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c=t[r];if(null===e||"function"!=typeof c)i(e);else{var u=c(nt.a({},e),n);Object(it.m)(u)?u.then((function(e){return o._notifyEventProcessors(t,e,n,r+1).then(i)})).then(null,a):o._notifyEventProcessors(t,u,n,r+1).then(i).then(null,a)}}))},t.prototype.setUser=function(t){return this._user=t||{},this._notifyScopeListeners(),this},t.prototype.setTags=function(t){return this._tags=nt.a({},this._tags,t),this._notifyScopeListeners(),this},t.prototype.setTag=function(t,e){var n;return this._tags=nt.a({},this._tags,((n={})[t]=e,n)),this._notifyScopeListeners(),this},t.prototype.setExtras=function(t){return this._extra=nt.a({},this._extra,t),this._notifyScopeListeners(),this},t.prototype.setExtra=function(t,e){var n;return this._extra=nt.a({},this._extra,((n={})[t]=e,n)),this._notifyScopeListeners(),this},t.prototype.setFingerprint=function(t){return this._fingerprint=t,this._notifyScopeListeners(),this},t.prototype.setLevel=function(t){return 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this._extra&&Object.keys(this._extra).length&&(t.extra=nt.a({},this._extra,t.extra)),this._tags&&Object.keys(this._tags).length&&(t.tags=nt.a({},this._tags,t.tags)),this._user&&Object.keys(this._user).length&&(t.user=nt.a({},this._user,t.user)),this._context&&Object.keys(this._context).length&&(t.contexts=nt.a({},this._context,t.contexts)),this._level&&(t.level=this._level),this._transaction&&(t.transaction=this._transaction),this._span&&(t.contexts=nt.a({trace:this._span.getTraceContext()},t.contexts)),this._applyFingerprint(t),t.breadcrumbs=nt.d(t.breadcrumbs||[],this._breadcrumbs),t.breadcrumbs=t.breadcrumbs.length>0?t.breadcrumbs:void 0,this._notifyEventProcessors(nt.d(r(),this._eventProcessors),t,e)},t}(),ht=n("HhP1"),dt=function(){function t(t,e,n){void 0===e&&(e=new pt),void 0===n&&(n=3),this._version=n,this._stack=[],this._stack.push({client:t,scope:e})}return t.prototype._invokeClient=function(t){for(var e,n=[],r=1;r0?t[t.length-1].scope:void 0);return this.getStack().push({client:this.getClient(),scope:e}),e},t.prototype.popScope=function(){return void 0!==this.getStack().pop()},t.prototype.withScope=function(t){var e=this.pushScope();try{t(e)}finally{this.popScope()}},t.prototype.getClient=function(){return this.getStackTop().client},t.prototype.getScope=function(){return this.getStackTop().scope},t.prototype.getStack=function(){return this._stack},t.prototype.getStackTop=function(){return this._stack[this._stack.length-1]},t.prototype.captureException=function(t,e){var n=this._lastEventId=Object(ft.m)(),r=e;if(!e){var o=void 0;try{throw new Error("Sentry syntheticException")}catch(t){o=t}r={originalException:t,syntheticException:o}}return this._invokeClient("captureException",t,nt.a({},r,{event_id:n})),n},t.prototype.captureMessage=function(t,e,n){var r=this._lastEventId=Object(ft.m)(),o=n;if(!n){var i=void 0;try{throw new Error(t)}catch(t){i=t}o={originalException:t,syntheticException:i}}return 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r=this,o=e&&e.event_id;return this._processing=!0,this._processEvent(t,e,n).then((function(t){o=t&&t.event_id,r._processing=!1})).then(null,(function(t){ht.a.error(t),r._processing=!1})),o},t.prototype.getDsn=function(){return this._dsn},t.prototype.getOptions=function(){return this._options},t.prototype.flush=function(t){var e=this;return this._isClientProcessing(t).then((function(n){return clearInterval(n.interval),e._getBackend().getTransport().close(t).then((function(t){return n.ready&&t}))}))},t.prototype.close=function(t){var e=this;return this.flush(t).then((function(t){return e.getOptions().enabled=!1,t}))},t.prototype.setupIntegrations=function(){this._isEnabled()&&(this._integrations=w(this._options))},t.prototype.getIntegration=function(t){try{return this._integrations[t.id]||null}catch(e){return ht.a.warn("Cannot retrieve integration "+t.id+" from the current Client"),null}},t.prototype._isClientProcessing=function(t){var e=this;return new lt((function(n){var 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\t__webpack_require__.oe = function(err) { console.error(err); throw err; };\n\n \tvar jsonpArray = window[\"webpackJsonp\"] = window[\"webpackJsonp\"] || [];\n \tvar oldJsonpFunction = jsonpArray.push.bind(jsonpArray);\n \tjsonpArray.push = webpackJsonpCallback;\n \tjsonpArray = jsonpArray.slice();\n \tfor(var i = 0; i < jsonpArray.length; i++) webpackJsonpCallback(jsonpArray[i]);\n \tvar parentJsonpFunction = oldJsonpFunction;\n\n\n \t// Load entry module and return exports\n \treturn __webpack_require__(__webpack_require__.s = 0);\n","import { Event, Integration, StackFrame, WrappedFunction } from '@sentry/types';\n\nimport { isString } from './is';\nimport { snipLine } from './string';\n\n/** Internal */\ninterface SentryGlobal {\n Sentry?: {\n Integrations?: Integration[];\n };\n SENTRY_ENVIRONMENT?: string;\n SENTRY_DSN?: string;\n SENTRY_RELEASE?: {\n id?: string;\n };\n __SENTRY__: {\n globalEventProcessors: any;\n hub: any;\n logger: any;\n };\n}\n\n/**\n * Requires a module which is protected against bundler minification.\n *\n * @param request The module path to resolve\n */\nexport function dynamicRequire(mod: any, request: string): any {\n // tslint:disable-next-line: no-unsafe-any\n return mod.require(request);\n}\n\n/**\n * Checks whether we're in the Node.js or Browser environment\n *\n * @returns Answer to given question\n */\nexport function isNodeEnv(): boolean {\n // tslint:disable:strict-type-predicates\n return Object.prototype.toString.call(typeof process !== 'undefined' ? process : 0) === '[object process]';\n}\n\nconst fallbackGlobalObject = {};\n\n/**\n * Safely get global scope object\n *\n * @returns Global scope object\n */\nexport function getGlobalObject(): T & SentryGlobal {\n return (isNodeEnv()\n ? global\n : typeof window !== 'undefined'\n ? window\n : typeof self !== 'undefined'\n ? self\n : fallbackGlobalObject) as T & SentryGlobal;\n}\n// tslint:enable:strict-type-predicates\n\n/**\n * Extended Window interface that allows for Crypto API usage in IE browsers\n */\ninterface MsCryptoWindow extends Window {\n msCrypto?: Crypto;\n}\n\n/**\n * UUID4 generator\n *\n * @returns string Generated UUID4.\n */\nexport function uuid4(): string {\n const global = getGlobalObject() as MsCryptoWindow;\n const crypto = global.crypto || global.msCrypto;\n\n if (!(crypto === void 0) && crypto.getRandomValues) {\n // Use window.crypto API if available\n const arr = new Uint16Array(8);\n crypto.getRandomValues(arr);\n\n // set 4 in byte 7\n // tslint:disable-next-line:no-bitwise\n arr[3] = (arr[3] & 0xfff) | 0x4000;\n // set 2 most significant bits of byte 9 to '10'\n // tslint:disable-next-line:no-bitwise\n arr[4] = (arr[4] & 0x3fff) | 0x8000;\n\n const pad = (num: number): string => {\n let v = num.toString(16);\n while (v.length < 4) {\n v = `0${v}`;\n }\n return v;\n };\n\n return (\n pad(arr[0]) + pad(arr[1]) + pad(arr[2]) + pad(arr[3]) + pad(arr[4]) + pad(arr[5]) + pad(arr[6]) + pad(arr[7])\n );\n }\n // http://stackoverflow.com/questions/105034/how-to-create-a-guid-uuid-in-javascript/2117523#2117523\n return 'xxxxxxxxxxxx4xxxyxxxxxxxxxxxxxxx'.replace(/[xy]/g, c => {\n // tslint:disable-next-line:no-bitwise\n const r = (Math.random() * 16) | 0;\n // tslint:disable-next-line:no-bitwise\n const v = c === 'x' ? r : (r & 0x3) | 0x8;\n return v.toString(16);\n });\n}\n\n/**\n * Parses string form of URL into an object\n * // borrowed from https://tools.ietf.org/html/rfc3986#appendix-B\n * // intentionally using regex and not href parsing trick because React Native and other\n * // environments where DOM might not be available\n * @returns parsed URL object\n */\nexport function parseUrl(\n url: string,\n): {\n host?: string;\n path?: string;\n protocol?: string;\n relative?: string;\n} {\n if (!url) {\n return {};\n }\n\n const match = url.match(/^(([^:\\/?#]+):)?(\\/\\/([^\\/?#]*))?([^?#]*)(\\?([^#]*))?(#(.*))?$/);\n\n if (!match) {\n return {};\n }\n\n // coerce to undefined values to empty string so we don't get 'undefined'\n const query = match[6] || '';\n const fragment = match[8] || '';\n return {\n host: match[4],\n path: match[5],\n protocol: match[2],\n relative: match[5] + query + fragment, // everything minus origin\n };\n}\n\n/**\n * Extracts either message or type+value from an event that can be used for user-facing logs\n * @returns event's description\n */\nexport function getEventDescription(event: Event): string {\n if (event.message) {\n return event.message;\n }\n if (event.exception && event.exception.values && event.exception.values[0]) {\n const exception = event.exception.values[0];\n\n if (exception.type && exception.value) {\n return `${exception.type}: ${exception.value}`;\n }\n return exception.type || exception.value || event.event_id || '';\n }\n return event.event_id || '';\n}\n\n/** JSDoc */\ninterface ExtensibleConsole extends Console {\n [key: string]: any;\n}\n\n/** JSDoc */\nexport function consoleSandbox(callback: () => any): any {\n const global = getGlobalObject();\n const levels = ['debug', 'info', 'warn', 'error', 'log', 'assert'];\n\n if (!('console' in global)) {\n return callback();\n }\n\n const originalConsole = global.console as ExtensibleConsole;\n const wrappedLevels: { [key: string]: any } = {};\n\n // Restore all wrapped console methods\n levels.forEach(level => {\n if (level in global.console && (originalConsole[level] as WrappedFunction).__sentry_original__) {\n wrappedLevels[level] = originalConsole[level] as WrappedFunction;\n originalConsole[level] = (originalConsole[level] as WrappedFunction).__sentry_original__;\n }\n });\n\n // Perform callback manipulations\n const result = callback();\n\n // Revert restoration to wrapped state\n Object.keys(wrappedLevels).forEach(level => {\n originalConsole[level] = wrappedLevels[level];\n });\n\n return result;\n}\n\n/**\n * Adds exception values, type and value to an synthetic Exception.\n * @param event The event to modify.\n * @param value Value of the exception.\n * @param type Type of the exception.\n * @hidden\n */\nexport function addExceptionTypeValue(event: Event, value?: string, type?: string): void {\n event.exception = event.exception || {};\n event.exception.values = event.exception.values || [];\n event.exception.values[0] = event.exception.values[0] || {};\n event.exception.values[0].value = event.exception.values[0].value || value || '';\n event.exception.values[0].type = event.exception.values[0].type || type || 'Error';\n}\n\n/**\n * Adds exception mechanism to a given event.\n * @param event The event to modify.\n * @param mechanism Mechanism of the mechanism.\n * @hidden\n */\nexport function addExceptionMechanism(\n event: Event,\n mechanism: {\n [key: string]: any;\n } = {},\n): void {\n // TODO: Use real type with `keyof Mechanism` thingy and maybe make it better?\n try {\n // @ts-ignore\n // tslint:disable:no-non-null-assertion\n event.exception!.values![0].mechanism = event.exception!.values![0].mechanism || {};\n Object.keys(mechanism).forEach(key => {\n // @ts-ignore\n event.exception!.values![0].mechanism[key] = mechanism[key];\n });\n } catch (_oO) {\n // no-empty\n }\n}\n\n/**\n * A safe form of location.href\n */\nexport function getLocationHref(): string {\n try {\n return document.location.href;\n } catch (oO) {\n return '';\n }\n}\n\n/**\n * Given a child DOM element, returns a query-selector statement describing that\n * and its ancestors\n * e.g. [HTMLElement] => body > div > input#foo.btn[name=baz]\n * @returns generated DOM path\n */\nexport function htmlTreeAsString(elem: unknown): string {\n type SimpleNode = {\n parentNode: SimpleNode;\n } | null;\n\n // try/catch both:\n // - accessing event.target (see getsentry/raven-js#838, #768)\n // - `htmlTreeAsString` because it's complex, and just accessing the DOM incorrectly\n // - can throw an exception in some circumstances.\n try {\n let currentElem = elem as SimpleNode;\n const MAX_TRAVERSE_HEIGHT = 5;\n const MAX_OUTPUT_LEN = 80;\n const out = [];\n let height = 0;\n let len = 0;\n const separator = ' > ';\n const sepLength = separator.length;\n let nextStr;\n\n while (currentElem && height++ < MAX_TRAVERSE_HEIGHT) {\n nextStr = _htmlElementAsString(currentElem);\n // bail out if\n // - nextStr is the 'html' element\n // - the length of the string that would be created exceeds MAX_OUTPUT_LEN\n // (ignore this limit if we are on the first iteration)\n if (nextStr === 'html' || (height > 1 && len + out.length * sepLength + nextStr.length >= MAX_OUTPUT_LEN)) {\n break;\n }\n\n out.push(nextStr);\n\n len += nextStr.length;\n currentElem = currentElem.parentNode;\n }\n\n return out.reverse().join(separator);\n } catch (_oO) {\n return '';\n }\n}\n\n/**\n * Returns a simple, query-selector representation of a DOM element\n * e.g. [HTMLElement] => input#foo.btn[name=baz]\n * @returns generated DOM path\n */\nfunction _htmlElementAsString(el: unknown): string {\n const elem = el as {\n getAttribute(key: string): string; // tslint:disable-line:completed-docs\n tagName?: string;\n id?: string;\n className?: string;\n };\n\n const out = [];\n let className;\n let classes;\n let key;\n let attr;\n let i;\n\n if (!elem || !elem.tagName) {\n return '';\n }\n\n out.push(elem.tagName.toLowerCase());\n if (elem.id) {\n out.push(`#${elem.id}`);\n }\n\n className = elem.className;\n if (className && isString(className)) {\n classes = className.split(/\\s+/);\n for (i = 0; i < classes.length; i++) {\n out.push(`.${classes[i]}`);\n }\n }\n const attrWhitelist = ['type', 'name', 'title', 'alt'];\n for (i = 0; i < attrWhitelist.length; i++) {\n key = attrWhitelist[i];\n attr = elem.getAttribute(key);\n if (attr) {\n out.push(`[${key}=\"${attr}\"]`);\n }\n }\n return out.join('');\n}\n\nconst INITIAL_TIME = Date.now();\nlet prevNow = 0;\n\n/**\n * Cross platform compatible partial performance implementation\n */\ninterface CrossPlatformPerformance {\n /**\n * Returns the current timestamp in ms\n */\n now(): number;\n timeOrigin: number;\n}\n\nconst performanceFallback: CrossPlatformPerformance = {\n now(): number {\n let now = Date.now() - INITIAL_TIME;\n if (now < prevNow) {\n now = prevNow;\n }\n prevNow = now;\n return now;\n },\n timeOrigin: INITIAL_TIME,\n};\n\nexport const crossPlatformPerformance: CrossPlatformPerformance = (() => {\n if (isNodeEnv()) {\n try {\n const perfHooks = dynamicRequire(module, 'perf_hooks') as { performance: CrossPlatformPerformance };\n return perfHooks.performance;\n } catch (_) {\n return performanceFallback;\n }\n }\n\n if (getGlobalObject().performance) {\n // Polyfill for performance.timeOrigin.\n //\n // While performance.timing.navigationStart is deprecated in favor of performance.timeOrigin, performance.timeOrigin\n // is not as widely supported. Namely, performance.timeOrigin is undefined in Safari as of writing.\n // tslint:disable-next-line:strict-type-predicates\n if (performance.timeOrigin === undefined) {\n // As of writing, performance.timing is not available in Web Workers in mainstream browsers, so it is not always a\n // valid fallback. In the absence of a initial time provided by the browser, fallback to INITIAL_TIME.\n // @ts-ignore\n // tslint:disable-next-line:deprecation\n performance.timeOrigin = (performance.timing && performance.timing.navigationStart) || INITIAL_TIME;\n }\n }\n\n return getGlobalObject().performance || performanceFallback;\n})();\n\n/**\n * Returns a timestamp in seconds with milliseconds precision since the UNIX epoch calculated with the monotonic clock.\n */\nexport function timestampWithMs(): number {\n return (crossPlatformPerformance.timeOrigin + crossPlatformPerformance.now()) / 1000;\n}\n\n// https://semver.org/#is-there-a-suggested-regular-expression-regex-to-check-a-semver-string\nconst SEMVER_REGEXP = /^(0|[1-9]\\d*)\\.(0|[1-9]\\d*)\\.(0|[1-9]\\d*)(?:-((?:0|[1-9]\\d*|\\d*[a-zA-Z-][0-9a-zA-Z-]*)(?:\\.(?:0|[1-9]\\d*|\\d*[a-zA-Z-][0-9a-zA-Z-]*))*))?(?:\\+([0-9a-zA-Z-]+(?:\\.[0-9a-zA-Z-]+)*))?$/;\n\n/**\n * Represents Semantic Versioning object\n */\ninterface SemVer {\n major?: number;\n minor?: number;\n patch?: number;\n prerelease?: string;\n buildmetadata?: string;\n}\n\n/**\n * Parses input into a SemVer interface\n * @param input string representation of a semver version\n */\nexport function parseSemver(input: string): SemVer {\n const match = input.match(SEMVER_REGEXP) || [];\n const major = parseInt(match[1], 10);\n const minor = parseInt(match[2], 10);\n const patch = parseInt(match[3], 10);\n return {\n buildmetadata: match[5],\n major: isNaN(major) ? undefined : major,\n minor: isNaN(minor) ? undefined : minor,\n patch: isNaN(patch) ? undefined : patch,\n prerelease: match[4],\n };\n}\n\nconst defaultRetryAfter = 60 * 1000; // 60 seconds\n\n/**\n * Extracts Retry-After value from the request header or returns default value\n * @param now current unix timestamp\n * @param header string representation of 'Retry-After' header\n */\nexport function parseRetryAfterHeader(now: number, header?: string | number | null): number {\n if (!header) {\n return defaultRetryAfter;\n }\n\n const headerDelay = parseInt(`${header}`, 10);\n if (!isNaN(headerDelay)) {\n return headerDelay * 1000;\n }\n\n const headerDate = Date.parse(`${header}`);\n if (!isNaN(headerDate)) {\n return headerDate - now;\n }\n\n return defaultRetryAfter;\n}\n\nconst defaultFunctionName = '';\n\n/**\n * Safely extract function name from itself\n */\nexport function getFunctionName(fn: unknown): string {\n try {\n if (!fn || typeof fn !== 'function') {\n return defaultFunctionName;\n }\n return fn.name || defaultFunctionName;\n } catch (e) {\n // Just accessing custom props in some Selenium environments\n // can cause a \"Permission denied\" exception (see raven-js#495).\n return defaultFunctionName;\n }\n}\n\n/**\n * This function adds context (pre/post/line) lines to the provided frame\n *\n * @param lines string[] containing all lines\n * @param frame StackFrame that will be mutated\n * @param linesOfContext number of context lines we want to add pre/post\n */\nexport function addContextToFrame(lines: string[], frame: StackFrame, linesOfContext: number = 5): void {\n const lineno = frame.lineno || 0;\n const maxLines = lines.length;\n const sourceLine = Math.max(Math.min(maxLines, lineno - 1), 0);\n\n frame.pre_context = lines\n .slice(Math.max(0, sourceLine - linesOfContext), sourceLine)\n .map((line: string) => snipLine(line, 0));\n\n frame.context_line = snipLine(lines[Math.min(maxLines - 1, sourceLine)], frame.colno || 0);\n\n frame.post_context = lines\n .slice(Math.min(sourceLine + 1, maxLines), sourceLine + 1 + linesOfContext)\n .map((line: string) => snipLine(line, 0));\n}\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./NetLogo.js\") );\n\t\t\t}, \"route-NetLogo\");\n\t\t}\n\n\t\texport default Async(load);\n\t","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./VlDiGeometria.js\") );\n\t\t\t}, \"route-VlDiGeometria\");\n\t\t}\n\n\t\texport default Async(load);\n\t","// tslint:disable:no-unsafe-any\n/**\n * Memo class used for decycle json objects. Uses WeakSet if available otherwise array.\n */\nexport class Memo {\n /** Determines if WeakSet is available */\n private readonly _hasWeakSet: boolean;\n /** Either WeakSet or Array */\n private readonly _inner: any;\n\n public constructor() {\n // tslint:disable-next-line\n this._hasWeakSet = typeof WeakSet === 'function';\n this._inner = this._hasWeakSet ? new WeakSet() : [];\n }\n\n /**\n * Sets obj to remember.\n * @param obj Object to remember\n */\n public memoize(obj: any): boolean {\n if (this._hasWeakSet) {\n if (this._inner.has(obj)) {\n return true;\n }\n this._inner.add(obj);\n return false;\n }\n // tslint:disable-next-line:prefer-for-of\n for (let i = 0; i < this._inner.length; i++) {\n const value = this._inner[i];\n if (value === obj) {\n return true;\n }\n }\n this._inner.push(obj);\n return false;\n }\n\n /**\n * Removes object from internal storage.\n * @param obj Object to forget\n */\n public unmemoize(obj: any): void {\n if (this._hasWeakSet) {\n this._inner.delete(obj);\n } else {\n for (let i = 0; i < this._inner.length; i++) {\n if (this._inner[i] === obj) {\n this._inner.splice(i, 1);\n break;\n }\n }\n }\n }\n}\n","import {createContext} from \"preact\";\n\nexport default createContext(\"White\");\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./BasiDiDati.js\") );\n\t\t\t}, \"route-BasiDiDati\");\n\t\t}\n\n\t\texport default Async(load);\n\t","/**\n * Checks whether given value's type is one of a few Error or Error-like\n * {@link isError}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isError(wat: any): boolean {\n switch (Object.prototype.toString.call(wat)) {\n case '[object Error]':\n return true;\n case '[object Exception]':\n return true;\n case '[object DOMException]':\n return true;\n default:\n return isInstanceOf(wat, Error);\n }\n}\n\n/**\n * Checks whether given value's type is ErrorEvent\n * {@link isErrorEvent}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isErrorEvent(wat: any): boolean {\n return Object.prototype.toString.call(wat) === '[object ErrorEvent]';\n}\n\n/**\n * Checks whether given value's type is DOMError\n * {@link isDOMError}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isDOMError(wat: any): boolean {\n return Object.prototype.toString.call(wat) === '[object DOMError]';\n}\n\n/**\n * Checks whether given value's type is DOMException\n * {@link isDOMException}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isDOMException(wat: any): boolean {\n return Object.prototype.toString.call(wat) === '[object DOMException]';\n}\n\n/**\n * Checks whether given value's type is a string\n * {@link isString}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isString(wat: any): boolean {\n return Object.prototype.toString.call(wat) === '[object String]';\n}\n\n/**\n * Checks whether given value's is a primitive (undefined, null, number, boolean, string)\n * {@link isPrimitive}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isPrimitive(wat: any): boolean {\n return wat === null || (typeof wat !== 'object' && typeof wat !== 'function');\n}\n\n/**\n * Checks whether given value's type is an object literal\n * {@link isPlainObject}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isPlainObject(wat: any): boolean {\n return Object.prototype.toString.call(wat) === '[object Object]';\n}\n\n/**\n * Checks whether given value's type is an Event instance\n * {@link isEvent}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isEvent(wat: any): boolean {\n // tslint:disable-next-line:strict-type-predicates\n return typeof Event !== 'undefined' && isInstanceOf(wat, Event);\n}\n\n/**\n * Checks whether given value's type is an Element instance\n * {@link isElement}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isElement(wat: any): boolean {\n // tslint:disable-next-line:strict-type-predicates\n return typeof Element !== 'undefined' && isInstanceOf(wat, Element);\n}\n\n/**\n * Checks whether given value's type is an regexp\n * {@link isRegExp}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isRegExp(wat: any): boolean {\n return Object.prototype.toString.call(wat) === '[object RegExp]';\n}\n\n/**\n * Checks whether given value has a then function.\n * @param wat A value to be checked.\n */\nexport function isThenable(wat: any): boolean {\n // tslint:disable:no-unsafe-any\n return Boolean(wat && wat.then && typeof wat.then === 'function');\n // tslint:enable:no-unsafe-any\n}\n\n/**\n * Checks whether given value's type is a SyntheticEvent\n * {@link isSyntheticEvent}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isSyntheticEvent(wat: any): boolean {\n // tslint:disable-next-line:no-unsafe-any\n return isPlainObject(wat) && 'nativeEvent' in wat && 'preventDefault' in wat && 'stopPropagation' in wat;\n}\n/**\n * Checks whether given value's type is an instance of provided constructor.\n * {@link isInstanceOf}.\n *\n * @param wat A value to be checked.\n * @param base A constructor to be used in a check.\n * @returns A boolean representing the result.\n */\nexport function isInstanceOf(wat: any, base: any): boolean {\n try {\n // tslint:disable-next-line:no-unsafe-any\n return wat instanceof base;\n } catch (_e) {\n return false;\n }\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"footer\":\"footer__3lyac\"};","// Slightly modified (no IE8 support, ES6) and transcribed to TypeScript\n// https://raw.githubusercontent.com/calvinmetcalf/rollup-plugin-node-builtins/master/src/es6/path.js\n\n/** JSDoc */\nfunction normalizeArray(parts: string[], allowAboveRoot?: boolean): string[] {\n // if the path tries to go above the root, `up` ends up > 0\n let up = 0;\n for (let i = parts.length - 1; i >= 0; i--) {\n const last = parts[i];\n if (last === '.') {\n parts.splice(i, 1);\n } else if (last === '..') {\n parts.splice(i, 1);\n up++;\n } else if (up) {\n parts.splice(i, 1);\n up--;\n }\n }\n\n // if the path is allowed to go above the root, restore leading ..s\n if (allowAboveRoot) {\n for (; up--; up) {\n parts.unshift('..');\n }\n }\n\n return parts;\n}\n\n// Split a filename into [root, dir, basename, ext], unix version\n// 'root' is just a slash, or nothing.\nconst splitPathRe = /^(\\/?|)([\\s\\S]*?)((?:\\.{1,2}|[^\\/]+?|)(\\.[^.\\/]*|))(?:[\\/]*)$/;\n/** JSDoc */\nfunction splitPath(filename: string): string[] {\n const parts = splitPathRe.exec(filename);\n return parts ? parts.slice(1) : [];\n}\n\n// path.resolve([from ...], to)\n// posix version\n/** JSDoc */\nexport function resolve(...args: string[]): string {\n let resolvedPath = '';\n let resolvedAbsolute = false;\n\n for (let i = args.length - 1; i >= -1 && !resolvedAbsolute; i--) {\n const path = i >= 0 ? args[i] : '/';\n\n // Skip empty entries\n if (!path) {\n continue;\n }\n\n resolvedPath = `${path}/${resolvedPath}`;\n resolvedAbsolute = path.charAt(0) === '/';\n }\n\n // At this point the path should be resolved to a full absolute path, but\n // handle relative paths to be safe (might happen when process.cwd() fails)\n\n // Normalize the path\n resolvedPath = normalizeArray(resolvedPath.split('/').filter(p => !!p), !resolvedAbsolute).join('/');\n\n return (resolvedAbsolute ? '/' : '') + resolvedPath || '.';\n}\n\n/** JSDoc */\nfunction trim(arr: string[]): string[] {\n let start = 0;\n for (; start < arr.length; start++) {\n if (arr[start] !== '') {\n break;\n }\n }\n\n let end = arr.length - 1;\n for (; end >= 0; end--) {\n if (arr[end] !== '') {\n break;\n }\n }\n\n if (start > end) {\n return [];\n }\n return arr.slice(start, end - start + 1);\n}\n\n// path.relative(from, to)\n// posix version\n/** JSDoc */\nexport function relative(from: string, to: string): string {\n // tslint:disable:no-parameter-reassignment\n from = resolve(from).substr(1);\n to = resolve(to).substr(1);\n\n const fromParts = trim(from.split('/'));\n const toParts = trim(to.split('/'));\n\n const length = Math.min(fromParts.length, toParts.length);\n let samePartsLength = length;\n for (let i = 0; i < length; i++) {\n if (fromParts[i] !== toParts[i]) {\n samePartsLength = i;\n break;\n }\n }\n\n let outputParts = [];\n for (let i = samePartsLength; i < fromParts.length; i++) {\n outputParts.push('..');\n }\n\n outputParts = outputParts.concat(toParts.slice(samePartsLength));\n\n return outputParts.join('/');\n}\n\n// path.normalize(path)\n// posix version\n/** JSDoc */\nexport function normalizePath(path: string): string {\n const isPathAbsolute = isAbsolute(path);\n const trailingSlash = path.substr(-1) === '/';\n\n // Normalize the path\n let normalizedPath = normalizeArray(path.split('/').filter(p => !!p), !isPathAbsolute).join('/');\n\n if (!normalizedPath && !isPathAbsolute) {\n normalizedPath = '.';\n }\n if (normalizedPath && trailingSlash) {\n normalizedPath += '/';\n }\n\n return (isPathAbsolute ? '/' : '') + normalizedPath;\n}\n\n// posix version\n/** JSDoc */\nexport function isAbsolute(path: string): boolean {\n return path.charAt(0) === '/';\n}\n\n// posix version\n/** JSDoc */\nexport function join(...args: string[]): string {\n return normalizePath(args.join('/'));\n}\n\n/** JSDoc */\nexport function dirname(path: string): string {\n const result = splitPath(path);\n const root = result[0];\n let dir = result[1];\n\n if (!root && !dir) {\n // No dirname whatsoever\n return '.';\n }\n\n if (dir) {\n // It has a dirname, strip trailing slash\n dir = dir.substr(0, dir.length - 1);\n }\n\n return root + dir;\n}\n\n/** JSDoc */\nexport function basename(path: string, ext?: string): string {\n let f = splitPath(path)[2];\n if (ext && f.substr(ext.length * -1) === ext) {\n f = f.substr(0, f.length - ext.length);\n }\n return f;\n}\n","import { EventProcessor, Hub, Integration } from '@sentry/types';\nimport { getGlobalObject, supportsReportingObserver } from '@sentry/utils';\n\n/** JSDoc */\ninterface Report {\n [key: string]: any;\n type: ReportTypes;\n url: string;\n body?: ReportBody;\n}\n\n/** JSDoc */\nenum ReportTypes {\n /** JSDoc */\n Crash = 'crash',\n /** JSDoc */\n Deprecation = 'deprecation',\n /** JSDoc */\n Intervention = 'intervention',\n}\n\n/** JSDoc */\ntype ReportBody = CrashReportBody | DeprecationReportBody | InterventionReportBody;\n\n/** JSDoc */\ninterface CrashReportBody {\n [key: string]: any;\n crashId: string;\n reason?: string;\n}\n\n/** JSDoc */\ninterface DeprecationReportBody {\n [key: string]: any;\n id: string;\n anticipatedRemoval?: Date;\n message: string;\n sourceFile?: string;\n lineNumber?: number;\n columnNumber?: number;\n}\n\n/** JSDoc */\ninterface InterventionReportBody {\n [key: string]: any;\n id: string;\n message: string;\n sourceFile?: string;\n lineNumber?: number;\n columnNumber?: number;\n}\n\n/** Reporting API integration - https://w3c.github.io/reporting/ */\nexport class ReportingObserver implements Integration {\n /**\n * @inheritDoc\n */\n public readonly name: string = ReportingObserver.id;\n /**\n * @inheritDoc\n */\n public static id: string = 'ReportingObserver';\n\n /**\n * Returns current hub.\n */\n private _getCurrentHub?: () => Hub;\n\n /**\n * @inheritDoc\n */\n public constructor(\n private readonly _options: {\n types?: ReportTypes[];\n } = {\n types: [ReportTypes.Crash, ReportTypes.Deprecation, ReportTypes.Intervention],\n },\n ) {}\n\n /**\n * @inheritDoc\n */\n public setupOnce(_: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n // tslint:disable:no-unsafe-any\n\n if (!supportsReportingObserver()) {\n return;\n }\n\n this._getCurrentHub = getCurrentHub;\n\n const observer = new (getGlobalObject()).ReportingObserver(this.handler.bind(this), {\n buffered: true,\n types: this._options.types,\n });\n\n observer.observe();\n }\n\n /**\n * @inheritDoc\n */\n public handler(reports: Report[]): void {\n const hub = this._getCurrentHub && this._getCurrentHub();\n if (!hub || !hub.getIntegration(ReportingObserver)) {\n return;\n }\n for (const report of reports) {\n hub.withScope(scope => {\n scope.setExtra('url', report.url);\n\n const label = `ReportingObserver [${report.type}]`;\n let details = 'No details available';\n\n if (report.body) {\n // Object.keys doesn't work on ReportBody, as all properties are inheirted\n const plainBody: {\n [key: string]: any;\n } = {};\n\n // tslint:disable-next-line:forin\n for (const prop in report.body) {\n plainBody[prop] = report.body[prop];\n }\n\n scope.setExtra('body', plainBody);\n\n if (report.type === ReportTypes.Crash) {\n const body = report.body as CrashReportBody;\n // A fancy way to create a message out of crashId OR reason OR both OR fallback\n details = [body.crashId || '', body.reason || ''].join(' ').trim() || details;\n } else {\n const body = report.body as DeprecationReportBody | InterventionReportBody;\n details = body.message || details;\n }\n }\n\n hub.captureMessage(`${label}: ${details}`);\n });\n }\n }\n}\n","import { Event, EventProcessor, Hub, Integration } from '@sentry/types';\nimport { getGlobalObject, logger } from '@sentry/utils';\n\n// See https://github.com/angular/angular.js/blob/v1.4.7/src/minErr.js\nconst angularPattern = /^\\[((?:[$a-zA-Z0-9]+:)?(?:[$a-zA-Z0-9]+))\\] (.*?)\\n?(\\S+)$/;\n\n/**\n * AngularJS integration\n *\n * Provides an $exceptionHandler for AngularJS\n */\nexport class Angular implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = Angular.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'AngularJS';\n\n /**\n * moduleName used in Angular's DI resolution algorithm\n */\n public static moduleName: string = 'ngSentry';\n\n /**\n * Angular's instance\n */\n private readonly _angular: any;\n\n /**\n * Returns current hub.\n */\n private _getCurrentHub?: () => Hub;\n\n /**\n * @inheritDoc\n */\n public constructor(options: { angular?: any } = {}) {\n // tslint:disable-next-line: no-unsafe-any\n this._angular = options.angular || getGlobalObject().angular;\n }\n\n /**\n * @inheritDoc\n */\n public setupOnce(_: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n if (!this._angular) {\n logger.error('AngularIntegration is missing an Angular instance');\n return;\n }\n\n this._getCurrentHub = getCurrentHub;\n\n // tslint:disable: no-unsafe-any\n this._angular.module(Angular.moduleName, []).config([\n '$provide',\n ($provide: any) => {\n $provide.decorator('$exceptionHandler', ['$delegate', this._$exceptionHandlerDecorator.bind(this)]);\n },\n ]);\n // tslint:enable: no-unsafe-any\n }\n\n /**\n * Angular's exceptionHandler for Sentry integration\n */\n // tslint:disable-next-line: no-unsafe-any\n private _$exceptionHandlerDecorator($delegate: any): any {\n return (exception: Error, cause?: string) => {\n const hub = this._getCurrentHub && this._getCurrentHub();\n\n if (hub && hub.getIntegration(Angular)) {\n hub.withScope(scope => {\n if (cause) {\n scope.setExtra('cause', cause);\n }\n\n scope.addEventProcessor((event: Event) => {\n const ex = event.exception && event.exception.values && event.exception.values[0];\n\n if (ex) {\n const matches = angularPattern.exec(ex.value || '');\n\n if (matches) {\n // This type now becomes something like: $rootScope:inprog\n ex.type = matches[1];\n ex.value = matches[2];\n event.message = `${ex.type}: ${ex.value}`;\n // auto set a new tag specifically for the angular error url\n event.extra = {\n ...event.extra,\n angularDocs: matches[3].substr(0, 250),\n };\n }\n }\n\n return event;\n });\n\n hub.captureException(exception);\n });\n }\n // tslint:disable-next-line: no-unsafe-any\n $delegate(exception, cause);\n };\n }\n}\n","import { EventProcessor, Hub, Integration, Severity } from '@sentry/types';\nimport { fill, getGlobalObject, safeJoin } from '@sentry/utils';\n\nconst global = getGlobalObject();\n\n/** Send Console API calls as Sentry Events */\nexport class CaptureConsole implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = CaptureConsole.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'CaptureConsole';\n\n /**\n * @inheritDoc\n */\n private readonly _levels: string[] = ['log', 'info', 'warn', 'error', 'debug', 'assert'];\n\n /**\n * @inheritDoc\n */\n public constructor(options: { levels?: string[] } = {}) {\n if (options.levels) {\n this._levels = options.levels;\n }\n }\n\n /**\n * @inheritDoc\n */\n public setupOnce(_: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n if (!('console' in global)) {\n return;\n }\n\n this._levels.forEach((level: string) => {\n if (!(level in global.console)) {\n return;\n }\n\n fill(global.console, level, (originalConsoleLevel: () => any) => (...args: any[]) => {\n const hub = getCurrentHub();\n\n if (hub.getIntegration(CaptureConsole)) {\n hub.withScope(scope => {\n scope.setLevel(Severity.fromString(level));\n scope.setExtra('arguments', args);\n scope.addEventProcessor(event => {\n event.logger = 'console';\n return event;\n });\n\n let message = safeJoin(args, ' ');\n if (level === 'assert') {\n if (args[0] === false) {\n message = `Assertion failed: ${safeJoin(args.slice(1), ' ') || 'console.assert'}`;\n scope.setExtra('arguments', args.slice(1));\n hub.captureMessage(message);\n }\n } else {\n hub.captureMessage(message);\n }\n });\n }\n\n // this fails for some browsers. :(\n if (originalConsoleLevel) {\n Function.prototype.apply.call(originalConsoleLevel, global.console, args);\n }\n });\n });\n }\n}\n","import { Event, EventHint, EventProcessor, Hub, Integration } from '@sentry/types';\nimport { consoleSandbox } from '@sentry/utils';\n\n/** JSDoc */\ninterface DebugOptions {\n stringify?: boolean;\n debugger?: boolean;\n}\n\n/** JSDoc */\nexport class Debug implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = Debug.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'Debug';\n\n /** JSDoc */\n private readonly _options: DebugOptions;\n\n /**\n * @inheritDoc\n */\n public constructor(options?: DebugOptions) {\n this._options = {\n debugger: false,\n stringify: false,\n ...options,\n };\n }\n\n /**\n * @inheritDoc\n */\n public setupOnce(addGlobalEventProcessor: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n addGlobalEventProcessor((event: Event, hint?: EventHint) => {\n const self = getCurrentHub().getIntegration(Debug);\n if (self) {\n // tslint:disable:no-console\n // tslint:disable:no-debugger\n if (self._options.debugger) {\n debugger;\n }\n\n consoleSandbox(() => {\n if (self._options.stringify) {\n console.log(JSON.stringify(event, null, 2));\n if (hint) {\n console.log(JSON.stringify(hint, null, 2));\n }\n } else {\n console.log(event);\n if (hint) {\n console.log(hint);\n }\n }\n });\n }\n return event;\n });\n }\n}\n","import { Event, EventProcessor, Exception, Hub, Integration, StackFrame } from '@sentry/types';\n\n/** Deduplication filter */\nexport class Dedupe implements Integration {\n /**\n * @inheritDoc\n */\n private _previousEvent?: Event;\n\n /**\n * @inheritDoc\n */\n public name: string = Dedupe.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'Dedupe';\n\n /**\n * @inheritDoc\n */\n public setupOnce(addGlobalEventProcessor: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n addGlobalEventProcessor((currentEvent: Event) => {\n const self = getCurrentHub().getIntegration(Dedupe);\n if (self) {\n // Juuust in case something goes wrong\n try {\n if (self._shouldDropEvent(currentEvent, self._previousEvent)) {\n return null;\n }\n } catch (_oO) {\n return (self._previousEvent = currentEvent);\n }\n\n return (self._previousEvent = currentEvent);\n }\n return currentEvent;\n });\n }\n\n /** JSDoc */\n private _shouldDropEvent(currentEvent: Event, previousEvent?: Event): boolean {\n if (!previousEvent) {\n return false;\n }\n\n if (this._isSameMessageEvent(currentEvent, previousEvent)) {\n return true;\n }\n\n if (this._isSameExceptionEvent(currentEvent, previousEvent)) {\n return true;\n }\n\n return false;\n }\n\n /** JSDoc */\n private _isSameMessageEvent(currentEvent: Event, previousEvent: Event): boolean {\n const currentMessage = currentEvent.message;\n const previousMessage = previousEvent.message;\n\n // If neither event has a message property, they were both exceptions, so bail out\n if (!currentMessage && !previousMessage) {\n return false;\n }\n\n // If only one event has a stacktrace, but not the other one, they are not the same\n if ((currentMessage && !previousMessage) || (!currentMessage && previousMessage)) {\n return false;\n }\n\n if (currentMessage !== previousMessage) {\n return false;\n }\n\n if (!this._isSameFingerprint(currentEvent, previousEvent)) {\n return false;\n }\n\n if (!this._isSameStacktrace(currentEvent, previousEvent)) {\n return false;\n }\n\n return true;\n }\n\n /** JSDoc */\n private _getFramesFromEvent(event: Event): StackFrame[] | undefined {\n const exception = event.exception;\n\n if (exception) {\n try {\n // @ts-ignore\n return exception.values[0].stacktrace.frames;\n } catch (_oO) {\n return undefined;\n }\n } else if (event.stacktrace) {\n return event.stacktrace.frames;\n }\n return undefined;\n }\n\n /** JSDoc */\n private _isSameStacktrace(currentEvent: Event, previousEvent: Event): boolean {\n let currentFrames = this._getFramesFromEvent(currentEvent);\n let previousFrames = this._getFramesFromEvent(previousEvent);\n\n // If neither event has a stacktrace, they are assumed to be the same\n if (!currentFrames && !previousFrames) {\n return true;\n }\n\n // If only one event has a stacktrace, but not the other one, they are not the same\n if ((currentFrames && !previousFrames) || (!currentFrames && previousFrames)) {\n return false;\n }\n\n currentFrames = currentFrames as StackFrame[];\n previousFrames = previousFrames as StackFrame[];\n\n // If number of frames differ, they are not the same\n if (previousFrames.length !== currentFrames.length) {\n return false;\n }\n\n // Otherwise, compare the two\n for (let i = 0; i < previousFrames.length; i++) {\n const frameA = previousFrames[i];\n const frameB = currentFrames[i];\n\n if (\n frameA.filename !== frameB.filename ||\n frameA.lineno !== frameB.lineno ||\n frameA.colno !== frameB.colno ||\n frameA.function !== frameB.function\n ) {\n return false;\n }\n }\n\n return true;\n }\n\n /** JSDoc */\n private _getExceptionFromEvent(event: Event): Exception | undefined {\n return event.exception && event.exception.values && event.exception.values[0];\n }\n\n /** JSDoc */\n private _isSameExceptionEvent(currentEvent: Event, previousEvent: Event): boolean {\n const previousException = this._getExceptionFromEvent(previousEvent);\n const currentException = this._getExceptionFromEvent(currentEvent);\n\n if (!previousException || !currentException) {\n return false;\n }\n\n if (previousException.type !== currentException.type || previousException.value !== currentException.value) {\n return false;\n }\n\n if (!this._isSameFingerprint(currentEvent, previousEvent)) {\n return false;\n }\n\n if (!this._isSameStacktrace(currentEvent, previousEvent)) {\n return false;\n }\n\n return true;\n }\n\n /** JSDoc */\n private _isSameFingerprint(currentEvent: Event, previousEvent: Event): boolean {\n let currentFingerprint = currentEvent.fingerprint;\n let previousFingerprint = previousEvent.fingerprint;\n\n // If neither event has a fingerprint, they are assumed to be the same\n if (!currentFingerprint && !previousFingerprint) {\n return true;\n }\n\n // If only one event has a fingerprint, but not the other one, they are not the same\n if ((currentFingerprint && !previousFingerprint) || (!currentFingerprint && previousFingerprint)) {\n return false;\n }\n\n currentFingerprint = currentFingerprint as string[];\n previousFingerprint = previousFingerprint as string[];\n\n // Otherwise, compare the two\n try {\n return !!(currentFingerprint.join('') === previousFingerprint.join(''));\n } catch (_oO) {\n return false;\n }\n }\n}\n","import { EventProcessor, Hub, Integration } from '@sentry/types';\nimport { getGlobalObject, isInstanceOf, logger } from '@sentry/utils';\n\n/** JSDoc */\nexport class Ember implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = Ember.id;\n /**\n * @inheritDoc\n */\n public static id: string = 'Ember';\n\n /**\n * @inheritDoc\n */\n private readonly _Ember: any; // tslint:disable-line:variable-name\n\n /**\n * @inheritDoc\n */\n public constructor(options: { Ember?: any } = {}) {\n // tslint:disable-next-line: no-unsafe-any\n this._Ember = options.Ember || getGlobalObject().Ember;\n }\n\n /**\n * @inheritDoc\n */\n public setupOnce(_: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n // tslint:disable:no-unsafe-any\n\n if (!this._Ember) {\n logger.error('EmberIntegration is missing an Ember instance');\n return;\n }\n\n const oldOnError = this._Ember.onerror;\n\n this._Ember.onerror = (error: Error): void => {\n if (getCurrentHub().getIntegration(Ember)) {\n getCurrentHub().captureException(error, { originalException: error });\n }\n\n if (typeof oldOnError === 'function') {\n oldOnError.call(this._Ember, error);\n } else if (this._Ember.testing) {\n throw error;\n }\n };\n\n this._Ember.RSVP.on(\n 'error',\n (reason: any): void => {\n if (getCurrentHub().getIntegration(Ember)) {\n getCurrentHub().withScope(scope => {\n if (isInstanceOf(reason, Error)) {\n scope.setExtra('context', 'Unhandled Promise error detected');\n getCurrentHub().captureException(reason, { originalException: reason });\n } else {\n scope.setExtra('reason', reason);\n getCurrentHub().captureMessage('Unhandled Promise error detected');\n }\n });\n }\n },\n );\n }\n}\n","import { Event, EventHint, EventProcessor, ExtendedError, Hub, Integration } from '@sentry/types';\nimport { isError, isPlainObject, logger, normalize } from '@sentry/utils';\n\n/** JSDoc */\ninterface ExtraErrorDataOptions {\n depth?: number;\n}\n\n/** Patch toString calls to return proper name for wrapped functions */\nexport class ExtraErrorData implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = ExtraErrorData.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'ExtraErrorData';\n\n /**\n * @inheritDoc\n */\n public constructor(private readonly _options: ExtraErrorDataOptions = { depth: 3 }) {}\n\n /**\n * @inheritDoc\n */\n public setupOnce(addGlobalEventProcessor: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n addGlobalEventProcessor((event: Event, hint?: EventHint) => {\n const self = getCurrentHub().getIntegration(ExtraErrorData);\n if (!self) {\n return event;\n }\n return self.enhanceEventWithErrorData(event, hint);\n });\n }\n\n /**\n * Attaches extracted information from the Error object to extra field in the Event\n */\n public enhanceEventWithErrorData(event: Event, hint?: EventHint): Event {\n if (!hint || !hint.originalException || !isError(hint.originalException)) {\n return event;\n }\n const name = (hint.originalException as ExtendedError).name || hint.originalException.constructor.name;\n\n const errorData = this._extractErrorData(hint.originalException as ExtendedError);\n\n if (errorData) {\n let contexts = {\n ...event.contexts,\n };\n\n const normalizedErrorData = normalize(errorData, this._options.depth);\n if (isPlainObject(normalizedErrorData)) {\n contexts = {\n ...event.contexts,\n [name]: {\n ...normalizedErrorData,\n },\n };\n }\n\n return {\n ...event,\n contexts,\n };\n }\n\n return event;\n }\n\n /**\n * Extract extra information from the Error object\n */\n private _extractErrorData(error: ExtendedError): { [key: string]: unknown } | null {\n let result = null;\n // We are trying to enhance already existing event, so no harm done if it won't succeed\n try {\n const nativeKeys = ['name', 'message', 'stack', 'line', 'column', 'fileName', 'lineNumber', 'columnNumber'];\n const errorKeys = Object.getOwnPropertyNames(error).filter(key => nativeKeys.indexOf(key) === -1);\n\n if (errorKeys.length) {\n const extraErrorInfo: { [key: string]: unknown } = {};\n for (const key of errorKeys) {\n let value = error[key];\n if (isError(value)) {\n value = (value as Error).toString();\n }\n // tslint:disable:no-unsafe-any\n extraErrorInfo[key] = value;\n }\n result = extraErrorInfo;\n }\n } catch (oO) {\n logger.error('Unable to extract extra data from the Error object:', oO);\n }\n\n return result;\n }\n}\n","import { Event, EventProcessor, Hub, Integration, StackFrame, Stacktrace } from '@sentry/types';\nimport { basename, relative } from '@sentry/utils';\n\ntype StackFrameIteratee = (frame: StackFrame) => StackFrame;\n\n/** Rewrite event frames paths */\nexport class RewriteFrames implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = RewriteFrames.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'RewriteFrames';\n\n /**\n * @inheritDoc\n */\n private readonly _root?: string;\n\n /**\n * @inheritDoc\n */\n private readonly _iteratee: StackFrameIteratee = (frame: StackFrame) => {\n if (!frame.filename) {\n return frame;\n }\n // Check if the frame filename begins with `/` or a Windows-style prefix such as `C:\\`\n const isWindowsFrame = /^[A-Z]:\\\\/.test(frame.filename);\n const startsWithSlash = /^\\//.test(frame.filename);\n if (frame.filename && (isWindowsFrame || startsWithSlash)) {\n const filename = isWindowsFrame\n ? frame.filename\n .replace(/^[A-Z]:/, '') // remove Windows-style prefix\n .replace(/\\\\/g, '/') // replace all `\\\\` instances with `/`\n : frame.filename;\n const base = this._root ? relative(this._root, filename) : basename(filename);\n frame.filename = `app:///${base}`;\n }\n return frame;\n };\n\n /**\n * @inheritDoc\n */\n public constructor(options: { root?: string; iteratee?: StackFrameIteratee } = {}) {\n if (options.root) {\n this._root = options.root;\n }\n if (options.iteratee) {\n this._iteratee = options.iteratee;\n }\n }\n\n /**\n * @inheritDoc\n */\n public setupOnce(addGlobalEventProcessor: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n addGlobalEventProcessor(event => {\n const self = getCurrentHub().getIntegration(RewriteFrames);\n if (self) {\n return self.process(event);\n }\n return event;\n });\n }\n\n /** JSDoc */\n public process(event: Event): Event {\n if (event.exception && Array.isArray(event.exception.values)) {\n return this._processExceptionsEvent(event);\n }\n\n if (event.stacktrace) {\n return this._processStacktraceEvent(event);\n }\n\n return event;\n }\n\n /** JSDoc */\n private _processExceptionsEvent(event: Event): Event {\n try {\n return {\n ...event,\n exception: {\n ...event.exception,\n // The check for this is performed inside `process` call itself, safe to skip here\n // tslint:disable-next-line:no-non-null-assertion\n values: event.exception!.values!.map(value => ({\n ...value,\n stacktrace: this._processStacktrace(value.stacktrace),\n })),\n },\n };\n } catch (_oO) {\n return event;\n }\n }\n\n /** JSDoc */\n private _processStacktraceEvent(event: Event): Event {\n try {\n return {\n ...event,\n stacktrace: this._processStacktrace(event.stacktrace),\n };\n } catch (_oO) {\n return event;\n }\n }\n\n /** JSDoc */\n private _processStacktrace(stacktrace?: Stacktrace): Stacktrace {\n return {\n ...stacktrace,\n frames: stacktrace && stacktrace.frames && stacktrace.frames.map(f => this._iteratee(f)),\n };\n }\n}\n","import { Event, EventProcessor, Hub, Integration } from '@sentry/types';\n\n/** This function adds duration since Sentry was initialized till the time event was sent */\nexport class SessionTiming implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = SessionTiming.id;\n /**\n * @inheritDoc\n */\n public static id: string = 'SessionTiming';\n\n /** Exact time Client was initialized expressed in milliseconds since Unix Epoch. */\n protected readonly _startTime: number = Date.now();\n\n /**\n * @inheritDoc\n */\n public setupOnce(addGlobalEventProcessor: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n addGlobalEventProcessor(event => {\n const self = getCurrentHub().getIntegration(SessionTiming);\n if (self) {\n return self.process(event);\n }\n return event;\n });\n }\n\n /**\n * @inheritDoc\n */\n public process(event: Event): Event {\n const now = Date.now();\n\n return {\n ...event,\n extra: {\n ...event.extra,\n ['session:start']: this._startTime,\n ['session:duration']: now - this._startTime,\n ['session:end']: now,\n },\n };\n }\n}\n","import { Event, EventProcessor, Hub, Integration, StackFrame } from '@sentry/types';\n\n/** Add node transaction to the event */\nexport class Transaction implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = Transaction.id;\n /**\n * @inheritDoc\n */\n public static id: string = 'Transaction';\n\n /**\n * @inheritDoc\n */\n public setupOnce(addGlobalEventProcessor: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n addGlobalEventProcessor(event => {\n const self = getCurrentHub().getIntegration(Transaction);\n if (self) {\n return self.process(event);\n }\n return event;\n });\n }\n\n /**\n * @inheritDoc\n */\n public process(event: Event): Event {\n const frames = this._getFramesFromEvent(event);\n\n // use for loop so we don't have to reverse whole frames array\n for (let i = frames.length - 1; i >= 0; i--) {\n const frame = frames[i];\n\n if (frame.in_app === true) {\n event.transaction = this._getTransaction(frame);\n break;\n }\n }\n\n return event;\n }\n\n /** JSDoc */\n private _getFramesFromEvent(event: Event): StackFrame[] {\n const exception = event.exception && event.exception.values && event.exception.values[0];\n return (exception && exception.stacktrace && exception.stacktrace.frames) || [];\n }\n\n /** JSDoc */\n private _getTransaction(frame: StackFrame): string {\n return frame.module || frame.function ? `${frame.module || '?'}/${frame.function || '?'}` : '';\n }\n}\n","import { EventProcessor, Hub, Integration } from '@sentry/types';\nimport { getGlobalObject, isPlainObject, logger } from '@sentry/utils';\n\n/** JSDoc */\ninterface Metadata {\n [key: string]: any;\n componentName?: string;\n propsData?: {\n [key: string]: any;\n };\n lifecycleHook?: string;\n}\n\n/** JSDoc */\nexport class Vue implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = Vue.id;\n /**\n * @inheritDoc\n */\n public static id: string = 'Vue';\n\n /**\n * @inheritDoc\n */\n private readonly _Vue: any; // tslint:disable-line:variable-name\n\n /**\n * When set to false, Sentry will suppress reporting all props data\n * from your Vue components for privacy concerns.\n */\n private readonly _attachProps: boolean = true;\n\n /**\n * When set to true, original Vue's `logError` will be called as well.\n * https://github.com/vuejs/vue/blob/c2b1cfe9ccd08835f2d99f6ce60f67b4de55187f/src/core/util/error.js#L38-L48\n */\n private readonly _logErrors: boolean = false;\n\n /**\n * @inheritDoc\n */\n public constructor(options: { Vue?: any; attachProps?: boolean; logErrors?: boolean } = {}) {\n // tslint:disable-next-line: no-unsafe-any\n this._Vue = options.Vue || getGlobalObject().Vue;\n\n if (options.logErrors !== undefined) {\n this._logErrors = options.logErrors;\n }\n if (options.attachProps === false) {\n this._attachProps = false;\n }\n }\n\n /** JSDoc */\n private _formatComponentName(vm: any): string {\n // tslint:disable:no-unsafe-any\n\n if (vm.$root === vm) {\n return 'root instance';\n }\n const name = vm._isVue ? vm.$options.name || vm.$options._componentTag : vm.name;\n return (\n (name ? `component <${name}>` : 'anonymous component') +\n (vm._isVue && vm.$options.__file ? ` at ${vm.$options.__file}` : '')\n );\n }\n\n /**\n * @inheritDoc\n */\n public setupOnce(_: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n // tslint:disable:no-unsafe-any\n\n if (!this._Vue || !this._Vue.config) {\n logger.error('VueIntegration is missing a Vue instance');\n return;\n }\n\n const oldOnError = this._Vue.config.errorHandler;\n\n this._Vue.config.errorHandler = (error: Error, vm: { [key: string]: any }, info: string): void => {\n const metadata: Metadata = {};\n\n if (isPlainObject(vm)) {\n metadata.componentName = this._formatComponentName(vm);\n\n if (this._attachProps) {\n metadata.propsData = vm.$options.propsData;\n }\n }\n\n if (info !== void 0) {\n metadata.lifecycleHook = info;\n }\n\n if (getCurrentHub().getIntegration(Vue)) {\n // This timeout makes sure that any breadcrumbs are recorded before sending it off the sentry\n setTimeout(() => {\n getCurrentHub().withScope(scope => {\n scope.setContext('vue', metadata);\n getCurrentHub().captureException(error);\n });\n });\n }\n\n if (typeof oldOnError === 'function') {\n oldOnError.call(this._Vue, error, vm, info);\n }\n\n if (this._logErrors) {\n this._Vue.util.warn(`Error in ${info}: \"${error.toString()}\"`, vm);\n // tslint:disable-next-line:no-console\n console.error(error);\n }\n };\n }\n}\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./OttimizzazioneLineare.js\") );\n\t\t\t}, \"route-OttimizzazioneLineare\");\n\t\t}\n\n\t\texport default Async(load);\n\t","import { consoleSandbox, getGlobalObject } from './misc';\n\n// TODO: Implement different loggers for different environments\nconst global = getGlobalObject();\n\n/** Prefix for logging strings */\nconst PREFIX = 'Sentry Logger ';\n\n/** JSDoc */\nclass Logger {\n /** JSDoc */\n private _enabled: boolean;\n\n /** JSDoc */\n public constructor() {\n this._enabled = false;\n }\n\n /** JSDoc */\n public disable(): void {\n this._enabled = false;\n }\n\n /** JSDoc */\n public enable(): void {\n this._enabled = true;\n }\n\n /** JSDoc */\n public log(...args: any[]): void {\n if (!this._enabled) {\n return;\n }\n consoleSandbox(() => {\n global.console.log(`${PREFIX}[Log]: ${args.join(' ')}`); // tslint:disable-line:no-console\n });\n }\n\n /** JSDoc */\n public warn(...args: any[]): void {\n if (!this._enabled) {\n return;\n }\n consoleSandbox(() => {\n global.console.warn(`${PREFIX}[Warn]: ${args.join(' ')}`); // tslint:disable-line:no-console\n });\n }\n\n /** JSDoc */\n public error(...args: any[]): void {\n if (!this._enabled) {\n return;\n }\n consoleSandbox(() => {\n global.console.error(`${PREFIX}[Error]: ${args.join(' ')}`); // tslint:disable-line:no-console\n });\n }\n}\n\n// Ensure we only have a single logger instance, even if multiple versions of @sentry/utils are being used\nglobal.__SENTRY__ = global.__SENTRY__ || {};\nconst logger = (global.__SENTRY__.logger as Logger) || (global.__SENTRY__.logger = new Logger());\n\nexport { logger };\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./CalcoloNumerico.js\") );\n\t\t\t}, \"route-CalcoloNumerico\");\n\t\t}\n\n\t\texport default Async(load);\n\t","import { logger } from './logger';\nimport { getGlobalObject } from './misc';\n\n/**\n * Tells whether current environment supports ErrorEvent objects\n * {@link supportsErrorEvent}.\n *\n * @returns Answer to the given question.\n */\nexport function supportsErrorEvent(): boolean {\n try {\n // tslint:disable:no-unused-expression\n new ErrorEvent('');\n return true;\n } catch (e) {\n return false;\n }\n}\n\n/**\n * Tells whether current environment supports DOMError objects\n * {@link supportsDOMError}.\n *\n * @returns Answer to the given question.\n */\nexport function supportsDOMError(): boolean {\n try {\n // It really needs 1 argument, not 0.\n // Chrome: VM89:1 Uncaught TypeError: Failed to construct 'DOMError':\n // 1 argument required, but only 0 present.\n // @ts-ignore\n // tslint:disable:no-unused-expression\n new DOMError('');\n return true;\n } catch (e) {\n return false;\n }\n}\n\n/**\n * Tells whether current environment supports DOMException objects\n * {@link supportsDOMException}.\n *\n * @returns Answer to the given question.\n */\nexport function supportsDOMException(): boolean {\n try {\n // tslint:disable:no-unused-expression\n new DOMException('');\n return true;\n } catch (e) {\n return false;\n }\n}\n\n/**\n * Tells whether current environment supports Fetch API\n * {@link supportsFetch}.\n *\n * @returns Answer to the given question.\n */\nexport function supportsFetch(): boolean {\n if (!('fetch' in getGlobalObject())) {\n return false;\n }\n\n try {\n // tslint:disable-next-line:no-unused-expression\n new Headers();\n // tslint:disable-next-line:no-unused-expression\n new Request('');\n // tslint:disable-next-line:no-unused-expression\n new Response();\n return true;\n } catch (e) {\n return false;\n }\n}\n/**\n * isNativeFetch checks if the given function is a native implementation of fetch()\n */\nfunction isNativeFetch(func: Function): boolean {\n return func && /^function fetch\\(\\)\\s+\\{\\s+\\[native code\\]\\s+\\}$/.test(func.toString());\n}\n\n/**\n * Tells whether current environment supports Fetch API natively\n * {@link supportsNativeFetch}.\n *\n * @returns true if `window.fetch` is natively implemented, false otherwise\n */\nexport function supportsNativeFetch(): boolean {\n if (!supportsFetch()) {\n return false;\n }\n\n const global = getGlobalObject();\n\n // Fast path to avoid DOM I/O\n // tslint:disable-next-line:no-unbound-method\n if (isNativeFetch(global.fetch)) {\n return true;\n }\n\n // window.fetch is implemented, but is polyfilled or already wrapped (e.g: by a chrome extension)\n // so create a \"pure\" iframe to see if that has native fetch\n let result = false;\n const doc = global.document;\n // tslint:disable-next-line:no-unbound-method deprecation\n if (doc && typeof (doc.createElement as unknown) === `function`) {\n try {\n const sandbox = doc.createElement('iframe');\n sandbox.hidden = true;\n doc.head.appendChild(sandbox);\n if (sandbox.contentWindow && sandbox.contentWindow.fetch) {\n // tslint:disable-next-line:no-unbound-method\n result = isNativeFetch(sandbox.contentWindow.fetch);\n }\n doc.head.removeChild(sandbox);\n } catch (err) {\n logger.warn('Could not create sandbox iframe for pure fetch check, bailing to window.fetch: ', err);\n }\n }\n\n return result;\n}\n\n/**\n * Tells whether current environment supports ReportingObserver API\n * {@link supportsReportingObserver}.\n *\n * @returns Answer to the given question.\n */\nexport function supportsReportingObserver(): boolean {\n // tslint:disable-next-line: no-unsafe-any\n return 'ReportingObserver' in getGlobalObject();\n}\n\n/**\n * Tells whether current environment supports Referrer Policy API\n * {@link supportsReferrerPolicy}.\n *\n * @returns Answer to the given question.\n */\nexport function supportsReferrerPolicy(): boolean {\n // Despite all stars in the sky saying that Edge supports old draft syntax, aka 'never', 'always', 'origin' and 'default\n // https://caniuse.com/#feat=referrer-policy\n // It doesn't. And it throw exception instead of ignoring this parameter...\n // REF: https://github.com/getsentry/raven-js/issues/1233\n\n if (!supportsFetch()) {\n return false;\n }\n\n try {\n // tslint:disable:no-unused-expression\n new Request('_', {\n referrerPolicy: 'origin' as ReferrerPolicy,\n });\n return true;\n } catch (e) {\n return false;\n }\n}\n\n/**\n * Tells whether current environment supports History API\n * {@link supportsHistory}.\n *\n * @returns Answer to the given question.\n */\nexport function supportsHistory(): boolean {\n // NOTE: in Chrome App environment, touching history.pushState, *even inside\n // a try/catch block*, will cause Chrome to output an error to console.error\n // borrowed from: https://github.com/angular/angular.js/pull/13945/files\n const global = getGlobalObject();\n const chrome = (global as any).chrome;\n // tslint:disable-next-line:no-unsafe-any\n const isChromePackagedApp = chrome && chrome.app && chrome.app.runtime;\n const hasHistoryApi = 'history' in global && !!global.history.pushState && !!global.history.replaceState;\n\n return !isChromePackagedApp && hasHistoryApi;\n}\n","/** JSDoc */\nexport enum Severity {\n /** JSDoc */\n Fatal = 'fatal',\n /** JSDoc */\n Error = 'error',\n /** JSDoc */\n Warning = 'warning',\n /** JSDoc */\n Log = 'log',\n /** JSDoc */\n Info = 'info',\n /** JSDoc */\n Debug = 'debug',\n /** JSDoc */\n Critical = 'critical',\n}\n// tslint:disable:completed-docs\n// tslint:disable:no-unnecessary-qualifier no-namespace\nexport namespace Severity {\n /**\n * Converts a string-based level into a {@link Severity}.\n *\n * @param level string representation of Severity\n * @returns Severity\n */\n export function fromString(level: string): Severity {\n switch (level) {\n case 'debug':\n return Severity.Debug;\n case 'info':\n return Severity.Info;\n case 'warn':\n case 'warning':\n return Severity.Warning;\n case 'error':\n return Severity.Error;\n case 'fatal':\n return Severity.Fatal;\n case 'critical':\n return Severity.Critical;\n case 'log':\n default:\n return Severity.Log;\n }\n }\n}\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./MingwInstall.js\") );\n\t\t\t}, \"route-MingwInstall\");\n\t\t}\n\n\t\texport default Async(load);\n\t","module.exports = function(originalModule) {\n\tif (!originalModule.webpackPolyfill) {\n\t\tvar module = Object.create(originalModule);\n\t\t// module.parent = undefined by default\n\t\tif (!module.children) module.children = [];\n\t\tObject.defineProperty(module, \"loaded\", {\n\t\t\tenumerable: true,\n\t\t\tget: function() {\n\t\t\t\treturn module.l;\n\t\t\t}\n\t\t});\n\t\tObject.defineProperty(module, \"id\", {\n\t\t\tenumerable: true,\n\t\t\tget: function() {\n\t\t\t\treturn module.i;\n\t\t\t}\n\t\t});\n\t\tObject.defineProperty(module, \"exports\", {\n\t\t\tenumerable: true\n\t\t});\n\t\tmodule.webpackPolyfill = 1;\n\t}\n\treturn module;\n};\n","// Import debugging tools\nlet Sentry = null;\nif(process.env.NODE_ENV === \"development\") {\n\tconsole.debug(\"Initializing Preact Debugger...\")\n\trequire(\"preact/debug\");\n}\nelse if(process.env.NODE_ENV === \"production\") {\n\tconsole.debug(\"Initializing Sentry...\")\n\tSentry = require(\"@sentry/browser\");\n\tlet SentryIntegrations = require(\"@sentry/integrations\")\n\t// noinspection JSUnresolvedVariable\n\tSentry.init({\n\t\tdsn: \"https://9f5089346fd14e04a6f412638474dfec@o40131.ingest.sentry.io/5255500\",\n\t\trelease: process.env.RELEASE,\n\t\tenvironment: \"production\",\n\t\tbeforeSend(event, hint) {\n\t\t\tif (event.exception) {\n\t\t\t\tSentry.showReportDialog({ eventId: event.event_id });\n\t\t\t}\n\t\t\treturn event;\n\t\t}\n\t});\n}\n\n// noinspection ES6UnusedImports\nimport _style from './index.less';\n// noinspection ES6UnusedImports\nimport _manifest from './meta/manifest.json';\n// noinspection ES6UnusedImports\nimport _cname from './meta/CNAME';\n// noinspection ES6UnusedImports\nimport _nojekyll from './meta/.nojekyll';\n\nimport Router from 'preact-router';\nimport {createHashHistory} from \"history\";\nimport Home from './routes/Home';\nimport Fisica from './routes/Fisica';\nimport VlDiGeometria from './routes/VlDiGeometria';\nimport MingwInstall from './routes/MingwInstall';\nimport Footer from './components/Layout/Footer';\nimport Statistica from './routes/Statistica';\nimport OttimizzazioneLineare from \"./routes/OttimizzazioneLineare\";\nimport BasiDiDati from './routes/BasiDiDati';\nimport CalcoloNumerico from './routes/CalcoloNumerico';\nimport ApprendimentoSistemiArtificiali from \"./routes/ApprendimentoSistemiArtificiali\";\nimport LatexRenderColor from \"./contexts/LatexRenderColor\";\nimport NetLogo from \"./routes/NetLogo\";\nimport AlgoritmiEStruttureDati from \"./routes/AlgoritmiEStruttureDati\";\n\n// noinspection JSUnusedGlobalSymbols\nexport default function(props) {\n\treturn (\n\t\t
\n\t\t\t\n\t\t\t\t

Appuntiweb di Steffo

\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\t
\n\t\t\t\n\t\t
\n\t);\n}\n","import { h, Component } from 'preact';\n\nexport default function(req) {\n\tfunction Async() {\n\t\tComponent.call(this);\n\n\t\tlet b, old;\n\t\tthis.componentWillMount = () => {\n\t\t\tb = this.base = this.nextBase || this.__b; // short circuits 1st render\n\t\t\treq(m => {\n\t\t\t\tthis.setState({ child: m.default || m });\n\t\t\t});\n\t\t};\n\n\t\tthis.shouldComponentUpdate = (_, nxt) => {\n\t\t\tnxt = nxt.child === void 0;\n\t\t\tif (nxt && old === void 0 && b) {\n\t\t\t\t// Node.TEXT_NODE\n\t\t\t\tif (b.nodeType === 3) {\n\t\t\t\t\told = b.data;\n\t\t\t\t} else {\n\t\t\t\t\told = h(b.nodeName, {\n\t\t\t\t\t\tdangerouslySetInnerHTML: { __html: b.innerHTML },\n\t\t\t\t\t});\n\t\t\t\t}\n\t\t\t} else {\n\t\t\t\told = ''; // dump it\n\t\t\t}\n\t\t\treturn !nxt;\n\t\t};\n\n\t\tthis.render = (p, s) => (s.child ? h(s.child, p) : old);\n\t}\n\t(Async.prototype = new Component()).constructor = Async;\n\treturn Async;\n}\n","/**\n * Assign properties from `props` to `obj`\n * @template O, P The obj and props types\n * @param {O} obj The object to copy properties to\n * @param {P} props The object to copy properties from\n * @returns {O & P}\n */\nexport function assign(obj, props) {\n\tfor (let i in props) obj[i] = props[i];\n\treturn /** @type {O & P} */ (obj);\n}\n\n/**\n * Remove a child node from its parent if attached. This is a workaround for\n * IE11 which doesn't support `Element.prototype.remove()`. Using this function\n * is smaller than including a dedicated polyfill.\n * @param {Node} node The node to remove\n */\nexport function removeNode(node) {\n\tlet parentNode = node.parentNode;\n\tif (parentNode) parentNode.removeChild(node);\n}\n","import { cloneElement, createElement, Component, toChildArray } from 'preact';\nimport { exec, prepareVNodeForRanking, assign, pathRankSort } from './util';\n\nlet customHistory = null;\n\nconst ROUTERS = [];\n\nconst subscribers = [];\n\nconst EMPTY = {};\n\nfunction setUrl(url, type='push') {\n\tif (customHistory && customHistory[type]) {\n\t\tcustomHistory[type](url);\n\t}\n\telse if (typeof history!=='undefined' && history[type+'State']) {\n\t\thistory[type+'State'](null, null, url);\n\t}\n}\n\n\nfunction getCurrentUrl() {\n\tlet url;\n\tif (customHistory && customHistory.location) {\n\t\turl = customHistory.location;\n\t}\n\telse if (customHistory && customHistory.getCurrentLocation) {\n\t\turl = customHistory.getCurrentLocation();\n\t}\n\telse {\n\t\turl = typeof location!=='undefined' ? location : EMPTY;\n\t}\n\treturn `${url.pathname || ''}${url.search || ''}`;\n}\n\n\n\nfunction route(url, replace=false) {\n\tif (typeof url!=='string' && url.url) {\n\t\treplace = url.replace;\n\t\turl = url.url;\n\t}\n\n\t// only push URL into history if we can handle it\n\tif (canRoute(url)) {\n\t\tsetUrl(url, replace ? 'replace' : 'push');\n\t}\n\n\treturn routeTo(url);\n}\n\n\n/** Check if the given URL can be handled by any router instances. */\nfunction canRoute(url) {\n\tfor (let i=ROUTERS.length; i--; ) {\n\t\tif (ROUTERS[i].canRoute(url)) return true;\n\t}\n\treturn false;\n}\n\n\n/** Tell all router instances to handle the given URL. */\nfunction routeTo(url) {\n\tlet didRoute = false;\n\tfor (let i=0; i {\n\t\t\t\trouteTo(getCurrentUrl());\n\t\t\t});\n\t\t}\n\t\taddEventListener('click', delegateLinkHandler);\n\t}\n\teventListenersInitialized = true;\n}\n\n\nclass Router extends Component {\n\tconstructor(props) {\n\t\tsuper(props);\n\t\tif (props.history) {\n\t\t\tcustomHistory = props.history;\n\t\t}\n\n\t\tthis.state = {\n\t\t\turl: props.url || getCurrentUrl()\n\t\t};\n\n\t\tinitEventListeners();\n\t}\n\n\tshouldComponentUpdate(props) {\n\t\tif (props.static!==true) return true;\n\t\treturn props.url!==this.props.url || props.onChange!==this.props.onChange;\n\t}\n\n\t/** Check if the given URL can be matched against any children */\n\tcanRoute(url) {\n\t\tconst children = toChildArray(this.props.children);\n\t\treturn this.getMatchingChildren(children, url, false).length > 0;\n\t}\n\n\t/** Re-render children with a new URL to match against. */\n\trouteTo(url) {\n\t\tthis.setState({ url });\n\n\t\tconst didRoute = this.canRoute(url);\n\n\t\t// trigger a manual re-route if we're not in the middle of an update:\n\t\tif (!this.updating) this.forceUpdate();\n\n\t\treturn didRoute;\n\t}\n\n\tcomponentWillMount() {\n\t\tROUTERS.push(this);\n\t\tthis.updating = true;\n\t}\n\n\tcomponentDidMount() {\n\t\tif (customHistory) {\n\t\t\tthis.unlisten = customHistory.listen((location) => {\n\t\t\t\tthis.routeTo(`${location.pathname || ''}${location.search || ''}`);\n\t\t\t});\n\t\t}\n\t\tthis.updating = false;\n\t}\n\n\tcomponentWillUnmount() {\n\t\tif (typeof this.unlisten==='function') this.unlisten();\n\t\tROUTERS.splice(ROUTERS.indexOf(this), 1);\n\t}\n\n\tcomponentWillUpdate() {\n\t\tthis.updating = true;\n\t}\n\n\tcomponentDidUpdate() {\n\t\tthis.updating = false;\n\t}\n\n\tgetMatchingChildren(children, url, invoke) {\n\t\treturn children\n\t\t\t.filter(prepareVNodeForRanking)\n\t\t\t.sort(pathRankSort)\n\t\t\t.map( vnode => {\n\t\t\t\tlet matches = exec(url, vnode.props.path, vnode.props);\n\t\t\t\tif (matches) {\n\t\t\t\t\tif (invoke !== false) {\n\t\t\t\t\t\tlet newProps = { url, matches };\n\t\t\t\t\t\tassign(newProps, matches);\n\t\t\t\t\t\tdelete newProps.ref;\n\t\t\t\t\t\tdelete newProps.key;\n\t\t\t\t\t\treturn cloneElement(vnode, newProps);\n\t\t\t\t\t}\n\t\t\t\t\treturn vnode;\n\t\t\t\t}\n\t\t\t}).filter(Boolean);\n\t}\n\n\trender({ children, onChange }, { url }) {\n\t\tlet active = this.getMatchingChildren(toChildArray(children), url, true);\n\n\t\tlet current = active[0] || null;\n\n\t\tlet previous = this.previousUrl;\n\t\tif (url!==previous) {\n\t\t\tthis.previousUrl = url;\n\t\t\tif (typeof onChange==='function') {\n\t\t\t\tonChange({\n\t\t\t\t\trouter: this,\n\t\t\t\t\turl,\n\t\t\t\t\tprevious,\n\t\t\t\t\tactive,\n\t\t\t\t\tcurrent\n\t\t\t\t});\n\t\t\t}\n\t\t}\n\n\t\treturn current;\n\t}\n}\n\nconst Link = (props) => (\n\tcreateElement('a', assign({ onClick: handleLinkClick }, props))\n);\n\nconst Route = props => createElement(props.component, props);\n\nRouter.subscribers = subscribers;\nRouter.getCurrentUrl = getCurrentUrl;\nRouter.route = route;\nRouter.Router = Router;\nRouter.Route = Route;\nRouter.Link = Link;\nRouter.exec = exec;\n\nexport { subscribers, getCurrentUrl, route, Router, Route, Link, exec };\nexport default Router;\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./ApprendimentoSistemiArtificiali.js\") );\n\t\t\t}, \"route-ApprendimentoSistemiArtificiali\");\n\t\t}\n\n\t\texport default Async(load);\n\t","/*! *****************************************************************************\r\nCopyright (c) Microsoft Corporation. All rights reserved.\r\nLicensed under the Apache License, Version 2.0 (the \"License\"); you may not use\r\nthis file except in compliance with the License. You may obtain a copy of the\r\nLicense at http://www.apache.org/licenses/LICENSE-2.0\r\n\r\nTHIS CODE IS PROVIDED ON AN *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY\r\nKIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED\r\nWARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,\r\nMERCHANTABLITY OR NON-INFRINGEMENT.\r\n\r\nSee the Apache Version 2.0 License for specific language governing permissions\r\nand limitations under the License.\r\n***************************************************************************** */\r\n/* global Reflect, Promise */\r\n\r\nvar extendStatics = function(d, b) {\r\n extendStatics = Object.setPrototypeOf ||\r\n ({ __proto__: [] } instanceof Array && function (d, b) { d.__proto__ = b; }) ||\r\n function (d, b) { for (var p in b) if (b.hasOwnProperty(p)) d[p] = b[p]; };\r\n return extendStatics(d, b);\r\n};\r\n\r\nexport function __extends(d, b) {\r\n extendStatics(d, b);\r\n function __() { this.constructor = d; }\r\n d.prototype = b === null ? Object.create(b) : (__.prototype = b.prototype, new __());\r\n}\r\n\r\nexport var __assign = function() {\r\n __assign = Object.assign || function __assign(t) {\r\n for (var s, i = 1, n = arguments.length; i < n; i++) {\r\n s = arguments[i];\r\n for (var p in s) if (Object.prototype.hasOwnProperty.call(s, p)) t[p] = s[p];\r\n }\r\n return t;\r\n }\r\n return __assign.apply(this, arguments);\r\n}\r\n\r\nexport function __rest(s, e) {\r\n var t = {};\r\n for (var p in s) if (Object.prototype.hasOwnProperty.call(s, p) && e.indexOf(p) < 0)\r\n t[p] = s[p];\r\n if (s != null && typeof Object.getOwnPropertySymbols === \"function\")\r\n for (var i = 0, p = Object.getOwnPropertySymbols(s); i < p.length; i++) {\r\n if (e.indexOf(p[i]) < 0 && Object.prototype.propertyIsEnumerable.call(s, p[i]))\r\n t[p[i]] = s[p[i]];\r\n }\r\n return t;\r\n}\r\n\r\nexport function __decorate(decorators, target, key, desc) {\r\n var c = arguments.length, r = c < 3 ? target : desc === null ? desc = Object.getOwnPropertyDescriptor(target, key) : desc, d;\r\n if (typeof Reflect === \"object\" && typeof Reflect.decorate === \"function\") r = Reflect.decorate(decorators, target, key, desc);\r\n else for (var i = decorators.length - 1; i >= 0; i--) if (d = decorators[i]) r = (c < 3 ? d(r) : c > 3 ? d(target, key, r) : d(target, key)) || r;\r\n return c > 3 && r && Object.defineProperty(target, key, r), r;\r\n}\r\n\r\nexport function __param(paramIndex, decorator) {\r\n return function (target, key) { decorator(target, key, paramIndex); }\r\n}\r\n\r\nexport function __metadata(metadataKey, metadataValue) {\r\n if (typeof Reflect === \"object\" && typeof Reflect.metadata === \"function\") return Reflect.metadata(metadataKey, metadataValue);\r\n}\r\n\r\nexport function __awaiter(thisArg, _arguments, P, generator) {\r\n function adopt(value) { return value instanceof P ? value : new P(function (resolve) { resolve(value); }); }\r\n return new (P || (P = Promise))(function (resolve, reject) {\r\n function fulfilled(value) { try { step(generator.next(value)); } catch (e) { reject(e); } }\r\n function rejected(value) { try { step(generator[\"throw\"](value)); } catch (e) { reject(e); } }\r\n function step(result) { result.done ? resolve(result.value) : adopt(result.value).then(fulfilled, rejected); }\r\n step((generator = generator.apply(thisArg, _arguments || [])).next());\r\n });\r\n}\r\n\r\nexport function __generator(thisArg, body) {\r\n var _ = { label: 0, sent: function() { if (t[0] & 1) throw t[1]; return t[1]; }, trys: [], ops: [] }, f, y, t, g;\r\n return g = { next: verb(0), \"throw\": verb(1), \"return\": verb(2) }, typeof Symbol === \"function\" && (g[Symbol.iterator] = function() { return this; }), g;\r\n function verb(n) { return function (v) { return step([n, v]); }; }\r\n function step(op) {\r\n if (f) throw new TypeError(\"Generator is already executing.\");\r\n while (_) try {\r\n if (f = 1, y && (t = op[0] & 2 ? y[\"return\"] : op[0] ? y[\"throw\"] || ((t = y[\"return\"]) && t.call(y), 0) : y.next) && !(t = t.call(y, op[1])).done) return t;\r\n if (y = 0, t) op = [op[0] & 2, t.value];\r\n switch (op[0]) {\r\n case 0: case 1: t = op; break;\r\n case 4: _.label++; return { value: op[1], done: false };\r\n case 5: _.label++; y = op[1]; op = [0]; continue;\r\n case 7: op = _.ops.pop(); _.trys.pop(); continue;\r\n default:\r\n if (!(t = _.trys, t = t.length > 0 && t[t.length - 1]) && (op[0] === 6 || op[0] === 2)) { _ = 0; continue; }\r\n if (op[0] === 3 && (!t || (op[1] > t[0] && op[1] < t[3]))) { _.label = op[1]; break; }\r\n if (op[0] === 6 && _.label < t[1]) { _.label = t[1]; t = op; break; }\r\n if (t && _.label < t[2]) { _.label = t[2]; _.ops.push(op); break; }\r\n if (t[2]) _.ops.pop();\r\n _.trys.pop(); continue;\r\n }\r\n op = body.call(thisArg, _);\r\n } catch (e) { op = [6, e]; y = 0; } finally { f = t = 0; }\r\n if (op[0] & 5) throw op[1]; return { value: op[0] ? op[1] : void 0, done: true };\r\n }\r\n}\r\n\r\nexport function __exportStar(m, exports) {\r\n for (var p in m) if (!exports.hasOwnProperty(p)) exports[p] = m[p];\r\n}\r\n\r\nexport function __values(o) {\r\n var s = typeof Symbol === \"function\" && Symbol.iterator, m = s && o[s], i = 0;\r\n if (m) return m.call(o);\r\n if (o && typeof o.length === \"number\") return {\r\n next: function () {\r\n if (o && i >= o.length) o = void 0;\r\n return { value: o && o[i++], done: !o };\r\n }\r\n };\r\n throw new TypeError(s ? \"Object is not iterable.\" : \"Symbol.iterator is not defined.\");\r\n}\r\n\r\nexport function __read(o, n) {\r\n var m = typeof Symbol === \"function\" && o[Symbol.iterator];\r\n if (!m) return o;\r\n var i = m.call(o), r, ar = [], e;\r\n try {\r\n while ((n === void 0 || n-- > 0) && !(r = i.next()).done) ar.push(r.value);\r\n }\r\n catch (error) { e = { error: error }; }\r\n finally {\r\n try {\r\n if (r && !r.done && (m = i[\"return\"])) m.call(i);\r\n }\r\n finally { if (e) throw e.error; }\r\n }\r\n return ar;\r\n}\r\n\r\nexport function __spread() {\r\n for (var ar = [], i = 0; i < arguments.length; i++)\r\n ar = ar.concat(__read(arguments[i]));\r\n return ar;\r\n}\r\n\r\nexport function __spreadArrays() {\r\n for (var s = 0, i = 0, il = arguments.length; i < il; i++) s += arguments[i].length;\r\n for (var r = Array(s), k = 0, i = 0; i < il; i++)\r\n for (var a = arguments[i], j = 0, jl = a.length; j < jl; j++, k++)\r\n r[k] = a[j];\r\n return r;\r\n};\r\n\r\nexport function __await(v) {\r\n return this instanceof __await ? (this.v = v, this) : new __await(v);\r\n}\r\n\r\nexport function __asyncGenerator(thisArg, _arguments, generator) {\r\n if (!Symbol.asyncIterator) throw new TypeError(\"Symbol.asyncIterator is not defined.\");\r\n var g = generator.apply(thisArg, _arguments || []), i, q = [];\r\n return i = {}, verb(\"next\"), verb(\"throw\"), verb(\"return\"), i[Symbol.asyncIterator] = function () { return this; }, i;\r\n function verb(n) { if (g[n]) i[n] = function (v) { return new Promise(function (a, b) { q.push([n, v, a, b]) > 1 || resume(n, v); }); }; }\r\n function resume(n, v) { try { step(g[n](v)); } catch (e) { settle(q[0][3], e); } }\r\n function step(r) { r.value instanceof __await ? Promise.resolve(r.value.v).then(fulfill, reject) : settle(q[0][2], r); }\r\n function fulfill(value) { resume(\"next\", value); }\r\n function reject(value) { resume(\"throw\", value); }\r\n function settle(f, v) { if (f(v), q.shift(), q.length) resume(q[0][0], q[0][1]); }\r\n}\r\n\r\nexport function __asyncDelegator(o) {\r\n var i, p;\r\n return i = {}, verb(\"next\"), verb(\"throw\", function (e) { throw e; }), verb(\"return\"), i[Symbol.iterator] = function () { return this; }, i;\r\n function verb(n, f) { i[n] = o[n] ? function (v) { return (p = !p) ? { value: __await(o[n](v)), done: n === \"return\" } : f ? f(v) : v; } : f; }\r\n}\r\n\r\nexport function __asyncValues(o) {\r\n if (!Symbol.asyncIterator) throw new TypeError(\"Symbol.asyncIterator is not defined.\");\r\n var m = o[Symbol.asyncIterator], i;\r\n return m ? m.call(o) : (o = typeof __values === \"function\" ? __values(o) : o[Symbol.iterator](), i = {}, verb(\"next\"), verb(\"throw\"), verb(\"return\"), i[Symbol.asyncIterator] = function () { return this; }, i);\r\n function verb(n) { i[n] = o[n] && function (v) { return new Promise(function (resolve, reject) { v = o[n](v), settle(resolve, reject, v.done, v.value); }); }; }\r\n function settle(resolve, reject, d, v) { Promise.resolve(v).then(function(v) { resolve({ value: v, done: d }); }, reject); }\r\n}\r\n\r\nexport function __makeTemplateObject(cooked, raw) {\r\n if (Object.defineProperty) { Object.defineProperty(cooked, \"raw\", { value: raw }); } else { cooked.raw = raw; }\r\n return cooked;\r\n};\r\n\r\nexport function __importStar(mod) {\r\n if (mod && mod.__esModule) return mod;\r\n var result = {};\r\n if (mod != null) for (var k in mod) if (Object.hasOwnProperty.call(mod, k)) result[k] = mod[k];\r\n result.default = mod;\r\n return result;\r\n}\r\n\r\nexport function __importDefault(mod) {\r\n return (mod && mod.__esModule) ? mod : { default: mod };\r\n}\r\n\r\nexport function __classPrivateFieldGet(receiver, privateMap) {\r\n if (!privateMap.has(receiver)) {\r\n throw new TypeError(\"attempted to get private field on non-instance\");\r\n }\r\n return privateMap.get(receiver);\r\n}\r\n\r\nexport function __classPrivateFieldSet(receiver, privateMap, value) {\r\n if (!privateMap.has(receiver)) {\r\n throw new TypeError(\"attempted to set private field on non-instance\");\r\n }\r\n privateMap.set(receiver, value);\r\n return value;\r\n}\r\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./AlgoritmiEStruttureDati.js\") );\n\t\t\t}, \"route-AlgoritmiEStruttureDati\");\n\t\t}\n\n\t\texport default Async(load);\n\t","import { isRegExp, isString } from './is';\n\n/**\n * Truncates given string to the maximum characters count\n *\n * @param str An object that contains serializable values\n * @param max Maximum number of characters in truncated string\n * @returns string Encoded\n */\nexport function truncate(str: string, max: number = 0): string {\n // tslint:disable-next-line:strict-type-predicates\n if (typeof str !== 'string' || max === 0) {\n return str;\n }\n return str.length <= max ? str : `${str.substr(0, max)}...`;\n}\n\n/**\n * This is basically just `trim_line` from\n * https://github.com/getsentry/sentry/blob/master/src/sentry/lang/javascript/processor.py#L67\n *\n * @param str An object that contains serializable values\n * @param max Maximum number of characters in truncated string\n * @returns string Encoded\n */\n\nexport function snipLine(line: string, colno: number): string {\n let newLine = line;\n const ll = newLine.length;\n if (ll <= 150) {\n return newLine;\n }\n if (colno > ll) {\n colno = ll; // tslint:disable-line:no-parameter-reassignment\n }\n\n let start = Math.max(colno - 60, 0);\n if (start < 5) {\n start = 0;\n }\n\n let end = Math.min(start + 140, ll);\n if (end > ll - 5) {\n end = ll;\n }\n if (end === ll) {\n start = Math.max(end - 140, 0);\n }\n\n newLine = newLine.slice(start, end);\n if (start > 0) {\n newLine = `'{snip} ${newLine}`;\n }\n if (end < ll) {\n newLine += ' {snip}';\n }\n\n return newLine;\n}\n\n/**\n * Join values in array\n * @param input array of values to be joined together\n * @param delimiter string to be placed in-between values\n * @returns Joined values\n */\nexport function safeJoin(input: any[], delimiter?: string): string {\n if (!Array.isArray(input)) {\n return '';\n }\n\n const output = [];\n // tslint:disable-next-line:prefer-for-of\n for (let i = 0; i < input.length; i++) {\n const value = input[i];\n try {\n output.push(String(value));\n } catch (e) {\n output.push('[value cannot be serialized]');\n }\n }\n\n return output.join(delimiter);\n}\n\n/**\n * Checks if the value matches a regex or includes the string\n * @param value The string value to be checked against\n * @param pattern Either a regex or a string that must be contained in value\n */\nexport function isMatchingPattern(value: string, pattern: RegExp | string): boolean {\n if (!isString(value)) {\n return false;\n }\n\n if (isRegExp(pattern)) {\n return (pattern as RegExp).test(value);\n }\n if (typeof pattern === 'string') {\n return value.indexOf(pattern) !== -1;\n }\n return false;\n}\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./Home.js\") );\n\t\t\t}, \"route-Home\");\n\t\t}\n\n\t\texport default Async(load);\n\t","import options from './options';\n\n/**\n * Create an virtual node (used for JSX)\n * @param {import('./internal').VNode[\"type\"]} type The node name or Component\n * constructor for this virtual node\n * @param {object | null | undefined} [props] The properties of the virtual node\n * @param {Array} [children] The children of the virtual node\n * @returns {import('./internal').VNode}\n */\nexport function createElement(type, props, children) {\n\tlet normalizedProps = {},\n\t\ti;\n\tfor (i in props) {\n\t\tif (i !== 'key' && i !== 'ref') normalizedProps[i] = props[i];\n\t}\n\n\tif (arguments.length > 3) {\n\t\tchildren = [children];\n\t\t// https://github.com/preactjs/preact/issues/1916\n\t\tfor (i = 3; i < arguments.length; i++) {\n\t\t\tchildren.push(arguments[i]);\n\t\t}\n\t}\n\tif (children != null) {\n\t\tnormalizedProps.children = children;\n\t}\n\n\t// If a Component VNode, check for and apply defaultProps\n\t// Note: type may be undefined in development, must never error here.\n\tif (typeof type == 'function' && type.defaultProps != null) {\n\t\tfor (i in type.defaultProps) {\n\t\t\tif (normalizedProps[i] === undefined) {\n\t\t\t\tnormalizedProps[i] = type.defaultProps[i];\n\t\t\t}\n\t\t}\n\t}\n\n\treturn createVNode(\n\t\ttype,\n\t\tnormalizedProps,\n\t\tprops && props.key,\n\t\tprops && props.ref,\n\t\tnull\n\t);\n}\n\n/**\n * Create a VNode (used internally by Preact)\n * @param {import('./internal').VNode[\"type\"]} type The node name or Component\n * Constructor for this virtual node\n * @param {object | string | number | null} props The properties of this virtual node.\n * If this virtual node represents a text node, this is the text of the node (string or number).\n * @param {string | number | null} key The key for this virtual node, used when\n * diffing it against its children\n * @param {import('./internal').VNode[\"ref\"]} ref The ref property that will\n * receive a reference to its created child\n * @returns {import('./internal').VNode}\n */\nexport function createVNode(type, props, key, ref, original) {\n\t// V8 seems to be better at detecting type shapes if the object is allocated from the same call site\n\t// Do not inline into createElement and coerceToVNode!\n\tconst vnode = {\n\t\ttype,\n\t\tprops,\n\t\tkey,\n\t\tref,\n\t\t_children: null,\n\t\t_parent: null,\n\t\t_depth: 0,\n\t\t_dom: null,\n\t\t// _nextDom must be initialized to undefined b/c it will eventually\n\t\t// be set to dom.nextSibling which can return `null` and it is important\n\t\t// to be able to distinguish between an uninitialized _nextDom and\n\t\t// a _nextDom that has been set to `null`\n\t\t_nextDom: undefined,\n\t\t_component: null,\n\t\tconstructor: undefined,\n\t\t_original: original\n\t};\n\n\tif (original == null) vnode._original = vnode;\n\tif (options.vnode) options.vnode(vnode);\n\n\treturn vnode;\n}\n\nexport function createRef() {\n\treturn {};\n}\n\nexport function Fragment(props) {\n\treturn props.children;\n}\n\n/**\n * Check if a the argument is a valid Preact VNode.\n * @param {*} vnode\n * @returns {vnode is import('./internal').VNode}\n */\nexport const isValidElement = vnode =>\n\tvnode != null && vnode.constructor === undefined;\n","import { assign } from './util';\nimport { diff, commitRoot } from './diff/index';\nimport options from './options';\nimport { Fragment } from './create-element';\n\n/**\n * Base Component class. Provides `setState()` and `forceUpdate()`, which\n * trigger rendering\n * @param {object} props The initial component props\n * @param {object} context The initial context from parent components'\n * getChildContext\n */\nexport function Component(props, context) {\n\tthis.props = props;\n\tthis.context = context;\n}\n\n/**\n * Update component state and schedule a re-render.\n * @param {object | ((s: object, p: object) => object)} update A hash of state\n * properties to update with new values or a function that given the current\n * state and props returns a new partial state\n * @param {() => void} [callback] A function to be called once component state is\n * updated\n */\nComponent.prototype.setState = function(update, callback) {\n\t// only clone state when copying to nextState the first time.\n\tlet s;\n\tif (this._nextState !== this.state) {\n\t\ts = this._nextState;\n\t} else {\n\t\ts = this._nextState = assign({}, this.state);\n\t}\n\n\tif (typeof update == 'function') {\n\t\tupdate = update(s, this.props);\n\t}\n\n\tif (update) {\n\t\tassign(s, update);\n\t}\n\n\t// Skip update if updater function returned null\n\tif (update == null) return;\n\n\tif (this._vnode) {\n\t\tif (callback) this._renderCallbacks.push(callback);\n\t\tenqueueRender(this);\n\t}\n};\n\n/**\n * Immediately perform a synchronous re-render of the component\n * @param {() => void} [callback] A function to be called after component is\n * re-rendered\n */\nComponent.prototype.forceUpdate = function(callback) {\n\tif (this._vnode) {\n\t\t// Set render mode so that we can differentiate where the render request\n\t\t// is coming from. We need this because forceUpdate should never call\n\t\t// shouldComponentUpdate\n\t\tthis._force = true;\n\t\tif (callback) this._renderCallbacks.push(callback);\n\t\tenqueueRender(this);\n\t}\n};\n\n/**\n * Accepts `props` and `state`, and returns a new Virtual DOM tree to build.\n * Virtual DOM is generally constructed via [JSX](http://jasonformat.com/wtf-is-jsx).\n * @param {object} props Props (eg: JSX attributes) received from parent\n * element/component\n * @param {object} state The component's current state\n * @param {object} context Context object, as returned by the nearest\n * ancestor's `getChildContext()`\n * @returns {import('./index').ComponentChildren | void}\n */\nComponent.prototype.render = Fragment;\n\n/**\n * @param {import('./internal').VNode} vnode\n * @param {number | null} [childIndex]\n */\nexport function getDomSibling(vnode, childIndex) {\n\tif (childIndex == null) {\n\t\t// Use childIndex==null as a signal to resume the search from the vnode's sibling\n\t\treturn vnode._parent\n\t\t\t? getDomSibling(vnode._parent, vnode._parent._children.indexOf(vnode) + 1)\n\t\t\t: null;\n\t}\n\n\tlet sibling;\n\tfor (; childIndex < vnode._children.length; childIndex++) {\n\t\tsibling = vnode._children[childIndex];\n\n\t\tif (sibling != null && sibling._dom != null) {\n\t\t\t// Since updateParentDomPointers keeps _dom pointer correct,\n\t\t\t// we can rely on _dom to tell us if this subtree contains a\n\t\t\t// rendered DOM node, and what the first rendered DOM node is\n\t\t\treturn sibling._dom;\n\t\t}\n\t}\n\n\t// If we get here, we have not found a DOM node in this vnode's children.\n\t// We must resume from this vnode's sibling (in it's parent _children array)\n\t// Only climb up and search the parent if we aren't searching through a DOM\n\t// VNode (meaning we reached the DOM parent of the original vnode that began\n\t// the search)\n\treturn typeof vnode.type == 'function' ? getDomSibling(vnode) : null;\n}\n\n/**\n * Trigger in-place re-rendering of a component.\n * @param {import('./internal').Component} component The component to rerender\n */\nfunction renderComponent(component) {\n\tlet vnode = component._vnode,\n\t\toldDom = vnode._dom,\n\t\tparentDom = component._parentDom;\n\n\tif (parentDom) {\n\t\tlet commitQueue = [];\n\t\tconst oldVNode = assign({}, vnode);\n\t\toldVNode._original = oldVNode;\n\n\t\tlet newDom = diff(\n\t\t\tparentDom,\n\t\t\tvnode,\n\t\t\toldVNode,\n\t\t\tcomponent._globalContext,\n\t\t\tparentDom.ownerSVGElement !== undefined,\n\t\t\tnull,\n\t\t\tcommitQueue,\n\t\t\toldDom == null ? getDomSibling(vnode) : oldDom\n\t\t);\n\t\tcommitRoot(commitQueue, vnode);\n\n\t\tif (newDom != oldDom) {\n\t\t\tupdateParentDomPointers(vnode);\n\t\t}\n\t}\n}\n\n/**\n * @param {import('./internal').VNode} vnode\n */\nfunction updateParentDomPointers(vnode) {\n\tif ((vnode = vnode._parent) != null && vnode._component != null) {\n\t\tvnode._dom = vnode._component.base = null;\n\t\tfor (let i = 0; i < vnode._children.length; i++) {\n\t\t\tlet child = vnode._children[i];\n\t\t\tif (child != null && child._dom != null) {\n\t\t\t\tvnode._dom = vnode._component.base = child._dom;\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\n\t\treturn updateParentDomPointers(vnode);\n\t}\n}\n\n/**\n * The render queue\n * @type {Array}\n */\nlet rerenderQueue = [];\nlet rerenderCount = 0;\n\n/**\n * Asynchronously schedule a callback\n * @type {(cb: () => void) => void}\n */\n/* istanbul ignore next */\n// Note the following line isn't tree-shaken by rollup cuz of rollup/rollup#2566\nconst defer =\n\ttypeof Promise == 'function'\n\t\t? Promise.prototype.then.bind(Promise.resolve())\n\t\t: setTimeout;\n\n/*\n * The value of `Component.debounce` must asynchronously invoke the passed in callback. It is\n * important that contributors to Preact can consistently reason about what calls to `setState`, etc.\n * do, and when their effects will be applied. See the links below for some further reading on designing\n * asynchronous APIs.\n * * [Designing APIs for Asynchrony](https://blog.izs.me/2013/08/designing-apis-for-asynchrony)\n * * [Callbacks synchronous and asynchronous](https://blog.ometer.com/2011/07/24/callbacks-synchronous-and-asynchronous/)\n */\n\nlet prevDebounce;\n\n/**\n * Enqueue a rerender of a component\n * @param {import('./internal').Component} c The component to rerender\n */\nexport function enqueueRender(c) {\n\tif (\n\t\t(!c._dirty &&\n\t\t\t(c._dirty = true) &&\n\t\t\trerenderQueue.push(c) &&\n\t\t\t!rerenderCount++) ||\n\t\tprevDebounce !== options.debounceRendering\n\t) {\n\t\tprevDebounce = options.debounceRendering;\n\t\t(prevDebounce || defer)(process);\n\t}\n}\n\n/** Flush the render queue by rerendering all queued components */\nfunction process() {\n\tlet queue;\n\twhile ((rerenderCount = rerenderQueue.length)) {\n\t\tqueue = rerenderQueue.sort((a, b) => a._vnode._depth - b._vnode._depth);\n\t\trerenderQueue = [];\n\t\t// Don't update `renderCount` yet. Keep its value non-zero to prevent unnecessary\n\t\t// process() calls from getting scheduled while `queue` is still being consumed.\n\t\tqueue.some(c => {\n\t\t\tif (c._dirty) renderComponent(c);\n\t\t});\n\t}\n}\n","import { diff, unmount, applyRef } from './index';\nimport { createVNode, Fragment } from '../create-element';\nimport { EMPTY_OBJ, EMPTY_ARR } from '../constants';\nimport { removeNode } from '../util';\nimport { getDomSibling } from '../component';\n\n/**\n * Diff the children of a virtual node\n * @param {import('../internal').PreactElement} parentDom The DOM element whose\n * children are being diffed\n * @param {import('../index').ComponentChildren[]} renderResult\n * @param {import('../internal').VNode} newParentVNode The new virtual\n * node whose children should be diff'ed against oldParentVNode\n * @param {import('../internal').VNode} oldParentVNode The old virtual\n * node whose children should be diff'ed against newParentVNode\n * @param {object} globalContext The current context object - modified by getChildContext\n * @param {boolean} isSvg Whether or not this DOM node is an SVG node\n * @param {Array} excessDomChildren\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {Node | Text} oldDom The current attached DOM\n * element any new dom elements should be placed around. Likely `null` on first\n * render (except when hydrating). Can be a sibling DOM element when diffing\n * Fragments that have siblings. In most cases, it starts out as `oldChildren[0]._dom`.\n * @param {boolean} isHydrating Whether or not we are in hydration\n */\nexport function diffChildren(\n\tparentDom,\n\trenderResult,\n\tnewParentVNode,\n\toldParentVNode,\n\tglobalContext,\n\tisSvg,\n\texcessDomChildren,\n\tcommitQueue,\n\toldDom,\n\tisHydrating\n) {\n\tlet i, j, oldVNode, childVNode, newDom, sibDom, firstChildDom, refs;\n\n\t// This is a compression of oldParentVNode!=null && oldParentVNode != EMPTY_OBJ && oldParentVNode._children || EMPTY_ARR\n\t// as EMPTY_OBJ._children should be `undefined`.\n\tlet oldChildren = (oldParentVNode && oldParentVNode._children) || EMPTY_ARR;\n\n\tlet oldChildrenLength = oldChildren.length;\n\n\t// Only in very specific places should this logic be invoked (top level `render` and `diffElementNodes`).\n\t// I'm using `EMPTY_OBJ` to signal when `diffChildren` is invoked in these situations. I can't use `null`\n\t// for this purpose, because `null` is a valid value for `oldDom` which can mean to skip to this logic\n\t// (e.g. if mounting a new tree in which the old DOM should be ignored (usually for Fragments).\n\tif (oldDom == EMPTY_OBJ) {\n\t\tif (excessDomChildren != null) {\n\t\t\toldDom = excessDomChildren[0];\n\t\t} else if (oldChildrenLength) {\n\t\t\toldDom = getDomSibling(oldParentVNode, 0);\n\t\t} else {\n\t\t\toldDom = null;\n\t\t}\n\t}\n\n\tnewParentVNode._children = [];\n\tfor (i = 0; i < renderResult.length; i++) {\n\t\tchildVNode = renderResult[i];\n\n\t\tif (childVNode == null || typeof childVNode == 'boolean') {\n\t\t\tchildVNode = newParentVNode._children[i] = null;\n\t\t}\n\t\t// If this newVNode is being reused (e.g.
{reuse}{reuse}
) in the same diff,\n\t\t// or we are rendering a component (e.g. setState) copy the oldVNodes so it can have\n\t\t// it's own DOM & etc. pointers\n\t\telse if (typeof childVNode == 'string' || typeof childVNode == 'number') {\n\t\t\tchildVNode = newParentVNode._children[i] = createVNode(\n\t\t\t\tnull,\n\t\t\t\tchildVNode,\n\t\t\t\tnull,\n\t\t\t\tnull,\n\t\t\t\tchildVNode\n\t\t\t);\n\t\t} else if (Array.isArray(childVNode)) {\n\t\t\tchildVNode = newParentVNode._children[i] = createVNode(\n\t\t\t\tFragment,\n\t\t\t\t{ children: childVNode },\n\t\t\t\tnull,\n\t\t\t\tnull,\n\t\t\t\tnull\n\t\t\t);\n\t\t} else if (childVNode._dom != null || childVNode._component != null) {\n\t\t\tchildVNode = newParentVNode._children[i] = createVNode(\n\t\t\t\tchildVNode.type,\n\t\t\t\tchildVNode.props,\n\t\t\t\tchildVNode.key,\n\t\t\t\tnull,\n\t\t\t\tchildVNode._original\n\t\t\t);\n\t\t} else {\n\t\t\tchildVNode = newParentVNode._children[i] = childVNode;\n\t\t}\n\n\t\t// Terser removes the `continue` here and wraps the loop body\n\t\t// in a `if (childVNode) { ... } condition\n\t\tif (childVNode == null) {\n\t\t\tcontinue;\n\t\t}\n\n\t\tchildVNode._parent = newParentVNode;\n\t\tchildVNode._depth = newParentVNode._depth + 1;\n\n\t\t// Check if we find a corresponding element in oldChildren.\n\t\t// If found, delete the array item by setting to `undefined`.\n\t\t// We use `undefined`, as `null` is reserved for empty placeholders\n\t\t// (holes).\n\t\toldVNode = oldChildren[i];\n\n\t\tif (\n\t\t\toldVNode === null ||\n\t\t\t(oldVNode &&\n\t\t\t\tchildVNode.key == oldVNode.key &&\n\t\t\t\tchildVNode.type === oldVNode.type)\n\t\t) {\n\t\t\toldChildren[i] = undefined;\n\t\t} else {\n\t\t\t// Either oldVNode === undefined or oldChildrenLength > 0,\n\t\t\t// so after this loop oldVNode == null or oldVNode is a valid value.\n\t\t\tfor (j = 0; j < oldChildrenLength; j++) {\n\t\t\t\toldVNode = oldChildren[j];\n\t\t\t\t// If childVNode is unkeyed, we only match similarly unkeyed nodes, otherwise we match by key.\n\t\t\t\t// We always match by type (in either case).\n\t\t\t\tif (\n\t\t\t\t\toldVNode &&\n\t\t\t\t\tchildVNode.key == oldVNode.key &&\n\t\t\t\t\tchildVNode.type === oldVNode.type\n\t\t\t\t) {\n\t\t\t\t\toldChildren[j] = undefined;\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t\toldVNode = null;\n\t\t\t}\n\t\t}\n\n\t\toldVNode = oldVNode || EMPTY_OBJ;\n\n\t\t// Morph the old element into the new one, but don't append it to the dom yet\n\t\tnewDom = diff(\n\t\t\tparentDom,\n\t\t\tchildVNode,\n\t\t\toldVNode,\n\t\t\tglobalContext,\n\t\t\tisSvg,\n\t\t\texcessDomChildren,\n\t\t\tcommitQueue,\n\t\t\toldDom,\n\t\t\tisHydrating\n\t\t);\n\n\t\tif ((j = childVNode.ref) && oldVNode.ref != j) {\n\t\t\tif (!refs) refs = [];\n\t\t\tif (oldVNode.ref) refs.push(oldVNode.ref, null, childVNode);\n\t\t\trefs.push(j, childVNode._component || newDom, childVNode);\n\t\t}\n\n\t\t// Only proceed if the vnode has not been unmounted by `diff()` above.\n\t\tif (newDom != null) {\n\t\t\tif (firstChildDom == null) {\n\t\t\t\tfirstChildDom = newDom;\n\t\t\t}\n\n\t\t\tlet nextDom;\n\t\t\tif (childVNode._nextDom !== undefined) {\n\t\t\t\t// Only Fragments or components that return Fragment like VNodes will\n\t\t\t\t// have a non-undefined _nextDom. Continue the diff from the sibling\n\t\t\t\t// of last DOM child of this child VNode\n\t\t\t\tnextDom = childVNode._nextDom;\n\n\t\t\t\t// Eagerly cleanup _nextDom. We don't need to persist the value because\n\t\t\t\t// it is only used by `diffChildren` to determine where to resume the diff after\n\t\t\t\t// diffing Components and Fragments. Once we store it the nextDOM local var, we\n\t\t\t\t// can clean up the property\n\t\t\t\tchildVNode._nextDom = undefined;\n\t\t\t} else if (\n\t\t\t\texcessDomChildren == oldVNode ||\n\t\t\t\tnewDom != oldDom ||\n\t\t\t\tnewDom.parentNode == null\n\t\t\t) {\n\t\t\t\t// NOTE: excessDomChildren==oldVNode above:\n\t\t\t\t// This is a compression of excessDomChildren==null && oldVNode==null!\n\t\t\t\t// The values only have the same type when `null`.\n\n\t\t\t\touter: if (oldDom == null || oldDom.parentNode !== parentDom) {\n\t\t\t\t\tparentDom.appendChild(newDom);\n\t\t\t\t\tnextDom = null;\n\t\t\t\t} else {\n\t\t\t\t\t// `j} excessDomChildren\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {Element | Text} oldDom The current attached DOM\n * element any new dom elements should be placed around. Likely `null` on first\n * render (except when hydrating). Can be a sibling DOM element when diffing\n * Fragments that have siblings. In most cases, it starts out as `oldChildren[0]._dom`.\n * @param {boolean} [isHydrating] Whether or not we are in hydration\n */\nexport function diff(\n\tparentDom,\n\tnewVNode,\n\toldVNode,\n\tglobalContext,\n\tisSvg,\n\texcessDomChildren,\n\tcommitQueue,\n\toldDom,\n\tisHydrating\n) {\n\tlet tmp,\n\t\tnewType = newVNode.type;\n\n\t// When passing through createElement it assigns the object\n\t// constructor as undefined. This to prevent JSON-injection.\n\tif (newVNode.constructor !== undefined) return null;\n\n\tif ((tmp = options._diff)) tmp(newVNode);\n\n\ttry {\n\t\touter: if (typeof newType == 'function') {\n\t\t\tlet c, isNew, oldProps, oldState, snapshot, clearProcessingException;\n\t\t\tlet newProps = newVNode.props;\n\n\t\t\t// Necessary for createContext api. Setting this property will pass\n\t\t\t// the context value as `this.context` just for this component.\n\t\t\ttmp = newType.contextType;\n\t\t\tlet provider = tmp && globalContext[tmp._id];\n\t\t\tlet componentContext = tmp\n\t\t\t\t? provider\n\t\t\t\t\t? provider.props.value\n\t\t\t\t\t: tmp._defaultValue\n\t\t\t\t: globalContext;\n\n\t\t\t// Get component and set it to `c`\n\t\t\tif (oldVNode._component) {\n\t\t\t\tc = newVNode._component = oldVNode._component;\n\t\t\t\tclearProcessingException = c._processingException = c._pendingError;\n\t\t\t} else {\n\t\t\t\t// Instantiate the new component\n\t\t\t\tif ('prototype' in newType && newType.prototype.render) {\n\t\t\t\t\tnewVNode._component = c = new newType(newProps, componentContext); // eslint-disable-line new-cap\n\t\t\t\t} else {\n\t\t\t\t\tnewVNode._component = c = new Component(newProps, componentContext);\n\t\t\t\t\tc.constructor = newType;\n\t\t\t\t\tc.render = doRender;\n\t\t\t\t}\n\t\t\t\tif (provider) provider.sub(c);\n\n\t\t\t\tc.props = newProps;\n\t\t\t\tif (!c.state) c.state = {};\n\t\t\t\tc.context = componentContext;\n\t\t\t\tc._globalContext = globalContext;\n\t\t\t\tisNew = c._dirty = true;\n\t\t\t\tc._renderCallbacks = [];\n\t\t\t}\n\n\t\t\t// Invoke getDerivedStateFromProps\n\t\t\tif (c._nextState == null) {\n\t\t\t\tc._nextState = c.state;\n\t\t\t}\n\t\t\tif (newType.getDerivedStateFromProps != null) {\n\t\t\t\tif (c._nextState == c.state) {\n\t\t\t\t\tc._nextState = assign({}, c._nextState);\n\t\t\t\t}\n\n\t\t\t\tassign(\n\t\t\t\t\tc._nextState,\n\t\t\t\t\tnewType.getDerivedStateFromProps(newProps, c._nextState)\n\t\t\t\t);\n\t\t\t}\n\n\t\t\toldProps = c.props;\n\t\t\toldState = c.state;\n\n\t\t\t// Invoke pre-render lifecycle methods\n\t\t\tif (isNew) {\n\t\t\t\tif (\n\t\t\t\t\tnewType.getDerivedStateFromProps == null &&\n\t\t\t\t\tc.componentWillMount != null\n\t\t\t\t) {\n\t\t\t\t\tc.componentWillMount();\n\t\t\t\t}\n\n\t\t\t\tif (c.componentDidMount != null) {\n\t\t\t\t\tc._renderCallbacks.push(c.componentDidMount);\n\t\t\t\t}\n\t\t\t} else {\n\t\t\t\tif (\n\t\t\t\t\tnewType.getDerivedStateFromProps == null &&\n\t\t\t\t\tnewProps !== oldProps &&\n\t\t\t\t\tc.componentWillReceiveProps != null\n\t\t\t\t) {\n\t\t\t\t\tc.componentWillReceiveProps(newProps, componentContext);\n\t\t\t\t}\n\n\t\t\t\tif (\n\t\t\t\t\t(!c._force &&\n\t\t\t\t\t\tc.shouldComponentUpdate != null &&\n\t\t\t\t\t\tc.shouldComponentUpdate(\n\t\t\t\t\t\t\tnewProps,\n\t\t\t\t\t\t\tc._nextState,\n\t\t\t\t\t\t\tcomponentContext\n\t\t\t\t\t\t) === false) ||\n\t\t\t\t\tnewVNode._original === oldVNode._original\n\t\t\t\t) {\n\t\t\t\t\tc.props = newProps;\n\t\t\t\t\tc.state = c._nextState;\n\t\t\t\t\t// More info about this here: https://gist.github.com/JoviDeCroock/bec5f2ce93544d2e6070ef8e0036e4e8\n\t\t\t\t\tif (newVNode._original !== oldVNode._original) c._dirty = false;\n\t\t\t\t\tc._vnode = newVNode;\n\t\t\t\t\tnewVNode._dom = oldVNode._dom;\n\t\t\t\t\tnewVNode._children = oldVNode._children;\n\t\t\t\t\tif (c._renderCallbacks.length) {\n\t\t\t\t\t\tcommitQueue.push(c);\n\t\t\t\t\t}\n\n\t\t\t\t\tfor (tmp = 0; tmp < newVNode._children.length; tmp++) {\n\t\t\t\t\t\tif (newVNode._children[tmp]) {\n\t\t\t\t\t\t\tnewVNode._children[tmp]._parent = newVNode;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\n\t\t\t\t\tbreak outer;\n\t\t\t\t}\n\n\t\t\t\tif (c.componentWillUpdate != null) {\n\t\t\t\t\tc.componentWillUpdate(newProps, c._nextState, componentContext);\n\t\t\t\t}\n\n\t\t\t\tif (c.componentDidUpdate != null) {\n\t\t\t\t\tc._renderCallbacks.push(() => {\n\t\t\t\t\t\tc.componentDidUpdate(oldProps, oldState, snapshot);\n\t\t\t\t\t});\n\t\t\t\t}\n\t\t\t}\n\n\t\t\tc.context = componentContext;\n\t\t\tc.props = newProps;\n\t\t\tc.state = c._nextState;\n\n\t\t\tif ((tmp = options._render)) tmp(newVNode);\n\n\t\t\tc._dirty = false;\n\t\t\tc._vnode = newVNode;\n\t\t\tc._parentDom = parentDom;\n\n\t\t\ttmp = c.render(c.props, c.state, c.context);\n\n\t\t\tif (c.getChildContext != null) {\n\t\t\t\tglobalContext = assign(assign({}, globalContext), c.getChildContext());\n\t\t\t}\n\n\t\t\tif (!isNew && c.getSnapshotBeforeUpdate != null) {\n\t\t\t\tsnapshot = c.getSnapshotBeforeUpdate(oldProps, oldState);\n\t\t\t}\n\n\t\t\tlet isTopLevelFragment =\n\t\t\t\ttmp != null && tmp.type == Fragment && tmp.key == null;\n\t\t\tlet renderResult = isTopLevelFragment ? tmp.props.children : tmp;\n\n\t\t\tdiffChildren(\n\t\t\t\tparentDom,\n\t\t\t\tArray.isArray(renderResult) ? renderResult : [renderResult],\n\t\t\t\tnewVNode,\n\t\t\t\toldVNode,\n\t\t\t\tglobalContext,\n\t\t\t\tisSvg,\n\t\t\t\texcessDomChildren,\n\t\t\t\tcommitQueue,\n\t\t\t\toldDom,\n\t\t\t\tisHydrating\n\t\t\t);\n\n\t\t\tc.base = newVNode._dom;\n\n\t\t\tif (c._renderCallbacks.length) {\n\t\t\t\tcommitQueue.push(c);\n\t\t\t}\n\n\t\t\tif (clearProcessingException) {\n\t\t\t\tc._pendingError = c._processingException = null;\n\t\t\t}\n\n\t\t\tc._force = false;\n\t\t} else if (\n\t\t\texcessDomChildren == null &&\n\t\t\tnewVNode._original === oldVNode._original\n\t\t) {\n\t\t\tnewVNode._children = oldVNode._children;\n\t\t\tnewVNode._dom = oldVNode._dom;\n\t\t} else {\n\t\t\tnewVNode._dom = diffElementNodes(\n\t\t\t\toldVNode._dom,\n\t\t\t\tnewVNode,\n\t\t\t\toldVNode,\n\t\t\t\tglobalContext,\n\t\t\t\tisSvg,\n\t\t\t\texcessDomChildren,\n\t\t\t\tcommitQueue,\n\t\t\t\tisHydrating\n\t\t\t);\n\t\t}\n\n\t\tif ((tmp = options.diffed)) tmp(newVNode);\n\t} catch (e) {\n\t\tnewVNode._original = null;\n\t\toptions._catchError(e, newVNode, oldVNode);\n\t}\n\n\treturn newVNode._dom;\n}\n\n/**\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {import('../internal').VNode} root\n */\nexport function commitRoot(commitQueue, root) {\n\tif (options._commit) options._commit(root, commitQueue);\n\n\tcommitQueue.some(c => {\n\t\ttry {\n\t\t\tcommitQueue = c._renderCallbacks;\n\t\t\tc._renderCallbacks = [];\n\t\t\tcommitQueue.some(cb => {\n\t\t\t\tcb.call(c);\n\t\t\t});\n\t\t} catch (e) {\n\t\t\toptions._catchError(e, c._vnode);\n\t\t}\n\t});\n}\n\n/**\n * Diff two virtual nodes representing DOM element\n * @param {import('../internal').PreactElement} dom The DOM element representing\n * the virtual nodes being diffed\n * @param {import('../internal').VNode} newVNode The new virtual node\n * @param {import('../internal').VNode} oldVNode The old virtual node\n * @param {object} globalContext The current context object\n * @param {boolean} isSvg Whether or not this DOM node is an SVG node\n * @param {*} excessDomChildren\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {boolean} isHydrating Whether or not we are in hydration\n * @returns {import('../internal').PreactElement}\n */\nfunction diffElementNodes(\n\tdom,\n\tnewVNode,\n\toldVNode,\n\tglobalContext,\n\tisSvg,\n\texcessDomChildren,\n\tcommitQueue,\n\tisHydrating\n) {\n\tlet i;\n\tlet oldProps = oldVNode.props;\n\tlet newProps = newVNode.props;\n\n\t// Tracks entering and exiting SVG namespace when descending through the tree.\n\tisSvg = newVNode.type === 'svg' || isSvg;\n\n\tif (excessDomChildren != null) {\n\t\tfor (i = 0; i < excessDomChildren.length; i++) {\n\t\t\tconst child = excessDomChildren[i];\n\n\t\t\t// if newVNode matches an element in excessDomChildren or the `dom`\n\t\t\t// argument matches an element in excessDomChildren, remove it from\n\t\t\t// excessDomChildren so it isn't later removed in diffChildren\n\t\t\tif (\n\t\t\t\tchild != null &&\n\t\t\t\t((newVNode.type === null\n\t\t\t\t\t? child.nodeType === 3\n\t\t\t\t\t: child.localName === newVNode.type) ||\n\t\t\t\t\tdom == child)\n\t\t\t) {\n\t\t\t\tdom = child;\n\t\t\t\texcessDomChildren[i] = null;\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\t}\n\n\tif (dom == null) {\n\t\tif (newVNode.type === null) {\n\t\t\treturn document.createTextNode(newProps);\n\t\t}\n\n\t\tdom = isSvg\n\t\t\t? document.createElementNS('http://www.w3.org/2000/svg', newVNode.type)\n\t\t\t: document.createElement(\n\t\t\t\t\tnewVNode.type,\n\t\t\t\t\tnewProps.is && { is: newProps.is }\n\t\t\t );\n\t\t// we created a new parent, so none of the previously attached children can be reused:\n\t\texcessDomChildren = null;\n\t\t// we are creating a new node, so we can assume this is a new subtree (in case we are hydrating), this deopts the hydrate\n\t\tisHydrating = false;\n\t}\n\n\tif (newVNode.type === null) {\n\t\tif (oldProps !== newProps && dom.data != newProps) {\n\t\t\tdom.data = newProps;\n\t\t}\n\t} else {\n\t\tif (excessDomChildren != null) {\n\t\t\texcessDomChildren = EMPTY_ARR.slice.call(dom.childNodes);\n\t\t}\n\n\t\toldProps = oldVNode.props || EMPTY_OBJ;\n\n\t\tlet oldHtml = oldProps.dangerouslySetInnerHTML;\n\t\tlet newHtml = newProps.dangerouslySetInnerHTML;\n\n\t\t// During hydration, props are not diffed at all (including dangerouslySetInnerHTML)\n\t\t// @TODO we should warn in debug mode when props don't match here.\n\t\tif (!isHydrating) {\n\t\t\t// But, if we are in a situation where we are using existing DOM (e.g. replaceNode)\n\t\t\t// we should read the existing DOM attributes to diff them\n\t\t\tif (excessDomChildren != null) {\n\t\t\t\toldProps = {};\n\t\t\t\tfor (let i = 0; i < dom.attributes.length; i++) {\n\t\t\t\t\toldProps[dom.attributes[i].name] = dom.attributes[i].value;\n\t\t\t\t}\n\t\t\t}\n\n\t\t\tif (newHtml || oldHtml) {\n\t\t\t\t// Avoid re-applying the same '__html' if it did not changed between re-render\n\t\t\t\tif (!newHtml || !oldHtml || newHtml.__html != oldHtml.__html) {\n\t\t\t\t\tdom.innerHTML = (newHtml && newHtml.__html) || '';\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t\tdiffProps(dom, newProps, oldProps, isSvg, isHydrating);\n\n\t\t// If the new vnode didn't have dangerouslySetInnerHTML, diff its children\n\t\tif (newHtml) {\n\t\t\tnewVNode._children = [];\n\t\t} else {\n\t\t\ti = newVNode.props.children;\n\t\t\tdiffChildren(\n\t\t\t\tdom,\n\t\t\t\tArray.isArray(i) ? i : [i],\n\t\t\t\tnewVNode,\n\t\t\t\toldVNode,\n\t\t\t\tglobalContext,\n\t\t\t\tnewVNode.type === 'foreignObject' ? false : isSvg,\n\t\t\t\texcessDomChildren,\n\t\t\t\tcommitQueue,\n\t\t\t\tEMPTY_OBJ,\n\t\t\t\tisHydrating\n\t\t\t);\n\t\t}\n\n\t\t// (as above, don't diff props during hydration)\n\t\tif (!isHydrating) {\n\t\t\tif (\n\t\t\t\t'value' in newProps &&\n\t\t\t\t(i = newProps.value) !== undefined &&\n\t\t\t\ti !== dom.value\n\t\t\t) {\n\t\t\t\tsetProperty(dom, 'value', i, oldProps.value, false);\n\t\t\t}\n\t\t\tif (\n\t\t\t\t'checked' in newProps &&\n\t\t\t\t(i = newProps.checked) !== undefined &&\n\t\t\t\ti !== dom.checked\n\t\t\t) {\n\t\t\t\tsetProperty(dom, 'checked', i, oldProps.checked, false);\n\t\t\t}\n\t\t}\n\t}\n\n\treturn dom;\n}\n\n/**\n * Invoke or update a ref, depending on whether it is a function or object ref.\n * @param {object|function} ref\n * @param {any} value\n * @param {import('../internal').VNode} vnode\n */\nexport function applyRef(ref, value, vnode) {\n\ttry {\n\t\tif (typeof ref == 'function') ref(value);\n\t\telse ref.current = value;\n\t} catch (e) {\n\t\toptions._catchError(e, vnode);\n\t}\n}\n\n/**\n * Unmount a virtual node from the tree and apply DOM changes\n * @param {import('../internal').VNode} vnode The virtual node to unmount\n * @param {import('../internal').VNode} parentVNode The parent of the VNode that\n * initiated the unmount\n * @param {boolean} [skipRemove] Flag that indicates that a parent node of the\n * current element is already detached from the DOM.\n */\nexport function unmount(vnode, parentVNode, skipRemove) {\n\tlet r;\n\tif (options.unmount) options.unmount(vnode);\n\n\tif ((r = vnode.ref)) {\n\t\tif (!r.current || r.current === vnode._dom) applyRef(r, null, parentVNode);\n\t}\n\n\tlet dom;\n\tif (!skipRemove && typeof vnode.type != 'function') {\n\t\tskipRemove = (dom = vnode._dom) != null;\n\t}\n\n\t// Must be set to `undefined` to properly clean up `_nextDom`\n\t// for which `null` is a valid value. See comment in `create-element.js`\n\tvnode._dom = vnode._nextDom = undefined;\n\n\tif ((r = vnode._component) != null) {\n\t\tif (r.componentWillUnmount) {\n\t\t\ttry {\n\t\t\t\tr.componentWillUnmount();\n\t\t\t} catch (e) {\n\t\t\t\toptions._catchError(e, parentVNode);\n\t\t\t}\n\t\t}\n\n\t\tr.base = r._parentDom = null;\n\t}\n\n\tif ((r = vnode._children)) {\n\t\tfor (let i = 0; i < r.length; i++) {\n\t\t\tif (r[i]) unmount(r[i], parentVNode, skipRemove);\n\t\t}\n\t}\n\n\tif (dom != null) removeNode(dom);\n}\n\n/** The `.render()` method for a PFC backing instance. */\nfunction doRender(props, state, context) {\n\treturn this.constructor(props, context);\n}\n","import { EMPTY_OBJ, EMPTY_ARR } from './constants';\nimport { commitRoot, diff } from './diff/index';\nimport { createElement, Fragment } from './create-element';\nimport options from './options';\n\nconst IS_HYDRATE = EMPTY_OBJ;\n\n/**\n * Render a Preact virtual node into a DOM element\n * @param {import('./index').ComponentChild} vnode The virtual node to render\n * @param {import('./internal').PreactElement} parentDom The DOM element to\n * render into\n * @param {Element | Text} [replaceNode] Optional: Attempt to re-use an\n * existing DOM tree rooted at `replaceNode`\n */\nexport function render(vnode, parentDom, replaceNode) {\n\tif (options._root) options._root(vnode, parentDom);\n\n\t// We abuse the `replaceNode` parameter in `hydrate()` to signal if we\n\t// are in hydration mode or not by passing `IS_HYDRATE` instead of a\n\t// DOM element.\n\tlet isHydrating = replaceNode === IS_HYDRATE;\n\n\t// To be able to support calling `render()` multiple times on the same\n\t// DOM node, we need to obtain a reference to the previous tree. We do\n\t// this by assigning a new `_children` property to DOM nodes which points\n\t// to the last rendered tree. By default this property is not present, which\n\t// means that we are mounting a new tree for the first time.\n\tlet oldVNode = isHydrating\n\t\t? null\n\t\t: (replaceNode && replaceNode._children) || parentDom._children;\n\tvnode = createElement(Fragment, null, [vnode]);\n\n\t// List of effects that need to be called after diffing.\n\tlet commitQueue = [];\n\tdiff(\n\t\tparentDom,\n\t\t// Determine the new vnode tree and store it on the DOM element on\n\t\t// our custom `_children` property.\n\t\t((isHydrating ? parentDom : replaceNode || parentDom)._children = vnode),\n\t\toldVNode || EMPTY_OBJ,\n\t\tEMPTY_OBJ,\n\t\tparentDom.ownerSVGElement !== undefined,\n\t\treplaceNode && !isHydrating\n\t\t\t? [replaceNode]\n\t\t\t: oldVNode\n\t\t\t? null\n\t\t\t: parentDom.childNodes.length\n\t\t\t? EMPTY_ARR.slice.call(parentDom.childNodes)\n\t\t\t: null,\n\t\tcommitQueue,\n\t\treplaceNode || EMPTY_OBJ,\n\t\tisHydrating\n\t);\n\n\t// Flush all queued effects\n\tcommitRoot(commitQueue, vnode);\n}\n\n/**\n * Update an existing DOM element with data from a Preact virtual node\n * @param {import('./index').ComponentChild} vnode The virtual node to render\n * @param {import('./internal').PreactElement} parentDom The DOM element to\n * update\n */\nexport function hydrate(vnode, parentDom) {\n\trender(vnode, parentDom, IS_HYDRATE);\n}\n","import { assign } from './util';\nimport { EMPTY_ARR } from './constants';\nimport { createVNode } from './create-element';\n\n/**\n * Clones the given VNode, optionally adding attributes/props and replacing its children.\n * @param {import('./internal').VNode} vnode The virtual DOM element to clone\n * @param {object} props Attributes/props to add when cloning\n * @param {Array} rest Any additional arguments will be used as replacement children.\n * @returns {import('./internal').VNode}\n */\nexport function cloneElement(vnode, props) {\n\tprops = assign(assign({}, vnode.props), props);\n\tif (arguments.length > 2) props.children = EMPTY_ARR.slice.call(arguments, 2);\n\tlet normalizedProps = {};\n\tfor (const i in props) {\n\t\tif (i !== 'key' && i !== 'ref') normalizedProps[i] = props[i];\n\t}\n\n\treturn createVNode(\n\t\tvnode.type,\n\t\tnormalizedProps,\n\t\tprops.key || vnode.key,\n\t\tprops.ref || vnode.ref,\n\t\tnull\n\t);\n}\n","import { enqueueRender } from './component';\n\nexport let i = 0;\n\nexport function createContext(defaultValue) {\n\tconst ctx = {};\n\n\tconst context = {\n\t\t_id: '__cC' + i++,\n\t\t_defaultValue: defaultValue,\n\t\tConsumer(props, context) {\n\t\t\treturn props.children(context);\n\t\t},\n\t\tProvider(props) {\n\t\t\tif (!this.getChildContext) {\n\t\t\t\tconst subs = [];\n\t\t\t\tthis.getChildContext = () => {\n\t\t\t\t\tctx[context._id] = this;\n\t\t\t\t\treturn ctx;\n\t\t\t\t};\n\n\t\t\t\tthis.shouldComponentUpdate = _props => {\n\t\t\t\t\tif (this.props.value !== _props.value) {\n\t\t\t\t\t\tsubs.some(c => {\n\t\t\t\t\t\t\tc.context = _props.value;\n\t\t\t\t\t\t\tenqueueRender(c);\n\t\t\t\t\t\t});\n\t\t\t\t\t}\n\t\t\t\t};\n\n\t\t\t\tthis.sub = c => {\n\t\t\t\t\tsubs.push(c);\n\t\t\t\t\tlet old = c.componentWillUnmount;\n\t\t\t\t\tc.componentWillUnmount = () => {\n\t\t\t\t\t\tsubs.splice(subs.indexOf(c), 1);\n\t\t\t\t\t\told && old.call(c);\n\t\t\t\t\t};\n\t\t\t\t};\n\t\t\t}\n\n\t\t\treturn props.children;\n\t\t}\n\t};\n\n\tcontext.Consumer.contextType = context;\n\n\t// Devtools needs access to the context object when it\n\t// encounters a Provider. This is necessary to support\n\t// setting `displayName` on the context object instead\n\t// of on the component itself. See:\n\t// https://reactjs.org/docs/context.html#contextdisplayname\n\tcontext.Provider._contextRef = context;\n\n\treturn context;\n}\n","export const EMPTY_OBJ = {};\nexport const EMPTY_ARR = [];\nexport const IS_NON_DIMENSIONAL = /acit|ex(?:s|g|n|p|$)|rph|grid|ows|mnc|ntw|ine[ch]|zoo|^ord|itera/i;\n","import { _catchError } from './diff/catch-error';\n\n/**\n * The `option` object can potentially contain callback functions\n * that are called during various stages of our renderer. This is the\n * foundation on which all our addons like `preact/debug`, `preact/compat`,\n * and `preact/hooks` are based on. See the `Options` type in `internal.d.ts`\n * for a full list of available option hooks (most editors/IDEs allow you to\n * ctrl+click or cmd+click on mac the type definition below).\n * @type {import('./internal').Options}\n */\nconst options = {\n\t_catchError\n};\n\nexport default options;\n","import { enqueueRender } from '../component';\n\n/**\n * Find the closest error boundary to a thrown error and call it\n * @param {object} error The thrown value\n * @param {import('../internal').VNode} vnode The vnode that threw\n * the error that was caught (except for unmounting when this parameter\n * is the highest parent that was being unmounted)\n */\nexport function _catchError(error, vnode) {\n\t/** @type {import('../internal').Component} */\n\tlet component, hasCaught;\n\n\tfor (; (vnode = vnode._parent); ) {\n\t\tif ((component = vnode._component) && !component._processingException) {\n\t\t\ttry {\n\t\t\t\tif (\n\t\t\t\t\tcomponent.constructor &&\n\t\t\t\t\tcomponent.constructor.getDerivedStateFromError != null\n\t\t\t\t) {\n\t\t\t\t\thasCaught = true;\n\t\t\t\t\tcomponent.setState(\n\t\t\t\t\t\tcomponent.constructor.getDerivedStateFromError(error)\n\t\t\t\t\t);\n\t\t\t\t}\n\n\t\t\t\tif (component.componentDidCatch != null) {\n\t\t\t\t\thasCaught = true;\n\t\t\t\t\tcomponent.componentDidCatch(error);\n\t\t\t\t}\n\n\t\t\t\tif (hasCaught)\n\t\t\t\t\treturn enqueueRender((component._pendingError = component));\n\t\t\t} catch (e) {\n\t\t\t\terror = e;\n\t\t\t}\n\t\t}\n\t}\n\n\tthrow error;\n}\n","/* global __webpack_public_path__ */\n\nimport * as Preact from 'preact';\nconst { h, render, hydrate } = Preact;\n\nconst interopDefault = m => (m && m.default ? m.default : m);\n\nconst normalizeURL = url => (url[url.length - 1] === '/' ? url : url + '/');\n\nif (process.env.NODE_ENV === 'development') {\n\t// enable preact devtools\n\trequire('preact/debug');\n\tif (process.env.RHL) {\n\t\t// enable hot loader\n\t\tconst hotLoader = interopDefault(require('react-hot-loader'));\n\t\thotLoader.preact(interopDefault(require('preact')));\n\t}\n\t// only add a debug sw if webpack service worker is not requested.\n\tif (process.env.ADD_SW === undefined && 'serviceWorker' in navigator) {\n\t\t// eslint-disable-next-line no-undef\n\t\tnavigator.serviceWorker.register(__webpack_public_path__ + 'sw-debug.js');\n\t} else if (process.env.ADD_SW && 'serviceWorker' in navigator) {\n\t\t// eslint-disable-next-line no-undef\n\t\tnavigator.serviceWorker.register(\n\t\t\t__webpack_public_path__ + (process.env.ES_BUILD ? 'sw-esm.js' : 'sw.js')\n\t\t);\n\t}\n} else if (process.env.ADD_SW && 'serviceWorker' in navigator) {\n\t// eslint-disable-next-line no-undef\n\tnavigator.serviceWorker.register(\n\t\t__webpack_public_path__ + (process.env.ES_BUILD ? 'sw-esm.js' : 'sw.js')\n\t);\n}\n\nlet app = interopDefault(require('preact-cli-entrypoint'));\n\nif (typeof app === 'function') {\n\tlet root =\n\t\tdocument.getElementById('preact_root') || document.body.firstElementChild;\n\n\tlet init = () => {\n\t\tlet app = interopDefault(require('preact-cli-entrypoint'));\n\t\tlet preRenderData = {};\n\t\tconst inlineDataElement = document.querySelector(\n\t\t\t'[type=\"__PREACT_CLI_DATA__\"]'\n\t\t);\n\t\tif (inlineDataElement) {\n\t\t\tpreRenderData =\n\t\t\t\tJSON.parse(inlineDataElement.innerHTML).preRenderData || preRenderData;\n\t\t}\n\t\t/* An object named CLI_DATA is passed as a prop,\n\t\t * this keeps us future proof if in case we decide,\n\t\t * to send other data like at some point in time.\n\t\t */\n\t\tconst CLI_DATA = { preRenderData };\n\t\tconst currentURL = preRenderData.url ? normalizeURL(preRenderData.url) : '';\n\t\tconst canHydrate =\n\t\t\tprocess.env.PRERENDER &&\n\t\t\tprocess.env.NODE_ENV === 'production' &&\n\t\t\thydrate &&\n\t\t\tcurrentURL === location.pathname;\n\t\tconst doRender = canHydrate ? hydrate : render;\n\t\troot = doRender(h(app, { CLI_DATA }), document.body, root);\n\t};\n\n\tif (module.hot) module.hot.accept('preact-cli-entrypoint', init);\n\n\tinit();\n}\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./Statistica.js\") );\n\t\t\t}, \"route-Statistica\");\n\t\t}\n\n\t\texport default Async(load);\n\t","var g;\n\n// This works in non-strict mode\ng = (function() {\n\treturn this;\n})();\n\ntry {\n\t// This works if eval is allowed (see CSP)\n\tg = g || new Function(\"return this\")();\n} catch (e) {\n\t// This works if the window reference is available\n\tif (typeof window === \"object\") g = window;\n}\n\n// g can still be undefined, but nothing to do about it...\n// We return undefined, instead of nothing here, so it's\n// easier to handle this case. if(!global) { ...}\n\nmodule.exports = g;\n","import { ExtendedError, WrappedFunction } from '@sentry/types';\n\nimport { isElement, isError, isEvent, isInstanceOf, isPlainObject, isPrimitive, isSyntheticEvent } from './is';\nimport { Memo } from './memo';\nimport { getFunctionName, htmlTreeAsString } from './misc';\nimport { truncate } from './string';\n\n/**\n * Wrap a given object method with a higher-order function\n *\n * @param source An object that contains a method to be wrapped.\n * @param name A name of method to be wrapped.\n * @param replacement A function that should be used to wrap a given method.\n * @returns void\n */\nexport function fill(source: { [key: string]: any }, name: string, replacement: (...args: any[]) => any): void {\n if (!(name in source)) {\n return;\n }\n\n const original = source[name] as () => any;\n const wrapped = replacement(original) as WrappedFunction;\n\n // Make sure it's a function first, as we need to attach an empty prototype for `defineProperties` to work\n // otherwise it'll throw \"TypeError: Object.defineProperties called on non-object\"\n // tslint:disable-next-line:strict-type-predicates\n if (typeof wrapped === 'function') {\n try {\n wrapped.prototype = wrapped.prototype || {};\n Object.defineProperties(wrapped, {\n __sentry_original__: {\n enumerable: false,\n value: original,\n },\n });\n } catch (_Oo) {\n // This can throw if multiple fill happens on a global object like XMLHttpRequest\n // Fixes https://github.com/getsentry/sentry-javascript/issues/2043\n }\n }\n\n source[name] = wrapped;\n}\n\n/**\n * Encodes given object into url-friendly format\n *\n * @param object An object that contains serializable values\n * @returns string Encoded\n */\nexport function urlEncode(object: { [key: string]: any }): string {\n return Object.keys(object)\n .map(\n // tslint:disable-next-line:no-unsafe-any\n key => `${encodeURIComponent(key)}=${encodeURIComponent(object[key])}`,\n )\n .join('&');\n}\n\n/**\n * Transforms any object into an object literal with all it's attributes\n * attached to it.\n *\n * @param value Initial source that we have to transform in order to be usable by the serializer\n */\nfunction getWalkSource(\n value: any,\n): {\n [key: string]: any;\n} {\n if (isError(value)) {\n const error = value as ExtendedError;\n const err: {\n stack: string | undefined;\n message: string;\n name: string;\n [key: string]: any;\n } = {\n message: error.message,\n name: error.name,\n stack: error.stack,\n };\n\n for (const i in error) {\n if (Object.prototype.hasOwnProperty.call(error, i)) {\n err[i] = error[i];\n }\n }\n\n return err;\n }\n\n if (isEvent(value)) {\n /**\n * Event-like interface that's usable in browser and node\n */\n interface SimpleEvent {\n [key: string]: unknown;\n type: string;\n target?: unknown;\n currentTarget?: unknown;\n }\n\n const event = value as SimpleEvent;\n\n const source: {\n [key: string]: any;\n } = {};\n\n source.type = event.type;\n\n // Accessing event.target can throw (see getsentry/raven-js#838, #768)\n try {\n source.target = isElement(event.target)\n ? htmlTreeAsString(event.target)\n : Object.prototype.toString.call(event.target);\n } catch (_oO) {\n source.target = '';\n }\n\n try {\n source.currentTarget = isElement(event.currentTarget)\n ? htmlTreeAsString(event.currentTarget)\n : Object.prototype.toString.call(event.currentTarget);\n } catch (_oO) {\n source.currentTarget = '';\n }\n\n // tslint:disable-next-line:strict-type-predicates\n if (typeof CustomEvent !== 'undefined' && isInstanceOf(value, CustomEvent)) {\n source.detail = event.detail;\n }\n\n for (const i in event) {\n if (Object.prototype.hasOwnProperty.call(event, i)) {\n source[i] = event;\n }\n }\n\n return source;\n }\n\n return value as {\n [key: string]: any;\n };\n}\n\n/** Calculates bytes size of input string */\nfunction utf8Length(value: string): number {\n // tslint:disable-next-line:no-bitwise\n return ~-encodeURI(value).split(/%..|./).length;\n}\n\n/** Calculates bytes size of input object */\nfunction jsonSize(value: any): number {\n return utf8Length(JSON.stringify(value));\n}\n\n/** JSDoc */\nexport function normalizeToSize(\n object: { [key: string]: any },\n // Default Node.js REPL depth\n depth: number = 3,\n // 100kB, as 200kB is max payload size, so half sounds reasonable\n maxSize: number = 100 * 1024,\n): T {\n const serialized = normalize(object, depth);\n\n if (jsonSize(serialized) > maxSize) {\n return normalizeToSize(object, depth - 1, maxSize);\n }\n\n return serialized as T;\n}\n\n/** Transforms any input value into a string form, either primitive value or a type of the input */\nfunction serializeValue(value: any): any {\n const type = Object.prototype.toString.call(value);\n\n // Node.js REPL notation\n if (typeof value === 'string') {\n return value;\n }\n if (type === '[object Object]') {\n return '[Object]';\n }\n if (type === '[object Array]') {\n return '[Array]';\n }\n\n const normalized = normalizeValue(value);\n return isPrimitive(normalized) ? normalized : type;\n}\n\n/**\n * normalizeValue()\n *\n * Takes unserializable input and make it serializable friendly\n *\n * - translates undefined/NaN values to \"[undefined]\"/\"[NaN]\" respectively,\n * - serializes Error objects\n * - filter global objects\n */\n// tslint:disable-next-line:cyclomatic-complexity\nfunction normalizeValue(value: T, key?: any): T | string {\n if (key === 'domain' && value && typeof value === 'object' && ((value as unknown) as { _events: any })._events) {\n return '[Domain]';\n }\n\n if (key === 'domainEmitter') {\n return '[DomainEmitter]';\n }\n\n if (typeof (global as any) !== 'undefined' && (value as unknown) === global) {\n return '[Global]';\n }\n\n if (typeof (window as any) !== 'undefined' && (value as unknown) === window) {\n return '[Window]';\n }\n\n if (typeof (document as any) !== 'undefined' && (value as unknown) === document) {\n return '[Document]';\n }\n\n // React's SyntheticEvent thingy\n if (isSyntheticEvent(value)) {\n return '[SyntheticEvent]';\n }\n\n // tslint:disable-next-line:no-tautology-expression\n if (typeof value === 'number' && value !== value) {\n return '[NaN]';\n }\n\n if (value === void 0) {\n return '[undefined]';\n }\n\n if (typeof value === 'function') {\n return `[Function: ${getFunctionName(value)}]`;\n }\n\n return value;\n}\n\n/**\n * Walks an object to perform a normalization on it\n *\n * @param key of object that's walked in current iteration\n * @param value object to be walked\n * @param depth Optional number indicating how deep should walking be performed\n * @param memo Optional Memo class handling decycling\n */\nexport function walk(key: string, value: any, depth: number = +Infinity, memo: Memo = new Memo()): any {\n // If we reach the maximum depth, serialize whatever has left\n if (depth === 0) {\n return serializeValue(value);\n }\n\n // If value implements `toJSON` method, call it and return early\n // tslint:disable:no-unsafe-any\n if (value !== null && value !== undefined && typeof value.toJSON === 'function') {\n return value.toJSON();\n }\n // tslint:enable:no-unsafe-any\n\n // If normalized value is a primitive, there are no branches left to walk, so we can just bail out, as theres no point in going down that branch any further\n const normalized = normalizeValue(value, key);\n if (isPrimitive(normalized)) {\n return normalized;\n }\n\n // Create source that we will use for next itterations, either objectified error object (Error type with extracted keys:value pairs) or the input itself\n const source = getWalkSource(value);\n\n // Create an accumulator that will act as a parent for all future itterations of that branch\n const acc = Array.isArray(value) ? [] : {};\n\n // If we already walked that branch, bail out, as it's circular reference\n if (memo.memoize(value)) {\n return '[Circular ~]';\n }\n\n // Walk all keys of the source\n for (const innerKey in source) {\n // Avoid iterating over fields in the prototype if they've somehow been exposed to enumeration.\n if (!Object.prototype.hasOwnProperty.call(source, innerKey)) {\n continue;\n }\n // Recursively walk through all the child nodes\n (acc as { [key: string]: any })[innerKey] = walk(innerKey, source[innerKey], depth - 1, memo);\n }\n\n // Once walked through all the branches, remove the parent from memo storage\n memo.unmemoize(value);\n\n // Return accumulated values\n return acc;\n}\n\n/**\n * normalize()\n *\n * - Creates a copy to prevent original input mutation\n * - Skip non-enumerablers\n * - Calls `toJSON` if implemented\n * - Removes circular references\n * - Translates non-serializeable values (undefined/NaN/Functions) to serializable format\n * - Translates known global objects/Classes to a string representations\n * - Takes care of Error objects serialization\n * - Optionally limit depth of final output\n */\nexport function normalize(input: any, depth?: number): any {\n try {\n // tslint:disable-next-line:no-unsafe-any\n return JSON.parse(JSON.stringify(input, (key: string, value: any) => walk(key, value, depth)));\n } catch (_oO) {\n return '**non-serializable**';\n }\n}\n\n/**\n * Given any captured exception, extract its keys and create a sorted\n * and truncated list that will be used inside the event message.\n * eg. `Non-error exception captured with keys: foo, bar, baz`\n */\nexport function extractExceptionKeysForMessage(exception: any, maxLength: number = 40): string {\n // tslint:disable:strict-type-predicates\n const keys = Object.keys(getWalkSource(exception));\n keys.sort();\n\n if (!keys.length) {\n return '[object has no keys]';\n }\n\n if (keys[0].length >= maxLength) {\n return truncate(keys[0], maxLength);\n }\n\n for (let includedKeys = keys.length; includedKeys > 0; includedKeys--) {\n const serialized = keys.slice(0, includedKeys).join(', ');\n if (serialized.length > maxLength) {\n continue;\n }\n if (includedKeys === keys.length) {\n return serialized;\n }\n return truncate(serialized, maxLength);\n }\n\n return '';\n}\n\n/**\n * Given any object, return the new object with removed keys that value was `undefined`.\n * Works recursively on objects and arrays.\n */\nexport function dropUndefinedKeys(val: T): T {\n if (isPlainObject(val)) {\n const obj = val as { [key: string]: any };\n const rv: { [key: string]: any } = {};\n for (const key of Object.keys(obj)) {\n if (typeof obj[key] !== 'undefined') {\n rv[key] = dropUndefinedKeys(obj[key]);\n }\n }\n return rv as T;\n }\n\n if (Array.isArray(val)) {\n return val.map(dropUndefinedKeys) as any;\n }\n\n return val;\n}\n","import style from './Footer.less';\nimport { Component } from 'preact';\n\nexport default function(props) {\n\treturn (\n\t\t
\n\t\t\t© {new Date().getFullYear()}\n\t\t\t - \n\t\t\tStefano Pigozzi\n\t\t\t - \n\t\t\tCC BY-SA 4.0\n\t\t\t - \n\t\t\tuni.steffo.eu {process.env.RELEASE}\n\t\t\t - \n\t\t\tSupportami\n\t\t
\n\t);\n}\n","export default function _extends() {\n _extends = Object.assign || function (target) {\n for (var i = 1; i < arguments.length; i++) {\n var source = arguments[i];\n\n for (var key in source) {\n if (Object.prototype.hasOwnProperty.call(source, key)) {\n target[key] = source[key];\n }\n }\n }\n\n return target;\n };\n\n return _extends.apply(this, arguments);\n}","function isAbsolute(pathname) {\n return pathname.charAt(0) === '/';\n}\n\n// About 1.5x faster than the two-arg version of Array#splice()\nfunction spliceOne(list, index) {\n for (var i = index, k = i + 1, n = list.length; k < n; i += 1, k += 1) {\n list[i] = list[k];\n }\n\n list.pop();\n}\n\n// This implementation is based heavily on node's url.parse\nfunction resolvePathname(to, from) {\n if (from === undefined) from = '';\n\n var toParts = (to && to.split('/')) || [];\n var fromParts = (from && from.split('/')) || [];\n\n var isToAbs = to && isAbsolute(to);\n var isFromAbs = from && isAbsolute(from);\n var mustEndAbs = isToAbs || isFromAbs;\n\n if (to && isAbsolute(to)) {\n // to is absolute\n fromParts = toParts;\n } else if (toParts.length) {\n // to is relative, drop the filename\n fromParts.pop();\n fromParts = fromParts.concat(toParts);\n }\n\n if (!fromParts.length) return '/';\n\n var hasTrailingSlash;\n if (fromParts.length) {\n var last = fromParts[fromParts.length - 1];\n hasTrailingSlash = last === '.' || last === '..' || last === '';\n } else {\n hasTrailingSlash = false;\n }\n\n var up = 0;\n for (var i = fromParts.length; i >= 0; i--) {\n var part = fromParts[i];\n\n if (part === '.') {\n spliceOne(fromParts, i);\n } else if (part === '..') {\n spliceOne(fromParts, i);\n up++;\n } else if (up) {\n spliceOne(fromParts, i);\n up--;\n }\n }\n\n if (!mustEndAbs) for (; up--; up) fromParts.unshift('..');\n\n if (\n mustEndAbs &&\n fromParts[0] !== '' &&\n (!fromParts[0] || !isAbsolute(fromParts[0]))\n )\n fromParts.unshift('');\n\n var result = fromParts.join('/');\n\n if (hasTrailingSlash && result.substr(-1) !== '/') result += '/';\n\n return result;\n}\n\nexport default resolvePathname;\n","import _extends from '@babel/runtime/helpers/esm/extends';\nimport resolvePathname from 'resolve-pathname';\nimport valueEqual from 'value-equal';\nimport warning from 'tiny-warning';\nimport invariant from 'tiny-invariant';\n\nfunction addLeadingSlash(path) {\n return path.charAt(0) === '/' ? path : '/' + path;\n}\nfunction stripLeadingSlash(path) {\n return path.charAt(0) === '/' ? path.substr(1) : path;\n}\nfunction hasBasename(path, prefix) {\n return path.toLowerCase().indexOf(prefix.toLowerCase()) === 0 && '/?#'.indexOf(path.charAt(prefix.length)) !== -1;\n}\nfunction stripBasename(path, prefix) {\n return hasBasename(path, prefix) ? path.substr(prefix.length) : path;\n}\nfunction stripTrailingSlash(path) {\n return path.charAt(path.length - 1) === '/' ? path.slice(0, -1) : path;\n}\nfunction parsePath(path) {\n var pathname = path || '/';\n var search = '';\n var hash = '';\n var hashIndex = pathname.indexOf('#');\n\n if (hashIndex !== -1) {\n hash = pathname.substr(hashIndex);\n pathname = pathname.substr(0, hashIndex);\n }\n\n var searchIndex = pathname.indexOf('?');\n\n if (searchIndex !== -1) {\n search = pathname.substr(searchIndex);\n pathname = pathname.substr(0, searchIndex);\n }\n\n return {\n pathname: pathname,\n search: search === '?' ? '' : search,\n hash: hash === '#' ? '' : hash\n };\n}\nfunction createPath(location) {\n var pathname = location.pathname,\n search = location.search,\n hash = location.hash;\n var path = pathname || '/';\n if (search && search !== '?') path += search.charAt(0) === '?' ? search : \"?\" + search;\n if (hash && hash !== '#') path += hash.charAt(0) === '#' ? hash : \"#\" + hash;\n return path;\n}\n\nfunction createLocation(path, state, key, currentLocation) {\n var location;\n\n if (typeof path === 'string') {\n // Two-arg form: push(path, state)\n location = parsePath(path);\n location.state = state;\n } else {\n // One-arg form: push(location)\n location = _extends({}, path);\n if (location.pathname === undefined) location.pathname = '';\n\n if (location.search) {\n if (location.search.charAt(0) !== '?') location.search = '?' + location.search;\n } else {\n location.search = '';\n }\n\n if (location.hash) {\n if (location.hash.charAt(0) !== '#') location.hash = '#' + location.hash;\n } else {\n location.hash = '';\n }\n\n if (state !== undefined && location.state === undefined) location.state = state;\n }\n\n try {\n location.pathname = decodeURI(location.pathname);\n } catch (e) {\n if (e instanceof URIError) {\n throw new URIError('Pathname \"' + location.pathname + '\" could not be decoded. ' + 'This is likely caused by an invalid percent-encoding.');\n } else {\n throw e;\n }\n }\n\n if (key) location.key = key;\n\n if (currentLocation) {\n // Resolve incomplete/relative pathname relative to current location.\n if (!location.pathname) {\n location.pathname = currentLocation.pathname;\n } else if (location.pathname.charAt(0) !== '/') {\n location.pathname = resolvePathname(location.pathname, currentLocation.pathname);\n }\n } else {\n // When there is no prior location and pathname is empty, set it to /\n if (!location.pathname) {\n location.pathname = '/';\n }\n }\n\n return location;\n}\nfunction locationsAreEqual(a, b) {\n return a.pathname === b.pathname && a.search === b.search && a.hash === b.hash && a.key === b.key && valueEqual(a.state, b.state);\n}\n\nfunction createTransitionManager() {\n var prompt = null;\n\n function setPrompt(nextPrompt) {\n process.env.NODE_ENV !== \"production\" ? warning(prompt == null, 'A history supports only one prompt at a time') : void 0;\n prompt = nextPrompt;\n return function () {\n if (prompt === nextPrompt) prompt = null;\n };\n }\n\n function confirmTransitionTo(location, action, getUserConfirmation, callback) {\n // TODO: If another transition starts while we're still confirming\n // the previous one, we may end up in a weird state. Figure out the\n // best way to handle this.\n if (prompt != null) {\n var result = typeof prompt === 'function' ? prompt(location, action) : prompt;\n\n if (typeof result === 'string') {\n if (typeof getUserConfirmation === 'function') {\n getUserConfirmation(result, callback);\n } else {\n process.env.NODE_ENV !== \"production\" ? warning(false, 'A history needs a getUserConfirmation function in order to use a prompt message') : void 0;\n callback(true);\n }\n } else {\n // Return false from a transition hook to cancel the transition.\n callback(result !== false);\n }\n } else {\n callback(true);\n }\n }\n\n var listeners = [];\n\n function appendListener(fn) {\n var isActive = true;\n\n function listener() {\n if (isActive) fn.apply(void 0, arguments);\n }\n\n listeners.push(listener);\n return function () {\n isActive = false;\n listeners = listeners.filter(function (item) {\n return item !== listener;\n });\n };\n }\n\n function notifyListeners() {\n for (var _len = arguments.length, args = new Array(_len), _key = 0; _key < _len; _key++) {\n args[_key] = arguments[_key];\n }\n\n listeners.forEach(function (listener) {\n return listener.apply(void 0, args);\n });\n }\n\n return {\n setPrompt: setPrompt,\n confirmTransitionTo: confirmTransitionTo,\n appendListener: appendListener,\n notifyListeners: notifyListeners\n };\n}\n\nvar canUseDOM = !!(typeof window !== 'undefined' && window.document && window.document.createElement);\nfunction getConfirmation(message, callback) {\n callback(window.confirm(message)); // eslint-disable-line no-alert\n}\n/**\n * Returns true if the HTML5 history API is supported. Taken from Modernizr.\n *\n * https://github.com/Modernizr/Modernizr/blob/master/LICENSE\n * https://github.com/Modernizr/Modernizr/blob/master/feature-detects/history.js\n * changed to avoid false negatives for Windows Phones: https://github.com/reactjs/react-router/issues/586\n */\n\nfunction supportsHistory() {\n var ua = window.navigator.userAgent;\n if ((ua.indexOf('Android 2.') !== -1 || ua.indexOf('Android 4.0') !== -1) && ua.indexOf('Mobile Safari') !== -1 && ua.indexOf('Chrome') === -1 && ua.indexOf('Windows Phone') === -1) return false;\n return window.history && 'pushState' in window.history;\n}\n/**\n * Returns true if browser fires popstate on hash change.\n * IE10 and IE11 do not.\n */\n\nfunction supportsPopStateOnHashChange() {\n return window.navigator.userAgent.indexOf('Trident') === -1;\n}\n/**\n * Returns false if using go(n) with hash history causes a full page reload.\n */\n\nfunction supportsGoWithoutReloadUsingHash() {\n return window.navigator.userAgent.indexOf('Firefox') === -1;\n}\n/**\n * Returns true if a given popstate event is an extraneous WebKit event.\n * Accounts for the fact that Chrome on iOS fires real popstate events\n * containing undefined state when pressing the back button.\n */\n\nfunction isExtraneousPopstateEvent(event) {\n return event.state === undefined && navigator.userAgent.indexOf('CriOS') === -1;\n}\n\nvar PopStateEvent = 'popstate';\nvar HashChangeEvent = 'hashchange';\n\nfunction getHistoryState() {\n try {\n return window.history.state || {};\n } catch (e) {\n // IE 11 sometimes throws when accessing window.history.state\n // See https://github.com/ReactTraining/history/pull/289\n return {};\n }\n}\n/**\n * Creates a history object that uses the HTML5 history API including\n * pushState, replaceState, and the popstate event.\n */\n\n\nfunction createBrowserHistory(props) {\n if (props === void 0) {\n props = {};\n }\n\n !canUseDOM ? process.env.NODE_ENV !== \"production\" ? invariant(false, 'Browser history needs a DOM') : invariant(false) : void 0;\n var globalHistory = window.history;\n var canUseHistory = supportsHistory();\n var needsHashChangeListener = !supportsPopStateOnHashChange();\n var _props = props,\n _props$forceRefresh = _props.forceRefresh,\n forceRefresh = _props$forceRefresh === void 0 ? false : _props$forceRefresh,\n _props$getUserConfirm = _props.getUserConfirmation,\n getUserConfirmation = _props$getUserConfirm === void 0 ? getConfirmation : _props$getUserConfirm,\n _props$keyLength = _props.keyLength,\n keyLength = _props$keyLength === void 0 ? 6 : _props$keyLength;\n var basename = props.basename ? stripTrailingSlash(addLeadingSlash(props.basename)) : '';\n\n function getDOMLocation(historyState) {\n var _ref = historyState || {},\n key = _ref.key,\n state = _ref.state;\n\n var _window$location = window.location,\n pathname = _window$location.pathname,\n search = _window$location.search,\n hash = _window$location.hash;\n var path = pathname + search + hash;\n process.env.NODE_ENV !== \"production\" ? warning(!basename || hasBasename(path, basename), 'You are attempting to use a basename on a page whose URL path does not begin ' + 'with the basename. Expected path \"' + path + '\" to begin with \"' + basename + '\".') : void 0;\n if (basename) path = stripBasename(path, basename);\n return createLocation(path, state, key);\n }\n\n function createKey() {\n return Math.random().toString(36).substr(2, keyLength);\n }\n\n var transitionManager = createTransitionManager();\n\n function setState(nextState) {\n _extends(history, nextState);\n\n history.length = globalHistory.length;\n transitionManager.notifyListeners(history.location, history.action);\n }\n\n function handlePopState(event) {\n // Ignore extraneous popstate events in WebKit.\n if (isExtraneousPopstateEvent(event)) return;\n handlePop(getDOMLocation(event.state));\n }\n\n function handleHashChange() {\n handlePop(getDOMLocation(getHistoryState()));\n }\n\n var forceNextPop = false;\n\n function handlePop(location) {\n if (forceNextPop) {\n forceNextPop = false;\n setState();\n } else {\n var action = 'POP';\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (ok) {\n setState({\n action: action,\n location: location\n });\n } else {\n revertPop(location);\n }\n });\n }\n }\n\n function revertPop(fromLocation) {\n var toLocation = history.location; // TODO: We could probably make this more reliable by\n // keeping a list of keys we've seen in sessionStorage.\n // Instead, we just default to 0 for keys we don't know.\n\n var toIndex = allKeys.indexOf(toLocation.key);\n if (toIndex === -1) toIndex = 0;\n var fromIndex = allKeys.indexOf(fromLocation.key);\n if (fromIndex === -1) fromIndex = 0;\n var delta = toIndex - fromIndex;\n\n if (delta) {\n forceNextPop = true;\n go(delta);\n }\n }\n\n var initialLocation = getDOMLocation(getHistoryState());\n var allKeys = [initialLocation.key]; // Public interface\n\n function createHref(location) {\n return basename + createPath(location);\n }\n\n function push(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to push when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n var action = 'PUSH';\n var location = createLocation(path, state, createKey(), history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var href = createHref(location);\n var key = location.key,\n state = location.state;\n\n if (canUseHistory) {\n globalHistory.pushState({\n key: key,\n state: state\n }, null, href);\n\n if (forceRefresh) {\n window.location.href = href;\n } else {\n var prevIndex = allKeys.indexOf(history.location.key);\n var nextKeys = allKeys.slice(0, prevIndex + 1);\n nextKeys.push(location.key);\n allKeys = nextKeys;\n setState({\n action: action,\n location: location\n });\n }\n } else {\n process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Browser history cannot push state in browsers that do not support HTML5 history') : void 0;\n window.location.href = href;\n }\n });\n }\n\n function replace(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to replace when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n var action = 'REPLACE';\n var location = createLocation(path, state, createKey(), history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var href = createHref(location);\n var key = location.key,\n state = location.state;\n\n if (canUseHistory) {\n globalHistory.replaceState({\n key: key,\n state: state\n }, null, href);\n\n if (forceRefresh) {\n window.location.replace(href);\n } else {\n var prevIndex = allKeys.indexOf(history.location.key);\n if (prevIndex !== -1) allKeys[prevIndex] = location.key;\n setState({\n action: action,\n location: location\n });\n }\n } else {\n process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Browser history cannot replace state in browsers that do not support HTML5 history') : void 0;\n window.location.replace(href);\n }\n });\n }\n\n function go(n) {\n globalHistory.go(n);\n }\n\n function goBack() {\n go(-1);\n }\n\n function goForward() {\n go(1);\n }\n\n var listenerCount = 0;\n\n function checkDOMListeners(delta) {\n listenerCount += delta;\n\n if (listenerCount === 1 && delta === 1) {\n window.addEventListener(PopStateEvent, handlePopState);\n if (needsHashChangeListener) window.addEventListener(HashChangeEvent, handleHashChange);\n } else if (listenerCount === 0) {\n window.removeEventListener(PopStateEvent, handlePopState);\n if (needsHashChangeListener) window.removeEventListener(HashChangeEvent, handleHashChange);\n }\n }\n\n var isBlocked = false;\n\n function block(prompt) {\n if (prompt === void 0) {\n prompt = false;\n }\n\n var unblock = transitionManager.setPrompt(prompt);\n\n if (!isBlocked) {\n checkDOMListeners(1);\n isBlocked = true;\n }\n\n return function () {\n if (isBlocked) {\n isBlocked = false;\n checkDOMListeners(-1);\n }\n\n return unblock();\n };\n }\n\n function listen(listener) {\n var unlisten = transitionManager.appendListener(listener);\n checkDOMListeners(1);\n return function () {\n checkDOMListeners(-1);\n unlisten();\n };\n }\n\n var history = {\n length: globalHistory.length,\n action: 'POP',\n location: initialLocation,\n createHref: createHref,\n push: push,\n replace: replace,\n go: go,\n goBack: goBack,\n goForward: goForward,\n block: block,\n listen: listen\n };\n return history;\n}\n\nvar HashChangeEvent$1 = 'hashchange';\nvar HashPathCoders = {\n hashbang: {\n encodePath: function encodePath(path) {\n return path.charAt(0) === '!' ? path : '!/' + stripLeadingSlash(path);\n },\n decodePath: function decodePath(path) {\n return path.charAt(0) === '!' ? path.substr(1) : path;\n }\n },\n noslash: {\n encodePath: stripLeadingSlash,\n decodePath: addLeadingSlash\n },\n slash: {\n encodePath: addLeadingSlash,\n decodePath: addLeadingSlash\n }\n};\n\nfunction stripHash(url) {\n var hashIndex = url.indexOf('#');\n return hashIndex === -1 ? url : url.slice(0, hashIndex);\n}\n\nfunction getHashPath() {\n // We can't use window.location.hash here because it's not\n // consistent across browsers - Firefox will pre-decode it!\n var href = window.location.href;\n var hashIndex = href.indexOf('#');\n return hashIndex === -1 ? '' : href.substring(hashIndex + 1);\n}\n\nfunction pushHashPath(path) {\n window.location.hash = path;\n}\n\nfunction replaceHashPath(path) {\n window.location.replace(stripHash(window.location.href) + '#' + path);\n}\n\nfunction createHashHistory(props) {\n if (props === void 0) {\n props = {};\n }\n\n !canUseDOM ? process.env.NODE_ENV !== \"production\" ? invariant(false, 'Hash history needs a DOM') : invariant(false) : void 0;\n var globalHistory = window.history;\n var canGoWithoutReload = supportsGoWithoutReloadUsingHash();\n var _props = props,\n _props$getUserConfirm = _props.getUserConfirmation,\n getUserConfirmation = _props$getUserConfirm === void 0 ? getConfirmation : _props$getUserConfirm,\n _props$hashType = _props.hashType,\n hashType = _props$hashType === void 0 ? 'slash' : _props$hashType;\n var basename = props.basename ? stripTrailingSlash(addLeadingSlash(props.basename)) : '';\n var _HashPathCoders$hashT = HashPathCoders[hashType],\n encodePath = _HashPathCoders$hashT.encodePath,\n decodePath = _HashPathCoders$hashT.decodePath;\n\n function getDOMLocation() {\n var path = decodePath(getHashPath());\n process.env.NODE_ENV !== \"production\" ? warning(!basename || hasBasename(path, basename), 'You are attempting to use a basename on a page whose URL path does not begin ' + 'with the basename. Expected path \"' + path + '\" to begin with \"' + basename + '\".') : void 0;\n if (basename) path = stripBasename(path, basename);\n return createLocation(path);\n }\n\n var transitionManager = createTransitionManager();\n\n function setState(nextState) {\n _extends(history, nextState);\n\n history.length = globalHistory.length;\n transitionManager.notifyListeners(history.location, history.action);\n }\n\n var forceNextPop = false;\n var ignorePath = null;\n\n function locationsAreEqual$$1(a, b) {\n return a.pathname === b.pathname && a.search === b.search && a.hash === b.hash;\n }\n\n function handleHashChange() {\n var path = getHashPath();\n var encodedPath = encodePath(path);\n\n if (path !== encodedPath) {\n // Ensure we always have a properly-encoded hash.\n replaceHashPath(encodedPath);\n } else {\n var location = getDOMLocation();\n var prevLocation = history.location;\n if (!forceNextPop && locationsAreEqual$$1(prevLocation, location)) return; // A hashchange doesn't always == location change.\n\n if (ignorePath === createPath(location)) return; // Ignore this change; we already setState in push/replace.\n\n ignorePath = null;\n handlePop(location);\n }\n }\n\n function handlePop(location) {\n if (forceNextPop) {\n forceNextPop = false;\n setState();\n } else {\n var action = 'POP';\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (ok) {\n setState({\n action: action,\n location: location\n });\n } else {\n revertPop(location);\n }\n });\n }\n }\n\n function revertPop(fromLocation) {\n var toLocation = history.location; // TODO: We could probably make this more reliable by\n // keeping a list of paths we've seen in sessionStorage.\n // Instead, we just default to 0 for paths we don't know.\n\n var toIndex = allPaths.lastIndexOf(createPath(toLocation));\n if (toIndex === -1) toIndex = 0;\n var fromIndex = allPaths.lastIndexOf(createPath(fromLocation));\n if (fromIndex === -1) fromIndex = 0;\n var delta = toIndex - fromIndex;\n\n if (delta) {\n forceNextPop = true;\n go(delta);\n }\n } // Ensure the hash is encoded properly before doing anything else.\n\n\n var path = getHashPath();\n var encodedPath = encodePath(path);\n if (path !== encodedPath) replaceHashPath(encodedPath);\n var initialLocation = getDOMLocation();\n var allPaths = [createPath(initialLocation)]; // Public interface\n\n function createHref(location) {\n var baseTag = document.querySelector('base');\n var href = '';\n\n if (baseTag && baseTag.getAttribute('href')) {\n href = stripHash(window.location.href);\n }\n\n return href + '#' + encodePath(basename + createPath(location));\n }\n\n function push(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Hash history cannot push state; it is ignored') : void 0;\n var action = 'PUSH';\n var location = createLocation(path, undefined, undefined, history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var path = createPath(location);\n var encodedPath = encodePath(basename + path);\n var hashChanged = getHashPath() !== encodedPath;\n\n if (hashChanged) {\n // We cannot tell if a hashchange was caused by a PUSH, so we'd\n // rather setState here and ignore the hashchange. The caveat here\n // is that other hash histories in the page will consider it a POP.\n ignorePath = path;\n pushHashPath(encodedPath);\n var prevIndex = allPaths.lastIndexOf(createPath(history.location));\n var nextPaths = allPaths.slice(0, prevIndex + 1);\n nextPaths.push(path);\n allPaths = nextPaths;\n setState({\n action: action,\n location: location\n });\n } else {\n process.env.NODE_ENV !== \"production\" ? warning(false, 'Hash history cannot PUSH the same path; a new entry will not be added to the history stack') : void 0;\n setState();\n }\n });\n }\n\n function replace(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Hash history cannot replace state; it is ignored') : void 0;\n var action = 'REPLACE';\n var location = createLocation(path, undefined, undefined, history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var path = createPath(location);\n var encodedPath = encodePath(basename + path);\n var hashChanged = getHashPath() !== encodedPath;\n\n if (hashChanged) {\n // We cannot tell if a hashchange was caused by a REPLACE, so we'd\n // rather setState here and ignore the hashchange. The caveat here\n // is that other hash histories in the page will consider it a POP.\n ignorePath = path;\n replaceHashPath(encodedPath);\n }\n\n var prevIndex = allPaths.indexOf(createPath(history.location));\n if (prevIndex !== -1) allPaths[prevIndex] = path;\n setState({\n action: action,\n location: location\n });\n });\n }\n\n function go(n) {\n process.env.NODE_ENV !== \"production\" ? warning(canGoWithoutReload, 'Hash history go(n) causes a full page reload in this browser') : void 0;\n globalHistory.go(n);\n }\n\n function goBack() {\n go(-1);\n }\n\n function goForward() {\n go(1);\n }\n\n var listenerCount = 0;\n\n function checkDOMListeners(delta) {\n listenerCount += delta;\n\n if (listenerCount === 1 && delta === 1) {\n window.addEventListener(HashChangeEvent$1, handleHashChange);\n } else if (listenerCount === 0) {\n window.removeEventListener(HashChangeEvent$1, handleHashChange);\n }\n }\n\n var isBlocked = false;\n\n function block(prompt) {\n if (prompt === void 0) {\n prompt = false;\n }\n\n var unblock = transitionManager.setPrompt(prompt);\n\n if (!isBlocked) {\n checkDOMListeners(1);\n isBlocked = true;\n }\n\n return function () {\n if (isBlocked) {\n isBlocked = false;\n checkDOMListeners(-1);\n }\n\n return unblock();\n };\n }\n\n function listen(listener) {\n var unlisten = transitionManager.appendListener(listener);\n checkDOMListeners(1);\n return function () {\n checkDOMListeners(-1);\n unlisten();\n };\n }\n\n var history = {\n length: globalHistory.length,\n action: 'POP',\n location: initialLocation,\n createHref: createHref,\n push: push,\n replace: replace,\n go: go,\n goBack: goBack,\n goForward: goForward,\n block: block,\n listen: listen\n };\n return history;\n}\n\nfunction clamp(n, lowerBound, upperBound) {\n return Math.min(Math.max(n, lowerBound), upperBound);\n}\n/**\n * Creates a history object that stores locations in memory.\n */\n\n\nfunction createMemoryHistory(props) {\n if (props === void 0) {\n props = {};\n }\n\n var _props = props,\n getUserConfirmation = _props.getUserConfirmation,\n _props$initialEntries = _props.initialEntries,\n initialEntries = _props$initialEntries === void 0 ? ['/'] : _props$initialEntries,\n _props$initialIndex = _props.initialIndex,\n initialIndex = _props$initialIndex === void 0 ? 0 : _props$initialIndex,\n _props$keyLength = _props.keyLength,\n keyLength = _props$keyLength === void 0 ? 6 : _props$keyLength;\n var transitionManager = createTransitionManager();\n\n function setState(nextState) {\n _extends(history, nextState);\n\n history.length = history.entries.length;\n transitionManager.notifyListeners(history.location, history.action);\n }\n\n function createKey() {\n return Math.random().toString(36).substr(2, keyLength);\n }\n\n var index = clamp(initialIndex, 0, initialEntries.length - 1);\n var entries = initialEntries.map(function (entry) {\n return typeof entry === 'string' ? createLocation(entry, undefined, createKey()) : createLocation(entry, undefined, entry.key || createKey());\n }); // Public interface\n\n var createHref = createPath;\n\n function push(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to push when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n var action = 'PUSH';\n var location = createLocation(path, state, createKey(), history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var prevIndex = history.index;\n var nextIndex = prevIndex + 1;\n var nextEntries = history.entries.slice(0);\n\n if (nextEntries.length > nextIndex) {\n nextEntries.splice(nextIndex, nextEntries.length - nextIndex, location);\n } else {\n nextEntries.push(location);\n }\n\n setState({\n action: action,\n location: location,\n index: nextIndex,\n entries: nextEntries\n });\n });\n }\n\n function replace(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to replace when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n var action = 'REPLACE';\n var location = createLocation(path, state, createKey(), history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n history.entries[history.index] = location;\n setState({\n action: action,\n location: location\n });\n });\n }\n\n function go(n) {\n var nextIndex = clamp(history.index + n, 0, history.entries.length - 1);\n var action = 'POP';\n var location = history.entries[nextIndex];\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (ok) {\n setState({\n action: action,\n location: location,\n index: nextIndex\n });\n } else {\n // Mimic the behavior of DOM histories by\n // causing a render after a cancelled POP.\n setState();\n }\n });\n }\n\n function goBack() {\n go(-1);\n }\n\n function goForward() {\n go(1);\n }\n\n function canGo(n) {\n var nextIndex = history.index + n;\n return nextIndex >= 0 && nextIndex < history.entries.length;\n }\n\n function block(prompt) {\n if (prompt === void 0) {\n prompt = false;\n }\n\n return transitionManager.setPrompt(prompt);\n }\n\n function listen(listener) {\n return transitionManager.appendListener(listener);\n }\n\n var history = {\n length: entries.length,\n action: 'POP',\n location: entries[index],\n index: index,\n entries: entries,\n createHref: createHref,\n push: push,\n replace: replace,\n go: go,\n goBack: goBack,\n goForward: goForward,\n canGo: canGo,\n block: block,\n listen: listen\n };\n return history;\n}\n\nexport { createBrowserHistory, createHashHistory, createMemoryHistory, createLocation, locationsAreEqual, parsePath, createPath };\n","var isProduction = process.env.NODE_ENV === 'production';\nvar prefix = 'Invariant failed';\nfunction invariant(condition, message) {\n if (condition) {\n return;\n }\n if (isProduction) {\n throw new Error(prefix);\n }\n throw new Error(prefix + \": \" + (message || ''));\n}\n\nexport default invariant;\n","// This will be replaced\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./Fisica.js\") );\n\t\t\t}, \"route-Fisica\");\n\t\t}\n\n\t\texport default Async(load);\n\t","import {\n Breadcrumb,\n Event,\n EventHint,\n EventProcessor,\n Scope as ScopeInterface,\n Severity,\n Span,\n User,\n} from '@sentry/types';\nimport { getGlobalObject, isThenable, SyncPromise, timestampWithMs } from '@sentry/utils';\n\n/**\n * Holds additional event information. {@link Scope.applyToEvent} will be\n * called by the client before an event will be sent.\n */\nexport class Scope implements ScopeInterface {\n /** Flag if notifiying is happening. */\n protected _notifyingListeners: boolean = false;\n\n /** Callback for client to receive scope changes. */\n protected _scopeListeners: Array<(scope: Scope) => void> = [];\n\n /** Callback list that will be called after {@link applyToEvent}. */\n protected _eventProcessors: EventProcessor[] = [];\n\n /** Array of breadcrumbs. */\n protected _breadcrumbs: Breadcrumb[] = [];\n\n /** User */\n protected _user: User = {};\n\n /** Tags */\n protected _tags: { [key: string]: string } = {};\n\n /** Extra */\n protected _extra: { [key: string]: any } = {};\n\n /** Contexts */\n protected _context: { [key: string]: any } = {};\n\n /** Fingerprint */\n protected _fingerprint?: string[];\n\n /** Severity */\n protected _level?: Severity;\n\n /** Transaction */\n protected _transaction?: string;\n\n /** Span */\n protected _span?: Span;\n\n /**\n * Add internal on change listener. Used for sub SDKs that need to store the scope.\n * @hidden\n */\n public addScopeListener(callback: (scope: Scope) => void): void {\n this._scopeListeners.push(callback);\n }\n\n /**\n * @inheritDoc\n */\n public addEventProcessor(callback: EventProcessor): this {\n this._eventProcessors.push(callback);\n return this;\n }\n\n /**\n * This will be called on every set call.\n */\n protected _notifyScopeListeners(): void {\n if (!this._notifyingListeners) {\n this._notifyingListeners = true;\n setTimeout(() => {\n this._scopeListeners.forEach(callback => {\n callback(this);\n });\n this._notifyingListeners = false;\n });\n }\n }\n\n /**\n * This will be called after {@link applyToEvent} is finished.\n */\n protected _notifyEventProcessors(\n processors: EventProcessor[],\n event: Event | null,\n hint?: EventHint,\n index: number = 0,\n ): PromiseLike {\n return new SyncPromise((resolve, reject) => {\n const processor = processors[index];\n // tslint:disable-next-line:strict-type-predicates\n if (event === null || typeof processor !== 'function') {\n resolve(event);\n } else {\n const result = processor({ ...event }, hint) as Event | null;\n if (isThenable(result)) {\n (result as PromiseLike)\n .then(final => this._notifyEventProcessors(processors, final, hint, index + 1).then(resolve))\n .then(null, reject);\n } else {\n this._notifyEventProcessors(processors, result, hint, index + 1)\n .then(resolve)\n .then(null, reject);\n }\n }\n });\n }\n\n /**\n * @inheritDoc\n */\n public setUser(user: User | null): this {\n this._user = user || {};\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public setTags(tags: { [key: string]: string }): this {\n this._tags = {\n ...this._tags,\n ...tags,\n };\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public setTag(key: string, value: string): this {\n this._tags = { ...this._tags, [key]: value };\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public setExtras(extras: { [key: string]: any }): this {\n this._extra = {\n ...this._extra,\n ...extras,\n };\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public setExtra(key: string, extra: any): this {\n this._extra = { ...this._extra, [key]: extra };\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public setFingerprint(fingerprint: string[]): this {\n this._fingerprint = fingerprint;\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public setLevel(level: Severity): this {\n this._level = level;\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public setTransaction(transaction?: string): this {\n this._transaction = transaction;\n if (this._span) {\n (this._span as any).transaction = transaction;\n }\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public setContext(key: string, context: { [key: string]: any } | null): this {\n this._context = { ...this._context, [key]: context };\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public setSpan(span?: Span): this {\n this._span = span;\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * Internal getter for Span, used in Hub.\n * @hidden\n */\n public getSpan(): Span | undefined {\n return this._span;\n }\n\n /**\n * Inherit values from the parent scope.\n * @param scope to clone.\n */\n public static clone(scope?: Scope): Scope {\n const newScope = new Scope();\n if (scope) {\n newScope._breadcrumbs = [...scope._breadcrumbs];\n newScope._tags = { ...scope._tags };\n newScope._extra = { ...scope._extra };\n newScope._context = { ...scope._context };\n newScope._user = scope._user;\n newScope._level = scope._level;\n newScope._span = scope._span;\n newScope._transaction = scope._transaction;\n newScope._fingerprint = scope._fingerprint;\n newScope._eventProcessors = [...scope._eventProcessors];\n }\n return newScope;\n }\n\n /**\n * @inheritDoc\n */\n public clear(): this {\n this._breadcrumbs = [];\n this._tags = {};\n this._extra = {};\n this._user = {};\n this._context = {};\n this._level = undefined;\n this._transaction = undefined;\n this._fingerprint = undefined;\n this._span = undefined;\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public addBreadcrumb(breadcrumb: Breadcrumb, maxBreadcrumbs?: number): this {\n const mergedBreadcrumb = {\n timestamp: timestampWithMs(),\n ...breadcrumb,\n };\n\n this._breadcrumbs =\n maxBreadcrumbs !== undefined && maxBreadcrumbs >= 0\n ? [...this._breadcrumbs, mergedBreadcrumb].slice(-maxBreadcrumbs)\n : [...this._breadcrumbs, mergedBreadcrumb];\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public clearBreadcrumbs(): this {\n this._breadcrumbs = [];\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * Applies fingerprint from the scope to the event if there's one,\n * uses message if there's one instead or get rid of empty fingerprint\n */\n private _applyFingerprint(event: Event): void {\n // Make sure it's an array first and we actually have something in place\n event.fingerprint = event.fingerprint\n ? Array.isArray(event.fingerprint)\n ? event.fingerprint\n : [event.fingerprint]\n : [];\n\n // If we have something on the scope, then merge it with event\n if (this._fingerprint) {\n event.fingerprint = event.fingerprint.concat(this._fingerprint);\n }\n\n // If we have no data at all, remove empty array default\n if (event.fingerprint && !event.fingerprint.length) {\n delete event.fingerprint;\n }\n }\n\n /**\n * Applies the current context and fingerprint to the event.\n * Note that breadcrumbs will be added by the client.\n * Also if the event has already breadcrumbs on it, we do not merge them.\n * @param event Event\n * @param hint May contain additional informartion about the original exception.\n * @hidden\n */\n public applyToEvent(event: Event, hint?: EventHint): PromiseLike {\n if (this._extra && Object.keys(this._extra).length) {\n event.extra = { ...this._extra, ...event.extra };\n }\n if (this._tags && Object.keys(this._tags).length) {\n event.tags = { ...this._tags, ...event.tags };\n }\n if (this._user && Object.keys(this._user).length) {\n event.user = { ...this._user, ...event.user };\n }\n if (this._context && Object.keys(this._context).length) {\n event.contexts = { ...this._context, ...event.contexts };\n }\n if (this._level) {\n event.level = this._level;\n }\n if (this._transaction) {\n event.transaction = this._transaction;\n }\n if (this._span) {\n event.contexts = { trace: this._span.getTraceContext(), ...event.contexts };\n }\n\n this._applyFingerprint(event);\n\n event.breadcrumbs = [...(event.breadcrumbs || []), ...this._breadcrumbs];\n event.breadcrumbs = event.breadcrumbs.length > 0 ? event.breadcrumbs : undefined;\n\n return this._notifyEventProcessors([...getGlobalEventProcessors(), ...this._eventProcessors], event, hint);\n }\n}\n\n/**\n * Retruns the global event processors.\n */\nfunction getGlobalEventProcessors(): EventProcessor[] {\n const global = getGlobalObject();\n global.__SENTRY__ = global.__SENTRY__ || {};\n global.__SENTRY__.globalEventProcessors = global.__SENTRY__.globalEventProcessors || [];\n return global.__SENTRY__.globalEventProcessors;\n}\n\n/**\n * Add a EventProcessor to be kept globally.\n * @param callback EventProcessor to add\n */\nexport function addGlobalEventProcessor(callback: EventProcessor): void {\n getGlobalEventProcessors().push(callback);\n}\n","import {\n Breadcrumb,\n BreadcrumbHint,\n Client,\n Event,\n EventHint,\n Hub as HubInterface,\n Integration,\n IntegrationClass,\n Severity,\n Span,\n SpanContext,\n User,\n} from '@sentry/types';\nimport { consoleSandbox, getGlobalObject, isNodeEnv, logger, timestampWithMs, uuid4 } from '@sentry/utils';\n\nimport { Carrier, Layer } from './interfaces';\nimport { Scope } from './scope';\n\n/**\n * API compatibility version of this hub.\n *\n * WARNING: This number should only be incresed when the global interface\n * changes a and new methods are introduced.\n *\n * @hidden\n */\nexport const API_VERSION = 3;\n\n/**\n * Default maximum number of breadcrumbs added to an event. Can be overwritten\n * with {@link Options.maxBreadcrumbs}.\n */\nconst DEFAULT_BREADCRUMBS = 100;\n\n/**\n * Absolute maximum number of breadcrumbs added to an event. The\n * `maxBreadcrumbs` option cannot be higher than this value.\n */\nconst MAX_BREADCRUMBS = 100;\n\n/**\n * @inheritDoc\n */\nexport class Hub implements HubInterface {\n /** Is a {@link Layer}[] containing the client and scope */\n private readonly _stack: Layer[] = [];\n\n /** Contains the last event id of a captured event. */\n private _lastEventId?: string;\n\n /**\n * Creates a new instance of the hub, will push one {@link Layer} into the\n * internal stack on creation.\n *\n * @param client bound to the hub.\n * @param scope bound to the hub.\n * @param version number, higher number means higher priority.\n */\n public constructor(client?: Client, scope: Scope = new Scope(), private readonly _version: number = API_VERSION) {\n this._stack.push({ client, scope });\n }\n\n /**\n * Internal helper function to call a method on the top client if it exists.\n *\n * @param method The method to call on the client.\n * @param args Arguments to pass to the client function.\n */\n private _invokeClient(method: M, ...args: any[]): void {\n const top = this.getStackTop();\n if (top && top.client && top.client[method]) {\n (top.client as any)[method](...args, top.scope);\n }\n }\n\n /**\n * @inheritDoc\n */\n public isOlderThan(version: number): boolean {\n return this._version < version;\n }\n\n /**\n * @inheritDoc\n */\n public bindClient(client?: Client): void {\n const top = this.getStackTop();\n top.client = client;\n if (client && client.setupIntegrations) {\n client.setupIntegrations();\n }\n }\n\n /**\n * @inheritDoc\n */\n public pushScope(): Scope {\n // We want to clone the content of prev scope\n const stack = this.getStack();\n const parentScope = stack.length > 0 ? stack[stack.length - 1].scope : undefined;\n const scope = Scope.clone(parentScope);\n this.getStack().push({\n client: this.getClient(),\n scope,\n });\n return scope;\n }\n\n /**\n * @inheritDoc\n */\n public popScope(): boolean {\n return this.getStack().pop() !== undefined;\n }\n\n /**\n * @inheritDoc\n */\n public withScope(callback: (scope: Scope) => void): void {\n const scope = this.pushScope();\n try {\n callback(scope);\n } finally {\n this.popScope();\n }\n }\n\n /**\n * @inheritDoc\n */\n public getClient(): C | undefined {\n return this.getStackTop().client as C;\n }\n\n /** Returns the scope of the top stack. */\n public getScope(): Scope | undefined {\n return this.getStackTop().scope;\n }\n\n /** Returns the scope stack for domains or the process. */\n public getStack(): Layer[] {\n return this._stack;\n }\n\n /** Returns the topmost scope layer in the order domain > local > process. */\n public getStackTop(): Layer {\n return this._stack[this._stack.length - 1];\n }\n\n /**\n * @inheritDoc\n */\n public captureException(exception: any, hint?: EventHint): string {\n const eventId = (this._lastEventId = uuid4());\n let finalHint = hint;\n\n // If there's no explicit hint provided, mimick the same thing that would happen\n // in the minimal itself to create a consistent behavior.\n // We don't do this in the client, as it's the lowest level API, and doing this,\n // would prevent user from having full control over direct calls.\n if (!hint) {\n let syntheticException: Error;\n try {\n throw new Error('Sentry syntheticException');\n } catch (exception) {\n syntheticException = exception as Error;\n }\n finalHint = {\n originalException: exception,\n syntheticException,\n };\n }\n\n this._invokeClient('captureException', exception, {\n ...finalHint,\n event_id: eventId,\n });\n return eventId;\n }\n\n /**\n * @inheritDoc\n */\n public captureMessage(message: string, level?: Severity, hint?: EventHint): string {\n const eventId = (this._lastEventId = uuid4());\n let finalHint = hint;\n\n // If there's no explicit hint provided, mimick the same thing that would happen\n // in the minimal itself to create a consistent behavior.\n // We don't do this in the client, as it's the lowest level API, and doing this,\n // would prevent user from having full control over direct calls.\n if (!hint) {\n let syntheticException: Error;\n try {\n throw new Error(message);\n } catch (exception) {\n syntheticException = exception as Error;\n }\n finalHint = {\n originalException: message,\n syntheticException,\n };\n }\n\n this._invokeClient('captureMessage', message, level, {\n ...finalHint,\n event_id: eventId,\n });\n return eventId;\n }\n\n /**\n * @inheritDoc\n */\n public captureEvent(event: Event, hint?: EventHint): string {\n const eventId = (this._lastEventId = uuid4());\n this._invokeClient('captureEvent', event, {\n ...hint,\n event_id: eventId,\n });\n return eventId;\n }\n\n /**\n * @inheritDoc\n */\n public lastEventId(): string | undefined {\n return this._lastEventId;\n }\n\n /**\n * @inheritDoc\n */\n public addBreadcrumb(breadcrumb: Breadcrumb, hint?: BreadcrumbHint): void {\n const top = this.getStackTop();\n\n if (!top.scope || !top.client) {\n return;\n }\n\n const { beforeBreadcrumb = null, maxBreadcrumbs = DEFAULT_BREADCRUMBS } =\n (top.client.getOptions && top.client.getOptions()) || {};\n\n if (maxBreadcrumbs <= 0) {\n return;\n }\n\n const timestamp = timestampWithMs();\n const mergedBreadcrumb = { timestamp, ...breadcrumb };\n const finalBreadcrumb = beforeBreadcrumb\n ? (consoleSandbox(() => beforeBreadcrumb(mergedBreadcrumb, hint)) as Breadcrumb | null)\n : mergedBreadcrumb;\n\n if (finalBreadcrumb === null) {\n return;\n }\n\n top.scope.addBreadcrumb(finalBreadcrumb, Math.min(maxBreadcrumbs, MAX_BREADCRUMBS));\n }\n\n /**\n * @inheritDoc\n */\n public setUser(user: User | null): void {\n const top = this.getStackTop();\n if (!top.scope) {\n return;\n }\n top.scope.setUser(user);\n }\n\n /**\n * @inheritDoc\n */\n public setTags(tags: { [key: string]: string }): void {\n const top = this.getStackTop();\n if (!top.scope) {\n return;\n }\n top.scope.setTags(tags);\n }\n\n /**\n * @inheritDoc\n */\n public setExtras(extras: { [key: string]: any }): void {\n const top = this.getStackTop();\n if (!top.scope) {\n return;\n }\n top.scope.setExtras(extras);\n }\n\n /**\n * @inheritDoc\n */\n public setTag(key: string, value: string): void {\n const top = this.getStackTop();\n if (!top.scope) {\n return;\n }\n top.scope.setTag(key, value);\n }\n\n /**\n * @inheritDoc\n */\n public setExtra(key: string, extra: any): void {\n const top = this.getStackTop();\n if (!top.scope) {\n return;\n }\n top.scope.setExtra(key, extra);\n }\n\n /**\n * @inheritDoc\n */\n public setContext(name: string, context: { [key: string]: any } | null): void {\n const top = this.getStackTop();\n if (!top.scope) {\n return;\n }\n top.scope.setContext(name, context);\n }\n\n /**\n * @inheritDoc\n */\n public configureScope(callback: (scope: Scope) => void): void {\n const top = this.getStackTop();\n if (top.scope && top.client) {\n callback(top.scope);\n }\n }\n\n /**\n * @inheritDoc\n */\n public run(callback: (hub: Hub) => void): void {\n const oldHub = makeMain(this);\n try {\n callback(this);\n } finally {\n makeMain(oldHub);\n }\n }\n\n /**\n * @inheritDoc\n */\n public getIntegration(integration: IntegrationClass): T | null {\n const client = this.getClient();\n if (!client) {\n return null;\n }\n try {\n return client.getIntegration(integration);\n } catch (_oO) {\n logger.warn(`Cannot retrieve integration ${integration.id} from the current Hub`);\n return null;\n }\n }\n\n /**\n * @inheritDoc\n */\n public startSpan(spanOrSpanContext?: Span | SpanContext, forceNoChild: boolean = false): Span {\n return this._callExtensionMethod('startSpan', spanOrSpanContext, forceNoChild);\n }\n\n /**\n * @inheritDoc\n */\n public traceHeaders(): { [key: string]: string } {\n return this._callExtensionMethod<{ [key: string]: string }>('traceHeaders');\n }\n\n /**\n * Calls global extension method and binding current instance to the function call\n */\n // @ts-ignore\n private _callExtensionMethod(method: string, ...args: any[]): T {\n const carrier = getMainCarrier();\n const sentry = carrier.__SENTRY__;\n // tslint:disable-next-line: strict-type-predicates\n if (sentry && sentry.extensions && typeof sentry.extensions[method] === 'function') {\n return sentry.extensions[method].apply(this, args);\n }\n logger.warn(`Extension method ${method} couldn't be found, doing nothing.`);\n }\n}\n\n/** Returns the global shim registry. */\nexport function getMainCarrier(): Carrier {\n const carrier = getGlobalObject();\n carrier.__SENTRY__ = carrier.__SENTRY__ || {\n extensions: {},\n hub: undefined,\n };\n return carrier;\n}\n\n/**\n * Replaces the current main hub with the passed one on the global object\n *\n * @returns The old replaced hub\n */\nexport function makeMain(hub: Hub): Hub {\n const registry = getMainCarrier();\n const oldHub = getHubFromCarrier(registry);\n setHubOnCarrier(registry, hub);\n return oldHub;\n}\n\n/**\n * Returns the default hub instance.\n *\n * If a hub is already registered in the global carrier but this module\n * contains a more recent version, it replaces the registered version.\n * Otherwise, the currently registered hub will be returned.\n */\nexport function getCurrentHub(): Hub {\n // Get main carrier (global for every environment)\n const registry = getMainCarrier();\n\n // If there's no hub, or its an old API, assign a new one\n if (!hasHubOnCarrier(registry) || getHubFromCarrier(registry).isOlderThan(API_VERSION)) {\n setHubOnCarrier(registry, new Hub());\n }\n\n // Prefer domains over global if they are there (applicable only to Node environment)\n if (isNodeEnv()) {\n return getHubFromActiveDomain(registry);\n }\n // Return hub that lives on a global object\n return getHubFromCarrier(registry);\n}\n\n/**\n * Try to read the hub from an active domain, fallback to the registry if one doesnt exist\n * @returns discovered hub\n */\nfunction getHubFromActiveDomain(registry: Carrier): Hub {\n try {\n const property = 'domain';\n const carrier = getMainCarrier();\n const sentry = carrier.__SENTRY__;\n // tslint:disable-next-line: strict-type-predicates\n if (!sentry || !sentry.extensions || !sentry.extensions[property]) {\n return getHubFromCarrier(registry);\n }\n const domain = sentry.extensions[property] as any;\n const activeDomain = domain.active;\n\n // If there no active domain, just return global hub\n if (!activeDomain) {\n return getHubFromCarrier(registry);\n }\n\n // If there's no hub on current domain, or its an old API, assign a new one\n if (!hasHubOnCarrier(activeDomain) || getHubFromCarrier(activeDomain).isOlderThan(API_VERSION)) {\n const registryHubTopStack = getHubFromCarrier(registry).getStackTop();\n setHubOnCarrier(activeDomain, new Hub(registryHubTopStack.client, Scope.clone(registryHubTopStack.scope)));\n }\n\n // Return hub that lives on a domain\n return getHubFromCarrier(activeDomain);\n } catch (_Oo) {\n // Return hub that lives on a global object\n return getHubFromCarrier(registry);\n }\n}\n\n/**\n * This will tell whether a carrier has a hub on it or not\n * @param carrier object\n */\nfunction hasHubOnCarrier(carrier: Carrier): boolean {\n if (carrier && carrier.__SENTRY__ && carrier.__SENTRY__.hub) {\n return true;\n }\n return false;\n}\n\n/**\n * This will create a new {@link Hub} and add to the passed object on\n * __SENTRY__.hub.\n * @param carrier object\n * @hidden\n */\nexport function getHubFromCarrier(carrier: Carrier): Hub {\n if (carrier && carrier.__SENTRY__ && carrier.__SENTRY__.hub) {\n return carrier.__SENTRY__.hub;\n }\n carrier.__SENTRY__ = carrier.__SENTRY__ || {};\n carrier.__SENTRY__.hub = new Hub();\n return carrier.__SENTRY__.hub;\n}\n\n/**\n * This will set passed {@link Hub} on the passed object's __SENTRY__.hub attribute\n * @param carrier object\n * @param hub Hub\n */\nexport function setHubOnCarrier(carrier: Carrier, hub: Hub): boolean {\n if (!carrier) {\n return false;\n }\n carrier.__SENTRY__ = carrier.__SENTRY__ || {};\n carrier.__SENTRY__.hub = hub;\n return true;\n}\n","export * from './exports';\n\nimport { Integrations as CoreIntegrations } from '@sentry/core';\nimport { getGlobalObject } from '@sentry/utils';\n\nimport * as BrowserIntegrations from './integrations';\nimport * as Transports from './transports';\n\nlet windowIntegrations = {};\n\n// This block is needed to add compatibility with the integrations packages when used with a CDN\n// tslint:disable: no-unsafe-any\nconst _window = getGlobalObject();\nif (_window.Sentry && _window.Sentry.Integrations) {\n windowIntegrations = _window.Sentry.Integrations;\n}\n// tslint:enable: no-unsafe-any\n\nconst INTEGRATIONS = {\n ...windowIntegrations,\n ...CoreIntegrations,\n ...BrowserIntegrations,\n};\n\nexport { INTEGRATIONS as Integrations, Transports };\n","import { addGlobalEventProcessor, getCurrentHub } from '@sentry/hub';\nimport { Integration, Options } from '@sentry/types';\nimport { logger } from '@sentry/utils';\n\nexport const installedIntegrations: string[] = [];\n\n/** Map of integrations assigned to a client */\nexport interface IntegrationIndex {\n [key: string]: Integration;\n}\n\n/** Gets integration to install */\nexport function getIntegrationsToSetup(options: Options): Integration[] {\n const defaultIntegrations = (options.defaultIntegrations && [...options.defaultIntegrations]) || [];\n const userIntegrations = options.integrations;\n let integrations: Integration[] = [];\n if (Array.isArray(userIntegrations)) {\n const userIntegrationsNames = userIntegrations.map(i => i.name);\n const pickedIntegrationsNames: string[] = [];\n\n // Leave only unique default integrations, that were not overridden with provided user integrations\n defaultIntegrations.forEach(defaultIntegration => {\n if (\n userIntegrationsNames.indexOf(defaultIntegration.name) === -1 &&\n pickedIntegrationsNames.indexOf(defaultIntegration.name) === -1\n ) {\n integrations.push(defaultIntegration);\n pickedIntegrationsNames.push(defaultIntegration.name);\n }\n });\n\n // Don't add same user integration twice\n userIntegrations.forEach(userIntegration => {\n if (pickedIntegrationsNames.indexOf(userIntegration.name) === -1) {\n integrations.push(userIntegration);\n pickedIntegrationsNames.push(userIntegration.name);\n }\n });\n } else if (typeof userIntegrations === 'function') {\n integrations = userIntegrations(defaultIntegrations);\n integrations = Array.isArray(integrations) ? integrations : [integrations];\n } else {\n integrations = [...defaultIntegrations];\n }\n\n // Make sure that if present, `Debug` integration will always run last\n const integrationsNames = integrations.map(i => i.name);\n const alwaysLastToRun = 'Debug';\n if (integrationsNames.indexOf(alwaysLastToRun) !== -1) {\n integrations.push(...integrations.splice(integrationsNames.indexOf(alwaysLastToRun), 1));\n }\n\n return integrations;\n}\n\n/** Setup given integration */\nexport function setupIntegration(integration: Integration): void {\n if (installedIntegrations.indexOf(integration.name) !== -1) {\n return;\n }\n integration.setupOnce(addGlobalEventProcessor, getCurrentHub);\n installedIntegrations.push(integration.name);\n logger.log(`Integration installed: ${integration.name}`);\n}\n\n/**\n * Given a list of integration instances this installs them all. When `withDefaults` is set to `true` then all default\n * integrations are added unless they were already provided before.\n * @param integrations array of integration instances\n * @param withDefault should enable default integrations\n */\nexport function setupIntegrations(options: O): IntegrationIndex {\n const integrations: IntegrationIndex = {};\n getIntegrationsToSetup(options).forEach(integration => {\n integrations[integration.name] = integration;\n setupIntegration(integration);\n });\n return integrations;\n}\n","// tslint:disable:object-literal-sort-keys\n\n/**\n * This was originally forked from https://github.com/occ/TraceKit, but has since been\n * largely modified and is now maintained as part of Sentry JS SDK.\n */\n\n/**\n * An object representing a single stack frame.\n * {Object} StackFrame\n * {string} url The JavaScript or HTML file URL.\n * {string} func The function name, or empty for anonymous functions (if guessing did not work).\n * {string[]?} args The arguments passed to the function, if known.\n * {number=} line The line number, if known.\n * {number=} column The column number, if known.\n * {string[]} context An array of source code lines; the middle element corresponds to the correct line#.\n */\nexport interface StackFrame {\n url: string;\n func: string;\n args: string[];\n line: number | null;\n column: number | null;\n}\n\n/**\n * An object representing a JavaScript stack trace.\n * {Object} StackTrace\n * {string} name The name of the thrown exception.\n * {string} message The exception error message.\n * {TraceKit.StackFrame[]} stack An array of stack frames.\n */\nexport interface StackTrace {\n name: string;\n message: string;\n mechanism?: string;\n stack: StackFrame[];\n failed?: boolean;\n}\n\n// global reference to slice\nconst UNKNOWN_FUNCTION = '?';\n\n// Chromium based browsers: Chrome, Brave, new Opera, new Edge\nconst chrome = /^\\s*at (?:(.*?) ?\\()?((?:file|https?|blob|chrome-extension|address|native|eval|webpack||[-a-z]+:|.*bundle|\\/).*?)(?::(\\d+))?(?::(\\d+))?\\)?\\s*$/i;\n// gecko regex: `(?:bundle|\\d+\\.js)`: `bundle` is for react native, `\\d+\\.js` also but specifically for ram bundles because it\n// generates filenames without a prefix like `file://` the filenames in the stacktrace are just 42.js\n// We need this specific case for now because we want no other regex to match.\nconst gecko = /^\\s*(.*?)(?:\\((.*?)\\))?(?:^|@)?((?:file|https?|blob|chrome|webpack|resource|moz-extension).*?:\\/.*?|\\[native code\\]|[^@]*(?:bundle|\\d+\\.js))(?::(\\d+))?(?::(\\d+))?\\s*$/i;\nconst winjs = /^\\s*at (?:((?:\\[object object\\])?.+) )?\\(?((?:file|ms-appx|https?|webpack|blob):.*?):(\\d+)(?::(\\d+))?\\)?\\s*$/i;\nconst geckoEval = /(\\S+) line (\\d+)(?: > eval line \\d+)* > eval/i;\nconst chromeEval = /\\((\\S*)(?::(\\d+))(?::(\\d+))\\)/;\n\n/** JSDoc */\nexport function computeStackTrace(ex: any): StackTrace {\n // tslint:disable:no-unsafe-any\n\n let stack = null;\n const popSize: number = ex && ex.framesToPop;\n\n try {\n // This must be tried first because Opera 10 *destroys*\n // its stacktrace property if you try to access the stack\n // property first!!\n stack = computeStackTraceFromStacktraceProp(ex);\n if (stack) {\n return popFrames(stack, popSize);\n }\n } catch (e) {\n // no-empty\n }\n\n try {\n stack = computeStackTraceFromStackProp(ex);\n if (stack) {\n return popFrames(stack, popSize);\n }\n } catch (e) {\n // no-empty\n }\n\n return {\n message: extractMessage(ex),\n name: ex && ex.name,\n stack: [],\n failed: true,\n };\n}\n\n/** JSDoc */\n// tslint:disable-next-line:cyclomatic-complexity\nfunction computeStackTraceFromStackProp(ex: any): StackTrace | null {\n // tslint:disable:no-conditional-assignment\n if (!ex || !ex.stack) {\n return null;\n }\n\n const stack = [];\n const lines = ex.stack.split('\\n');\n let isEval;\n let submatch;\n let parts;\n let element;\n\n for (let i = 0; i < lines.length; ++i) {\n if ((parts = chrome.exec(lines[i]))) {\n const isNative = parts[2] && parts[2].indexOf('native') === 0; // start of line\n isEval = parts[2] && parts[2].indexOf('eval') === 0; // start of line\n if (isEval && (submatch = chromeEval.exec(parts[2]))) {\n // throw out eval line/column and use top-most line/column number\n parts[2] = submatch[1]; // url\n parts[3] = submatch[2]; // line\n parts[4] = submatch[3]; // column\n }\n element = {\n // working with the regexp above is super painful. it is quite a hack, but just stripping the `address at `\n // prefix here seems like the quickest solution for now.\n url: parts[2] && parts[2].indexOf('address at ') === 0 ? parts[2].substr('address at '.length) : parts[2],\n func: parts[1] || UNKNOWN_FUNCTION,\n args: isNative ? [parts[2]] : [],\n line: parts[3] ? +parts[3] : null,\n column: parts[4] ? +parts[4] : null,\n };\n } else if ((parts = winjs.exec(lines[i]))) {\n element = {\n url: parts[2],\n func: parts[1] || UNKNOWN_FUNCTION,\n args: [],\n line: +parts[3],\n column: parts[4] ? +parts[4] : null,\n };\n } else if ((parts = gecko.exec(lines[i]))) {\n isEval = parts[3] && parts[3].indexOf(' > eval') > -1;\n if (isEval && (submatch = geckoEval.exec(parts[3]))) {\n // throw out eval line/column and use top-most line number\n parts[1] = parts[1] || `eval`;\n parts[3] = submatch[1];\n parts[4] = submatch[2];\n parts[5] = ''; // no column when eval\n } else if (i === 0 && !parts[5] && ex.columnNumber !== void 0) {\n // FireFox uses this awesome columnNumber property for its top frame\n // Also note, Firefox's column number is 0-based and everything else expects 1-based,\n // so adding 1\n // NOTE: this hack doesn't work if top-most frame is eval\n stack[0].column = (ex.columnNumber as number) + 1;\n }\n element = {\n url: parts[3],\n func: parts[1] || UNKNOWN_FUNCTION,\n args: parts[2] ? parts[2].split(',') : [],\n line: parts[4] ? +parts[4] : null,\n column: parts[5] ? +parts[5] : null,\n };\n } else {\n continue;\n }\n\n if (!element.func && element.line) {\n element.func = UNKNOWN_FUNCTION;\n }\n\n stack.push(element);\n }\n\n if (!stack.length) {\n return null;\n }\n\n return {\n message: extractMessage(ex),\n name: ex.name,\n stack,\n };\n}\n\n/** JSDoc */\nfunction computeStackTraceFromStacktraceProp(ex: any): StackTrace | null {\n if (!ex || !ex.stacktrace) {\n return null;\n }\n // Access and store the stacktrace property before doing ANYTHING\n // else to it because Opera is not very good at providing it\n // reliably in other circumstances.\n const stacktrace = ex.stacktrace;\n const opera10Regex = / line (\\d+).*script (?:in )?(\\S+)(?:: in function (\\S+))?$/i;\n const opera11Regex = / line (\\d+), column (\\d+)\\s*(?:in (?:]+)>|([^\\)]+))\\((.*)\\))? in (.*):\\s*$/i;\n const lines = stacktrace.split('\\n');\n const stack = [];\n let parts;\n\n for (let line = 0; line < lines.length; line += 2) {\n // tslint:disable:no-conditional-assignment\n let element = null;\n if ((parts = opera10Regex.exec(lines[line]))) {\n element = {\n url: parts[2],\n func: parts[3],\n args: [],\n line: +parts[1],\n column: null,\n };\n } else if ((parts = opera11Regex.exec(lines[line]))) {\n element = {\n url: parts[6],\n func: parts[3] || parts[4],\n args: parts[5] ? parts[5].split(',') : [],\n line: +parts[1],\n column: +parts[2],\n };\n }\n\n if (element) {\n if (!element.func && element.line) {\n element.func = UNKNOWN_FUNCTION;\n }\n stack.push(element);\n }\n }\n\n if (!stack.length) {\n return null;\n }\n\n return {\n message: extractMessage(ex),\n name: ex.name,\n stack,\n };\n}\n\n/** Remove N number of frames from the stack */\nfunction popFrames(stacktrace: StackTrace, popSize: number): StackTrace {\n try {\n return {\n ...stacktrace,\n stack: stacktrace.stack.slice(popSize),\n };\n } catch (e) {\n return stacktrace;\n }\n}\n\n/**\n * There are cases where stacktrace.message is an Event object\n * https://github.com/getsentry/sentry-javascript/issues/1949\n * In this specific case we try to extract stacktrace.message.error.message\n */\nfunction extractMessage(ex: any): string {\n const message = ex && ex.message;\n if (!message) {\n return 'No error message';\n }\n if (message.error && typeof message.error.message === 'string') {\n return message.error.message;\n }\n return message;\n}\n","import { Event, Exception, StackFrame } from '@sentry/types';\nimport { extractExceptionKeysForMessage, isEvent, normalizeToSize } from '@sentry/utils';\n\nimport { computeStackTrace, StackFrame as TraceKitStackFrame, StackTrace as TraceKitStackTrace } from './tracekit';\n\nconst STACKTRACE_LIMIT = 50;\n\n/**\n * This function creates an exception from an TraceKitStackTrace\n * @param stacktrace TraceKitStackTrace that will be converted to an exception\n * @hidden\n */\nexport function exceptionFromStacktrace(stacktrace: TraceKitStackTrace): Exception {\n const frames = prepareFramesForEvent(stacktrace.stack);\n\n const exception: Exception = {\n type: stacktrace.name,\n value: stacktrace.message,\n };\n\n if (frames && frames.length) {\n exception.stacktrace = { frames };\n }\n\n // tslint:disable-next-line:strict-type-predicates\n if (exception.type === undefined && exception.value === '') {\n exception.value = 'Unrecoverable error caught';\n }\n\n return exception;\n}\n\n/**\n * @hidden\n */\nexport function eventFromPlainObject(exception: {}, syntheticException?: Error, rejection?: boolean): Event {\n const event: Event = {\n exception: {\n values: [\n {\n type: isEvent(exception) ? exception.constructor.name : rejection ? 'UnhandledRejection' : 'Error',\n value: `Non-Error ${\n rejection ? 'promise rejection' : 'exception'\n } captured with keys: ${extractExceptionKeysForMessage(exception)}`,\n },\n ],\n },\n extra: {\n __serialized__: normalizeToSize(exception),\n },\n };\n\n if (syntheticException) {\n const stacktrace = computeStackTrace(syntheticException);\n const frames = prepareFramesForEvent(stacktrace.stack);\n event.stacktrace = {\n frames,\n };\n }\n\n return event;\n}\n\n/**\n * @hidden\n */\nexport function eventFromStacktrace(stacktrace: TraceKitStackTrace): Event {\n const exception = exceptionFromStacktrace(stacktrace);\n\n return {\n exception: {\n values: [exception],\n },\n };\n}\n\n/**\n * @hidden\n */\nexport function prepareFramesForEvent(stack: TraceKitStackFrame[]): StackFrame[] {\n if (!stack || !stack.length) {\n return [];\n }\n\n let localStack = stack;\n\n const firstFrameFunction = localStack[0].func || '';\n const lastFrameFunction = localStack[localStack.length - 1].func || '';\n\n // If stack starts with one of our API calls, remove it (starts, meaning it's the top of the stack - aka last call)\n if (firstFrameFunction.indexOf('captureMessage') !== -1 || firstFrameFunction.indexOf('captureException') !== -1) {\n localStack = localStack.slice(1);\n }\n\n // If stack ends with one of our internal API calls, remove it (ends, meaning it's the bottom of the stack - aka top-most call)\n if (lastFrameFunction.indexOf('sentryWrapped') !== -1) {\n localStack = localStack.slice(0, -1);\n }\n\n // The frame where the crash happened, should be the last entry in the array\n return localStack\n .map(\n (frame: TraceKitStackFrame): StackFrame => ({\n colno: frame.column === null ? undefined : frame.column,\n filename: frame.url || localStack[0].url,\n function: frame.func || '?',\n in_app: true,\n lineno: frame.line === null ? undefined : frame.line,\n }),\n )\n .slice(0, STACKTRACE_LIMIT)\n .reverse();\n}\n","import { Event } from '@sentry/types';\nimport {\n addExceptionMechanism,\n addExceptionTypeValue,\n isDOMError,\n isDOMException,\n isError,\n isErrorEvent,\n isEvent,\n isPlainObject,\n} from '@sentry/utils';\n\nimport { eventFromPlainObject, eventFromStacktrace, prepareFramesForEvent } from './parsers';\nimport { computeStackTrace } from './tracekit';\n\n/** JSDoc */\nexport function eventFromUnknownInput(\n exception: unknown,\n syntheticException?: Error,\n options: {\n rejection?: boolean;\n attachStacktrace?: boolean;\n } = {},\n): Event {\n let event: Event;\n\n if (isErrorEvent(exception as ErrorEvent) && (exception as ErrorEvent).error) {\n // If it is an ErrorEvent with `error` property, extract it to get actual Error\n const errorEvent = exception as ErrorEvent;\n exception = errorEvent.error; // tslint:disable-line:no-parameter-reassignment\n event = eventFromStacktrace(computeStackTrace(exception as Error));\n return event;\n }\n if (isDOMError(exception as DOMError) || isDOMException(exception as DOMException)) {\n // If it is a DOMError or DOMException (which are legacy APIs, but still supported in some browsers)\n // then we just extract the name and message, as they don't provide anything else\n // https://developer.mozilla.org/en-US/docs/Web/API/DOMError\n // https://developer.mozilla.org/en-US/docs/Web/API/DOMException\n const domException = exception as DOMException;\n const name = domException.name || (isDOMError(domException) ? 'DOMError' : 'DOMException');\n const message = domException.message ? `${name}: ${domException.message}` : name;\n\n event = eventFromString(message, syntheticException, options);\n addExceptionTypeValue(event, message);\n return event;\n }\n if (isError(exception as Error)) {\n // we have a real Error object, do nothing\n event = eventFromStacktrace(computeStackTrace(exception as Error));\n return event;\n }\n if (isPlainObject(exception) || isEvent(exception)) {\n // If it is plain Object or Event, serialize it manually and extract options\n // This will allow us to group events based on top-level keys\n // which is much better than creating new group when any key/value change\n const objectException = exception as {};\n event = eventFromPlainObject(objectException, syntheticException, options.rejection);\n addExceptionMechanism(event, {\n synthetic: true,\n });\n return event;\n }\n\n // If none of previous checks were valid, then it means that it's not:\n // - an instance of DOMError\n // - an instance of DOMException\n // - an instance of Event\n // - an instance of Error\n // - a valid ErrorEvent (one with an error property)\n // - a plain Object\n //\n // So bail out and capture it as a simple message:\n event = eventFromString(exception as string, syntheticException, options);\n addExceptionTypeValue(event, `${exception}`, undefined);\n addExceptionMechanism(event, {\n synthetic: true,\n });\n\n return event;\n}\n\n// this._options.attachStacktrace\n/** JSDoc */\nexport function eventFromString(\n input: string,\n syntheticException?: Error,\n options: {\n attachStacktrace?: boolean;\n } = {},\n): Event {\n const event: Event = {\n message: input,\n };\n\n if (options.attachStacktrace && syntheticException) {\n const stacktrace = computeStackTrace(syntheticException);\n const frames = prepareFramesForEvent(stacktrace.stack);\n event.stacktrace = {\n frames,\n };\n }\n\n return event;\n}\n","import { captureException, withScope } from '@sentry/core';\nimport { Event as SentryEvent, Mechanism, Scope, WrappedFunction } from '@sentry/types';\nimport { addExceptionMechanism, addExceptionTypeValue } from '@sentry/utils';\n\nlet ignoreOnError: number = 0;\n\n/**\n * @hidden\n */\nexport function shouldIgnoreOnError(): boolean {\n return ignoreOnError > 0;\n}\n\n/**\n * @hidden\n */\nexport function ignoreNextOnError(): void {\n // onerror should trigger before setTimeout\n ignoreOnError += 1;\n setTimeout(() => {\n ignoreOnError -= 1;\n });\n}\n\n/**\n * Instruments the given function and sends an event to Sentry every time the\n * function throws an exception.\n *\n * @param fn A function to wrap.\n * @returns The wrapped function.\n * @hidden\n */\nexport function wrap(\n fn: WrappedFunction,\n options: {\n mechanism?: Mechanism;\n } = {},\n before?: WrappedFunction,\n): any {\n // tslint:disable-next-line:strict-type-predicates\n if (typeof fn !== 'function') {\n return fn;\n }\n\n try {\n // We don't wanna wrap it twice\n if (fn.__sentry__) {\n return fn;\n }\n\n // If this has already been wrapped in the past, return that wrapped function\n if (fn.__sentry_wrapped__) {\n return fn.__sentry_wrapped__;\n }\n } catch (e) {\n // Just accessing custom props in some Selenium environments\n // can cause a \"Permission denied\" exception (see raven-js#495).\n // Bail on wrapping and return the function as-is (defers to window.onerror).\n return fn;\n }\n\n const sentryWrapped: WrappedFunction = function(this: any): void {\n const args = Array.prototype.slice.call(arguments);\n\n // tslint:disable:no-unsafe-any\n try {\n // tslint:disable-next-line:strict-type-predicates\n if (before && typeof before === 'function') {\n before.apply(this, arguments);\n }\n\n const wrappedArguments = args.map((arg: any) => wrap(arg, options));\n\n if (fn.handleEvent) {\n // Attempt to invoke user-land function\n // NOTE: If you are a Sentry user, and you are seeing this stack frame, it\n // means the sentry.javascript SDK caught an error invoking your application code. This\n // is expected behavior and NOT indicative of a bug with sentry.javascript.\n return fn.handleEvent.apply(this, wrappedArguments);\n }\n // Attempt to invoke user-land function\n // NOTE: If you are a Sentry user, and you are seeing this stack frame, it\n // means the sentry.javascript SDK caught an error invoking your application code. This\n // is expected behavior and NOT indicative of a bug with sentry.javascript.\n return fn.apply(this, wrappedArguments);\n // tslint:enable:no-unsafe-any\n } catch (ex) {\n ignoreNextOnError();\n\n withScope((scope: Scope) => {\n scope.addEventProcessor((event: SentryEvent) => {\n const processedEvent = { ...event };\n\n if (options.mechanism) {\n addExceptionTypeValue(processedEvent, undefined, undefined);\n addExceptionMechanism(processedEvent, options.mechanism);\n }\n\n processedEvent.extra = {\n ...processedEvent.extra,\n arguments: args,\n };\n\n return processedEvent;\n });\n\n captureException(ex);\n });\n\n throw ex;\n }\n };\n\n // Accessing some objects may throw\n // ref: https://github.com/getsentry/sentry-javascript/issues/1168\n try {\n for (const property in fn) {\n if (Object.prototype.hasOwnProperty.call(fn, property)) {\n sentryWrapped[property] = fn[property];\n }\n }\n } catch (_oO) {} // tslint:disable-line:no-empty\n\n fn.prototype = fn.prototype || {};\n sentryWrapped.prototype = fn.prototype;\n\n Object.defineProperty(fn, '__sentry_wrapped__', {\n enumerable: false,\n value: sentryWrapped,\n });\n\n // Signal that this function has been wrapped/filled already\n // for both debugging and to prevent it to being wrapped/filled twice\n Object.defineProperties(sentryWrapped, {\n __sentry__: {\n enumerable: false,\n value: true,\n },\n __sentry_original__: {\n enumerable: false,\n value: fn,\n },\n });\n\n // Restore original function name (not all browsers allow that)\n try {\n const descriptor = Object.getOwnPropertyDescriptor(sentryWrapped, 'name') as PropertyDescriptor;\n if (descriptor.configurable) {\n Object.defineProperty(sentryWrapped, 'name', {\n get(): string {\n return fn.name;\n },\n });\n }\n } catch (_oO) {\n /*no-empty*/\n }\n\n return sentryWrapped;\n}\n","/* tslint:disable:only-arrow-functions no-unsafe-any */\n\nimport { WrappedFunction } from '@sentry/types';\n\nimport { isInstanceOf, isString } from './is';\nimport { logger } from './logger';\nimport { getFunctionName, getGlobalObject } from './misc';\nimport { fill } from './object';\nimport { supportsHistory, supportsNativeFetch } from './supports';\n\nconst global = getGlobalObject();\n\n/** Object describing handler that will be triggered for a given `type` of instrumentation */\ninterface InstrumentHandler {\n type: InstrumentHandlerType;\n callback: InstrumentHandlerCallback;\n}\ntype InstrumentHandlerType =\n | 'console'\n | 'dom'\n | 'fetch'\n | 'history'\n | 'sentry'\n | 'xhr'\n | 'error'\n | 'unhandledrejection';\ntype InstrumentHandlerCallback = (data: any) => void;\n\n/**\n * Instrument native APIs to call handlers that can be used to create breadcrumbs, APM spans etc.\n * - Console API\n * - Fetch API\n * - XHR API\n * - History API\n * - DOM API (click/typing)\n * - Error API\n * - UnhandledRejection API\n */\n\nconst handlers: { [key in InstrumentHandlerType]?: InstrumentHandlerCallback[] } = {};\nconst instrumented: { [key in InstrumentHandlerType]?: boolean } = {};\n\n/** Instruments given API */\nfunction instrument(type: InstrumentHandlerType): void {\n if (instrumented[type]) {\n return;\n }\n\n instrumented[type] = true;\n\n switch (type) {\n case 'console':\n instrumentConsole();\n break;\n case 'dom':\n instrumentDOM();\n break;\n case 'xhr':\n instrumentXHR();\n break;\n case 'fetch':\n instrumentFetch();\n break;\n case 'history':\n instrumentHistory();\n break;\n case 'error':\n instrumentError();\n break;\n case 'unhandledrejection':\n instrumentUnhandledRejection();\n break;\n default:\n logger.warn('unknown instrumentation type:', type);\n }\n}\n\n/**\n * Add handler that will be called when given type of instrumentation triggers.\n * Use at your own risk, this might break without changelog notice, only used internally.\n * @hidden\n */\nexport function addInstrumentationHandler(handler: InstrumentHandler): void {\n // tslint:disable-next-line:strict-type-predicates\n if (!handler || typeof handler.type !== 'string' || typeof handler.callback !== 'function') {\n return;\n }\n handlers[handler.type] = handlers[handler.type] || [];\n (handlers[handler.type] as InstrumentHandlerCallback[]).push(handler.callback);\n instrument(handler.type);\n}\n\n/** JSDoc */\nfunction triggerHandlers(type: InstrumentHandlerType, data: any): void {\n if (!type || !handlers[type]) {\n return;\n }\n\n for (const handler of handlers[type] || []) {\n try {\n handler(data);\n } catch (e) {\n logger.error(\n `Error while triggering instrumentation handler.\\nType: ${type}\\nName: ${getFunctionName(\n handler,\n )}\\nError: ${e}`,\n );\n }\n }\n}\n\n/** JSDoc */\nfunction instrumentConsole(): void {\n if (!('console' in global)) {\n return;\n }\n\n ['debug', 'info', 'warn', 'error', 'log', 'assert'].forEach(function(level: string): void {\n if (!(level in global.console)) {\n return;\n }\n\n fill(global.console, level, function(originalConsoleLevel: () => any): Function {\n return function(...args: any[]): void {\n triggerHandlers('console', { args, level });\n\n // this fails for some browsers. :(\n if (originalConsoleLevel) {\n Function.prototype.apply.call(originalConsoleLevel, global.console, args);\n }\n };\n });\n });\n}\n\n/** JSDoc */\nfunction instrumentFetch(): void {\n if (!supportsNativeFetch()) {\n return;\n }\n\n fill(global, 'fetch', function(originalFetch: () => void): () => void {\n return function(...args: any[]): void {\n const commonHandlerData = {\n args,\n fetchData: {\n method: getFetchMethod(args),\n url: getFetchUrl(args),\n },\n startTimestamp: Date.now(),\n };\n\n triggerHandlers('fetch', {\n ...commonHandlerData,\n });\n\n return originalFetch.apply(global, args).then(\n (response: Response) => {\n triggerHandlers('fetch', {\n ...commonHandlerData,\n endTimestamp: Date.now(),\n response,\n });\n return response;\n },\n (error: Error) => {\n triggerHandlers('fetch', {\n ...commonHandlerData,\n endTimestamp: Date.now(),\n error,\n });\n throw error;\n },\n );\n };\n });\n}\n\n/** JSDoc */\ninterface SentryWrappedXMLHttpRequest extends XMLHttpRequest {\n [key: string]: any;\n __sentry_xhr__?: {\n method?: string;\n url?: string;\n status_code?: number;\n };\n}\n\n/** Extract `method` from fetch call arguments */\nfunction getFetchMethod(fetchArgs: any[] = []): string {\n if ('Request' in global && isInstanceOf(fetchArgs[0], Request) && fetchArgs[0].method) {\n return String(fetchArgs[0].method).toUpperCase();\n }\n if (fetchArgs[1] && fetchArgs[1].method) {\n return String(fetchArgs[1].method).toUpperCase();\n }\n return 'GET';\n}\n\n/** Extract `url` from fetch call arguments */\nfunction getFetchUrl(fetchArgs: any[] = []): string {\n if (typeof fetchArgs[0] === 'string') {\n return fetchArgs[0];\n }\n if ('Request' in global && isInstanceOf(fetchArgs[0], Request)) {\n return fetchArgs[0].url;\n }\n return String(fetchArgs[0]);\n}\n\n/** JSDoc */\nfunction instrumentXHR(): void {\n if (!('XMLHttpRequest' in global)) {\n return;\n }\n\n const xhrproto = XMLHttpRequest.prototype;\n\n fill(xhrproto, 'open', function(originalOpen: () => void): () => void {\n return function(this: SentryWrappedXMLHttpRequest, ...args: any[]): void {\n const url = args[1];\n this.__sentry_xhr__ = {\n method: isString(args[0]) ? args[0].toUpperCase() : args[0],\n url: args[1],\n };\n\n // if Sentry key appears in URL, don't capture it as a request\n if (isString(url) && this.__sentry_xhr__.method === 'POST' && url.match(/sentry_key/)) {\n this.__sentry_own_request__ = true;\n }\n\n return originalOpen.apply(this, args);\n };\n });\n\n fill(xhrproto, 'send', function(originalSend: () => void): () => void {\n return function(this: SentryWrappedXMLHttpRequest, ...args: any[]): void {\n const xhr = this; // tslint:disable-line:no-this-assignment\n const commonHandlerData = {\n args,\n startTimestamp: Date.now(),\n xhr,\n };\n\n triggerHandlers('xhr', {\n ...commonHandlerData,\n });\n\n xhr.addEventListener('readystatechange', function(): void {\n if (xhr.readyState === 4) {\n try {\n // touching statusCode in some platforms throws\n // an exception\n if (xhr.__sentry_xhr__) {\n xhr.__sentry_xhr__.status_code = xhr.status;\n }\n } catch (e) {\n /* do nothing */\n }\n triggerHandlers('xhr', {\n ...commonHandlerData,\n endTimestamp: Date.now(),\n });\n }\n });\n\n return originalSend.apply(this, args);\n };\n });\n}\n\nlet lastHref: string;\n\n/** JSDoc */\nfunction instrumentHistory(): void {\n if (!supportsHistory()) {\n return;\n }\n\n const oldOnPopState = global.onpopstate;\n global.onpopstate = function(this: WindowEventHandlers, ...args: any[]): any {\n const to = global.location.href;\n // keep track of the current URL state, as we always receive only the updated state\n const from = lastHref;\n lastHref = to;\n triggerHandlers('history', {\n from,\n to,\n });\n if (oldOnPopState) {\n return oldOnPopState.apply(this, args);\n }\n };\n\n /** @hidden */\n function historyReplacementFunction(originalHistoryFunction: () => void): () => void {\n return function(this: History, ...args: any[]): void {\n const url = args.length > 2 ? args[2] : undefined;\n if (url) {\n // coerce to string (this is what pushState does)\n const from = lastHref;\n const to = String(url);\n // keep track of the current URL state, as we always receive only the updated state\n lastHref = to;\n triggerHandlers('history', {\n from,\n to,\n });\n }\n return originalHistoryFunction.apply(this, args);\n };\n }\n\n fill(global.history, 'pushState', historyReplacementFunction);\n fill(global.history, 'replaceState', historyReplacementFunction);\n}\n\n/** JSDoc */\nfunction instrumentDOM(): void {\n if (!('document' in global)) {\n return;\n }\n\n // Capture breadcrumbs from any click that is unhandled / bubbled up all the way\n // to the document. Do this before we instrument addEventListener.\n global.document.addEventListener('click', domEventHandler('click', triggerHandlers.bind(null, 'dom')), false);\n global.document.addEventListener('keypress', keypressEventHandler(triggerHandlers.bind(null, 'dom')), false);\n\n // After hooking into document bubbled up click and keypresses events, we also hook into user handled click & keypresses.\n ['EventTarget', 'Node'].forEach((target: string) => {\n const proto = (global as any)[target] && (global as any)[target].prototype;\n\n if (!proto || !proto.hasOwnProperty || !proto.hasOwnProperty('addEventListener')) {\n return;\n }\n\n fill(proto, 'addEventListener', function(\n original: () => void,\n ): (\n eventName: string,\n fn: EventListenerOrEventListenerObject,\n options?: boolean | AddEventListenerOptions,\n ) => void {\n return function(\n this: any,\n eventName: string,\n fn: EventListenerOrEventListenerObject,\n options?: boolean | AddEventListenerOptions,\n ): (eventName: string, fn: EventListenerOrEventListenerObject, capture?: boolean, secure?: boolean) => void {\n if (fn && (fn as EventListenerObject).handleEvent) {\n if (eventName === 'click') {\n fill(fn, 'handleEvent', function(innerOriginal: () => void): (caughtEvent: Event) => void {\n return function(this: any, event: Event): (event: Event) => void {\n domEventHandler('click', triggerHandlers.bind(null, 'dom'))(event);\n return innerOriginal.call(this, event);\n };\n });\n }\n if (eventName === 'keypress') {\n fill(fn, 'handleEvent', function(innerOriginal: () => void): (caughtEvent: Event) => void {\n return function(this: any, event: Event): (event: Event) => void {\n keypressEventHandler(triggerHandlers.bind(null, 'dom'))(event);\n return innerOriginal.call(this, event);\n };\n });\n }\n } else {\n if (eventName === 'click') {\n domEventHandler('click', triggerHandlers.bind(null, 'dom'), true)(this);\n }\n if (eventName === 'keypress') {\n keypressEventHandler(triggerHandlers.bind(null, 'dom'))(this);\n }\n }\n\n return original.call(this, eventName, fn, options);\n };\n });\n\n fill(proto, 'removeEventListener', function(\n original: () => void,\n ): (\n this: any,\n eventName: string,\n fn: EventListenerOrEventListenerObject,\n options?: boolean | EventListenerOptions,\n ) => () => void {\n return function(\n this: any,\n eventName: string,\n fn: EventListenerOrEventListenerObject,\n options?: boolean | EventListenerOptions,\n ): () => void {\n let callback = fn as WrappedFunction;\n try {\n callback = callback && (callback.__sentry_wrapped__ || callback);\n } catch (e) {\n // ignore, accessing __sentry_wrapped__ will throw in some Selenium environments\n }\n return original.call(this, eventName, callback, options);\n };\n });\n });\n}\n\nconst debounceDuration: number = 1000;\nlet debounceTimer: number = 0;\nlet keypressTimeout: number | undefined;\nlet lastCapturedEvent: Event | undefined;\n\n/**\n * Wraps addEventListener to capture UI breadcrumbs\n * @param name the event name (e.g. \"click\")\n * @param handler function that will be triggered\n * @param debounce decides whether it should wait till another event loop\n * @returns wrapped breadcrumb events handler\n * @hidden\n */\nfunction domEventHandler(name: string, handler: Function, debounce: boolean = false): (event: Event) => void {\n return (event: Event) => {\n // reset keypress timeout; e.g. triggering a 'click' after\n // a 'keypress' will reset the keypress debounce so that a new\n // set of keypresses can be recorded\n keypressTimeout = undefined;\n // It's possible this handler might trigger multiple times for the same\n // event (e.g. event propagation through node ancestors). Ignore if we've\n // already captured the event.\n if (!event || lastCapturedEvent === event) {\n return;\n }\n\n lastCapturedEvent = event;\n\n if (debounceTimer) {\n clearTimeout(debounceTimer);\n }\n\n if (debounce) {\n debounceTimer = setTimeout(() => {\n handler({ event, name });\n });\n } else {\n handler({ event, name });\n }\n };\n}\n\n/**\n * Wraps addEventListener to capture keypress UI events\n * @param handler function that will be triggered\n * @returns wrapped keypress events handler\n * @hidden\n */\nfunction keypressEventHandler(handler: Function): (event: Event) => void {\n // TODO: if somehow user switches keypress target before\n // debounce timeout is triggered, we will only capture\n // a single breadcrumb from the FIRST target (acceptable?)\n return (event: Event) => {\n let target;\n\n try {\n target = event.target;\n } catch (e) {\n // just accessing event properties can throw an exception in some rare circumstances\n // see: https://github.com/getsentry/raven-js/issues/838\n return;\n }\n\n const tagName = target && (target as HTMLElement).tagName;\n\n // only consider keypress events on actual input elements\n // this will disregard keypresses targeting body (e.g. tabbing\n // through elements, hotkeys, etc)\n if (!tagName || (tagName !== 'INPUT' && tagName !== 'TEXTAREA' && !(target as HTMLElement).isContentEditable)) {\n return;\n }\n\n // record first keypress in a series, but ignore subsequent\n // keypresses until debounce clears\n if (!keypressTimeout) {\n domEventHandler('input', handler)(event);\n }\n clearTimeout(keypressTimeout);\n\n keypressTimeout = (setTimeout(() => {\n keypressTimeout = undefined;\n }, debounceDuration) as any) as number;\n };\n}\n\nlet _oldOnErrorHandler: OnErrorEventHandler = null;\n/** JSDoc */\nfunction instrumentError(): void {\n _oldOnErrorHandler = global.onerror;\n\n global.onerror = function(msg: any, url: any, line: any, column: any, error: any): boolean {\n triggerHandlers('error', {\n column,\n error,\n line,\n msg,\n url,\n });\n\n if (_oldOnErrorHandler) {\n return _oldOnErrorHandler.apply(this, arguments);\n }\n\n return false;\n };\n}\n\nlet _oldOnUnhandledRejectionHandler: ((e: any) => void) | null = null;\n/** JSDoc */\nfunction instrumentUnhandledRejection(): void {\n _oldOnUnhandledRejectionHandler = global.onunhandledrejection;\n\n global.onunhandledrejection = function(e: any): boolean {\n triggerHandlers('unhandledrejection', e);\n\n if (_oldOnUnhandledRejectionHandler) {\n return _oldOnUnhandledRejectionHandler.apply(this, arguments);\n }\n\n return true;\n };\n}\n","import { API, getCurrentHub } from '@sentry/core';\nimport { Integration, Severity } from '@sentry/types';\nimport {\n addInstrumentationHandler,\n getEventDescription,\n getGlobalObject,\n htmlTreeAsString,\n logger,\n parseUrl,\n safeJoin,\n} from '@sentry/utils';\n\nimport { BrowserClient } from '../client';\n\n/**\n * @hidden\n */\nexport interface SentryWrappedXMLHttpRequest extends XMLHttpRequest {\n [key: string]: any;\n __sentry_xhr__?: {\n method?: string;\n url?: string;\n status_code?: number;\n };\n}\n\n/** JSDoc */\ninterface BreadcrumbIntegrations {\n console?: boolean;\n dom?: boolean;\n fetch?: boolean;\n history?: boolean;\n sentry?: boolean;\n xhr?: boolean;\n}\n\n/**\n * Default Breadcrumbs instrumentations\n * TODO: Deprecated - with v6, this will be renamed to `Instrument`\n */\nexport class Breadcrumbs implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = Breadcrumbs.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'Breadcrumbs';\n\n /** JSDoc */\n private readonly _options: BreadcrumbIntegrations;\n\n /**\n * @inheritDoc\n */\n public constructor(options?: BreadcrumbIntegrations) {\n this._options = {\n console: true,\n dom: true,\n fetch: true,\n history: true,\n sentry: true,\n xhr: true,\n ...options,\n };\n }\n\n /**\n * Creates breadcrumbs from console API calls\n */\n private _consoleBreadcrumb(handlerData: { [key: string]: any }): void {\n const breadcrumb = {\n category: 'console',\n data: {\n arguments: handlerData.args,\n logger: 'console',\n },\n level: Severity.fromString(handlerData.level),\n message: safeJoin(handlerData.args, ' '),\n };\n\n if (handlerData.level === 'assert') {\n if (handlerData.args[0] === false) {\n breadcrumb.message = `Assertion failed: ${safeJoin(handlerData.args.slice(1), ' ') || 'console.assert'}`;\n breadcrumb.data.arguments = handlerData.args.slice(1);\n } else {\n // Don't capture a breadcrumb for passed assertions\n return;\n }\n }\n\n getCurrentHub().addBreadcrumb(breadcrumb, {\n input: handlerData.args,\n level: handlerData.level,\n });\n }\n\n /**\n * Creates breadcrumbs from DOM API calls\n */\n private _domBreadcrumb(handlerData: { [key: string]: any }): void {\n let target;\n\n // Accessing event.target can throw (see getsentry/raven-js#838, #768)\n try {\n target = handlerData.event.target\n ? htmlTreeAsString(handlerData.event.target as Node)\n : htmlTreeAsString((handlerData.event as unknown) as Node);\n } catch (e) {\n target = '';\n }\n\n if (target.length === 0) {\n return;\n }\n\n getCurrentHub().addBreadcrumb(\n {\n category: `ui.${handlerData.name}`,\n message: target,\n },\n {\n event: handlerData.event,\n name: handlerData.name,\n },\n );\n }\n\n /**\n * Creates breadcrumbs from XHR API calls\n */\n private _xhrBreadcrumb(handlerData: { [key: string]: any }): void {\n if (handlerData.endTimestamp) {\n // We only capture complete, non-sentry requests\n if (handlerData.xhr.__sentry_own_request__) {\n return;\n }\n\n getCurrentHub().addBreadcrumb(\n {\n category: 'xhr',\n data: handlerData.xhr.__sentry_xhr__,\n type: 'http',\n },\n {\n xhr: handlerData.xhr,\n },\n );\n\n return;\n }\n\n // We only capture issued sentry requests\n if (this._options.sentry && handlerData.xhr.__sentry_own_request__) {\n addSentryBreadcrumb(handlerData.args[0]);\n }\n }\n\n /**\n * Creates breadcrumbs from fetch API calls\n */\n private _fetchBreadcrumb(handlerData: { [key: string]: any }): void {\n // We only capture complete fetch requests\n if (!handlerData.endTimestamp) {\n return;\n }\n\n const client = getCurrentHub().getClient();\n const dsn = client && client.getDsn();\n if (this._options.sentry && dsn) {\n const filterUrl = new API(dsn).getStoreEndpoint();\n // if Sentry key appears in URL, don't capture it as a request\n // but rather as our own 'sentry' type breadcrumb\n if (\n filterUrl &&\n handlerData.fetchData.url.indexOf(filterUrl) !== -1 &&\n handlerData.fetchData.method === 'POST' &&\n handlerData.args[1] &&\n handlerData.args[1].body\n ) {\n addSentryBreadcrumb(handlerData.args[1].body);\n return;\n }\n }\n\n if (handlerData.error) {\n getCurrentHub().addBreadcrumb(\n {\n category: 'fetch',\n data: {\n ...handlerData.fetchData,\n status_code: handlerData.response.status,\n },\n level: Severity.Error,\n type: 'http',\n },\n {\n data: handlerData.error,\n input: handlerData.args,\n },\n );\n } else {\n getCurrentHub().addBreadcrumb(\n {\n category: 'fetch',\n data: {\n ...handlerData.fetchData,\n status_code: handlerData.response.status,\n },\n type: 'http',\n },\n {\n input: handlerData.args,\n response: handlerData.response,\n },\n );\n }\n }\n\n /**\n * Creates breadcrumbs from history API calls\n */\n private _historyBreadcrumb(handlerData: { [key: string]: any }): void {\n const global = getGlobalObject();\n let from = handlerData.from;\n let to = handlerData.to;\n const parsedLoc = parseUrl(global.location.href);\n let parsedFrom = parseUrl(from);\n const parsedTo = parseUrl(to);\n\n // Initial pushState doesn't provide `from` information\n if (!parsedFrom.path) {\n parsedFrom = parsedLoc;\n }\n\n // Use only the path component of the URL if the URL matches the current\n // document (almost all the time when using pushState)\n if (parsedLoc.protocol === parsedTo.protocol && parsedLoc.host === parsedTo.host) {\n // tslint:disable-next-line:no-parameter-reassignment\n to = parsedTo.relative;\n }\n if (parsedLoc.protocol === parsedFrom.protocol && parsedLoc.host === parsedFrom.host) {\n // tslint:disable-next-line:no-parameter-reassignment\n from = parsedFrom.relative;\n }\n\n getCurrentHub().addBreadcrumb({\n category: 'navigation',\n data: {\n from,\n to,\n },\n });\n }\n\n /**\n * Instrument browser built-ins w/ breadcrumb capturing\n * - Console API\n * - DOM API (click/typing)\n * - XMLHttpRequest API\n * - Fetch API\n * - History API\n */\n public setupOnce(): void {\n if (this._options.console) {\n addInstrumentationHandler({\n callback: (...args) => {\n this._consoleBreadcrumb(...args);\n },\n type: 'console',\n });\n }\n if (this._options.dom) {\n addInstrumentationHandler({\n callback: (...args) => {\n this._domBreadcrumb(...args);\n },\n type: 'dom',\n });\n }\n if (this._options.xhr) {\n addInstrumentationHandler({\n callback: (...args) => {\n this._xhrBreadcrumb(...args);\n },\n type: 'xhr',\n });\n }\n if (this._options.fetch) {\n addInstrumentationHandler({\n callback: (...args) => {\n this._fetchBreadcrumb(...args);\n },\n type: 'fetch',\n });\n }\n if (this._options.history) {\n addInstrumentationHandler({\n callback: (...args) => {\n this._historyBreadcrumb(...args);\n },\n type: 'history',\n });\n }\n }\n}\n\n/**\n * Create a breadcrumb of `sentry` from the events themselves\n */\nfunction addSentryBreadcrumb(serializedData: string): void {\n // There's always something that can go wrong with deserialization...\n try {\n const event = JSON.parse(serializedData);\n getCurrentHub().addBreadcrumb(\n {\n category: `sentry.${event.type === 'transaction' ? 'transaction' : 'event'}`,\n event_id: event.event_id,\n level: event.level || Severity.fromString('error'),\n message: getEventDescription(event),\n },\n {\n event,\n },\n );\n } catch (_oO) {\n logger.error('Error while adding sentry type breadcrumb');\n }\n}\n","import { getCurrentHub, initAndBind, Integrations as CoreIntegrations } from '@sentry/core';\nimport { getGlobalObject, SyncPromise } from '@sentry/utils';\n\nimport { BrowserOptions } from './backend';\nimport { BrowserClient, ReportDialogOptions } from './client';\nimport { wrap as internalWrap } from './helpers';\nimport { Breadcrumbs, GlobalHandlers, LinkedErrors, TryCatch, UserAgent } from './integrations';\n\nexport const defaultIntegrations = [\n new CoreIntegrations.InboundFilters(),\n new CoreIntegrations.FunctionToString(),\n new TryCatch(),\n new Breadcrumbs(),\n new GlobalHandlers(),\n new LinkedErrors(),\n new UserAgent(),\n];\n\n/**\n * The Sentry Browser SDK Client.\n *\n * To use this SDK, call the {@link init} function as early as possible when\n * loading the web page. To set context information or send manual events, use\n * the provided methods.\n *\n * @example\n *\n * ```\n *\n * import { init } from '@sentry/browser';\n *\n * init({\n * dsn: '__DSN__',\n * // ...\n * });\n * ```\n *\n * @example\n * ```\n *\n * import { configureScope } from '@sentry/browser';\n * configureScope((scope: Scope) => {\n * scope.setExtra({ battery: 0.7 });\n * scope.setTag({ user_mode: 'admin' });\n * scope.setUser({ id: '4711' });\n * });\n * ```\n *\n * @example\n * ```\n *\n * import { addBreadcrumb } from '@sentry/browser';\n * addBreadcrumb({\n * message: 'My Breadcrumb',\n * // ...\n * });\n * ```\n *\n * @example\n *\n * ```\n *\n * import * as Sentry from '@sentry/browser';\n * Sentry.captureMessage('Hello, world!');\n * Sentry.captureException(new Error('Good bye'));\n * Sentry.captureEvent({\n * message: 'Manual',\n * stacktrace: [\n * // ...\n * ],\n * });\n * ```\n *\n * @see {@link BrowserOptions} for documentation on configuration options.\n */\nexport function init(options: BrowserOptions = {}): void {\n if (options.defaultIntegrations === undefined) {\n options.defaultIntegrations = defaultIntegrations;\n }\n if (options.release === undefined) {\n const window = getGlobalObject();\n // This supports the variable that sentry-webpack-plugin injects\n if (window.SENTRY_RELEASE && window.SENTRY_RELEASE.id) {\n options.release = window.SENTRY_RELEASE.id;\n }\n }\n initAndBind(BrowserClient, options);\n}\n\n/**\n * Present the user with a report dialog.\n *\n * @param options Everything is optional, we try to fetch all info need from the global scope.\n */\nexport function showReportDialog(options: ReportDialogOptions = {}): void {\n if (!options.eventId) {\n options.eventId = getCurrentHub().lastEventId();\n }\n const client = getCurrentHub().getClient();\n if (client) {\n client.showReportDialog(options);\n }\n}\n\n/**\n * This is the getter for lastEventId.\n *\n * @returns The last event id of a captured event.\n */\nexport function lastEventId(): string | undefined {\n return getCurrentHub().lastEventId();\n}\n\n/**\n * This function is here to be API compatible with the loader.\n * @hidden\n */\nexport function forceLoad(): void {\n // Noop\n}\n\n/**\n * This function is here to be API compatible with the loader.\n * @hidden\n */\nexport function onLoad(callback: () => void): void {\n callback();\n}\n\n/**\n * A promise that resolves when all current events have been sent.\n * If you provide a timeout and the queue takes longer to drain the promise returns false.\n *\n * @param timeout Maximum time in ms the client should wait.\n */\nexport function flush(timeout?: number): PromiseLike {\n const client = getCurrentHub().getClient();\n if (client) {\n return client.flush(timeout);\n }\n return SyncPromise.reject(false);\n}\n\n/**\n * A promise that resolves when all current events have been sent.\n * If you provide a timeout and the queue takes longer to drain the promise returns false.\n *\n * @param timeout Maximum time in ms the client should wait.\n */\nexport function close(timeout?: number): PromiseLike {\n const client = getCurrentHub().getClient();\n if (client) {\n return client.close(timeout);\n }\n return SyncPromise.reject(false);\n}\n\n/**\n * Wrap code within a try/catch block so the SDK is able to capture errors.\n *\n * @param fn A function to wrap.\n *\n * @returns The result of wrapped function call.\n */\nexport function wrap(fn: Function): any {\n return internalWrap(fn)(); // tslint:disable-line:no-unsafe-any\n}\n","/** The status of an event. */\nexport enum Status {\n /** The status could not be determined. */\n Unknown = 'unknown',\n /** The event was skipped due to configuration or callbacks. */\n Skipped = 'skipped',\n /** The event was sent to Sentry successfully. */\n Success = 'success',\n /** The client is currently rate limited and will try again later. */\n RateLimit = 'rate_limit',\n /** The event could not be processed. */\n Invalid = 'invalid',\n /** A server-side error ocurred during submission. */\n Failed = 'failed',\n}\n// tslint:disable:completed-docs\n// tslint:disable:no-unnecessary-qualifier no-namespace\nexport namespace Status {\n /**\n * Converts a HTTP status code into a {@link Status}.\n *\n * @param code The HTTP response status code.\n * @returns The send status or {@link Status.Unknown}.\n */\n export function fromHttpCode(code: number): Status {\n if (code >= 200 && code < 300) {\n return Status.Success;\n }\n\n if (code === 429) {\n return Status.RateLimit;\n }\n\n if (code >= 400 && code < 500) {\n return Status.Invalid;\n }\n\n if (code >= 500) {\n return Status.Failed;\n }\n\n return Status.Unknown;\n }\n}\n","import { isThenable } from './is';\n\n/** SyncPromise internal states */\nenum States {\n /** Pending */\n PENDING = 'PENDING',\n /** Resolved / OK */\n RESOLVED = 'RESOLVED',\n /** Rejected / Error */\n REJECTED = 'REJECTED',\n}\n\n/**\n * Thenable class that behaves like a Promise and follows it's interface\n * but is not async internally\n */\nclass SyncPromise implements PromiseLike {\n private _state: States = States.PENDING;\n private _handlers: Array<{\n done: boolean;\n onfulfilled?: ((value: T) => T | PromiseLike) | null;\n onrejected?: ((reason: any) => any) | null;\n }> = [];\n private _value: any;\n\n public constructor(\n executor: (resolve: (value?: T | PromiseLike | null) => void, reject: (reason?: any) => void) => void,\n ) {\n try {\n executor(this._resolve, this._reject);\n } catch (e) {\n this._reject(e);\n }\n }\n\n /** JSDoc */\n public toString(): string {\n return '[object SyncPromise]';\n }\n\n /** JSDoc */\n public static resolve(value: T | PromiseLike): PromiseLike {\n return new SyncPromise(resolve => {\n resolve(value);\n });\n }\n\n /** JSDoc */\n public static reject(reason?: any): PromiseLike {\n return new SyncPromise((_, reject) => {\n reject(reason);\n });\n }\n\n /** JSDoc */\n public static all(collection: Array>): PromiseLike {\n return new SyncPromise((resolve, reject) => {\n if (!Array.isArray(collection)) {\n reject(new TypeError(`Promise.all requires an array as input.`));\n return;\n }\n\n if (collection.length === 0) {\n resolve([]);\n return;\n }\n\n let counter = collection.length;\n const resolvedCollection: U[] = [];\n\n collection.forEach((item, index) => {\n SyncPromise.resolve(item)\n .then(value => {\n resolvedCollection[index] = value;\n counter -= 1;\n\n if (counter !== 0) {\n return;\n }\n resolve(resolvedCollection);\n })\n .then(null, reject);\n });\n });\n }\n\n /** JSDoc */\n public then(\n onfulfilled?: ((value: T) => TResult1 | PromiseLike) | null,\n onrejected?: ((reason: any) => TResult2 | PromiseLike) | null,\n ): PromiseLike {\n return new SyncPromise((resolve, reject) => {\n this._attachHandler({\n done: false,\n onfulfilled: result => {\n if (!onfulfilled) {\n // TODO: ¯\\_(ツ)_/¯\n // TODO: FIXME\n resolve(result as any);\n return;\n }\n try {\n resolve(onfulfilled(result));\n return;\n } catch (e) {\n reject(e);\n return;\n }\n },\n onrejected: reason => {\n if (!onrejected) {\n reject(reason);\n return;\n }\n try {\n resolve(onrejected(reason));\n return;\n } catch (e) {\n reject(e);\n return;\n }\n },\n });\n });\n }\n\n /** JSDoc */\n public catch(\n onrejected?: ((reason: any) => TResult | PromiseLike) | null,\n ): PromiseLike {\n return this.then(val => val, onrejected);\n }\n\n /** JSDoc */\n public finally(onfinally?: (() => void) | null): PromiseLike {\n return new SyncPromise((resolve, reject) => {\n let val: TResult | any;\n let isRejected: boolean;\n\n return this.then(\n value => {\n isRejected = false;\n val = value;\n if (onfinally) {\n onfinally();\n }\n },\n reason => {\n isRejected = true;\n val = reason;\n if (onfinally) {\n onfinally();\n }\n },\n ).then(() => {\n if (isRejected) {\n reject(val);\n return;\n }\n\n resolve((val as unknown) as any);\n });\n });\n }\n\n /** JSDoc */\n private readonly _resolve = (value?: T | PromiseLike | null) => {\n this._setResult(States.RESOLVED, value);\n };\n\n /** JSDoc */\n private readonly _reject = (reason?: any) => {\n this._setResult(States.REJECTED, reason);\n };\n\n /** JSDoc */\n private readonly _setResult = (state: States, value?: T | PromiseLike | any) => {\n if (this._state !== States.PENDING) {\n return;\n }\n\n if (isThenable(value)) {\n (value as PromiseLike).then(this._resolve, this._reject);\n return;\n }\n\n this._state = state;\n this._value = value;\n\n this._executeHandlers();\n };\n\n // TODO: FIXME\n /** JSDoc */\n private readonly _attachHandler = (handler: {\n /** JSDoc */\n done: boolean;\n /** JSDoc */\n onfulfilled?(value: T): any;\n /** JSDoc */\n onrejected?(reason: any): any;\n }) => {\n this._handlers = this._handlers.concat(handler);\n this._executeHandlers();\n };\n\n /** JSDoc */\n private readonly _executeHandlers = () => {\n if (this._state === States.PENDING) {\n return;\n }\n\n const cachedHandlers = this._handlers.slice();\n this._handlers = [];\n\n cachedHandlers.forEach(handler => {\n if (handler.done) {\n return;\n }\n\n if (this._state === States.RESOLVED) {\n if (handler.onfulfilled) {\n handler.onfulfilled((this._value as unknown) as any);\n }\n }\n\n if (this._state === States.REJECTED) {\n if (handler.onrejected) {\n handler.onrejected(this._value);\n }\n }\n\n handler.done = true;\n });\n };\n}\n\nexport { SyncPromise };\n","import { Integration, WrappedFunction } from '@sentry/types';\n\nlet originalFunctionToString: () => void;\n\n/** Patch toString calls to return proper name for wrapped functions */\nexport class FunctionToString implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = FunctionToString.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'FunctionToString';\n\n /**\n * @inheritDoc\n */\n public setupOnce(): void {\n originalFunctionToString = Function.prototype.toString;\n\n Function.prototype.toString = function(this: WrappedFunction, ...args: any[]): string {\n const context = this.__sentry_original__ || this;\n // tslint:disable-next-line:no-unsafe-any\n return originalFunctionToString.apply(context, args);\n };\n }\n}\n","export const setPrototypeOf =\n Object.setPrototypeOf || ({ __proto__: [] } instanceof Array ? setProtoOf : mixinProperties); // tslint:disable-line:no-unbound-method\n\n/**\n * setPrototypeOf polyfill using __proto__\n */\nfunction setProtoOf(obj: TTarget, proto: TProto): TTarget & TProto {\n // @ts-ignore\n obj.__proto__ = proto;\n return obj as TTarget & TProto;\n}\n\n/**\n * setPrototypeOf polyfill using mixin\n */\nfunction mixinProperties(obj: TTarget, proto: TProto): TTarget & TProto {\n for (const prop in proto) {\n if (!obj.hasOwnProperty(prop)) {\n // @ts-ignore\n obj[prop] = proto[prop];\n }\n }\n\n return obj as TTarget & TProto;\n}\n","import { setPrototypeOf } from './polyfill';\n\n/** An error emitted by Sentry SDKs and related utilities. */\nexport class SentryError extends Error {\n /** Display name of this error instance. */\n public name: string;\n\n public constructor(public message: string) {\n super(message);\n\n // tslint:disable:no-unsafe-any\n this.name = new.target.prototype.constructor.name;\n setPrototypeOf(this, new.target.prototype);\n }\n}\n","import { DsnComponents, DsnLike, DsnProtocol } from '@sentry/types';\n\nimport { SentryError } from './error';\n\n/** Regular expression used to parse a Dsn. */\nconst DSN_REGEX = /^(?:(\\w+):)\\/\\/(?:(\\w+)(?::(\\w+))?@)([\\w\\.-]+)(?::(\\d+))?\\/(.+)/;\n\n/** Error message */\nconst ERROR_MESSAGE = 'Invalid Dsn';\n\n/** The Sentry Dsn, identifying a Sentry instance and project. */\nexport class Dsn implements DsnComponents {\n /** Protocol used to connect to Sentry. */\n public protocol!: DsnProtocol;\n /** Public authorization key. */\n public user!: string;\n /** Private authorization key (deprecated, optional). */\n public pass!: string;\n /** Hostname of the Sentry instance. */\n public host!: string;\n /** Port of the Sentry instance. */\n public port!: string;\n /** Path */\n public path!: string;\n /** Project ID */\n public projectId!: string;\n\n /** Creates a new Dsn component */\n public constructor(from: DsnLike) {\n if (typeof from === 'string') {\n this._fromString(from);\n } else {\n this._fromComponents(from);\n }\n\n this._validate();\n }\n\n /**\n * Renders the string representation of this Dsn.\n *\n * By default, this will render the public representation without the password\n * component. To get the deprecated private representation, set `withPassword`\n * to true.\n *\n * @param withPassword When set to true, the password will be included.\n */\n public toString(withPassword: boolean = false): string {\n // tslint:disable-next-line:no-this-assignment\n const { host, path, pass, port, projectId, protocol, user } = this;\n return (\n `${protocol}://${user}${withPassword && pass ? `:${pass}` : ''}` +\n `@${host}${port ? `:${port}` : ''}/${path ? `${path}/` : path}${projectId}`\n );\n }\n\n /** Parses a string into this Dsn. */\n private _fromString(str: string): void {\n const match = DSN_REGEX.exec(str);\n\n if (!match) {\n throw new SentryError(ERROR_MESSAGE);\n }\n\n const [protocol, user, pass = '', host, port = '', lastPath] = match.slice(1);\n let path = '';\n let projectId = lastPath;\n\n const split = projectId.split('/');\n if (split.length > 1) {\n path = split.slice(0, -1).join('/');\n projectId = split.pop() as string;\n }\n\n this._fromComponents({ host, pass, path, projectId, port, protocol: protocol as DsnProtocol, user });\n }\n\n /** Maps Dsn components into this instance. */\n private _fromComponents(components: DsnComponents): void {\n this.protocol = components.protocol;\n this.user = components.user;\n this.pass = components.pass || '';\n this.host = components.host;\n this.port = components.port || '';\n this.path = components.path || '';\n this.projectId = components.projectId;\n }\n\n /** Validates this Dsn and throws on error. */\n private _validate(): void {\n ['protocol', 'user', 'host', 'projectId'].forEach(component => {\n if (!this[component as keyof DsnComponents]) {\n throw new SentryError(ERROR_MESSAGE);\n }\n });\n\n if (this.protocol !== 'http' && this.protocol !== 'https') {\n throw new SentryError(ERROR_MESSAGE);\n }\n\n if (this.port && isNaN(parseInt(this.port, 10))) {\n throw new SentryError(ERROR_MESSAGE);\n }\n }\n}\n","import { DsnLike } from '@sentry/types';\nimport { Dsn, urlEncode } from '@sentry/utils';\n\nconst SENTRY_API_VERSION = '7';\n\n/** Helper class to provide urls to different Sentry endpoints. */\nexport class API {\n /** The internally used Dsn object. */\n private readonly _dsnObject: Dsn;\n /** Create a new instance of API */\n public constructor(public dsn: DsnLike) {\n this._dsnObject = new Dsn(dsn);\n }\n\n /** Returns the Dsn object. */\n public getDsn(): Dsn {\n return this._dsnObject;\n }\n\n /** Returns a string with auth headers in the url to the store endpoint. */\n public getStoreEndpoint(): string {\n return `${this._getBaseUrl()}${this.getStoreEndpointPath()}`;\n }\n\n /** Returns the store endpoint with auth added in url encoded. */\n public getStoreEndpointWithUrlEncodedAuth(): string {\n const dsn = this._dsnObject;\n const auth = {\n sentry_key: dsn.user, // sentry_key is currently used in tracing integration to identify internal sentry requests\n sentry_version: SENTRY_API_VERSION,\n };\n // Auth is intentionally sent as part of query string (NOT as custom HTTP header)\n // to avoid preflight CORS requests\n return `${this.getStoreEndpoint()}?${urlEncode(auth)}`;\n }\n\n /** Returns the base path of the url including the port. */\n private _getBaseUrl(): string {\n const dsn = this._dsnObject;\n const protocol = dsn.protocol ? `${dsn.protocol}:` : '';\n const port = dsn.port ? `:${dsn.port}` : '';\n return `${protocol}//${dsn.host}${port}`;\n }\n\n /** Returns only the path component for the store endpoint. */\n public getStoreEndpointPath(): string {\n const dsn = this._dsnObject;\n return `${dsn.path ? `/${dsn.path}` : ''}/api/${dsn.projectId}/store/`;\n }\n\n /** Returns an object that can be used in request headers. */\n public getRequestHeaders(clientName: string, clientVersion: string): { [key: string]: string } {\n const dsn = this._dsnObject;\n const header = [`Sentry sentry_version=${SENTRY_API_VERSION}`];\n header.push(`sentry_client=${clientName}/${clientVersion}`);\n header.push(`sentry_key=${dsn.user}`);\n if (dsn.pass) {\n header.push(`sentry_secret=${dsn.pass}`);\n }\n return {\n 'Content-Type': 'application/json',\n 'X-Sentry-Auth': header.join(', '),\n };\n }\n\n /** Returns the url to the report dialog endpoint. */\n public getReportDialogEndpoint(\n dialogOptions: {\n [key: string]: any;\n user?: { name?: string; email?: string };\n } = {},\n ): string {\n const dsn = this._dsnObject;\n const endpoint = `${this._getBaseUrl()}${dsn.path ? `/${dsn.path}` : ''}/api/embed/error-page/`;\n\n const encodedOptions = [];\n encodedOptions.push(`dsn=${dsn.toString()}`);\n for (const key in dialogOptions) {\n if (key === 'user') {\n if (!dialogOptions.user) {\n continue;\n }\n if (dialogOptions.user.name) {\n encodedOptions.push(`name=${encodeURIComponent(dialogOptions.user.name)}`);\n }\n if (dialogOptions.user.email) {\n encodedOptions.push(`email=${encodeURIComponent(dialogOptions.user.email)}`);\n }\n } else {\n encodedOptions.push(`${encodeURIComponent(key)}=${encodeURIComponent(dialogOptions[key] as string)}`);\n }\n }\n if (encodedOptions.length) {\n return `${endpoint}?${encodedOptions.join('&')}`;\n }\n\n return endpoint;\n }\n}\n","import { Scope } from '@sentry/hub';\nimport { Client, Event, EventHint, Integration, IntegrationClass, Options, SdkInfo, Severity } from '@sentry/types';\nimport { Dsn, isPrimitive, isThenable, logger, normalize, SyncPromise, truncate, uuid4 } from '@sentry/utils';\n\nimport { Backend, BackendClass } from './basebackend';\nimport { IntegrationIndex, setupIntegrations } from './integration';\n\n/**\n * Base implementation for all JavaScript SDK clients.\n *\n * Call the constructor with the corresponding backend constructor and options\n * specific to the client subclass. To access these options later, use\n * {@link Client.getOptions}. Also, the Backend instance is available via\n * {@link Client.getBackend}.\n *\n * If a Dsn is specified in the options, it will be parsed and stored. Use\n * {@link Client.getDsn} to retrieve the Dsn at any moment. In case the Dsn is\n * invalid, the constructor will throw a {@link SentryException}. Note that\n * without a valid Dsn, the SDK will not send any events to Sentry.\n *\n * Before sending an event via the backend, it is passed through\n * {@link BaseClient.prepareEvent} to add SDK information and scope data\n * (breadcrumbs and context). To add more custom information, override this\n * method and extend the resulting prepared event.\n *\n * To issue automatically created events (e.g. via instrumentation), use\n * {@link Client.captureEvent}. It will prepare the event and pass it through\n * the callback lifecycle. To issue auto-breadcrumbs, use\n * {@link Client.addBreadcrumb}.\n *\n * @example\n * class NodeClient extends BaseClient {\n * public constructor(options: NodeOptions) {\n * super(NodeBackend, options);\n * }\n *\n * // ...\n * }\n */\nexport abstract class BaseClient implements Client {\n /**\n * The backend used to physically interact in the enviornment. Usually, this\n * will correspond to the client. When composing SDKs, however, the Backend\n * from the root SDK will be used.\n */\n protected readonly _backend: B;\n\n /** Options passed to the SDK. */\n protected readonly _options: O;\n\n /** The client Dsn, if specified in options. Without this Dsn, the SDK will be disabled. */\n protected readonly _dsn?: Dsn;\n\n /** Array of used integrations. */\n protected _integrations: IntegrationIndex = {};\n\n /** Is the client still processing a call? */\n protected _processing: boolean = false;\n\n /**\n * Initializes this client instance.\n *\n * @param backendClass A constructor function to create the backend.\n * @param options Options for the client.\n */\n protected constructor(backendClass: BackendClass, options: O) {\n this._backend = new backendClass(options);\n this._options = options;\n\n if (options.dsn) {\n this._dsn = new Dsn(options.dsn);\n }\n }\n\n /**\n * @inheritDoc\n */\n public captureException(exception: any, hint?: EventHint, scope?: Scope): string | undefined {\n let eventId: string | undefined = hint && hint.event_id;\n this._processing = true;\n\n this._getBackend()\n .eventFromException(exception, hint)\n .then(event => this._processEvent(event, hint, scope))\n .then(finalEvent => {\n // We need to check for finalEvent in case beforeSend returned null\n eventId = finalEvent && finalEvent.event_id;\n this._processing = false;\n })\n .then(null, reason => {\n logger.error(reason);\n this._processing = false;\n });\n\n return eventId;\n }\n\n /**\n * @inheritDoc\n */\n public captureMessage(message: string, level?: Severity, hint?: EventHint, scope?: Scope): string | undefined {\n let eventId: string | undefined = hint && hint.event_id;\n\n this._processing = true;\n\n const promisedEvent = isPrimitive(message)\n ? this._getBackend().eventFromMessage(`${message}`, level, hint)\n : this._getBackend().eventFromException(message, hint);\n\n promisedEvent\n .then(event => this._processEvent(event, hint, scope))\n .then(finalEvent => {\n // We need to check for finalEvent in case beforeSend returned null\n eventId = finalEvent && finalEvent.event_id;\n this._processing = false;\n })\n .then(null, reason => {\n logger.error(reason);\n this._processing = false;\n });\n\n return eventId;\n }\n\n /**\n * @inheritDoc\n */\n public captureEvent(event: Event, hint?: EventHint, scope?: Scope): string | undefined {\n let eventId: string | undefined = hint && hint.event_id;\n this._processing = true;\n\n this._processEvent(event, hint, scope)\n .then(finalEvent => {\n // We need to check for finalEvent in case beforeSend returned null\n eventId = finalEvent && finalEvent.event_id;\n this._processing = false;\n })\n .then(null, reason => {\n logger.error(reason);\n this._processing = false;\n });\n\n return eventId;\n }\n\n /**\n * @inheritDoc\n */\n public getDsn(): Dsn | undefined {\n return this._dsn;\n }\n\n /**\n * @inheritDoc\n */\n public getOptions(): O {\n return this._options;\n }\n\n /**\n * @inheritDoc\n */\n public flush(timeout?: number): PromiseLike {\n return this._isClientProcessing(timeout).then(status => {\n clearInterval(status.interval);\n return this._getBackend()\n .getTransport()\n .close(timeout)\n .then(transportFlushed => status.ready && transportFlushed);\n });\n }\n\n /**\n * @inheritDoc\n */\n public close(timeout?: number): PromiseLike {\n return this.flush(timeout).then(result => {\n this.getOptions().enabled = false;\n return result;\n });\n }\n\n /**\n * Sets up the integrations\n */\n public setupIntegrations(): void {\n if (this._isEnabled()) {\n this._integrations = setupIntegrations(this._options);\n }\n }\n\n /**\n * @inheritDoc\n */\n public getIntegration(integration: IntegrationClass): T | null {\n try {\n return (this._integrations[integration.id] as T) || null;\n } catch (_oO) {\n logger.warn(`Cannot retrieve integration ${integration.id} from the current Client`);\n return null;\n }\n }\n\n /** Waits for the client to be done with processing. */\n protected _isClientProcessing(timeout?: number): PromiseLike<{ ready: boolean; interval: number }> {\n return new SyncPromise<{ ready: boolean; interval: number }>(resolve => {\n let ticked: number = 0;\n const tick: number = 1;\n\n let interval = 0;\n clearInterval(interval);\n\n interval = (setInterval(() => {\n if (!this._processing) {\n resolve({\n interval,\n ready: true,\n });\n } else {\n ticked += tick;\n if (timeout && ticked >= timeout) {\n resolve({\n interval,\n ready: false,\n });\n }\n }\n }, tick) as unknown) as number;\n });\n }\n\n /** Returns the current backend. */\n protected _getBackend(): B {\n return this._backend;\n }\n\n /** Determines whether this SDK is enabled and a valid Dsn is present. */\n protected _isEnabled(): boolean {\n return this.getOptions().enabled !== false && this._dsn !== undefined;\n }\n\n /**\n * Adds common information to events.\n *\n * The information includes release and environment from `options`,\n * breadcrumbs and context (extra, tags and user) from the scope.\n *\n * Information that is already present in the event is never overwritten. For\n * nested objects, such as the context, keys are merged.\n *\n * @param event The original event.\n * @param hint May contain additional informartion about the original exception.\n * @param scope A scope containing event metadata.\n * @returns A new event with more information.\n */\n protected _prepareEvent(event: Event, scope?: Scope, hint?: EventHint): PromiseLike {\n const { environment, release, dist, maxValueLength = 250, normalizeDepth = 3 } = this.getOptions();\n\n const prepared: Event = { ...event };\n if (prepared.environment === undefined && environment !== undefined) {\n prepared.environment = environment;\n }\n if (prepared.release === undefined && release !== undefined) {\n prepared.release = release;\n }\n\n if (prepared.dist === undefined && dist !== undefined) {\n prepared.dist = dist;\n }\n\n if (prepared.message) {\n prepared.message = truncate(prepared.message, maxValueLength);\n }\n\n const exception = prepared.exception && prepared.exception.values && prepared.exception.values[0];\n if (exception && exception.value) {\n exception.value = truncate(exception.value, maxValueLength);\n }\n\n const request = prepared.request;\n if (request && request.url) {\n request.url = truncate(request.url, maxValueLength);\n }\n\n if (prepared.event_id === undefined) {\n prepared.event_id = hint && hint.event_id ? hint.event_id : uuid4();\n }\n\n this._addIntegrations(prepared.sdk);\n\n // We prepare the result here with a resolved Event.\n let result = SyncPromise.resolve(prepared);\n\n // This should be the last thing called, since we want that\n // {@link Hub.addEventProcessor} gets the finished prepared event.\n if (scope) {\n // In case we have a hub we reassign it.\n result = scope.applyToEvent(prepared, hint);\n }\n\n return result.then(evt => {\n // tslint:disable-next-line:strict-type-predicates\n if (typeof normalizeDepth === 'number' && normalizeDepth > 0) {\n return this._normalizeEvent(evt, normalizeDepth);\n }\n return evt;\n });\n }\n\n /**\n * Applies `normalize` function on necessary `Event` attributes to make them safe for serialization.\n * Normalized keys:\n * - `breadcrumbs.data`\n * - `user`\n * - `contexts`\n * - `extra`\n * @param event Event\n * @returns Normalized event\n */\n protected _normalizeEvent(event: Event | null, depth: number): Event | null {\n if (!event) {\n return null;\n }\n\n // tslint:disable:no-unsafe-any\n return {\n ...event,\n ...(event.breadcrumbs && {\n breadcrumbs: event.breadcrumbs.map(b => ({\n ...b,\n ...(b.data && {\n data: normalize(b.data, depth),\n }),\n })),\n }),\n ...(event.user && {\n user: normalize(event.user, depth),\n }),\n ...(event.contexts && {\n contexts: normalize(event.contexts, depth),\n }),\n ...(event.extra && {\n extra: normalize(event.extra, depth),\n }),\n };\n }\n\n /**\n * This function adds all used integrations to the SDK info in the event.\n * @param sdkInfo The sdkInfo of the event that will be filled with all integrations.\n */\n protected _addIntegrations(sdkInfo?: SdkInfo): void {\n const integrationsArray = Object.keys(this._integrations);\n if (sdkInfo && integrationsArray.length > 0) {\n sdkInfo.integrations = integrationsArray;\n }\n }\n\n /**\n * Processes an event (either error or message) and sends it to Sentry.\n *\n * This also adds breadcrumbs and context information to the event. However,\n * platform specific meta data (such as the User's IP address) must be added\n * by the SDK implementor.\n *\n *\n * @param event The event to send to Sentry.\n * @param hint May contain additional informartion about the original exception.\n * @param scope A scope containing event metadata.\n * @returns A SyncPromise that resolves with the event or rejects in case event was/will not be send.\n */\n protected _processEvent(event: Event, hint?: EventHint, scope?: Scope): PromiseLike {\n const { beforeSend, sampleRate } = this.getOptions();\n\n if (!this._isEnabled()) {\n return SyncPromise.reject('SDK not enabled, will not send event.');\n }\n\n // 1.0 === 100% events are sent\n // 0.0 === 0% events are sent\n if (typeof sampleRate === 'number' && Math.random() > sampleRate) {\n return SyncPromise.reject('This event has been sampled, will not send event.');\n }\n\n return new SyncPromise((resolve, reject) => {\n this._prepareEvent(event, scope, hint)\n .then(prepared => {\n if (prepared === null) {\n reject('An event processor returned null, will not send event.');\n return;\n }\n\n let finalEvent: Event | null = prepared;\n\n const isInternalException = hint && hint.data && (hint.data as { [key: string]: any }).__sentry__ === true;\n if (isInternalException || !beforeSend) {\n this._getBackend().sendEvent(finalEvent);\n resolve(finalEvent);\n return;\n }\n\n const beforeSendResult = beforeSend(prepared, hint);\n // tslint:disable-next-line:strict-type-predicates\n if (typeof beforeSendResult === 'undefined') {\n logger.error('`beforeSend` method has to return `null` or a valid event.');\n } else if (isThenable(beforeSendResult)) {\n this._handleAsyncBeforeSend(beforeSendResult as PromiseLike, resolve, reject);\n } else {\n finalEvent = beforeSendResult as Event | null;\n\n if (finalEvent === null) {\n logger.log('`beforeSend` returned `null`, will not send event.');\n resolve(null);\n return;\n }\n\n // From here on we are really async\n this._getBackend().sendEvent(finalEvent);\n resolve(finalEvent);\n }\n })\n .then(null, reason => {\n this.captureException(reason, {\n data: {\n __sentry__: true,\n },\n originalException: reason as Error,\n });\n reject(\n `Event processing pipeline threw an error, original event will not be sent. Details have been sent as a new event.\\nReason: ${reason}`,\n );\n });\n });\n }\n\n /**\n * Resolves before send Promise and calls resolve/reject on parent SyncPromise.\n */\n private _handleAsyncBeforeSend(\n beforeSend: PromiseLike,\n resolve: (event: Event) => void,\n reject: (reason: string) => void,\n ): void {\n beforeSend\n .then(processedEvent => {\n if (processedEvent === null) {\n reject('`beforeSend` returned `null`, will not send event.');\n return;\n }\n // From here on we are really async\n this._getBackend().sendEvent(processedEvent);\n resolve(processedEvent);\n })\n .then(null, e => {\n reject(`beforeSend rejected with ${e}`);\n });\n }\n}\n","import { Event, Response, Status, Transport } from '@sentry/types';\nimport { SyncPromise } from '@sentry/utils';\n\n/** Noop transport */\nexport class NoopTransport implements Transport {\n /**\n * @inheritDoc\n */\n public sendEvent(_: Event): PromiseLike {\n return SyncPromise.resolve({\n reason: `NoopTransport: Event has been skipped because no Dsn is configured.`,\n status: Status.Skipped,\n });\n }\n\n /**\n * @inheritDoc\n */\n public close(_?: number): PromiseLike {\n return SyncPromise.resolve(true);\n }\n}\n","import { Event, EventHint, Options, Severity, Transport } from '@sentry/types';\nimport { logger, SentryError } from '@sentry/utils';\n\nimport { NoopTransport } from './transports/noop';\n\n/**\n * Internal platform-dependent Sentry SDK Backend.\n *\n * While {@link Client} contains business logic specific to an SDK, the\n * Backend offers platform specific implementations for low-level operations.\n * These are persisting and loading information, sending events, and hooking\n * into the environment.\n *\n * Backends receive a handle to the Client in their constructor. When a\n * Backend automatically generates events, it must pass them to\n * the Client for validation and processing first.\n *\n * Usually, the Client will be of corresponding type, e.g. NodeBackend\n * receives NodeClient. However, higher-level SDKs can choose to instanciate\n * multiple Backends and delegate tasks between them. In this case, an event\n * generated by one backend might very well be sent by another one.\n *\n * The client also provides access to options via {@link Client.getOptions}.\n * @hidden\n */\nexport interface Backend {\n /** Creates a {@link Event} from an exception. */\n eventFromException(exception: any, hint?: EventHint): PromiseLike;\n\n /** Creates a {@link Event} from a plain message. */\n eventFromMessage(message: string, level?: Severity, hint?: EventHint): PromiseLike;\n\n /** Submits the event to Sentry */\n sendEvent(event: Event): void;\n\n /**\n * Returns the transport that is used by the backend.\n * Please note that the transport gets lazy initialized so it will only be there once the first event has been sent.\n *\n * @returns The transport.\n */\n getTransport(): Transport;\n}\n\n/**\n * A class object that can instanciate Backend objects.\n * @hidden\n */\nexport type BackendClass = new (options: O) => B;\n\n/**\n * This is the base implemention of a Backend.\n * @hidden\n */\nexport abstract class BaseBackend implements Backend {\n /** Options passed to the SDK. */\n protected readonly _options: O;\n\n /** Cached transport used internally. */\n protected _transport: Transport;\n\n /** Creates a new backend instance. */\n public constructor(options: O) {\n this._options = options;\n if (!this._options.dsn) {\n logger.warn('No DSN provided, backend will not do anything.');\n }\n this._transport = this._setupTransport();\n }\n\n /**\n * Sets up the transport so it can be used later to send requests.\n */\n protected _setupTransport(): Transport {\n return new NoopTransport();\n }\n\n /**\n * @inheritDoc\n */\n public eventFromException(_exception: any, _hint?: EventHint): PromiseLike {\n throw new SentryError('Backend has to implement `eventFromException` method');\n }\n\n /**\n * @inheritDoc\n */\n public eventFromMessage(_message: string, _level?: Severity, _hint?: EventHint): PromiseLike {\n throw new SentryError('Backend has to implement `eventFromMessage` method');\n }\n\n /**\n * @inheritDoc\n */\n public sendEvent(event: Event): void {\n this._transport.sendEvent(event).then(null, reason => {\n logger.error(`Error while sending event: ${reason}`);\n });\n }\n\n /**\n * @inheritDoc\n */\n public getTransport(): Transport {\n return this._transport;\n }\n}\n","import { SentryError } from './error';\nimport { SyncPromise } from './syncpromise';\n\n/** A simple queue that holds promises. */\nexport class PromiseBuffer {\n public constructor(protected _limit?: number) {}\n\n /** Internal set of queued Promises */\n private readonly _buffer: Array> = [];\n\n /**\n * Says if the buffer is ready to take more requests\n */\n public isReady(): boolean {\n return this._limit === undefined || this.length() < this._limit;\n }\n\n /**\n * Add a promise to the queue.\n *\n * @param task Can be any PromiseLike\n * @returns The original promise.\n */\n public add(task: PromiseLike): PromiseLike {\n if (!this.isReady()) {\n return SyncPromise.reject(new SentryError('Not adding Promise due to buffer limit reached.'));\n }\n if (this._buffer.indexOf(task) === -1) {\n this._buffer.push(task);\n }\n task\n .then(() => this.remove(task))\n .then(null, () =>\n this.remove(task).then(null, () => {\n // We have to add this catch here otherwise we have an unhandledPromiseRejection\n // because it's a new Promise chain.\n }),\n );\n return task;\n }\n\n /**\n * Remove a promise to the queue.\n *\n * @param task Can be any PromiseLike\n * @returns Removed promise.\n */\n public remove(task: PromiseLike): PromiseLike {\n const removedTask = this._buffer.splice(this._buffer.indexOf(task), 1)[0];\n return removedTask;\n }\n\n /**\n * This function returns the number of unresolved promises in the queue.\n */\n public length(): number {\n return this._buffer.length;\n }\n\n /**\n * This will drain the whole queue, returns true if queue is empty or drained.\n * If timeout is provided and the queue takes longer to drain, the promise still resolves but with false.\n *\n * @param timeout Number in ms to wait until it resolves with false.\n */\n public drain(timeout?: number): PromiseLike {\n return new SyncPromise(resolve => {\n const capturedSetTimeout = setTimeout(() => {\n if (timeout && timeout > 0) {\n resolve(false);\n }\n }, timeout);\n SyncPromise.all(this._buffer)\n .then(() => {\n clearTimeout(capturedSetTimeout);\n resolve(true);\n })\n .then(null, () => {\n resolve(true);\n });\n });\n }\n}\n","import { API } from '@sentry/core';\nimport { Event, Response, Transport, TransportOptions } from '@sentry/types';\nimport { PromiseBuffer, SentryError } from '@sentry/utils';\n\n/** Base Transport class implementation */\nexport abstract class BaseTransport implements Transport {\n /**\n * @inheritDoc\n */\n public url: string;\n\n /** A simple buffer holding all requests. */\n protected readonly _buffer: PromiseBuffer = new PromiseBuffer(30);\n\n public constructor(public options: TransportOptions) {\n this.url = new API(this.options.dsn).getStoreEndpointWithUrlEncodedAuth();\n }\n\n /**\n * @inheritDoc\n */\n public sendEvent(_: Event): PromiseLike {\n throw new SentryError('Transport Class has to implement `sendEvent` method');\n }\n\n /**\n * @inheritDoc\n */\n public close(timeout?: number): PromiseLike {\n return this._buffer.drain(timeout);\n }\n}\n","import { Event, Response, Status } from '@sentry/types';\nimport { getGlobalObject, logger, parseRetryAfterHeader, supportsReferrerPolicy, SyncPromise } from '@sentry/utils';\n\nimport { BaseTransport } from './base';\n\nconst global = getGlobalObject();\n\n/** `fetch` based transport */\nexport class FetchTransport extends BaseTransport {\n /** Locks transport after receiving 429 response */\n private _disabledUntil: Date = new Date(Date.now());\n\n /**\n * @inheritDoc\n */\n public sendEvent(event: Event): PromiseLike {\n if (new Date(Date.now()) < this._disabledUntil) {\n return Promise.reject({\n event,\n reason: `Transport locked till ${this._disabledUntil} due to too many requests.`,\n status: 429,\n });\n }\n\n const defaultOptions: RequestInit = {\n body: JSON.stringify(event),\n method: 'POST',\n // Despite all stars in the sky saying that Edge supports old draft syntax, aka 'never', 'always', 'origin' and 'default\n // https://caniuse.com/#feat=referrer-policy\n // It doesn't. And it throw exception instead of ignoring this parameter...\n // REF: https://github.com/getsentry/raven-js/issues/1233\n referrerPolicy: (supportsReferrerPolicy() ? 'origin' : '') as ReferrerPolicy,\n };\n\n if (this.options.headers !== undefined) {\n defaultOptions.headers = this.options.headers;\n }\n\n return this._buffer.add(\n new SyncPromise((resolve, reject) => {\n global\n .fetch(this.url, defaultOptions)\n .then(response => {\n const status = Status.fromHttpCode(response.status);\n\n if (status === Status.Success) {\n resolve({ status });\n return;\n }\n\n if (status === Status.RateLimit) {\n const now = Date.now();\n this._disabledUntil = new Date(now + parseRetryAfterHeader(now, response.headers.get('Retry-After')));\n logger.warn(`Too many requests, backing off till: ${this._disabledUntil}`);\n }\n\n reject(response);\n })\n .catch(reject);\n }),\n );\n }\n}\n","import { Event, Response, Status } from '@sentry/types';\nimport { logger, parseRetryAfterHeader, SyncPromise } from '@sentry/utils';\n\nimport { BaseTransport } from './base';\n\n/** `XHR` based transport */\nexport class XHRTransport extends BaseTransport {\n /** Locks transport after receiving 429 response */\n private _disabledUntil: Date = new Date(Date.now());\n\n /**\n * @inheritDoc\n */\n public sendEvent(event: Event): PromiseLike {\n if (new Date(Date.now()) < this._disabledUntil) {\n return Promise.reject({\n event,\n reason: `Transport locked till ${this._disabledUntil} due to too many requests.`,\n status: 429,\n });\n }\n\n return this._buffer.add(\n new SyncPromise((resolve, reject) => {\n const request = new XMLHttpRequest();\n\n request.onreadystatechange = () => {\n if (request.readyState !== 4) {\n return;\n }\n\n const status = Status.fromHttpCode(request.status);\n\n if (status === Status.Success) {\n resolve({ status });\n return;\n }\n\n if (status === Status.RateLimit) {\n const now = Date.now();\n this._disabledUntil = new Date(now + parseRetryAfterHeader(now, request.getResponseHeader('Retry-After')));\n logger.warn(`Too many requests, backing off till: ${this._disabledUntil}`);\n }\n\n reject(request);\n };\n\n request.open('POST', this.url);\n for (const header in this.options.headers) {\n if (this.options.headers.hasOwnProperty(header)) {\n request.setRequestHeader(header, this.options.headers[header]);\n }\n }\n request.send(JSON.stringify(event));\n }),\n );\n }\n}\n","import { BaseBackend } from '@sentry/core';\nimport { Event, EventHint, Options, Severity, Transport } from '@sentry/types';\nimport { addExceptionMechanism, supportsFetch, SyncPromise } from '@sentry/utils';\n\nimport { eventFromString, eventFromUnknownInput } from './eventbuilder';\nimport { FetchTransport, XHRTransport } from './transports';\n\n/**\n * Configuration options for the Sentry Browser SDK.\n * @see BrowserClient for more information.\n */\nexport interface BrowserOptions extends Options {\n /**\n * A pattern for error URLs which should not be sent to Sentry.\n * To whitelist certain errors instead, use {@link Options.whitelistUrls}.\n * By default, all errors will be sent.\n */\n blacklistUrls?: Array;\n\n /**\n * A pattern for error URLs which should exclusively be sent to Sentry.\n * This is the opposite of {@link Options.blacklistUrls}.\n * By default, all errors will be sent.\n */\n whitelistUrls?: Array;\n}\n\n/**\n * The Sentry Browser SDK Backend.\n * @hidden\n */\nexport class BrowserBackend extends BaseBackend {\n /**\n * @inheritDoc\n */\n protected _setupTransport(): Transport {\n if (!this._options.dsn) {\n // We return the noop transport here in case there is no Dsn.\n return super._setupTransport();\n }\n\n const transportOptions = {\n ...this._options.transportOptions,\n dsn: this._options.dsn,\n };\n\n if (this._options.transport) {\n return new this._options.transport(transportOptions);\n }\n if (supportsFetch()) {\n return new FetchTransport(transportOptions);\n }\n return new XHRTransport(transportOptions);\n }\n\n /**\n * @inheritDoc\n */\n public eventFromException(exception: any, hint?: EventHint): PromiseLike {\n const syntheticException = (hint && hint.syntheticException) || undefined;\n const event = eventFromUnknownInput(exception, syntheticException, {\n attachStacktrace: this._options.attachStacktrace,\n });\n addExceptionMechanism(event, {\n handled: true,\n type: 'generic',\n });\n event.level = Severity.Error;\n if (hint && hint.event_id) {\n event.event_id = hint.event_id;\n }\n return SyncPromise.resolve(event);\n }\n /**\n * @inheritDoc\n */\n public eventFromMessage(message: string, level: Severity = Severity.Info, hint?: EventHint): PromiseLike {\n const syntheticException = (hint && hint.syntheticException) || undefined;\n const event = eventFromString(message, syntheticException, {\n attachStacktrace: this._options.attachStacktrace,\n });\n event.level = level;\n if (hint && hint.event_id) {\n event.event_id = hint.event_id;\n }\n return SyncPromise.resolve(event);\n }\n}\n","export const SDK_NAME = 'sentry.javascript.browser';\nexport const SDK_VERSION = '5.15.5';\n","import { API, BaseClient, Scope } from '@sentry/core';\nimport { DsnLike, Event, EventHint } from '@sentry/types';\nimport { getGlobalObject, logger } from '@sentry/utils';\n\nimport { BrowserBackend, BrowserOptions } from './backend';\nimport { SDK_NAME, SDK_VERSION } from './version';\n\n/**\n * All properties the report dialog supports\n */\nexport interface ReportDialogOptions {\n [key: string]: any;\n eventId?: string;\n dsn?: DsnLike;\n user?: {\n email?: string;\n name?: string;\n };\n lang?: string;\n title?: string;\n subtitle?: string;\n subtitle2?: string;\n labelName?: string;\n labelEmail?: string;\n labelComments?: string;\n labelClose?: string;\n labelSubmit?: string;\n errorGeneric?: string;\n errorFormEntry?: string;\n successMessage?: string;\n /** Callback after reportDialog showed up */\n onLoad?(): void;\n}\n\n/**\n * The Sentry Browser SDK Client.\n *\n * @see BrowserOptions for documentation on configuration options.\n * @see SentryClient for usage documentation.\n */\nexport class BrowserClient extends BaseClient {\n /**\n * Creates a new Browser SDK instance.\n *\n * @param options Configuration options for this SDK.\n */\n public constructor(options: BrowserOptions = {}) {\n super(BrowserBackend, options);\n }\n\n /**\n * @inheritDoc\n */\n protected _prepareEvent(event: Event, scope?: Scope, hint?: EventHint): PromiseLike {\n event.platform = event.platform || 'javascript';\n event.sdk = {\n ...event.sdk,\n name: SDK_NAME,\n packages: [\n ...((event.sdk && event.sdk.packages) || []),\n {\n name: 'npm:@sentry/browser',\n version: SDK_VERSION,\n },\n ],\n version: SDK_VERSION,\n };\n\n return super._prepareEvent(event, scope, hint);\n }\n\n /**\n * Show a report dialog to the user to send feedback to a specific event.\n *\n * @param options Set individual options for the dialog\n */\n public showReportDialog(options: ReportDialogOptions = {}): void {\n // doesn't work without a document (React Native)\n const document = getGlobalObject().document;\n if (!document) {\n return;\n }\n\n if (!this._isEnabled()) {\n logger.error('Trying to call showReportDialog with Sentry Client is disabled');\n return;\n }\n\n const dsn = options.dsn || this.getDsn();\n\n if (!options.eventId) {\n logger.error('Missing `eventId` option in showReportDialog call');\n return;\n }\n\n if (!dsn) {\n logger.error('Missing `Dsn` option in showReportDialog call');\n return;\n }\n\n const script = document.createElement('script');\n script.async = true;\n script.src = new API(dsn).getReportDialogEndpoint(options);\n\n if (options.onLoad) {\n script.onload = options.onLoad;\n }\n\n (document.head || document.body).appendChild(script);\n }\n}\n","import { addGlobalEventProcessor, getCurrentHub } from '@sentry/hub';\nimport { Event, Integration } from '@sentry/types';\nimport { getEventDescription, isMatchingPattern, logger } from '@sentry/utils';\n\n// \"Script error.\" is hard coded into browsers for errors that it can't read.\n// this is the result of a script being pulled in from an external domain and CORS.\nconst DEFAULT_IGNORE_ERRORS = [/^Script error\\.?$/, /^Javascript error: Script error\\.? on line 0$/];\n\n/** JSDoc */\ninterface InboundFiltersOptions {\n blacklistUrls?: Array;\n ignoreErrors?: Array;\n ignoreInternal?: boolean;\n whitelistUrls?: Array;\n}\n\n/** Inbound filters configurable by the user */\nexport class InboundFilters implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = InboundFilters.id;\n /**\n * @inheritDoc\n */\n public static id: string = 'InboundFilters';\n\n public constructor(private readonly _options: InboundFiltersOptions = {}) {}\n\n /**\n * @inheritDoc\n */\n public setupOnce(): void {\n addGlobalEventProcessor((event: Event) => {\n const hub = getCurrentHub();\n if (!hub) {\n return event;\n }\n const self = hub.getIntegration(InboundFilters);\n if (self) {\n const client = hub.getClient();\n const clientOptions = client ? client.getOptions() : {};\n const options = self._mergeOptions(clientOptions);\n if (self._shouldDropEvent(event, options)) {\n return null;\n }\n }\n return event;\n });\n }\n\n /** JSDoc */\n private _shouldDropEvent(event: Event, options: InboundFiltersOptions): boolean {\n if (this._isSentryError(event, options)) {\n logger.warn(`Event dropped due to being internal Sentry Error.\\nEvent: ${getEventDescription(event)}`);\n return true;\n }\n if (this._isIgnoredError(event, options)) {\n logger.warn(\n `Event dropped due to being matched by \\`ignoreErrors\\` option.\\nEvent: ${getEventDescription(event)}`,\n );\n return true;\n }\n if (this._isBlacklistedUrl(event, options)) {\n logger.warn(\n `Event dropped due to being matched by \\`blacklistUrls\\` option.\\nEvent: ${getEventDescription(\n event,\n )}.\\nUrl: ${this._getEventFilterUrl(event)}`,\n );\n return true;\n }\n if (!this._isWhitelistedUrl(event, options)) {\n logger.warn(\n `Event dropped due to not being matched by \\`whitelistUrls\\` option.\\nEvent: ${getEventDescription(\n event,\n )}.\\nUrl: ${this._getEventFilterUrl(event)}`,\n );\n return true;\n }\n return false;\n }\n\n /** JSDoc */\n private _isSentryError(event: Event, options: InboundFiltersOptions = {}): boolean {\n if (!options.ignoreInternal) {\n return false;\n }\n\n try {\n return (\n (event &&\n event.exception &&\n event.exception.values &&\n event.exception.values[0] &&\n event.exception.values[0].type === 'SentryError') ||\n false\n );\n } catch (_oO) {\n return false;\n }\n }\n\n /** JSDoc */\n private _isIgnoredError(event: Event, options: InboundFiltersOptions = {}): boolean {\n if (!options.ignoreErrors || !options.ignoreErrors.length) {\n return false;\n }\n\n return this._getPossibleEventMessages(event).some(message =>\n // Not sure why TypeScript complains here...\n (options.ignoreErrors as Array).some(pattern => isMatchingPattern(message, pattern)),\n );\n }\n\n /** JSDoc */\n private _isBlacklistedUrl(event: Event, options: InboundFiltersOptions = {}): boolean {\n // TODO: Use Glob instead?\n if (!options.blacklistUrls || !options.blacklistUrls.length) {\n return false;\n }\n const url = this._getEventFilterUrl(event);\n return !url ? false : options.blacklistUrls.some(pattern => isMatchingPattern(url, pattern));\n }\n\n /** JSDoc */\n private _isWhitelistedUrl(event: Event, options: InboundFiltersOptions = {}): boolean {\n // TODO: Use Glob instead?\n if (!options.whitelistUrls || !options.whitelistUrls.length) {\n return true;\n }\n const url = this._getEventFilterUrl(event);\n return !url ? true : options.whitelistUrls.some(pattern => isMatchingPattern(url, pattern));\n }\n\n /** JSDoc */\n private _mergeOptions(clientOptions: InboundFiltersOptions = {}): InboundFiltersOptions {\n return {\n blacklistUrls: [...(this._options.blacklistUrls || []), ...(clientOptions.blacklistUrls || [])],\n ignoreErrors: [\n ...(this._options.ignoreErrors || []),\n ...(clientOptions.ignoreErrors || []),\n ...DEFAULT_IGNORE_ERRORS,\n ],\n ignoreInternal: typeof this._options.ignoreInternal !== 'undefined' ? this._options.ignoreInternal : true,\n whitelistUrls: [...(this._options.whitelistUrls || []), ...(clientOptions.whitelistUrls || [])],\n };\n }\n\n /** JSDoc */\n private _getPossibleEventMessages(event: Event): string[] {\n if (event.message) {\n return [event.message];\n }\n if (event.exception) {\n try {\n const { type = '', value = '' } = (event.exception.values && event.exception.values[0]) || {};\n return [`${value}`, `${type}: ${value}`];\n } catch (oO) {\n logger.error(`Cannot extract message for event ${getEventDescription(event)}`);\n return [];\n }\n }\n return [];\n }\n\n /** JSDoc */\n private _getEventFilterUrl(event: Event): string | null {\n try {\n if (event.stacktrace) {\n const frames = event.stacktrace.frames;\n return (frames && frames[frames.length - 1].filename) || null;\n }\n if (event.exception) {\n const frames =\n event.exception.values && event.exception.values[0].stacktrace && event.exception.values[0].stacktrace.frames;\n return (frames && frames[frames.length - 1].filename) || null;\n }\n return null;\n } catch (oO) {\n logger.error(`Cannot extract url for event ${getEventDescription(event)}`);\n return null;\n }\n }\n}\n","import { Integration, WrappedFunction } from '@sentry/types';\nimport { fill, getFunctionName, getGlobalObject } from '@sentry/utils';\n\nimport { wrap } from '../helpers';\n\ntype XMLHttpRequestProp = 'onload' | 'onerror' | 'onprogress' | 'onreadystatechange';\n\n/** Wrap timer functions and event targets to catch errors and provide better meta data */\nexport class TryCatch implements Integration {\n /** JSDoc */\n private _ignoreOnError: number = 0;\n\n /**\n * @inheritDoc\n */\n public name: string = TryCatch.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'TryCatch';\n\n /** JSDoc */\n private _wrapTimeFunction(original: () => void): () => number {\n return function(this: any, ...args: any[]): number {\n const originalCallback = args[0];\n args[0] = wrap(originalCallback, {\n mechanism: {\n data: { function: getFunctionName(original) },\n handled: true,\n type: 'instrument',\n },\n });\n return original.apply(this, args);\n };\n }\n\n /** JSDoc */\n private _wrapRAF(original: any): (callback: () => void) => any {\n return function(this: any, callback: () => void): () => void {\n return original(\n wrap(callback, {\n mechanism: {\n data: {\n function: 'requestAnimationFrame',\n handler: getFunctionName(original),\n },\n handled: true,\n type: 'instrument',\n },\n }),\n );\n };\n }\n\n /** JSDoc */\n private _wrapEventTarget(target: string): void {\n const global = getGlobalObject() as { [key: string]: any };\n const proto = global[target] && global[target].prototype;\n\n if (!proto || !proto.hasOwnProperty || !proto.hasOwnProperty('addEventListener')) {\n return;\n }\n\n fill(proto, 'addEventListener', function(\n original: () => void,\n ): (eventName: string, fn: EventListenerObject, options?: boolean | AddEventListenerOptions) => void {\n return function(\n this: any,\n eventName: string,\n fn: EventListenerObject,\n options?: boolean | AddEventListenerOptions,\n ): (eventName: string, fn: EventListenerObject, capture?: boolean, secure?: boolean) => void {\n try {\n // tslint:disable-next-line:no-unbound-method strict-type-predicates\n if (typeof fn.handleEvent === 'function') {\n fn.handleEvent = wrap(fn.handleEvent.bind(fn), {\n mechanism: {\n data: {\n function: 'handleEvent',\n handler: getFunctionName(fn),\n target,\n },\n handled: true,\n type: 'instrument',\n },\n });\n }\n } catch (err) {\n // can sometimes get 'Permission denied to access property \"handle Event'\n }\n\n return original.call(\n this,\n eventName,\n wrap((fn as any) as WrappedFunction, {\n mechanism: {\n data: {\n function: 'addEventListener',\n handler: getFunctionName(fn),\n target,\n },\n handled: true,\n type: 'instrument',\n },\n }),\n options,\n );\n };\n });\n\n fill(proto, 'removeEventListener', function(\n original: () => void,\n ): (this: any, eventName: string, fn: EventListenerObject, options?: boolean | EventListenerOptions) => () => void {\n return function(\n this: any,\n eventName: string,\n fn: EventListenerObject,\n options?: boolean | EventListenerOptions,\n ): () => void {\n let callback = (fn as any) as WrappedFunction;\n try {\n callback = callback && (callback.__sentry_wrapped__ || callback);\n } catch (e) {\n // ignore, accessing __sentry_wrapped__ will throw in some Selenium environments\n }\n return original.call(this, eventName, callback, options);\n };\n });\n }\n\n /** JSDoc */\n private _wrapXHR(originalSend: () => void): () => void {\n return function(this: XMLHttpRequest, ...args: any[]): void {\n const xhr = this; // tslint:disable-line:no-this-assignment\n const xmlHttpRequestProps: XMLHttpRequestProp[] = ['onload', 'onerror', 'onprogress', 'onreadystatechange'];\n\n xmlHttpRequestProps.forEach(prop => {\n if (prop in xhr && typeof xhr[prop] === 'function') {\n fill(xhr, prop, function(original: WrappedFunction): Function {\n const wrapOptions = {\n mechanism: {\n data: {\n function: prop,\n handler: getFunctionName(original),\n },\n handled: true,\n type: 'instrument',\n },\n };\n\n // If Instrument integration has been called before TryCatch, get the name of original function\n if (original.__sentry_original__) {\n wrapOptions.mechanism.data.handler = getFunctionName(original.__sentry_original__);\n }\n\n // Otherwise wrap directly\n return wrap(original, wrapOptions);\n });\n }\n });\n\n return originalSend.apply(this, args);\n };\n }\n\n /**\n * Wrap timer functions and event targets to catch errors\n * and provide better metadata.\n */\n public setupOnce(): void {\n this._ignoreOnError = this._ignoreOnError;\n\n const global = getGlobalObject();\n\n fill(global, 'setTimeout', this._wrapTimeFunction.bind(this));\n fill(global, 'setInterval', this._wrapTimeFunction.bind(this));\n fill(global, 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isString,\n logger,\n} from '@sentry/utils';\n\nimport { eventFromUnknownInput } from '../eventbuilder';\nimport { shouldIgnoreOnError } from '../helpers';\n\n/** JSDoc */\ninterface GlobalHandlersIntegrations {\n onerror: boolean;\n onunhandledrejection: boolean;\n}\n\n/** Global handlers */\nexport class GlobalHandlers implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = GlobalHandlers.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'GlobalHandlers';\n\n /** JSDoc */\n private readonly _options: GlobalHandlersIntegrations;\n\n /** JSDoc */\n private _onErrorHandlerInstalled: boolean = false;\n\n /** JSDoc */\n private _onUnhandledRejectionHandlerInstalled: boolean = false;\n\n /** JSDoc */\n public constructor(options?: GlobalHandlersIntegrations) {\n this._options = {\n onerror: true,\n onunhandledrejection: true,\n ...options,\n };\n }\n /**\n * @inheritDoc\n */\n public setupOnce(): void {\n Error.stackTraceLimit = 50;\n\n if 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true,\n });\n\n event.level = Severity.Error;\n\n addExceptionMechanism(event, {\n handled: false,\n type: 'onunhandledrejection',\n });\n\n currentHub.captureEvent(event, {\n originalException: error,\n });\n\n return;\n },\n type: 'unhandledrejection',\n });\n\n this._onUnhandledRejectionHandlerInstalled = true;\n }\n\n /**\n * This function creates a stack from an old, error-less onerror handler.\n */\n private _eventFromIncompleteOnError(msg: any, url: any, line: any, column: any): Event {\n const ERROR_TYPES_RE = /^(?:[Uu]ncaught (?:exception: )?)?(?:((?:Eval|Internal|Range|Reference|Syntax|Type|URI|)Error): )?(.*)$/i;\n\n // If 'message' is ErrorEvent, get real message from inside\n let message = isErrorEvent(msg) ? msg.message : msg;\n let name;\n\n if (isString(message)) {\n const groups = message.match(ERROR_TYPES_RE);\n if (groups) {\n name = groups[1];\n message = groups[2];\n }\n }\n\n const event = {\n exception: {\n values: [\n {\n type: name || 'Error',\n value: message,\n },\n ],\n },\n };\n\n return this._enhanceEventWithInitialFrame(event, url, line, column);\n }\n\n /**\n * This function creates an Event from an TraceKitStackTrace that has part of it missing.\n */\n private _eventFromIncompleteRejection(error: any): Event {\n return {\n exception: {\n values: [\n {\n type: 'UnhandledRejection',\n value: `Non-Error promise rejection captured with value: ${error}`,\n },\n ],\n },\n };\n }\n\n /** JSDoc */\n private _enhanceEventWithInitialFrame(event: Event, url: any, line: any, column: any): Event {\n event.exception = event.exception || {};\n event.exception.values = event.exception.values || [];\n event.exception.values[0] = event.exception.values[0] || {};\n event.exception.values[0].stacktrace = event.exception.values[0].stacktrace || {};\n event.exception.values[0].stacktrace.frames = event.exception.values[0].stacktrace.frames || [];\n\n const colno = isNaN(parseInt(column, 10)) ? undefined : column;\n const lineno = isNaN(parseInt(line, 10)) ? undefined : line;\n const filename = isString(url) && url.length > 0 ? url : getLocationHref();\n\n if (event.exception.values[0].stacktrace.frames.length === 0) {\n event.exception.values[0].stacktrace.frames.push({\n colno,\n filename,\n function: '?',\n in_app: true,\n lineno,\n });\n }\n\n return event;\n }\n}\n","import { addGlobalEventProcessor, getCurrentHub } from '@sentry/core';\nimport { Event, EventHint, Exception, ExtendedError, Integration } from '@sentry/types';\nimport { isInstanceOf } from '@sentry/utils';\n\nimport { exceptionFromStacktrace } from '../parsers';\nimport { computeStackTrace } from '../tracekit';\n\nconst DEFAULT_KEY = 'cause';\nconst DEFAULT_LIMIT = 5;\n\n/** Adds SDK info to an event. */\nexport class LinkedErrors implements Integration {\n /**\n * @inheritDoc\n */\n public readonly name: string = LinkedErrors.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'LinkedErrors';\n\n /**\n * @inheritDoc\n */\n private 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this._level=t,this._notifyScopeListeners(),this},t.prototype.setTransaction=function(t){return this._transaction=t,this._span&&(this._span.transaction=t),this._notifyScopeListeners(),this},t.prototype.setContext=function(t,e){var n;return this._context=nt.a({},this._context,((n={})[t]=e,n)),this._notifyScopeListeners(),this},t.prototype.setSpan=function(t){return this._span=t,this._notifyScopeListeners(),this},t.prototype.getSpan=function(){return this._span},t.clone=function(e){var n=new t;return e&&(n._breadcrumbs=nt.d(e._breadcrumbs),n._tags=nt.a({},e._tags),n._extra=nt.a({},e._extra),n._context=nt.a({},e._context),n._user=e._user,n._level=e._level,n._span=e._span,n._transaction=e._transaction,n._fingerprint=e._fingerprint,n._eventProcessors=nt.d(e._eventProcessors)),n},t.prototype.clear=function(){return this._breadcrumbs=[],this._tags={},this._extra={},this._user={},this._context={},this._level=void 0,this._transaction=void 0,this._fingerprint=void 0,this._span=void 0,this._notifyScopeListeners(),this},t.prototype.addBreadcrumb=function(t,e){var n=nt.a({timestamp:Object(ft.l)()},t);return this._breadcrumbs=void 0!==e&&e>=0?nt.d(this._breadcrumbs,[n]).slice(-e):nt.d(this._breadcrumbs,[n]),this._notifyScopeListeners(),this},t.prototype.clearBreadcrumbs=function(){return this._breadcrumbs=[],this._notifyScopeListeners(),this},t.prototype._applyFingerprint=function(t){t.fingerprint=t.fingerprint?Array.isArray(t.fingerprint)?t.fingerprint:[t.fingerprint]:[],this._fingerprint&&(t.fingerprint=t.fingerprint.concat(this._fingerprint)),t.fingerprint&&!t.fingerprint.length&&delete t.fingerprint},t.prototype.applyToEvent=function(t,e){return this._extra&&Object.keys(this._extra).length&&(t.extra=nt.a({},this._extra,t.extra)),this._tags&&Object.keys(this._tags).length&&(t.tags=nt.a({},this._tags,t.tags)),this._user&&Object.keys(this._user).length&&(t.user=nt.a({},this._user,t.user)),this._context&&Object.keys(this._context).length&&(t.contexts=nt.a({},this._context,t.contexts)),this._level&&(t.level=this._level),this._transaction&&(t.transaction=this._transaction),this._span&&(t.contexts=nt.a({trace:this._span.getTraceContext()},t.contexts)),this._applyFingerprint(t),t.breadcrumbs=nt.d(t.breadcrumbs||[],this._breadcrumbs),t.breadcrumbs=t.breadcrumbs.length>0?t.breadcrumbs:void 0,this._notifyEventProcessors(nt.d(r(),this._eventProcessors),t,e)},t}(),ht=n("HhP1"),dt=function(){function t(t,e,n){void 0===e&&(e=new pt),void 0===n&&(n=3),this._version=n,this._stack=[],this._stack.push({client:t,scope:e})}return t.prototype._invokeClient=function(t){for(var e,n=[],r=1;r0?t[t.length-1].scope:void 0);return this.getStack().push({client:this.getClient(),scope:e}),e},t.prototype.popScope=function(){return void 0!==this.getStack().pop()},t.prototype.withScope=function(t){var e=this.pushScope();try{t(e)}finally{this.popScope()}},t.prototype.getClient=function(){return this.getStackTop().client},t.prototype.getScope=function(){return this.getStackTop().scope},t.prototype.getStack=function(){return this._stack},t.prototype.getStackTop=function(){return this._stack[this._stack.length-1]},t.prototype.captureException=function(t,e){var n=this._lastEventId=Object(ft.m)(),r=e;if(!e){var o=void 0;try{throw new Error("Sentry syntheticException")}catch(t){o=t}r={originalException:t,syntheticException:o}}return this._invokeClient("captureException",t,nt.a({},r,{event_id:n})),n},t.prototype.captureMessage=function(t,e,n){var r=this._lastEventId=Object(ft.m)(),o=n;if(!n){var i=void 0;try{throw new Error(t)}catch(t){i=t}o={originalException:t,syntheticException:i}}return 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n=this.getStackTop();n.scope&&n.scope.setTag(t,e)},t.prototype.setExtra=function(t,e){var n=this.getStackTop();n.scope&&n.scope.setExtra(t,e)},t.prototype.setContext=function(t,e){var n=this.getStackTop();n.scope&&n.scope.setContext(t,e)},t.prototype.configureScope=function(t){var e=this.getStackTop();e.scope&&e.client&&t(e.scope)},t.prototype.run=function(t){var e=a(this);try{t(this)}finally{a(e)}},t.prototype.getIntegration=function(t){var e=this.getClient();if(!e)return null;try{return e.getIntegration(t)}catch(e){return ht.a.warn("Cannot retrieve integration "+t.id+" from the current Hub"),null}},t.prototype.startSpan=function(t,e){return void 0===e&&(e=!1),this._callExtensionMethod("startSpan",t,e)},t.prototype.traceHeaders=function(){return this._callExtensionMethod("traceHeaders")},t.prototype._callExtensionMethod=function(t){for(var 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r=this,o=e&&e.event_id;return this._processing=!0,this._processEvent(t,e,n).then((function(t){o=t&&t.event_id,r._processing=!1})).then(null,(function(t){ht.a.error(t),r._processing=!1})),o},t.prototype.getDsn=function(){return this._dsn},t.prototype.getOptions=function(){return this._options},t.prototype.flush=function(t){var e=this;return this._isClientProcessing(t).then((function(n){return clearInterval(n.interval),e._getBackend().getTransport().close(t).then((function(t){return n.ready&&t}))}))},t.prototype.close=function(t){var e=this;return this.flush(t).then((function(t){return e.getOptions().enabled=!1,t}))},t.prototype.setupIntegrations=function(){this._isEnabled()&&(this._integrations=w(this._options))},t.prototype.getIntegration=function(t){try{return this._integrations[t.id]||null}catch(e){return ht.a.warn("Cannot retrieve integration "+t.id+" from the current Client"),null}},t.prototype._isClientProcessing=function(t){var e=this;return new lt((function(n){var 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\t__webpack_require__.d = function(exports, name, getter) {\n \t\tif(!__webpack_require__.o(exports, name)) {\n \t\t\tObject.defineProperty(exports, name, { enumerable: true, get: getter });\n \t\t}\n \t};\n\n \t// define __esModule on exports\n \t__webpack_require__.r = function(exports) {\n \t\tif(typeof Symbol !== 'undefined' && Symbol.toStringTag) {\n \t\t\tObject.defineProperty(exports, Symbol.toStringTag, { value: 'Module' });\n \t\t}\n \t\tObject.defineProperty(exports, '__esModule', { value: true });\n \t};\n\n \t// create a fake namespace object\n \t// mode & 1: value is a module id, require it\n \t// mode & 2: merge all properties of value into the ns\n \t// mode & 4: return value when already ns object\n \t// mode & 8|1: behave like require\n \t__webpack_require__.t = function(value, mode) {\n \t\tif(mode & 1) value = __webpack_require__(value);\n \t\tif(mode & 8) return value;\n \t\tif((mode & 4) && typeof value === 'object' && value && value.__esModule) return value;\n 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\t__webpack_require__.oe = function(err) { console.error(err); throw err; };\n\n \tvar jsonpArray = window[\"webpackJsonp\"] = window[\"webpackJsonp\"] || [];\n \tvar oldJsonpFunction = jsonpArray.push.bind(jsonpArray);\n \tjsonpArray.push = webpackJsonpCallback;\n \tjsonpArray = jsonpArray.slice();\n \tfor(var i = 0; i < jsonpArray.length; i++) webpackJsonpCallback(jsonpArray[i]);\n \tvar parentJsonpFunction = oldJsonpFunction;\n\n\n \t// Load entry module and return exports\n \treturn __webpack_require__(__webpack_require__.s = 0);\n","import { Event, Integration, StackFrame, WrappedFunction } from '@sentry/types';\n\nimport { isString } from './is';\nimport { snipLine } from './string';\n\n/** Internal */\ninterface SentryGlobal {\n Sentry?: {\n Integrations?: Integration[];\n };\n SENTRY_ENVIRONMENT?: string;\n SENTRY_DSN?: string;\n SENTRY_RELEASE?: {\n id?: string;\n };\n __SENTRY__: {\n globalEventProcessors: any;\n hub: any;\n logger: any;\n };\n}\n\n/**\n * Requires a module which is protected against bundler minification.\n *\n * @param request The module path to resolve\n */\nexport function dynamicRequire(mod: any, request: string): any {\n // tslint:disable-next-line: no-unsafe-any\n return mod.require(request);\n}\n\n/**\n * Checks whether we're in the Node.js or Browser environment\n *\n * @returns Answer to given question\n */\nexport function isNodeEnv(): boolean {\n // tslint:disable:strict-type-predicates\n return Object.prototype.toString.call(typeof process !== 'undefined' ? process : 0) === '[object process]';\n}\n\nconst fallbackGlobalObject = {};\n\n/**\n * Safely get global scope object\n *\n * @returns Global scope object\n */\nexport function getGlobalObject(): T & SentryGlobal {\n return (isNodeEnv()\n ? global\n : typeof window !== 'undefined'\n ? window\n : typeof self !== 'undefined'\n ? self\n : fallbackGlobalObject) as T & SentryGlobal;\n}\n// tslint:enable:strict-type-predicates\n\n/**\n * Extended Window interface that allows for Crypto API usage in IE browsers\n */\ninterface MsCryptoWindow extends Window {\n msCrypto?: Crypto;\n}\n\n/**\n * UUID4 generator\n *\n * @returns string Generated UUID4.\n */\nexport function uuid4(): string {\n const global = getGlobalObject() as MsCryptoWindow;\n const crypto = global.crypto || global.msCrypto;\n\n if (!(crypto === void 0) && crypto.getRandomValues) {\n // Use window.crypto API if available\n const arr = new Uint16Array(8);\n crypto.getRandomValues(arr);\n\n // set 4 in byte 7\n // tslint:disable-next-line:no-bitwise\n arr[3] = (arr[3] & 0xfff) | 0x4000;\n // set 2 most significant bits of byte 9 to '10'\n // tslint:disable-next-line:no-bitwise\n arr[4] = (arr[4] & 0x3fff) | 0x8000;\n\n const pad = (num: number): string => {\n let v = num.toString(16);\n while (v.length < 4) {\n v = `0${v}`;\n }\n return v;\n };\n\n return (\n pad(arr[0]) + pad(arr[1]) + pad(arr[2]) + pad(arr[3]) + pad(arr[4]) + pad(arr[5]) + pad(arr[6]) + pad(arr[7])\n );\n }\n // http://stackoverflow.com/questions/105034/how-to-create-a-guid-uuid-in-javascript/2117523#2117523\n return 'xxxxxxxxxxxx4xxxyxxxxxxxxxxxxxxx'.replace(/[xy]/g, c => {\n // tslint:disable-next-line:no-bitwise\n const r = (Math.random() * 16) | 0;\n // tslint:disable-next-line:no-bitwise\n const v = c === 'x' ? r : (r & 0x3) | 0x8;\n return v.toString(16);\n });\n}\n\n/**\n * Parses string form of URL into an object\n * // borrowed from https://tools.ietf.org/html/rfc3986#appendix-B\n * // intentionally using regex and not href parsing trick because React Native and other\n * // environments where DOM might not be available\n * @returns parsed URL object\n */\nexport function parseUrl(\n url: string,\n): {\n host?: string;\n path?: string;\n protocol?: string;\n relative?: string;\n} {\n if (!url) {\n return {};\n }\n\n const match = url.match(/^(([^:\\/?#]+):)?(\\/\\/([^\\/?#]*))?([^?#]*)(\\?([^#]*))?(#(.*))?$/);\n\n if (!match) {\n return {};\n }\n\n // coerce to undefined values to empty string so we don't get 'undefined'\n const query = match[6] || '';\n const fragment = match[8] || '';\n return {\n host: match[4],\n path: match[5],\n protocol: match[2],\n relative: match[5] + query + fragment, // everything minus origin\n };\n}\n\n/**\n * Extracts either message or type+value from an event that can be used for user-facing logs\n * @returns event's description\n */\nexport function getEventDescription(event: Event): string {\n if (event.message) {\n return event.message;\n }\n if (event.exception && event.exception.values && event.exception.values[0]) {\n const exception = event.exception.values[0];\n\n if (exception.type && exception.value) {\n return `${exception.type}: ${exception.value}`;\n }\n return exception.type || exception.value || event.event_id || '';\n }\n return event.event_id || '';\n}\n\n/** JSDoc */\ninterface ExtensibleConsole extends Console {\n [key: string]: any;\n}\n\n/** JSDoc */\nexport function consoleSandbox(callback: () => any): any {\n const global = getGlobalObject();\n const levels = ['debug', 'info', 'warn', 'error', 'log', 'assert'];\n\n if (!('console' in global)) {\n return callback();\n }\n\n const originalConsole = global.console as ExtensibleConsole;\n const wrappedLevels: { [key: string]: any } = {};\n\n // Restore all wrapped console methods\n levels.forEach(level => {\n if (level in global.console && (originalConsole[level] as WrappedFunction).__sentry_original__) {\n wrappedLevels[level] = originalConsole[level] as WrappedFunction;\n originalConsole[level] = (originalConsole[level] as WrappedFunction).__sentry_original__;\n }\n });\n\n // Perform callback manipulations\n const result = callback();\n\n // Revert restoration to wrapped state\n Object.keys(wrappedLevels).forEach(level => {\n originalConsole[level] = wrappedLevels[level];\n });\n\n return result;\n}\n\n/**\n * Adds exception values, type and value to an synthetic Exception.\n * @param event The event to modify.\n * @param value Value of the exception.\n * @param type Type of the exception.\n * @hidden\n */\nexport function addExceptionTypeValue(event: Event, value?: string, type?: string): void {\n event.exception = event.exception || {};\n event.exception.values = event.exception.values || [];\n event.exception.values[0] = event.exception.values[0] || {};\n event.exception.values[0].value = event.exception.values[0].value || value || '';\n event.exception.values[0].type = event.exception.values[0].type || type || 'Error';\n}\n\n/**\n * Adds exception mechanism to a given event.\n * @param event The event to modify.\n * @param mechanism Mechanism of the mechanism.\n * @hidden\n */\nexport function addExceptionMechanism(\n event: Event,\n mechanism: {\n [key: string]: any;\n } = {},\n): void {\n // TODO: Use real type with `keyof Mechanism` thingy and maybe make it better?\n try {\n // @ts-ignore\n // tslint:disable:no-non-null-assertion\n event.exception!.values![0].mechanism = event.exception!.values![0].mechanism || {};\n Object.keys(mechanism).forEach(key => {\n // @ts-ignore\n event.exception!.values![0].mechanism[key] = mechanism[key];\n });\n } catch (_oO) {\n // no-empty\n }\n}\n\n/**\n * A safe form of location.href\n */\nexport function getLocationHref(): string {\n try {\n return document.location.href;\n } catch (oO) {\n return '';\n }\n}\n\n/**\n * Given a child DOM element, returns a query-selector statement describing that\n * and its ancestors\n * e.g. [HTMLElement] => body > div > input#foo.btn[name=baz]\n * @returns generated DOM path\n */\nexport function htmlTreeAsString(elem: unknown): string {\n type SimpleNode = {\n parentNode: SimpleNode;\n } | null;\n\n // try/catch both:\n // - accessing event.target (see getsentry/raven-js#838, #768)\n // - `htmlTreeAsString` because it's complex, and just accessing the DOM incorrectly\n // - can throw an exception in some circumstances.\n try {\n let currentElem = elem as SimpleNode;\n const MAX_TRAVERSE_HEIGHT = 5;\n const MAX_OUTPUT_LEN = 80;\n const out = [];\n let height = 0;\n let len = 0;\n const separator = ' > ';\n const sepLength = separator.length;\n let nextStr;\n\n while (currentElem && height++ < MAX_TRAVERSE_HEIGHT) {\n nextStr = _htmlElementAsString(currentElem);\n // bail out if\n // - nextStr is the 'html' element\n // - the length of the string that would be created exceeds MAX_OUTPUT_LEN\n // (ignore this limit if we are on the first iteration)\n if (nextStr === 'html' || (height > 1 && len + out.length * sepLength + nextStr.length >= MAX_OUTPUT_LEN)) {\n break;\n }\n\n out.push(nextStr);\n\n len += nextStr.length;\n currentElem = currentElem.parentNode;\n }\n\n return out.reverse().join(separator);\n } catch (_oO) {\n return '';\n }\n}\n\n/**\n * Returns a simple, query-selector representation of a DOM element\n * e.g. [HTMLElement] => input#foo.btn[name=baz]\n * @returns generated DOM path\n */\nfunction _htmlElementAsString(el: unknown): string {\n const elem = el as {\n getAttribute(key: string): string; // tslint:disable-line:completed-docs\n tagName?: string;\n id?: string;\n className?: string;\n };\n\n const out = [];\n let className;\n let classes;\n let key;\n let attr;\n let i;\n\n if (!elem || !elem.tagName) {\n return '';\n }\n\n out.push(elem.tagName.toLowerCase());\n if (elem.id) {\n out.push(`#${elem.id}`);\n }\n\n className = elem.className;\n if (className && isString(className)) {\n classes = className.split(/\\s+/);\n for (i = 0; i < classes.length; i++) {\n out.push(`.${classes[i]}`);\n }\n }\n const attrWhitelist = ['type', 'name', 'title', 'alt'];\n for (i = 0; i < attrWhitelist.length; i++) {\n key = attrWhitelist[i];\n attr = elem.getAttribute(key);\n if (attr) {\n out.push(`[${key}=\"${attr}\"]`);\n }\n }\n return out.join('');\n}\n\nconst INITIAL_TIME = Date.now();\nlet prevNow = 0;\n\n/**\n * Cross platform compatible partial performance implementation\n */\ninterface CrossPlatformPerformance {\n /**\n * Returns the current timestamp in ms\n */\n now(): number;\n timeOrigin: number;\n}\n\nconst performanceFallback: CrossPlatformPerformance = {\n now(): number {\n let now = Date.now() - INITIAL_TIME;\n if (now < prevNow) {\n now = prevNow;\n }\n prevNow = now;\n return now;\n },\n timeOrigin: INITIAL_TIME,\n};\n\nexport const crossPlatformPerformance: CrossPlatformPerformance = (() => {\n if (isNodeEnv()) {\n try {\n const perfHooks = dynamicRequire(module, 'perf_hooks') as { performance: CrossPlatformPerformance };\n return perfHooks.performance;\n } catch (_) {\n return performanceFallback;\n }\n }\n\n if (getGlobalObject().performance) {\n // Polyfill for performance.timeOrigin.\n //\n // While performance.timing.navigationStart is deprecated in favor of performance.timeOrigin, performance.timeOrigin\n // is not as widely supported. Namely, performance.timeOrigin is undefined in Safari as of writing.\n // tslint:disable-next-line:strict-type-predicates\n if (performance.timeOrigin === undefined) {\n // As of writing, performance.timing is not available in Web Workers in mainstream browsers, so it is not always a\n // valid fallback. In the absence of a initial time provided by the browser, fallback to INITIAL_TIME.\n // @ts-ignore\n // tslint:disable-next-line:deprecation\n performance.timeOrigin = (performance.timing && performance.timing.navigationStart) || INITIAL_TIME;\n }\n }\n\n return getGlobalObject().performance || performanceFallback;\n})();\n\n/**\n * Returns a timestamp in seconds with milliseconds precision since the UNIX epoch calculated with the monotonic clock.\n */\nexport function timestampWithMs(): number {\n return (crossPlatformPerformance.timeOrigin + crossPlatformPerformance.now()) / 1000;\n}\n\n// https://semver.org/#is-there-a-suggested-regular-expression-regex-to-check-a-semver-string\nconst SEMVER_REGEXP = /^(0|[1-9]\\d*)\\.(0|[1-9]\\d*)\\.(0|[1-9]\\d*)(?:-((?:0|[1-9]\\d*|\\d*[a-zA-Z-][0-9a-zA-Z-]*)(?:\\.(?:0|[1-9]\\d*|\\d*[a-zA-Z-][0-9a-zA-Z-]*))*))?(?:\\+([0-9a-zA-Z-]+(?:\\.[0-9a-zA-Z-]+)*))?$/;\n\n/**\n * Represents Semantic Versioning object\n */\ninterface SemVer {\n major?: number;\n minor?: number;\n patch?: number;\n prerelease?: string;\n buildmetadata?: string;\n}\n\n/**\n * Parses input into a SemVer interface\n * @param input string representation of a semver version\n */\nexport function parseSemver(input: string): SemVer {\n const match = input.match(SEMVER_REGEXP) || [];\n const major = parseInt(match[1], 10);\n const minor = parseInt(match[2], 10);\n const patch = parseInt(match[3], 10);\n return {\n buildmetadata: match[5],\n major: isNaN(major) ? undefined : major,\n minor: isNaN(minor) ? undefined : minor,\n patch: isNaN(patch) ? undefined : patch,\n prerelease: match[4],\n };\n}\n\nconst defaultRetryAfter = 60 * 1000; // 60 seconds\n\n/**\n * Extracts Retry-After value from the request header or returns default value\n * @param now current unix timestamp\n * @param header string representation of 'Retry-After' header\n */\nexport function parseRetryAfterHeader(now: number, header?: string | number | null): number {\n if (!header) {\n return defaultRetryAfter;\n }\n\n const headerDelay = parseInt(`${header}`, 10);\n if (!isNaN(headerDelay)) {\n return headerDelay * 1000;\n }\n\n const headerDate = Date.parse(`${header}`);\n if (!isNaN(headerDate)) {\n return headerDate - now;\n }\n\n return defaultRetryAfter;\n}\n\nconst defaultFunctionName = '';\n\n/**\n * Safely extract function name from itself\n */\nexport function getFunctionName(fn: unknown): string {\n try {\n if (!fn || typeof fn !== 'function') {\n return defaultFunctionName;\n }\n return fn.name || defaultFunctionName;\n } catch (e) {\n // Just accessing custom props in some Selenium environments\n // can cause a \"Permission denied\" exception (see raven-js#495).\n return defaultFunctionName;\n }\n}\n\n/**\n * This function adds context (pre/post/line) lines to the provided frame\n *\n * @param lines string[] containing all lines\n * @param frame StackFrame that will be mutated\n * @param linesOfContext number of context lines we want to add pre/post\n */\nexport function addContextToFrame(lines: string[], frame: StackFrame, linesOfContext: number = 5): void {\n const lineno = frame.lineno || 0;\n const maxLines = lines.length;\n const sourceLine = Math.max(Math.min(maxLines, lineno - 1), 0);\n\n frame.pre_context = lines\n .slice(Math.max(0, sourceLine - linesOfContext), sourceLine)\n .map((line: string) => snipLine(line, 0));\n\n frame.context_line = snipLine(lines[Math.min(maxLines - 1, sourceLine)], frame.colno || 0);\n\n frame.post_context = lines\n .slice(Math.min(sourceLine + 1, maxLines), sourceLine + 1 + linesOfContext)\n .map((line: string) => snipLine(line, 0));\n}\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./VlDiGeometria.js\") );\n\t\t\t}, \"route-VlDiGeometria\");\n\t\t}\n\n\t\texport default Async(load);\n\t","// tslint:disable:no-unsafe-any\n/**\n * Memo class used for decycle json objects. Uses WeakSet if available otherwise array.\n */\nexport class Memo {\n /** Determines if WeakSet is available */\n private readonly _hasWeakSet: boolean;\n /** Either WeakSet or Array */\n private readonly _inner: any;\n\n public constructor() {\n // tslint:disable-next-line\n this._hasWeakSet = typeof WeakSet === 'function';\n this._inner = this._hasWeakSet ? new WeakSet() : [];\n }\n\n /**\n * Sets obj to remember.\n * @param obj Object to remember\n */\n public memoize(obj: any): boolean {\n if (this._hasWeakSet) {\n if (this._inner.has(obj)) {\n return true;\n }\n this._inner.add(obj);\n return false;\n }\n // tslint:disable-next-line:prefer-for-of\n for (let i = 0; i < this._inner.length; i++) {\n const value = this._inner[i];\n if (value === obj) {\n return true;\n }\n }\n this._inner.push(obj);\n return false;\n }\n\n /**\n * Removes object from internal storage.\n * @param obj Object to forget\n */\n public unmemoize(obj: any): void {\n if (this._hasWeakSet) {\n this._inner.delete(obj);\n } else {\n for (let i = 0; i < this._inner.length; i++) {\n if (this._inner[i] === obj) {\n this._inner.splice(i, 1);\n break;\n }\n }\n }\n }\n}\n","import {createContext} from \"preact\";\n\nexport default createContext(\"White\");\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./BasiDiDati.js\") );\n\t\t\t}, \"route-BasiDiDati\");\n\t\t}\n\n\t\texport default Async(load);\n\t","/**\n * Checks whether given value's type is one of a few Error or Error-like\n * {@link isError}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isError(wat: any): boolean {\n switch (Object.prototype.toString.call(wat)) {\n case '[object Error]':\n return true;\n case '[object Exception]':\n return true;\n case '[object DOMException]':\n return true;\n default:\n return isInstanceOf(wat, Error);\n }\n}\n\n/**\n * Checks whether given value's type is ErrorEvent\n * {@link isErrorEvent}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isErrorEvent(wat: any): boolean {\n return Object.prototype.toString.call(wat) === '[object ErrorEvent]';\n}\n\n/**\n * Checks whether given value's type is DOMError\n * {@link isDOMError}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isDOMError(wat: any): boolean {\n return Object.prototype.toString.call(wat) === '[object DOMError]';\n}\n\n/**\n * Checks whether given value's type is DOMException\n * {@link isDOMException}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isDOMException(wat: any): boolean {\n return Object.prototype.toString.call(wat) === '[object DOMException]';\n}\n\n/**\n * Checks whether given value's type is a string\n * {@link isString}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isString(wat: any): boolean {\n return Object.prototype.toString.call(wat) === '[object String]';\n}\n\n/**\n * Checks whether given value's is a primitive (undefined, null, number, boolean, string)\n * {@link isPrimitive}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isPrimitive(wat: any): boolean {\n return wat === null || (typeof wat !== 'object' && typeof wat !== 'function');\n}\n\n/**\n * Checks whether given value's type is an object literal\n * {@link isPlainObject}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isPlainObject(wat: any): boolean {\n return Object.prototype.toString.call(wat) === '[object Object]';\n}\n\n/**\n * Checks whether given value's type is an Event instance\n * {@link isEvent}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isEvent(wat: any): boolean {\n // tslint:disable-next-line:strict-type-predicates\n return typeof Event !== 'undefined' && isInstanceOf(wat, Event);\n}\n\n/**\n * Checks whether given value's type is an Element instance\n * {@link isElement}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isElement(wat: any): boolean {\n // tslint:disable-next-line:strict-type-predicates\n return typeof Element !== 'undefined' && isInstanceOf(wat, Element);\n}\n\n/**\n * Checks whether given value's type is an regexp\n * {@link isRegExp}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isRegExp(wat: any): boolean {\n return Object.prototype.toString.call(wat) === '[object RegExp]';\n}\n\n/**\n * Checks whether given value has a then function.\n * @param wat A value to be checked.\n */\nexport function isThenable(wat: any): boolean {\n // tslint:disable:no-unsafe-any\n return Boolean(wat && wat.then && typeof wat.then === 'function');\n // tslint:enable:no-unsafe-any\n}\n\n/**\n * Checks whether given value's type is a SyntheticEvent\n * {@link isSyntheticEvent}.\n *\n * @param wat A value to be checked.\n * @returns A boolean representing the result.\n */\nexport function isSyntheticEvent(wat: any): boolean {\n // tslint:disable-next-line:no-unsafe-any\n return isPlainObject(wat) && 'nativeEvent' in wat && 'preventDefault' in wat && 'stopPropagation' in wat;\n}\n/**\n * Checks whether given value's type is an instance of provided constructor.\n * {@link isInstanceOf}.\n *\n * @param wat A value to be checked.\n * @param base A constructor to be used in a check.\n * @returns A boolean representing the result.\n */\nexport function isInstanceOf(wat: any, base: any): boolean {\n try {\n // tslint:disable-next-line:no-unsafe-any\n return wat instanceof base;\n } catch (_e) {\n return false;\n }\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"footer\":\"footer__3lyac\"};","// Slightly modified (no IE8 support, ES6) and transcribed to TypeScript\n// https://raw.githubusercontent.com/calvinmetcalf/rollup-plugin-node-builtins/master/src/es6/path.js\n\n/** JSDoc */\nfunction normalizeArray(parts: string[], allowAboveRoot?: boolean): string[] {\n // if the path tries to go above the root, `up` ends up > 0\n let up = 0;\n for (let i = parts.length - 1; i >= 0; i--) {\n const last = parts[i];\n if (last === '.') {\n parts.splice(i, 1);\n } else if (last === '..') {\n parts.splice(i, 1);\n up++;\n } else if (up) {\n parts.splice(i, 1);\n up--;\n }\n }\n\n // if the path is allowed to go above the root, restore leading ..s\n if (allowAboveRoot) {\n for (; up--; up) {\n parts.unshift('..');\n }\n }\n\n return parts;\n}\n\n// Split a filename into [root, dir, basename, ext], unix version\n// 'root' is just a slash, or nothing.\nconst splitPathRe = /^(\\/?|)([\\s\\S]*?)((?:\\.{1,2}|[^\\/]+?|)(\\.[^.\\/]*|))(?:[\\/]*)$/;\n/** JSDoc */\nfunction splitPath(filename: string): string[] {\n const parts = splitPathRe.exec(filename);\n return parts ? parts.slice(1) : [];\n}\n\n// path.resolve([from ...], to)\n// posix version\n/** JSDoc */\nexport function resolve(...args: string[]): string {\n let resolvedPath = '';\n let resolvedAbsolute = false;\n\n for (let i = args.length - 1; i >= -1 && !resolvedAbsolute; i--) {\n const path = i >= 0 ? args[i] : '/';\n\n // Skip empty entries\n if (!path) {\n continue;\n }\n\n resolvedPath = `${path}/${resolvedPath}`;\n resolvedAbsolute = path.charAt(0) === '/';\n }\n\n // At this point the path should be resolved to a full absolute path, but\n // handle relative paths to be safe (might happen when process.cwd() fails)\n\n // Normalize the path\n resolvedPath = normalizeArray(resolvedPath.split('/').filter(p => !!p), !resolvedAbsolute).join('/');\n\n return (resolvedAbsolute ? '/' : '') + resolvedPath || '.';\n}\n\n/** JSDoc */\nfunction trim(arr: string[]): string[] {\n let start = 0;\n for (; start < arr.length; start++) {\n if (arr[start] !== '') {\n break;\n }\n }\n\n let end = arr.length - 1;\n for (; end >= 0; end--) {\n if (arr[end] !== '') {\n break;\n }\n }\n\n if (start > end) {\n return [];\n }\n return arr.slice(start, end - start + 1);\n}\n\n// path.relative(from, to)\n// posix version\n/** JSDoc */\nexport function relative(from: string, to: string): string {\n // tslint:disable:no-parameter-reassignment\n from = resolve(from).substr(1);\n to = resolve(to).substr(1);\n\n const fromParts = trim(from.split('/'));\n const toParts = trim(to.split('/'));\n\n const length = Math.min(fromParts.length, toParts.length);\n let samePartsLength = length;\n for (let i = 0; i < length; i++) {\n if (fromParts[i] !== toParts[i]) {\n samePartsLength = i;\n break;\n }\n }\n\n let outputParts = [];\n for (let i = samePartsLength; i < fromParts.length; i++) {\n outputParts.push('..');\n }\n\n outputParts = outputParts.concat(toParts.slice(samePartsLength));\n\n return outputParts.join('/');\n}\n\n// path.normalize(path)\n// posix version\n/** JSDoc */\nexport function normalizePath(path: string): string {\n const isPathAbsolute = isAbsolute(path);\n const trailingSlash = path.substr(-1) === '/';\n\n // Normalize the path\n let normalizedPath = normalizeArray(path.split('/').filter(p => !!p), !isPathAbsolute).join('/');\n\n if (!normalizedPath && !isPathAbsolute) {\n normalizedPath = '.';\n }\n if (normalizedPath && trailingSlash) {\n normalizedPath += '/';\n }\n\n return (isPathAbsolute ? '/' : '') + normalizedPath;\n}\n\n// posix version\n/** JSDoc */\nexport function isAbsolute(path: string): boolean {\n return path.charAt(0) === '/';\n}\n\n// posix version\n/** JSDoc */\nexport function join(...args: string[]): string {\n return normalizePath(args.join('/'));\n}\n\n/** JSDoc */\nexport function dirname(path: string): string {\n const result = splitPath(path);\n const root = result[0];\n let dir = result[1];\n\n if (!root && !dir) {\n // No dirname whatsoever\n return '.';\n }\n\n if (dir) {\n // It has a dirname, strip trailing slash\n dir = dir.substr(0, dir.length - 1);\n }\n\n return root + dir;\n}\n\n/** JSDoc */\nexport function basename(path: string, ext?: string): string {\n let f = splitPath(path)[2];\n if (ext && f.substr(ext.length * -1) === ext) {\n f = f.substr(0, f.length - ext.length);\n }\n return f;\n}\n","import { EventProcessor, Hub, Integration } from '@sentry/types';\nimport { getGlobalObject, supportsReportingObserver } from '@sentry/utils';\n\n/** JSDoc */\ninterface Report {\n [key: string]: any;\n type: ReportTypes;\n url: string;\n body?: ReportBody;\n}\n\n/** JSDoc */\nenum ReportTypes {\n /** JSDoc */\n Crash = 'crash',\n /** JSDoc */\n Deprecation = 'deprecation',\n /** JSDoc */\n Intervention = 'intervention',\n}\n\n/** JSDoc */\ntype ReportBody = CrashReportBody | DeprecationReportBody | InterventionReportBody;\n\n/** JSDoc */\ninterface CrashReportBody {\n [key: string]: any;\n crashId: string;\n reason?: string;\n}\n\n/** JSDoc */\ninterface DeprecationReportBody {\n [key: string]: any;\n id: string;\n anticipatedRemoval?: Date;\n message: string;\n sourceFile?: string;\n lineNumber?: number;\n columnNumber?: number;\n}\n\n/** JSDoc */\ninterface InterventionReportBody {\n [key: string]: any;\n id: string;\n message: string;\n sourceFile?: string;\n lineNumber?: number;\n columnNumber?: number;\n}\n\n/** Reporting API integration - https://w3c.github.io/reporting/ */\nexport class ReportingObserver implements Integration {\n /**\n * @inheritDoc\n */\n public readonly name: string = ReportingObserver.id;\n /**\n * @inheritDoc\n */\n public static id: string = 'ReportingObserver';\n\n /**\n * Returns current hub.\n */\n private _getCurrentHub?: () => Hub;\n\n /**\n * @inheritDoc\n */\n public constructor(\n private readonly _options: {\n types?: ReportTypes[];\n } = {\n types: [ReportTypes.Crash, ReportTypes.Deprecation, ReportTypes.Intervention],\n },\n ) {}\n\n /**\n * @inheritDoc\n */\n public setupOnce(_: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n // tslint:disable:no-unsafe-any\n\n if (!supportsReportingObserver()) {\n return;\n }\n\n this._getCurrentHub = getCurrentHub;\n\n const observer = new (getGlobalObject()).ReportingObserver(this.handler.bind(this), {\n buffered: true,\n types: this._options.types,\n });\n\n observer.observe();\n }\n\n /**\n * @inheritDoc\n */\n public handler(reports: Report[]): void {\n const hub = this._getCurrentHub && this._getCurrentHub();\n if (!hub || !hub.getIntegration(ReportingObserver)) {\n return;\n }\n for (const report of reports) {\n hub.withScope(scope => {\n scope.setExtra('url', report.url);\n\n const label = `ReportingObserver [${report.type}]`;\n let details = 'No details available';\n\n if (report.body) {\n // Object.keys doesn't work on ReportBody, as all properties are inheirted\n const plainBody: {\n [key: string]: any;\n } = {};\n\n // tslint:disable-next-line:forin\n for (const prop in report.body) {\n plainBody[prop] = report.body[prop];\n }\n\n scope.setExtra('body', plainBody);\n\n if (report.type === ReportTypes.Crash) {\n const body = report.body as CrashReportBody;\n // A fancy way to create a message out of crashId OR reason OR both OR fallback\n details = [body.crashId || '', body.reason || ''].join(' ').trim() || details;\n } else {\n const body = report.body as DeprecationReportBody | InterventionReportBody;\n details = body.message || details;\n }\n }\n\n hub.captureMessage(`${label}: ${details}`);\n });\n }\n }\n}\n","import { Event, EventProcessor, Hub, Integration } from '@sentry/types';\nimport { getGlobalObject, logger } from '@sentry/utils';\n\n// See https://github.com/angular/angular.js/blob/v1.4.7/src/minErr.js\nconst angularPattern = /^\\[((?:[$a-zA-Z0-9]+:)?(?:[$a-zA-Z0-9]+))\\] (.*?)\\n?(\\S+)$/;\n\n/**\n * AngularJS integration\n *\n * Provides an $exceptionHandler for AngularJS\n */\nexport class Angular implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = Angular.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'AngularJS';\n\n /**\n * moduleName used in Angular's DI resolution algorithm\n */\n public static moduleName: string = 'ngSentry';\n\n /**\n * Angular's instance\n */\n private readonly _angular: any;\n\n /**\n * Returns current hub.\n */\n private _getCurrentHub?: () => Hub;\n\n /**\n * @inheritDoc\n */\n public constructor(options: { angular?: any } = {}) {\n // tslint:disable-next-line: no-unsafe-any\n this._angular = options.angular || getGlobalObject().angular;\n }\n\n /**\n * @inheritDoc\n */\n public setupOnce(_: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n if (!this._angular) {\n logger.error('AngularIntegration is missing an Angular instance');\n return;\n }\n\n this._getCurrentHub = getCurrentHub;\n\n // tslint:disable: no-unsafe-any\n this._angular.module(Angular.moduleName, []).config([\n '$provide',\n ($provide: any) => {\n $provide.decorator('$exceptionHandler', ['$delegate', this._$exceptionHandlerDecorator.bind(this)]);\n },\n ]);\n // tslint:enable: no-unsafe-any\n }\n\n /**\n * Angular's exceptionHandler for Sentry integration\n */\n // tslint:disable-next-line: no-unsafe-any\n private _$exceptionHandlerDecorator($delegate: any): any {\n return (exception: Error, cause?: string) => {\n const hub = this._getCurrentHub && this._getCurrentHub();\n\n if (hub && hub.getIntegration(Angular)) {\n hub.withScope(scope => {\n if (cause) {\n scope.setExtra('cause', cause);\n }\n\n scope.addEventProcessor((event: Event) => {\n const ex = event.exception && event.exception.values && event.exception.values[0];\n\n if (ex) {\n const matches = angularPattern.exec(ex.value || '');\n\n if (matches) {\n // This type now becomes something like: $rootScope:inprog\n ex.type = matches[1];\n ex.value = matches[2];\n event.message = `${ex.type}: ${ex.value}`;\n // auto set a new tag specifically for the angular error url\n event.extra = {\n ...event.extra,\n angularDocs: matches[3].substr(0, 250),\n };\n }\n }\n\n return event;\n });\n\n hub.captureException(exception);\n });\n }\n // tslint:disable-next-line: no-unsafe-any\n $delegate(exception, cause);\n };\n }\n}\n","import { EventProcessor, Hub, Integration, Severity } from '@sentry/types';\nimport { fill, getGlobalObject, safeJoin } from '@sentry/utils';\n\nconst global = getGlobalObject();\n\n/** Send Console API calls as Sentry Events */\nexport class CaptureConsole implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = CaptureConsole.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'CaptureConsole';\n\n /**\n * @inheritDoc\n */\n private readonly _levels: string[] = ['log', 'info', 'warn', 'error', 'debug', 'assert'];\n\n /**\n * @inheritDoc\n */\n public constructor(options: { levels?: string[] } = {}) {\n if (options.levels) {\n this._levels = options.levels;\n }\n }\n\n /**\n * @inheritDoc\n */\n public setupOnce(_: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n if (!('console' in global)) {\n return;\n }\n\n this._levels.forEach((level: string) => {\n if (!(level in global.console)) {\n return;\n }\n\n fill(global.console, level, (originalConsoleLevel: () => any) => (...args: any[]) => {\n const hub = getCurrentHub();\n\n if (hub.getIntegration(CaptureConsole)) {\n hub.withScope(scope => {\n scope.setLevel(Severity.fromString(level));\n scope.setExtra('arguments', args);\n scope.addEventProcessor(event => {\n event.logger = 'console';\n return event;\n });\n\n let message = safeJoin(args, ' ');\n if (level === 'assert') {\n if (args[0] === false) {\n message = `Assertion failed: ${safeJoin(args.slice(1), ' ') || 'console.assert'}`;\n scope.setExtra('arguments', args.slice(1));\n hub.captureMessage(message);\n }\n } else {\n hub.captureMessage(message);\n }\n });\n }\n\n // this fails for some browsers. :(\n if (originalConsoleLevel) {\n Function.prototype.apply.call(originalConsoleLevel, global.console, args);\n }\n });\n });\n }\n}\n","import { Event, EventHint, EventProcessor, Hub, Integration } from '@sentry/types';\nimport { consoleSandbox } from '@sentry/utils';\n\n/** JSDoc */\ninterface DebugOptions {\n stringify?: boolean;\n debugger?: boolean;\n}\n\n/** JSDoc */\nexport class Debug implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = Debug.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'Debug';\n\n /** JSDoc */\n private readonly _options: DebugOptions;\n\n /**\n * @inheritDoc\n */\n public constructor(options?: DebugOptions) {\n this._options = {\n debugger: false,\n stringify: false,\n ...options,\n };\n }\n\n /**\n * @inheritDoc\n */\n public setupOnce(addGlobalEventProcessor: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n addGlobalEventProcessor((event: Event, hint?: EventHint) => {\n const self = getCurrentHub().getIntegration(Debug);\n if (self) {\n // tslint:disable:no-console\n // tslint:disable:no-debugger\n if (self._options.debugger) {\n debugger;\n }\n\n consoleSandbox(() => {\n if (self._options.stringify) {\n console.log(JSON.stringify(event, null, 2));\n if (hint) {\n console.log(JSON.stringify(hint, null, 2));\n }\n } else {\n console.log(event);\n if (hint) {\n console.log(hint);\n }\n }\n });\n }\n return event;\n });\n }\n}\n","import { Event, EventProcessor, Exception, Hub, Integration, StackFrame } from '@sentry/types';\n\n/** Deduplication filter */\nexport class Dedupe implements Integration {\n /**\n * @inheritDoc\n */\n private _previousEvent?: Event;\n\n /**\n * @inheritDoc\n */\n public name: string = Dedupe.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'Dedupe';\n\n /**\n * @inheritDoc\n */\n public setupOnce(addGlobalEventProcessor: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n addGlobalEventProcessor((currentEvent: Event) => {\n const self = getCurrentHub().getIntegration(Dedupe);\n if (self) {\n // Juuust in case something goes wrong\n try {\n if (self._shouldDropEvent(currentEvent, self._previousEvent)) {\n return null;\n }\n } catch (_oO) {\n return (self._previousEvent = currentEvent);\n }\n\n return (self._previousEvent = currentEvent);\n }\n return currentEvent;\n });\n }\n\n /** JSDoc */\n private _shouldDropEvent(currentEvent: Event, previousEvent?: Event): boolean {\n if (!previousEvent) {\n return false;\n }\n\n if (this._isSameMessageEvent(currentEvent, previousEvent)) {\n return true;\n }\n\n if (this._isSameExceptionEvent(currentEvent, previousEvent)) {\n return true;\n }\n\n return false;\n }\n\n /** JSDoc */\n private _isSameMessageEvent(currentEvent: Event, previousEvent: Event): boolean {\n const currentMessage = currentEvent.message;\n const previousMessage = previousEvent.message;\n\n // If neither event has a message property, they were both exceptions, so bail out\n if (!currentMessage && !previousMessage) {\n return false;\n }\n\n // If only one event has a stacktrace, but not the other one, they are not the same\n if ((currentMessage && !previousMessage) || (!currentMessage && previousMessage)) {\n return false;\n }\n\n if (currentMessage !== previousMessage) {\n return false;\n }\n\n if (!this._isSameFingerprint(currentEvent, previousEvent)) {\n return false;\n }\n\n if (!this._isSameStacktrace(currentEvent, previousEvent)) {\n return false;\n }\n\n return true;\n }\n\n /** JSDoc */\n private _getFramesFromEvent(event: Event): StackFrame[] | undefined {\n const exception = event.exception;\n\n if (exception) {\n try {\n // @ts-ignore\n return exception.values[0].stacktrace.frames;\n } catch (_oO) {\n return undefined;\n }\n } else if (event.stacktrace) {\n return event.stacktrace.frames;\n }\n return undefined;\n }\n\n /** JSDoc */\n private _isSameStacktrace(currentEvent: Event, previousEvent: Event): boolean {\n let currentFrames = this._getFramesFromEvent(currentEvent);\n let previousFrames = this._getFramesFromEvent(previousEvent);\n\n // If neither event has a stacktrace, they are assumed to be the same\n if (!currentFrames && !previousFrames) {\n return true;\n }\n\n // If only one event has a stacktrace, but not the other one, they are not the same\n if ((currentFrames && !previousFrames) || (!currentFrames && previousFrames)) {\n return false;\n }\n\n currentFrames = currentFrames as StackFrame[];\n previousFrames = previousFrames as StackFrame[];\n\n // If number of frames differ, they are not the same\n if (previousFrames.length !== currentFrames.length) {\n return false;\n }\n\n // Otherwise, compare the two\n for (let i = 0; i < previousFrames.length; i++) {\n const frameA = previousFrames[i];\n const frameB = currentFrames[i];\n\n if (\n frameA.filename !== frameB.filename ||\n frameA.lineno !== frameB.lineno ||\n frameA.colno !== frameB.colno ||\n frameA.function !== frameB.function\n ) {\n return false;\n }\n }\n\n return true;\n }\n\n /** JSDoc */\n private _getExceptionFromEvent(event: Event): Exception | undefined {\n return event.exception && event.exception.values && event.exception.values[0];\n }\n\n /** JSDoc */\n private _isSameExceptionEvent(currentEvent: Event, previousEvent: Event): boolean {\n const previousException = this._getExceptionFromEvent(previousEvent);\n const currentException = this._getExceptionFromEvent(currentEvent);\n\n if (!previousException || !currentException) {\n return false;\n }\n\n if (previousException.type !== currentException.type || previousException.value !== currentException.value) {\n return false;\n }\n\n if (!this._isSameFingerprint(currentEvent, previousEvent)) {\n return false;\n }\n\n if (!this._isSameStacktrace(currentEvent, previousEvent)) {\n return false;\n }\n\n return true;\n }\n\n /** JSDoc */\n private _isSameFingerprint(currentEvent: Event, previousEvent: Event): boolean {\n let currentFingerprint = currentEvent.fingerprint;\n let previousFingerprint = previousEvent.fingerprint;\n\n // If neither event has a fingerprint, they are assumed to be the same\n if (!currentFingerprint && !previousFingerprint) {\n return true;\n }\n\n // If only one event has a fingerprint, but not the other one, they are not the same\n if ((currentFingerprint && !previousFingerprint) || (!currentFingerprint && previousFingerprint)) {\n return false;\n }\n\n currentFingerprint = currentFingerprint as string[];\n previousFingerprint = previousFingerprint as string[];\n\n // Otherwise, compare the two\n try {\n return !!(currentFingerprint.join('') === previousFingerprint.join(''));\n } catch (_oO) {\n return false;\n }\n }\n}\n","import { EventProcessor, Hub, Integration } from '@sentry/types';\nimport { getGlobalObject, isInstanceOf, logger } from '@sentry/utils';\n\n/** JSDoc */\nexport class Ember implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = Ember.id;\n /**\n * @inheritDoc\n */\n public static id: string = 'Ember';\n\n /**\n * @inheritDoc\n */\n private readonly _Ember: any; // tslint:disable-line:variable-name\n\n /**\n * @inheritDoc\n */\n public constructor(options: { Ember?: any } = {}) {\n // tslint:disable-next-line: no-unsafe-any\n this._Ember = options.Ember || getGlobalObject().Ember;\n }\n\n /**\n * @inheritDoc\n */\n public setupOnce(_: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n // tslint:disable:no-unsafe-any\n\n if (!this._Ember) {\n logger.error('EmberIntegration is missing an Ember instance');\n return;\n }\n\n const oldOnError = this._Ember.onerror;\n\n this._Ember.onerror = (error: Error): void => {\n if (getCurrentHub().getIntegration(Ember)) {\n getCurrentHub().captureException(error, { originalException: error });\n }\n\n if (typeof oldOnError === 'function') {\n oldOnError.call(this._Ember, error);\n } else if (this._Ember.testing) {\n throw error;\n }\n };\n\n this._Ember.RSVP.on(\n 'error',\n (reason: any): void => {\n if (getCurrentHub().getIntegration(Ember)) {\n getCurrentHub().withScope(scope => {\n if (isInstanceOf(reason, Error)) {\n scope.setExtra('context', 'Unhandled Promise error detected');\n getCurrentHub().captureException(reason, { originalException: reason });\n } else {\n scope.setExtra('reason', reason);\n getCurrentHub().captureMessage('Unhandled Promise error detected');\n }\n });\n }\n },\n );\n }\n}\n","import { Event, EventHint, EventProcessor, ExtendedError, Hub, Integration } from '@sentry/types';\nimport { isError, isPlainObject, logger, normalize } from '@sentry/utils';\n\n/** JSDoc */\ninterface ExtraErrorDataOptions {\n depth?: number;\n}\n\n/** Patch toString calls to return proper name for wrapped functions */\nexport class ExtraErrorData implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = ExtraErrorData.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'ExtraErrorData';\n\n /**\n * @inheritDoc\n */\n public constructor(private readonly _options: ExtraErrorDataOptions = { depth: 3 }) {}\n\n /**\n * @inheritDoc\n */\n public setupOnce(addGlobalEventProcessor: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n addGlobalEventProcessor((event: Event, hint?: EventHint) => {\n const self = getCurrentHub().getIntegration(ExtraErrorData);\n if (!self) {\n return event;\n }\n return self.enhanceEventWithErrorData(event, hint);\n });\n }\n\n /**\n * Attaches extracted information from the Error object to extra field in the Event\n */\n public enhanceEventWithErrorData(event: Event, hint?: EventHint): Event {\n if (!hint || !hint.originalException || !isError(hint.originalException)) {\n return event;\n }\n const name = (hint.originalException as ExtendedError).name || hint.originalException.constructor.name;\n\n const errorData = this._extractErrorData(hint.originalException as ExtendedError);\n\n if (errorData) {\n let contexts = {\n ...event.contexts,\n };\n\n const normalizedErrorData = normalize(errorData, this._options.depth);\n if (isPlainObject(normalizedErrorData)) {\n contexts = {\n ...event.contexts,\n [name]: {\n ...normalizedErrorData,\n },\n };\n }\n\n return {\n ...event,\n contexts,\n };\n }\n\n return event;\n }\n\n /**\n * Extract extra information from the Error object\n */\n private _extractErrorData(error: ExtendedError): { [key: string]: unknown } | null {\n let result = null;\n // We are trying to enhance already existing event, so no harm done if it won't succeed\n try {\n const nativeKeys = ['name', 'message', 'stack', 'line', 'column', 'fileName', 'lineNumber', 'columnNumber'];\n const errorKeys = Object.getOwnPropertyNames(error).filter(key => nativeKeys.indexOf(key) === -1);\n\n if (errorKeys.length) {\n const extraErrorInfo: { [key: string]: unknown } = {};\n for (const key of errorKeys) {\n let value = error[key];\n if (isError(value)) {\n value = (value as Error).toString();\n }\n // tslint:disable:no-unsafe-any\n extraErrorInfo[key] = value;\n }\n result = extraErrorInfo;\n }\n } catch (oO) {\n logger.error('Unable to extract extra data from the Error object:', oO);\n }\n\n return result;\n }\n}\n","import { Event, EventProcessor, Hub, Integration, StackFrame, Stacktrace } from '@sentry/types';\nimport { basename, relative } from '@sentry/utils';\n\ntype StackFrameIteratee = (frame: StackFrame) => StackFrame;\n\n/** Rewrite event frames paths */\nexport class RewriteFrames implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = RewriteFrames.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'RewriteFrames';\n\n /**\n * @inheritDoc\n */\n private readonly _root?: string;\n\n /**\n * @inheritDoc\n */\n private readonly _iteratee: StackFrameIteratee = (frame: StackFrame) => {\n if (!frame.filename) {\n return frame;\n }\n // Check if the frame filename begins with `/` or a Windows-style prefix such as `C:\\`\n const isWindowsFrame = /^[A-Z]:\\\\/.test(frame.filename);\n const startsWithSlash = /^\\//.test(frame.filename);\n if (frame.filename && (isWindowsFrame || startsWithSlash)) {\n const filename = isWindowsFrame\n ? frame.filename\n .replace(/^[A-Z]:/, '') // remove Windows-style prefix\n .replace(/\\\\/g, '/') // replace all `\\\\` instances with `/`\n : frame.filename;\n const base = this._root ? relative(this._root, filename) : basename(filename);\n frame.filename = `app:///${base}`;\n }\n return frame;\n };\n\n /**\n * @inheritDoc\n */\n public constructor(options: { root?: string; iteratee?: StackFrameIteratee } = {}) {\n if (options.root) {\n this._root = options.root;\n }\n if (options.iteratee) {\n this._iteratee = options.iteratee;\n }\n }\n\n /**\n * @inheritDoc\n */\n public setupOnce(addGlobalEventProcessor: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n addGlobalEventProcessor(event => {\n const self = getCurrentHub().getIntegration(RewriteFrames);\n if (self) {\n return self.process(event);\n }\n return event;\n });\n }\n\n /** JSDoc */\n public process(event: Event): Event {\n if (event.exception && Array.isArray(event.exception.values)) {\n return this._processExceptionsEvent(event);\n }\n\n if (event.stacktrace) {\n return this._processStacktraceEvent(event);\n }\n\n return event;\n }\n\n /** JSDoc */\n private _processExceptionsEvent(event: Event): Event {\n try {\n return {\n ...event,\n exception: {\n ...event.exception,\n // The check for this is performed inside `process` call itself, safe to skip here\n // tslint:disable-next-line:no-non-null-assertion\n values: event.exception!.values!.map(value => ({\n ...value,\n stacktrace: this._processStacktrace(value.stacktrace),\n })),\n },\n };\n } catch (_oO) {\n return event;\n }\n }\n\n /** JSDoc */\n private _processStacktraceEvent(event: Event): Event {\n try {\n return {\n ...event,\n stacktrace: this._processStacktrace(event.stacktrace),\n };\n } catch (_oO) {\n return event;\n }\n }\n\n /** JSDoc */\n private _processStacktrace(stacktrace?: Stacktrace): Stacktrace {\n return {\n ...stacktrace,\n frames: stacktrace && stacktrace.frames && stacktrace.frames.map(f => this._iteratee(f)),\n };\n }\n}\n","import { Event, EventProcessor, Hub, Integration } from '@sentry/types';\n\n/** This function adds duration since Sentry was initialized till the time event was sent */\nexport class SessionTiming implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = SessionTiming.id;\n /**\n * @inheritDoc\n */\n public static id: string = 'SessionTiming';\n\n /** Exact time Client was initialized expressed in milliseconds since Unix Epoch. */\n protected readonly _startTime: number = Date.now();\n\n /**\n * @inheritDoc\n */\n public setupOnce(addGlobalEventProcessor: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n addGlobalEventProcessor(event => {\n const self = getCurrentHub().getIntegration(SessionTiming);\n if (self) {\n return self.process(event);\n }\n return event;\n });\n }\n\n /**\n * @inheritDoc\n */\n public process(event: Event): Event {\n const now = Date.now();\n\n return {\n ...event,\n extra: {\n ...event.extra,\n ['session:start']: this._startTime,\n ['session:duration']: now - this._startTime,\n ['session:end']: now,\n },\n };\n }\n}\n","import { Event, EventProcessor, Hub, Integration, StackFrame } from '@sentry/types';\n\n/** Add node transaction to the event */\nexport class Transaction implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = Transaction.id;\n /**\n * @inheritDoc\n */\n public static id: string = 'Transaction';\n\n /**\n * @inheritDoc\n */\n public setupOnce(addGlobalEventProcessor: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n addGlobalEventProcessor(event => {\n const self = getCurrentHub().getIntegration(Transaction);\n if (self) {\n return self.process(event);\n }\n return event;\n });\n }\n\n /**\n * @inheritDoc\n */\n public process(event: Event): Event {\n const frames = this._getFramesFromEvent(event);\n\n // use for loop so we don't have to reverse whole frames array\n for (let i = frames.length - 1; i >= 0; i--) {\n const frame = frames[i];\n\n if (frame.in_app === true) {\n event.transaction = this._getTransaction(frame);\n break;\n }\n }\n\n return event;\n }\n\n /** JSDoc */\n private _getFramesFromEvent(event: Event): StackFrame[] {\n const exception = event.exception && event.exception.values && event.exception.values[0];\n return (exception && exception.stacktrace && exception.stacktrace.frames) || [];\n }\n\n /** JSDoc */\n private _getTransaction(frame: StackFrame): string {\n return frame.module || frame.function ? `${frame.module || '?'}/${frame.function || '?'}` : '';\n }\n}\n","import { EventProcessor, Hub, Integration } from '@sentry/types';\nimport { getGlobalObject, isPlainObject, logger } from '@sentry/utils';\n\n/** JSDoc */\ninterface Metadata {\n [key: string]: any;\n componentName?: string;\n propsData?: {\n [key: string]: any;\n };\n lifecycleHook?: string;\n}\n\n/** JSDoc */\nexport class Vue implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = Vue.id;\n /**\n * @inheritDoc\n */\n public static id: string = 'Vue';\n\n /**\n * @inheritDoc\n */\n private readonly _Vue: any; // tslint:disable-line:variable-name\n\n /**\n * When set to false, Sentry will suppress reporting all props data\n * from your Vue components for privacy concerns.\n */\n private readonly _attachProps: boolean = true;\n\n /**\n * When set to true, original Vue's `logError` will be called as well.\n * https://github.com/vuejs/vue/blob/c2b1cfe9ccd08835f2d99f6ce60f67b4de55187f/src/core/util/error.js#L38-L48\n */\n private readonly _logErrors: boolean = false;\n\n /**\n * @inheritDoc\n */\n public constructor(options: { Vue?: any; attachProps?: boolean; logErrors?: boolean } = {}) {\n // tslint:disable-next-line: no-unsafe-any\n this._Vue = options.Vue || getGlobalObject().Vue;\n\n if (options.logErrors !== undefined) {\n this._logErrors = options.logErrors;\n }\n if (options.attachProps === false) {\n this._attachProps = false;\n }\n }\n\n /** JSDoc */\n private _formatComponentName(vm: any): string {\n // tslint:disable:no-unsafe-any\n\n if (vm.$root === vm) {\n return 'root instance';\n }\n const name = vm._isVue ? vm.$options.name || vm.$options._componentTag : vm.name;\n return (\n (name ? `component <${name}>` : 'anonymous component') +\n (vm._isVue && vm.$options.__file ? ` at ${vm.$options.__file}` : '')\n );\n }\n\n /**\n * @inheritDoc\n */\n public setupOnce(_: (callback: EventProcessor) => void, getCurrentHub: () => Hub): void {\n // tslint:disable:no-unsafe-any\n\n if (!this._Vue || !this._Vue.config) {\n logger.error('VueIntegration is missing a Vue instance');\n return;\n }\n\n const oldOnError = this._Vue.config.errorHandler;\n\n this._Vue.config.errorHandler = (error: Error, vm: { [key: string]: any }, info: string): void => {\n const metadata: Metadata = {};\n\n if (isPlainObject(vm)) {\n metadata.componentName = this._formatComponentName(vm);\n\n if (this._attachProps) {\n metadata.propsData = vm.$options.propsData;\n }\n }\n\n if (info !== void 0) {\n metadata.lifecycleHook = info;\n }\n\n if (getCurrentHub().getIntegration(Vue)) {\n // This timeout makes sure that any breadcrumbs are recorded before sending it off the sentry\n setTimeout(() => {\n getCurrentHub().withScope(scope => {\n scope.setContext('vue', metadata);\n getCurrentHub().captureException(error);\n });\n });\n }\n\n if (typeof oldOnError === 'function') {\n oldOnError.call(this._Vue, error, vm, info);\n }\n\n if (this._logErrors) {\n this._Vue.util.warn(`Error in ${info}: \"${error.toString()}\"`, vm);\n // tslint:disable-next-line:no-console\n console.error(error);\n }\n };\n }\n}\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./OttimizzazioneLineare.js\") );\n\t\t\t}, \"route-OttimizzazioneLineare\");\n\t\t}\n\n\t\texport default Async(load);\n\t","import { consoleSandbox, getGlobalObject } from './misc';\n\n// TODO: Implement different loggers for different environments\nconst global = getGlobalObject();\n\n/** Prefix for logging strings */\nconst PREFIX = 'Sentry Logger ';\n\n/** JSDoc */\nclass Logger {\n /** JSDoc */\n private _enabled: boolean;\n\n /** JSDoc */\n public constructor() {\n this._enabled = false;\n }\n\n /** JSDoc */\n public disable(): void {\n this._enabled = false;\n }\n\n /** JSDoc */\n public enable(): void {\n this._enabled = true;\n }\n\n /** JSDoc */\n public log(...args: any[]): void {\n if (!this._enabled) {\n return;\n }\n consoleSandbox(() => {\n global.console.log(`${PREFIX}[Log]: ${args.join(' ')}`); // tslint:disable-line:no-console\n });\n }\n\n /** JSDoc */\n public warn(...args: any[]): void {\n if (!this._enabled) {\n return;\n }\n consoleSandbox(() => {\n global.console.warn(`${PREFIX}[Warn]: ${args.join(' ')}`); // tslint:disable-line:no-console\n });\n }\n\n /** JSDoc */\n public error(...args: any[]): void {\n if (!this._enabled) {\n return;\n }\n consoleSandbox(() => {\n global.console.error(`${PREFIX}[Error]: ${args.join(' ')}`); // tslint:disable-line:no-console\n });\n }\n}\n\n// Ensure we only have a single logger instance, even if multiple versions of @sentry/utils are being used\nglobal.__SENTRY__ = global.__SENTRY__ || {};\nconst logger = (global.__SENTRY__.logger as Logger) || (global.__SENTRY__.logger = new Logger());\n\nexport { logger };\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./CalcoloNumerico.js\") );\n\t\t\t}, \"route-CalcoloNumerico\");\n\t\t}\n\n\t\texport default Async(load);\n\t","import { logger } from './logger';\nimport { getGlobalObject } from './misc';\n\n/**\n * Tells whether current environment supports ErrorEvent objects\n * {@link supportsErrorEvent}.\n *\n * @returns Answer to the given question.\n */\nexport function supportsErrorEvent(): boolean {\n try {\n // tslint:disable:no-unused-expression\n new ErrorEvent('');\n return true;\n } catch (e) {\n return false;\n }\n}\n\n/**\n * Tells whether current environment supports DOMError objects\n * {@link supportsDOMError}.\n *\n * @returns Answer to the given question.\n */\nexport function supportsDOMError(): boolean {\n try {\n // It really needs 1 argument, not 0.\n // Chrome: VM89:1 Uncaught TypeError: Failed to construct 'DOMError':\n // 1 argument required, but only 0 present.\n // @ts-ignore\n // tslint:disable:no-unused-expression\n new DOMError('');\n return true;\n } catch (e) {\n return false;\n }\n}\n\n/**\n * Tells whether current environment supports DOMException objects\n * {@link supportsDOMException}.\n *\n * @returns Answer to the given question.\n */\nexport function supportsDOMException(): boolean {\n try {\n // tslint:disable:no-unused-expression\n new DOMException('');\n return true;\n } catch (e) {\n return false;\n }\n}\n\n/**\n * Tells whether current environment supports Fetch API\n * {@link supportsFetch}.\n *\n * @returns Answer to the given question.\n */\nexport function supportsFetch(): boolean {\n if (!('fetch' in getGlobalObject())) {\n return false;\n }\n\n try {\n // tslint:disable-next-line:no-unused-expression\n new Headers();\n // tslint:disable-next-line:no-unused-expression\n new Request('');\n // tslint:disable-next-line:no-unused-expression\n new Response();\n return true;\n } catch (e) {\n return false;\n }\n}\n/**\n * isNativeFetch checks if the given function is a native implementation of fetch()\n */\nfunction isNativeFetch(func: Function): boolean {\n return func && /^function fetch\\(\\)\\s+\\{\\s+\\[native code\\]\\s+\\}$/.test(func.toString());\n}\n\n/**\n * Tells whether current environment supports Fetch API natively\n * {@link supportsNativeFetch}.\n *\n * @returns true if `window.fetch` is natively implemented, false otherwise\n */\nexport function supportsNativeFetch(): boolean {\n if (!supportsFetch()) {\n return false;\n }\n\n const global = getGlobalObject();\n\n // Fast path to avoid DOM I/O\n // tslint:disable-next-line:no-unbound-method\n if (isNativeFetch(global.fetch)) {\n return true;\n }\n\n // window.fetch is implemented, but is polyfilled or already wrapped (e.g: by a chrome extension)\n // so create a \"pure\" iframe to see if that has native fetch\n let result = false;\n const doc = global.document;\n // tslint:disable-next-line:no-unbound-method deprecation\n if (doc && typeof (doc.createElement as unknown) === `function`) {\n try {\n const sandbox = doc.createElement('iframe');\n sandbox.hidden = true;\n doc.head.appendChild(sandbox);\n if (sandbox.contentWindow && sandbox.contentWindow.fetch) {\n // tslint:disable-next-line:no-unbound-method\n result = isNativeFetch(sandbox.contentWindow.fetch);\n }\n doc.head.removeChild(sandbox);\n } catch (err) {\n logger.warn('Could not create sandbox iframe for pure fetch check, bailing to window.fetch: ', err);\n }\n }\n\n return result;\n}\n\n/**\n * Tells whether current environment supports ReportingObserver API\n * {@link supportsReportingObserver}.\n *\n * @returns Answer to the given question.\n */\nexport function supportsReportingObserver(): boolean {\n // tslint:disable-next-line: no-unsafe-any\n return 'ReportingObserver' in getGlobalObject();\n}\n\n/**\n * Tells whether current environment supports Referrer Policy API\n * {@link supportsReferrerPolicy}.\n *\n * @returns Answer to the given question.\n */\nexport function supportsReferrerPolicy(): boolean {\n // Despite all stars in the sky saying that Edge supports old draft syntax, aka 'never', 'always', 'origin' and 'default\n // https://caniuse.com/#feat=referrer-policy\n // It doesn't. And it throw exception instead of ignoring this parameter...\n // REF: https://github.com/getsentry/raven-js/issues/1233\n\n if (!supportsFetch()) {\n return false;\n }\n\n try {\n // tslint:disable:no-unused-expression\n new Request('_', {\n referrerPolicy: 'origin' as ReferrerPolicy,\n });\n return true;\n } catch (e) {\n return false;\n }\n}\n\n/**\n * Tells whether current environment supports History API\n * {@link supportsHistory}.\n *\n * @returns Answer to the given question.\n */\nexport function supportsHistory(): boolean {\n // NOTE: in Chrome App environment, touching history.pushState, *even inside\n // a try/catch block*, will cause Chrome to output an error to console.error\n // borrowed from: https://github.com/angular/angular.js/pull/13945/files\n const global = getGlobalObject();\n const chrome = (global as any).chrome;\n // tslint:disable-next-line:no-unsafe-any\n const isChromePackagedApp = chrome && chrome.app && chrome.app.runtime;\n const hasHistoryApi = 'history' in global && !!global.history.pushState && !!global.history.replaceState;\n\n return !isChromePackagedApp && hasHistoryApi;\n}\n","/** JSDoc */\nexport enum Severity {\n /** JSDoc */\n Fatal = 'fatal',\n /** JSDoc */\n Error = 'error',\n /** JSDoc */\n Warning = 'warning',\n /** JSDoc */\n Log = 'log',\n /** JSDoc */\n Info = 'info',\n /** JSDoc */\n Debug = 'debug',\n /** JSDoc */\n Critical = 'critical',\n}\n// tslint:disable:completed-docs\n// tslint:disable:no-unnecessary-qualifier no-namespace\nexport namespace Severity {\n /**\n * Converts a string-based level into a {@link Severity}.\n *\n * @param level string representation of Severity\n * @returns Severity\n */\n export function fromString(level: string): Severity {\n switch (level) {\n case 'debug':\n return Severity.Debug;\n case 'info':\n return Severity.Info;\n case 'warn':\n case 'warning':\n return Severity.Warning;\n case 'error':\n return Severity.Error;\n case 'fatal':\n return Severity.Fatal;\n case 'critical':\n return Severity.Critical;\n case 'log':\n default:\n return Severity.Log;\n }\n }\n}\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./MingwInstall.js\") );\n\t\t\t}, \"route-MingwInstall\");\n\t\t}\n\n\t\texport default Async(load);\n\t","module.exports = function(originalModule) {\n\tif (!originalModule.webpackPolyfill) {\n\t\tvar module = Object.create(originalModule);\n\t\t// module.parent = undefined by default\n\t\tif (!module.children) module.children = [];\n\t\tObject.defineProperty(module, \"loaded\", {\n\t\t\tenumerable: true,\n\t\t\tget: function() {\n\t\t\t\treturn module.l;\n\t\t\t}\n\t\t});\n\t\tObject.defineProperty(module, \"id\", {\n\t\t\tenumerable: true,\n\t\t\tget: function() {\n\t\t\t\treturn module.i;\n\t\t\t}\n\t\t});\n\t\tObject.defineProperty(module, \"exports\", {\n\t\t\tenumerable: true\n\t\t});\n\t\tmodule.webpackPolyfill = 1;\n\t}\n\treturn module;\n};\n","// Import debugging tools\nimport AlgoritmiEStruttureDati from \"./routes/AlgoritmiEStruttureDati\";\n\nlet Sentry = null;\nif(process.env.NODE_ENV === \"development\") {\n\tconsole.debug(\"Initializing Preact Debugger...\")\n\trequire(\"preact/debug\");\n}\nelse if(process.env.NODE_ENV === \"production\") {\n\tconsole.debug(\"Initializing Sentry...\")\n\tSentry = require(\"@sentry/browser\");\n\tlet SentryIntegrations = require(\"@sentry/integrations\")\n\t// noinspection JSUnresolvedVariable\n\tSentry.init({\n\t\tdsn: \"https://9f5089346fd14e04a6f412638474dfec@o40131.ingest.sentry.io/5255500\",\n\t\trelease: process.env.RELEASE,\n\t\tenvironment: \"production\",\n\t\tbeforeSend(event, hint) {\n\t\t\tif (event.exception) {\n\t\t\t\tSentry.showReportDialog({ eventId: event.event_id });\n\t\t\t}\n\t\t\treturn event;\n\t\t}\n\t});\n}\n\n// noinspection ES6UnusedImports\nimport _style from './index.less';\n// noinspection ES6UnusedImports\nimport _manifest from './meta/manifest.json';\n// noinspection ES6UnusedImports\nimport _cname from './meta/CNAME';\n// noinspection ES6UnusedImports\nimport _nojekyll from './meta/.nojekyll';\n\nimport Router from 'preact-router';\nimport {createHashHistory} from \"history\";\nimport Home from './routes/Home';\nimport Fisica from './routes/Fisica';\nimport VlDiGeometria from './routes/VlDiGeometria';\nimport MingwInstall from './routes/MingwInstall';\nimport Footer from './components/Layout/Footer';\nimport Statistica from './routes/Statistica';\nimport OttimizzazioneLineare from \"./routes/OttimizzazioneLineare\";\nimport BasiDiDati from './routes/BasiDiDati';\nimport CalcoloNumerico from './routes/CalcoloNumerico';\nimport ApprendimentoSistemiArtificiali from \"./routes/ApprendimentoSistemiArtificiali\";\nimport LatexRenderColor from \"./contexts/LatexRenderColor\";\n\n// noinspection JSUnusedGlobalSymbols\nexport default function(props) {\n\treturn (\n\t\t
\n\t\t\t\n\t\t\t\t

Appuntiweb di Steffo

\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\t
\n\t\t\t\n\t\t
\n\t);\n}\n","import { h, Component } from 'preact';\n\nexport default function(req) {\n\tfunction Async() {\n\t\tComponent.call(this);\n\n\t\tlet b, old;\n\t\tthis.componentWillMount = () => {\n\t\t\tb = this.base = this.nextBase || this.__b; // short circuits 1st render\n\t\t\treq(m => {\n\t\t\t\tthis.setState({ child: m.default || m });\n\t\t\t});\n\t\t};\n\n\t\tthis.shouldComponentUpdate = (_, nxt) => {\n\t\t\tnxt = nxt.child === void 0;\n\t\t\tif (nxt && old === void 0 && b) {\n\t\t\t\t// Node.TEXT_NODE\n\t\t\t\tif (b.nodeType === 3) {\n\t\t\t\t\told = b.data;\n\t\t\t\t} else {\n\t\t\t\t\told = h(b.nodeName, {\n\t\t\t\t\t\tdangerouslySetInnerHTML: { __html: b.innerHTML },\n\t\t\t\t\t});\n\t\t\t\t}\n\t\t\t} else {\n\t\t\t\told = ''; // dump it\n\t\t\t}\n\t\t\treturn !nxt;\n\t\t};\n\n\t\tthis.render = (p, s) => (s.child ? h(s.child, p) : old);\n\t}\n\t(Async.prototype = new Component()).constructor = Async;\n\treturn Async;\n}\n","/**\n * Assign properties from `props` to `obj`\n * @template O, P The obj and props types\n * @param {O} obj The object to copy properties to\n * @param {P} props The object to copy properties from\n * @returns {O & P}\n */\nexport function assign(obj, props) {\n\tfor (let i in props) obj[i] = props[i];\n\treturn /** @type {O & P} */ (obj);\n}\n\n/**\n * Remove a child node from its parent if attached. This is a workaround for\n * IE11 which doesn't support `Element.prototype.remove()`. Using this function\n * is smaller than including a dedicated polyfill.\n * @param {Node} node The node to remove\n */\nexport function removeNode(node) {\n\tlet parentNode = node.parentNode;\n\tif (parentNode) parentNode.removeChild(node);\n}\n","import { cloneElement, createElement, Component, toChildArray } from 'preact';\nimport { exec, prepareVNodeForRanking, assign, pathRankSort } from './util';\n\nlet customHistory = null;\n\nconst ROUTERS = [];\n\nconst subscribers = [];\n\nconst EMPTY = {};\n\nfunction setUrl(url, type='push') {\n\tif (customHistory && customHistory[type]) {\n\t\tcustomHistory[type](url);\n\t}\n\telse if (typeof history!=='undefined' && history[type+'State']) {\n\t\thistory[type+'State'](null, null, url);\n\t}\n}\n\n\nfunction getCurrentUrl() {\n\tlet url;\n\tif (customHistory && customHistory.location) {\n\t\turl = customHistory.location;\n\t}\n\telse if (customHistory && customHistory.getCurrentLocation) {\n\t\turl = customHistory.getCurrentLocation();\n\t}\n\telse {\n\t\turl = typeof location!=='undefined' ? location : EMPTY;\n\t}\n\treturn `${url.pathname || ''}${url.search || ''}`;\n}\n\n\n\nfunction route(url, replace=false) {\n\tif (typeof url!=='string' && url.url) {\n\t\treplace = url.replace;\n\t\turl = url.url;\n\t}\n\n\t// only push URL into history if we can handle it\n\tif (canRoute(url)) {\n\t\tsetUrl(url, replace ? 'replace' : 'push');\n\t}\n\n\treturn routeTo(url);\n}\n\n\n/** Check if the given URL can be handled by any router instances. */\nfunction canRoute(url) {\n\tfor (let i=ROUTERS.length; i--; ) {\n\t\tif (ROUTERS[i].canRoute(url)) return true;\n\t}\n\treturn false;\n}\n\n\n/** Tell all router instances to handle the given URL. */\nfunction routeTo(url) {\n\tlet didRoute = false;\n\tfor (let i=0; i {\n\t\t\t\trouteTo(getCurrentUrl());\n\t\t\t});\n\t\t}\n\t\taddEventListener('click', delegateLinkHandler);\n\t}\n\teventListenersInitialized = true;\n}\n\n\nclass Router extends Component {\n\tconstructor(props) {\n\t\tsuper(props);\n\t\tif (props.history) {\n\t\t\tcustomHistory = props.history;\n\t\t}\n\n\t\tthis.state = {\n\t\t\turl: props.url || getCurrentUrl()\n\t\t};\n\n\t\tinitEventListeners();\n\t}\n\n\tshouldComponentUpdate(props) {\n\t\tif (props.static!==true) return true;\n\t\treturn props.url!==this.props.url || props.onChange!==this.props.onChange;\n\t}\n\n\t/** Check if the given URL can be matched against any children */\n\tcanRoute(url) {\n\t\tconst children = toChildArray(this.props.children);\n\t\treturn this.getMatchingChildren(children, url, false).length > 0;\n\t}\n\n\t/** Re-render children with a new URL to match against. */\n\trouteTo(url) {\n\t\tthis.setState({ url });\n\n\t\tconst didRoute = this.canRoute(url);\n\n\t\t// trigger a manual re-route if we're not in the middle of an update:\n\t\tif (!this.updating) this.forceUpdate();\n\n\t\treturn didRoute;\n\t}\n\n\tcomponentWillMount() {\n\t\tROUTERS.push(this);\n\t\tthis.updating = true;\n\t}\n\n\tcomponentDidMount() {\n\t\tif (customHistory) {\n\t\t\tthis.unlisten = customHistory.listen((location) => {\n\t\t\t\tthis.routeTo(`${location.pathname || ''}${location.search || ''}`);\n\t\t\t});\n\t\t}\n\t\tthis.updating = false;\n\t}\n\n\tcomponentWillUnmount() {\n\t\tif (typeof this.unlisten==='function') this.unlisten();\n\t\tROUTERS.splice(ROUTERS.indexOf(this), 1);\n\t}\n\n\tcomponentWillUpdate() {\n\t\tthis.updating = true;\n\t}\n\n\tcomponentDidUpdate() {\n\t\tthis.updating = false;\n\t}\n\n\tgetMatchingChildren(children, url, invoke) {\n\t\treturn children\n\t\t\t.filter(prepareVNodeForRanking)\n\t\t\t.sort(pathRankSort)\n\t\t\t.map( vnode => {\n\t\t\t\tlet matches = exec(url, vnode.props.path, vnode.props);\n\t\t\t\tif (matches) {\n\t\t\t\t\tif (invoke !== false) {\n\t\t\t\t\t\tlet newProps = { url, matches };\n\t\t\t\t\t\tassign(newProps, matches);\n\t\t\t\t\t\tdelete newProps.ref;\n\t\t\t\t\t\tdelete newProps.key;\n\t\t\t\t\t\treturn cloneElement(vnode, newProps);\n\t\t\t\t\t}\n\t\t\t\t\treturn vnode;\n\t\t\t\t}\n\t\t\t}).filter(Boolean);\n\t}\n\n\trender({ children, onChange }, { url }) {\n\t\tlet active = this.getMatchingChildren(toChildArray(children), url, true);\n\n\t\tlet current = active[0] || null;\n\n\t\tlet previous = this.previousUrl;\n\t\tif (url!==previous) {\n\t\t\tthis.previousUrl = url;\n\t\t\tif (typeof onChange==='function') {\n\t\t\t\tonChange({\n\t\t\t\t\trouter: this,\n\t\t\t\t\turl,\n\t\t\t\t\tprevious,\n\t\t\t\t\tactive,\n\t\t\t\t\tcurrent\n\t\t\t\t});\n\t\t\t}\n\t\t}\n\n\t\treturn current;\n\t}\n}\n\nconst Link = (props) => (\n\tcreateElement('a', assign({ onClick: handleLinkClick }, props))\n);\n\nconst Route = props => createElement(props.component, props);\n\nRouter.subscribers = subscribers;\nRouter.getCurrentUrl = getCurrentUrl;\nRouter.route = route;\nRouter.Router = Router;\nRouter.Route = Route;\nRouter.Link = Link;\nRouter.exec = exec;\n\nexport { subscribers, getCurrentUrl, route, Router, Route, Link, exec };\nexport default Router;\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./ApprendimentoSistemiArtificiali.js\") );\n\t\t\t}, \"route-ApprendimentoSistemiArtificiali\");\n\t\t}\n\n\t\texport default Async(load);\n\t","/*! *****************************************************************************\r\nCopyright (c) Microsoft Corporation. All rights reserved.\r\nLicensed under the Apache License, Version 2.0 (the \"License\"); you may not use\r\nthis file except in compliance with the License. You may obtain a copy of the\r\nLicense at http://www.apache.org/licenses/LICENSE-2.0\r\n\r\nTHIS CODE IS PROVIDED ON AN *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY\r\nKIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED\r\nWARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,\r\nMERCHANTABLITY OR NON-INFRINGEMENT.\r\n\r\nSee the Apache Version 2.0 License for specific language governing permissions\r\nand limitations under the License.\r\n***************************************************************************** */\r\n/* global Reflect, Promise */\r\n\r\nvar extendStatics = function(d, b) {\r\n extendStatics = Object.setPrototypeOf ||\r\n ({ __proto__: [] } instanceof Array && function (d, b) { d.__proto__ = b; }) ||\r\n function (d, b) { for (var p in b) if (b.hasOwnProperty(p)) d[p] = b[p]; };\r\n return extendStatics(d, b);\r\n};\r\n\r\nexport function __extends(d, b) {\r\n extendStatics(d, b);\r\n function __() { this.constructor = d; }\r\n d.prototype = b === null ? Object.create(b) : (__.prototype = b.prototype, new __());\r\n}\r\n\r\nexport var __assign = function() {\r\n __assign = Object.assign || function __assign(t) {\r\n for (var s, i = 1, n = arguments.length; i < n; i++) {\r\n s = arguments[i];\r\n for (var p in s) if (Object.prototype.hasOwnProperty.call(s, p)) t[p] = s[p];\r\n }\r\n return t;\r\n }\r\n return __assign.apply(this, arguments);\r\n}\r\n\r\nexport function __rest(s, e) {\r\n var t = {};\r\n for (var p in s) if (Object.prototype.hasOwnProperty.call(s, p) && e.indexOf(p) < 0)\r\n t[p] = s[p];\r\n if (s != null && typeof Object.getOwnPropertySymbols === \"function\")\r\n for (var i = 0, p = Object.getOwnPropertySymbols(s); i < p.length; i++) {\r\n if (e.indexOf(p[i]) < 0 && Object.prototype.propertyIsEnumerable.call(s, p[i]))\r\n t[p[i]] = s[p[i]];\r\n }\r\n return t;\r\n}\r\n\r\nexport function __decorate(decorators, target, key, desc) {\r\n var c = arguments.length, r = c < 3 ? target : desc === null ? desc = Object.getOwnPropertyDescriptor(target, key) : desc, d;\r\n if (typeof Reflect === \"object\" && typeof Reflect.decorate === \"function\") r = Reflect.decorate(decorators, target, key, desc);\r\n else for (var i = decorators.length - 1; i >= 0; i--) if (d = decorators[i]) r = (c < 3 ? d(r) : c > 3 ? d(target, key, r) : d(target, key)) || r;\r\n return c > 3 && r && Object.defineProperty(target, key, r), r;\r\n}\r\n\r\nexport function __param(paramIndex, decorator) {\r\n return function (target, key) { decorator(target, key, paramIndex); }\r\n}\r\n\r\nexport function __metadata(metadataKey, metadataValue) {\r\n if (typeof Reflect === \"object\" && typeof Reflect.metadata === \"function\") return Reflect.metadata(metadataKey, metadataValue);\r\n}\r\n\r\nexport function __awaiter(thisArg, _arguments, P, generator) {\r\n function adopt(value) { return value instanceof P ? value : new P(function (resolve) { resolve(value); }); }\r\n return new (P || (P = Promise))(function (resolve, reject) {\r\n function fulfilled(value) { try { step(generator.next(value)); } catch (e) { reject(e); } }\r\n function rejected(value) { try { step(generator[\"throw\"](value)); } catch (e) { reject(e); } }\r\n function step(result) { result.done ? resolve(result.value) : adopt(result.value).then(fulfilled, rejected); }\r\n step((generator = generator.apply(thisArg, _arguments || [])).next());\r\n });\r\n}\r\n\r\nexport function __generator(thisArg, body) {\r\n var _ = { label: 0, sent: function() { if (t[0] & 1) throw t[1]; return t[1]; }, trys: [], ops: [] }, f, y, t, g;\r\n return g = { next: verb(0), \"throw\": verb(1), \"return\": verb(2) }, typeof Symbol === \"function\" && (g[Symbol.iterator] = function() { return this; }), g;\r\n function verb(n) { return function (v) { return step([n, v]); }; }\r\n function step(op) {\r\n if (f) throw new TypeError(\"Generator is already executing.\");\r\n while (_) try {\r\n if (f = 1, y && (t = op[0] & 2 ? y[\"return\"] : op[0] ? y[\"throw\"] || ((t = y[\"return\"]) && t.call(y), 0) : y.next) && !(t = t.call(y, op[1])).done) return t;\r\n if (y = 0, t) op = [op[0] & 2, t.value];\r\n switch (op[0]) {\r\n case 0: case 1: t = op; break;\r\n case 4: _.label++; return { value: op[1], done: false };\r\n case 5: _.label++; y = op[1]; op = [0]; continue;\r\n case 7: op = _.ops.pop(); _.trys.pop(); continue;\r\n default:\r\n if (!(t = _.trys, t = t.length > 0 && t[t.length - 1]) && (op[0] === 6 || op[0] === 2)) { _ = 0; continue; }\r\n if (op[0] === 3 && (!t || (op[1] > t[0] && op[1] < t[3]))) { _.label = op[1]; break; }\r\n if (op[0] === 6 && _.label < t[1]) { _.label = t[1]; t = op; break; }\r\n if (t && _.label < t[2]) { _.label = t[2]; _.ops.push(op); break; }\r\n if (t[2]) _.ops.pop();\r\n _.trys.pop(); continue;\r\n }\r\n op = body.call(thisArg, _);\r\n } catch (e) { op = [6, e]; y = 0; } finally { f = t = 0; }\r\n if (op[0] & 5) throw op[1]; return { value: op[0] ? op[1] : void 0, done: true };\r\n }\r\n}\r\n\r\nexport function __exportStar(m, exports) {\r\n for (var p in m) if (!exports.hasOwnProperty(p)) exports[p] = m[p];\r\n}\r\n\r\nexport function __values(o) {\r\n var s = typeof Symbol === \"function\" && Symbol.iterator, m = s && o[s], i = 0;\r\n if (m) return m.call(o);\r\n if (o && typeof o.length === \"number\") return {\r\n next: function () {\r\n if (o && i >= o.length) o = void 0;\r\n return { value: o && o[i++], done: !o };\r\n }\r\n };\r\n throw new TypeError(s ? \"Object is not iterable.\" : \"Symbol.iterator is not defined.\");\r\n}\r\n\r\nexport function __read(o, n) {\r\n var m = typeof Symbol === \"function\" && o[Symbol.iterator];\r\n if (!m) return o;\r\n var i = m.call(o), r, ar = [], e;\r\n try {\r\n while ((n === void 0 || n-- > 0) && !(r = i.next()).done) ar.push(r.value);\r\n }\r\n catch (error) { e = { error: error }; }\r\n finally {\r\n try {\r\n if (r && !r.done && (m = i[\"return\"])) m.call(i);\r\n }\r\n finally { if (e) throw e.error; }\r\n }\r\n return ar;\r\n}\r\n\r\nexport function __spread() {\r\n for (var ar = [], i = 0; i < arguments.length; i++)\r\n ar = ar.concat(__read(arguments[i]));\r\n return ar;\r\n}\r\n\r\nexport function __spreadArrays() {\r\n for (var s = 0, i = 0, il = arguments.length; i < il; i++) s += arguments[i].length;\r\n for (var r = Array(s), k = 0, i = 0; i < il; i++)\r\n for (var a = arguments[i], j = 0, jl = a.length; j < jl; j++, k++)\r\n r[k] = a[j];\r\n return r;\r\n};\r\n\r\nexport function __await(v) {\r\n return this instanceof __await ? (this.v = v, this) : new __await(v);\r\n}\r\n\r\nexport function __asyncGenerator(thisArg, _arguments, generator) {\r\n if (!Symbol.asyncIterator) throw new TypeError(\"Symbol.asyncIterator is not defined.\");\r\n var g = generator.apply(thisArg, _arguments || []), i, q = [];\r\n return i = {}, verb(\"next\"), verb(\"throw\"), verb(\"return\"), i[Symbol.asyncIterator] = function () { return this; }, i;\r\n function verb(n) { if (g[n]) i[n] = function (v) { return new Promise(function (a, b) { q.push([n, v, a, b]) > 1 || resume(n, v); }); }; }\r\n function resume(n, v) { try { step(g[n](v)); } catch (e) { settle(q[0][3], e); } }\r\n function step(r) { r.value instanceof __await ? Promise.resolve(r.value.v).then(fulfill, reject) : settle(q[0][2], r); }\r\n function fulfill(value) { resume(\"next\", value); }\r\n function reject(value) { resume(\"throw\", value); }\r\n function settle(f, v) { if (f(v), q.shift(), q.length) resume(q[0][0], q[0][1]); }\r\n}\r\n\r\nexport function __asyncDelegator(o) {\r\n var i, p;\r\n return i = {}, verb(\"next\"), verb(\"throw\", function (e) { throw e; }), verb(\"return\"), i[Symbol.iterator] = function () { return this; }, i;\r\n function verb(n, f) { i[n] = o[n] ? function (v) { return (p = !p) ? { value: __await(o[n](v)), done: n === \"return\" } : f ? f(v) : v; } : f; }\r\n}\r\n\r\nexport function __asyncValues(o) {\r\n if (!Symbol.asyncIterator) throw new TypeError(\"Symbol.asyncIterator is not defined.\");\r\n var m = o[Symbol.asyncIterator], i;\r\n return m ? m.call(o) : (o = typeof __values === \"function\" ? __values(o) : o[Symbol.iterator](), i = {}, verb(\"next\"), verb(\"throw\"), verb(\"return\"), i[Symbol.asyncIterator] = function () { return this; }, i);\r\n function verb(n) { i[n] = o[n] && function (v) { return new Promise(function (resolve, reject) { v = o[n](v), settle(resolve, reject, v.done, v.value); }); }; }\r\n function settle(resolve, reject, d, v) { Promise.resolve(v).then(function(v) { resolve({ value: v, done: d }); }, reject); }\r\n}\r\n\r\nexport function __makeTemplateObject(cooked, raw) {\r\n if (Object.defineProperty) { Object.defineProperty(cooked, \"raw\", { value: raw }); } else { cooked.raw = raw; }\r\n return cooked;\r\n};\r\n\r\nexport function __importStar(mod) {\r\n if (mod && mod.__esModule) return mod;\r\n var result = {};\r\n if (mod != null) for (var k in mod) if (Object.hasOwnProperty.call(mod, k)) result[k] = mod[k];\r\n result.default = mod;\r\n return result;\r\n}\r\n\r\nexport function __importDefault(mod) {\r\n return (mod && mod.__esModule) ? mod : { default: mod };\r\n}\r\n\r\nexport function __classPrivateFieldGet(receiver, privateMap) {\r\n if (!privateMap.has(receiver)) {\r\n throw new TypeError(\"attempted to get private field on non-instance\");\r\n }\r\n return privateMap.get(receiver);\r\n}\r\n\r\nexport function __classPrivateFieldSet(receiver, privateMap, value) {\r\n if (!privateMap.has(receiver)) {\r\n throw new TypeError(\"attempted to set private field on non-instance\");\r\n }\r\n privateMap.set(receiver, value);\r\n return value;\r\n}\r\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./AlgoritmiEStruttureDati.js\") );\n\t\t\t}, \"route-AlgoritmiEStruttureDati\");\n\t\t}\n\n\t\texport default Async(load);\n\t","import { isRegExp, isString } from './is';\n\n/**\n * Truncates given string to the maximum characters count\n *\n * @param str An object that contains serializable values\n * @param max Maximum number of characters in truncated string\n * @returns string Encoded\n */\nexport function truncate(str: string, max: number = 0): string {\n // tslint:disable-next-line:strict-type-predicates\n if (typeof str !== 'string' || max === 0) {\n return str;\n }\n return str.length <= max ? str : `${str.substr(0, max)}...`;\n}\n\n/**\n * This is basically just `trim_line` from\n * https://github.com/getsentry/sentry/blob/master/src/sentry/lang/javascript/processor.py#L67\n *\n * @param str An object that contains serializable values\n * @param max Maximum number of characters in truncated string\n * @returns string Encoded\n */\n\nexport function snipLine(line: string, colno: number): string {\n let newLine = line;\n const ll = newLine.length;\n if (ll <= 150) {\n return newLine;\n }\n if (colno > ll) {\n colno = ll; // tslint:disable-line:no-parameter-reassignment\n }\n\n let start = Math.max(colno - 60, 0);\n if (start < 5) {\n start = 0;\n }\n\n let end = Math.min(start + 140, ll);\n if (end > ll - 5) {\n end = ll;\n }\n if (end === ll) {\n start = Math.max(end - 140, 0);\n }\n\n newLine = newLine.slice(start, end);\n if (start > 0) {\n newLine = `'{snip} ${newLine}`;\n }\n if (end < ll) {\n newLine += ' {snip}';\n }\n\n return newLine;\n}\n\n/**\n * Join values in array\n * @param input array of values to be joined together\n * @param delimiter string to be placed in-between values\n * @returns Joined values\n */\nexport function safeJoin(input: any[], delimiter?: string): string {\n if (!Array.isArray(input)) {\n return '';\n }\n\n const output = [];\n // tslint:disable-next-line:prefer-for-of\n for (let i = 0; i < input.length; i++) {\n const value = input[i];\n try {\n output.push(String(value));\n } catch (e) {\n output.push('[value cannot be serialized]');\n }\n }\n\n return output.join(delimiter);\n}\n\n/**\n * Checks if the value matches a regex or includes the string\n * @param value The string value to be checked against\n * @param pattern Either a regex or a string that must be contained in value\n */\nexport function isMatchingPattern(value: string, pattern: RegExp | string): boolean {\n if (!isString(value)) {\n return false;\n }\n\n if (isRegExp(pattern)) {\n return (pattern as RegExp).test(value);\n }\n if (typeof pattern === 'string') {\n return value.indexOf(pattern) !== -1;\n }\n return false;\n}\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./Home.js\") );\n\t\t\t}, \"route-Home\");\n\t\t}\n\n\t\texport default Async(load);\n\t","import options from './options';\n\n/**\n * Create an virtual node (used for JSX)\n * @param {import('./internal').VNode[\"type\"]} type The node name or Component\n * constructor for this virtual node\n * @param {object | null | undefined} [props] The properties of the virtual node\n * @param {Array} [children] The children of the virtual node\n * @returns {import('./internal').VNode}\n */\nexport function createElement(type, props, children) {\n\tlet normalizedProps = {},\n\t\ti;\n\tfor (i in props) {\n\t\tif (i !== 'key' && i !== 'ref') normalizedProps[i] = props[i];\n\t}\n\n\tif (arguments.length > 3) {\n\t\tchildren = [children];\n\t\t// https://github.com/preactjs/preact/issues/1916\n\t\tfor (i = 3; i < arguments.length; i++) {\n\t\t\tchildren.push(arguments[i]);\n\t\t}\n\t}\n\tif (children != null) {\n\t\tnormalizedProps.children = children;\n\t}\n\n\t// If a Component VNode, check for and apply defaultProps\n\t// Note: type may be undefined in development, must never error here.\n\tif (typeof type == 'function' && type.defaultProps != null) {\n\t\tfor (i in type.defaultProps) {\n\t\t\tif (normalizedProps[i] === undefined) {\n\t\t\t\tnormalizedProps[i] = type.defaultProps[i];\n\t\t\t}\n\t\t}\n\t}\n\n\treturn createVNode(\n\t\ttype,\n\t\tnormalizedProps,\n\t\tprops && props.key,\n\t\tprops && props.ref,\n\t\tnull\n\t);\n}\n\n/**\n * Create a VNode (used internally by Preact)\n * @param {import('./internal').VNode[\"type\"]} type The node name or Component\n * Constructor for this virtual node\n * @param {object | string | number | null} props The properties of this virtual node.\n * If this virtual node represents a text node, this is the text of the node (string or number).\n * @param {string | number | null} key The key for this virtual node, used when\n * diffing it against its children\n * @param {import('./internal').VNode[\"ref\"]} ref The ref property that will\n * receive a reference to its created child\n * @returns {import('./internal').VNode}\n */\nexport function createVNode(type, props, key, ref, original) {\n\t// V8 seems to be better at detecting type shapes if the object is allocated from the same call site\n\t// Do not inline into createElement and coerceToVNode!\n\tconst vnode = {\n\t\ttype,\n\t\tprops,\n\t\tkey,\n\t\tref,\n\t\t_children: null,\n\t\t_parent: null,\n\t\t_depth: 0,\n\t\t_dom: null,\n\t\t// _nextDom must be initialized to undefined b/c it will eventually\n\t\t// be set to dom.nextSibling which can return `null` and it is important\n\t\t// to be able to distinguish between an uninitialized _nextDom and\n\t\t// a _nextDom that has been set to `null`\n\t\t_nextDom: undefined,\n\t\t_component: null,\n\t\tconstructor: undefined,\n\t\t_original: original\n\t};\n\n\tif (original == null) vnode._original = vnode;\n\tif (options.vnode) options.vnode(vnode);\n\n\treturn vnode;\n}\n\nexport function createRef() {\n\treturn {};\n}\n\nexport function Fragment(props) {\n\treturn props.children;\n}\n\n/**\n * Check if a the argument is a valid Preact VNode.\n * @param {*} vnode\n * @returns {vnode is import('./internal').VNode}\n */\nexport const isValidElement = vnode =>\n\tvnode != null && vnode.constructor === undefined;\n","import { assign } from './util';\nimport { diff, commitRoot } from './diff/index';\nimport options from './options';\nimport { Fragment } from './create-element';\n\n/**\n * Base Component class. Provides `setState()` and `forceUpdate()`, which\n * trigger rendering\n * @param {object} props The initial component props\n * @param {object} context The initial context from parent components'\n * getChildContext\n */\nexport function Component(props, context) {\n\tthis.props = props;\n\tthis.context = context;\n}\n\n/**\n * Update component state and schedule a re-render.\n * @param {object | ((s: object, p: object) => object)} update A hash of state\n * properties to update with new values or a function that given the current\n * state and props returns a new partial state\n * @param {() => void} [callback] A function to be called once component state is\n * updated\n */\nComponent.prototype.setState = function(update, callback) {\n\t// only clone state when copying to nextState the first time.\n\tlet s;\n\tif (this._nextState !== this.state) {\n\t\ts = this._nextState;\n\t} else {\n\t\ts = this._nextState = assign({}, this.state);\n\t}\n\n\tif (typeof update == 'function') {\n\t\tupdate = update(s, this.props);\n\t}\n\n\tif (update) {\n\t\tassign(s, update);\n\t}\n\n\t// Skip update if updater function returned null\n\tif (update == null) return;\n\n\tif (this._vnode) {\n\t\tif (callback) this._renderCallbacks.push(callback);\n\t\tenqueueRender(this);\n\t}\n};\n\n/**\n * Immediately perform a synchronous re-render of the component\n * @param {() => void} [callback] A function to be called after component is\n * re-rendered\n */\nComponent.prototype.forceUpdate = function(callback) {\n\tif (this._vnode) {\n\t\t// Set render mode so that we can differentiate where the render request\n\t\t// is coming from. We need this because forceUpdate should never call\n\t\t// shouldComponentUpdate\n\t\tthis._force = true;\n\t\tif (callback) this._renderCallbacks.push(callback);\n\t\tenqueueRender(this);\n\t}\n};\n\n/**\n * Accepts `props` and `state`, and returns a new Virtual DOM tree to build.\n * Virtual DOM is generally constructed via [JSX](http://jasonformat.com/wtf-is-jsx).\n * @param {object} props Props (eg: JSX attributes) received from parent\n * element/component\n * @param {object} state The component's current state\n * @param {object} context Context object, as returned by the nearest\n * ancestor's `getChildContext()`\n * @returns {import('./index').ComponentChildren | void}\n */\nComponent.prototype.render = Fragment;\n\n/**\n * @param {import('./internal').VNode} vnode\n * @param {number | null} [childIndex]\n */\nexport function getDomSibling(vnode, childIndex) {\n\tif (childIndex == null) {\n\t\t// Use childIndex==null as a signal to resume the search from the vnode's sibling\n\t\treturn vnode._parent\n\t\t\t? getDomSibling(vnode._parent, vnode._parent._children.indexOf(vnode) + 1)\n\t\t\t: null;\n\t}\n\n\tlet sibling;\n\tfor (; childIndex < vnode._children.length; childIndex++) {\n\t\tsibling = vnode._children[childIndex];\n\n\t\tif (sibling != null && sibling._dom != null) {\n\t\t\t// Since updateParentDomPointers keeps _dom pointer correct,\n\t\t\t// we can rely on _dom to tell us if this subtree contains a\n\t\t\t// rendered DOM node, and what the first rendered DOM node is\n\t\t\treturn sibling._dom;\n\t\t}\n\t}\n\n\t// If we get here, we have not found a DOM node in this vnode's children.\n\t// We must resume from this vnode's sibling (in it's parent _children array)\n\t// Only climb up and search the parent if we aren't searching through a DOM\n\t// VNode (meaning we reached the DOM parent of the original vnode that began\n\t// the search)\n\treturn typeof vnode.type == 'function' ? getDomSibling(vnode) : null;\n}\n\n/**\n * Trigger in-place re-rendering of a component.\n * @param {import('./internal').Component} component The component to rerender\n */\nfunction renderComponent(component) {\n\tlet vnode = component._vnode,\n\t\toldDom = vnode._dom,\n\t\tparentDom = component._parentDom;\n\n\tif (parentDom) {\n\t\tlet commitQueue = [];\n\t\tconst oldVNode = assign({}, vnode);\n\t\toldVNode._original = oldVNode;\n\n\t\tlet newDom = diff(\n\t\t\tparentDom,\n\t\t\tvnode,\n\t\t\toldVNode,\n\t\t\tcomponent._globalContext,\n\t\t\tparentDom.ownerSVGElement !== undefined,\n\t\t\tnull,\n\t\t\tcommitQueue,\n\t\t\toldDom == null ? getDomSibling(vnode) : oldDom\n\t\t);\n\t\tcommitRoot(commitQueue, vnode);\n\n\t\tif (newDom != oldDom) {\n\t\t\tupdateParentDomPointers(vnode);\n\t\t}\n\t}\n}\n\n/**\n * @param {import('./internal').VNode} vnode\n */\nfunction updateParentDomPointers(vnode) {\n\tif ((vnode = vnode._parent) != null && vnode._component != null) {\n\t\tvnode._dom = vnode._component.base = null;\n\t\tfor (let i = 0; i < vnode._children.length; i++) {\n\t\t\tlet child = vnode._children[i];\n\t\t\tif (child != null && child._dom != null) {\n\t\t\t\tvnode._dom = vnode._component.base = child._dom;\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\n\t\treturn updateParentDomPointers(vnode);\n\t}\n}\n\n/**\n * The render queue\n * @type {Array}\n */\nlet rerenderQueue = [];\nlet rerenderCount = 0;\n\n/**\n * Asynchronously schedule a callback\n * @type {(cb: () => void) => void}\n */\n/* istanbul ignore next */\n// Note the following line isn't tree-shaken by rollup cuz of rollup/rollup#2566\nconst defer =\n\ttypeof Promise == 'function'\n\t\t? Promise.prototype.then.bind(Promise.resolve())\n\t\t: setTimeout;\n\n/*\n * The value of `Component.debounce` must asynchronously invoke the passed in callback. It is\n * important that contributors to Preact can consistently reason about what calls to `setState`, etc.\n * do, and when their effects will be applied. See the links below for some further reading on designing\n * asynchronous APIs.\n * * [Designing APIs for Asynchrony](https://blog.izs.me/2013/08/designing-apis-for-asynchrony)\n * * [Callbacks synchronous and asynchronous](https://blog.ometer.com/2011/07/24/callbacks-synchronous-and-asynchronous/)\n */\n\nlet prevDebounce;\n\n/**\n * Enqueue a rerender of a component\n * @param {import('./internal').Component} c The component to rerender\n */\nexport function enqueueRender(c) {\n\tif (\n\t\t(!c._dirty &&\n\t\t\t(c._dirty = true) &&\n\t\t\trerenderQueue.push(c) &&\n\t\t\t!rerenderCount++) ||\n\t\tprevDebounce !== options.debounceRendering\n\t) {\n\t\tprevDebounce = options.debounceRendering;\n\t\t(prevDebounce || defer)(process);\n\t}\n}\n\n/** Flush the render queue by rerendering all queued components */\nfunction process() {\n\tlet queue;\n\twhile ((rerenderCount = rerenderQueue.length)) {\n\t\tqueue = rerenderQueue.sort((a, b) => a._vnode._depth - b._vnode._depth);\n\t\trerenderQueue = [];\n\t\t// Don't update `renderCount` yet. Keep its value non-zero to prevent unnecessary\n\t\t// process() calls from getting scheduled while `queue` is still being consumed.\n\t\tqueue.some(c => {\n\t\t\tif (c._dirty) renderComponent(c);\n\t\t});\n\t}\n}\n","import { diff, unmount, applyRef } from './index';\nimport { createVNode, Fragment } from '../create-element';\nimport { EMPTY_OBJ, EMPTY_ARR } from '../constants';\nimport { removeNode } from '../util';\nimport { getDomSibling } from '../component';\n\n/**\n * Diff the children of a virtual node\n * @param {import('../internal').PreactElement} parentDom The DOM element whose\n * children are being diffed\n * @param {import('../index').ComponentChildren[]} renderResult\n * @param {import('../internal').VNode} newParentVNode The new virtual\n * node whose children should be diff'ed against oldParentVNode\n * @param {import('../internal').VNode} oldParentVNode The old virtual\n * node whose children should be diff'ed against newParentVNode\n * @param {object} globalContext The current context object - modified by getChildContext\n * @param {boolean} isSvg Whether or not this DOM node is an SVG node\n * @param {Array} excessDomChildren\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {Node | Text} oldDom The current attached DOM\n * element any new dom elements should be placed around. Likely `null` on first\n * render (except when hydrating). Can be a sibling DOM element when diffing\n * Fragments that have siblings. In most cases, it starts out as `oldChildren[0]._dom`.\n * @param {boolean} isHydrating Whether or not we are in hydration\n */\nexport function diffChildren(\n\tparentDom,\n\trenderResult,\n\tnewParentVNode,\n\toldParentVNode,\n\tglobalContext,\n\tisSvg,\n\texcessDomChildren,\n\tcommitQueue,\n\toldDom,\n\tisHydrating\n) {\n\tlet i, j, oldVNode, childVNode, newDom, sibDom, firstChildDom, refs;\n\n\t// This is a compression of oldParentVNode!=null && oldParentVNode != EMPTY_OBJ && oldParentVNode._children || EMPTY_ARR\n\t// as EMPTY_OBJ._children should be `undefined`.\n\tlet oldChildren = (oldParentVNode && oldParentVNode._children) || EMPTY_ARR;\n\n\tlet oldChildrenLength = oldChildren.length;\n\n\t// Only in very specific places should this logic be invoked (top level `render` and `diffElementNodes`).\n\t// I'm using `EMPTY_OBJ` to signal when `diffChildren` is invoked in these situations. I can't use `null`\n\t// for this purpose, because `null` is a valid value for `oldDom` which can mean to skip to this logic\n\t// (e.g. if mounting a new tree in which the old DOM should be ignored (usually for Fragments).\n\tif (oldDom == EMPTY_OBJ) {\n\t\tif (excessDomChildren != null) {\n\t\t\toldDom = excessDomChildren[0];\n\t\t} else if (oldChildrenLength) {\n\t\t\toldDom = getDomSibling(oldParentVNode, 0);\n\t\t} else {\n\t\t\toldDom = null;\n\t\t}\n\t}\n\n\tnewParentVNode._children = [];\n\tfor (i = 0; i < renderResult.length; i++) {\n\t\tchildVNode = renderResult[i];\n\n\t\tif (childVNode == null || typeof childVNode == 'boolean') {\n\t\t\tchildVNode = newParentVNode._children[i] = null;\n\t\t}\n\t\t// If this newVNode is being reused (e.g.
{reuse}{reuse}
) in the same diff,\n\t\t// or we are rendering a component (e.g. setState) copy the oldVNodes so it can have\n\t\t// it's own DOM & etc. pointers\n\t\telse if (typeof childVNode == 'string' || typeof childVNode == 'number') {\n\t\t\tchildVNode = newParentVNode._children[i] = createVNode(\n\t\t\t\tnull,\n\t\t\t\tchildVNode,\n\t\t\t\tnull,\n\t\t\t\tnull,\n\t\t\t\tchildVNode\n\t\t\t);\n\t\t} else if (Array.isArray(childVNode)) {\n\t\t\tchildVNode = newParentVNode._children[i] = createVNode(\n\t\t\t\tFragment,\n\t\t\t\t{ children: childVNode },\n\t\t\t\tnull,\n\t\t\t\tnull,\n\t\t\t\tnull\n\t\t\t);\n\t\t} else if (childVNode._dom != null || childVNode._component != null) {\n\t\t\tchildVNode = newParentVNode._children[i] = createVNode(\n\t\t\t\tchildVNode.type,\n\t\t\t\tchildVNode.props,\n\t\t\t\tchildVNode.key,\n\t\t\t\tnull,\n\t\t\t\tchildVNode._original\n\t\t\t);\n\t\t} else {\n\t\t\tchildVNode = newParentVNode._children[i] = childVNode;\n\t\t}\n\n\t\t// Terser removes the `continue` here and wraps the loop body\n\t\t// in a `if (childVNode) { ... } condition\n\t\tif (childVNode == null) {\n\t\t\tcontinue;\n\t\t}\n\n\t\tchildVNode._parent = newParentVNode;\n\t\tchildVNode._depth = newParentVNode._depth + 1;\n\n\t\t// Check if we find a corresponding element in oldChildren.\n\t\t// If found, delete the array item by setting to `undefined`.\n\t\t// We use `undefined`, as `null` is reserved for empty placeholders\n\t\t// (holes).\n\t\toldVNode = oldChildren[i];\n\n\t\tif (\n\t\t\toldVNode === null ||\n\t\t\t(oldVNode &&\n\t\t\t\tchildVNode.key == oldVNode.key &&\n\t\t\t\tchildVNode.type === oldVNode.type)\n\t\t) {\n\t\t\toldChildren[i] = undefined;\n\t\t} else {\n\t\t\t// Either oldVNode === undefined or oldChildrenLength > 0,\n\t\t\t// so after this loop oldVNode == null or oldVNode is a valid value.\n\t\t\tfor (j = 0; j < oldChildrenLength; j++) {\n\t\t\t\toldVNode = oldChildren[j];\n\t\t\t\t// If childVNode is unkeyed, we only match similarly unkeyed nodes, otherwise we match by key.\n\t\t\t\t// We always match by type (in either case).\n\t\t\t\tif (\n\t\t\t\t\toldVNode &&\n\t\t\t\t\tchildVNode.key == oldVNode.key &&\n\t\t\t\t\tchildVNode.type === oldVNode.type\n\t\t\t\t) {\n\t\t\t\t\toldChildren[j] = undefined;\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t\toldVNode = null;\n\t\t\t}\n\t\t}\n\n\t\toldVNode = oldVNode || EMPTY_OBJ;\n\n\t\t// Morph the old element into the new one, but don't append it to the dom yet\n\t\tnewDom = diff(\n\t\t\tparentDom,\n\t\t\tchildVNode,\n\t\t\toldVNode,\n\t\t\tglobalContext,\n\t\t\tisSvg,\n\t\t\texcessDomChildren,\n\t\t\tcommitQueue,\n\t\t\toldDom,\n\t\t\tisHydrating\n\t\t);\n\n\t\tif ((j = childVNode.ref) && oldVNode.ref != j) {\n\t\t\tif (!refs) refs = [];\n\t\t\tif (oldVNode.ref) refs.push(oldVNode.ref, null, childVNode);\n\t\t\trefs.push(j, childVNode._component || newDom, childVNode);\n\t\t}\n\n\t\t// Only proceed if the vnode has not been unmounted by `diff()` above.\n\t\tif (newDom != null) {\n\t\t\tif (firstChildDom == null) {\n\t\t\t\tfirstChildDom = newDom;\n\t\t\t}\n\n\t\t\tlet nextDom;\n\t\t\tif (childVNode._nextDom !== undefined) {\n\t\t\t\t// Only Fragments or components that return Fragment like VNodes will\n\t\t\t\t// have a non-undefined _nextDom. Continue the diff from the sibling\n\t\t\t\t// of last DOM child of this child VNode\n\t\t\t\tnextDom = childVNode._nextDom;\n\n\t\t\t\t// Eagerly cleanup _nextDom. We don't need to persist the value because\n\t\t\t\t// it is only used by `diffChildren` to determine where to resume the diff after\n\t\t\t\t// diffing Components and Fragments. Once we store it the nextDOM local var, we\n\t\t\t\t// can clean up the property\n\t\t\t\tchildVNode._nextDom = undefined;\n\t\t\t} else if (\n\t\t\t\texcessDomChildren == oldVNode ||\n\t\t\t\tnewDom != oldDom ||\n\t\t\t\tnewDom.parentNode == null\n\t\t\t) {\n\t\t\t\t// NOTE: excessDomChildren==oldVNode above:\n\t\t\t\t// This is a compression of excessDomChildren==null && oldVNode==null!\n\t\t\t\t// The values only have the same type when `null`.\n\n\t\t\t\touter: if (oldDom == null || oldDom.parentNode !== parentDom) {\n\t\t\t\t\tparentDom.appendChild(newDom);\n\t\t\t\t\tnextDom = null;\n\t\t\t\t} else {\n\t\t\t\t\t// `j} excessDomChildren\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {Element | Text} oldDom The current attached DOM\n * element any new dom elements should be placed around. Likely `null` on first\n * render (except when hydrating). Can be a sibling DOM element when diffing\n * Fragments that have siblings. In most cases, it starts out as `oldChildren[0]._dom`.\n * @param {boolean} [isHydrating] Whether or not we are in hydration\n */\nexport function diff(\n\tparentDom,\n\tnewVNode,\n\toldVNode,\n\tglobalContext,\n\tisSvg,\n\texcessDomChildren,\n\tcommitQueue,\n\toldDom,\n\tisHydrating\n) {\n\tlet tmp,\n\t\tnewType = newVNode.type;\n\n\t// When passing through createElement it assigns the object\n\t// constructor as undefined. This to prevent JSON-injection.\n\tif (newVNode.constructor !== undefined) return null;\n\n\tif ((tmp = options._diff)) tmp(newVNode);\n\n\ttry {\n\t\touter: if (typeof newType == 'function') {\n\t\t\tlet c, isNew, oldProps, oldState, snapshot, clearProcessingException;\n\t\t\tlet newProps = newVNode.props;\n\n\t\t\t// Necessary for createContext api. Setting this property will pass\n\t\t\t// the context value as `this.context` just for this component.\n\t\t\ttmp = newType.contextType;\n\t\t\tlet provider = tmp && globalContext[tmp._id];\n\t\t\tlet componentContext = tmp\n\t\t\t\t? provider\n\t\t\t\t\t? provider.props.value\n\t\t\t\t\t: tmp._defaultValue\n\t\t\t\t: globalContext;\n\n\t\t\t// Get component and set it to `c`\n\t\t\tif (oldVNode._component) {\n\t\t\t\tc = newVNode._component = oldVNode._component;\n\t\t\t\tclearProcessingException = c._processingException = c._pendingError;\n\t\t\t} else {\n\t\t\t\t// Instantiate the new component\n\t\t\t\tif ('prototype' in newType && newType.prototype.render) {\n\t\t\t\t\tnewVNode._component = c = new newType(newProps, componentContext); // eslint-disable-line new-cap\n\t\t\t\t} else {\n\t\t\t\t\tnewVNode._component = c = new Component(newProps, componentContext);\n\t\t\t\t\tc.constructor = newType;\n\t\t\t\t\tc.render = doRender;\n\t\t\t\t}\n\t\t\t\tif (provider) provider.sub(c);\n\n\t\t\t\tc.props = newProps;\n\t\t\t\tif (!c.state) c.state = {};\n\t\t\t\tc.context = componentContext;\n\t\t\t\tc._globalContext = globalContext;\n\t\t\t\tisNew = c._dirty = true;\n\t\t\t\tc._renderCallbacks = [];\n\t\t\t}\n\n\t\t\t// Invoke getDerivedStateFromProps\n\t\t\tif (c._nextState == null) {\n\t\t\t\tc._nextState = c.state;\n\t\t\t}\n\t\t\tif (newType.getDerivedStateFromProps != null) {\n\t\t\t\tif (c._nextState == c.state) {\n\t\t\t\t\tc._nextState = assign({}, c._nextState);\n\t\t\t\t}\n\n\t\t\t\tassign(\n\t\t\t\t\tc._nextState,\n\t\t\t\t\tnewType.getDerivedStateFromProps(newProps, c._nextState)\n\t\t\t\t);\n\t\t\t}\n\n\t\t\toldProps = c.props;\n\t\t\toldState = c.state;\n\n\t\t\t// Invoke pre-render lifecycle methods\n\t\t\tif (isNew) {\n\t\t\t\tif (\n\t\t\t\t\tnewType.getDerivedStateFromProps == null &&\n\t\t\t\t\tc.componentWillMount != null\n\t\t\t\t) {\n\t\t\t\t\tc.componentWillMount();\n\t\t\t\t}\n\n\t\t\t\tif (c.componentDidMount != null) {\n\t\t\t\t\tc._renderCallbacks.push(c.componentDidMount);\n\t\t\t\t}\n\t\t\t} else {\n\t\t\t\tif (\n\t\t\t\t\tnewType.getDerivedStateFromProps == null &&\n\t\t\t\t\tnewProps !== oldProps &&\n\t\t\t\t\tc.componentWillReceiveProps != null\n\t\t\t\t) {\n\t\t\t\t\tc.componentWillReceiveProps(newProps, componentContext);\n\t\t\t\t}\n\n\t\t\t\tif (\n\t\t\t\t\t(!c._force &&\n\t\t\t\t\t\tc.shouldComponentUpdate != null &&\n\t\t\t\t\t\tc.shouldComponentUpdate(\n\t\t\t\t\t\t\tnewProps,\n\t\t\t\t\t\t\tc._nextState,\n\t\t\t\t\t\t\tcomponentContext\n\t\t\t\t\t\t) === false) ||\n\t\t\t\t\tnewVNode._original === oldVNode._original\n\t\t\t\t) {\n\t\t\t\t\tc.props = newProps;\n\t\t\t\t\tc.state = c._nextState;\n\t\t\t\t\t// More info about this here: https://gist.github.com/JoviDeCroock/bec5f2ce93544d2e6070ef8e0036e4e8\n\t\t\t\t\tif (newVNode._original !== oldVNode._original) c._dirty = false;\n\t\t\t\t\tc._vnode = newVNode;\n\t\t\t\t\tnewVNode._dom = oldVNode._dom;\n\t\t\t\t\tnewVNode._children = oldVNode._children;\n\t\t\t\t\tif (c._renderCallbacks.length) {\n\t\t\t\t\t\tcommitQueue.push(c);\n\t\t\t\t\t}\n\n\t\t\t\t\tfor (tmp = 0; tmp < newVNode._children.length; tmp++) {\n\t\t\t\t\t\tif (newVNode._children[tmp]) {\n\t\t\t\t\t\t\tnewVNode._children[tmp]._parent = newVNode;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\n\t\t\t\t\tbreak outer;\n\t\t\t\t}\n\n\t\t\t\tif (c.componentWillUpdate != null) {\n\t\t\t\t\tc.componentWillUpdate(newProps, c._nextState, componentContext);\n\t\t\t\t}\n\n\t\t\t\tif (c.componentDidUpdate != null) {\n\t\t\t\t\tc._renderCallbacks.push(() => {\n\t\t\t\t\t\tc.componentDidUpdate(oldProps, oldState, snapshot);\n\t\t\t\t\t});\n\t\t\t\t}\n\t\t\t}\n\n\t\t\tc.context = componentContext;\n\t\t\tc.props = newProps;\n\t\t\tc.state = c._nextState;\n\n\t\t\tif ((tmp = options._render)) tmp(newVNode);\n\n\t\t\tc._dirty = false;\n\t\t\tc._vnode = newVNode;\n\t\t\tc._parentDom = parentDom;\n\n\t\t\ttmp = c.render(c.props, c.state, c.context);\n\n\t\t\tif (c.getChildContext != null) {\n\t\t\t\tglobalContext = assign(assign({}, globalContext), c.getChildContext());\n\t\t\t}\n\n\t\t\tif (!isNew && c.getSnapshotBeforeUpdate != null) {\n\t\t\t\tsnapshot = c.getSnapshotBeforeUpdate(oldProps, oldState);\n\t\t\t}\n\n\t\t\tlet isTopLevelFragment =\n\t\t\t\ttmp != null && tmp.type == Fragment && tmp.key == null;\n\t\t\tlet renderResult = isTopLevelFragment ? tmp.props.children : tmp;\n\n\t\t\tdiffChildren(\n\t\t\t\tparentDom,\n\t\t\t\tArray.isArray(renderResult) ? renderResult : [renderResult],\n\t\t\t\tnewVNode,\n\t\t\t\toldVNode,\n\t\t\t\tglobalContext,\n\t\t\t\tisSvg,\n\t\t\t\texcessDomChildren,\n\t\t\t\tcommitQueue,\n\t\t\t\toldDom,\n\t\t\t\tisHydrating\n\t\t\t);\n\n\t\t\tc.base = newVNode._dom;\n\n\t\t\tif (c._renderCallbacks.length) {\n\t\t\t\tcommitQueue.push(c);\n\t\t\t}\n\n\t\t\tif (clearProcessingException) {\n\t\t\t\tc._pendingError = c._processingException = null;\n\t\t\t}\n\n\t\t\tc._force = false;\n\t\t} else if (\n\t\t\texcessDomChildren == null &&\n\t\t\tnewVNode._original === oldVNode._original\n\t\t) {\n\t\t\tnewVNode._children = oldVNode._children;\n\t\t\tnewVNode._dom = oldVNode._dom;\n\t\t} else {\n\t\t\tnewVNode._dom = diffElementNodes(\n\t\t\t\toldVNode._dom,\n\t\t\t\tnewVNode,\n\t\t\t\toldVNode,\n\t\t\t\tglobalContext,\n\t\t\t\tisSvg,\n\t\t\t\texcessDomChildren,\n\t\t\t\tcommitQueue,\n\t\t\t\tisHydrating\n\t\t\t);\n\t\t}\n\n\t\tif ((tmp = options.diffed)) tmp(newVNode);\n\t} catch (e) {\n\t\tnewVNode._original = null;\n\t\toptions._catchError(e, newVNode, oldVNode);\n\t}\n\n\treturn newVNode._dom;\n}\n\n/**\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {import('../internal').VNode} root\n */\nexport function commitRoot(commitQueue, root) {\n\tif (options._commit) options._commit(root, commitQueue);\n\n\tcommitQueue.some(c => {\n\t\ttry {\n\t\t\tcommitQueue = c._renderCallbacks;\n\t\t\tc._renderCallbacks = [];\n\t\t\tcommitQueue.some(cb => {\n\t\t\t\tcb.call(c);\n\t\t\t});\n\t\t} catch (e) {\n\t\t\toptions._catchError(e, c._vnode);\n\t\t}\n\t});\n}\n\n/**\n * Diff two virtual nodes representing DOM element\n * @param {import('../internal').PreactElement} dom The DOM element representing\n * the virtual nodes being diffed\n * @param {import('../internal').VNode} newVNode The new virtual node\n * @param {import('../internal').VNode} oldVNode The old virtual node\n * @param {object} globalContext The current context object\n * @param {boolean} isSvg Whether or not this DOM node is an SVG node\n * @param {*} excessDomChildren\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {boolean} isHydrating Whether or not we are in hydration\n * @returns {import('../internal').PreactElement}\n */\nfunction diffElementNodes(\n\tdom,\n\tnewVNode,\n\toldVNode,\n\tglobalContext,\n\tisSvg,\n\texcessDomChildren,\n\tcommitQueue,\n\tisHydrating\n) {\n\tlet i;\n\tlet oldProps = oldVNode.props;\n\tlet newProps = newVNode.props;\n\n\t// Tracks entering and exiting SVG namespace when descending through the tree.\n\tisSvg = newVNode.type === 'svg' || isSvg;\n\n\tif (excessDomChildren != null) {\n\t\tfor (i = 0; i < excessDomChildren.length; i++) {\n\t\t\tconst child = excessDomChildren[i];\n\n\t\t\t// if newVNode matches an element in excessDomChildren or the `dom`\n\t\t\t// argument matches an element in excessDomChildren, remove it from\n\t\t\t// excessDomChildren so it isn't later removed in diffChildren\n\t\t\tif (\n\t\t\t\tchild != null &&\n\t\t\t\t((newVNode.type === null\n\t\t\t\t\t? child.nodeType === 3\n\t\t\t\t\t: child.localName === newVNode.type) ||\n\t\t\t\t\tdom == child)\n\t\t\t) {\n\t\t\t\tdom = child;\n\t\t\t\texcessDomChildren[i] = null;\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\t}\n\n\tif (dom == null) {\n\t\tif (newVNode.type === null) {\n\t\t\treturn document.createTextNode(newProps);\n\t\t}\n\n\t\tdom = isSvg\n\t\t\t? document.createElementNS('http://www.w3.org/2000/svg', newVNode.type)\n\t\t\t: document.createElement(\n\t\t\t\t\tnewVNode.type,\n\t\t\t\t\tnewProps.is && { is: newProps.is }\n\t\t\t );\n\t\t// we created a new parent, so none of the previously attached children can be reused:\n\t\texcessDomChildren = null;\n\t\t// we are creating a new node, so we can assume this is a new subtree (in case we are hydrating), this deopts the hydrate\n\t\tisHydrating = false;\n\t}\n\n\tif (newVNode.type === null) {\n\t\tif (oldProps !== newProps && dom.data != newProps) {\n\t\t\tdom.data = newProps;\n\t\t}\n\t} else {\n\t\tif (excessDomChildren != null) {\n\t\t\texcessDomChildren = EMPTY_ARR.slice.call(dom.childNodes);\n\t\t}\n\n\t\toldProps = oldVNode.props || EMPTY_OBJ;\n\n\t\tlet oldHtml = oldProps.dangerouslySetInnerHTML;\n\t\tlet newHtml = newProps.dangerouslySetInnerHTML;\n\n\t\t// During hydration, props are not diffed at all (including dangerouslySetInnerHTML)\n\t\t// @TODO we should warn in debug mode when props don't match here.\n\t\tif (!isHydrating) {\n\t\t\t// But, if we are in a situation where we are using existing DOM (e.g. replaceNode)\n\t\t\t// we should read the existing DOM attributes to diff them\n\t\t\tif (excessDomChildren != null) {\n\t\t\t\toldProps = {};\n\t\t\t\tfor (let i = 0; i < dom.attributes.length; i++) {\n\t\t\t\t\toldProps[dom.attributes[i].name] = dom.attributes[i].value;\n\t\t\t\t}\n\t\t\t}\n\n\t\t\tif (newHtml || oldHtml) {\n\t\t\t\t// Avoid re-applying the same '__html' if it did not changed between re-render\n\t\t\t\tif (!newHtml || !oldHtml || newHtml.__html != oldHtml.__html) {\n\t\t\t\t\tdom.innerHTML = (newHtml && newHtml.__html) || '';\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t\tdiffProps(dom, newProps, oldProps, isSvg, isHydrating);\n\n\t\t// If the new vnode didn't have dangerouslySetInnerHTML, diff its children\n\t\tif (newHtml) {\n\t\t\tnewVNode._children = [];\n\t\t} else {\n\t\t\ti = newVNode.props.children;\n\t\t\tdiffChildren(\n\t\t\t\tdom,\n\t\t\t\tArray.isArray(i) ? i : [i],\n\t\t\t\tnewVNode,\n\t\t\t\toldVNode,\n\t\t\t\tglobalContext,\n\t\t\t\tnewVNode.type === 'foreignObject' ? false : isSvg,\n\t\t\t\texcessDomChildren,\n\t\t\t\tcommitQueue,\n\t\t\t\tEMPTY_OBJ,\n\t\t\t\tisHydrating\n\t\t\t);\n\t\t}\n\n\t\t// (as above, don't diff props during hydration)\n\t\tif (!isHydrating) {\n\t\t\tif (\n\t\t\t\t'value' in newProps &&\n\t\t\t\t(i = newProps.value) !== undefined &&\n\t\t\t\ti !== dom.value\n\t\t\t) {\n\t\t\t\tsetProperty(dom, 'value', i, oldProps.value, false);\n\t\t\t}\n\t\t\tif (\n\t\t\t\t'checked' in newProps &&\n\t\t\t\t(i = newProps.checked) !== undefined &&\n\t\t\t\ti !== dom.checked\n\t\t\t) {\n\t\t\t\tsetProperty(dom, 'checked', i, oldProps.checked, false);\n\t\t\t}\n\t\t}\n\t}\n\n\treturn dom;\n}\n\n/**\n * Invoke or update a ref, depending on whether it is a function or object ref.\n * @param {object|function} ref\n * @param {any} value\n * @param {import('../internal').VNode} vnode\n */\nexport function applyRef(ref, value, vnode) {\n\ttry {\n\t\tif (typeof ref == 'function') ref(value);\n\t\telse ref.current = value;\n\t} catch (e) {\n\t\toptions._catchError(e, vnode);\n\t}\n}\n\n/**\n * Unmount a virtual node from the tree and apply DOM changes\n * @param {import('../internal').VNode} vnode The virtual node to unmount\n * @param {import('../internal').VNode} parentVNode The parent of the VNode that\n * initiated the unmount\n * @param {boolean} [skipRemove] Flag that indicates that a parent node of the\n * current element is already detached from the DOM.\n */\nexport function unmount(vnode, parentVNode, skipRemove) {\n\tlet r;\n\tif (options.unmount) options.unmount(vnode);\n\n\tif ((r = vnode.ref)) {\n\t\tif (!r.current || r.current === vnode._dom) applyRef(r, null, parentVNode);\n\t}\n\n\tlet dom;\n\tif (!skipRemove && typeof vnode.type != 'function') {\n\t\tskipRemove = (dom = vnode._dom) != null;\n\t}\n\n\t// Must be set to `undefined` to properly clean up `_nextDom`\n\t// for which `null` is a valid value. See comment in `create-element.js`\n\tvnode._dom = vnode._nextDom = undefined;\n\n\tif ((r = vnode._component) != null) {\n\t\tif (r.componentWillUnmount) {\n\t\t\ttry {\n\t\t\t\tr.componentWillUnmount();\n\t\t\t} catch (e) {\n\t\t\t\toptions._catchError(e, parentVNode);\n\t\t\t}\n\t\t}\n\n\t\tr.base = r._parentDom = null;\n\t}\n\n\tif ((r = vnode._children)) {\n\t\tfor (let i = 0; i < r.length; i++) {\n\t\t\tif (r[i]) unmount(r[i], parentVNode, skipRemove);\n\t\t}\n\t}\n\n\tif (dom != null) removeNode(dom);\n}\n\n/** The `.render()` method for a PFC backing instance. */\nfunction doRender(props, state, context) {\n\treturn this.constructor(props, context);\n}\n","import { EMPTY_OBJ, EMPTY_ARR } from './constants';\nimport { commitRoot, diff } from './diff/index';\nimport { createElement, Fragment } from './create-element';\nimport options from './options';\n\nconst IS_HYDRATE = EMPTY_OBJ;\n\n/**\n * Render a Preact virtual node into a DOM element\n * @param {import('./index').ComponentChild} vnode The virtual node to render\n * @param {import('./internal').PreactElement} parentDom The DOM element to\n * render into\n * @param {Element | Text} [replaceNode] Optional: Attempt to re-use an\n * existing DOM tree rooted at `replaceNode`\n */\nexport function render(vnode, parentDom, replaceNode) {\n\tif (options._root) options._root(vnode, parentDom);\n\n\t// We abuse the `replaceNode` parameter in `hydrate()` to signal if we\n\t// are in hydration mode or not by passing `IS_HYDRATE` instead of a\n\t// DOM element.\n\tlet isHydrating = replaceNode === IS_HYDRATE;\n\n\t// To be able to support calling `render()` multiple times on the same\n\t// DOM node, we need to obtain a reference to the previous tree. We do\n\t// this by assigning a new `_children` property to DOM nodes which points\n\t// to the last rendered tree. By default this property is not present, which\n\t// means that we are mounting a new tree for the first time.\n\tlet oldVNode = isHydrating\n\t\t? null\n\t\t: (replaceNode && replaceNode._children) || parentDom._children;\n\tvnode = createElement(Fragment, null, [vnode]);\n\n\t// List of effects that need to be called after diffing.\n\tlet commitQueue = [];\n\tdiff(\n\t\tparentDom,\n\t\t// Determine the new vnode tree and store it on the DOM element on\n\t\t// our custom `_children` property.\n\t\t((isHydrating ? parentDom : replaceNode || parentDom)._children = vnode),\n\t\toldVNode || EMPTY_OBJ,\n\t\tEMPTY_OBJ,\n\t\tparentDom.ownerSVGElement !== undefined,\n\t\treplaceNode && !isHydrating\n\t\t\t? [replaceNode]\n\t\t\t: oldVNode\n\t\t\t? null\n\t\t\t: parentDom.childNodes.length\n\t\t\t? EMPTY_ARR.slice.call(parentDom.childNodes)\n\t\t\t: null,\n\t\tcommitQueue,\n\t\treplaceNode || EMPTY_OBJ,\n\t\tisHydrating\n\t);\n\n\t// Flush all queued effects\n\tcommitRoot(commitQueue, vnode);\n}\n\n/**\n * Update an existing DOM element with data from a Preact virtual node\n * @param {import('./index').ComponentChild} vnode The virtual node to render\n * @param {import('./internal').PreactElement} parentDom The DOM element to\n * update\n */\nexport function hydrate(vnode, parentDom) {\n\trender(vnode, parentDom, IS_HYDRATE);\n}\n","import { assign } from './util';\nimport { EMPTY_ARR } from './constants';\nimport { createVNode } from './create-element';\n\n/**\n * Clones the given VNode, optionally adding attributes/props and replacing its children.\n * @param {import('./internal').VNode} vnode The virtual DOM element to clone\n * @param {object} props Attributes/props to add when cloning\n * @param {Array} rest Any additional arguments will be used as replacement children.\n * @returns {import('./internal').VNode}\n */\nexport function cloneElement(vnode, props) {\n\tprops = assign(assign({}, vnode.props), props);\n\tif (arguments.length > 2) props.children = EMPTY_ARR.slice.call(arguments, 2);\n\tlet normalizedProps = {};\n\tfor (const i in props) {\n\t\tif (i !== 'key' && i !== 'ref') normalizedProps[i] = props[i];\n\t}\n\n\treturn createVNode(\n\t\tvnode.type,\n\t\tnormalizedProps,\n\t\tprops.key || vnode.key,\n\t\tprops.ref || vnode.ref,\n\t\tnull\n\t);\n}\n","import { enqueueRender } from './component';\n\nexport let i = 0;\n\nexport function createContext(defaultValue) {\n\tconst ctx = {};\n\n\tconst context = {\n\t\t_id: '__cC' + i++,\n\t\t_defaultValue: defaultValue,\n\t\tConsumer(props, context) {\n\t\t\treturn props.children(context);\n\t\t},\n\t\tProvider(props) {\n\t\t\tif (!this.getChildContext) {\n\t\t\t\tconst subs = [];\n\t\t\t\tthis.getChildContext = () => {\n\t\t\t\t\tctx[context._id] = this;\n\t\t\t\t\treturn ctx;\n\t\t\t\t};\n\n\t\t\t\tthis.shouldComponentUpdate = _props => {\n\t\t\t\t\tif (this.props.value !== _props.value) {\n\t\t\t\t\t\tsubs.some(c => {\n\t\t\t\t\t\t\tc.context = _props.value;\n\t\t\t\t\t\t\tenqueueRender(c);\n\t\t\t\t\t\t});\n\t\t\t\t\t}\n\t\t\t\t};\n\n\t\t\t\tthis.sub = c => {\n\t\t\t\t\tsubs.push(c);\n\t\t\t\t\tlet old = c.componentWillUnmount;\n\t\t\t\t\tc.componentWillUnmount = () => {\n\t\t\t\t\t\tsubs.splice(subs.indexOf(c), 1);\n\t\t\t\t\t\told && old.call(c);\n\t\t\t\t\t};\n\t\t\t\t};\n\t\t\t}\n\n\t\t\treturn props.children;\n\t\t}\n\t};\n\n\tcontext.Consumer.contextType = context;\n\n\t// Devtools needs access to the context object when it\n\t// encounters a Provider. This is necessary to support\n\t// setting `displayName` on the context object instead\n\t// of on the component itself. See:\n\t// https://reactjs.org/docs/context.html#contextdisplayname\n\tcontext.Provider._contextRef = context;\n\n\treturn context;\n}\n","export const EMPTY_OBJ = {};\nexport const EMPTY_ARR = [];\nexport const IS_NON_DIMENSIONAL = /acit|ex(?:s|g|n|p|$)|rph|grid|ows|mnc|ntw|ine[ch]|zoo|^ord|itera/i;\n","import { _catchError } from './diff/catch-error';\n\n/**\n * The `option` object can potentially contain callback functions\n * that are called during various stages of our renderer. This is the\n * foundation on which all our addons like `preact/debug`, `preact/compat`,\n * and `preact/hooks` are based on. See the `Options` type in `internal.d.ts`\n * for a full list of available option hooks (most editors/IDEs allow you to\n * ctrl+click or cmd+click on mac the type definition below).\n * @type {import('./internal').Options}\n */\nconst options = {\n\t_catchError\n};\n\nexport default options;\n","import { enqueueRender } from '../component';\n\n/**\n * Find the closest error boundary to a thrown error and call it\n * @param {object} error The thrown value\n * @param {import('../internal').VNode} vnode The vnode that threw\n * the error that was caught (except for unmounting when this parameter\n * is the highest parent that was being unmounted)\n */\nexport function _catchError(error, vnode) {\n\t/** @type {import('../internal').Component} */\n\tlet component, hasCaught;\n\n\tfor (; (vnode = vnode._parent); ) {\n\t\tif ((component = vnode._component) && !component._processingException) {\n\t\t\ttry {\n\t\t\t\tif (\n\t\t\t\t\tcomponent.constructor &&\n\t\t\t\t\tcomponent.constructor.getDerivedStateFromError != null\n\t\t\t\t) {\n\t\t\t\t\thasCaught = true;\n\t\t\t\t\tcomponent.setState(\n\t\t\t\t\t\tcomponent.constructor.getDerivedStateFromError(error)\n\t\t\t\t\t);\n\t\t\t\t}\n\n\t\t\t\tif (component.componentDidCatch != null) {\n\t\t\t\t\thasCaught = true;\n\t\t\t\t\tcomponent.componentDidCatch(error);\n\t\t\t\t}\n\n\t\t\t\tif (hasCaught)\n\t\t\t\t\treturn enqueueRender((component._pendingError = component));\n\t\t\t} catch (e) {\n\t\t\t\terror = e;\n\t\t\t}\n\t\t}\n\t}\n\n\tthrow error;\n}\n","/* global __webpack_public_path__ */\n\nimport * as Preact from 'preact';\nconst { h, render, hydrate } = Preact;\n\nconst interopDefault = m => (m && m.default ? m.default : m);\n\nconst normalizeURL = url => (url[url.length - 1] === '/' ? url : url + '/');\n\nif (process.env.NODE_ENV === 'development') {\n\t// enable preact devtools\n\trequire('preact/debug');\n\tif (process.env.RHL) {\n\t\t// enable hot loader\n\t\tconst hotLoader = interopDefault(require('react-hot-loader'));\n\t\thotLoader.preact(interopDefault(require('preact')));\n\t}\n\t// only add a debug sw if webpack service worker is not requested.\n\tif (process.env.ADD_SW === undefined && 'serviceWorker' in navigator) {\n\t\t// eslint-disable-next-line no-undef\n\t\tnavigator.serviceWorker.register(__webpack_public_path__ + 'sw-debug.js');\n\t} else if (process.env.ADD_SW && 'serviceWorker' in navigator) {\n\t\t// eslint-disable-next-line no-undef\n\t\tnavigator.serviceWorker.register(\n\t\t\t__webpack_public_path__ + (process.env.ES_BUILD ? 'sw-esm.js' : 'sw.js')\n\t\t);\n\t}\n} else if (process.env.ADD_SW && 'serviceWorker' in navigator) {\n\t// eslint-disable-next-line no-undef\n\tnavigator.serviceWorker.register(\n\t\t__webpack_public_path__ + (process.env.ES_BUILD ? 'sw-esm.js' : 'sw.js')\n\t);\n}\n\nlet app = interopDefault(require('preact-cli-entrypoint'));\n\nif (typeof app === 'function') {\n\tlet root =\n\t\tdocument.getElementById('preact_root') || document.body.firstElementChild;\n\n\tlet init = () => {\n\t\tlet app = interopDefault(require('preact-cli-entrypoint'));\n\t\tlet preRenderData = {};\n\t\tconst inlineDataElement = document.querySelector(\n\t\t\t'[type=\"__PREACT_CLI_DATA__\"]'\n\t\t);\n\t\tif (inlineDataElement) {\n\t\t\tpreRenderData =\n\t\t\t\tJSON.parse(inlineDataElement.innerHTML).preRenderData || preRenderData;\n\t\t}\n\t\t/* An object named CLI_DATA is passed as a prop,\n\t\t * this keeps us future proof if in case we decide,\n\t\t * to send other data like at some point in time.\n\t\t */\n\t\tconst CLI_DATA = { preRenderData };\n\t\tconst currentURL = preRenderData.url ? normalizeURL(preRenderData.url) : '';\n\t\tconst canHydrate =\n\t\t\tprocess.env.PRERENDER &&\n\t\t\tprocess.env.NODE_ENV === 'production' &&\n\t\t\thydrate &&\n\t\t\tcurrentURL === location.pathname;\n\t\tconst doRender = canHydrate ? hydrate : render;\n\t\troot = doRender(h(app, { CLI_DATA }), document.body, root);\n\t};\n\n\tif (module.hot) module.hot.accept('preact-cli-entrypoint', init);\n\n\tinit();\n}\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./Statistica.js\") );\n\t\t\t}, \"route-Statistica\");\n\t\t}\n\n\t\texport default Async(load);\n\t","var g;\n\n// This works in non-strict mode\ng = (function() {\n\treturn this;\n})();\n\ntry {\n\t// This works if eval is allowed (see CSP)\n\tg = g || new Function(\"return this\")();\n} catch (e) {\n\t// This works if the window reference is available\n\tif (typeof window === \"object\") g = window;\n}\n\n// g can still be undefined, but nothing to do about it...\n// We return undefined, instead of nothing here, so it's\n// easier to handle this case. if(!global) { ...}\n\nmodule.exports = g;\n","import { ExtendedError, WrappedFunction } from '@sentry/types';\n\nimport { isElement, isError, isEvent, isInstanceOf, isPlainObject, isPrimitive, isSyntheticEvent } from './is';\nimport { Memo } from './memo';\nimport { getFunctionName, htmlTreeAsString } from './misc';\nimport { truncate } from './string';\n\n/**\n * Wrap a given object method with a higher-order function\n *\n * @param source An object that contains a method to be wrapped.\n * @param name A name of method to be wrapped.\n * @param replacement A function that should be used to wrap a given method.\n * @returns void\n */\nexport function fill(source: { [key: string]: any }, name: string, replacement: (...args: any[]) => any): void {\n if (!(name in source)) {\n return;\n }\n\n const original = source[name] as () => any;\n const wrapped = replacement(original) as WrappedFunction;\n\n // Make sure it's a function first, as we need to attach an empty prototype for `defineProperties` to work\n // otherwise it'll throw \"TypeError: Object.defineProperties called on non-object\"\n // tslint:disable-next-line:strict-type-predicates\n if (typeof wrapped === 'function') {\n try {\n wrapped.prototype = wrapped.prototype || {};\n Object.defineProperties(wrapped, {\n __sentry_original__: {\n enumerable: false,\n value: original,\n },\n });\n } catch (_Oo) {\n // This can throw if multiple fill happens on a global object like XMLHttpRequest\n // Fixes https://github.com/getsentry/sentry-javascript/issues/2043\n }\n }\n\n source[name] = wrapped;\n}\n\n/**\n * Encodes given object into url-friendly format\n *\n * @param object An object that contains serializable values\n * @returns string Encoded\n */\nexport function urlEncode(object: { [key: string]: any }): string {\n return Object.keys(object)\n .map(\n // tslint:disable-next-line:no-unsafe-any\n key => `${encodeURIComponent(key)}=${encodeURIComponent(object[key])}`,\n )\n .join('&');\n}\n\n/**\n * Transforms any object into an object literal with all it's attributes\n * attached to it.\n *\n * @param value Initial source that we have to transform in order to be usable by the serializer\n */\nfunction getWalkSource(\n value: any,\n): {\n [key: string]: any;\n} {\n if (isError(value)) {\n const error = value as ExtendedError;\n const err: {\n stack: string | undefined;\n message: string;\n name: string;\n [key: string]: any;\n } = {\n message: error.message,\n name: error.name,\n stack: error.stack,\n };\n\n for (const i in error) {\n if (Object.prototype.hasOwnProperty.call(error, i)) {\n err[i] = error[i];\n }\n }\n\n return err;\n }\n\n if (isEvent(value)) {\n /**\n * Event-like interface that's usable in browser and node\n */\n interface SimpleEvent {\n [key: string]: unknown;\n type: string;\n target?: unknown;\n currentTarget?: unknown;\n }\n\n const event = value as SimpleEvent;\n\n const source: {\n [key: string]: any;\n } = {};\n\n source.type = event.type;\n\n // Accessing event.target can throw (see getsentry/raven-js#838, #768)\n try {\n source.target = isElement(event.target)\n ? htmlTreeAsString(event.target)\n : Object.prototype.toString.call(event.target);\n } catch (_oO) {\n source.target = '';\n }\n\n try {\n source.currentTarget = isElement(event.currentTarget)\n ? htmlTreeAsString(event.currentTarget)\n : Object.prototype.toString.call(event.currentTarget);\n } catch (_oO) {\n source.currentTarget = '';\n }\n\n // tslint:disable-next-line:strict-type-predicates\n if (typeof CustomEvent !== 'undefined' && isInstanceOf(value, CustomEvent)) {\n source.detail = event.detail;\n }\n\n for (const i in event) {\n if (Object.prototype.hasOwnProperty.call(event, i)) {\n source[i] = event;\n }\n }\n\n return source;\n }\n\n return value as {\n [key: string]: any;\n };\n}\n\n/** Calculates bytes size of input string */\nfunction utf8Length(value: string): number {\n // tslint:disable-next-line:no-bitwise\n return ~-encodeURI(value).split(/%..|./).length;\n}\n\n/** Calculates bytes size of input object */\nfunction jsonSize(value: any): number {\n return utf8Length(JSON.stringify(value));\n}\n\n/** JSDoc */\nexport function normalizeToSize(\n object: { [key: string]: any },\n // Default Node.js REPL depth\n depth: number = 3,\n // 100kB, as 200kB is max payload size, so half sounds reasonable\n maxSize: number = 100 * 1024,\n): T {\n const serialized = normalize(object, depth);\n\n if (jsonSize(serialized) > maxSize) {\n return normalizeToSize(object, depth - 1, maxSize);\n }\n\n return serialized as T;\n}\n\n/** Transforms any input value into a string form, either primitive value or a type of the input */\nfunction serializeValue(value: any): any {\n const type = Object.prototype.toString.call(value);\n\n // Node.js REPL notation\n if (typeof value === 'string') {\n return value;\n }\n if (type === '[object Object]') {\n return '[Object]';\n }\n if (type === '[object Array]') {\n return '[Array]';\n }\n\n const normalized = normalizeValue(value);\n return isPrimitive(normalized) ? normalized : type;\n}\n\n/**\n * normalizeValue()\n *\n * Takes unserializable input and make it serializable friendly\n *\n * - translates undefined/NaN values to \"[undefined]\"/\"[NaN]\" respectively,\n * - serializes Error objects\n * - filter global objects\n */\n// tslint:disable-next-line:cyclomatic-complexity\nfunction normalizeValue(value: T, key?: any): T | string {\n if (key === 'domain' && value && typeof value === 'object' && ((value as unknown) as { _events: any })._events) {\n return '[Domain]';\n }\n\n if (key === 'domainEmitter') {\n return '[DomainEmitter]';\n }\n\n if (typeof (global as any) !== 'undefined' && (value as unknown) === global) {\n return '[Global]';\n }\n\n if (typeof (window as any) !== 'undefined' && (value as unknown) === window) {\n return '[Window]';\n }\n\n if (typeof (document as any) !== 'undefined' && (value as unknown) === document) {\n return '[Document]';\n }\n\n // React's SyntheticEvent thingy\n if (isSyntheticEvent(value)) {\n return '[SyntheticEvent]';\n }\n\n // tslint:disable-next-line:no-tautology-expression\n if (typeof value === 'number' && value !== value) {\n return '[NaN]';\n }\n\n if (value === void 0) {\n return '[undefined]';\n }\n\n if (typeof value === 'function') {\n return `[Function: ${getFunctionName(value)}]`;\n }\n\n return value;\n}\n\n/**\n * Walks an object to perform a normalization on it\n *\n * @param key of object that's walked in current iteration\n * @param value object to be walked\n * @param depth Optional number indicating how deep should walking be performed\n * @param memo Optional Memo class handling decycling\n */\nexport function walk(key: string, value: any, depth: number = +Infinity, memo: Memo = new Memo()): any {\n // If we reach the maximum depth, serialize whatever has left\n if (depth === 0) {\n return serializeValue(value);\n }\n\n // If value implements `toJSON` method, call it and return early\n // tslint:disable:no-unsafe-any\n if (value !== null && value !== undefined && typeof value.toJSON === 'function') {\n return value.toJSON();\n }\n // tslint:enable:no-unsafe-any\n\n // If normalized value is a primitive, there are no branches left to walk, so we can just bail out, as theres no point in going down that branch any further\n const normalized = normalizeValue(value, key);\n if (isPrimitive(normalized)) {\n return normalized;\n }\n\n // Create source that we will use for next itterations, either objectified error object (Error type with extracted keys:value pairs) or the input itself\n const source = getWalkSource(value);\n\n // Create an accumulator that will act as a parent for all future itterations of that branch\n const acc = Array.isArray(value) ? [] : {};\n\n // If we already walked that branch, bail out, as it's circular reference\n if (memo.memoize(value)) {\n return '[Circular ~]';\n }\n\n // Walk all keys of the source\n for (const innerKey in source) {\n // Avoid iterating over fields in the prototype if they've somehow been exposed to enumeration.\n if (!Object.prototype.hasOwnProperty.call(source, innerKey)) {\n continue;\n }\n // Recursively walk through all the child nodes\n (acc as { [key: string]: any })[innerKey] = walk(innerKey, source[innerKey], depth - 1, memo);\n }\n\n // Once walked through all the branches, remove the parent from memo storage\n memo.unmemoize(value);\n\n // Return accumulated values\n return acc;\n}\n\n/**\n * normalize()\n *\n * - Creates a copy to prevent original input mutation\n * - Skip non-enumerablers\n * - Calls `toJSON` if implemented\n * - Removes circular references\n * - Translates non-serializeable values (undefined/NaN/Functions) to serializable format\n * - Translates known global objects/Classes to a string representations\n * - Takes care of Error objects serialization\n * - Optionally limit depth of final output\n */\nexport function normalize(input: any, depth?: number): any {\n try {\n // tslint:disable-next-line:no-unsafe-any\n return JSON.parse(JSON.stringify(input, (key: string, value: any) => walk(key, value, depth)));\n } catch (_oO) {\n return '**non-serializable**';\n }\n}\n\n/**\n * Given any captured exception, extract its keys and create a sorted\n * and truncated list that will be used inside the event message.\n * eg. `Non-error exception captured with keys: foo, bar, baz`\n */\nexport function extractExceptionKeysForMessage(exception: any, maxLength: number = 40): string {\n // tslint:disable:strict-type-predicates\n const keys = Object.keys(getWalkSource(exception));\n keys.sort();\n\n if (!keys.length) {\n return '[object has no keys]';\n }\n\n if (keys[0].length >= maxLength) {\n return truncate(keys[0], maxLength);\n }\n\n for (let includedKeys = keys.length; includedKeys > 0; includedKeys--) {\n const serialized = keys.slice(0, includedKeys).join(', ');\n if (serialized.length > maxLength) {\n continue;\n }\n if (includedKeys === keys.length) {\n return serialized;\n }\n return truncate(serialized, maxLength);\n }\n\n return '';\n}\n\n/**\n * Given any object, return the new object with removed keys that value was `undefined`.\n * Works recursively on objects and arrays.\n */\nexport function dropUndefinedKeys(val: T): T {\n if (isPlainObject(val)) {\n const obj = val as { [key: string]: any };\n const rv: { [key: string]: any } = {};\n for (const key of Object.keys(obj)) {\n if (typeof obj[key] !== 'undefined') {\n rv[key] = dropUndefinedKeys(obj[key]);\n }\n }\n return rv as T;\n }\n\n if (Array.isArray(val)) {\n return val.map(dropUndefinedKeys) as any;\n }\n\n return val;\n}\n","import style from './Footer.less';\nimport { Component } from 'preact';\n\nexport default function(props) {\n\treturn (\n\t\t
\n\t\t\t© {new Date().getFullYear()}\n\t\t\t - \n\t\t\tStefano Pigozzi\n\t\t\t - \n\t\t\tCC BY-SA 4.0\n\t\t\t - \n\t\t\tuni.steffo.eu {process.env.RELEASE}\n\t\t\t - \n\t\t\tSupportami\n\t\t
\n\t);\n}\n","export default function _extends() {\n _extends = Object.assign || function (target) {\n for (var i = 1; i < arguments.length; i++) {\n var source = arguments[i];\n\n for (var key in source) {\n if (Object.prototype.hasOwnProperty.call(source, key)) {\n target[key] = source[key];\n }\n }\n }\n\n return target;\n };\n\n return _extends.apply(this, arguments);\n}","function isAbsolute(pathname) {\n return pathname.charAt(0) === '/';\n}\n\n// About 1.5x faster than the two-arg version of Array#splice()\nfunction spliceOne(list, index) {\n for (var i = index, k = i + 1, n = list.length; k < n; i += 1, k += 1) {\n list[i] = list[k];\n }\n\n list.pop();\n}\n\n// This implementation is based heavily on node's url.parse\nfunction resolvePathname(to, from) {\n if (from === undefined) from = '';\n\n var toParts = (to && to.split('/')) || [];\n var fromParts = (from && from.split('/')) || [];\n\n var isToAbs = to && isAbsolute(to);\n var isFromAbs = from && isAbsolute(from);\n var mustEndAbs = isToAbs || isFromAbs;\n\n if (to && isAbsolute(to)) {\n // to is absolute\n fromParts = toParts;\n } else if (toParts.length) {\n // to is relative, drop the filename\n fromParts.pop();\n fromParts = fromParts.concat(toParts);\n }\n\n if (!fromParts.length) return '/';\n\n var hasTrailingSlash;\n if (fromParts.length) {\n var last = fromParts[fromParts.length - 1];\n hasTrailingSlash = last === '.' || last === '..' || last === '';\n } else {\n hasTrailingSlash = false;\n }\n\n var up = 0;\n for (var i = fromParts.length; i >= 0; i--) {\n var part = fromParts[i];\n\n if (part === '.') {\n spliceOne(fromParts, i);\n } else if (part === '..') {\n spliceOne(fromParts, i);\n up++;\n } else if (up) {\n spliceOne(fromParts, i);\n up--;\n }\n }\n\n if (!mustEndAbs) for (; up--; up) fromParts.unshift('..');\n\n if (\n mustEndAbs &&\n fromParts[0] !== '' &&\n (!fromParts[0] || !isAbsolute(fromParts[0]))\n )\n fromParts.unshift('');\n\n var result = fromParts.join('/');\n\n if (hasTrailingSlash && result.substr(-1) !== '/') result += '/';\n\n return result;\n}\n\nexport default resolvePathname;\n","import _extends from '@babel/runtime/helpers/esm/extends';\nimport resolvePathname from 'resolve-pathname';\nimport valueEqual from 'value-equal';\nimport warning from 'tiny-warning';\nimport invariant from 'tiny-invariant';\n\nfunction addLeadingSlash(path) {\n return path.charAt(0) === '/' ? path : '/' + path;\n}\nfunction stripLeadingSlash(path) {\n return path.charAt(0) === '/' ? path.substr(1) : path;\n}\nfunction hasBasename(path, prefix) {\n return path.toLowerCase().indexOf(prefix.toLowerCase()) === 0 && '/?#'.indexOf(path.charAt(prefix.length)) !== -1;\n}\nfunction stripBasename(path, prefix) {\n return hasBasename(path, prefix) ? path.substr(prefix.length) : path;\n}\nfunction stripTrailingSlash(path) {\n return path.charAt(path.length - 1) === '/' ? path.slice(0, -1) : path;\n}\nfunction parsePath(path) {\n var pathname = path || '/';\n var search = '';\n var hash = '';\n var hashIndex = pathname.indexOf('#');\n\n if (hashIndex !== -1) {\n hash = pathname.substr(hashIndex);\n pathname = pathname.substr(0, hashIndex);\n }\n\n var searchIndex = pathname.indexOf('?');\n\n if (searchIndex !== -1) {\n search = pathname.substr(searchIndex);\n pathname = pathname.substr(0, searchIndex);\n }\n\n return {\n pathname: pathname,\n search: search === '?' ? '' : search,\n hash: hash === '#' ? '' : hash\n };\n}\nfunction createPath(location) {\n var pathname = location.pathname,\n search = location.search,\n hash = location.hash;\n var path = pathname || '/';\n if (search && search !== '?') path += search.charAt(0) === '?' ? search : \"?\" + search;\n if (hash && hash !== '#') path += hash.charAt(0) === '#' ? hash : \"#\" + hash;\n return path;\n}\n\nfunction createLocation(path, state, key, currentLocation) {\n var location;\n\n if (typeof path === 'string') {\n // Two-arg form: push(path, state)\n location = parsePath(path);\n location.state = state;\n } else {\n // One-arg form: push(location)\n location = _extends({}, path);\n if (location.pathname === undefined) location.pathname = '';\n\n if (location.search) {\n if (location.search.charAt(0) !== '?') location.search = '?' + location.search;\n } else {\n location.search = '';\n }\n\n if (location.hash) {\n if (location.hash.charAt(0) !== '#') location.hash = '#' + location.hash;\n } else {\n location.hash = '';\n }\n\n if (state !== undefined && location.state === undefined) location.state = state;\n }\n\n try {\n location.pathname = decodeURI(location.pathname);\n } catch (e) {\n if (e instanceof URIError) {\n throw new URIError('Pathname \"' + location.pathname + '\" could not be decoded. ' + 'This is likely caused by an invalid percent-encoding.');\n } else {\n throw e;\n }\n }\n\n if (key) location.key = key;\n\n if (currentLocation) {\n // Resolve incomplete/relative pathname relative to current location.\n if (!location.pathname) {\n location.pathname = currentLocation.pathname;\n } else if (location.pathname.charAt(0) !== '/') {\n location.pathname = resolvePathname(location.pathname, currentLocation.pathname);\n }\n } else {\n // When there is no prior location and pathname is empty, set it to /\n if (!location.pathname) {\n location.pathname = '/';\n }\n }\n\n return location;\n}\nfunction locationsAreEqual(a, b) {\n return a.pathname === b.pathname && a.search === b.search && a.hash === b.hash && a.key === b.key && valueEqual(a.state, b.state);\n}\n\nfunction createTransitionManager() {\n var prompt = null;\n\n function setPrompt(nextPrompt) {\n process.env.NODE_ENV !== \"production\" ? warning(prompt == null, 'A history supports only one prompt at a time') : void 0;\n prompt = nextPrompt;\n return function () {\n if (prompt === nextPrompt) prompt = null;\n };\n }\n\n function confirmTransitionTo(location, action, getUserConfirmation, callback) {\n // TODO: If another transition starts while we're still confirming\n // the previous one, we may end up in a weird state. Figure out the\n // best way to handle this.\n if (prompt != null) {\n var result = typeof prompt === 'function' ? prompt(location, action) : prompt;\n\n if (typeof result === 'string') {\n if (typeof getUserConfirmation === 'function') {\n getUserConfirmation(result, callback);\n } else {\n process.env.NODE_ENV !== \"production\" ? warning(false, 'A history needs a getUserConfirmation function in order to use a prompt message') : void 0;\n callback(true);\n }\n } else {\n // Return false from a transition hook to cancel the transition.\n callback(result !== false);\n }\n } else {\n callback(true);\n }\n }\n\n var listeners = [];\n\n function appendListener(fn) {\n var isActive = true;\n\n function listener() {\n if (isActive) fn.apply(void 0, arguments);\n }\n\n listeners.push(listener);\n return function () {\n isActive = false;\n listeners = listeners.filter(function (item) {\n return item !== listener;\n });\n };\n }\n\n function notifyListeners() {\n for (var _len = arguments.length, args = new Array(_len), _key = 0; _key < _len; _key++) {\n args[_key] = arguments[_key];\n }\n\n listeners.forEach(function (listener) {\n return listener.apply(void 0, args);\n });\n }\n\n return {\n setPrompt: setPrompt,\n confirmTransitionTo: confirmTransitionTo,\n appendListener: appendListener,\n notifyListeners: notifyListeners\n };\n}\n\nvar canUseDOM = !!(typeof window !== 'undefined' && window.document && window.document.createElement);\nfunction getConfirmation(message, callback) {\n callback(window.confirm(message)); // eslint-disable-line no-alert\n}\n/**\n * Returns true if the HTML5 history API is supported. Taken from Modernizr.\n *\n * https://github.com/Modernizr/Modernizr/blob/master/LICENSE\n * https://github.com/Modernizr/Modernizr/blob/master/feature-detects/history.js\n * changed to avoid false negatives for Windows Phones: https://github.com/reactjs/react-router/issues/586\n */\n\nfunction supportsHistory() {\n var ua = window.navigator.userAgent;\n if ((ua.indexOf('Android 2.') !== -1 || ua.indexOf('Android 4.0') !== -1) && ua.indexOf('Mobile Safari') !== -1 && ua.indexOf('Chrome') === -1 && ua.indexOf('Windows Phone') === -1) return false;\n return window.history && 'pushState' in window.history;\n}\n/**\n * Returns true if browser fires popstate on hash change.\n * IE10 and IE11 do not.\n */\n\nfunction supportsPopStateOnHashChange() {\n return window.navigator.userAgent.indexOf('Trident') === -1;\n}\n/**\n * Returns false if using go(n) with hash history causes a full page reload.\n */\n\nfunction supportsGoWithoutReloadUsingHash() {\n return window.navigator.userAgent.indexOf('Firefox') === -1;\n}\n/**\n * Returns true if a given popstate event is an extraneous WebKit event.\n * Accounts for the fact that Chrome on iOS fires real popstate events\n * containing undefined state when pressing the back button.\n */\n\nfunction isExtraneousPopstateEvent(event) {\n return event.state === undefined && navigator.userAgent.indexOf('CriOS') === -1;\n}\n\nvar PopStateEvent = 'popstate';\nvar HashChangeEvent = 'hashchange';\n\nfunction getHistoryState() {\n try {\n return window.history.state || {};\n } catch (e) {\n // IE 11 sometimes throws when accessing window.history.state\n // See https://github.com/ReactTraining/history/pull/289\n return {};\n }\n}\n/**\n * Creates a history object that uses the HTML5 history API including\n * pushState, replaceState, and the popstate event.\n */\n\n\nfunction createBrowserHistory(props) {\n if (props === void 0) {\n props = {};\n }\n\n !canUseDOM ? process.env.NODE_ENV !== \"production\" ? invariant(false, 'Browser history needs a DOM') : invariant(false) : void 0;\n var globalHistory = window.history;\n var canUseHistory = supportsHistory();\n var needsHashChangeListener = !supportsPopStateOnHashChange();\n var _props = props,\n _props$forceRefresh = _props.forceRefresh,\n forceRefresh = _props$forceRefresh === void 0 ? false : _props$forceRefresh,\n _props$getUserConfirm = _props.getUserConfirmation,\n getUserConfirmation = _props$getUserConfirm === void 0 ? getConfirmation : _props$getUserConfirm,\n _props$keyLength = _props.keyLength,\n keyLength = _props$keyLength === void 0 ? 6 : _props$keyLength;\n var basename = props.basename ? stripTrailingSlash(addLeadingSlash(props.basename)) : '';\n\n function getDOMLocation(historyState) {\n var _ref = historyState || {},\n key = _ref.key,\n state = _ref.state;\n\n var _window$location = window.location,\n pathname = _window$location.pathname,\n search = _window$location.search,\n hash = _window$location.hash;\n var path = pathname + search + hash;\n process.env.NODE_ENV !== \"production\" ? warning(!basename || hasBasename(path, basename), 'You are attempting to use a basename on a page whose URL path does not begin ' + 'with the basename. Expected path \"' + path + '\" to begin with \"' + basename + '\".') : void 0;\n if (basename) path = stripBasename(path, basename);\n return createLocation(path, state, key);\n }\n\n function createKey() {\n return Math.random().toString(36).substr(2, keyLength);\n }\n\n var transitionManager = createTransitionManager();\n\n function setState(nextState) {\n _extends(history, nextState);\n\n history.length = globalHistory.length;\n transitionManager.notifyListeners(history.location, history.action);\n }\n\n function handlePopState(event) {\n // Ignore extraneous popstate events in WebKit.\n if (isExtraneousPopstateEvent(event)) return;\n handlePop(getDOMLocation(event.state));\n }\n\n function handleHashChange() {\n handlePop(getDOMLocation(getHistoryState()));\n }\n\n var forceNextPop = false;\n\n function handlePop(location) {\n if (forceNextPop) {\n forceNextPop = false;\n setState();\n } else {\n var action = 'POP';\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (ok) {\n setState({\n action: action,\n location: location\n });\n } else {\n revertPop(location);\n }\n });\n }\n }\n\n function revertPop(fromLocation) {\n var toLocation = history.location; // TODO: We could probably make this more reliable by\n // keeping a list of keys we've seen in sessionStorage.\n // Instead, we just default to 0 for keys we don't know.\n\n var toIndex = allKeys.indexOf(toLocation.key);\n if (toIndex === -1) toIndex = 0;\n var fromIndex = allKeys.indexOf(fromLocation.key);\n if (fromIndex === -1) fromIndex = 0;\n var delta = toIndex - fromIndex;\n\n if (delta) {\n forceNextPop = true;\n go(delta);\n }\n }\n\n var initialLocation = getDOMLocation(getHistoryState());\n var allKeys = [initialLocation.key]; // Public interface\n\n function createHref(location) {\n return basename + createPath(location);\n }\n\n function push(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to push when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n var action = 'PUSH';\n var location = createLocation(path, state, createKey(), history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var href = createHref(location);\n var key = location.key,\n state = location.state;\n\n if (canUseHistory) {\n globalHistory.pushState({\n key: key,\n state: state\n }, null, href);\n\n if (forceRefresh) {\n window.location.href = href;\n } else {\n var prevIndex = allKeys.indexOf(history.location.key);\n var nextKeys = allKeys.slice(0, prevIndex + 1);\n nextKeys.push(location.key);\n allKeys = nextKeys;\n setState({\n action: action,\n location: location\n });\n }\n } else {\n process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Browser history cannot push state in browsers that do not support HTML5 history') : void 0;\n window.location.href = href;\n }\n });\n }\n\n function replace(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to replace when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n var action = 'REPLACE';\n var location = createLocation(path, state, createKey(), history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var href = createHref(location);\n var key = location.key,\n state = location.state;\n\n if (canUseHistory) {\n globalHistory.replaceState({\n key: key,\n state: state\n }, null, href);\n\n if (forceRefresh) {\n window.location.replace(href);\n } else {\n var prevIndex = allKeys.indexOf(history.location.key);\n if (prevIndex !== -1) allKeys[prevIndex] = location.key;\n setState({\n action: action,\n location: location\n });\n }\n } else {\n process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Browser history cannot replace state in browsers that do not support HTML5 history') : void 0;\n window.location.replace(href);\n }\n });\n }\n\n function go(n) {\n globalHistory.go(n);\n }\n\n function goBack() {\n go(-1);\n }\n\n function goForward() {\n go(1);\n }\n\n var listenerCount = 0;\n\n function checkDOMListeners(delta) {\n listenerCount += delta;\n\n if (listenerCount === 1 && delta === 1) {\n window.addEventListener(PopStateEvent, handlePopState);\n if (needsHashChangeListener) window.addEventListener(HashChangeEvent, handleHashChange);\n } else if (listenerCount === 0) {\n window.removeEventListener(PopStateEvent, handlePopState);\n if (needsHashChangeListener) window.removeEventListener(HashChangeEvent, handleHashChange);\n }\n }\n\n var isBlocked = false;\n\n function block(prompt) {\n if (prompt === void 0) {\n prompt = false;\n }\n\n var unblock = transitionManager.setPrompt(prompt);\n\n if (!isBlocked) {\n checkDOMListeners(1);\n isBlocked = true;\n }\n\n return function () {\n if (isBlocked) {\n isBlocked = false;\n checkDOMListeners(-1);\n }\n\n return unblock();\n };\n }\n\n function listen(listener) {\n var unlisten = transitionManager.appendListener(listener);\n checkDOMListeners(1);\n return function () {\n checkDOMListeners(-1);\n unlisten();\n };\n }\n\n var history = {\n length: globalHistory.length,\n action: 'POP',\n location: initialLocation,\n createHref: createHref,\n push: push,\n replace: replace,\n go: go,\n goBack: goBack,\n goForward: goForward,\n block: block,\n listen: listen\n };\n return history;\n}\n\nvar HashChangeEvent$1 = 'hashchange';\nvar HashPathCoders = {\n hashbang: {\n encodePath: function encodePath(path) {\n return path.charAt(0) === '!' ? path : '!/' + stripLeadingSlash(path);\n },\n decodePath: function decodePath(path) {\n return path.charAt(0) === '!' ? path.substr(1) : path;\n }\n },\n noslash: {\n encodePath: stripLeadingSlash,\n decodePath: addLeadingSlash\n },\n slash: {\n encodePath: addLeadingSlash,\n decodePath: addLeadingSlash\n }\n};\n\nfunction stripHash(url) {\n var hashIndex = url.indexOf('#');\n return hashIndex === -1 ? url : url.slice(0, hashIndex);\n}\n\nfunction getHashPath() {\n // We can't use window.location.hash here because it's not\n // consistent across browsers - Firefox will pre-decode it!\n var href = window.location.href;\n var hashIndex = href.indexOf('#');\n return hashIndex === -1 ? '' : href.substring(hashIndex + 1);\n}\n\nfunction pushHashPath(path) {\n window.location.hash = path;\n}\n\nfunction replaceHashPath(path) {\n window.location.replace(stripHash(window.location.href) + '#' + path);\n}\n\nfunction createHashHistory(props) {\n if (props === void 0) {\n props = {};\n }\n\n !canUseDOM ? process.env.NODE_ENV !== \"production\" ? invariant(false, 'Hash history needs a DOM') : invariant(false) : void 0;\n var globalHistory = window.history;\n var canGoWithoutReload = supportsGoWithoutReloadUsingHash();\n var _props = props,\n _props$getUserConfirm = _props.getUserConfirmation,\n getUserConfirmation = _props$getUserConfirm === void 0 ? getConfirmation : _props$getUserConfirm,\n _props$hashType = _props.hashType,\n hashType = _props$hashType === void 0 ? 'slash' : _props$hashType;\n var basename = props.basename ? stripTrailingSlash(addLeadingSlash(props.basename)) : '';\n var _HashPathCoders$hashT = HashPathCoders[hashType],\n encodePath = _HashPathCoders$hashT.encodePath,\n decodePath = _HashPathCoders$hashT.decodePath;\n\n function getDOMLocation() {\n var path = decodePath(getHashPath());\n process.env.NODE_ENV !== \"production\" ? warning(!basename || hasBasename(path, basename), 'You are attempting to use a basename on a page whose URL path does not begin ' + 'with the basename. Expected path \"' + path + '\" to begin with \"' + basename + '\".') : void 0;\n if (basename) path = stripBasename(path, basename);\n return createLocation(path);\n }\n\n var transitionManager = createTransitionManager();\n\n function setState(nextState) {\n _extends(history, nextState);\n\n history.length = globalHistory.length;\n transitionManager.notifyListeners(history.location, history.action);\n }\n\n var forceNextPop = false;\n var ignorePath = null;\n\n function locationsAreEqual$$1(a, b) {\n return a.pathname === b.pathname && a.search === b.search && a.hash === b.hash;\n }\n\n function handleHashChange() {\n var path = getHashPath();\n var encodedPath = encodePath(path);\n\n if (path !== encodedPath) {\n // Ensure we always have a properly-encoded hash.\n replaceHashPath(encodedPath);\n } else {\n var location = getDOMLocation();\n var prevLocation = history.location;\n if (!forceNextPop && locationsAreEqual$$1(prevLocation, location)) return; // A hashchange doesn't always == location change.\n\n if (ignorePath === createPath(location)) return; // Ignore this change; we already setState in push/replace.\n\n ignorePath = null;\n handlePop(location);\n }\n }\n\n function handlePop(location) {\n if (forceNextPop) {\n forceNextPop = false;\n setState();\n } else {\n var action = 'POP';\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (ok) {\n setState({\n action: action,\n location: location\n });\n } else {\n revertPop(location);\n }\n });\n }\n }\n\n function revertPop(fromLocation) {\n var toLocation = history.location; // TODO: We could probably make this more reliable by\n // keeping a list of paths we've seen in sessionStorage.\n // Instead, we just default to 0 for paths we don't know.\n\n var toIndex = allPaths.lastIndexOf(createPath(toLocation));\n if (toIndex === -1) toIndex = 0;\n var fromIndex = allPaths.lastIndexOf(createPath(fromLocation));\n if (fromIndex === -1) fromIndex = 0;\n var delta = toIndex - fromIndex;\n\n if (delta) {\n forceNextPop = true;\n go(delta);\n }\n } // Ensure the hash is encoded properly before doing anything else.\n\n\n var path = getHashPath();\n var encodedPath = encodePath(path);\n if (path !== encodedPath) replaceHashPath(encodedPath);\n var initialLocation = getDOMLocation();\n var allPaths = [createPath(initialLocation)]; // Public interface\n\n function createHref(location) {\n var baseTag = document.querySelector('base');\n var href = '';\n\n if (baseTag && baseTag.getAttribute('href')) {\n href = stripHash(window.location.href);\n }\n\n return href + '#' + encodePath(basename + createPath(location));\n }\n\n function push(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Hash history cannot push state; it is ignored') : void 0;\n var action = 'PUSH';\n var location = createLocation(path, undefined, undefined, history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var path = createPath(location);\n var encodedPath = encodePath(basename + path);\n var hashChanged = getHashPath() !== encodedPath;\n\n if (hashChanged) {\n // We cannot tell if a hashchange was caused by a PUSH, so we'd\n // rather setState here and ignore the hashchange. The caveat here\n // is that other hash histories in the page will consider it a POP.\n ignorePath = path;\n pushHashPath(encodedPath);\n var prevIndex = allPaths.lastIndexOf(createPath(history.location));\n var nextPaths = allPaths.slice(0, prevIndex + 1);\n nextPaths.push(path);\n allPaths = nextPaths;\n setState({\n action: action,\n location: location\n });\n } else {\n process.env.NODE_ENV !== \"production\" ? warning(false, 'Hash history cannot PUSH the same path; a new entry will not be added to the history stack') : void 0;\n setState();\n }\n });\n }\n\n function replace(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Hash history cannot replace state; it is ignored') : void 0;\n var action = 'REPLACE';\n var location = createLocation(path, undefined, undefined, history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var path = createPath(location);\n var encodedPath = encodePath(basename + path);\n var hashChanged = getHashPath() !== encodedPath;\n\n if (hashChanged) {\n // We cannot tell if a hashchange was caused by a REPLACE, so we'd\n // rather setState here and ignore the hashchange. The caveat here\n // is that other hash histories in the page will consider it a POP.\n ignorePath = path;\n replaceHashPath(encodedPath);\n }\n\n var prevIndex = allPaths.indexOf(createPath(history.location));\n if (prevIndex !== -1) allPaths[prevIndex] = path;\n setState({\n action: action,\n location: location\n });\n });\n }\n\n function go(n) {\n process.env.NODE_ENV !== \"production\" ? warning(canGoWithoutReload, 'Hash history go(n) causes a full page reload in this browser') : void 0;\n globalHistory.go(n);\n }\n\n function goBack() {\n go(-1);\n }\n\n function goForward() {\n go(1);\n }\n\n var listenerCount = 0;\n\n function checkDOMListeners(delta) {\n listenerCount += delta;\n\n if (listenerCount === 1 && delta === 1) {\n window.addEventListener(HashChangeEvent$1, handleHashChange);\n } else if (listenerCount === 0) {\n window.removeEventListener(HashChangeEvent$1, handleHashChange);\n }\n }\n\n var isBlocked = false;\n\n function block(prompt) {\n if (prompt === void 0) {\n prompt = false;\n }\n\n var unblock = transitionManager.setPrompt(prompt);\n\n if (!isBlocked) {\n checkDOMListeners(1);\n isBlocked = true;\n }\n\n return function () {\n if (isBlocked) {\n isBlocked = false;\n checkDOMListeners(-1);\n }\n\n return unblock();\n };\n }\n\n function listen(listener) {\n var unlisten = transitionManager.appendListener(listener);\n checkDOMListeners(1);\n return function () {\n checkDOMListeners(-1);\n unlisten();\n };\n }\n\n var history = {\n length: globalHistory.length,\n action: 'POP',\n location: initialLocation,\n createHref: createHref,\n push: push,\n replace: replace,\n go: go,\n goBack: goBack,\n goForward: goForward,\n block: block,\n listen: listen\n };\n return history;\n}\n\nfunction clamp(n, lowerBound, upperBound) {\n return Math.min(Math.max(n, lowerBound), upperBound);\n}\n/**\n * Creates a history object that stores locations in memory.\n */\n\n\nfunction createMemoryHistory(props) {\n if (props === void 0) {\n props = {};\n }\n\n var _props = props,\n getUserConfirmation = _props.getUserConfirmation,\n _props$initialEntries = _props.initialEntries,\n initialEntries = _props$initialEntries === void 0 ? ['/'] : _props$initialEntries,\n _props$initialIndex = _props.initialIndex,\n initialIndex = _props$initialIndex === void 0 ? 0 : _props$initialIndex,\n _props$keyLength = _props.keyLength,\n keyLength = _props$keyLength === void 0 ? 6 : _props$keyLength;\n var transitionManager = createTransitionManager();\n\n function setState(nextState) {\n _extends(history, nextState);\n\n history.length = history.entries.length;\n transitionManager.notifyListeners(history.location, history.action);\n }\n\n function createKey() {\n return Math.random().toString(36).substr(2, keyLength);\n }\n\n var index = clamp(initialIndex, 0, initialEntries.length - 1);\n var entries = initialEntries.map(function (entry) {\n return typeof entry === 'string' ? createLocation(entry, undefined, createKey()) : createLocation(entry, undefined, entry.key || createKey());\n }); // Public interface\n\n var createHref = createPath;\n\n function push(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to push when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n var action = 'PUSH';\n var location = createLocation(path, state, createKey(), history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var prevIndex = history.index;\n var nextIndex = prevIndex + 1;\n var nextEntries = history.entries.slice(0);\n\n if (nextEntries.length > nextIndex) {\n nextEntries.splice(nextIndex, nextEntries.length - nextIndex, location);\n } else {\n nextEntries.push(location);\n }\n\n setState({\n action: action,\n location: location,\n index: nextIndex,\n entries: nextEntries\n });\n });\n }\n\n function replace(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to replace when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n var action = 'REPLACE';\n var location = createLocation(path, state, createKey(), history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n history.entries[history.index] = location;\n setState({\n action: action,\n location: location\n });\n });\n }\n\n function go(n) {\n var nextIndex = clamp(history.index + n, 0, history.entries.length - 1);\n var action = 'POP';\n var location = history.entries[nextIndex];\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (ok) {\n setState({\n action: action,\n location: location,\n index: nextIndex\n });\n } else {\n // Mimic the behavior of DOM histories by\n // causing a render after a cancelled POP.\n setState();\n }\n });\n }\n\n function goBack() {\n go(-1);\n }\n\n function goForward() {\n go(1);\n }\n\n function canGo(n) {\n var nextIndex = history.index + n;\n return nextIndex >= 0 && nextIndex < history.entries.length;\n }\n\n function block(prompt) {\n if (prompt === void 0) {\n prompt = false;\n }\n\n return transitionManager.setPrompt(prompt);\n }\n\n function listen(listener) {\n return transitionManager.appendListener(listener);\n }\n\n var history = {\n length: entries.length,\n action: 'POP',\n location: entries[index],\n index: index,\n entries: entries,\n createHref: createHref,\n push: push,\n replace: replace,\n go: go,\n goBack: goBack,\n goForward: goForward,\n canGo: canGo,\n block: block,\n listen: listen\n };\n return history;\n}\n\nexport { createBrowserHistory, createHashHistory, createMemoryHistory, createLocation, locationsAreEqual, parsePath, createPath };\n","var isProduction = process.env.NODE_ENV === 'production';\nvar prefix = 'Invariant failed';\nfunction invariant(condition, message) {\n if (condition) {\n return;\n }\n if (isProduction) {\n throw new Error(prefix);\n }\n throw new Error(prefix + \": \" + (message || ''));\n}\n\nexport default invariant;\n","// This will be replaced\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./Fisica.js\") );\n\t\t\t}, \"route-Fisica\");\n\t\t}\n\n\t\texport default Async(load);\n\t","import {\n Breadcrumb,\n Event,\n EventHint,\n EventProcessor,\n Scope as ScopeInterface,\n Severity,\n Span,\n User,\n} from '@sentry/types';\nimport { getGlobalObject, isThenable, SyncPromise, timestampWithMs } from '@sentry/utils';\n\n/**\n * Holds additional event information. {@link Scope.applyToEvent} will be\n * called by the client before an event will be sent.\n */\nexport class Scope implements ScopeInterface {\n /** Flag if notifiying is happening. */\n protected _notifyingListeners: boolean = false;\n\n /** Callback for client to receive scope changes. */\n protected _scopeListeners: Array<(scope: Scope) => void> = [];\n\n /** Callback list that will be called after {@link applyToEvent}. */\n protected _eventProcessors: EventProcessor[] = [];\n\n /** Array of breadcrumbs. */\n protected _breadcrumbs: Breadcrumb[] = [];\n\n /** User */\n protected _user: User = {};\n\n /** Tags */\n protected _tags: { [key: string]: string } = {};\n\n /** Extra */\n protected _extra: { [key: string]: any } = {};\n\n /** Contexts */\n protected _context: { [key: string]: any } = {};\n\n /** Fingerprint */\n protected _fingerprint?: string[];\n\n /** Severity */\n protected _level?: Severity;\n\n /** Transaction */\n protected _transaction?: string;\n\n /** Span */\n protected _span?: Span;\n\n /**\n * Add internal on change listener. Used for sub SDKs that need to store the scope.\n * @hidden\n */\n public addScopeListener(callback: (scope: Scope) => void): void {\n this._scopeListeners.push(callback);\n }\n\n /**\n * @inheritDoc\n */\n public addEventProcessor(callback: EventProcessor): this {\n this._eventProcessors.push(callback);\n return this;\n }\n\n /**\n * This will be called on every set call.\n */\n protected _notifyScopeListeners(): void {\n if (!this._notifyingListeners) {\n this._notifyingListeners = true;\n setTimeout(() => {\n this._scopeListeners.forEach(callback => {\n callback(this);\n });\n this._notifyingListeners = false;\n });\n }\n }\n\n /**\n * This will be called after {@link applyToEvent} is finished.\n */\n protected _notifyEventProcessors(\n processors: EventProcessor[],\n event: Event | null,\n hint?: EventHint,\n index: number = 0,\n ): PromiseLike {\n return new SyncPromise((resolve, reject) => {\n const processor = processors[index];\n // tslint:disable-next-line:strict-type-predicates\n if (event === null || typeof processor !== 'function') {\n resolve(event);\n } else {\n const result = processor({ ...event }, hint) as Event | null;\n if (isThenable(result)) {\n (result as PromiseLike)\n .then(final => this._notifyEventProcessors(processors, final, hint, index + 1).then(resolve))\n .then(null, reject);\n } else {\n this._notifyEventProcessors(processors, result, hint, index + 1)\n .then(resolve)\n .then(null, reject);\n }\n }\n });\n }\n\n /**\n * @inheritDoc\n */\n public setUser(user: User | null): this {\n this._user = user || {};\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public setTags(tags: { [key: string]: string }): this {\n this._tags = {\n ...this._tags,\n ...tags,\n };\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public setTag(key: string, value: string): this {\n this._tags = { ...this._tags, [key]: value };\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public setExtras(extras: { [key: string]: any }): this {\n this._extra = {\n ...this._extra,\n ...extras,\n };\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public setExtra(key: string, extra: any): this {\n this._extra = { ...this._extra, [key]: extra };\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public setFingerprint(fingerprint: string[]): this {\n this._fingerprint = fingerprint;\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public setLevel(level: Severity): this {\n this._level = level;\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public setTransaction(transaction?: string): this {\n this._transaction = transaction;\n if (this._span) {\n (this._span as any).transaction = transaction;\n }\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public setContext(key: string, context: { [key: string]: any } | null): this {\n this._context = { ...this._context, [key]: context };\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public setSpan(span?: Span): this {\n this._span = span;\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * Internal getter for Span, used in Hub.\n * @hidden\n */\n public getSpan(): Span | undefined {\n return this._span;\n }\n\n /**\n * Inherit values from the parent scope.\n * @param scope to clone.\n */\n public static clone(scope?: Scope): Scope {\n const newScope = new Scope();\n if (scope) {\n newScope._breadcrumbs = [...scope._breadcrumbs];\n newScope._tags = { ...scope._tags };\n newScope._extra = { ...scope._extra };\n newScope._context = { ...scope._context };\n newScope._user = scope._user;\n newScope._level = scope._level;\n newScope._span = scope._span;\n newScope._transaction = scope._transaction;\n newScope._fingerprint = scope._fingerprint;\n newScope._eventProcessors = [...scope._eventProcessors];\n }\n return newScope;\n }\n\n /**\n * @inheritDoc\n */\n public clear(): this {\n this._breadcrumbs = [];\n this._tags = {};\n this._extra = {};\n this._user = {};\n this._context = {};\n this._level = undefined;\n this._transaction = undefined;\n this._fingerprint = undefined;\n this._span = undefined;\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public addBreadcrumb(breadcrumb: Breadcrumb, maxBreadcrumbs?: number): this {\n const mergedBreadcrumb = {\n timestamp: timestampWithMs(),\n ...breadcrumb,\n };\n\n this._breadcrumbs =\n maxBreadcrumbs !== undefined && maxBreadcrumbs >= 0\n ? [...this._breadcrumbs, mergedBreadcrumb].slice(-maxBreadcrumbs)\n : [...this._breadcrumbs, mergedBreadcrumb];\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * @inheritDoc\n */\n public clearBreadcrumbs(): this {\n this._breadcrumbs = [];\n this._notifyScopeListeners();\n return this;\n }\n\n /**\n * Applies fingerprint from the scope to the event if there's one,\n * uses message if there's one instead or get rid of empty fingerprint\n */\n private _applyFingerprint(event: Event): void {\n // Make sure it's an array first and we actually have something in place\n event.fingerprint = event.fingerprint\n ? Array.isArray(event.fingerprint)\n ? event.fingerprint\n : [event.fingerprint]\n : [];\n\n // If we have something on the scope, then merge it with event\n if (this._fingerprint) {\n event.fingerprint = event.fingerprint.concat(this._fingerprint);\n }\n\n // If we have no data at all, remove empty array default\n if (event.fingerprint && !event.fingerprint.length) {\n delete event.fingerprint;\n }\n }\n\n /**\n * Applies the current context and fingerprint to the event.\n * Note that breadcrumbs will be added by the client.\n * Also if the event has already breadcrumbs on it, we do not merge them.\n * @param event Event\n * @param hint May contain additional informartion about the original exception.\n * @hidden\n */\n public applyToEvent(event: Event, hint?: EventHint): PromiseLike {\n if (this._extra && Object.keys(this._extra).length) {\n event.extra = { ...this._extra, ...event.extra };\n }\n if (this._tags && Object.keys(this._tags).length) {\n event.tags = { ...this._tags, ...event.tags };\n }\n if (this._user && Object.keys(this._user).length) {\n event.user = { ...this._user, ...event.user };\n }\n if (this._context && Object.keys(this._context).length) {\n event.contexts = { ...this._context, ...event.contexts };\n }\n if (this._level) {\n event.level = this._level;\n }\n if (this._transaction) {\n event.transaction = this._transaction;\n }\n if (this._span) {\n event.contexts = { trace: this._span.getTraceContext(), ...event.contexts };\n }\n\n this._applyFingerprint(event);\n\n event.breadcrumbs = [...(event.breadcrumbs || []), ...this._breadcrumbs];\n event.breadcrumbs = event.breadcrumbs.length > 0 ? event.breadcrumbs : undefined;\n\n return this._notifyEventProcessors([...getGlobalEventProcessors(), ...this._eventProcessors], event, hint);\n }\n}\n\n/**\n * Retruns the global event processors.\n */\nfunction getGlobalEventProcessors(): EventProcessor[] {\n const global = getGlobalObject();\n global.__SENTRY__ = global.__SENTRY__ || {};\n global.__SENTRY__.globalEventProcessors = global.__SENTRY__.globalEventProcessors || [];\n return global.__SENTRY__.globalEventProcessors;\n}\n\n/**\n * Add a EventProcessor to be kept globally.\n * @param callback EventProcessor to add\n */\nexport function addGlobalEventProcessor(callback: EventProcessor): void {\n getGlobalEventProcessors().push(callback);\n}\n","import {\n Breadcrumb,\n BreadcrumbHint,\n Client,\n Event,\n EventHint,\n Hub as HubInterface,\n Integration,\n IntegrationClass,\n Severity,\n Span,\n SpanContext,\n User,\n} from '@sentry/types';\nimport { consoleSandbox, getGlobalObject, isNodeEnv, logger, timestampWithMs, uuid4 } from '@sentry/utils';\n\nimport { Carrier, Layer } from './interfaces';\nimport { Scope } from './scope';\n\n/**\n * API compatibility version of this hub.\n *\n * WARNING: This number should only be incresed when the global interface\n * changes a and new methods are introduced.\n *\n * @hidden\n */\nexport const API_VERSION = 3;\n\n/**\n * Default maximum number of breadcrumbs added to an event. Can be overwritten\n * with {@link Options.maxBreadcrumbs}.\n */\nconst DEFAULT_BREADCRUMBS = 100;\n\n/**\n * Absolute maximum number of breadcrumbs added to an event. The\n * `maxBreadcrumbs` option cannot be higher than this value.\n */\nconst MAX_BREADCRUMBS = 100;\n\n/**\n * @inheritDoc\n */\nexport class Hub implements HubInterface {\n /** Is a {@link Layer}[] containing the client and scope */\n private readonly _stack: Layer[] = [];\n\n /** Contains the last event id of a captured event. */\n private _lastEventId?: string;\n\n /**\n * Creates a new instance of the hub, will push one {@link Layer} into the\n * internal stack on creation.\n *\n * @param client bound to the hub.\n * @param scope bound to the hub.\n * @param version number, higher number means higher priority.\n */\n public constructor(client?: Client, scope: Scope = new Scope(), private readonly _version: number = API_VERSION) {\n this._stack.push({ client, scope });\n }\n\n /**\n * Internal helper function to call a method on the top client if it exists.\n *\n * @param method The method to call on the client.\n * @param args Arguments to pass to the client function.\n */\n private _invokeClient(method: M, ...args: any[]): void {\n const top = this.getStackTop();\n if (top && top.client && top.client[method]) {\n (top.client as any)[method](...args, top.scope);\n }\n }\n\n /**\n * @inheritDoc\n */\n public isOlderThan(version: number): boolean {\n return this._version < version;\n }\n\n /**\n * @inheritDoc\n */\n public bindClient(client?: Client): void {\n const top = this.getStackTop();\n top.client = client;\n if (client && client.setupIntegrations) {\n client.setupIntegrations();\n }\n }\n\n /**\n * @inheritDoc\n */\n public pushScope(): Scope {\n // We want to clone the content of prev scope\n const stack = this.getStack();\n const parentScope = stack.length > 0 ? stack[stack.length - 1].scope : undefined;\n const scope = Scope.clone(parentScope);\n this.getStack().push({\n client: this.getClient(),\n scope,\n });\n return scope;\n }\n\n /**\n * @inheritDoc\n */\n public popScope(): boolean {\n return this.getStack().pop() !== undefined;\n }\n\n /**\n * @inheritDoc\n */\n public withScope(callback: (scope: Scope) => void): void {\n const scope = this.pushScope();\n try {\n callback(scope);\n } finally {\n this.popScope();\n }\n }\n\n /**\n * @inheritDoc\n */\n public getClient(): C | undefined {\n return this.getStackTop().client as C;\n }\n\n /** Returns the scope of the top stack. */\n public getScope(): Scope | undefined {\n return this.getStackTop().scope;\n }\n\n /** Returns the scope stack for domains or the process. */\n public getStack(): Layer[] {\n return this._stack;\n }\n\n /** Returns the topmost scope layer in the order domain > local > process. */\n public getStackTop(): Layer {\n return this._stack[this._stack.length - 1];\n }\n\n /**\n * @inheritDoc\n */\n public captureException(exception: any, hint?: EventHint): string {\n const eventId = (this._lastEventId = uuid4());\n let finalHint = hint;\n\n // If there's no explicit hint provided, mimick the same thing that would happen\n // in the minimal itself to create a consistent behavior.\n // We don't do this in the client, as it's the lowest level API, and doing this,\n // would prevent user from having full control over direct calls.\n if (!hint) {\n let syntheticException: Error;\n try {\n throw new Error('Sentry syntheticException');\n } catch (exception) {\n syntheticException = exception as Error;\n }\n finalHint = {\n originalException: exception,\n syntheticException,\n };\n }\n\n this._invokeClient('captureException', exception, {\n ...finalHint,\n event_id: eventId,\n });\n return eventId;\n }\n\n /**\n * @inheritDoc\n */\n public captureMessage(message: string, level?: Severity, hint?: EventHint): string {\n const eventId = (this._lastEventId = uuid4());\n let finalHint = hint;\n\n // If there's no explicit hint provided, mimick the same thing that would happen\n // in the minimal itself to create a consistent behavior.\n // We don't do this in the client, as it's the lowest level API, and doing this,\n // would prevent user from having full control over direct calls.\n if (!hint) {\n let syntheticException: Error;\n try {\n throw new Error(message);\n } catch (exception) {\n syntheticException = exception as Error;\n }\n finalHint = {\n originalException: message,\n syntheticException,\n };\n }\n\n this._invokeClient('captureMessage', message, level, {\n ...finalHint,\n event_id: eventId,\n });\n return eventId;\n }\n\n /**\n * @inheritDoc\n */\n public captureEvent(event: Event, hint?: EventHint): string {\n const eventId = (this._lastEventId = uuid4());\n this._invokeClient('captureEvent', event, {\n ...hint,\n event_id: eventId,\n });\n return eventId;\n }\n\n /**\n * @inheritDoc\n */\n public lastEventId(): string | undefined {\n return this._lastEventId;\n }\n\n /**\n * @inheritDoc\n */\n public addBreadcrumb(breadcrumb: Breadcrumb, hint?: BreadcrumbHint): void {\n const top = this.getStackTop();\n\n if (!top.scope || !top.client) {\n return;\n }\n\n const { beforeBreadcrumb = null, maxBreadcrumbs = DEFAULT_BREADCRUMBS } =\n (top.client.getOptions && top.client.getOptions()) || {};\n\n if (maxBreadcrumbs <= 0) {\n return;\n }\n\n const timestamp = timestampWithMs();\n const mergedBreadcrumb = { timestamp, ...breadcrumb };\n const finalBreadcrumb = beforeBreadcrumb\n ? (consoleSandbox(() => beforeBreadcrumb(mergedBreadcrumb, hint)) as Breadcrumb | null)\n : mergedBreadcrumb;\n\n if (finalBreadcrumb === null) {\n return;\n }\n\n top.scope.addBreadcrumb(finalBreadcrumb, Math.min(maxBreadcrumbs, MAX_BREADCRUMBS));\n }\n\n /**\n * @inheritDoc\n */\n public setUser(user: User | null): void {\n const top = this.getStackTop();\n if (!top.scope) {\n return;\n }\n top.scope.setUser(user);\n }\n\n /**\n * @inheritDoc\n */\n public setTags(tags: { [key: string]: string }): void {\n const top = this.getStackTop();\n if (!top.scope) {\n return;\n }\n top.scope.setTags(tags);\n }\n\n /**\n * @inheritDoc\n */\n public setExtras(extras: { [key: string]: any }): void {\n const top = this.getStackTop();\n if (!top.scope) {\n return;\n }\n top.scope.setExtras(extras);\n }\n\n /**\n * @inheritDoc\n */\n public setTag(key: string, value: string): void {\n const top = this.getStackTop();\n if (!top.scope) {\n return;\n }\n top.scope.setTag(key, value);\n }\n\n /**\n * @inheritDoc\n */\n public setExtra(key: string, extra: any): void {\n const top = this.getStackTop();\n if (!top.scope) {\n return;\n }\n top.scope.setExtra(key, extra);\n }\n\n /**\n * @inheritDoc\n */\n public setContext(name: string, context: { [key: string]: any } | null): void {\n const top = this.getStackTop();\n if (!top.scope) {\n return;\n }\n top.scope.setContext(name, context);\n }\n\n /**\n * @inheritDoc\n */\n public configureScope(callback: (scope: Scope) => void): void {\n const top = this.getStackTop();\n if (top.scope && top.client) {\n callback(top.scope);\n }\n }\n\n /**\n * @inheritDoc\n */\n public run(callback: (hub: Hub) => void): void {\n const oldHub = makeMain(this);\n try {\n callback(this);\n } finally {\n makeMain(oldHub);\n }\n }\n\n /**\n * @inheritDoc\n */\n public getIntegration(integration: IntegrationClass): T | null {\n const client = this.getClient();\n if (!client) {\n return null;\n }\n try {\n return client.getIntegration(integration);\n } catch (_oO) {\n logger.warn(`Cannot retrieve integration ${integration.id} from the current Hub`);\n return null;\n }\n }\n\n /**\n * @inheritDoc\n */\n public startSpan(spanOrSpanContext?: Span | SpanContext, forceNoChild: boolean = false): Span {\n return this._callExtensionMethod('startSpan', spanOrSpanContext, forceNoChild);\n }\n\n /**\n * @inheritDoc\n */\n public traceHeaders(): { [key: string]: string } {\n return this._callExtensionMethod<{ [key: string]: string }>('traceHeaders');\n }\n\n /**\n * Calls global extension method and binding current instance to the function call\n */\n // @ts-ignore\n private _callExtensionMethod(method: string, ...args: any[]): T {\n const carrier = getMainCarrier();\n const sentry = carrier.__SENTRY__;\n // tslint:disable-next-line: strict-type-predicates\n if (sentry && sentry.extensions && typeof sentry.extensions[method] === 'function') {\n return sentry.extensions[method].apply(this, args);\n }\n logger.warn(`Extension method ${method} couldn't be found, doing nothing.`);\n }\n}\n\n/** Returns the global shim registry. */\nexport function getMainCarrier(): Carrier {\n const carrier = getGlobalObject();\n carrier.__SENTRY__ = carrier.__SENTRY__ || {\n extensions: {},\n hub: undefined,\n };\n return carrier;\n}\n\n/**\n * Replaces the current main hub with the passed one on the global object\n *\n * @returns The old replaced hub\n */\nexport function makeMain(hub: Hub): Hub {\n const registry = getMainCarrier();\n const oldHub = getHubFromCarrier(registry);\n setHubOnCarrier(registry, hub);\n return oldHub;\n}\n\n/**\n * Returns the default hub instance.\n *\n * If a hub is already registered in the global carrier but this module\n * contains a more recent version, it replaces the registered version.\n * Otherwise, the currently registered hub will be returned.\n */\nexport function getCurrentHub(): Hub {\n // Get main carrier (global for every environment)\n const registry = getMainCarrier();\n\n // If there's no hub, or its an old API, assign a new one\n if (!hasHubOnCarrier(registry) || getHubFromCarrier(registry).isOlderThan(API_VERSION)) {\n setHubOnCarrier(registry, new Hub());\n }\n\n // Prefer domains over global if they are there (applicable only to Node environment)\n if (isNodeEnv()) {\n return getHubFromActiveDomain(registry);\n }\n // Return hub that lives on a global object\n return getHubFromCarrier(registry);\n}\n\n/**\n * Try to read the hub from an active domain, fallback to the registry if one doesnt exist\n * @returns discovered hub\n */\nfunction getHubFromActiveDomain(registry: Carrier): Hub {\n try {\n const property = 'domain';\n const carrier = getMainCarrier();\n const sentry = carrier.__SENTRY__;\n // tslint:disable-next-line: strict-type-predicates\n if (!sentry || !sentry.extensions || !sentry.extensions[property]) {\n return getHubFromCarrier(registry);\n }\n const domain = sentry.extensions[property] as any;\n const activeDomain = domain.active;\n\n // If there no active domain, just return global hub\n if (!activeDomain) {\n return getHubFromCarrier(registry);\n }\n\n // If there's no hub on current domain, or its an old API, assign a new one\n if (!hasHubOnCarrier(activeDomain) || getHubFromCarrier(activeDomain).isOlderThan(API_VERSION)) {\n const registryHubTopStack = getHubFromCarrier(registry).getStackTop();\n setHubOnCarrier(activeDomain, new Hub(registryHubTopStack.client, Scope.clone(registryHubTopStack.scope)));\n }\n\n // Return hub that lives on a domain\n return getHubFromCarrier(activeDomain);\n } catch (_Oo) {\n // Return hub that lives on a global object\n return getHubFromCarrier(registry);\n }\n}\n\n/**\n * This will tell whether a carrier has a hub on it or not\n * @param carrier object\n */\nfunction hasHubOnCarrier(carrier: Carrier): boolean {\n if (carrier && carrier.__SENTRY__ && carrier.__SENTRY__.hub) {\n return true;\n }\n return false;\n}\n\n/**\n * This will create a new {@link Hub} and add to the passed object on\n * __SENTRY__.hub.\n * @param carrier object\n * @hidden\n */\nexport function getHubFromCarrier(carrier: Carrier): Hub {\n if (carrier && carrier.__SENTRY__ && carrier.__SENTRY__.hub) {\n return carrier.__SENTRY__.hub;\n }\n carrier.__SENTRY__ = carrier.__SENTRY__ || {};\n carrier.__SENTRY__.hub = new Hub();\n return carrier.__SENTRY__.hub;\n}\n\n/**\n * This will set passed {@link Hub} on the passed object's __SENTRY__.hub attribute\n * @param carrier object\n * @param hub Hub\n */\nexport function setHubOnCarrier(carrier: Carrier, hub: Hub): boolean {\n if (!carrier) {\n return false;\n }\n carrier.__SENTRY__ = carrier.__SENTRY__ || {};\n carrier.__SENTRY__.hub = hub;\n return true;\n}\n","export * from './exports';\n\nimport { Integrations as CoreIntegrations } from '@sentry/core';\nimport { getGlobalObject } from '@sentry/utils';\n\nimport * as BrowserIntegrations from './integrations';\nimport * as Transports from './transports';\n\nlet windowIntegrations = {};\n\n// This block is needed to add compatibility with the integrations packages when used with a CDN\n// tslint:disable: no-unsafe-any\nconst _window = getGlobalObject();\nif (_window.Sentry && _window.Sentry.Integrations) {\n windowIntegrations = _window.Sentry.Integrations;\n}\n// tslint:enable: no-unsafe-any\n\nconst INTEGRATIONS = {\n ...windowIntegrations,\n ...CoreIntegrations,\n ...BrowserIntegrations,\n};\n\nexport { INTEGRATIONS as Integrations, Transports };\n","import { addGlobalEventProcessor, getCurrentHub } from '@sentry/hub';\nimport { Integration, Options } from '@sentry/types';\nimport { logger } from '@sentry/utils';\n\nexport const installedIntegrations: string[] = [];\n\n/** Map of integrations assigned to a client */\nexport interface IntegrationIndex {\n [key: string]: Integration;\n}\n\n/** Gets integration to install */\nexport function getIntegrationsToSetup(options: Options): Integration[] {\n const defaultIntegrations = (options.defaultIntegrations && [...options.defaultIntegrations]) || [];\n const userIntegrations = options.integrations;\n let integrations: Integration[] = [];\n if (Array.isArray(userIntegrations)) {\n const userIntegrationsNames = userIntegrations.map(i => i.name);\n const pickedIntegrationsNames: string[] = [];\n\n // Leave only unique default integrations, that were not overridden with provided user integrations\n defaultIntegrations.forEach(defaultIntegration => {\n if (\n userIntegrationsNames.indexOf(defaultIntegration.name) === -1 &&\n pickedIntegrationsNames.indexOf(defaultIntegration.name) === -1\n ) {\n integrations.push(defaultIntegration);\n pickedIntegrationsNames.push(defaultIntegration.name);\n }\n });\n\n // Don't add same user integration twice\n userIntegrations.forEach(userIntegration => {\n if (pickedIntegrationsNames.indexOf(userIntegration.name) === -1) {\n integrations.push(userIntegration);\n pickedIntegrationsNames.push(userIntegration.name);\n }\n });\n } else if (typeof userIntegrations === 'function') {\n integrations = userIntegrations(defaultIntegrations);\n integrations = Array.isArray(integrations) ? integrations : [integrations];\n } else {\n integrations = [...defaultIntegrations];\n }\n\n // Make sure that if present, `Debug` integration will always run last\n const integrationsNames = integrations.map(i => i.name);\n const alwaysLastToRun = 'Debug';\n if (integrationsNames.indexOf(alwaysLastToRun) !== -1) {\n integrations.push(...integrations.splice(integrationsNames.indexOf(alwaysLastToRun), 1));\n }\n\n return integrations;\n}\n\n/** Setup given integration */\nexport function setupIntegration(integration: Integration): void {\n if (installedIntegrations.indexOf(integration.name) !== -1) {\n return;\n }\n integration.setupOnce(addGlobalEventProcessor, getCurrentHub);\n installedIntegrations.push(integration.name);\n logger.log(`Integration installed: ${integration.name}`);\n}\n\n/**\n * Given a list of integration instances this installs them all. When `withDefaults` is set to `true` then all default\n * integrations are added unless they were already provided before.\n * @param integrations array of integration instances\n * @param withDefault should enable default integrations\n */\nexport function setupIntegrations(options: O): IntegrationIndex {\n const integrations: IntegrationIndex = {};\n getIntegrationsToSetup(options).forEach(integration => {\n integrations[integration.name] = integration;\n setupIntegration(integration);\n });\n return integrations;\n}\n","// tslint:disable:object-literal-sort-keys\n\n/**\n * This was originally forked from https://github.com/occ/TraceKit, but has since been\n * largely modified and is now maintained as part of Sentry JS SDK.\n */\n\n/**\n * An object representing a single stack frame.\n * {Object} StackFrame\n * {string} url The JavaScript or HTML file URL.\n * {string} func The function name, or empty for anonymous functions (if guessing did not work).\n * {string[]?} args The arguments passed to the function, if known.\n * {number=} line The line number, if known.\n * {number=} column The column number, if known.\n * {string[]} context An array of source code lines; the middle element corresponds to the correct line#.\n */\nexport interface StackFrame {\n url: string;\n func: string;\n args: string[];\n line: number | null;\n column: number | null;\n}\n\n/**\n * An object representing a JavaScript stack trace.\n * {Object} StackTrace\n * {string} name The name of the thrown exception.\n * {string} message The exception error message.\n * {TraceKit.StackFrame[]} stack An array of stack frames.\n */\nexport interface StackTrace {\n name: string;\n message: string;\n mechanism?: string;\n stack: StackFrame[];\n failed?: boolean;\n}\n\n// global reference to slice\nconst UNKNOWN_FUNCTION = '?';\n\n// Chromium based browsers: Chrome, Brave, new Opera, new Edge\nconst chrome = /^\\s*at (?:(.*?) ?\\()?((?:file|https?|blob|chrome-extension|address|native|eval|webpack||[-a-z]+:|.*bundle|\\/).*?)(?::(\\d+))?(?::(\\d+))?\\)?\\s*$/i;\n// gecko regex: `(?:bundle|\\d+\\.js)`: `bundle` is for react native, `\\d+\\.js` also but specifically for ram bundles because it\n// generates filenames without a prefix like `file://` the filenames in the stacktrace are just 42.js\n// We need this specific case for now because we want no other regex to match.\nconst gecko = /^\\s*(.*?)(?:\\((.*?)\\))?(?:^|@)?((?:file|https?|blob|chrome|webpack|resource|moz-extension).*?:\\/.*?|\\[native code\\]|[^@]*(?:bundle|\\d+\\.js))(?::(\\d+))?(?::(\\d+))?\\s*$/i;\nconst winjs = /^\\s*at (?:((?:\\[object object\\])?.+) )?\\(?((?:file|ms-appx|https?|webpack|blob):.*?):(\\d+)(?::(\\d+))?\\)?\\s*$/i;\nconst geckoEval = /(\\S+) line (\\d+)(?: > eval line \\d+)* > eval/i;\nconst chromeEval = /\\((\\S*)(?::(\\d+))(?::(\\d+))\\)/;\n\n/** JSDoc */\nexport function computeStackTrace(ex: any): StackTrace {\n // tslint:disable:no-unsafe-any\n\n let stack = null;\n const popSize: number = ex && ex.framesToPop;\n\n try {\n // This must be tried first because Opera 10 *destroys*\n // its stacktrace property if you try to access the stack\n // property first!!\n stack = computeStackTraceFromStacktraceProp(ex);\n if (stack) {\n return popFrames(stack, popSize);\n }\n } catch (e) {\n // no-empty\n }\n\n try {\n stack = computeStackTraceFromStackProp(ex);\n if (stack) {\n return popFrames(stack, popSize);\n }\n } catch (e) {\n // no-empty\n }\n\n return {\n message: extractMessage(ex),\n name: ex && ex.name,\n stack: [],\n failed: true,\n };\n}\n\n/** JSDoc */\n// tslint:disable-next-line:cyclomatic-complexity\nfunction computeStackTraceFromStackProp(ex: any): StackTrace | null {\n // tslint:disable:no-conditional-assignment\n if (!ex || !ex.stack) {\n return null;\n }\n\n const stack = [];\n const lines = ex.stack.split('\\n');\n let isEval;\n let submatch;\n let parts;\n let element;\n\n for (let i = 0; i < lines.length; ++i) {\n if ((parts = chrome.exec(lines[i]))) {\n const isNative = parts[2] && parts[2].indexOf('native') === 0; // start of line\n isEval = parts[2] && parts[2].indexOf('eval') === 0; // start of line\n if (isEval && (submatch = chromeEval.exec(parts[2]))) {\n // throw out eval line/column and use top-most line/column number\n parts[2] = submatch[1]; // url\n parts[3] = submatch[2]; // line\n parts[4] = submatch[3]; // column\n }\n element = {\n // working with the regexp above is super painful. it is quite a hack, but just stripping the `address at `\n // prefix here seems like the quickest solution for now.\n url: parts[2] && parts[2].indexOf('address at ') === 0 ? parts[2].substr('address at '.length) : parts[2],\n func: parts[1] || UNKNOWN_FUNCTION,\n args: isNative ? [parts[2]] : [],\n line: parts[3] ? +parts[3] : null,\n column: parts[4] ? +parts[4] : null,\n };\n } else if ((parts = winjs.exec(lines[i]))) {\n element = {\n url: parts[2],\n func: parts[1] || UNKNOWN_FUNCTION,\n args: [],\n line: +parts[3],\n column: parts[4] ? +parts[4] : null,\n };\n } else if ((parts = gecko.exec(lines[i]))) {\n isEval = parts[3] && parts[3].indexOf(' > eval') > -1;\n if (isEval && (submatch = geckoEval.exec(parts[3]))) {\n // throw out eval line/column and use top-most line number\n parts[1] = parts[1] || `eval`;\n parts[3] = submatch[1];\n parts[4] = submatch[2];\n parts[5] = ''; // no column when eval\n } else if (i === 0 && !parts[5] && ex.columnNumber !== void 0) {\n // FireFox uses this awesome columnNumber property for its top frame\n // Also note, Firefox's column number is 0-based and everything else expects 1-based,\n // so adding 1\n // NOTE: this hack doesn't work if top-most frame is eval\n stack[0].column = (ex.columnNumber as number) + 1;\n }\n element = {\n url: parts[3],\n func: parts[1] || UNKNOWN_FUNCTION,\n args: parts[2] ? parts[2].split(',') : [],\n line: parts[4] ? +parts[4] : null,\n column: parts[5] ? +parts[5] : null,\n };\n } else {\n continue;\n }\n\n if (!element.func && element.line) {\n element.func = UNKNOWN_FUNCTION;\n }\n\n stack.push(element);\n }\n\n if (!stack.length) {\n return null;\n }\n\n return {\n message: extractMessage(ex),\n name: ex.name,\n stack,\n };\n}\n\n/** JSDoc */\nfunction computeStackTraceFromStacktraceProp(ex: any): StackTrace | null {\n if (!ex || !ex.stacktrace) {\n return null;\n }\n // Access and store the stacktrace property before doing ANYTHING\n // else to it because Opera is not very good at providing it\n // reliably in other circumstances.\n const stacktrace = ex.stacktrace;\n const opera10Regex = / line (\\d+).*script (?:in )?(\\S+)(?:: in function (\\S+))?$/i;\n const opera11Regex = / line (\\d+), column (\\d+)\\s*(?:in (?:]+)>|([^\\)]+))\\((.*)\\))? in (.*):\\s*$/i;\n const lines = stacktrace.split('\\n');\n const stack = [];\n let parts;\n\n for (let line = 0; line < lines.length; line += 2) {\n // tslint:disable:no-conditional-assignment\n let element = null;\n if ((parts = opera10Regex.exec(lines[line]))) {\n element = {\n url: parts[2],\n func: parts[3],\n args: [],\n line: +parts[1],\n column: null,\n };\n } else if ((parts = opera11Regex.exec(lines[line]))) {\n element = {\n url: parts[6],\n func: parts[3] || parts[4],\n args: parts[5] ? parts[5].split(',') : [],\n line: +parts[1],\n column: +parts[2],\n };\n }\n\n if (element) {\n if (!element.func && element.line) {\n element.func = UNKNOWN_FUNCTION;\n }\n stack.push(element);\n }\n }\n\n if (!stack.length) {\n return null;\n }\n\n return {\n message: extractMessage(ex),\n name: ex.name,\n stack,\n };\n}\n\n/** Remove N number of frames from the stack */\nfunction popFrames(stacktrace: StackTrace, popSize: number): StackTrace {\n try {\n return {\n ...stacktrace,\n stack: stacktrace.stack.slice(popSize),\n };\n } catch (e) {\n return stacktrace;\n }\n}\n\n/**\n * There are cases where stacktrace.message is an Event object\n * https://github.com/getsentry/sentry-javascript/issues/1949\n * In this specific case we try to extract stacktrace.message.error.message\n */\nfunction extractMessage(ex: any): string {\n const message = ex && ex.message;\n if (!message) {\n return 'No error message';\n }\n if (message.error && typeof message.error.message === 'string') {\n return message.error.message;\n }\n return message;\n}\n","import { Event, Exception, StackFrame } from '@sentry/types';\nimport { extractExceptionKeysForMessage, isEvent, normalizeToSize } from '@sentry/utils';\n\nimport { computeStackTrace, StackFrame as TraceKitStackFrame, StackTrace as TraceKitStackTrace } from './tracekit';\n\nconst STACKTRACE_LIMIT = 50;\n\n/**\n * This function creates an exception from an TraceKitStackTrace\n * @param stacktrace TraceKitStackTrace that will be converted to an exception\n * @hidden\n */\nexport function exceptionFromStacktrace(stacktrace: TraceKitStackTrace): Exception {\n const frames = prepareFramesForEvent(stacktrace.stack);\n\n const exception: Exception = {\n type: stacktrace.name,\n value: stacktrace.message,\n };\n\n if (frames && frames.length) {\n exception.stacktrace = { frames };\n }\n\n // tslint:disable-next-line:strict-type-predicates\n if (exception.type === undefined && exception.value === '') {\n exception.value = 'Unrecoverable error caught';\n }\n\n return exception;\n}\n\n/**\n * @hidden\n */\nexport function eventFromPlainObject(exception: {}, syntheticException?: Error, rejection?: boolean): Event {\n const event: Event = {\n exception: {\n values: [\n {\n type: isEvent(exception) ? exception.constructor.name : rejection ? 'UnhandledRejection' : 'Error',\n value: `Non-Error ${\n rejection ? 'promise rejection' : 'exception'\n } captured with keys: ${extractExceptionKeysForMessage(exception)}`,\n },\n ],\n },\n extra: {\n __serialized__: normalizeToSize(exception),\n },\n };\n\n if (syntheticException) {\n const stacktrace = computeStackTrace(syntheticException);\n const frames = prepareFramesForEvent(stacktrace.stack);\n event.stacktrace = {\n frames,\n };\n }\n\n return event;\n}\n\n/**\n * @hidden\n */\nexport function eventFromStacktrace(stacktrace: TraceKitStackTrace): Event {\n const exception = exceptionFromStacktrace(stacktrace);\n\n return {\n exception: {\n values: [exception],\n },\n };\n}\n\n/**\n * @hidden\n */\nexport function prepareFramesForEvent(stack: TraceKitStackFrame[]): StackFrame[] {\n if (!stack || !stack.length) {\n return [];\n }\n\n let localStack = stack;\n\n const firstFrameFunction = localStack[0].func || '';\n const lastFrameFunction = localStack[localStack.length - 1].func || '';\n\n // If stack starts with one of our API calls, remove it (starts, meaning it's the top of the stack - aka last call)\n if (firstFrameFunction.indexOf('captureMessage') !== -1 || firstFrameFunction.indexOf('captureException') !== -1) {\n localStack = localStack.slice(1);\n }\n\n // If stack ends with one of our internal API calls, remove it (ends, meaning it's the bottom of the stack - aka top-most call)\n if (lastFrameFunction.indexOf('sentryWrapped') !== -1) {\n localStack = localStack.slice(0, -1);\n }\n\n // The frame where the crash happened, should be the last entry in the array\n return localStack\n .map(\n (frame: TraceKitStackFrame): StackFrame => ({\n colno: frame.column === null ? undefined : frame.column,\n filename: frame.url || localStack[0].url,\n function: frame.func || '?',\n in_app: true,\n lineno: frame.line === null ? undefined : frame.line,\n }),\n )\n .slice(0, STACKTRACE_LIMIT)\n .reverse();\n}\n","import { Event } from '@sentry/types';\nimport {\n addExceptionMechanism,\n addExceptionTypeValue,\n isDOMError,\n isDOMException,\n isError,\n isErrorEvent,\n isEvent,\n isPlainObject,\n} from '@sentry/utils';\n\nimport { eventFromPlainObject, eventFromStacktrace, prepareFramesForEvent } from './parsers';\nimport { computeStackTrace } from './tracekit';\n\n/** JSDoc */\nexport function eventFromUnknownInput(\n exception: unknown,\n syntheticException?: Error,\n options: {\n rejection?: boolean;\n attachStacktrace?: boolean;\n } = {},\n): Event {\n let event: Event;\n\n if (isErrorEvent(exception as ErrorEvent) && (exception as ErrorEvent).error) {\n // If it is an ErrorEvent with `error` property, extract it to get actual Error\n const errorEvent = exception as ErrorEvent;\n exception = errorEvent.error; // tslint:disable-line:no-parameter-reassignment\n event = eventFromStacktrace(computeStackTrace(exception as Error));\n return event;\n }\n if (isDOMError(exception as DOMError) || isDOMException(exception as DOMException)) {\n // If it is a DOMError or DOMException (which are legacy APIs, but still supported in some browsers)\n // then we just extract the name and message, as they don't provide anything else\n // https://developer.mozilla.org/en-US/docs/Web/API/DOMError\n // https://developer.mozilla.org/en-US/docs/Web/API/DOMException\n const domException = exception as DOMException;\n const name = domException.name || (isDOMError(domException) ? 'DOMError' : 'DOMException');\n const message = domException.message ? `${name}: ${domException.message}` : name;\n\n event = eventFromString(message, syntheticException, options);\n addExceptionTypeValue(event, message);\n return event;\n }\n if (isError(exception as Error)) {\n // we have a real Error object, do nothing\n event = eventFromStacktrace(computeStackTrace(exception as Error));\n return event;\n }\n if (isPlainObject(exception) || isEvent(exception)) {\n // If it is plain Object or Event, serialize it manually and extract options\n // This will allow us to group events based on top-level keys\n // which is much better than creating new group when any key/value change\n const objectException = exception as {};\n event = eventFromPlainObject(objectException, syntheticException, options.rejection);\n addExceptionMechanism(event, {\n synthetic: true,\n });\n return event;\n }\n\n // If none of previous checks were valid, then it means that it's not:\n // - an instance of DOMError\n // - an instance of DOMException\n // - an instance of Event\n // - an instance of Error\n // - a valid ErrorEvent (one with an error property)\n // - a plain Object\n //\n // So bail out and capture it as a simple message:\n event = eventFromString(exception as string, syntheticException, options);\n addExceptionTypeValue(event, `${exception}`, undefined);\n addExceptionMechanism(event, {\n synthetic: true,\n });\n\n return event;\n}\n\n// this._options.attachStacktrace\n/** JSDoc */\nexport function eventFromString(\n input: string,\n syntheticException?: Error,\n options: {\n attachStacktrace?: boolean;\n } = {},\n): Event {\n const event: Event = {\n message: input,\n };\n\n if (options.attachStacktrace && syntheticException) {\n const stacktrace = computeStackTrace(syntheticException);\n const frames = prepareFramesForEvent(stacktrace.stack);\n event.stacktrace = {\n frames,\n };\n }\n\n return event;\n}\n","import { captureException, withScope } from '@sentry/core';\nimport { Event as SentryEvent, Mechanism, Scope, WrappedFunction } from '@sentry/types';\nimport { addExceptionMechanism, addExceptionTypeValue } from '@sentry/utils';\n\nlet ignoreOnError: number = 0;\n\n/**\n * @hidden\n */\nexport function shouldIgnoreOnError(): boolean {\n return ignoreOnError > 0;\n}\n\n/**\n * @hidden\n */\nexport function ignoreNextOnError(): void {\n // onerror should trigger before setTimeout\n ignoreOnError += 1;\n setTimeout(() => {\n ignoreOnError -= 1;\n });\n}\n\n/**\n * Instruments the given function and sends an event to Sentry every time the\n * function throws an exception.\n *\n * @param fn A function to wrap.\n * @returns The wrapped function.\n * @hidden\n */\nexport function wrap(\n fn: WrappedFunction,\n options: {\n mechanism?: Mechanism;\n } = {},\n before?: WrappedFunction,\n): any {\n // tslint:disable-next-line:strict-type-predicates\n if (typeof fn !== 'function') {\n return fn;\n }\n\n try {\n // We don't wanna wrap it twice\n if (fn.__sentry__) {\n return fn;\n }\n\n // If this has already been wrapped in the past, return that wrapped function\n if (fn.__sentry_wrapped__) {\n return fn.__sentry_wrapped__;\n }\n } catch (e) {\n // Just accessing custom props in some Selenium environments\n // can cause a \"Permission denied\" exception (see raven-js#495).\n // Bail on wrapping and return the function as-is (defers to window.onerror).\n return fn;\n }\n\n const sentryWrapped: WrappedFunction = function(this: any): void {\n const args = Array.prototype.slice.call(arguments);\n\n // tslint:disable:no-unsafe-any\n try {\n // tslint:disable-next-line:strict-type-predicates\n if (before && typeof before === 'function') {\n before.apply(this, arguments);\n }\n\n const wrappedArguments = args.map((arg: any) => wrap(arg, options));\n\n if (fn.handleEvent) {\n // Attempt to invoke user-land function\n // NOTE: If you are a Sentry user, and you are seeing this stack frame, it\n // means the sentry.javascript SDK caught an error invoking your application code. This\n // is expected behavior and NOT indicative of a bug with sentry.javascript.\n return fn.handleEvent.apply(this, wrappedArguments);\n }\n // Attempt to invoke user-land function\n // NOTE: If you are a Sentry user, and you are seeing this stack frame, it\n // means the sentry.javascript SDK caught an error invoking your application code. This\n // is expected behavior and NOT indicative of a bug with sentry.javascript.\n return fn.apply(this, wrappedArguments);\n // tslint:enable:no-unsafe-any\n } catch (ex) {\n ignoreNextOnError();\n\n withScope((scope: Scope) => {\n scope.addEventProcessor((event: SentryEvent) => {\n const processedEvent = { ...event };\n\n if (options.mechanism) {\n addExceptionTypeValue(processedEvent, undefined, undefined);\n addExceptionMechanism(processedEvent, options.mechanism);\n }\n\n processedEvent.extra = {\n ...processedEvent.extra,\n arguments: args,\n };\n\n return processedEvent;\n });\n\n captureException(ex);\n });\n\n throw ex;\n }\n };\n\n // Accessing some objects may throw\n // ref: https://github.com/getsentry/sentry-javascript/issues/1168\n try {\n for (const property in fn) {\n if (Object.prototype.hasOwnProperty.call(fn, property)) {\n sentryWrapped[property] = fn[property];\n }\n }\n } catch (_oO) {} // tslint:disable-line:no-empty\n\n fn.prototype = fn.prototype || {};\n sentryWrapped.prototype = fn.prototype;\n\n Object.defineProperty(fn, '__sentry_wrapped__', {\n enumerable: false,\n value: sentryWrapped,\n });\n\n // Signal that this function has been wrapped/filled already\n // for both debugging and to prevent it to being wrapped/filled twice\n Object.defineProperties(sentryWrapped, {\n __sentry__: {\n enumerable: false,\n value: true,\n },\n __sentry_original__: {\n enumerable: false,\n value: fn,\n },\n });\n\n // Restore original function name (not all browsers allow that)\n try {\n const descriptor = Object.getOwnPropertyDescriptor(sentryWrapped, 'name') as PropertyDescriptor;\n if (descriptor.configurable) {\n Object.defineProperty(sentryWrapped, 'name', {\n get(): string {\n return fn.name;\n },\n });\n }\n } catch (_oO) {\n /*no-empty*/\n }\n\n return sentryWrapped;\n}\n","/* tslint:disable:only-arrow-functions no-unsafe-any */\n\nimport { WrappedFunction } from '@sentry/types';\n\nimport { isInstanceOf, isString } from './is';\nimport { logger } from './logger';\nimport { getFunctionName, getGlobalObject } from './misc';\nimport { fill } from './object';\nimport { supportsHistory, supportsNativeFetch } from './supports';\n\nconst global = getGlobalObject();\n\n/** Object describing handler that will be triggered for a given `type` of instrumentation */\ninterface InstrumentHandler {\n type: InstrumentHandlerType;\n callback: InstrumentHandlerCallback;\n}\ntype InstrumentHandlerType =\n | 'console'\n | 'dom'\n | 'fetch'\n | 'history'\n | 'sentry'\n | 'xhr'\n | 'error'\n | 'unhandledrejection';\ntype InstrumentHandlerCallback = (data: any) => void;\n\n/**\n * Instrument native APIs to call handlers that can be used to create breadcrumbs, APM spans etc.\n * - Console API\n * - Fetch API\n * - XHR API\n * - History API\n * - DOM API (click/typing)\n * - Error API\n * - UnhandledRejection API\n */\n\nconst handlers: { [key in InstrumentHandlerType]?: InstrumentHandlerCallback[] } = {};\nconst instrumented: { [key in InstrumentHandlerType]?: boolean } = {};\n\n/** Instruments given API */\nfunction instrument(type: InstrumentHandlerType): void {\n if (instrumented[type]) {\n return;\n }\n\n instrumented[type] = true;\n\n switch (type) {\n case 'console':\n instrumentConsole();\n break;\n case 'dom':\n instrumentDOM();\n break;\n case 'xhr':\n instrumentXHR();\n break;\n case 'fetch':\n instrumentFetch();\n break;\n case 'history':\n instrumentHistory();\n break;\n case 'error':\n instrumentError();\n break;\n case 'unhandledrejection':\n instrumentUnhandledRejection();\n break;\n default:\n logger.warn('unknown instrumentation type:', type);\n }\n}\n\n/**\n * Add handler that will be called when given type of instrumentation triggers.\n * Use at your own risk, this might break without changelog notice, only used internally.\n * @hidden\n */\nexport function addInstrumentationHandler(handler: InstrumentHandler): void {\n // tslint:disable-next-line:strict-type-predicates\n if (!handler || typeof handler.type !== 'string' || typeof handler.callback !== 'function') {\n return;\n }\n handlers[handler.type] = handlers[handler.type] || [];\n (handlers[handler.type] as InstrumentHandlerCallback[]).push(handler.callback);\n instrument(handler.type);\n}\n\n/** JSDoc */\nfunction triggerHandlers(type: InstrumentHandlerType, data: any): void {\n if (!type || !handlers[type]) {\n return;\n }\n\n for (const handler of handlers[type] || []) {\n try {\n handler(data);\n } catch (e) {\n logger.error(\n `Error while triggering instrumentation handler.\\nType: ${type}\\nName: ${getFunctionName(\n handler,\n )}\\nError: ${e}`,\n );\n }\n }\n}\n\n/** JSDoc */\nfunction instrumentConsole(): void {\n if (!('console' in global)) {\n return;\n }\n\n ['debug', 'info', 'warn', 'error', 'log', 'assert'].forEach(function(level: string): void {\n if (!(level in global.console)) {\n return;\n }\n\n fill(global.console, level, function(originalConsoleLevel: () => any): Function {\n return function(...args: any[]): void {\n triggerHandlers('console', { args, level });\n\n // this fails for some browsers. :(\n if (originalConsoleLevel) {\n Function.prototype.apply.call(originalConsoleLevel, global.console, args);\n }\n };\n });\n });\n}\n\n/** JSDoc */\nfunction instrumentFetch(): void {\n if (!supportsNativeFetch()) {\n return;\n }\n\n fill(global, 'fetch', function(originalFetch: () => void): () => void {\n return function(...args: any[]): void {\n const commonHandlerData = {\n args,\n fetchData: {\n method: getFetchMethod(args),\n url: getFetchUrl(args),\n },\n startTimestamp: Date.now(),\n };\n\n triggerHandlers('fetch', {\n ...commonHandlerData,\n });\n\n return originalFetch.apply(global, args).then(\n (response: Response) => {\n triggerHandlers('fetch', {\n ...commonHandlerData,\n endTimestamp: Date.now(),\n response,\n });\n return response;\n },\n (error: Error) => {\n triggerHandlers('fetch', {\n ...commonHandlerData,\n endTimestamp: Date.now(),\n error,\n });\n throw error;\n },\n );\n };\n });\n}\n\n/** JSDoc */\ninterface SentryWrappedXMLHttpRequest extends XMLHttpRequest {\n [key: string]: any;\n __sentry_xhr__?: {\n method?: string;\n url?: string;\n status_code?: number;\n };\n}\n\n/** Extract `method` from fetch call arguments */\nfunction getFetchMethod(fetchArgs: any[] = []): string {\n if ('Request' in global && isInstanceOf(fetchArgs[0], Request) && fetchArgs[0].method) {\n return String(fetchArgs[0].method).toUpperCase();\n }\n if (fetchArgs[1] && fetchArgs[1].method) {\n return String(fetchArgs[1].method).toUpperCase();\n }\n return 'GET';\n}\n\n/** Extract `url` from fetch call arguments */\nfunction getFetchUrl(fetchArgs: any[] = []): string {\n if (typeof fetchArgs[0] === 'string') {\n return fetchArgs[0];\n }\n if ('Request' in global && isInstanceOf(fetchArgs[0], Request)) {\n return fetchArgs[0].url;\n }\n return String(fetchArgs[0]);\n}\n\n/** JSDoc */\nfunction instrumentXHR(): void {\n if (!('XMLHttpRequest' in global)) {\n return;\n }\n\n const xhrproto = XMLHttpRequest.prototype;\n\n fill(xhrproto, 'open', function(originalOpen: () => void): () => void {\n return function(this: SentryWrappedXMLHttpRequest, ...args: any[]): void {\n const url = args[1];\n this.__sentry_xhr__ = {\n method: isString(args[0]) ? args[0].toUpperCase() : args[0],\n url: args[1],\n };\n\n // if Sentry key appears in URL, don't capture it as a request\n if (isString(url) && this.__sentry_xhr__.method === 'POST' && url.match(/sentry_key/)) {\n this.__sentry_own_request__ = true;\n }\n\n return originalOpen.apply(this, args);\n };\n });\n\n fill(xhrproto, 'send', function(originalSend: () => void): () => void {\n return function(this: SentryWrappedXMLHttpRequest, ...args: any[]): void {\n const xhr = this; // tslint:disable-line:no-this-assignment\n const commonHandlerData = {\n args,\n startTimestamp: Date.now(),\n xhr,\n };\n\n triggerHandlers('xhr', {\n ...commonHandlerData,\n });\n\n xhr.addEventListener('readystatechange', function(): void {\n if (xhr.readyState === 4) {\n try {\n // touching statusCode in some platforms throws\n // an exception\n if (xhr.__sentry_xhr__) {\n xhr.__sentry_xhr__.status_code = xhr.status;\n }\n } catch (e) {\n /* do nothing */\n }\n triggerHandlers('xhr', {\n ...commonHandlerData,\n endTimestamp: Date.now(),\n });\n }\n });\n\n return originalSend.apply(this, args);\n };\n });\n}\n\nlet lastHref: string;\n\n/** JSDoc */\nfunction instrumentHistory(): void {\n if (!supportsHistory()) {\n return;\n }\n\n const oldOnPopState = global.onpopstate;\n global.onpopstate = function(this: WindowEventHandlers, ...args: any[]): any {\n const to = global.location.href;\n // keep track of the current URL state, as we always receive only the updated state\n const from = lastHref;\n lastHref = to;\n triggerHandlers('history', {\n from,\n to,\n });\n if (oldOnPopState) {\n return oldOnPopState.apply(this, args);\n }\n };\n\n /** @hidden */\n function historyReplacementFunction(originalHistoryFunction: () => void): () => void {\n return function(this: History, ...args: any[]): void {\n const url = args.length > 2 ? args[2] : undefined;\n if (url) {\n // coerce to string (this is what pushState does)\n const from = lastHref;\n const to = String(url);\n // keep track of the current URL state, as we always receive only the updated state\n lastHref = to;\n triggerHandlers('history', {\n from,\n to,\n });\n }\n return originalHistoryFunction.apply(this, args);\n };\n }\n\n fill(global.history, 'pushState', historyReplacementFunction);\n fill(global.history, 'replaceState', historyReplacementFunction);\n}\n\n/** JSDoc */\nfunction instrumentDOM(): void {\n if (!('document' in global)) {\n return;\n }\n\n // Capture breadcrumbs from any click that is unhandled / bubbled up all the way\n // to the document. Do this before we instrument addEventListener.\n global.document.addEventListener('click', domEventHandler('click', triggerHandlers.bind(null, 'dom')), false);\n global.document.addEventListener('keypress', keypressEventHandler(triggerHandlers.bind(null, 'dom')), false);\n\n // After hooking into document bubbled up click and keypresses events, we also hook into user handled click & keypresses.\n ['EventTarget', 'Node'].forEach((target: string) => {\n const proto = (global as any)[target] && (global as any)[target].prototype;\n\n if (!proto || !proto.hasOwnProperty || !proto.hasOwnProperty('addEventListener')) {\n return;\n }\n\n fill(proto, 'addEventListener', function(\n original: () => void,\n ): (\n eventName: string,\n fn: EventListenerOrEventListenerObject,\n options?: boolean | AddEventListenerOptions,\n ) => void {\n return function(\n this: any,\n eventName: string,\n fn: EventListenerOrEventListenerObject,\n options?: boolean | AddEventListenerOptions,\n ): (eventName: string, fn: EventListenerOrEventListenerObject, capture?: boolean, secure?: boolean) => void {\n if (fn && (fn as EventListenerObject).handleEvent) {\n if (eventName === 'click') {\n fill(fn, 'handleEvent', function(innerOriginal: () => void): (caughtEvent: Event) => void {\n return function(this: any, event: Event): (event: Event) => void {\n domEventHandler('click', triggerHandlers.bind(null, 'dom'))(event);\n return innerOriginal.call(this, event);\n };\n });\n }\n if (eventName === 'keypress') {\n fill(fn, 'handleEvent', function(innerOriginal: () => void): (caughtEvent: Event) => void {\n return function(this: any, event: Event): (event: Event) => void {\n keypressEventHandler(triggerHandlers.bind(null, 'dom'))(event);\n return innerOriginal.call(this, event);\n };\n });\n }\n } else {\n if (eventName === 'click') {\n domEventHandler('click', triggerHandlers.bind(null, 'dom'), true)(this);\n }\n if (eventName === 'keypress') {\n keypressEventHandler(triggerHandlers.bind(null, 'dom'))(this);\n }\n }\n\n return original.call(this, eventName, fn, options);\n };\n });\n\n fill(proto, 'removeEventListener', function(\n original: () => void,\n ): (\n this: any,\n eventName: string,\n fn: EventListenerOrEventListenerObject,\n options?: boolean | EventListenerOptions,\n ) => () => void {\n return function(\n this: any,\n eventName: string,\n fn: EventListenerOrEventListenerObject,\n options?: boolean | EventListenerOptions,\n ): () => void {\n let callback = fn as WrappedFunction;\n try {\n callback = callback && (callback.__sentry_wrapped__ || callback);\n } catch (e) {\n // ignore, accessing __sentry_wrapped__ will throw in some Selenium environments\n }\n return original.call(this, eventName, callback, options);\n };\n });\n });\n}\n\nconst debounceDuration: number = 1000;\nlet debounceTimer: number = 0;\nlet keypressTimeout: number | undefined;\nlet lastCapturedEvent: Event | undefined;\n\n/**\n * Wraps addEventListener to capture UI breadcrumbs\n * @param name the event name (e.g. \"click\")\n * @param handler function that will be triggered\n * @param debounce decides whether it should wait till another event loop\n * @returns wrapped breadcrumb events handler\n * @hidden\n */\nfunction domEventHandler(name: string, handler: Function, debounce: boolean = false): (event: Event) => void {\n return (event: Event) => {\n // reset keypress timeout; e.g. triggering a 'click' after\n // a 'keypress' will reset the keypress debounce so that a new\n // set of keypresses can be recorded\n keypressTimeout = undefined;\n // It's possible this handler might trigger multiple times for the same\n // event (e.g. event propagation through node ancestors). Ignore if we've\n // already captured the event.\n if (!event || lastCapturedEvent === event) {\n return;\n }\n\n lastCapturedEvent = event;\n\n if (debounceTimer) {\n clearTimeout(debounceTimer);\n }\n\n if (debounce) {\n debounceTimer = setTimeout(() => {\n handler({ event, name });\n });\n } else {\n handler({ event, name });\n }\n };\n}\n\n/**\n * Wraps addEventListener to capture keypress UI events\n * @param handler function that will be triggered\n * @returns wrapped keypress events handler\n * @hidden\n */\nfunction keypressEventHandler(handler: Function): (event: Event) => void {\n // TODO: if somehow user switches keypress target before\n // debounce timeout is triggered, we will only capture\n // a single breadcrumb from the FIRST target (acceptable?)\n return (event: Event) => {\n let target;\n\n try {\n target = event.target;\n } catch (e) {\n // just accessing event properties can throw an exception in some rare circumstances\n // see: https://github.com/getsentry/raven-js/issues/838\n return;\n }\n\n const tagName = target && (target as HTMLElement).tagName;\n\n // only consider keypress events on actual input elements\n // this will disregard keypresses targeting body (e.g. tabbing\n // through elements, hotkeys, etc)\n if (!tagName || (tagName !== 'INPUT' && tagName !== 'TEXTAREA' && !(target as HTMLElement).isContentEditable)) {\n return;\n }\n\n // record first keypress in a series, but ignore subsequent\n // keypresses until debounce clears\n if (!keypressTimeout) {\n domEventHandler('input', handler)(event);\n }\n clearTimeout(keypressTimeout);\n\n keypressTimeout = (setTimeout(() => {\n keypressTimeout = undefined;\n }, debounceDuration) as any) as number;\n };\n}\n\nlet _oldOnErrorHandler: OnErrorEventHandler = null;\n/** JSDoc */\nfunction instrumentError(): void {\n _oldOnErrorHandler = global.onerror;\n\n global.onerror = function(msg: any, url: any, line: any, column: any, error: any): boolean {\n triggerHandlers('error', {\n column,\n error,\n line,\n msg,\n url,\n });\n\n if (_oldOnErrorHandler) {\n return _oldOnErrorHandler.apply(this, arguments);\n }\n\n return false;\n };\n}\n\nlet _oldOnUnhandledRejectionHandler: ((e: any) => void) | null = null;\n/** JSDoc */\nfunction instrumentUnhandledRejection(): void {\n _oldOnUnhandledRejectionHandler = global.onunhandledrejection;\n\n global.onunhandledrejection = function(e: any): boolean {\n triggerHandlers('unhandledrejection', e);\n\n if (_oldOnUnhandledRejectionHandler) {\n return _oldOnUnhandledRejectionHandler.apply(this, arguments);\n }\n\n return true;\n };\n}\n","import { API, getCurrentHub } from '@sentry/core';\nimport { Integration, Severity } from '@sentry/types';\nimport {\n addInstrumentationHandler,\n getEventDescription,\n getGlobalObject,\n htmlTreeAsString,\n logger,\n parseUrl,\n safeJoin,\n} from '@sentry/utils';\n\nimport { BrowserClient } from '../client';\n\n/**\n * @hidden\n */\nexport interface SentryWrappedXMLHttpRequest extends XMLHttpRequest {\n [key: string]: any;\n __sentry_xhr__?: {\n method?: string;\n url?: string;\n status_code?: number;\n };\n}\n\n/** JSDoc */\ninterface BreadcrumbIntegrations {\n console?: boolean;\n dom?: boolean;\n fetch?: boolean;\n history?: boolean;\n sentry?: boolean;\n xhr?: boolean;\n}\n\n/**\n * Default Breadcrumbs instrumentations\n * TODO: Deprecated - with v6, this will be renamed to `Instrument`\n */\nexport class Breadcrumbs implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = Breadcrumbs.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'Breadcrumbs';\n\n /** JSDoc */\n private readonly _options: BreadcrumbIntegrations;\n\n /**\n * @inheritDoc\n */\n public constructor(options?: BreadcrumbIntegrations) {\n this._options = {\n console: true,\n dom: true,\n fetch: true,\n history: true,\n sentry: true,\n xhr: true,\n ...options,\n };\n }\n\n /**\n * Creates breadcrumbs from console API calls\n */\n private _consoleBreadcrumb(handlerData: { [key: string]: any }): void {\n const breadcrumb = {\n category: 'console',\n data: {\n arguments: handlerData.args,\n logger: 'console',\n },\n level: Severity.fromString(handlerData.level),\n message: safeJoin(handlerData.args, ' '),\n };\n\n if (handlerData.level === 'assert') {\n if (handlerData.args[0] === false) {\n breadcrumb.message = `Assertion failed: ${safeJoin(handlerData.args.slice(1), ' ') || 'console.assert'}`;\n breadcrumb.data.arguments = handlerData.args.slice(1);\n } else {\n // Don't capture a breadcrumb for passed assertions\n return;\n }\n }\n\n getCurrentHub().addBreadcrumb(breadcrumb, {\n input: handlerData.args,\n level: handlerData.level,\n });\n }\n\n /**\n * Creates breadcrumbs from DOM API calls\n */\n private _domBreadcrumb(handlerData: { [key: string]: any }): void {\n let target;\n\n // Accessing event.target can throw (see getsentry/raven-js#838, #768)\n try {\n target = handlerData.event.target\n ? htmlTreeAsString(handlerData.event.target as Node)\n : htmlTreeAsString((handlerData.event as unknown) as Node);\n } catch (e) {\n target = '';\n }\n\n if (target.length === 0) {\n return;\n }\n\n getCurrentHub().addBreadcrumb(\n {\n category: `ui.${handlerData.name}`,\n message: target,\n },\n {\n event: handlerData.event,\n name: handlerData.name,\n },\n );\n }\n\n /**\n * Creates breadcrumbs from XHR API calls\n */\n private _xhrBreadcrumb(handlerData: { [key: string]: any }): void {\n if (handlerData.endTimestamp) {\n // We only capture complete, non-sentry requests\n if (handlerData.xhr.__sentry_own_request__) {\n return;\n }\n\n getCurrentHub().addBreadcrumb(\n {\n category: 'xhr',\n data: handlerData.xhr.__sentry_xhr__,\n type: 'http',\n },\n {\n xhr: handlerData.xhr,\n },\n );\n\n return;\n }\n\n // We only capture issued sentry requests\n if (this._options.sentry && handlerData.xhr.__sentry_own_request__) {\n addSentryBreadcrumb(handlerData.args[0]);\n }\n }\n\n /**\n * Creates breadcrumbs from fetch API calls\n */\n private _fetchBreadcrumb(handlerData: { [key: string]: any }): void {\n // We only capture complete fetch requests\n if (!handlerData.endTimestamp) {\n return;\n }\n\n const client = getCurrentHub().getClient();\n const dsn = client && client.getDsn();\n if (this._options.sentry && dsn) {\n const filterUrl = new API(dsn).getStoreEndpoint();\n // if Sentry key appears in URL, don't capture it as a request\n // but rather as our own 'sentry' type breadcrumb\n if (\n filterUrl &&\n handlerData.fetchData.url.indexOf(filterUrl) !== -1 &&\n handlerData.fetchData.method === 'POST' &&\n handlerData.args[1] &&\n handlerData.args[1].body\n ) {\n addSentryBreadcrumb(handlerData.args[1].body);\n return;\n }\n }\n\n if (handlerData.error) {\n getCurrentHub().addBreadcrumb(\n {\n category: 'fetch',\n data: {\n ...handlerData.fetchData,\n status_code: handlerData.response.status,\n },\n level: Severity.Error,\n type: 'http',\n },\n {\n data: handlerData.error,\n input: handlerData.args,\n },\n );\n } else {\n getCurrentHub().addBreadcrumb(\n {\n category: 'fetch',\n data: {\n ...handlerData.fetchData,\n status_code: handlerData.response.status,\n },\n type: 'http',\n },\n {\n input: handlerData.args,\n response: handlerData.response,\n },\n );\n }\n }\n\n /**\n * Creates breadcrumbs from history API calls\n */\n private _historyBreadcrumb(handlerData: { [key: string]: any }): void {\n const global = getGlobalObject();\n let from = handlerData.from;\n let to = handlerData.to;\n const parsedLoc = parseUrl(global.location.href);\n let parsedFrom = parseUrl(from);\n const parsedTo = parseUrl(to);\n\n // Initial pushState doesn't provide `from` information\n if (!parsedFrom.path) {\n parsedFrom = parsedLoc;\n }\n\n // Use only the path component of the URL if the URL matches the current\n // document (almost all the time when using pushState)\n if (parsedLoc.protocol === parsedTo.protocol && parsedLoc.host === parsedTo.host) {\n // tslint:disable-next-line:no-parameter-reassignment\n to = parsedTo.relative;\n }\n if (parsedLoc.protocol === parsedFrom.protocol && parsedLoc.host === parsedFrom.host) {\n // tslint:disable-next-line:no-parameter-reassignment\n from = parsedFrom.relative;\n }\n\n getCurrentHub().addBreadcrumb({\n category: 'navigation',\n data: {\n from,\n to,\n },\n });\n }\n\n /**\n * Instrument browser built-ins w/ breadcrumb capturing\n * - Console API\n * - DOM API (click/typing)\n * - XMLHttpRequest API\n * - Fetch API\n * - History API\n */\n public setupOnce(): void {\n if (this._options.console) {\n addInstrumentationHandler({\n callback: (...args) => {\n this._consoleBreadcrumb(...args);\n },\n type: 'console',\n });\n }\n if (this._options.dom) {\n addInstrumentationHandler({\n callback: (...args) => {\n this._domBreadcrumb(...args);\n },\n type: 'dom',\n });\n }\n if (this._options.xhr) {\n addInstrumentationHandler({\n callback: (...args) => {\n this._xhrBreadcrumb(...args);\n },\n type: 'xhr',\n });\n }\n if (this._options.fetch) {\n addInstrumentationHandler({\n callback: (...args) => {\n this._fetchBreadcrumb(...args);\n },\n type: 'fetch',\n });\n }\n if (this._options.history) {\n addInstrumentationHandler({\n callback: (...args) => {\n this._historyBreadcrumb(...args);\n },\n type: 'history',\n });\n }\n }\n}\n\n/**\n * Create a breadcrumb of `sentry` from the events themselves\n */\nfunction addSentryBreadcrumb(serializedData: string): void {\n // There's always something that can go wrong with deserialization...\n try {\n const event = JSON.parse(serializedData);\n getCurrentHub().addBreadcrumb(\n {\n category: `sentry.${event.type === 'transaction' ? 'transaction' : 'event'}`,\n event_id: event.event_id,\n level: event.level || Severity.fromString('error'),\n message: getEventDescription(event),\n },\n {\n event,\n },\n );\n } catch (_oO) {\n logger.error('Error while adding sentry type breadcrumb');\n }\n}\n","import { getCurrentHub, initAndBind, Integrations as CoreIntegrations } from '@sentry/core';\nimport { getGlobalObject, SyncPromise } from '@sentry/utils';\n\nimport { BrowserOptions } from './backend';\nimport { BrowserClient, ReportDialogOptions } from './client';\nimport { wrap as internalWrap } from './helpers';\nimport { Breadcrumbs, GlobalHandlers, LinkedErrors, TryCatch, UserAgent } from './integrations';\n\nexport const defaultIntegrations = [\n new CoreIntegrations.InboundFilters(),\n new CoreIntegrations.FunctionToString(),\n new TryCatch(),\n new Breadcrumbs(),\n new GlobalHandlers(),\n new LinkedErrors(),\n new UserAgent(),\n];\n\n/**\n * The Sentry Browser SDK Client.\n *\n * To use this SDK, call the {@link init} function as early as possible when\n * loading the web page. To set context information or send manual events, use\n * the provided methods.\n *\n * @example\n *\n * ```\n *\n * import { init } from '@sentry/browser';\n *\n * init({\n * dsn: '__DSN__',\n * // ...\n * });\n * ```\n *\n * @example\n * ```\n *\n * import { configureScope } from '@sentry/browser';\n * configureScope((scope: Scope) => {\n * scope.setExtra({ battery: 0.7 });\n * scope.setTag({ user_mode: 'admin' });\n * scope.setUser({ id: '4711' });\n * });\n * ```\n *\n * @example\n * ```\n *\n * import { addBreadcrumb } from '@sentry/browser';\n * addBreadcrumb({\n * message: 'My Breadcrumb',\n * // ...\n * });\n * ```\n *\n * @example\n *\n * ```\n *\n * import * as Sentry from '@sentry/browser';\n * Sentry.captureMessage('Hello, world!');\n * Sentry.captureException(new Error('Good bye'));\n * Sentry.captureEvent({\n * message: 'Manual',\n * stacktrace: [\n * // ...\n * ],\n * });\n * ```\n *\n * @see {@link BrowserOptions} for documentation on configuration options.\n */\nexport function init(options: BrowserOptions = {}): void {\n if (options.defaultIntegrations === undefined) {\n options.defaultIntegrations = defaultIntegrations;\n }\n if (options.release === undefined) {\n const window = getGlobalObject();\n // This supports the variable that sentry-webpack-plugin injects\n if (window.SENTRY_RELEASE && window.SENTRY_RELEASE.id) {\n options.release = window.SENTRY_RELEASE.id;\n }\n }\n initAndBind(BrowserClient, options);\n}\n\n/**\n * Present the user with a report dialog.\n *\n * @param options Everything is optional, we try to fetch all info need from the global scope.\n */\nexport function showReportDialog(options: ReportDialogOptions = {}): void {\n if (!options.eventId) {\n options.eventId = getCurrentHub().lastEventId();\n }\n const client = getCurrentHub().getClient();\n if (client) {\n client.showReportDialog(options);\n }\n}\n\n/**\n * This is the getter for lastEventId.\n *\n * @returns The last event id of a captured event.\n */\nexport function lastEventId(): string | undefined {\n return getCurrentHub().lastEventId();\n}\n\n/**\n * This function is here to be API compatible with the loader.\n * @hidden\n */\nexport function forceLoad(): void {\n // Noop\n}\n\n/**\n * This function is here to be API compatible with the loader.\n * @hidden\n */\nexport function onLoad(callback: () => void): void {\n callback();\n}\n\n/**\n * A promise that resolves when all current events have been sent.\n * If you provide a timeout and the queue takes longer to drain the promise returns false.\n *\n * @param timeout Maximum time in ms the client should wait.\n */\nexport function flush(timeout?: number): PromiseLike {\n const client = getCurrentHub().getClient();\n if (client) {\n return client.flush(timeout);\n }\n return SyncPromise.reject(false);\n}\n\n/**\n * A promise that resolves when all current events have been sent.\n * If you provide a timeout and the queue takes longer to drain the promise returns false.\n *\n * @param timeout Maximum time in ms the client should wait.\n */\nexport function close(timeout?: number): PromiseLike {\n const client = getCurrentHub().getClient();\n if (client) {\n return client.close(timeout);\n }\n return SyncPromise.reject(false);\n}\n\n/**\n * Wrap code within a try/catch block so the SDK is able to capture errors.\n *\n * @param fn A function to wrap.\n *\n * @returns The result of wrapped function call.\n */\nexport function wrap(fn: Function): any {\n return internalWrap(fn)(); // tslint:disable-line:no-unsafe-any\n}\n","/** The status of an event. */\nexport enum Status {\n /** The status could not be determined. */\n Unknown = 'unknown',\n /** The event was skipped due to configuration or callbacks. */\n Skipped = 'skipped',\n /** The event was sent to Sentry successfully. */\n Success = 'success',\n /** The client is currently rate limited and will try again later. */\n RateLimit = 'rate_limit',\n /** The event could not be processed. */\n Invalid = 'invalid',\n /** A server-side error ocurred during submission. */\n Failed = 'failed',\n}\n// tslint:disable:completed-docs\n// tslint:disable:no-unnecessary-qualifier no-namespace\nexport namespace Status {\n /**\n * Converts a HTTP status code into a {@link Status}.\n *\n * @param code The HTTP response status code.\n * @returns The send status or {@link Status.Unknown}.\n */\n export function fromHttpCode(code: number): Status {\n if (code >= 200 && code < 300) {\n return Status.Success;\n }\n\n if (code === 429) {\n return Status.RateLimit;\n }\n\n if (code >= 400 && code < 500) {\n return Status.Invalid;\n }\n\n if (code >= 500) {\n return Status.Failed;\n }\n\n return Status.Unknown;\n }\n}\n","import { isThenable } from './is';\n\n/** SyncPromise internal states */\nenum States {\n /** Pending */\n PENDING = 'PENDING',\n /** Resolved / OK */\n RESOLVED = 'RESOLVED',\n /** Rejected / Error */\n REJECTED = 'REJECTED',\n}\n\n/**\n * Thenable class that behaves like a Promise and follows it's interface\n * but is not async internally\n */\nclass SyncPromise implements PromiseLike {\n private _state: States = States.PENDING;\n private _handlers: Array<{\n done: boolean;\n onfulfilled?: ((value: T) => T | PromiseLike) | null;\n onrejected?: ((reason: any) => any) | null;\n }> = [];\n private _value: any;\n\n public constructor(\n executor: (resolve: (value?: T | PromiseLike | null) => void, reject: (reason?: any) => void) => void,\n ) {\n try {\n executor(this._resolve, this._reject);\n } catch (e) {\n this._reject(e);\n }\n }\n\n /** JSDoc */\n public toString(): string {\n return '[object SyncPromise]';\n }\n\n /** JSDoc */\n public static resolve(value: T | PromiseLike): PromiseLike {\n return new SyncPromise(resolve => {\n resolve(value);\n });\n }\n\n /** JSDoc */\n public static reject(reason?: any): PromiseLike {\n return new SyncPromise((_, reject) => {\n reject(reason);\n });\n }\n\n /** JSDoc */\n public static all(collection: Array>): PromiseLike {\n return new SyncPromise((resolve, reject) => {\n if (!Array.isArray(collection)) {\n reject(new TypeError(`Promise.all requires an array as input.`));\n return;\n }\n\n if (collection.length === 0) {\n resolve([]);\n return;\n }\n\n let counter = collection.length;\n const resolvedCollection: U[] = [];\n\n collection.forEach((item, index) => {\n SyncPromise.resolve(item)\n .then(value => {\n resolvedCollection[index] = value;\n counter -= 1;\n\n if (counter !== 0) {\n return;\n }\n resolve(resolvedCollection);\n })\n .then(null, reject);\n });\n });\n }\n\n /** JSDoc */\n public then(\n onfulfilled?: ((value: T) => TResult1 | PromiseLike) | null,\n onrejected?: ((reason: any) => TResult2 | PromiseLike) | null,\n ): PromiseLike {\n return new SyncPromise((resolve, reject) => {\n this._attachHandler({\n done: false,\n onfulfilled: result => {\n if (!onfulfilled) {\n // TODO: ¯\\_(ツ)_/¯\n // TODO: FIXME\n resolve(result as any);\n return;\n }\n try {\n resolve(onfulfilled(result));\n return;\n } catch (e) {\n reject(e);\n return;\n }\n },\n onrejected: reason => {\n if (!onrejected) {\n reject(reason);\n return;\n }\n try {\n resolve(onrejected(reason));\n return;\n } catch (e) {\n reject(e);\n return;\n }\n },\n });\n });\n }\n\n /** JSDoc */\n public catch(\n onrejected?: ((reason: any) => TResult | PromiseLike) | null,\n ): PromiseLike {\n return this.then(val => val, onrejected);\n }\n\n /** JSDoc */\n public finally(onfinally?: (() => void) | null): PromiseLike {\n return new SyncPromise((resolve, reject) => {\n let val: TResult | any;\n let isRejected: boolean;\n\n return this.then(\n value => {\n isRejected = false;\n val = value;\n if (onfinally) {\n onfinally();\n }\n },\n reason => {\n isRejected = true;\n val = reason;\n if (onfinally) {\n onfinally();\n }\n },\n ).then(() => {\n if (isRejected) {\n reject(val);\n return;\n }\n\n resolve((val as unknown) as any);\n });\n });\n }\n\n /** JSDoc */\n private readonly _resolve = (value?: T | PromiseLike | null) => {\n this._setResult(States.RESOLVED, value);\n };\n\n /** JSDoc */\n private readonly _reject = (reason?: any) => {\n this._setResult(States.REJECTED, reason);\n };\n\n /** JSDoc */\n private readonly _setResult = (state: States, value?: T | PromiseLike | any) => {\n if (this._state !== States.PENDING) {\n return;\n }\n\n if (isThenable(value)) {\n (value as PromiseLike).then(this._resolve, this._reject);\n return;\n }\n\n this._state = state;\n this._value = value;\n\n this._executeHandlers();\n };\n\n // TODO: FIXME\n /** JSDoc */\n private readonly _attachHandler = (handler: {\n /** JSDoc */\n done: boolean;\n /** JSDoc */\n onfulfilled?(value: T): any;\n /** JSDoc */\n onrejected?(reason: any): any;\n }) => {\n this._handlers = this._handlers.concat(handler);\n this._executeHandlers();\n };\n\n /** JSDoc */\n private readonly _executeHandlers = () => {\n if (this._state === States.PENDING) {\n return;\n }\n\n const cachedHandlers = this._handlers.slice();\n this._handlers = [];\n\n cachedHandlers.forEach(handler => {\n if (handler.done) {\n return;\n }\n\n if (this._state === States.RESOLVED) {\n if (handler.onfulfilled) {\n handler.onfulfilled((this._value as unknown) as any);\n }\n }\n\n if (this._state === States.REJECTED) {\n if (handler.onrejected) {\n handler.onrejected(this._value);\n }\n }\n\n handler.done = true;\n });\n };\n}\n\nexport { SyncPromise };\n","import { Integration, WrappedFunction } from '@sentry/types';\n\nlet originalFunctionToString: () => void;\n\n/** Patch toString calls to return proper name for wrapped functions */\nexport class FunctionToString implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = FunctionToString.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'FunctionToString';\n\n /**\n * @inheritDoc\n */\n public setupOnce(): void {\n originalFunctionToString = Function.prototype.toString;\n\n Function.prototype.toString = function(this: WrappedFunction, ...args: any[]): string {\n const context = this.__sentry_original__ || this;\n // tslint:disable-next-line:no-unsafe-any\n return originalFunctionToString.apply(context, args);\n };\n }\n}\n","export const setPrototypeOf =\n Object.setPrototypeOf || ({ __proto__: [] } instanceof Array ? setProtoOf : mixinProperties); // tslint:disable-line:no-unbound-method\n\n/**\n * setPrototypeOf polyfill using __proto__\n */\nfunction setProtoOf(obj: TTarget, proto: TProto): TTarget & TProto {\n // @ts-ignore\n obj.__proto__ = proto;\n return obj as TTarget & TProto;\n}\n\n/**\n * setPrototypeOf polyfill using mixin\n */\nfunction mixinProperties(obj: TTarget, proto: TProto): TTarget & TProto {\n for (const prop in proto) {\n if (!obj.hasOwnProperty(prop)) {\n // @ts-ignore\n obj[prop] = proto[prop];\n }\n }\n\n return obj as TTarget & TProto;\n}\n","import { setPrototypeOf } from './polyfill';\n\n/** An error emitted by Sentry SDKs and related utilities. */\nexport class SentryError extends Error {\n /** Display name of this error instance. */\n public name: string;\n\n public constructor(public message: string) {\n super(message);\n\n // tslint:disable:no-unsafe-any\n this.name = new.target.prototype.constructor.name;\n setPrototypeOf(this, new.target.prototype);\n }\n}\n","import { DsnComponents, DsnLike, DsnProtocol } from '@sentry/types';\n\nimport { SentryError } from './error';\n\n/** Regular expression used to parse a Dsn. */\nconst DSN_REGEX = /^(?:(\\w+):)\\/\\/(?:(\\w+)(?::(\\w+))?@)([\\w\\.-]+)(?::(\\d+))?\\/(.+)/;\n\n/** Error message */\nconst ERROR_MESSAGE = 'Invalid Dsn';\n\n/** The Sentry Dsn, identifying a Sentry instance and project. */\nexport class Dsn implements DsnComponents {\n /** Protocol used to connect to Sentry. */\n public protocol!: DsnProtocol;\n /** Public authorization key. */\n public user!: string;\n /** Private authorization key (deprecated, optional). */\n public pass!: string;\n /** Hostname of the Sentry instance. */\n public host!: string;\n /** Port of the Sentry instance. */\n public port!: string;\n /** Path */\n public path!: string;\n /** Project ID */\n public projectId!: string;\n\n /** Creates a new Dsn component */\n public constructor(from: DsnLike) {\n if (typeof from === 'string') {\n this._fromString(from);\n } else {\n this._fromComponents(from);\n }\n\n this._validate();\n }\n\n /**\n * Renders the string representation of this Dsn.\n *\n * By default, this will render the public representation without the password\n * component. To get the deprecated private representation, set `withPassword`\n * to true.\n *\n * @param withPassword When set to true, the password will be included.\n */\n public toString(withPassword: boolean = false): string {\n // tslint:disable-next-line:no-this-assignment\n const { host, path, pass, port, projectId, protocol, user } = this;\n return (\n `${protocol}://${user}${withPassword && pass ? `:${pass}` : ''}` +\n `@${host}${port ? `:${port}` : ''}/${path ? `${path}/` : path}${projectId}`\n );\n }\n\n /** Parses a string into this Dsn. */\n private _fromString(str: string): void {\n const match = DSN_REGEX.exec(str);\n\n if (!match) {\n throw new SentryError(ERROR_MESSAGE);\n }\n\n const [protocol, user, pass = '', host, port = '', lastPath] = match.slice(1);\n let path = '';\n let projectId = lastPath;\n\n const split = projectId.split('/');\n if (split.length > 1) {\n path = split.slice(0, -1).join('/');\n projectId = split.pop() as string;\n }\n\n this._fromComponents({ host, pass, path, projectId, port, protocol: protocol as DsnProtocol, user });\n }\n\n /** Maps Dsn components into this instance. */\n private _fromComponents(components: DsnComponents): void {\n this.protocol = components.protocol;\n this.user = components.user;\n this.pass = components.pass || '';\n this.host = components.host;\n this.port = components.port || '';\n this.path = components.path || '';\n this.projectId = components.projectId;\n }\n\n /** Validates this Dsn and throws on error. */\n private _validate(): void {\n ['protocol', 'user', 'host', 'projectId'].forEach(component => {\n if (!this[component as keyof DsnComponents]) {\n throw new SentryError(ERROR_MESSAGE);\n }\n });\n\n if (this.protocol !== 'http' && this.protocol !== 'https') {\n throw new SentryError(ERROR_MESSAGE);\n }\n\n if (this.port && isNaN(parseInt(this.port, 10))) {\n throw new SentryError(ERROR_MESSAGE);\n }\n }\n}\n","import { DsnLike } from '@sentry/types';\nimport { Dsn, urlEncode } from '@sentry/utils';\n\nconst SENTRY_API_VERSION = '7';\n\n/** Helper class to provide urls to different Sentry endpoints. */\nexport class API {\n /** The internally used Dsn object. */\n private readonly _dsnObject: Dsn;\n /** Create a new instance of API */\n public constructor(public dsn: DsnLike) {\n this._dsnObject = new Dsn(dsn);\n }\n\n /** Returns the Dsn object. */\n public getDsn(): Dsn {\n return this._dsnObject;\n }\n\n /** Returns a string with auth headers in the url to the store endpoint. */\n public getStoreEndpoint(): string {\n return `${this._getBaseUrl()}${this.getStoreEndpointPath()}`;\n }\n\n /** Returns the store endpoint with auth added in url encoded. */\n public getStoreEndpointWithUrlEncodedAuth(): string {\n const dsn = this._dsnObject;\n const auth = {\n sentry_key: dsn.user, // sentry_key is currently used in tracing integration to identify internal sentry requests\n sentry_version: SENTRY_API_VERSION,\n };\n // Auth is intentionally sent as part of query string (NOT as custom HTTP header)\n // to avoid preflight CORS requests\n return `${this.getStoreEndpoint()}?${urlEncode(auth)}`;\n }\n\n /** Returns the base path of the url including the port. */\n private _getBaseUrl(): string {\n const dsn = this._dsnObject;\n const protocol = dsn.protocol ? `${dsn.protocol}:` : '';\n const port = dsn.port ? `:${dsn.port}` : '';\n return `${protocol}//${dsn.host}${port}`;\n }\n\n /** Returns only the path component for the store endpoint. */\n public getStoreEndpointPath(): string {\n const dsn = this._dsnObject;\n return `${dsn.path ? `/${dsn.path}` : ''}/api/${dsn.projectId}/store/`;\n }\n\n /** Returns an object that can be used in request headers. */\n public getRequestHeaders(clientName: string, clientVersion: string): { [key: string]: string } {\n const dsn = this._dsnObject;\n const header = [`Sentry sentry_version=${SENTRY_API_VERSION}`];\n header.push(`sentry_client=${clientName}/${clientVersion}`);\n header.push(`sentry_key=${dsn.user}`);\n if (dsn.pass) {\n header.push(`sentry_secret=${dsn.pass}`);\n }\n return {\n 'Content-Type': 'application/json',\n 'X-Sentry-Auth': header.join(', '),\n };\n }\n\n /** Returns the url to the report dialog endpoint. */\n public getReportDialogEndpoint(\n dialogOptions: {\n [key: string]: any;\n user?: { name?: string; email?: string };\n } = {},\n ): string {\n const dsn = this._dsnObject;\n const endpoint = `${this._getBaseUrl()}${dsn.path ? `/${dsn.path}` : ''}/api/embed/error-page/`;\n\n const encodedOptions = [];\n encodedOptions.push(`dsn=${dsn.toString()}`);\n for (const key in dialogOptions) {\n if (key === 'user') {\n if (!dialogOptions.user) {\n continue;\n }\n if (dialogOptions.user.name) {\n encodedOptions.push(`name=${encodeURIComponent(dialogOptions.user.name)}`);\n }\n if (dialogOptions.user.email) {\n encodedOptions.push(`email=${encodeURIComponent(dialogOptions.user.email)}`);\n }\n } else {\n encodedOptions.push(`${encodeURIComponent(key)}=${encodeURIComponent(dialogOptions[key] as string)}`);\n }\n }\n if (encodedOptions.length) {\n return `${endpoint}?${encodedOptions.join('&')}`;\n }\n\n return endpoint;\n }\n}\n","import { Scope } from '@sentry/hub';\nimport { Client, Event, EventHint, Integration, IntegrationClass, Options, SdkInfo, Severity } from '@sentry/types';\nimport { Dsn, isPrimitive, isThenable, logger, normalize, SyncPromise, truncate, uuid4 } from '@sentry/utils';\n\nimport { Backend, BackendClass } from './basebackend';\nimport { IntegrationIndex, setupIntegrations } from './integration';\n\n/**\n * Base implementation for all JavaScript SDK clients.\n *\n * Call the constructor with the corresponding backend constructor and options\n * specific to the client subclass. To access these options later, use\n * {@link Client.getOptions}. Also, the Backend instance is available via\n * {@link Client.getBackend}.\n *\n * If a Dsn is specified in the options, it will be parsed and stored. Use\n * {@link Client.getDsn} to retrieve the Dsn at any moment. In case the Dsn is\n * invalid, the constructor will throw a {@link SentryException}. Note that\n * without a valid Dsn, the SDK will not send any events to Sentry.\n *\n * Before sending an event via the backend, it is passed through\n * {@link BaseClient.prepareEvent} to add SDK information and scope data\n * (breadcrumbs and context). To add more custom information, override this\n * method and extend the resulting prepared event.\n *\n * To issue automatically created events (e.g. via instrumentation), use\n * {@link Client.captureEvent}. It will prepare the event and pass it through\n * the callback lifecycle. To issue auto-breadcrumbs, use\n * {@link Client.addBreadcrumb}.\n *\n * @example\n * class NodeClient extends BaseClient {\n * public constructor(options: NodeOptions) {\n * super(NodeBackend, options);\n * }\n *\n * // ...\n * }\n */\nexport abstract class BaseClient implements Client {\n /**\n * The backend used to physically interact in the enviornment. Usually, this\n * will correspond to the client. When composing SDKs, however, the Backend\n * from the root SDK will be used.\n */\n protected readonly _backend: B;\n\n /** Options passed to the SDK. */\n protected readonly _options: O;\n\n /** The client Dsn, if specified in options. Without this Dsn, the SDK will be disabled. */\n protected readonly _dsn?: Dsn;\n\n /** Array of used integrations. */\n protected _integrations: IntegrationIndex = {};\n\n /** Is the client still processing a call? */\n protected _processing: boolean = false;\n\n /**\n * Initializes this client instance.\n *\n * @param backendClass A constructor function to create the backend.\n * @param options Options for the client.\n */\n protected constructor(backendClass: BackendClass, options: O) {\n this._backend = new backendClass(options);\n this._options = options;\n\n if (options.dsn) {\n this._dsn = new Dsn(options.dsn);\n }\n }\n\n /**\n * @inheritDoc\n */\n public captureException(exception: any, hint?: EventHint, scope?: Scope): string | undefined {\n let eventId: string | undefined = hint && hint.event_id;\n this._processing = true;\n\n this._getBackend()\n .eventFromException(exception, hint)\n .then(event => this._processEvent(event, hint, scope))\n .then(finalEvent => {\n // We need to check for finalEvent in case beforeSend returned null\n eventId = finalEvent && finalEvent.event_id;\n this._processing = false;\n })\n .then(null, reason => {\n logger.error(reason);\n this._processing = false;\n });\n\n return eventId;\n }\n\n /**\n * @inheritDoc\n */\n public captureMessage(message: string, level?: Severity, hint?: EventHint, scope?: Scope): string | undefined {\n let eventId: string | undefined = hint && hint.event_id;\n\n this._processing = true;\n\n const promisedEvent = isPrimitive(message)\n ? this._getBackend().eventFromMessage(`${message}`, level, hint)\n : this._getBackend().eventFromException(message, hint);\n\n promisedEvent\n .then(event => this._processEvent(event, hint, scope))\n .then(finalEvent => {\n // We need to check for finalEvent in case beforeSend returned null\n eventId = finalEvent && finalEvent.event_id;\n this._processing = false;\n })\n .then(null, reason => {\n logger.error(reason);\n this._processing = false;\n });\n\n return eventId;\n }\n\n /**\n * @inheritDoc\n */\n public captureEvent(event: Event, hint?: EventHint, scope?: Scope): string | undefined {\n let eventId: string | undefined = hint && hint.event_id;\n this._processing = true;\n\n this._processEvent(event, hint, scope)\n .then(finalEvent => {\n // We need to check for finalEvent in case beforeSend returned null\n eventId = finalEvent && finalEvent.event_id;\n this._processing = false;\n })\n .then(null, reason => {\n logger.error(reason);\n this._processing = false;\n });\n\n return eventId;\n }\n\n /**\n * @inheritDoc\n */\n public getDsn(): Dsn | undefined {\n return this._dsn;\n }\n\n /**\n * @inheritDoc\n */\n public getOptions(): O {\n return this._options;\n }\n\n /**\n * @inheritDoc\n */\n public flush(timeout?: number): PromiseLike {\n return this._isClientProcessing(timeout).then(status => {\n clearInterval(status.interval);\n return this._getBackend()\n .getTransport()\n .close(timeout)\n .then(transportFlushed => status.ready && transportFlushed);\n });\n }\n\n /**\n * @inheritDoc\n */\n public close(timeout?: number): PromiseLike {\n return this.flush(timeout).then(result => {\n this.getOptions().enabled = false;\n return result;\n });\n }\n\n /**\n * Sets up the integrations\n */\n public setupIntegrations(): void {\n if (this._isEnabled()) {\n this._integrations = setupIntegrations(this._options);\n }\n }\n\n /**\n * @inheritDoc\n */\n public getIntegration(integration: IntegrationClass): T | null {\n try {\n return (this._integrations[integration.id] as T) || null;\n } catch (_oO) {\n logger.warn(`Cannot retrieve integration ${integration.id} from the current Client`);\n return null;\n }\n }\n\n /** Waits for the client to be done with processing. */\n protected _isClientProcessing(timeout?: number): PromiseLike<{ ready: boolean; interval: number }> {\n return new SyncPromise<{ ready: boolean; interval: number }>(resolve => {\n let ticked: number = 0;\n const tick: number = 1;\n\n let interval = 0;\n clearInterval(interval);\n\n interval = (setInterval(() => {\n if (!this._processing) {\n resolve({\n interval,\n ready: true,\n });\n } else {\n ticked += tick;\n if (timeout && ticked >= timeout) {\n resolve({\n interval,\n ready: false,\n });\n }\n }\n }, tick) as unknown) as number;\n });\n }\n\n /** Returns the current backend. */\n protected _getBackend(): B {\n return this._backend;\n }\n\n /** Determines whether this SDK is enabled and a valid Dsn is present. */\n protected _isEnabled(): boolean {\n return this.getOptions().enabled !== false && this._dsn !== undefined;\n }\n\n /**\n * Adds common information to events.\n *\n * The information includes release and environment from `options`,\n * breadcrumbs and context (extra, tags and user) from the scope.\n *\n * Information that is already present in the event is never overwritten. For\n * nested objects, such as the context, keys are merged.\n *\n * @param event The original event.\n * @param hint May contain additional informartion about the original exception.\n * @param scope A scope containing event metadata.\n * @returns A new event with more information.\n */\n protected _prepareEvent(event: Event, scope?: Scope, hint?: EventHint): PromiseLike {\n const { environment, release, dist, maxValueLength = 250, normalizeDepth = 3 } = this.getOptions();\n\n const prepared: Event = { ...event };\n if (prepared.environment === undefined && environment !== undefined) {\n prepared.environment = environment;\n }\n if (prepared.release === undefined && release !== undefined) {\n prepared.release = release;\n }\n\n if (prepared.dist === undefined && dist !== undefined) {\n prepared.dist = dist;\n }\n\n if (prepared.message) {\n prepared.message = truncate(prepared.message, maxValueLength);\n }\n\n const exception = prepared.exception && prepared.exception.values && prepared.exception.values[0];\n if (exception && exception.value) {\n exception.value = truncate(exception.value, maxValueLength);\n }\n\n const request = prepared.request;\n if (request && request.url) {\n request.url = truncate(request.url, maxValueLength);\n }\n\n if (prepared.event_id === undefined) {\n prepared.event_id = hint && hint.event_id ? hint.event_id : uuid4();\n }\n\n this._addIntegrations(prepared.sdk);\n\n // We prepare the result here with a resolved Event.\n let result = SyncPromise.resolve(prepared);\n\n // This should be the last thing called, since we want that\n // {@link Hub.addEventProcessor} gets the finished prepared event.\n if (scope) {\n // In case we have a hub we reassign it.\n result = scope.applyToEvent(prepared, hint);\n }\n\n return result.then(evt => {\n // tslint:disable-next-line:strict-type-predicates\n if (typeof normalizeDepth === 'number' && normalizeDepth > 0) {\n return this._normalizeEvent(evt, normalizeDepth);\n }\n return evt;\n });\n }\n\n /**\n * Applies `normalize` function on necessary `Event` attributes to make them safe for serialization.\n * Normalized keys:\n * - `breadcrumbs.data`\n * - `user`\n * - `contexts`\n * - `extra`\n * @param event Event\n * @returns Normalized event\n */\n protected _normalizeEvent(event: Event | null, depth: number): Event | null {\n if (!event) {\n return null;\n }\n\n // tslint:disable:no-unsafe-any\n return {\n ...event,\n ...(event.breadcrumbs && {\n breadcrumbs: event.breadcrumbs.map(b => ({\n ...b,\n ...(b.data && {\n data: normalize(b.data, depth),\n }),\n })),\n }),\n ...(event.user && {\n user: normalize(event.user, depth),\n }),\n ...(event.contexts && {\n contexts: normalize(event.contexts, depth),\n }),\n ...(event.extra && {\n extra: normalize(event.extra, depth),\n }),\n };\n }\n\n /**\n * This function adds all used integrations to the SDK info in the event.\n * @param sdkInfo The sdkInfo of the event that will be filled with all integrations.\n */\n protected _addIntegrations(sdkInfo?: SdkInfo): void {\n const integrationsArray = Object.keys(this._integrations);\n if (sdkInfo && integrationsArray.length > 0) {\n sdkInfo.integrations = integrationsArray;\n }\n }\n\n /**\n * Processes an event (either error or message) and sends it to Sentry.\n *\n * This also adds breadcrumbs and context information to the event. However,\n * platform specific meta data (such as the User's IP address) must be added\n * by the SDK implementor.\n *\n *\n * @param event The event to send to Sentry.\n * @param hint May contain additional informartion about the original exception.\n * @param scope A scope containing event metadata.\n * @returns A SyncPromise that resolves with the event or rejects in case event was/will not be send.\n */\n protected _processEvent(event: Event, hint?: EventHint, scope?: Scope): PromiseLike {\n const { beforeSend, sampleRate } = this.getOptions();\n\n if (!this._isEnabled()) {\n return SyncPromise.reject('SDK not enabled, will not send event.');\n }\n\n // 1.0 === 100% events are sent\n // 0.0 === 0% events are sent\n if (typeof sampleRate === 'number' && Math.random() > sampleRate) {\n return SyncPromise.reject('This event has been sampled, will not send event.');\n }\n\n return new SyncPromise((resolve, reject) => {\n this._prepareEvent(event, scope, hint)\n .then(prepared => {\n if (prepared === null) {\n reject('An event processor returned null, will not send event.');\n return;\n }\n\n let finalEvent: Event | null = prepared;\n\n const isInternalException = hint && hint.data && (hint.data as { [key: string]: any }).__sentry__ === true;\n if (isInternalException || !beforeSend) {\n this._getBackend().sendEvent(finalEvent);\n resolve(finalEvent);\n return;\n }\n\n const beforeSendResult = beforeSend(prepared, hint);\n // tslint:disable-next-line:strict-type-predicates\n if (typeof beforeSendResult === 'undefined') {\n logger.error('`beforeSend` method has to return `null` or a valid event.');\n } else if (isThenable(beforeSendResult)) {\n this._handleAsyncBeforeSend(beforeSendResult as PromiseLike, resolve, reject);\n } else {\n finalEvent = beforeSendResult as Event | null;\n\n if (finalEvent === null) {\n logger.log('`beforeSend` returned `null`, will not send event.');\n resolve(null);\n return;\n }\n\n // From here on we are really async\n this._getBackend().sendEvent(finalEvent);\n resolve(finalEvent);\n }\n })\n .then(null, reason => {\n this.captureException(reason, {\n data: {\n __sentry__: true,\n },\n originalException: reason as Error,\n });\n reject(\n `Event processing pipeline threw an error, original event will not be sent. Details have been sent as a new event.\\nReason: ${reason}`,\n );\n });\n });\n }\n\n /**\n * Resolves before send Promise and calls resolve/reject on parent SyncPromise.\n */\n private _handleAsyncBeforeSend(\n beforeSend: PromiseLike,\n resolve: (event: Event) => void,\n reject: (reason: string) => void,\n ): void {\n beforeSend\n .then(processedEvent => {\n if (processedEvent === null) {\n reject('`beforeSend` returned `null`, will not send event.');\n return;\n }\n // From here on we are really async\n this._getBackend().sendEvent(processedEvent);\n resolve(processedEvent);\n })\n .then(null, e => {\n reject(`beforeSend rejected with ${e}`);\n });\n }\n}\n","import { Event, Response, Status, Transport } from '@sentry/types';\nimport { SyncPromise } from '@sentry/utils';\n\n/** Noop transport */\nexport class NoopTransport implements Transport {\n /**\n * @inheritDoc\n */\n public sendEvent(_: Event): PromiseLike {\n return SyncPromise.resolve({\n reason: `NoopTransport: Event has been skipped because no Dsn is configured.`,\n status: Status.Skipped,\n });\n }\n\n /**\n * @inheritDoc\n */\n public close(_?: number): PromiseLike {\n return SyncPromise.resolve(true);\n }\n}\n","import { Event, EventHint, Options, Severity, Transport } from '@sentry/types';\nimport { logger, SentryError } from '@sentry/utils';\n\nimport { NoopTransport } from './transports/noop';\n\n/**\n * Internal platform-dependent Sentry SDK Backend.\n *\n * While {@link Client} contains business logic specific to an SDK, the\n * Backend offers platform specific implementations for low-level operations.\n * These are persisting and loading information, sending events, and hooking\n * into the environment.\n *\n * Backends receive a handle to the Client in their constructor. When a\n * Backend automatically generates events, it must pass them to\n * the Client for validation and processing first.\n *\n * Usually, the Client will be of corresponding type, e.g. NodeBackend\n * receives NodeClient. However, higher-level SDKs can choose to instanciate\n * multiple Backends and delegate tasks between them. In this case, an event\n * generated by one backend might very well be sent by another one.\n *\n * The client also provides access to options via {@link Client.getOptions}.\n * @hidden\n */\nexport interface Backend {\n /** Creates a {@link Event} from an exception. */\n eventFromException(exception: any, hint?: EventHint): PromiseLike;\n\n /** Creates a {@link Event} from a plain message. */\n eventFromMessage(message: string, level?: Severity, hint?: EventHint): PromiseLike;\n\n /** Submits the event to Sentry */\n sendEvent(event: Event): void;\n\n /**\n * Returns the transport that is used by the backend.\n * Please note that the transport gets lazy initialized so it will only be there once the first event has been sent.\n *\n * @returns The transport.\n */\n getTransport(): Transport;\n}\n\n/**\n * A class object that can instanciate Backend objects.\n * @hidden\n */\nexport type BackendClass = new (options: O) => B;\n\n/**\n * This is the base implemention of a Backend.\n * @hidden\n */\nexport abstract class BaseBackend implements Backend {\n /** Options passed to the SDK. */\n protected readonly _options: O;\n\n /** Cached transport used internally. */\n protected _transport: Transport;\n\n /** Creates a new backend instance. */\n public constructor(options: O) {\n this._options = options;\n if (!this._options.dsn) {\n logger.warn('No DSN provided, backend will not do anything.');\n }\n this._transport = this._setupTransport();\n }\n\n /**\n * Sets up the transport so it can be used later to send requests.\n */\n protected _setupTransport(): Transport {\n return new NoopTransport();\n }\n\n /**\n * @inheritDoc\n */\n public eventFromException(_exception: any, _hint?: EventHint): PromiseLike {\n throw new SentryError('Backend has to implement `eventFromException` method');\n }\n\n /**\n * @inheritDoc\n */\n public eventFromMessage(_message: string, _level?: Severity, _hint?: EventHint): PromiseLike {\n throw new SentryError('Backend has to implement `eventFromMessage` method');\n }\n\n /**\n * @inheritDoc\n */\n public sendEvent(event: Event): void {\n this._transport.sendEvent(event).then(null, reason => {\n logger.error(`Error while sending event: ${reason}`);\n });\n }\n\n /**\n * @inheritDoc\n */\n public getTransport(): Transport {\n return this._transport;\n }\n}\n","import { SentryError } from './error';\nimport { SyncPromise } from './syncpromise';\n\n/** A simple queue that holds promises. */\nexport class PromiseBuffer {\n public constructor(protected _limit?: number) {}\n\n /** Internal set of queued Promises */\n private readonly _buffer: Array> = [];\n\n /**\n * Says if the buffer is ready to take more requests\n */\n public isReady(): boolean {\n return this._limit === undefined || this.length() < this._limit;\n }\n\n /**\n * Add a promise to the queue.\n *\n * @param task Can be any PromiseLike\n * @returns The original promise.\n */\n public add(task: PromiseLike): PromiseLike {\n if (!this.isReady()) {\n return SyncPromise.reject(new SentryError('Not adding Promise due to buffer limit reached.'));\n }\n if (this._buffer.indexOf(task) === -1) {\n this._buffer.push(task);\n }\n task\n .then(() => this.remove(task))\n .then(null, () =>\n this.remove(task).then(null, () => {\n // We have to add this catch here otherwise we have an unhandledPromiseRejection\n // because it's a new Promise chain.\n }),\n );\n return task;\n }\n\n /**\n * Remove a promise to the queue.\n *\n * @param task Can be any PromiseLike\n * @returns Removed promise.\n */\n public remove(task: PromiseLike): PromiseLike {\n const removedTask = this._buffer.splice(this._buffer.indexOf(task), 1)[0];\n return removedTask;\n }\n\n /**\n * This function returns the number of unresolved promises in the queue.\n */\n public length(): number {\n return this._buffer.length;\n }\n\n /**\n * This will drain the whole queue, returns true if queue is empty or drained.\n * If timeout is provided and the queue takes longer to drain, the promise still resolves but with false.\n *\n * @param timeout Number in ms to wait until it resolves with false.\n */\n public drain(timeout?: number): PromiseLike {\n return new SyncPromise(resolve => {\n const capturedSetTimeout = setTimeout(() => {\n if (timeout && timeout > 0) {\n resolve(false);\n }\n }, timeout);\n SyncPromise.all(this._buffer)\n .then(() => {\n clearTimeout(capturedSetTimeout);\n resolve(true);\n })\n .then(null, () => {\n resolve(true);\n });\n });\n }\n}\n","import { API } from '@sentry/core';\nimport { Event, Response, Transport, TransportOptions } from '@sentry/types';\nimport { PromiseBuffer, SentryError } from '@sentry/utils';\n\n/** Base Transport class implementation */\nexport abstract class BaseTransport implements Transport {\n /**\n * @inheritDoc\n */\n public url: string;\n\n /** A simple buffer holding all requests. */\n protected readonly _buffer: PromiseBuffer = new PromiseBuffer(30);\n\n public constructor(public options: TransportOptions) {\n this.url = new API(this.options.dsn).getStoreEndpointWithUrlEncodedAuth();\n }\n\n /**\n * @inheritDoc\n */\n public sendEvent(_: Event): PromiseLike {\n throw new SentryError('Transport Class has to implement `sendEvent` method');\n }\n\n /**\n * @inheritDoc\n */\n public close(timeout?: number): PromiseLike {\n return this._buffer.drain(timeout);\n }\n}\n","import { Event, Response, Status } from '@sentry/types';\nimport { getGlobalObject, logger, parseRetryAfterHeader, supportsReferrerPolicy, SyncPromise } from '@sentry/utils';\n\nimport { BaseTransport } from './base';\n\nconst global = getGlobalObject();\n\n/** `fetch` based transport */\nexport class FetchTransport extends BaseTransport {\n /** Locks transport after receiving 429 response */\n private _disabledUntil: Date = new Date(Date.now());\n\n /**\n * @inheritDoc\n */\n public sendEvent(event: Event): PromiseLike {\n if (new Date(Date.now()) < this._disabledUntil) {\n return Promise.reject({\n event,\n reason: `Transport locked till ${this._disabledUntil} due to too many requests.`,\n status: 429,\n });\n }\n\n const defaultOptions: RequestInit = {\n body: JSON.stringify(event),\n method: 'POST',\n // Despite all stars in the sky saying that Edge supports old draft syntax, aka 'never', 'always', 'origin' and 'default\n // https://caniuse.com/#feat=referrer-policy\n // It doesn't. And it throw exception instead of ignoring this parameter...\n // REF: https://github.com/getsentry/raven-js/issues/1233\n referrerPolicy: (supportsReferrerPolicy() ? 'origin' : '') as ReferrerPolicy,\n };\n\n if (this.options.headers !== undefined) {\n defaultOptions.headers = this.options.headers;\n }\n\n return this._buffer.add(\n new SyncPromise((resolve, reject) => {\n global\n .fetch(this.url, defaultOptions)\n .then(response => {\n const status = Status.fromHttpCode(response.status);\n\n if (status === Status.Success) {\n resolve({ status });\n return;\n }\n\n if (status === Status.RateLimit) {\n const now = Date.now();\n this._disabledUntil = new Date(now + parseRetryAfterHeader(now, response.headers.get('Retry-After')));\n logger.warn(`Too many requests, backing off till: ${this._disabledUntil}`);\n }\n\n reject(response);\n })\n .catch(reject);\n }),\n );\n }\n}\n","import { Event, Response, Status } from '@sentry/types';\nimport { logger, parseRetryAfterHeader, SyncPromise } from '@sentry/utils';\n\nimport { BaseTransport } from './base';\n\n/** `XHR` based transport */\nexport class XHRTransport extends BaseTransport {\n /** Locks transport after receiving 429 response */\n private _disabledUntil: Date = new Date(Date.now());\n\n /**\n * @inheritDoc\n */\n public sendEvent(event: Event): PromiseLike {\n if (new Date(Date.now()) < this._disabledUntil) {\n return Promise.reject({\n event,\n reason: `Transport locked till ${this._disabledUntil} due to too many requests.`,\n status: 429,\n });\n }\n\n return this._buffer.add(\n new SyncPromise((resolve, reject) => {\n const request = new XMLHttpRequest();\n\n request.onreadystatechange = () => {\n if (request.readyState !== 4) {\n return;\n }\n\n const status = Status.fromHttpCode(request.status);\n\n if (status === Status.Success) {\n resolve({ status });\n return;\n }\n\n if (status === Status.RateLimit) {\n const now = Date.now();\n this._disabledUntil = new Date(now + parseRetryAfterHeader(now, request.getResponseHeader('Retry-After')));\n logger.warn(`Too many requests, backing off till: ${this._disabledUntil}`);\n }\n\n reject(request);\n };\n\n request.open('POST', this.url);\n for (const header in this.options.headers) {\n if (this.options.headers.hasOwnProperty(header)) {\n request.setRequestHeader(header, this.options.headers[header]);\n }\n }\n request.send(JSON.stringify(event));\n }),\n );\n }\n}\n","import { BaseBackend } from '@sentry/core';\nimport { Event, EventHint, Options, Severity, Transport } from '@sentry/types';\nimport { addExceptionMechanism, supportsFetch, SyncPromise } from '@sentry/utils';\n\nimport { eventFromString, eventFromUnknownInput } from './eventbuilder';\nimport { FetchTransport, XHRTransport } from './transports';\n\n/**\n * Configuration options for the Sentry Browser SDK.\n * @see BrowserClient for more information.\n */\nexport interface BrowserOptions extends Options {\n /**\n * A pattern for error URLs which should not be sent to Sentry.\n * To whitelist certain errors instead, use {@link Options.whitelistUrls}.\n * By default, all errors will be sent.\n */\n blacklistUrls?: Array;\n\n /**\n * A pattern for error URLs which should exclusively be sent to Sentry.\n * This is the opposite of {@link Options.blacklistUrls}.\n * By default, all errors will be sent.\n */\n whitelistUrls?: Array;\n}\n\n/**\n * The Sentry Browser SDK Backend.\n * @hidden\n */\nexport class BrowserBackend extends BaseBackend {\n /**\n * @inheritDoc\n */\n protected _setupTransport(): Transport {\n if (!this._options.dsn) {\n // We return the noop transport here in case there is no Dsn.\n return super._setupTransport();\n }\n\n const transportOptions = {\n ...this._options.transportOptions,\n dsn: this._options.dsn,\n };\n\n if (this._options.transport) {\n return new this._options.transport(transportOptions);\n }\n if (supportsFetch()) {\n return new FetchTransport(transportOptions);\n }\n return new XHRTransport(transportOptions);\n }\n\n /**\n * @inheritDoc\n */\n public eventFromException(exception: any, hint?: EventHint): PromiseLike {\n const syntheticException = (hint && hint.syntheticException) || undefined;\n const event = eventFromUnknownInput(exception, syntheticException, {\n attachStacktrace: this._options.attachStacktrace,\n });\n addExceptionMechanism(event, {\n handled: true,\n type: 'generic',\n });\n event.level = Severity.Error;\n if (hint && hint.event_id) {\n event.event_id = hint.event_id;\n }\n return SyncPromise.resolve(event);\n }\n /**\n * @inheritDoc\n */\n public eventFromMessage(message: string, level: Severity = Severity.Info, hint?: EventHint): PromiseLike {\n const syntheticException = (hint && hint.syntheticException) || undefined;\n const event = eventFromString(message, syntheticException, {\n attachStacktrace: this._options.attachStacktrace,\n });\n event.level = level;\n if (hint && hint.event_id) {\n event.event_id = hint.event_id;\n }\n return SyncPromise.resolve(event);\n }\n}\n","export const SDK_NAME = 'sentry.javascript.browser';\nexport const SDK_VERSION = '5.15.5';\n","import { API, BaseClient, Scope } from '@sentry/core';\nimport { DsnLike, Event, EventHint } from '@sentry/types';\nimport { getGlobalObject, logger } from '@sentry/utils';\n\nimport { BrowserBackend, BrowserOptions } from './backend';\nimport { SDK_NAME, SDK_VERSION } from './version';\n\n/**\n * All properties the report dialog supports\n */\nexport interface ReportDialogOptions {\n [key: string]: any;\n eventId?: string;\n dsn?: DsnLike;\n user?: {\n email?: string;\n name?: string;\n };\n lang?: string;\n title?: string;\n subtitle?: string;\n subtitle2?: string;\n labelName?: string;\n labelEmail?: string;\n labelComments?: string;\n labelClose?: string;\n labelSubmit?: string;\n errorGeneric?: string;\n errorFormEntry?: string;\n successMessage?: string;\n /** Callback after reportDialog showed up */\n onLoad?(): void;\n}\n\n/**\n * The Sentry Browser SDK Client.\n *\n * @see BrowserOptions for documentation on configuration options.\n * @see SentryClient for usage documentation.\n */\nexport class BrowserClient extends BaseClient {\n /**\n * Creates a new Browser SDK instance.\n *\n * @param options Configuration options for this SDK.\n */\n public constructor(options: BrowserOptions = {}) {\n super(BrowserBackend, options);\n }\n\n /**\n * @inheritDoc\n */\n protected _prepareEvent(event: Event, scope?: Scope, hint?: EventHint): PromiseLike {\n event.platform = event.platform || 'javascript';\n event.sdk = {\n ...event.sdk,\n name: SDK_NAME,\n packages: [\n ...((event.sdk && event.sdk.packages) || []),\n {\n name: 'npm:@sentry/browser',\n version: SDK_VERSION,\n },\n ],\n version: SDK_VERSION,\n };\n\n return super._prepareEvent(event, scope, hint);\n }\n\n /**\n * Show a report dialog to the user to send feedback to a specific event.\n *\n * @param options Set individual options for the dialog\n */\n public showReportDialog(options: ReportDialogOptions = {}): void {\n // doesn't work without a document (React Native)\n const document = getGlobalObject().document;\n if (!document) {\n return;\n }\n\n if (!this._isEnabled()) {\n logger.error('Trying to call showReportDialog with Sentry Client is disabled');\n return;\n }\n\n const dsn = options.dsn || this.getDsn();\n\n if (!options.eventId) {\n logger.error('Missing `eventId` option in showReportDialog call');\n return;\n }\n\n if (!dsn) {\n logger.error('Missing `Dsn` option in showReportDialog call');\n return;\n }\n\n const script = document.createElement('script');\n script.async = true;\n script.src = new API(dsn).getReportDialogEndpoint(options);\n\n if (options.onLoad) {\n script.onload = options.onLoad;\n }\n\n (document.head || document.body).appendChild(script);\n }\n}\n","import { addGlobalEventProcessor, getCurrentHub } from '@sentry/hub';\nimport { Event, Integration } from '@sentry/types';\nimport { getEventDescription, isMatchingPattern, logger } from '@sentry/utils';\n\n// \"Script error.\" is hard coded into browsers for errors that it can't read.\n// this is the result of a script being pulled in from an external domain and CORS.\nconst DEFAULT_IGNORE_ERRORS = [/^Script error\\.?$/, /^Javascript error: Script error\\.? on line 0$/];\n\n/** JSDoc */\ninterface InboundFiltersOptions {\n blacklistUrls?: Array;\n ignoreErrors?: Array;\n ignoreInternal?: boolean;\n whitelistUrls?: Array;\n}\n\n/** Inbound filters configurable by the user */\nexport class InboundFilters implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = InboundFilters.id;\n /**\n * @inheritDoc\n */\n public static id: string = 'InboundFilters';\n\n public constructor(private readonly _options: InboundFiltersOptions = {}) {}\n\n /**\n * @inheritDoc\n */\n public setupOnce(): void {\n addGlobalEventProcessor((event: Event) => {\n const hub = getCurrentHub();\n if (!hub) {\n return event;\n }\n const self = hub.getIntegration(InboundFilters);\n if (self) {\n const client = hub.getClient();\n const clientOptions = client ? client.getOptions() : {};\n const options = self._mergeOptions(clientOptions);\n if (self._shouldDropEvent(event, options)) {\n return null;\n }\n }\n return event;\n });\n }\n\n /** JSDoc */\n private _shouldDropEvent(event: Event, options: InboundFiltersOptions): boolean {\n if (this._isSentryError(event, options)) {\n logger.warn(`Event dropped due to being internal Sentry Error.\\nEvent: ${getEventDescription(event)}`);\n return true;\n }\n if (this._isIgnoredError(event, options)) {\n logger.warn(\n `Event dropped due to being matched by \\`ignoreErrors\\` option.\\nEvent: ${getEventDescription(event)}`,\n );\n return true;\n }\n if (this._isBlacklistedUrl(event, options)) {\n logger.warn(\n `Event dropped due to being matched by \\`blacklistUrls\\` option.\\nEvent: ${getEventDescription(\n event,\n )}.\\nUrl: ${this._getEventFilterUrl(event)}`,\n );\n return true;\n }\n if (!this._isWhitelistedUrl(event, options)) {\n logger.warn(\n `Event dropped due to not being matched by \\`whitelistUrls\\` option.\\nEvent: ${getEventDescription(\n event,\n )}.\\nUrl: ${this._getEventFilterUrl(event)}`,\n );\n return true;\n }\n return false;\n }\n\n /** JSDoc */\n private _isSentryError(event: Event, options: InboundFiltersOptions = {}): boolean {\n if (!options.ignoreInternal) {\n return false;\n }\n\n try {\n return (\n (event &&\n event.exception &&\n event.exception.values &&\n event.exception.values[0] &&\n event.exception.values[0].type === 'SentryError') ||\n false\n );\n } catch (_oO) {\n return false;\n }\n }\n\n /** JSDoc */\n private _isIgnoredError(event: Event, options: InboundFiltersOptions = {}): boolean {\n if (!options.ignoreErrors || !options.ignoreErrors.length) {\n return false;\n }\n\n return this._getPossibleEventMessages(event).some(message =>\n // Not sure why TypeScript complains here...\n (options.ignoreErrors as Array).some(pattern => isMatchingPattern(message, pattern)),\n );\n }\n\n /** JSDoc */\n private _isBlacklistedUrl(event: Event, options: InboundFiltersOptions = {}): boolean {\n // TODO: Use Glob instead?\n if (!options.blacklistUrls || !options.blacklistUrls.length) {\n return false;\n }\n const url = this._getEventFilterUrl(event);\n return !url ? false : options.blacklistUrls.some(pattern => isMatchingPattern(url, pattern));\n }\n\n /** JSDoc */\n private _isWhitelistedUrl(event: Event, options: InboundFiltersOptions = {}): boolean {\n // TODO: Use Glob instead?\n if (!options.whitelistUrls || !options.whitelistUrls.length) {\n return true;\n }\n const url = this._getEventFilterUrl(event);\n return !url ? true : options.whitelistUrls.some(pattern => isMatchingPattern(url, pattern));\n }\n\n /** JSDoc */\n private _mergeOptions(clientOptions: InboundFiltersOptions = {}): InboundFiltersOptions {\n return {\n blacklistUrls: [...(this._options.blacklistUrls || []), ...(clientOptions.blacklistUrls || [])],\n ignoreErrors: [\n ...(this._options.ignoreErrors || []),\n ...(clientOptions.ignoreErrors || []),\n ...DEFAULT_IGNORE_ERRORS,\n ],\n ignoreInternal: typeof this._options.ignoreInternal !== 'undefined' ? this._options.ignoreInternal : true,\n whitelistUrls: [...(this._options.whitelistUrls || []), ...(clientOptions.whitelistUrls || [])],\n };\n }\n\n /** JSDoc */\n private _getPossibleEventMessages(event: Event): string[] {\n if (event.message) {\n return [event.message];\n }\n if (event.exception) {\n try {\n const { type = '', value = '' } = (event.exception.values && event.exception.values[0]) || {};\n return [`${value}`, `${type}: ${value}`];\n } catch (oO) {\n logger.error(`Cannot extract message for event ${getEventDescription(event)}`);\n return [];\n }\n }\n return [];\n }\n\n /** JSDoc */\n private _getEventFilterUrl(event: Event): string | null {\n try {\n if (event.stacktrace) {\n const frames = event.stacktrace.frames;\n return (frames && frames[frames.length - 1].filename) || null;\n }\n if (event.exception) {\n const frames =\n event.exception.values && event.exception.values[0].stacktrace && event.exception.values[0].stacktrace.frames;\n return (frames && frames[frames.length - 1].filename) || null;\n }\n return null;\n } catch (oO) {\n logger.error(`Cannot extract url for event ${getEventDescription(event)}`);\n return null;\n }\n }\n}\n","import { Integration, WrappedFunction } from '@sentry/types';\nimport { fill, getFunctionName, getGlobalObject } from '@sentry/utils';\n\nimport { wrap } from '../helpers';\n\ntype XMLHttpRequestProp = 'onload' | 'onerror' | 'onprogress' | 'onreadystatechange';\n\n/** Wrap timer functions and event targets to catch errors and provide better meta data */\nexport class TryCatch implements Integration {\n /** JSDoc */\n private _ignoreOnError: number = 0;\n\n /**\n * @inheritDoc\n */\n public name: string = TryCatch.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'TryCatch';\n\n /** JSDoc */\n private _wrapTimeFunction(original: () => void): () => number {\n return function(this: any, ...args: any[]): number {\n const originalCallback = args[0];\n args[0] = wrap(originalCallback, {\n mechanism: {\n data: { function: getFunctionName(original) },\n handled: true,\n type: 'instrument',\n },\n });\n return original.apply(this, args);\n };\n }\n\n /** JSDoc */\n private _wrapRAF(original: any): (callback: () => void) => any {\n return function(this: any, callback: () => void): () => void {\n return original(\n wrap(callback, {\n mechanism: {\n data: {\n function: 'requestAnimationFrame',\n handler: getFunctionName(original),\n },\n handled: true,\n type: 'instrument',\n },\n }),\n );\n };\n }\n\n /** JSDoc */\n private _wrapEventTarget(target: string): void {\n const global = getGlobalObject() as { [key: string]: any };\n const proto = global[target] && global[target].prototype;\n\n if (!proto || !proto.hasOwnProperty || !proto.hasOwnProperty('addEventListener')) {\n return;\n }\n\n fill(proto, 'addEventListener', function(\n original: () => void,\n ): (eventName: string, fn: EventListenerObject, options?: boolean | AddEventListenerOptions) => void {\n return function(\n this: any,\n eventName: string,\n fn: EventListenerObject,\n options?: boolean | AddEventListenerOptions,\n ): (eventName: string, fn: EventListenerObject, capture?: boolean, secure?: boolean) => void {\n try {\n // tslint:disable-next-line:no-unbound-method strict-type-predicates\n if (typeof fn.handleEvent === 'function') {\n fn.handleEvent = wrap(fn.handleEvent.bind(fn), {\n mechanism: {\n data: {\n function: 'handleEvent',\n handler: getFunctionName(fn),\n target,\n },\n handled: true,\n type: 'instrument',\n },\n });\n }\n } catch (err) {\n // can sometimes get 'Permission denied to access property \"handle Event'\n }\n\n return original.call(\n this,\n eventName,\n wrap((fn as any) as WrappedFunction, {\n mechanism: {\n data: {\n function: 'addEventListener',\n handler: getFunctionName(fn),\n target,\n },\n handled: true,\n type: 'instrument',\n },\n }),\n options,\n );\n };\n });\n\n fill(proto, 'removeEventListener', function(\n original: () => void,\n ): (this: any, eventName: string, fn: EventListenerObject, options?: boolean | EventListenerOptions) => () => void {\n return function(\n this: any,\n eventName: string,\n fn: EventListenerObject,\n options?: boolean | EventListenerOptions,\n ): () => void {\n let callback = (fn as any) as WrappedFunction;\n try {\n callback = callback && (callback.__sentry_wrapped__ || callback);\n } catch (e) {\n // ignore, accessing __sentry_wrapped__ will throw in some Selenium environments\n }\n return original.call(this, eventName, callback, options);\n };\n });\n }\n\n /** JSDoc */\n private _wrapXHR(originalSend: () => void): () => void {\n return function(this: XMLHttpRequest, ...args: any[]): void {\n const xhr = this; // tslint:disable-line:no-this-assignment\n const xmlHttpRequestProps: XMLHttpRequestProp[] = ['onload', 'onerror', 'onprogress', 'onreadystatechange'];\n\n xmlHttpRequestProps.forEach(prop => {\n if (prop in xhr && typeof xhr[prop] === 'function') {\n fill(xhr, prop, function(original: WrappedFunction): Function {\n const wrapOptions = {\n mechanism: {\n data: {\n function: prop,\n handler: getFunctionName(original),\n },\n handled: true,\n type: 'instrument',\n },\n };\n\n // If Instrument integration has been called before TryCatch, get the name of original function\n if (original.__sentry_original__) {\n wrapOptions.mechanism.data.handler = getFunctionName(original.__sentry_original__);\n }\n\n // Otherwise wrap directly\n return wrap(original, wrapOptions);\n });\n }\n });\n\n return originalSend.apply(this, args);\n };\n }\n\n /**\n * Wrap timer functions and event targets to catch errors\n * and provide better metadata.\n */\n public setupOnce(): void {\n this._ignoreOnError = this._ignoreOnError;\n\n const global = getGlobalObject();\n\n fill(global, 'setTimeout', this._wrapTimeFunction.bind(this));\n fill(global, 'setInterval', this._wrapTimeFunction.bind(this));\n fill(global, 'requestAnimationFrame', this._wrapRAF.bind(this));\n\n if ('XMLHttpRequest' in global) {\n fill(XMLHttpRequest.prototype, 'send', this._wrapXHR.bind(this));\n }\n\n [\n 'EventTarget',\n 'Window',\n 'Node',\n 'ApplicationCache',\n 'AudioTrackList',\n 'ChannelMergerNode',\n 'CryptoOperation',\n 'EventSource',\n 'FileReader',\n 'HTMLUnknownElement',\n 'IDBDatabase',\n 'IDBRequest',\n 'IDBTransaction',\n 'KeyOperation',\n 'MediaController',\n 'MessagePort',\n 'ModalWindow',\n 'Notification',\n 'SVGElementInstance',\n 'Screen',\n 'TextTrack',\n 'TextTrackCue',\n 'TextTrackList',\n 'WebSocket',\n 'WebSocketWorker',\n 'Worker',\n 'XMLHttpRequest',\n 'XMLHttpRequestEventTarget',\n 'XMLHttpRequestUpload',\n ].forEach(this._wrapEventTarget.bind(this));\n }\n}\n","import { getCurrentHub } from '@sentry/core';\nimport { Event, Integration, Severity } from '@sentry/types';\nimport {\n addExceptionMechanism,\n addInstrumentationHandler,\n getLocationHref,\n isErrorEvent,\n isPrimitive,\n isString,\n logger,\n} from '@sentry/utils';\n\nimport { eventFromUnknownInput } from '../eventbuilder';\nimport { shouldIgnoreOnError } from '../helpers';\n\n/** JSDoc */\ninterface GlobalHandlersIntegrations {\n onerror: boolean;\n onunhandledrejection: boolean;\n}\n\n/** Global handlers */\nexport class GlobalHandlers implements Integration {\n /**\n * @inheritDoc\n */\n public name: string = GlobalHandlers.id;\n\n /**\n * @inheritDoc\n */\n public static id: string = 'GlobalHandlers';\n\n /** JSDoc */\n private readonly _options: GlobalHandlersIntegrations;\n\n /** JSDoc */\n private _onErrorHandlerInstalled: boolean = false;\n\n /** JSDoc */\n private _onUnhandledRejectionHandlerInstalled: boolean = false;\n\n /** JSDoc */\n public constructor(options?: GlobalHandlersIntegrations) {\n this._options = {\n onerror: true,\n onunhandledrejection: true,\n ...options,\n };\n }\n /**\n * @inheritDoc\n */\n public setupOnce(): void {\n Error.stackTraceLimit = 50;\n\n if (this._options.onerror) {\n logger.log('Global Handler attached: onerror');\n this._installGlobalOnErrorHandler();\n }\n\n if (this._options.onunhandledrejection) {\n logger.log('Global Handler attached: onunhandledrejection');\n this._installGlobalOnUnhandledRejectionHandler();\n }\n }\n\n /** JSDoc */\n private _installGlobalOnErrorHandler(): void {\n if (this._onErrorHandlerInstalled) {\n return;\n }\n\n addInstrumentationHandler({\n callback: (data: { msg: any; url: any; line: any; column: any; error: any }) => {\n const error = data.error;\n const currentHub = getCurrentHub();\n const hasIntegration = currentHub.getIntegration(GlobalHandlers);\n const isFailedOwnDelivery = error && error.__sentry_own_request__ === true;\n\n if (!hasIntegration || shouldIgnoreOnError() || isFailedOwnDelivery) {\n return;\n }\n\n const client = currentHub.getClient();\n const event = isPrimitive(error)\n ? this._eventFromIncompleteOnError(data.msg, data.url, data.line, data.column)\n : this._enhanceEventWithInitialFrame(\n eventFromUnknownInput(error, undefined, {\n attachStacktrace: client && client.getOptions().attachStacktrace,\n rejection: false,\n }),\n data.url,\n data.line,\n data.column,\n );\n\n addExceptionMechanism(event, {\n handled: false,\n type: 'onerror',\n });\n\n currentHub.captureEvent(event, {\n originalException: error,\n });\n },\n type: 'error',\n });\n\n this._onErrorHandlerInstalled = true;\n }\n\n /** JSDoc */\n private _installGlobalOnUnhandledRejectionHandler(): void {\n if (this._onUnhandledRejectionHandlerInstalled) {\n return;\n }\n\n addInstrumentationHandler({\n callback: (e: any) => {\n let error = e;\n\n // dig the object of the rejection out of known event types\n try {\n // PromiseRejectionEvents store the object of the rejection under 'reason'\n // see https://developer.mozilla.org/en-US/docs/Web/API/PromiseRejectionEvent\n if ('reason' in e) {\n error = e.reason;\n }\n // something, somewhere, (likely a browser extension) effectively casts PromiseRejectionEvents\n // to CustomEvents, moving the `promise` and `reason` attributes of the PRE into\n // the CustomEvent's `detail` attribute, since they're not part of CustomEvent's spec\n // see https://developer.mozilla.org/en-US/docs/Web/API/CustomEvent and\n // https://github.com/getsentry/sentry-javascript/issues/2380\n else if ('detail' in e && 'reason' in e.detail) {\n error = e.detail.reason;\n }\n } catch (_oO) {\n // no-empty\n }\n\n const currentHub = getCurrentHub();\n const hasIntegration = currentHub.getIntegration(GlobalHandlers);\n const isFailedOwnDelivery = error && error.__sentry_own_request__ === true;\n\n if (!hasIntegration || shouldIgnoreOnError() || isFailedOwnDelivery) {\n return true;\n }\n\n const client = currentHub.getClient();\n const event = isPrimitive(error)\n ? this._eventFromIncompleteRejection(error)\n : eventFromUnknownInput(error, undefined, {\n attachStacktrace: client && client.getOptions().attachStacktrace,\n rejection: 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dall'**account Unimore**\n\n ### Materiale\n\n Libri:\n - **Introduzione agli Algoritmi e Strutture Dati** di _T.H. Cormen, C. E. Leiserson, R. L. Rivest, C. Stein_\n\n **[Dolly (FIM)](https://dolly.fim.unimore.it/2018/course/view.php?id=26)**\n\n ### Tutorato\n\n Tutor: [**Gianluca d'Addese**](mailto:tutoratoalgoritmi@gmail.com)\n\n Cosa: **Esercizi sugli argomenti visti a lezione** e **preparatori all'esame**\n\n Quando: **Mercoledì dalle 09:00 alle 11:00**...?\n\n ### Esame\n\n Per iscriversi all'esame, bisogna aver passato:\n\n - Analisi matematica (propedeutica)\n - Programmazione I\n\n Formato:\n\n - Prima prova scritta\n - Risolvere problemi con algoritmi proposti a lezione\n - E' un test sulla preparazione\n - Dura 1h30m\n - Non si può usare nessun tipo di materiale\n - Seconda prova scritta\n - Proponi soluzioni per nuovi problemi non studiati a lezione\n - Domande teoriche sugli argomenti studiati\n - Dura 2h\n - E' il giorno dopo la prima prova\n - Si può utilizzare qualsiasi materiale, ma non deve permettere di comunicare\n - Orale facoltativo\n - Solo per chi supera entrambi gli scritti\n - Domande su quello che abbiamo visto a lezione (\"perchè gli algoritmi funzionano?\")\n - Informare via email entro 3 giorni dalla pubblicazione degli esiti della seconda prova\n - L'orale potrebbe migliorare o peggiorare il voto (anche \"molto\")\n\n **Attenzione:** Vengono verbalizzati anche i voti insufficienti; ricordarsi di rifiutarli!\n\n Ci sono i seguenti appelli:\n\n - 3 appelli tra Giugno e Luglio\n - 1 appello a Settembre\n - 2 appelli a Gennaio e Febbraio\n\n Vale il salto di appello se:\n\n - Uno studente regolarmente iscritto **non si presenta** all'appello e non ha avvisato via email almeno il giorno prima.\n - Uno studente ha riportato una **grave insufficienza** in uno dei due scritti, e l'appello successivo è nella stessa sessione\n\n\n ### Note\n\n Il corso è ben collegato con quello di Programmazione 2.\n\n Dormire non fa bene!\n "]);return o=function(){return n},n}var a=i("sJH0"),r=i("imVn"),t=(i("ox/y"),String.raw);e.default=function(){return n("div",null,n(r.a,null,n(a.a,null,t(o()))),n(r.a,null,n(a.a,null,"\n # Il nome del corso\n\n ## Cosa sono gli algoritmi?\n\n Gli algoritmi sono modi sistematici per risolvere problemi.\n\n Sono fondamentali per sviluppare software, in quanto i computer sono eccellenti esecutori di algoritmi.\n\n ## Come si sviluppa un algoritmo?\n\n Innanzitutto, bisogna conoscere gli _input_ e gli _output_ del problema, rispettivamente i dati di partenza e i dati di arrivo di esso; si ha quindi una fase di **ricerca**.\n\n Poi, si deve trovare un procedimento che ci faccia risolvere il nostro problema: è quello che faremo in questa materia!\n\n Infine, bisogna scrivere la soluzione in un modo che possa essere eseguita da un computer: questa è la **programmazione**.\n\n ## Che tipo di problemi possiamo risolvere?\n\n Un algoritmo risolve problemi di tipo generale, non ci interessa sapere _il risultato di 123+456_, ma vogliamo sapere _il risultato di x+y_, dove x e y sono due numeri naturali qualsiasi.\n\n Un problema può essere quindi considerato circa come una **funzione matematica**, che connette ogni input a un output corrispondente.\n\n ## Che caratteristiche ha un algoritmo?\n\n Per prima cosa, ripetendo l'algoritmo più volte con lo stesso ingresso deve dare sempre la stessa uscita come **risultato**, finendo in un **tempo finito**.\n\n Deve essere **ben ordinato**: cambiando l'ordine in cui vengono effettuate le operazioni, è probabile che anche il risultato cambi!\n\n Le sue istruzioni devono essere **non ambigue**, cioè che non possano essere interpretate in più modi, e **effettivamente realizzabili**, cioè realizzabili con l'esecutore che vogliamo usare per eseguire l'algoritmo.\n\n ## Esistono algoritmi equivalenti?\n\n **Sì!** Possono esserci due algoritmi che dati gli stessi input, hanno gli stessi output, e quindi risolvono lo stesso problema.\n\n In compenso, possono avere un numero di operazioni diverse, e quindi essere **uno più veloce** (da eseguire) dell'altro.\n\n ## Come si verifica la correttezza di un algoritmo?\n\n L'algoritmo deve essere **valido per tutti gli input**, anche se questi sono infiniti.\n\n Possiamo effettuare prove matematiche per verificarne la correttezza; il **principio di induzione** è dunque una dei teoremi fondamentali dell'algoritmica.\n\n Possiamo però verificare la _non correttezza_ di un algoritmo trovando un singolo controesempio.\n ")),n(r.a,null,n(a.a,null,"\n # Efficienza degli algoritmi\n \n Un buon algoritmo deve essere **efficiente**, ovvero deve usare il minimo delle risorse necessarie, come _usare il minimo di tempo possibile_.\n \n ## Come misuriamo il tempo necessario?\n \n Cerchiamo di astrarre il tempo dal particolare esecutore, e andiamo a contare il numero di operazioni elementari richieste per eseguire il nostro algoritmo nel caso peggiore.\n \n Un algoritmo efficiente, infatti, all'aumentare dei dati in ingresso, diventerà sempre più veloce rispetto a uno non efficiente, anche su computer più lenti!\n \n > Il [Bubble Sort](https://en.wikipedia.org/wiki/Bubble_sort) è sempre più lento di un [Tree Sort](https://en.wikipedia.org/wiki/Tree_sort), anche su computer più lenti, perchè, dovendo ordinare liste sempre più lunghe, prima o poi si raggiunge un punto in cui il primo è più veloce (in termini di tempo) dell'altro.\n \n Dobbiamo andare a vedere, quindi, _il numero di operazioni richieste per ottenere il risultato nel caso peggiore_.\n \n Consideriamo operazioni sia operazioni aritmetiche sia operazioni logiche, e diciamo che ciascuna costa 1.\n \n > L'[algoritmo di Euclide](https://it.wikipedia.org/wiki/Algoritmo_di_Euclide) per l'MCD costa `3` per ogni iterazione (un giro del ciclo `while`). Diciamo, allora, che costa `3n`, dove `n` è il numero più alto dei due, perchè nel caso peggiore (uno dei due numeri è 1) l'algoritmo compie `n` iterazioni.\n \n ## Altri parametri ottimizzabili\n \n È possibile che alcuni algoritmi per vari motivi cerchino di ottimizzare altri parametri diversi dal tempo, come ad esempio _la dimensione dell'input_ o la _memoria utilizzata_. \n \n > Generalmente, questo viene fatto sui dispositivi embedded, con memoria molto limitata.\n \n ### Criteri di costo di memoria\n \n Ci sono vari criteri con cui stimare la memoria richiesta da un dato: è possibile che il costo risultante vari in base al criterio scelto!\n \n #### Criterio di costo logaritmico\n \n Un dato costa il numero di bit necessari per rappresentarlo.\n \n > Un int che contiene il numero `n` costa `log_2(n)`. \n > Un array di `[n]` numeri tutti uguali costa `n log_2(n)`.\n \n #### Criterio di costo uniforme\n \n Un dato costa il numero di elementi che lo costituiscono.\n \n > Un int che contiene il numero `n` costa `1`. \n > Un array di `[n]` numeri costa `n`. \n > Una matrice `[m][n]` costa `m*n`.\n ")),n(r.a,null,n(a.a,null,"\n # Modelli algoritmici\n\n Per progettare un algoritmo, abbiamo bisogno di sapere le proprietà del nostro esecutore, ovvero il suo _modello algoritmico_.\n \n > Ad esempio, dobbiamo sapere quali istruzioni è in grado di eseguire, e quanto tempo queste istruzioni richiedono.\n \n ## Il modello RAM\n \n Il modello in uso su tutti i computer attuali è il _modello RAM_: \n \n - In ogni cella di memoria può essere archiviato un dato.\n - Il **tempo di accesso** alle celle è **costante** per tutte le celle.\n - La **memoria** principale è **infinita**.\n - Si ha **un solo processore**.\n ")),n(r.a,null,n(a.a,null,'\n # Notazione asintotica\n \n La _notazione asintotica_ è un sistema per **stimare** velocemente il costo di un algoritmo complesso.\n \n Ci permette di **confrontare velocemente il caso peggiore** degli algoritmi.\n \n In particolare, consideriamo il _rapporto tra il numero di operazioni nel caso peggiore e la dimensione dell\'input_.\n \n ## Limiti\n \n Possiamo dare a questa stima dei limiti, superiore e inferiore, che rappresenteranno rispettivamente un costo che non sarà **mai superato** e un costo che verrà **sempre superato**.\n \n Chiameremo questi limiti _upper bound_ e _lower bound_; la loro combinazione darà un _tight bound_.\n \n L\'obiettivo sarà di _ricavare i bound più precisi possibile_ per un dato algoritmo, ovvero l\'**upper bound più basso** e il **lower bound più alto**.\n \n ### O grande\n \n > "O grande" \n > O di g(n)\n > "big-O"\n \n Per rappresentare la stima, useremo una notazione particolare, detta _O grande_, con la seguente proprietà:\n - Date due funzioni `f(n) : N -> R` e `g(n) : N -> R`, diremo che `f(n) ∈ O(g(n))` se e soltanto se `∃ c > 0, n ≥ n_0` tali che `∀ n ≥ 0, f(n) ≤ c * g(n)`\n \n Quando una funzione è O grande di un altra, significa che **asintoticamente, la funzione in O grande è sempre maggiore di quella che sta venendo stimata**.\n \n > **Ipotesi** \n > - `f(n) = 2n² + 3n + 6` \n > - `g(n) = n²`\n >\n > **Tesi** \n > - `f(n) ∈ O(n²)`.\n >\n > **Svolgimento** \n > Scrivo una disequazione, lasciando intatto il termine noto: \n > 1. `2n² + 3n + 6 ≤ 2n² + 3n² + 6` \n > 2. `n² ≤ 2n² + 3n² + n² = 6n²` per `n ≥ 3`\n >\n > Sappiamo, allora, che `2n² + 3n + 6 ≤ 6n²`.\n \n #### Espressioni di O grande\n \n Questa tabella rappresenta le espressioni di O grande più comunemente utilizzate, in ordine **dalla più forte alla più debole**.\n \n > Più forte significa che, per ogni riga della tabella, tutte le righe sottostanti sono contenute nell\'espressione.\n >\n > Ad esempio, `O(n) ∈ O(1)`.\n \n | Espressione O() | Nome |\n |-----------------|------|\n | `O(1)` | Costante |\n | `O(log log n)` | loglog |\n | `O(log n)` | Logaritmica |\n | ![LaTeX](https://latex.codecogs.com/png.latex?O(n^{1/c})) (per c ≥ 1) | Sublineare |\n | `O(n)` | Lineare |\n | `O(n log n)` | nlogn |\n | `O(n²)` | Quadratica |\n | `O(n³)` | Cubica |\n | `O(n^k)` (per k ≥ 1) | Polinomiale |\n | `O(a^n)` (per a ≥ 1) | Esponenziale |\n | `O(n!)` | Fattoriale |\n \n #### Polinomiale\n \n Molto spesso, noteremo che il tempo richiesto da una funzione è O grande di un polinomio di grado K, ovvero `f(n) ∈ O(n^k)`.\n \n Notiamo che in questi casi, possiamo semplificare l\'O grande al grado massimo del polinomio.\n \n > Ad esempio, `O(n² + n + 1) = O(n²)`.\n \n ##### Dimostrazione\n \n Per `n > 0 \\and 0 ≤ i ≤ k`: \n ![LaTeX](https://latex.codecogs.com/png.latex?a_k%20n^k%20+%20a_{k-1}%20n^{k-1}%20+%20%E2%80%A6%20+%20a_1%20n%20+%20a_0%20%E2%89%A4%20|a_k|%20n^k%20+%20|a_{k-1}|%20n^k%20+%20%E2%80%A6%20+%20|a_1|%20n^k%20+%20|a_0|%20n^k%20=%20(|a_k|%20+%20|a_{k-1}|%20+%20%E2%80%A6%20+%20|a_1|%20+%20|a_0|)%20n^k)\n \n #### Proprietà di O grande\n \n 1. `f(n) ∈ O(g(n)) -> ∀ a > 0, a * f(n) ∈ O(g(n))`.\n 2. `f(n) ∈ O(g(n)), d(n) ∈ O(h(n)) -> f(n) + d(n) ∈ O(g(n) + h(n)) -> O(max\\{g(n), h(n)\\})`\n 3. `f(n) ∈ O(g(n)), d(n) ∈ O(h(n)) -> f(n) * d(n) ∈ O(g(n) * h(n))`\n \n In pratica, se una funzione è la _somma di più termini_, basta guardare l\'**`O()` più grande** tra tutti i suoi termini; se invece una funzione è un _prodotto di più termini_, si possono **omettere le costanti**, e l\'`O()` finale sarà dato dal **prodotto degli `O()`** dei termini.\n \n ## Lower bound\n \n Possiamo anche stimare il _lower bound_, il limite inferiore: il **numero minimo di operazioni** che viene effettuato **nel caso migliore** con la **massima dimensione dell\'ingresso**.\n \n ### Ω()\n \n > "Omega" \n > Omega di g(n)\n > "big-Omega"\n \n Esiste un equivalente di O grande per il lower bound: è detto _Omega grande_, o più semplicemente _Omega_, e funziona nello stesso identico modo, solo... al contrario.\n \n Diremo che `f(n) ∈ Ω(g(n))` se e solo se `∃ c > 0, n_0 ≥ 0 : ∀ n ≥ n_0 f(n) ≥ c * g(n)`.\n \n #### Espressioni di Ω()\n \n Anche in questa tabella le espressioni sono **dalla più forte alla più debole**.\n \n | Espressione Ω() | Nome |\n |-----------------|------|\n | `Ω(n!)` | Fattoriale |\n | `Ω(a^n)` (per a ≥ 1) | Esponenziale |\n | `Ω(n^k)` (per k ≥ 1) | Polinomiale |\n | `Ω(n³)` | Cubica |\n | `Ω(n²)` | Quadratica |\n | `Ω(n log n)` | nlogn |\n | `Ω(n)` | Lineare |\n | ![LaTeX](https://latex.codecogs.com/png.latex?\\Omega(n^{1/c})) (per c ≥ 1) | Sublineare |\n | `Ω(log n)` | Logaritmica |\n | `Ω(log log n)` | loglog |\n | `Ω(1)` | Costante |\n \n ## Tight bound\n \n Quando **upper e lower bound coincidono**, allora otteniamo un _tight bound_.\n \n ### θ()\n \n > "Theta" \n > Theta di g(n)\n > "big-Theta"\n \n Anche per il tight bound abbiamo una notazione equivalente a O grande e Omega grande: _Theta grande_!\n \n Diciamo che `f(n) ∈ θ(g(n))` se e solo se `∃ c_1, c_2 > 0, n_0 ≥ 0 : ∀ n ≥ n_0, c_1 * g(n) ≤ f(n) ≤ c_2 * g(n)`.\n \n Ha la particolarità che non valgono tutte le proprietà degli altri due: va usata quindi con cautela!\n \n ## Risorse utili\n \n [khanacademy.org](https://www.khanacademy.org/computing/computer-science/algorithms/asymptotic-notation/a/big-big-theta-notation)\n ')),n(r.a,null,n(a.a,null,"\n # Problemi algoritmici\n \n Un _problema algoritmico_ è un problema matematico che si vuole provare a risolvere con un algoritmo.\n \n > Dati 10 numeri, voglio sapere se sono in ordine crescente oppure no.\n \n ## Caterigorizzazione\n \n I problemi algoritmici si dividono in tre categorie: problemi _trattabili_, problemi _intrattabili_ e problemi _irrisolvibili_.\n \n ### Problema trattabile\n \n Perchè un problema algoritmico sia _trattabile_, deve avere **almeno un algoritmo con upper bound polinomiale**.\n \n > Questo significa che il tempo impiegato da un computer per risolvere il problema rimane ragionevole, e che quindi può essere utilizzato in maniera efficiente.\n \n La trattabilità è un campo ancora parecchio aperto: esistono anche tanti problemi di cui non si è ancora dimostrata la trattabilità o intrattabilità.\n \n > La [fattorizzazione](https://it.wikipedia.org/wiki/Fattorizzazione) è uno di questi problemi: l'assenza di una dimostrazione è ciò che la rende uno dei pilastri della sicurezza informatica moderna.\n \n ### Problema intrattabile\n \n Se **un problema non ha nessun algoritmo con upper bound polinomiale**, allora si dice che è **intrattabile**.\n \n ### Problema irrisolvibile\n \n Se **non esistono algoritmi per risolvere un problema**, allora questo si dice **irrisolvibile**.\n \n > [Dato un algoritmo con certi input, riusciamo a capire con un algoritmo se la sua esecuzione termina o no?](https://en.wikipedia.org/wiki/Halting_problem)\n \n ### Upper e lower bound di problemi\n \n Si può anche trovare un _upper bound_ e un _lower bound_ per un problema, ma bisogna generalizzare di più.\n \n L'**upper bound di un problema** è il minimo upper bound di tutti gli algoritmi che lo risolvono; deve esistere almeno un algoritmo che lo risolva che abbia lo stesso _upper bound_. E' praticamente il tempo migliore per risolvere il problema dato.\n \n Il **lower bound di un problema** è il minimo lower bound di tutti gli algoritmi che lo risolvono; non deve esistere nemmeno un algoritmo che abbia un lower bound migliore. E' il numero assolutamente minimo di operazioni richieste, non si può fare meglio di così.\n \n In particolare, abbiamo che l'_upper bound di un algoritmo_ -> l'_upper bound del suo problema_, \n e il _lower bound di un problema_ -> il _lower bound di un suo algoritmo_.\n \n Generalmente, il _lower bound di un problema_ è una rappresentazione abbastanza accurata della sua difficoltà.\n ")),n(r.a,null,n(a.a,null,"\n # Ricerca binaria\n \n Non credo di aver bisogno di studiare la ricerca binaria, quindi non ho preso appunti a riguardo.\n \n Se non siete me, e state cercando informazioni a riguardo, andate a vedere su Wikipedia!\n ")),n(r.a,null,n(a.a,null,"\n # Divide et impera\n \n Un modo efficace per risolvere un problema è di usare il metodo _divide et impera (et combina)_.\n \n - _Divide_: Divido il problema in **tanti sottoproblemi**.\n - _Impera_: **Risolvo indipendentemente dal resto** ciascuno dei sottoproblemi.\n - _Combina_: **Combino** i risultati dei sottoproblemi per **risolvere il problema principale**.\n \n ## Ricorsione\n \n Un algoritmo (o funzione) si dice _ricorsivo_ quando durante l'esecuzione **richiama sè stesso**.\n \n Dato che tutti gli algoritmi devono avere termine entro un tempo finito, se scriviamo una funzione ricorsiva è fondamentale finire con un **caso base**, che non chiami ulteriormente la ricorsione.\n \n Se esiste una funzione ricorsiva, allora esiste _sempre_ una _funzione iterativa_ che darà lo stesso risultato.\n \n > Sul pratico, una funzione ricorsiva tipicamente è **più costosa** del suo equivalente iterativo: se possibile, quindi, la ricorsione andrebbe evitata.\n \n #### Pseudocodice di esempio\n \n ```python\n def fattoriale(n):\n # Caso base; la ricorsione finisce e dà un risultato fisso\n if n <= 1:\n return 1\n # Caso ricorsivo; la funzione restituisce il risultato di sè stessa (ma con parametri diversi)\n else:\n return n * fattoriale(n - 1)\n ```\n ")),n(r.a,null,n(a.a,null,"\n # Master Theorem\n \n Il _Master Theorem_ è uno dei teoremi più importanti dell'algoritmica.\n \n Esso permette di **calcolare l'upper bound di un algoritmo ricorsivo** in modo piuttosto semplice.\n \n ## Ipotesi\n \n Dato un algoritmo:\n - Con uno o più casi base\n - Che richiama la funzione ricorsiva un numero n di volte\n \n ## Tesi\n \n Allora, il suo upper bound avrà la formula:\n \n ![](https://quicklatex.com/cache3/89/ql_08d29a7e55d561a900570bc83b93ff89_l3.png)\n ")),n(r.a,null,n(a.a,null,"\n # Caso particolare del Master Theorem\n \n ## Ipotesi\n \n Se: \n ![](https://quicklatex.com/cache3/57/ql_e34dc27b42831d3c3ff671b0f3861257_l3.png)\n \n Ovvero, se la dimensione dell'input viene divisa ad ogni ciclo da una costante b, è polinomiale e il caso base è costante...\n \n ## Tesi\n \n Allora: \n ![](https://quicklatex.com/cache3/ca/ql_26e3557a6ca2d6ac4b8481e7c5263fca_l3.png)\n \n > In pratica, se il costo dominante è quello della parte \"fissa\" dell'algoritmo, esso sarà `O(n^d)`, mentre se il costo dominante è quello delle chiamate ricorsive, esso sarà `O(n^{log_b e})`. \n > Se nessuno dei due è dominante... si dividono circa in parti uguali, creando un costo di `O(n^d log n)`.\n ")),n(r.a,null,n(a.a,null,"\n # Ordinamento\n \n Un problema molto frequente nell'informatica consiste nell'**ordinare efficientemente grandi quantità di elementi**.\n \n Esistono [tantissimi](https://it.wikipedia.org/wiki/Algoritmo_di_ordinamento) algoritmi per effettuare l'ordinamento. \n L'**efficienza** di ciascuno **varia** di caso in caso: alcuni sono estremamente efficienti se quasi tutti i numeri sono già nell'ordine giusto; altri, invece, potrebbero impiegare tantissimo tempo.\n \n In termini matematici, abbiamo:\n \n - **Input:** A[n]\n - **Output:** B, ∀ i < n, A[i] ≤ A[i+1]\n \n ## Ordinamento tramite confronto\n \n L'ordinamento \"tradizionale\" è detto _ordinamento tramite confronto_: funziona sempre, e **non ha altri modi di ottenere informazioni** se non con l'operazione logica di confronto tra i dati.\n \n ### Limiti\n \n E' un problema risolto: è dimostrabile che il suo **lower bound** è **`Ω(n log n)`**; possiamo quindi dire che qualsiasi algoritmo di ordinamento è in `Ω(n log n)`, e se riusciamo a trovare un algoritmo di ordinamento in `O(n log n)` siamo riusciti a raggiungere il massimo dell'efficienza.\n \n #### Dimostrazione\n \n Consideriamo **tutte le possibili permutazioni** della sequenza da ordinare: sono `n!`.\n \n Per ogni confronto che effettuiamo, **riduciamo la quantità di permutazioni** correttamente ordinate; prima o poi, rimarrà **una sola possibilità**.\n \n **TODO, non trovo la spiegazione corretta!**\n \n ### Esempi\n \n Algoritmi che effettuano l'ordinamento tramite confronto sono:\n - _Bubble sort_\n - _Merge sort_\n - _Insertion sort_\n - _Quick sort_\n - _Heap sort_\n - E tanti, tanti altri!\n \n ## Ordinamento con altri mezzi\n \n Esistono algoritmi che ricavano informazioni in altri modi, diversi dal confronto.\n \n Essi possono avere un lower bound più basso di `O(n log n)`, però hanno spesso limitazioni sul loro utilizzo.\n \n ### Esempi\n \n - _Counting sort_, indicizza i valori da ordinare\n - _Radix sort_, guarda singolarmente le cifre dei valori\n - _Sleep sort_, sfrutta i thread e la funzione sleep per ordinare valori\n - E altri ancora!\n ")),n(r.a,null,n(a.a,null,"\n # Insertion sort\n \n L'_insertion sort_ è una soluzione **iterativa** all'ordinamento per confronto.\n \n ## Funzionamento\n \n Considero la sequenza divisa in **due parti**: una parte **ordinata** e una parte **non ordinata**.\n \n Parto dal primo elemento della lista: è sempre ordinato con sè stesso. \n Poi, aggiungo uno alla volta i numeri della parte non ordinata a quella ordinata; prima trovo in quale posizione dovrò andare a mettere il numero, poi **faccio slittare tutti i numeri dopo quella posizione** avanti di 1, in modo da **creare lo spazio** in cui infine **inserirò** il numero.\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(n²)` | `Ω(n)` | - |\n \n Nel _caso migliore_ (**lista già ordinata**), il numero da inserire è già nella posizione giusta, quindi non devo effettuare altri confronti oltre il primo, rendendo il lower bound dell'algoritmo `Ω(n)`.\n \n Nel _caso peggiore_ (**lista nell'ordine inverso**), dobbiamo confrontare il numero da inserire con tutti gli altri nella parte ordinata: dobbiamo allora eseguire `1+2+3+4+5+… = \\frac{(n-1)(n)}{2}` confronti; ciò significa che l'upper bound è `O(n²)`!\n \n ## Pseudocodice\n \n ```python\n def insertion_sorted(lista):\n # Itero su tutti i numeri della lista, dal primo all'ultimo.\n for divisore_ord in range(len(lista)):\n # Partendo dalla posizione attuale, creo l'indice di divisione numeri ordinati maggiori e minori\n divisore_magg = divisore_ord\n # Faccio slittare avanti i numeri maggiori di quello che stiamo inserendo\n # Se l'indice divisore_magg raggiunge 0, vuol dire che tutti i numeri della lista sono maggiori del numero attuale \n while divisore_magg >= 0 and lista[divisore_magg-1] > lista[divisore_magg]:\n # Scambio la posizione dei due elementi con gli indici specificati\n # Funzione inventata \n lista[divisore_magg], lista[divisore_magg-1] = lista[divisore_magg-1], lista[divisore_magg]\n # Diminuisco il separatore di 1\n divisore_magg -= 1\n ```\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/bn/sorting)\n ")),n(r.a,null,n(a.a,null,"\n # Merge sort\n \n Il _merge sort_ è una soluzione **ricorsiva** all'ordinamento per confronto.\n \n ## Funzionamento\n \n Per questo algoritmo, utilizziamo la tecnica del **divide et impera**.\n \n 1. _Divide_: Divido A in **due parti**.\n 2. _Impera_: Metto **separatamente in ordine** le parti.\n 3. _Unisci_: **Unisco** le due parti.\n \n Consideriamo come **caso base** della ricorsione una parte composta da un numero, che ovviamente è già ordinata con sè stessa.\n \n ### Merge\n \n Per **unire le due parti** usiamo una funzione detta `merge()`.\n \n Costruiamo una nuova sequenza uguale alla sequenza 1, ma **aggiungiamo alla fine un valore sentinella** sempre maggiore di tutti gli elementi contenuti.\n \n > ```\n > | 1 | 3 | 7 | 8 | ∞ |\n > ```\n \n Facciamo **la stessa cosa** per la sequenza due.\n \n > ```\n > | 2 | 4 | 5 | 6 | ∞ |\n > ```\n \n Prendo i primi numeri delle due sequenze e **metto il più piccolo nella sequenza iniziale**.\n \n > ```\n > | 1 | 2 | 3 | | | | | | \n > | | | 7 | 8 | ∞ | \n > | | 4 | 5 | 6 | ∞ | \n > ```\n \n **Continuo** finchè non ho messo tutti i numeri; **grazie alla sentinella non usciremo mai dalla sequenza**, in quanto essa è sempre maggiore di tutti gli altri numeri.\n \n > ```\n > | 1 | 2 | 3 | 4 | 5 | 6 | | | \n > | | | 7 | 8 | ∞ | \n > | | | | | ∞ |\n > ```\n \n Quando **rimangono solo le sentinelle** significa che abbiamo aggiunto tutti gli elementi, e quindi abbiamo finito.\n \n > ```\n > | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | \n > | | | | | ∞ | \n > | | | | | ∞ | \n > ```\n \n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(n log n)` | `Ω(n log n)` | **`θ(n log n)`** |\n \n Il merge sort è un algoritmo ricorsivo con un **caso base in tempo costante** e che **richiama sè stesso 2 volte**.\n \n ```latex\n T(n) =\\\\\n \\\\\n Θ(1) \\qquad n=1\\\\\n 2 T(\\frac{n}{2}) + Θ(n) \\qquad n \\neq 1\n ```\n \n Applicando il **caso particolare del Master Theorem**, otteniamo:\n \n ```latex\n T(n) =\\\\\n \\\\\n Θ(1) \\qquad n=1\\\\\n Θ(n log n) \\qquad n \\neq 1\n ```\n \n ## Pseudocodice\n \n ```python\n def merge_sorted(part):\n # Caso base\n if len(part) == 1:\n return part\n # Divide\n middle = len(part) // 2\n part_a = part[:middle]\n part_b = part[middle:]\n # Impera\n sort_a = merge_sorted(part_a)\n sort_b = merge_sorted(part_b)\n # Combina\n return merge(sort_a, sort_b)\n ```\n \n ## Visualizzazione\n \n [hackerearth.com](https://www.hackerearth.com/practice/algorithms/sorting/merge-sort/visualize/)\n \n [visualgo.net](https://visualgo.net/bn/sorting) (Nota: visualizza solo la fase _Unisci_ del sort)\n ")),n(r.a,null,n(a.a,null,"\n # Quick sort\n \n Il _quick sort_ è un altro approccio **ricorsivo** all'ordinamento per confronto.\n \n ## Funzionamento\n \n Anche qui, applichiamo il **divide et impera**.\n \n 1. _Divide_: Scelgo un **pivot** qualsiasi all'interno della lista. Metto alla sua **sinistra tutti i numeri minori** e alla sua **destra tutti i numeri maggiori**.\n 2. _Impera_: Eseguo un **quick sort su entrambe le sottoliste**.\n \n ### Esempi\n \n #### Iterazione con partizioni bilanciate\n \n Osserviamo come si formi una partizione con tre elementi e una con quattro. \n \n ```\n |¦ [2] 8 7 1 3 5 6 {4}\n 2 |¦ [8] 7 1 3 5 6 {4}\n 2 |8 ¦ [7] 1 3 5 6 {4}\n 2 |8 ¦ [7] 1 3 5 6 {4}\n 2 |8 7 ¦ [1] 3 5 6 {4}\n 2 1 |7 8 ¦ [3] 5 6 {4}\n 2 1 3 |8 7 ¦ [5] 6 {4}\n 2 1 3 |8 7 5 ¦ [6] {4}\n 2 1 3 |8 7 5 6 ¦ [{4}]\n [2 1 3] {4} [8 5 6 7]\n ```\n \n #### Iterazione con partizioni sbilanciate\n \n Osserviamo come si formi una partizione con **zero elementi** e una con tre.\n \n ```\n |¦ [4] 7 3 {1}\n |4 ¦ [7] 3 {1}\n |4 7 |¦ [3] {1}\n |4 7 3 |¦ [{1}]\n [] {1} [4 7 3]\n ```\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(n²)` | `Ω(n log n)` | - |\n \n Il costo della funzione è dato dalla somma del costo per **dividere in due partizioni** con il costo per realizzare il **Quick sort delle due sottopartizioni**\n \n Possiamo applicare allora il **Master Theorem generale**:\n \n ```latex\n T(n)\\\\\n =\\\\\n Θ(1) \\qquad per\\ n = 1\\\\\n T(q) + T(dim_lista - pivot - 1) + Θ(n) \\qquad per\\ n > 1\n ```\n \n ### Il caso migliore\n \n Se il pivot `q` è la **mediana della partizione** che stiamo ordinando, si vengono a creare due _sottopartizioni bilanciate_, e sostituendo otteniamo:\n \n ```latex\n T(n)\\\\\n =\\\\\n Θ(1) \\qquad per\\ n = 1\\\\\n 2 T(\\frac{n}{2}) + Θ(n) \\qquad per\\ n > 1\n ``` \n \n Possiamo allora applicare il **Master Theorem particolare**:\n \n ```latex\n T(n)\\\\\n =\\\\\n Θ(1) \\qquad per\\ n = 1\\\\\n Θ(n log n) \\qquad per\\ n > 1\n ```\n \n ### Il caso peggiore\n \n Se il pivot è uno degli **estremi dell'array**, si creano due _partizioni sbilanciate_: una delle due sottoliste è sempre vuota! \n Allora:\n \n ```latex\n T(n) = T(n-1) + Θ(n)\\\\\n = T(n-2) + Θ(n-1) + Θ(n)\\\\\n = T(n-3) + Θ(n-2) + Θ(n-1) + Θ(n)\\\\\n = …\n ∈ Θ(n^2)\n ```\n \n > \"Non date da mangiare sequenze ordinate al Quicksort, gli sono indigeste.\"\n \n ## Pseudocodice\n \n ```python\n def partition(partizione, inizio, fine):\n \"\"\"Dividi una partizione in due, usando l'ultimo elemento come pivot.\n \n Note utili:\n partizione[fine] è il pivot\n partizione[maggiori] è il primo numero dei maggiori\n partizione[non_iterati] è l'elemento su cui si sta iterando al momento\"\"\"\n # Crea il primo separatore (la | pipe nell'esempio)\n maggiori = inizio\n # Crea il secondo separatore (la ¦ broken pipe nell'esempio)\n non_iterati = inizio\n # Itera su ogni numero tra inizio e fine (escluso!)\n while non_iterati < fine:\n # Se l'elemento su cui stiamo iterando è minore del pivot\n if partizione[non_iterati] <= partizione[fine]:\n # Mettilo nell'insieme dei minori, scambiandolo con il primo numero dei maggiori e incrementando il primo separatore\n partizione[maggiori], partizione[non_iterati] = partizione[non_iterati], partizione[maggiori]\n maggiori += 1\n # Incrementa sempre il secondo separatore\n non_iterati += 1\n # Inserisci il pivot tra le due sottopartizioni create, \n partizione[fine], partizione[non_iterati] = partizione[non_iterati], partizione[fine]\n return maggiori\n ```\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/bn/sorting) (Nota: invece che prendere l'ultimo numero come pivot prende il primo, cambiando leggermente l'algoritmo.)\n \n ## Note per l'esame\n \n > La domanda che fa sempre è **\"Qual è la sequenza di pivot utilizzata?\"**\n \n > Elementi da soli _non_ vengono presi come pivot!\n ")),n(r.a,null,n(a.a,null,'\n # Counting sort\n\n Il _counting sort_ è un approccio diverso all\'ordinamento: **non usa il confronto**!\n \n ## Requisiti\n \n Il counting sort può essere utilizzato solo su **sequenze di numeri interi**, e solo se **siamo a conoscenza del minimo e del massimo** dei numeri contenuti nell\'array, ed essi non sono troppo distanti uno dall\'altro. \n (La memoria occupata dal counting sort aumenta linearmente con la differenza tra minimo e massimo!)\n \n Per semplicità, consideriamo il **minimo `0`**. \n L\'input allora sarà una sequenza di interi `A`, e il valore del **massimo `k`**, tale che `∀ n ∈ A, 0 \\leq n \\leq K`.\n \n ## Funzionamento\n \n Il counting sort **conta le ripetizioni** delle chiavi nella sequenza originale e in seguito **sovrascrive i valori** della sequenza con i valori ordinati ripetuti il numero di volte che sono stati individuati nella sequenza.\n \n > ```\n > 1 4 5 3 4 1 4 2 5 1\n > ```\n >\n > L\'`1` appare 3 volte, il `2` 1 volta, il `3` 1 volta, il `4` tre volte e il `5` due volte.\n >\n > La sequenza viene quindi così sovrascritta:\n > ```\n > 1 1 1 3 4 1 4 2 5 1 # Sovrascriviamo la sequenza con 1 ripetuto 3 volte\n > 1 1 1 2 3 4 4 4 5 1 # Sovrascriviamo la sequenza con 2, 3, 4 ripetuti rispettivamente 1 1 e 3 volte\n > 1 1 1 2 3 4 4 4 5 5 # Sovrascriviamo la sequenza con 5 ripetuto 2 volte: abbiamo finito!\n > ``` \n \n Esiste anche una **versione stabile** del counting sort che, invece che sovrascrivere, **sposta i valori**, mantenendo le informazioni aggiuntive nel caso invece che interi fossero altri tipi di dati.\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(k + n)` | `Ω(k + n)` | **`θ(k + n)`** |\n \n L\'algoritmo è composto da quattro parti:\n - Ricerca del minimo e massimo (in `θ(n)`)\n - Inizializzazione dell\'indice (in `θ(k)`)\n - Conteggio dei numeri (in `θ(n)`)\n - Sovrascrittura dei numeri (in `θ(k + n)`)\n \n `2 + O(k) + O(n) + O(k + n) -> O(k + n)`\n \n Notiamo che `k` è costante, l\'algoritmo è `O(n)`, estremamente efficiente.\n \n ## Pseudocodice\n \n ```python\n def counting_sort(lista: typing.List[int]):\n """Ordina in-place una lista con il counting sort."""\n # Trovo la dimensione della lista\n dim = len(lista)\n # Trovo il massimo e il minimo all\'interno della lista\n minimo = min(lista)\n massimo = max(lista)\n # Creo l\'indice dei numeri, in modo che sia lungo k e pieno di 0\n indice = [0 for _ in range(minimo, massimo+1)]\n # Conto i numeri presenti, scorrendo su lista e aggiungendo 1 al numero corrispondente\n for i in range(dim):\n indice[lista[i]] += 1\n # Sovrascrivo i numeri nella lista\n count = 0\n for pos, val in enumerate(indice):\n for _ in range(val):\n indice[count] = pos\n count += 1\n \n def stable_counting_sorted(lista: typing.List[int], k: int) -> typing.List[int]:\n """Ordina stabilmente una lista con il counting sort stabile, e restituiscila."""\n # Trovo la dimensione della lista\n dim = len(lista)\n # Trovo il massimo e il minimo all\'interno della lista\n minimo = min(lista)\n massimo = max(lista)\n # Creo l\'indice dei numeri, in modo che sia lungo k e pieno di 0\n indice = [0 for _ in range(minimo, massimo+1)]\n # Conto i numeri presenti, scorrendo su lista e aggiungendo 1 al numero corrispondente\n for i in range(dim):\n indice[lista[i]] += 1\n # Faccio diventare l\'indice "il numero di numeri \\leq i"\n for i in range(len(indice)):\n if i == 0:\n continue\n indice[i] += indice[i-1]\n assert indice[-1] == dim\n # Creo una nuova lista, che sarà quella che verrà restituita\n nuova = [None for _ in range(dim)]\n # Inizio a posizionare i numeri, al contrario\n for i in range(0, dim, -1):\n nuova[indice[lista[i]]] = lista[i]\n indice[lista[i]] -= 1\n return nuova\n ```\n ')),n(r.a,null,n(a.a,null,"\n ## Introduzione alle Strutture Dati\n\n Una _struttura dati_ è un modo in cui si possono organizzare i dati di un programma.\n \n Si possono definire in due modi: **elementari** e **astratte**.\n \n ### Strutture dati elementari\n \n Le strutture _elementari_ dipendono strettamente dal modo in cui vengono memorizzati i dati.\n \n > **Array** e **liste** sono strutture dati elementari: sono definite dicendo come sono memorizzati i dati, rispettivamente, in celle contigue di memoria e da una serie di nodi con un valore e che puntano al successivo.\n \n ### Strutture dati astratte\n \n Le strutture _astratte_ sono separate dal modo in cui vengono memorizzati i dati, sono più ad alto livello, e si definiscono descrivendo le **proprietà** della struttura e i **metodi** che su di essa possono essere effettuate.\n \n > Una _classe_ in un qualsiasi linguaggio di programmazione è una struttura dati astratta.\n \n > Una _pila_ astratta:\n > - memorizza dati tutti dello stesso tipo\n > - `pop()`, estrae dalla pila l'ultimo valore inserito\n > - `push(val)`, aggiunge alla pila un valore\n > - `top()`, permette di vedere l'ultimo valore inserito nella pila\n > - `vuota()`, dice se la pila è vuota oppure no.\n ")),n(r.a,null,n(a.a,null,'\n # Array\n\n Un _array_ è sequenza di dati di **lunghezza conosciuta**, tutti dello **stesso tipo** e di una **dimensione fissa**, immagazzinata in **blocchi di memoria contigui**.\n \n ## Proprietà\n \n - E\' possibile accedere a tutti i blocchi di memoria conoscendo la loro **posizione relativa al primo** elemento.\n \n ## Metodi\n \n ```python\n class Array:\n def __init__(self, size, type=int): "Crea un array di dimensione size di elementi di tipo int."\n def __getitem__(self, index): "Restituisci il valore alla posizione index."\n def __setitem__(self, index, value): "Cambia il valore alla posizione index."\n ```\n \n ### Costo computazionale\n \n Tutte le operazioni su un array sono in **accesso immediato `O(1)`**!\n ')),n(r.a,null,n(a.a,null,'\n # Lista\n \n Una _lista_ è una sequenza di dati immagazzinata in **blocchi di memoria qualsiasi**.\n \n ## Proprietà\n \n Ogni dato ha un **riferimento** alla collocazione di memoria **successiva** (un puntatore): insieme, sono detti un _nodo_.\n \n E\' di **natura ricorsiva**: qualsiasi nodo di una lista può essere visto come inizio della lista con sè stesso e i suoi successivi.\n \n ## Metodi\n \n ```python\n class LinkedList:\n def __init__(self, value, next: typing.Optional[Node] = None):\n self.value = value\n self.next: typing.Optional[Node] = next\n \n def is_empty(self) -> bool: "Restituisce se la lista è vuota o no."\n def is_full(self) -> bool: "Restituisce se la lista è piena o no.\n def append(self, value): "Aggiunge un nuovo elemento in testa alla lista."\n def insert(self, value, index): "Inserisce un elemento dopo il nodo in posizione index."\n def insert_node(self, value, node): "Inserisce un nuovo elemento subito dopo un dato nodo."\n def find(self, node) -> int: "Trova l\'indice del nodo."\n def delete(self, value): "Elimina il primo nodo con quel valore dalla lista."\n def delete_node(self, node): "Elimina il nodo dalla lista."\n def forward(self, index) -> Node: "Restituisce il nodo in posizione index."\n ```\n \n ### Costo computazionale\n \n #### `List.forward(index)`\n \n Per raggiungere l\'`n`-esimo elemento, bisogna _scorrere tutti gli elementi prima di esso_: è dunque un **accesso sequenziale** in **`O(n)`**.\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/list)\n ')),n(r.a,null,n(a.a,null,'\n # Coda (Queue)\n\n Una _coda_ è come una pila, ma segue la strategia **First In, First Out** (il primo inserito sarà il primo a essere estratto).\n \n ## Proprietà\n \n - I dati vi possono essere aggiunti solo tramite il **metodo `enqueue()`**\n - I dati possono essere estratti solo tramite il **metodo `dequeue()`**\n - Verranno restituiti i valori inseriti secondo la strategia **First In, First Out** (il primo inserito sarà il primo a essere estratto).\n \n > Hai presente quando fai la fila per pagare al supermercato? Beh, è quello, però non si possono superare le altre persone in nessun modo.\n \n ## Metodi\n \n ```python\n class Queue:\n def __init__(self): "Crea una nuova coda."\n def is_empty(self) -> bool: "Restituisce vero se la coda è vuota."\n def enqueue(self, data): "Aggiunge un dato alla coda."\n def first(self) -> ...: "Restituisce il primo dato della coda."\n def dequeue(self) -> ...: "Restituisce il primo dato della coda e lo rimuove."\n ```\n \n ## Implementazione tramite lista\n \n Posso implementare la coda con una lista, ma per realizzare l\'implementazione più efficiente devo tenere anche un puntatore all\'ultimo elemento della coda, in modo da non doverla scorrere ogni volta che voglio effettuare un\'operazione.\n \n Chiamiamo i due puntatori `head` e `tail` rispettivamente.\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/list)\n ')),n(r.a,null,n(a.a,null,'\n # Pila (Stack)\n\n Una _pila_ è una struttura dati contenente **valori omogenei**.\n \n ## Proprietà\n \n - I dati vi possono essere aggiunti solo tramite il **metodo `push()`**\n - I dati possono essere estratti solo tramite il **metodo `pop()`**\n - Verranno restituiti i valori inseriti secondo la strategia **Last In, First Out** (l\'ultimo inserito sarà il primo a essere estratto).\n \n > Ci si può immaginare una pila di libri, da cui si può solo prendere un libro alla volta, quello più in alto.\n \n ## Metodi\n \n ```python\n class Stack:\n def __init__(self): "Crea una nuova pila."\n def is_empty(self) -> bool: "Restituisce vero se la pila è vuota."\n def push(self, data): "Aggiunge un dato alla pila."\n def top(self) -> ...: "Restituisce il primo dato della pila."\n def pop(self) -> ...: "Restituisce il primo dato della pila e lo rimuove."\n ```\n \n ## Implementazione tramite lista\n \n Utilizzando una lista possiamo realizzare una pila!\n \n La direzione dei puntatori sarà dall\'ultimo al primo, che non punterà più a nessuno.\n \n Il costo di tutti i metodi è `Θ(1)`!\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/list)\n ')),n(r.a,null,n(a.a,null,"\n # Albero radicato\n \n Un _albero radicato_ è una struttura dati di **natura ricorsiva** che organizza i dati in maniera **non-lineare**.\n \n ## Proprietà\n \n - Ogni nodo dell'albero ha un **unico genitore**: `∀ (padre, figlio), (padre' figlio) ∈ E \\implies padre = padre'`\n - Ogni nodo dell'albero può avere **un numero qualsiasi di figli**.\n \x3c!----\x3e\n - I **nodi superiori al padre** vengono chiamati _antenati_.\n - I **nodi inferiori ai figli** vengono chiamati _discendenti_.\n \x3c!----\x3e\n - Nodi **senza padre** sono detti _radice_: `\\notexists (padre, radice) ∈ E`\n - Nodi **con padre e figli** sono detti _rami_ o interni.\n - Nodi **senza figli** sono detti _foglie_.\n \x3c!----\x3e\n - La **distanza** tra il nodo radice e i suoi discendenti è detta _livello_:\n - I figli immediati sono di livello 1.\n - I \"nipoti\" (figli dei figli) sono di livello 2.\n - I figli dei nipoti sono livello 3.\n - E così via.\n - Il **livello massimo** all'interno di un albero è detto _altezza_, _profondità_ oppure _h_, ed è sempre `1 ≤ h ≤ n-1`.\n \x3c!----\x3e\n - Un albero ha sempre `n-1` archi.\n \n ## Alberi particolari\n \n ### Alberi `d`-ari\n \n Un albero _`d`-ario_ è un particolare tipo di albero che **limita il numero massimo di figli di un nodo** a `d`.\n \n > Un albero _binario_ può avere **massimo 2 figli** per ogni nodo; un albero _ternario_ ne può avere **3**; un albero _`17`-ario_ ne potrà avere **17**\n \n #### Alberi completi\n \n Un albero `d`-ario si dice _completo_ se **tutti i nodi hanno 0 o `d` figli**, e mai una numero in mezzo.\n \n #### Alberi bilanciati\n \n Un albero `d`-ario si dice _bilanciato_ se **tutti i livelli eccetto l'ultimo** hanno il numero massimo di figli.\n \n #### Alberi perfettamente bilanciati\n \n Un albero `d`-ario si dice _perfettamente bilanciato_ se **tutti i livelli incluso l'ultimo** hanno il numero massimo di figli.\n \n ##### Particolarità degli alberi binari perfettamente bilanciati\n \n Si può dimostrare per induzione che:\n - Hanno sempre `2^h` foglie.\n - Hanno sempre `2^{h+1}-1` (`\\sum_i=0^n 2^i`) nodi.\n - L'altezza è in `Θ(log n)`.\n \n ## Implementazione degli alberi\n \n Possiamo scegliere se usare una rappresentazione con array o con nodi e puntatori: ognuna ha vantaggi e svantaggi diversi.\n \n ### Implementazione tramite array\n \n E' suggerito se l'albero è regolare; più è simile a un albero d-ario completo, meglio è.\n \n ### Implementazione tramite nodi e puntatori\n \n Più adatta ad alberi irregolari.\n \n Se l'albero è regolare, creiamo il numero esatto di campi:\n \n - Valore\n - Figlio1\n - Figlio2\n - _Opzionale:_ Padre\n \n Se un albero è irregolare, creiamo una specie di lista:\n \n - Valore\n - Primo figlio\n - Prossimo fratello\n - _Opzionale:_ Padre\n ")),n(r.a,null,n(a.a,null,"\n #### Breadth-first search (BFS)\n\n La _breadth-first search_ è un algoritmo che visita **ogni livello** dell'albero in ordine, dal più basso al più alto.\n \n ## Funzionamento\n \n > 1. __Visita radice__\n > 2. __Visita figli__\n > 3. __Visita nipoti__\n > 4. __Visita pronipoti__\n \n Si può implementare con una coda, in cui verranno inseriti i figli del nodo visitato da visitare ed estratti dopo avere completato la visita del livello attuale.\n \n ## Pseudocodice \n \n ```python\n def bfs(radice):\n c = Queue()\n c.enqueue(radice)\n while not c.is_empty():\n nodo = c.dequeue()\n print(nodo)\n for figlio in nodo.figli:\n nodo.enqueue(figlio)\n ```\n ")),n(r.a,null,n(a.a,null,"\n # Depth-First Search\n\n La _depth-first search_ è un algoritmo che visita **tutti i sottoalberi di un figlio** prima di passare ad un altro sfruttando la natura ricorsiva degli alberi.\n \n ## Funzionamento\n \n Ci sono diverse versioni della depth-first search: ognuna visita la radice in un momento diverso.\n \n ### DFS previsita (pre-order)\n \n La _DFS pre-visita_ visita la **radice per prima**, poi tutti i sottoalberi formati dai figli uno dopo l'altro.\n \n > 1. __Visita radice__\n > 2. dfs_pre_order(figlio1)\n > 3. dfs_pre_order(figlio2)\n \n ### Postvisita (post-order)\n \n La _DFS postvisita_ visita prima tutti i sottoalberi dei figli, e **alla fine la radice**.\n \n > 1. dfs_post_order(figlio1)\n > 2. dfs_post_order(figlio2)\n > 3. __Visita radice__\n \n ### Invisita (in-order)\n \n La _DFS invisita_ visita **un certo numero di figli**, poi la radice, e infine i figli restanti.\n \n > 1. dfs_in_order(figlio1, 1)\n > 2. __Visita radice__\n > 3. dfs_in_order(figlio2, 1)\n ")),n(r.a,null,n(a.a,null,"\n # Albero binario di ricerca\n\n ## Proprietà\n \n - Albero **binario**\n - Chiavi appartenenti ad un **insieme totalmente ordinato** (N, Q, R, ma non C)\n \x3c!----\x3e\n - Per ogni nodo con valore `x`, se un valore `v` è nel sottoalbero di sinistra allora `v ≤ x`, mentre se è nel sottoalbero di destra allora `v > x`.\n \n ## Costo computazionale\n \n - Trovare un valore: `O(h)`\n - Ordinare i valori: `O(n)`\n - Trovare il minimo: `O(h)`\n - Trovare il massimo: `O(h)`\n - Inserire un elemento: `O(h)`\n - Cancellare un elemento: `O(h)`\n \n `h` vale `log n` in un albero perfettamente bilanciato, e più l'albero diventa sbilanciato, più si avvicina a `n`, raggiungendola nel caso l'albero sia una lista.\n \n ## Pseudocodice\n \n ### Cancellazione ricorsiva\n \n ```python\n def delete(tree, key):\n if tree is not None:\n # Se ho trovato il nodo che cercavo...\n if tree.key == key:\n # E c'è una sola diramazione...\n # Semplicemente stacca il nodo come in una lista.\n if tree.left is None:\n return tree.right\n if tree.right is None:\n return tree.left\n # Altrimenti, diventa il minimo dell'albero di destra\n tree.key = tree.right.min()\n # Ed eliminalo dal sottoalbero\n tree.right = delete(tree.right, tree.key)\n # Se la chiave attuale è diversa da quella che cerchiamo, continuo a navigare l'albero\n elif tree.key < key:\n tree.left = delete(tree.left, key)\n else:\n tree.right = delete(tree.right, key)\n return tree\n ```\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/bst)\n \n ## Approfondimenti\n \n Esistono alberi più avanzati che mantengono le proprietà degli alberi binari di ricerca, ma che si autobilanciano, come il [Red Black Tree](https://it.wikipedia.org/wiki/RB-Albero).\n ")),n(r.a,null,n(a.a,null,'\n # Heap binario\n \n L\'_heap binario_ è un **albero binario bilanciato a sinistra**.\n \n ## Proprietà\n \n - _Proprietà strutturale_:\n - L\'albero è **perfettamente bilanciato** in tutti i livelli tranne l\'ultimo\n - Nell\'ultimo livello, le foglie occupano le **posizioni più a sinistra** possibili\n - _Proprietà di ordinamento_:\n - La chiave di un qualsiasi nodo è **più piccola** di tutte quelle dei nodi **del suo sottoalbero**\n \n ## Metodi\n \n ```python\n class Heap:\n def __init__(self, H): ...\n def _heapify_ancestors(self, i): "Ripristina le proprietà dell\'heap per il nodo all\'indice specificato e i suoi genitori."\n def minimum(self): "Restituisce la chiave con il valore minimo in H."\n def decrease_value(self, index, new_value): "Diminuisce il valore della chiave all\'indice index a new_value."\n def insert(self, value): "Inserisci un nuovo valore nell\'albero."\n def _heapify_children(self, i): "Ripristina le proprietà dell\'heap per il nodo all\'indice specificato e i suoi figli."\n def pop(self): "Restituisce la chiave con il valore minimo, e la elimina."\n def from_list(l): "Crea un heap da una lista."\n ```\n \n ## Implementazione con un array\n \n Possiamo implementare l\'albero utilizzando un array con le chiavi dell\'albero memorizzate nell\'ordine _breadth-first_.\n \n L\'indice del figlio sinistro può essere trovato a `2i+1`, mentre l\'indice del figlio sinistro può essere trovato a `2i+2`; il genitore è a `i//2-1`.\n \n ### Pseudocodice\n \n ```python\n class Heap:\n def __init__(self, size):\n self.array = Array(size) # Il tipo Array non esiste; consideriamolo pseudocodice\n self.next_value = 0\n \n def _heapify_ancestors(self, index)\n """Ripristina le proprietà dell\'heap per il nodo all\'indice specificato e i suoi genitori.\n \n Costo:\n O(log n)"""\n # Trovo l\'indice del genitore\n parent = index // 2 - 1\n # Controllo se viene mantenuta la proprietà di ordinamento dell\'heap\n if self.array[index] < self.array[parent]:\n # Scambio i valori dei due nodi\n self.array[index], self.array[parent] = self.array[parent], self.array[index]\n # Faccio la stessa cosa con il genitore\n self._heapify(parent)\n \n \n def minimum(self):\n """Restituisce la chiave con il valore minimo in H.\n \n Costo:\n O(1)"""\n return self.array[0]\n \n def decrease_value(self, index, new_value):\n """Diminuisce il valore della chiave all\'indice index a new_value.\n \n Costo:\n O(log n)"""\n # Diminuisco il valore del nodo\n self.array[index] = new_value\n # Aggiorno l\'heap \n self._heapify(index)\n \n def insert(self, value):\n """Inserisci un nuovo valore nell\'albero.\n \n Costo:\n O(log n)"""\n # Trovo l\'indice in cui inserire il valore\n index = self.next_index \n # Aggiungo il valore in fondo\n self.array[index] = value\n # Aggiorno l\'heap\n self._heapify(index)\n \n def _heapify_children(self, index):\n """Ripristina le proprietà dell\'heap per il nodo all\'indice specificato e i suoi figli.\n \n Costo:\n O(log n)"""\n # Trovo l\'indice dei figli\n left = index * 2 + 1\n right = index * 2 + 2\n # Mi assicuro che i figli esistano\n try:\n # Guardo quale dei figli è maggiore\n if self.array[left] > self.array[right]:\n # Scambio i valori\n self.array[left], self.array[index] = self.array[index], self.array[left]\n # Ripeto la procedura sul figlio modificato\n self._heapify_children(left)\n else:\n # Scambio i valori\n self.array[right], self.array[index] = self.array[index], self.array[right]\n # Ripeto la procedura sul figlio modificato\n self._heapify_children(left)\n except IndexError:\n # La foglia non ha figli: ho finito!\n return\n \n def pop(self):\n """Restituisce la chiave con il valore minimo, e la elimina.\n \n Costo:\n O(log n)"""\n # Mi salvo il valore della radice\n value = self.array[0]\n # Sostituisco la radice con l\'ultima foglia a destra\n self.array[0], self.array[self.next_value] = self.array[self.next_value], self.array[0]\n ### Non bisognerebbe eliminare la foglia...?\n # Riordino l\'heap\n self._heapify_children(0)\n return value\n \n @staticmethod\n def from_list(l):\n """Crea un heap da una lista.\n \n Costo:\n O(n log n), ma si può abbassare"""\n heap = Heap(len(l)))\n heap.array = Array.from_list(l) # Pseudocodice\n heap.next_value = len(l)\n # Cominciamo a riordinare l\'heap dalla fine, in modo che rispetti le proprietà\n for index in range(heap.next_value, 0, -1):\n heap._heapify_children(index)\n ```\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/heap)\n ')),n(r.a,null,n(a.a,null,"\n # Coda con priorità\n \n La _coda con priorità_ è una struttura dati dal funzionamento molto simile a quello di una coda, ma invece che restituire il primo elemento inserito, essa restituisce l'**elemento con il valore di priorità minore**.\n \n ## Proprietà\n \n - Ogni elemento è una coppia costituita da **valore** e **priorità** (un numero intero).\n - Nuovi elementi possono essere aggiunti solo tramite il **metodo `insert()`**\n - Gli elementi possono essere estratti solo tramite il **metodo `pop()`**\n - Verranno restituiti i valori inseriti secondo la strategia **Lower Priority** (l'elemento con la priorità minore sarà il primo ad essere restituito).\n - E' possibile diminuire la priorità di un elemento (e quindi anticipare la sua estrazione)\n \n ## Metodi\n \n ```python\n class PriorityQueue:\n def __init__(self): ...\n def insert(self, new_elem: Element): ...\n def minimum(self) -> Element: ...\n def pop(self) -> Element: ...\n def decrease_priority_for(self, elem: Element, priority: int): ...\n ```\n \n ## Implementazione con lista\n \n E' possibile implementare la coda con priorità tramite una **lista**: l'inserimento di nuovi valori diventerà molto efficiente, ma tutte le altre operazioni saranno linearmente lente.\n \n ### Costo computazionale\n \n - *insert()*: `O(1)`\n - *minimum()*: `O(n)`\n - *pop()*: `O(n)`\n - *decrease_priority_for()*: `O(n)`\n \n ## Implementazione con lista ordinata\n \n Implementando la coda con priorità con una **lista ordinata** si avrà un costo di ordinamento elevato negli inserimenti e modifiche alla priorità, ma costi costanti nell'estrazione di un elemento.\n \n ### Costo computazionale\n \n - *insert()*: `O(n)`\n - *minimum()*: `O(1)`\n - *pop()*: `O(1)`\n - *decrease_priority_for()*: `O(n)`\n \n ## Implementazione con heap\n \n La **soluzione migliore** è quella di implementare la coda con priorità tramite un **heap**: tutti i costi saranno logaritmici, eccetto l'inserimento che sarà costante.\n \n - `insert()` costa `O(1)`\n - `minimum()` costa `O(log n)`\n - `pop()` costa `O(log n)`\n - `decrease_priority_for()` costa `O(log n)`\n \n ## Approfondimenti\n \n Esistono code con priorità che restituiscono **l'elemento con priorità maggiore**, invece che quello minore.\n ")),n(r.a,null,n(a.a,null,"\n # Heap sort\n\n L'_heap sort_ è un algoritmo di ordinamento per confronto **iterativo**.\n \n ## Funzionamento\n \n Per effettuare un heap sort, creiamo un **heap massimo** in cui inseriamo tutti i valori che vogliamo ordinare.\n \n Una volta applicate le proprietà dell'heap, chiamiamo una versione particolare di `heap.pop()` che invece che rimuovere dall'array i valori estratti li posiziona nello spazio creatosi in fondo.\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(n log n)` | `Ω(n log n)` | **`θ(n log n)`** |\n ")),n(r.a,null,n(a.a,null,"\n # Grafo\n \n Un _grafo_ è una struttura dati che rappresenta elementi interconnessi tra loro.\n \n Esistono due tipi di grafi: _orientati_ e _non orientati_.\n \n Per semplicità, consideriamo i nostri nodi numerati da 1 a `n`.\n \n ## Proprietà\n \n - Gli elementi sono rappresentati tramite _nodi_.\n - Il loro _grado_ è dato dal **numero degli archi** che vi incidono.\n - Se il grafo è orientato, hanno anche un _in-degree_ (**numero di archi entranti**) e un _out-degree_ (**numero di archi uscenti**).\n - Le connessioni tra elementi sono rappresentate tramite _archi_.\n - Un arco _incide_ esattamente su **due nodi**.\n - Se il grafo è orientato, sono _uscenti_ da uno dei due nodi ed _entranti_ nell'altro.\n - Sono matematicamente meno del **quadrato dei nodi**.\n \n ## Grafi particolari\n \n ### Catena\n \n Una _catena_ è un **grafo non orientato** composto da una **sequenza di nodi** aventi un **grado massimo di 2** tutti collegati tra loro.\n \n ### Cammino\n \n Un _cammino_ è un **grafo orientato** composto da una **sequenza di nodi** aventi un **in-degree** e un **out-degree** **massimo di 1**, collegati tra loro in modo che partendo dal primo e seguendo gli archi sia possibile arrivare all'ultimo.\n \n ### Cricca\n \n Una _cricca_ è un grafo in cui **tutti i nodi sono collegati tra loro**.\n \n Se il grafo è **non orientato**, la cricca ha `((n-1)n)/2` archi.\n \n Se il grafo è **orientato**, ha per ogni coppia un arco in entrambe le direzioni, quindi ha `(n-1)n` archi.\n \n ### Direct Acyclic Graph\n \n Un _DAG_ è un grafo diretto che non contiene nessun ciclo.\n \n Su di esso possiamo effettuare un ordinamento, detto _linearizzazione_, tra i nodi: otteniamo l'_ordine topologico_.\n \n I primi elementi dei DAG sono detti _Source_ (_Sorgente_), mentre gli ultimi sono detti _Sink_ (_Pozzo_).\n \n #### Albero\n \n Un **albero** può essere considerato un DAG con una **sorgente singola** e le **foglie come pozzi**.\n \n ### Grafo fortemente connesso\n \n Un insieme di nodi `V` di un **grafo diretto** `G` si dice una _componente fortemente connessa_ se:\n \n 1. Per ogni coppia di nodi `∀ u, v ∈ V' : ∃ un cammino u->v in G'`\n 2. Massimale (non può diventare più grande)\n \n > Praticamente una componente fortemente connessa è un gruppo di nodi tra i quali si può viaggiare liberamente da e a qualsiasi nodo al suo interno.\n \n Un grafo si dice _fortemente connesso_ se l'insieme `V` coincide con l'insieme dei nodi del grafo `G`.\n \n > Se partendo da qualsiasi nodo di un grafo riesco ad arrivare a qualsiasi altro nodo, allora il grafo è fortemente connesso.\n \n Inoltre, se creiamo un nuovo grafo, in cui **ogni nodo rappresenta una componente fortemente connessa** del nostro grafo iniziale, **otteniamo un DAG**, perchè tutti i cicli sono stati integrati nella componente.\n \n ### Trasposto di un grafo\n \n Il _trasposto_ di un **grafo diretto** `G` è il grafo stesso con gli archi che però vanno nella **direzione opposta**.\n \n ### Grafo pesato\n \n Un _grafo pesato_ è un particolare grafo che associa a ciascun arco un **costo** per attraversarlo.\n \n #### Costi negativi\n \n I costi possono anche essere negativi: rappresenteranno allora un **guadagno** ottenuto attraversando il nodo.\n \n ### Minimum spanning tree\n \n Un _minimum spanning tree_ è il **sottoinsieme degli archi** di un **grafo non diretto** che **connettono tutti i nodi** con il **minor costo possibile**.\n \n I MST hanno [molte proprietà](https://en.wikipedia.org/wiki/Minimum_spanning_tree#Properties); sono troppe da scrivere qui, e probabilmente non ci interesseranno nemmeno.\n \n ## Implementazione tramite matrice di adiacenza\n \n Possiamo implementare un grafo creando una **matrice di `bool` di dimensione `n * n`** in cui le **caselle collegate sono vere** e le caselle non collegate sono false.\n \n > Ad esempio, possiamo implementare un grafo non orientato in questo modo (`█` indica l'esistenza di un collegamento e ` ` indica la sua assenza):\n >\n > | |1|2|3|\n > |-|-|-|-|\n > |1|░|░|░|\n > |2|█|░|░|\n > |3|█| |░|\n >\n > Esistono gli archi `1-2` e `1-3`, ma non esiste un collegamento `2-3`.\n \n > Un grafo orientato invece si può implementare così:\n >\n > | |1|2|3|\n > |-|-|-|-|\n > |1|░|█| |\n > |2|█|░| |\n > |3|█| |░|\n >\n > Esistono gli archi `1->2`, `2->1` e `3->1`, ma non ci sono collegamenti `2->3`, `1->3` e `3->2`.\n \n ### Costo computazionale\n \n #### Tempo\n \n Le matrici di adiacenza portano alla realizzazione di algoritmi molto veloci: verificare l'esistenza di un arco è in `O(1)`!\n \n Abbiamo però penalità significative quando vogliamo effettuare operazioni sugli archi: ad esempio, trovare il trasposto di un grafo implementato con una matrice di adiacenza è in `O(nodi²)`.\n \n #### Memoria\n \n E' poco efficiente in quanto a memoria: l'upper bound è in `O(n^2)`. \n \n ## Implementazione tramite liste di adiacenza\n \n Un'alternativa alla matrice di adiacenza è quella di creare un'**array di liste**, le quali contengono i **vicini di ciascun nodo**.\n \n > |Posizione|Lista|\n > |-|-|\n > |1|[2, 3]|\n > |2|[]|\n > |3|[1]|\n >\n > Esistono gli archi `1->2`, `1->3`, e `3->1`, ma non esistono `2->1`, `2->3` e `3->2`.\n \n ### Costo computazionale\n \n #### Tempo\n \n Utilizzando le liste di adiacenza, il tempo richiesto per verificare l'esistenza di un arco sale a `O(max-out-degree)`.\n \n E' efficace però quando il problema che vogliamo risolvere riguarda operazioni su archi: trovare la trasposta è in `O(archi)`.\n \n #### Memoria \n \n La memoria richiesta dalle liste di adiacenza è minore di quella delle matrici: l'upper bound è in `O(nodi + archi)`.\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/graphds)\n ")),n(r.a,null,n(a.a,null,"\n # Visitare un grafo\n \n Come per gli alberi radicati, esistono due modi per visitare un grafo: _depth-first search_ e _breadth-first search_.\n \n In entrambi i casi, non visito mai due volte lo stesso nodo, e come risultato ottengo **molteplici alberi**, il cui insieme viene detto _foresta di copertura_.\n \n Se il grafo che vogliamo visitare è diretto, allora dobbiamo **considerare come vicini solo gli archi uscenti**\n \n ## Depth-first search\n \n La DFS ci può risultare utile per **identificare le componenti connesse** di un grafo e **identificare eventuali cicli**.\n \n ### Funzionamento\n \n Posso utilizzare la DFS per classificare gli archi di un grafo in quattro categorie:\n \n - _Tree_, archi che ci fanno **scoprire un nuovo nodo**\n - _Forward_, archi che ci portano a un **discendente**\n - _Back_, archi che ci portano ad un **antenato**\n - _Cross_, archi che **connettono due sottoalberi** diversi\n \n Usiamo due array inizializzati a 0 chiamati `pre` e `post`, grandi quanto il numero di archi del grafo, che ci indicano rispettivamente quando un nodo è stato scoperto e quando è terminata la visita. \n Inoltre, creiamo una variabile `clock` che avanza ad ogni evento. \n Alla scoperta di un nuovo nodo, mettiamo il valore attuale di `clock` all'interno di `pre[n]`. \n Alla fine della visita di un nodo invece mettiamo il valore di `clock` in `post[n]`.\n \n **Durante la visita**, gli archi avranno i seguenti valori:\n - _Tree_: `pre[dst] == 0`\n - _Forward_: `pre[src] < pre[dst] && post[dst] > 0`\n - _Back_: `pre[dst] < pre[src] && post[dst] == 0`\n - _Cross_: Tutti gli altri (`post[dst] < pre[src]`)\n \n **A fine visita**, gli archi avranno i seguenti valori:\n - _Tree_: `pre[dst] < pre[dst] < post[dst] < pre[src]`\n - _Forward_: `pre[dst] < pre[dst] < post[dst] < pre[src]`\n - _Back_: `pre[src] < pre[dst] < post[dst] < post[src]`\n - _Cross_: `pre[dst] < post[dst] < pre[src] < post[src]`\n \n Se un **grafo non diretto** contiene degli **archi Back**, allora esso **conterrà un ciclo**.\n \n #### DFS nel grafo trasposto\n \n Se effettuo una DFS sul trasposto di un grafo, posso **scoprire i nodi che hanno un cammino verso l'origine**.\n \n #### DFS nella componente fortemente connessa\n \n Se effettuo una DFS in una componente fortemente connessa e nella sua trasposta, il **`post` della trasposta sarà sempre minore** del `post` della componente originale.\n \n ### Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(nodi + archi)` | `Ω(nodi + archi)` | **`θ(nodi + archi)`** |\n | Memoria | `O(nodi)` | `Ω(nodi)` | **`θ(nodi)`** |\n \n ### Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/dfsbfs)\n \n ## Breadth-first search\n \n La BFS ci può risultare utile per **trovare tutti i nodi a una certa distanza** da un'origine.\n \n ### Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(nodi + archi)` | `Ω(nodi + archi)` | **`θ(nodi + archi)`** |\n | Memoria | `O(nodi + archi)` | `Ω(nodi + archi)` | **`θ(nodi + archi)`** |\n \n ### Pseudocodice\n \n Come per gli alberi, la implementiamo in modo **iterativo**:\n \n ```python\n queue = [starting_node]\n parents = [None for node in graph.nodes]\n distance = [-1 for node in graph.nodes]\n \n # TODO: controllami quando sei più sveglio\n \n while queue:\n node, source, distance = queue.pop(0)\n parents[node.number] = source\n distance[node.number] = distance\n for neighbour in node.neighbours:\n queue.append((neighbour, node, distance+1))\n ```\n \n > Nella coda, la distanza massima tra un nodo e l'altro è 1.\n \n ### Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/dfsbfs)\n ")),n(r.a,null,n(a.a,null,"\n # Algoritmi greedy\n\n Un modo per risolvere problemi algoritmici può essere usare una **tecnica** _greedy_.\n \n Le tecniche greedy consistono nel effettuare tanti piccoli passi, ed effettuare una **scelta** in base ai dati **locali al passo attuale**.\n \n > Scegli il numero di monete più piccole possibili per comporre €1.12.\n >\n > L'algoritmo cerca di scegliere sempre la moneta più grande possibile compatibile con il prezzo in quel momento, quindi:\n > | Moneta scelta | Rimanente |\n > |---------------|-----------|\n > | € 1.00 | € 0.12 |\n > | € 0.10 | € 0.02 |\n > | € 0.02 | € 0.00 |\n \n ## Esempi\n \n Sono algoritmi greedy:\n \n - L'_Algoritmo di Dijkstra_\n - L'_Algoritmo di Kruskal_\n - L'_Algoritmo di Prim_\n ")),n(r.a,null,n(a.a,null,"\n # Percorso più breve\n\n Trovare il _percorso più breve_ (o _cammino minimo_) tra due nodi di un **grafo pesato** è un problema frequente nell'informatica; per questo, sono stati sviluppati [numerosi algoritmi](https://en.wikipedia.org/wiki/Shortest_path_problem) per risolverlo.\n \n > Ad esempio, il pathfinding dei nemici nei videogiochi, oppure Google Maps!\n \n ## Percorso più breve da una sorgente singola\n \n Una sottocategoria del problema del percorso più breve è il caso in cui ci interessa sapere i percorsi più brevi che **partono da uno specifico nodo del grafo**: è detto problema del _percorso più breve da una sorgente singola_, o _single-source shortest path_.\n \n Si può notare che se il grafo contiene **costi negativi** allora è possibile che il percorso più breve non esista, in quanto diventa possibile la comparsa di **cicli di costo infinitamente negativo**.\n \n Possiamo notare che, se il percorso più breve tra `A` e `D` è `A-B-C-D`, allora il cammino minimo tra `B` e `D` passerà obbligatoriamente per `C` (`B-C-D`).\n Diremo più avanti che il percorso più breve ha una **sottostruttura ottimale**.\n \n ### Esempi\n \n Alcuni algoritmi che trovano il percorso più breve sono:\n - L'_Algoritmo di Dijkstra_\n - L'_Algoritmo di Bellman-Ford_\n - La [_ricerca A*_](https://en.wikipedia.org/wiki/A*_search_algorithm)\n ")),n(r.a,null,n(a.a,null,"\n # Algoritmo di Dijkstra\n \n L'_Algoritmo di [Dijkstra](https://upload.wikimedia.org/wikipedia/commons/8/85/Dijkstra.ogg)_ è un algoritmo che risolve il problema del **percorso più breve da una sorgente singola** per grafi con pesi **reali positivi** `\\mathbb{R}^+`.\n \n L'algoritmo trova tutti i percorsi più brevi per raggiungere qualsiasi nodo del grafo partendo da un dato nodo, assieme al costo richiesto per farlo.\n \n ## Funzionamento\n \n 1. Separiamo tutti i nodi del grafo in due gruppi: **visitati** e **non visitati**. \n - Tutti i nodi partono da **non visitati**.\n 2. Per ogni nodo, manteniamo un valore \"**costo richiesto per raggiungerlo**\", che verrà cambiato man mano che l'algoritmo avanza.\n - Il costo di partenza è `+∞`.\n - Il costo sarà **definitivo per i nodi visitati**, e **provvisorio per i non visitati**.\n 3. Creiamo un insieme detto _frontiera_ che conterrà tutti i **nodi non visitati adiacenti** a quelli visitati.\n 4. Prendiamo il nodo iniziale, che avrà un **costo di `0`**, e definiamolo il nodo _attuale_.\n 5. Finchè ci sono dei nodi non sono stati visitati, ripetiamo il seguente ciclo:\n 1. Aggiungiamo i nodi adiacenti al nodo attuale alla frontiera.\n - Il costo per raggiungerli sarà il **costo per il nodo attuale sommato al costo dell'arco** che li connette al nodo attuale. \n Se questo **costo** risulta essere **minore del costo provvisorio** precedente, esso **diventerà il nuovo costo**.\n - Questa operazione è detta _rilassamento dell'arco_.\n 2. Facciamo diventare **visitato** il nodo attuale.\n - Il percorso che abbiamo fatto per raggiungerlo è obbligatoriamente il più breve.\n 3. Il prossimo nodo attuale sarà il nodo di frontiera con un costo più basso.\n - Per questo, è possibile definire l'algoritmo di Dijkstra come un **algoritmo greedy**.\n \n ### Non funziona se...\n \n L'algoritmo smette di funzionare nel caso in cui siano presenti **costi negativi** e il grafo non sia **aciclico**, in quanto non saremmo mai in grado di rendere visitato un nodo.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | `O(nodi + archi) log nodi)` |\n \n ### Scomposizione\n \n - Inizializzazione: `O(nodi)`\n - Creazione coda priorità: `O(nodi log nodi)`\n - Ciclo: `O((nodi + archi) log nodi)`\n \n ## Pseudocodice\n \n ```python\n import math\n \n class Info:\n def __init__(self, distance=math.inf, previous=None):\n self.distance = distance\n self.previous = previous\n \n def dijkstra(graph, start):\n data = [Info() for node in graph.nodes]\n queue = PriorityQueue([start])\n while queue:\n node = queue.pop()\n for arc in node.connections:\n other = arc.other(node)\n if data[node.number].distance + arc.cost < data[other].distance:\n data[other].distance = data[node.number].distance + arc.cost\n queue.decrease_priority_for(other, data[other].distance)\n data[v].previous = node\n return data\n ```\n \n ## Visualizzazione\n \n [Visualgo](https://visualgo.net/en/sssp)\n ")),n(r.a,null,n(a.a,null,"\n # Algoritmo di Bellman-Ford\n\n L'_Algoritmo di Bellman-Ford_ è un algoritmo che, come l'Algoritmo di Dijkstra, risolve il problema del **percorso più breve da una sorgente singola**, però, a differenza da quest'ultimo, l'Algoritmo di Bellman-Ford accetta in input anche grafi con pesi **reali** `\\mathbb{R}` (sia positivi, sia negativi).\n \n ## Funzionamento\n \n L'approccio dell'algoritmo è simile a quello di Dijkstra: entrambi usano il **rilassamento** degli archi per ottenere un costo provvisorio per il raggiungimento di un nodo, ma invece che rilassare solo l'arco con costo inferiore, questo algoritmo **rilassa tutti gli archi** ripetutamente, eliminando la frontiera e il problema dei nodi negativi.\n \n L'operazione di rilassamento è ripetuta `nodi - 1` volte, ovvero la **lunghezza massima** di un cammino aciclico all'interno di un grafo.\n \n Possiamo individuare dopo i rilassamenti se è presente un nodo con un **ciclo negativo**: ci basta controllare se esiste un arco che connette due nodi con una distanza incompatibile: se `a.distanza + arco.costo < b.distanza`, allora è presente un ciclo negativo.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | `O(nodi * archi)` |\n \n ## Pseudocodice\n \n > TODO\n \n ## Visualizzazione\n \n [Visualgo](https://visualgo.net/en/sssp)\n ")),n(r.a,null,n(a.a,null,'\n # Disjoint set\n \n Il _disjoint set_ è una struttura dati che rappresenta elementi di un insieme raggruppati in **sottoinsiemi disgiunti**.\n \n ## Metodi\n \n ```python\n class DisjointNode:\n def __init__(self): ...\n def find_set(self): "Trova il rappresentante dell\'elemento."\n def union(self, other): "Unisce i sottoinsiemi che contengono questo nodo e `other`."\n ```\n \n ## Implementazione tramite array\n \n Possiamo implementare il disjoint set con due array: uno per l\'**indice del rappresentante** e uno per il **rango dell\'insieme**.\n \n Un singoletto avrà **sè stesso come rappresentante** e **rango `0`**.\n \n ### Costo computazionale\n \n - *create_set()*: `O(1)`\n - *find_set()*: `O(h)`\n - *union()*: `O(h)`\n \n ### Pseudocodice\n \n ```python\n class DisjointNode:\n def __init__(self):\n self.parent = self\n self.rank = 0\n \n def find_set(self):\n element = self\n while self.parent != element:\n element = self.parent\n return element\n \n def union(self, other):\n repres_self = self.find_set()\n repres_other = other.find_set()\n if repres_self == repres_other:\n return\n if repres_self.rank < repres_other.rank:\n repres_greater = repres_other\n repres_lesser = repres_self\n else:\n repres_greater = repres_self\n repres_lesser = repres_other\n repres_lesser.parent = repres_greater\n if repres_greater.rank == repres_lesser.rank:\n repres_greater.rank += 1\n ```\n \n ### Visualizzazione\n \n [cs.usfca.edu](https://www.cs.usfca.edu/~galles/JavascriptVisual/DisjointSets.html)\n ')),n(r.a,null,n(a.a,null,"\n # Trovare il minimum spanning tree\n\n Un altro problema ricorrente riguardante i grafi è trovare il _minimum spanning tree_ di un dato grafo non diretto.\n \n > E' utile per trovare il modo più efficiente per connettere le cose: ad esempio, per decidere la struttura di una rete internet!\n \n ## Esempi\n \n Gli algoritmi principali che risolvono il problema sono due, ed entrambi sono **algoritmi greedy**:\n \n - L'_Algoritmo di Kruskal_\n - L'_Algoritmo di Prim_\n ")),n(r.a,null,n(a.a,null,"\n # Algoritmo di Kruskal\n \n L'_Algoritmo di Kruskal_ è un algoritmo **greedy** che **trova il minimum spanning tree** di un grafo.\n \n ## Funzionamento\n \n 1. Ripetiamo questa procedura finchè tutti i nodi non sono connessi:\n 1. Prendiamo ad ogni passo **l'arco meno costoso** del grafo non ancora aggiunto all'insieme.\n 2. Assicuriamoci che **non si creino cicli**: se non se ne verrebbero a creare, possiamo **aggiungere l'arco all'insieme**.\n - Gli archi devono quindi connettere nodi in **componenti connesse diverse**.\n - Possiamo rappresentare le componenti connesse con un **Disjoint Set**.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | `O(archi²)` |\n \n ### Scomposizione\n \n - DisjointSet.__init__(): `O(archi)`\n - Per ogni ciclo: `O(archi²)`\n - DisjointSet.find_set(): `O(1)`\n - DisjointSet.union(): `O(archi)`\n \n ## Pseudocodice\n \n ```python\n def minimum_spanning_tree_kruskal(graph):\n ds = DisjointSet()\n for node in graph.nodes:\n ds.create_set(node)\n arcs = []\n sorted_arcs = sorted(graph.arcs, key=lambda arc: arc.cost)\n for arc in sorted_arcs:\n if ds.find_set(node.start) != ds.find_set(node.end):\n arcs.append(arc)\n ds.union(node.start, node.end)\n return arcs\n ```\n ")),n(r.a,null,n(a.a,null,"\n # Algoritmo di Prim\n \n L'_Algoritmo di Prim_ è un altro algoritmo **greedy** che **trova il minimum spanning tree** di un grafo.\n \n ## Funzionamento\n \n Creo una **coda con priorità** in cui inserisco tutti gli archi visibili dal mio albero, in cui la chiave è il **costo dell'arco**.\n \n Per trovare l'arco con costo più piccolo posso **estrarre un arco** dalla coda: la priorità ci garantisce che esso è l'**arco meno costoso**.\n \n Aggiungo allora un nuovo nodo all'albero, e con esso, **aggiungo alla coda** tutti gli **archi che scoprono un nuovo nodo**.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | `O(archi + nodi log nodi)` |\n \n ## Pseudocodice\n \n ```python\n import math\n \n def minimum_spanning_tree_prim(graph, cost_array, start_node):\n # E' un Array di bool: se l'indice corrispondente al nodo è uguale a true, vuol dire che il (nodo è contenuto nell'albero.\n contains = [False for _ in range(len(graph))]\n # Contiene il precedente di ogni nodo \n prev = [None for _ in range(len(graph))]\n # Contiene il costo per arrivare a quel nodo\n cost = [math.inf for _ in range(len(graph))]\n # Creo la priority queue\n pq = PriorityQueue(graph.arcs, key=lambda arc: arc.cost)\n # Parto dal nodo `start_index`\n # Il costo dell'origine è 0.\n cost[start_node.index] = 0\n contains[start_node.index] = True\n \n while not pq.is_empty():\n new_node = pq.pop()\n contains[new_node.index] = True\n for arc in new_node.connections:\n other_node = arc.other(new_node)\n if not contains[other_node.index] and cost[other_node.index] > arc.cost:\n cost[other_node.index] = arc.cost\n prev[other_node.index] = new_node\n pq.decrease_priority_for(other_node, arc.cost)\n # L'array di prev rappresenta un albero.\n return prev\n ```_\n ")),n(r.a,null,n(a.a,null,"\n # Compressione\n\n _Comprimere_ un file significa **ridurne le dimensioni** senza modificarne il significato.\n \n ## Categorie\n \n ### Compressione lossless\n \n Nella _compressione lossless_, i dati possono essere decompressi riottenendo una copia identica dell'originale.\n \n > Immaginiamo un file che contiene solo le lettere `a, b, c, d, e, f`.\n >\n > Le lettere compaiono con questa frequenza:\n > |a|b|c|d|e|f|\n > |45%|13%|12%|16%|9%|5%|\n >\n > Possiamo codificare le lettere nel seguente modo:\n > |a|b|c|d|e|f|\n > |`0b0`|`0b100`|`0b101`|`0b111`|`0b1100`|`0b1101`|\n >\n > Scrivere `abacadae` richiederebbe 64 bits con la codifica ASCII estesa, ma in questo modo riusciamo a scriverlo con soli 17 bits!\n \n Le codifiche di un file compresso devono rispettare la proprietà del _Codice a prefisso_, che dice che **nessun codice deve essere il prefisso di un altro codice**; altrimenti, si avrebbero ambiguità nella decodifica.\n \n > a = `1`\n > b = `11`\n >\n > `111` è `ab`, `ba` oppure `aaa`?\n \n Creiamo allora un _albero di decodifica_: un **albero binario** che, leggendo uno ad uno i bit codificati, ci permette di arrivare al **valore del codice presente sulle foglie** dell'albero.\n \n Gli alberi di decodifica sono sempre **completi**.\n \n > Un albero di decodifica incompleto sarebbe non ottimizzato!\n \n #### Esempi\n \n - .png\n - .flac\n - .zip\n - ...\n \n ### Compressione lossy\n \n Nella _compressione lossy_, alcuni dati [solitamente](http://needsmorejpeg.com/) irrilevanti vengono perduti: non si può, dunque, ricostruire l'originale.\n \n #### Esempi\n \n - .jpeg\n - .mp3\n - ...\n ")),n(r.a,null,n(a.a,null,"\n # Algoritmo di Huffman\n\n L'_Algoritmo di Huffman_ è un **algoritmo greedy** per la **costruzione di un albero di decodifica**.\n \n ## Funzionamento\n \n 1. Costruisco **un albero** (con un solo nodo) **per ogni elemento dell'alfabeto**.\n 2. Associo ad **ogni albero la frequenza dell'elemento** da cui è stato creato, per poi inserire tutti gli elementi in una coda con priorità.\n 3. Finchè non ho **un albero solo**:\n 1. Estraggo dalla coda i **due alberi con frequenza minore**.\n 2. **Li rendo fratelli**, creando un nuovo nodo in cui sono uno figlio destro e uno figlio sinistro.\n 3. Associo al nuovo nodo la **somma delle frequenze dei due alberi**, e inserisco il nuovo albero nella coda.\n \n > È molto raro che venga un albero \"dritto\"; se succede, probabilmente c'è qualcosa che non va.\n ")),n(r.a,null,n(a.a,null,"\n # Dizionario\n \n Un _dizionario_ è una struttura dati che **associa dei valori a delle chiavi**.\n \n ## Proprietà\n \n - Ogni elemento del dizionario è un **valore** che è stato **associato a una chiave**.\n - Possiamo aggiungere nuovi elementi con il **metodo `add(chiave, valore)`**.\n - Posiamo estrarre elementi con il **metodo `get(chiave)`**, che restituirà il valore associato a `chiave`.\n - E' possibile rimuovere elementi con il **metodo `delete(chiave)`**.\n - Due elementi con **chiavi diverse** non devono **mai restituire lo stesso valore**.\n \n ## Metodi\n \n Beh... Non ha molto senso in questo caso...\n \n ```python\n dict()\n ```\n \n ## Implementazione con tabella hash\n \n Una _tabella hash_ è un'array di coppie **chiave-valore**, che formano l'insieme _universo_.\n \n Per determinare l'**indice dell'array** in cui inserire una coppia, usiamo una [funzione _hash_](https://it.wikipedia.org/wiki/Hash#Algoritmo_di_hash) sulla chiave, che restituirà **numeri da `0` a `len(hash_table)`**.\n \n ### Risoluzione collisioni\n \n Potrebbe capitare però che **due chiavi diverse abbiano lo stesso indice**. Dobbiamo allora usare un metodo di _risoluzione collisioni_, che mi permetta di distinguere tra chiavi diverse.\n \n #### Lista di trabocco\n \n Possiamo salvare nell'array **liste di coppie** chiave-valore; in caso di collisione, **aggiungo un nuovo elemento alla lista**.\n \n In media, ciascuna di queste liste conterrà `elementi_inseriti / dimensione_tabella` elementi.\n \n #### Indirizzamento aperto\n \n Possiamo decidere di mettere le coppie che non trovano posto nel loro indice in **un altro indirizzo vuoto** dell'array.\n \n Ci sono diversi modi in cui decidere il nuovo indirizzo, ognuno con vantaggi e svantaggi: si può scegliere quello successivo, oppure il primo vuoto dell'array, oppure un indirizzo casuale.\n \n > Python, nei `dict`, usa indirizzamento aperto pseudorandom.\n \n ### Costo computazionale\n \n - Aggiungere una chiave: `O(n)`\n - Trovare una chiave: `O(n)`\n - Eliminare una chiave: `O(n)`\n ")),n(r.a,null,n(a.a,null,"\n # Programmazione dinamica\n \n La _programmazione dinamica_ è una **tecnica** di programmazione che prevede l'**estensione di una soluzione ottima precedente**.\n \n Tutti i problemi in cui si può applicare si possono risolvere anche con la **ricorsione**, ma a differenza della ricorsione, questa tecnica riesce ad evitare di ricalcolare la soluzione per ogni chiamata ricorsiva, ottenendo quindi tempi molto migliori.\n \n Si può applicare solo se un problema ha una **sottostruttura ottimale**, ovvero se la soluzione ottima di un sottoproblema è inclusa nella soluzione ottima del problema. \n \n ## Esempi\n \n - _Problema dello zaino_\n - ...\n \n > Il cammino minimo per raggiungere un nodo in un DAG è dato da `arco.costo + arco.primo_nodo.costo_cammino_minimo()`.\n >\n > ```python\n > def SPD_PD(graph, start):\n > distance = [float(inf) for node in graph.nodes]:\n > distance[start] = 0\n > # I nodi devono essere in ordine di linearizzazione\n > for node in graph.nodes:\n > distance[node] = min([(arc.cost + distance[arc.other(node)] for arc in node.connections])\n > ```\n \n > Ho una sequenza di interi da `a_1` a `a_n`. Voglio trovare la sottosequenza crescente più lunga.\n >\n > 5 2 3 4 7 3 6 3 1 6\n >\n > Trovo tutte le sequenze lunghe 1, e le rendo nodi di un grafo diretto.\n >\n > Da ogni nodo, creo una connessione verso i suoi maggiori.\n >\n > Infine, cerco i cammini massimi del grafo. \n > \n > Essi saranno la soluzione del problema.\n \n > Trova la lunghezza della sottosequenza più lunga che termina con `j`.\n >\n > `L[j]` = lunghezza della sottosequenza più lunga che termina in `j`\n > \n > ```python\n > L[j] = max([1 + L[node] for arc in node.connections)]\n > ```\n >\n > Esempio:\n > ```python\n > L[9] = max([1+L[8], 1+L[3], 1+L[6]])\n > ```\n ")),n(r.a,null,n(a.a,null,"\n # Problema dello zaino\n \n Il problema dello zaino è un problema _pseudo-trattabile_: non abbiamo dimostrazioni di se sia trattabile o intrattabile.\n \n ## Descrizione\n \n > Sei un ladro, e devi mettere **più refurtiva possibile** nello zaino per scappare. \n > Lo zaino può portare **al massimo `dim` kili**.\n >\n > **Quali** (e quanti) oggetti scegli?\n \n | Input | Output |\n |-------|--------|\n | `dim`ensione_zaino, `n`umero_oggetti, `oggetto.peso`, `oggetto.valore` | `profitto_massimo` |\n \n ## Categorie\n \n ### Problema con ripetizione\n \n Puoi prendere **tutte le copie che vuoi** di un oggetto.\n \n #### Soluzione\n \n `K(dim)` è il valore massimo ottenibile con uno zaino di capacità `dim`.\n \n > Se `i` appartenesse alla soluzione ottima, allora `K(dim) = i.valore + K(dim - i.peso)`...\n \n Possiamo dire che `K(dim) = max(i.valore + K(dim - i.peso))`.\n \n Inoltre, `K(0) = 0`.\n \n Ci salviamo tutte le soluzioni da `K(0)` a `K(dim)`, e le usiamo per calcolare il massimo in seguito.\n \n Calcolare `K(dim)` avrà allora un costo di `O(n * dim)`:\n - `n`, perchè trovare il massimo è un'operazione lineare\n - `dim`, perchè `dim` sono tutti i casi tra i quali devo andare a provare\n \n Il costo computazionale, allora, è in `O(n * dim)`. \n \n Però, il **tempo richiesto** dal nostro algoritmo dipende non dalla lunghezza dell'input, bensì dal **valore numerico** di `dim`, che corrisponde alla dimensione dell'array delle soluzioni. \n Allora, si dice che l'algoritmo è in **tempo _pseudo-polinomiale_**.\n \n ### Problema senza ripetizione\n \n Si può prendere **ogni oggetto una volta sola**.\n \n #### Soluzione _bruteforce_\n \n Scelgo se prendere o no l'item 1.\n \n Si creano due percorsi:\n - Non prendo l'oggetto: `valore = 0, peso = 0`\n - Prendo l'oggetto: `valore = oggetto.valore, peso = oggetto.peso`\n \n Continuo a creare percorsi, creando una specie di albero binario.\n \n Se a un certo punto vedo che `valore = x, peso = K` e `valore < x, peso = K`, allora posso escludere automaticamente tutto il sottoalbero destro, perchè non può essere migliore del sinistro: allora, sarò riuscito a ridurre il numero dei casi rispetto alla ricorsione.\n \n ### Problema in due variabili\n \n `K(j, w)` = massimo valore ottenibile con uno zaino di capacità `w` scegliendo gli item da `1` a `j`.\n \n Non possiamo più applicare la soluzione bruteforce, perchè abbiamo due variabili, `j` e `w`.\n \n Allora, prendo l'elemento `j`. Esso può essere o non essere nella soluzione: mi calcolo entrambe le alternative, e mi tengo l'alternativa dal valore più alto.\n \n Se `j` non è nella soluzione, il risultato diventerà `K(j-1, w)`; se invece è nella soluzione, il risultato sarà `j.valore + K(j-1, w-j.peso)`.\n \n In pratica, prendiamo\n \n ```latex\n K(j, w) = max\n \\begin{cases}\n V_j + K(j-1, w-w_j)\n K(j-1, w)\n \\end{cases}\n ```\n \n Costruisco allora una matrice con `j` su un asse e `w` sull'altro. \n Riempio le caselle con il valore di `K(j, w)`. \n Nella casella con `K(j, w)` avremo la soluzione ottima.\n \n Il tempo necessario per riempire tutte le caselle è nuovamente `O(n * w)`, ancora **pseudopolinomiale**.\n \n Per sapere che oggetti ho messo o no devo tenere traccia in qualche modo della catena del calcolo, usando, ad esempio, una pila.\n ")),n(r.a,null,n(a.a,null,"\n # Problemi intrattabili\n \n ## Problema di Set-Cover\n \n ### Input\n \n `U`niverso di `e`lementi\n \n `S`ottoinsieme di `s`ottoinsiemi di elementi di `U`\n \n ### Output\n \n Il minimo `S'`ottoinsieme di `s`ottoinsiemi che copra completamente `U`.\n \n ### Soluzione in `O(n^d)`\n \n Non c'è.\n \n ### Non-soluzione alternativa\n \n Faccio una scelta greedy, ma non posso dimostrare in alcun modo che la soluzione ottenuta sia quella ottima. \n Infatti, l'algoritmo non dà sempre la soluzione ottima, ma dà una soluzione accettabile in tempo polinomiale.\n \n Seleziono sempre il sottoinsieme che copre più elementi mancanti possibili.\n \n #### Costo computazionale\n \n `Costo greedy <= log(numero_elementi) * Costo ottimo`\n ")))}}.call(this,i("hosL").h)}}]); -//# sourceMappingURL=route-AlgoritmiEStruttureDati.chunk.59c45.js.map \ No newline at end of file +(window.webpackJsonp=window.webpackJsonp||[]).push([[4],{"ox/y":function(n,e,i){"use strict";function o(n,e){if(!n)throw new ReferenceError("this hasn't been initialised - super() hasn't been called");return!e||"object"!=typeof e&&"function"!=typeof e?n:e}Object.defineProperty(e,"__esModule",{value:!0}),e.Link=e.Match=void 0;var a=Object.assign||function(n){for(var e=1;e>>0,1)},e.prototype.render=function(n){var e=this.nextUrl||(0,t.getCurrentUrl)(),i=e.replace(/\?.+$/,"");return this.nextUrl=null,n.children({url:e,path:i,matches:!1!==(0,t.exec)(i,n.path,{})})},e}(r.Component),s=function(n){var e=n.activeClassName,i=n.path,o=function(n,e){var i={};for(var o in n)e.indexOf(o)>=0||Object.prototype.hasOwnProperty.call(n,o)&&(i[o]=n[o]);return i}(n,["activeClassName","path"]);return(0,r.h)(l,{path:i||o.href},(function(n){return(0,r.h)(t.Link,a({},o,{class:[o.class||o.className,n.matches&&e].filter(Boolean).join(" ")}))}))};e.Link=s,e.default=l,l.Link=s},w9qZ:function(n,e,i){"use strict";i.r(e),function(n){function o(){var n=function(n,e){e||(e=n.slice(0));return n.raw=e,n}(["\n # Algoritmi e Strutture Dati\n\n Docente: [**Manuela Montangero**](mailto:manuela.montangero@unimore.it)\n\n Crediti: **9 CFU** (72 ore di lezione)\n\n Orario di ricevimento: **Giovedì dalle 14:30 alle 16:30**\n _Mandare una mail prima, altrimenti potrebbe andarsene_\n\n\n #### Regole particolari per le email\n\n - Oggetto \"ASD\"\n - Mail **firmata** con **nome e cognome**\n - Mail spedita dall'**account Unimore**\n\n ### Materiale\n\n Libri:\n - **Introduzione agli Algoritmi e Strutture Dati** di _T.H. Cormen, C. E. Leiserson, R. L. Rivest, C. Stein_\n\n **[Dolly (FIM)](https://dolly.fim.unimore.it/2018/course/view.php?id=26)**\n\n ### Tutorato\n\n Tutor: [**Gianluca d'Addese**](mailto:tutoratoalgoritmi@gmail.com)\n\n Cosa: **Esercizi sugli argomenti visti a lezione** e **preparatori all'esame**\n\n Quando: **Mercoledì dalle 09:00 alle 11:00**...?\n\n ### Esame\n\n Per iscriversi all'esame, bisogna aver passato:\n\n - Analisi matematica (propedeutica)\n - Programmazione I\n\n Formato:\n\n - Prima prova scritta\n - Risolvere problemi con algoritmi proposti a lezione\n - E' un test sulla preparazione\n - Dura 1h30m\n - Non si può usare nessun tipo di materiale\n - Seconda prova scritta\n - Proponi soluzioni per nuovi problemi non studiati a lezione\n - Domande teoriche sugli argomenti studiati\n - Dura 2h\n - E' il giorno dopo la prima prova\n - Si può utilizzare qualsiasi materiale, ma non deve permettere di comunicare\n - Orale facoltativo\n - Solo per chi supera entrambi gli scritti\n - Domande su quello che abbiamo visto a lezione (\"perchè gli algoritmi funzionano?\")\n - Informare via email entro 3 giorni dalla pubblicazione degli esiti della seconda prova\n - L'orale potrebbe migliorare o peggiorare il voto (anche \"molto\")\n\n **Attenzione:** Vengono verbalizzati anche i voti insufficienti; ricordarsi di rifiutarli!\n\n Ci sono i seguenti appelli:\n\n - 3 appelli tra Giugno e Luglio\n - 1 appello a Settembre\n - 2 appelli a Gennaio e Febbraio\n\n Vale il salto di appello se:\n\n - Uno studente regolarmente iscritto **non si presenta** all'appello e non ha avvisato via email almeno il giorno prima.\n - Uno studente ha riportato una **grave insufficienza** in uno dei due scritti, e l'appello successivo è nella stessa sessione\n\n\n ### Note\n\n Il corso è ben collegato con quello di Programmazione 2.\n\n Dormire non fa bene!\n "]);return o=function(){return n},n}var a=i("sJH0"),r=i("imVn"),t=(i("ox/y"),String.raw);e.default=function(){return n("div",null,n(r.a,null,n(a.a,null,t(o()))),n(r.a,null,n(a.a,null,"\n # Il nome del corso\n\n ## Cosa sono gli algoritmi?\n\n Gli algoritmi sono modi sistematici per risolvere problemi.\n\n Sono fondamentali per sviluppare software, in quanto i computer sono eccellenti esecutori di algoritmi.\n\n ## Come si sviluppa un algoritmo?\n\n Innanzitutto, bisogna conoscere gli _input_ e gli _output_ del problema, rispettivamente i dati di partenza e i dati di arrivo di esso; si ha quindi una fase di **ricerca**.\n\n Poi, si deve trovare un procedimento che ci faccia risolvere il nostro problema: è quello che faremo in questa materia!\n\n Infine, bisogna scrivere la soluzione in un modo che possa essere eseguita da un computer: questa è la **programmazione**.\n\n ## Che tipo di problemi possiamo risolvere?\n\n Un algoritmo risolve problemi di tipo generale, non ci interessa sapere _il risultato di 123+456_, ma vogliamo sapere _il risultato di x+y_, dove x e y sono due numeri naturali qualsiasi.\n\n Un problema può essere quindi considerato circa come una **funzione matematica**, che connette ogni input a un output corrispondente.\n\n ## Che caratteristiche ha un algoritmo?\n\n Per prima cosa, ripetendo l'algoritmo più volte con lo stesso ingresso deve dare sempre la stessa uscita come **risultato**, finendo in un **tempo finito**.\n\n Deve essere **ben ordinato**: cambiando l'ordine in cui vengono effettuate le operazioni, è probabile che anche il risultato cambi!\n\n Le sue istruzioni devono essere **non ambigue**, cioè che non possano essere interpretate in più modi, e **effettivamente realizzabili**, cioè realizzabili con l'esecutore che vogliamo usare per eseguire l'algoritmo.\n\n ## Esistono algoritmi equivalenti?\n\n **Sì!** Possono esserci due algoritmi che dati gli stessi input, hanno gli stessi output, e quindi risolvono lo stesso problema.\n\n In compenso, possono avere un numero di operazioni diverse, e quindi essere **uno più veloce** (da eseguire) dell'altro.\n\n ## Come si verifica la correttezza di un algoritmo?\n\n L'algoritmo deve essere **valido per tutti gli input**, anche se questi sono infiniti.\n\n Possiamo effettuare prove matematiche per verificarne la correttezza; il **principio di induzione** è dunque una dei teoremi fondamentali dell'algoritmica.\n\n Possiamo però verificare la _non correttezza_ di un algoritmo trovando un singolo controesempio.\n ")),n(r.a,null,n(a.a,null,"\n # Efficienza degli algoritmi\n \n Un buon algoritmo deve essere **efficiente**, ovvero deve usare il minimo delle risorse necessarie, come _usare il minimo di tempo possibile_.\n \n ## Come misuriamo il tempo necessario?\n \n Cerchiamo di astrarre il tempo dal particolare esecutore, e andiamo a contare il numero di operazioni elementari richieste per eseguire il nostro algoritmo nel caso peggiore.\n \n Un algoritmo efficiente, infatti, all'aumentare dei dati in ingresso, diventerà sempre più veloce rispetto a uno non efficiente, anche su computer più lenti!\n \n > Il [Bubble Sort](https://en.wikipedia.org/wiki/Bubble_sort) è sempre più lento di un [Tree Sort](https://en.wikipedia.org/wiki/Tree_sort), anche su computer più lenti, perchè, dovendo ordinare liste sempre più lunghe, prima o poi si raggiunge un punto in cui il primo è più veloce (in termini di tempo) dell'altro.\n \n Dobbiamo andare a vedere, quindi, _il numero di operazioni richieste per ottenere il risultato nel caso peggiore_.\n \n Consideriamo operazioni sia operazioni aritmetiche sia operazioni logiche, e diciamo che ciascuna costa 1.\n \n > L'[algoritmo di Euclide](https://it.wikipedia.org/wiki/Algoritmo_di_Euclide) per l'MCD costa `3` per ogni iterazione (un giro del ciclo `while`). Diciamo, allora, che costa `3n`, dove `n` è il numero più alto dei due, perchè nel caso peggiore (uno dei due numeri è 1) l'algoritmo compie `n` iterazioni.\n \n ## Altri parametri ottimizzabili\n \n È possibile che alcuni algoritmi per vari motivi cerchino di ottimizzare altri parametri diversi dal tempo, come ad esempio _la dimensione dell'input_ o la _memoria utilizzata_. \n \n > Generalmente, questo viene fatto sui dispositivi embedded, con memoria molto limitata.\n \n ### Criteri di costo di memoria\n \n Ci sono vari criteri con cui stimare la memoria richiesta da un dato: è possibile che il costo risultante vari in base al criterio scelto!\n \n #### Criterio di costo logaritmico\n \n Un dato costa il numero di bit necessari per rappresentarlo.\n \n > Un int che contiene il numero `n` costa `log_2(n)`. \n > Un array di `[n]` numeri tutti uguali costa `n log_2(n)`.\n \n #### Criterio di costo uniforme\n \n Un dato costa il numero di elementi che lo costituiscono.\n \n > Un int che contiene il numero `n` costa `1`. \n > Un array di `[n]` numeri costa `n`. \n > Una matrice `[m][n]` costa `m*n`.\n ")),n(r.a,null,n(a.a,null,"\n # Modelli algoritmici\n\n Per progettare un algoritmo, abbiamo bisogno di sapere le proprietà del nostro esecutore, ovvero il suo _modello algoritmico_.\n \n > Ad esempio, dobbiamo sapere quali istruzioni è in grado di eseguire, e quanto tempo queste istruzioni richiedono.\n \n ## Il modello RAM\n \n Il modello in uso su tutti i computer attuali è il _modello RAM_: \n \n - In ogni cella di memoria può essere archiviato un dato.\n - Il **tempo di accesso** alle celle è **costante** per tutte le celle.\n - La **memoria** principale è **infinita**.\n - Si ha **un solo processore**.\n ")),n(r.a,null,n(a.a,null,'\n # Notazione asintotica\n \n La _notazione asintotica_ è un sistema per **stimare** velocemente il costo di un algoritmo complesso.\n \n Ci permette di **confrontare velocemente il caso peggiore** degli algoritmi.\n \n In particolare, consideriamo il _rapporto tra il numero di operazioni nel caso peggiore e la dimensione dell\'input_.\n \n ## Limiti\n \n Possiamo dare a questa stima dei limiti, superiore e inferiore, che rappresenteranno rispettivamente un costo che non sarà **mai superato** e un costo che verrà **sempre superato**.\n \n Chiameremo questi limiti _upper bound_ e _lower bound_; la loro combinazione darà un _tight bound_.\n \n L\'obiettivo sarà di _ricavare i bound più precisi possibile_ per un dato algoritmo, ovvero l\'**upper bound più basso** e il **lower bound più alto**.\n \n ### O grande\n \n > "O grande" \n > O di g(n)\n > "big-O"\n \n Per rappresentare la stima, useremo una notazione particolare, detta _O grande_, con la seguente proprietà:\n - Date due funzioni `f(n) : N -> R` e `g(n) : N -> R`, diremo che `f(n) ∈ O(g(n))` se e soltanto se `∃ c > 0, n ≥ n_0` tali che `∀ n ≥ 0, f(n) ≤ c * g(n)`\n \n Quando una funzione è O grande di un altra, significa che **asintoticamente, la funzione in O grande è sempre maggiore di quella che sta venendo stimata**.\n \n > **Ipotesi** \n > - `f(n) = 2n² + 3n + 6` \n > - `g(n) = n²`\n >\n > **Tesi** \n > - `f(n) ∈ O(n²)`.\n >\n > **Svolgimento** \n > Scrivo una disequazione, lasciando intatto il termine noto: \n > 1. `2n² + 3n + 6 ≤ 2n² + 3n² + 6` \n > 2. `n² ≤ 2n² + 3n² + n² = 6n²` per `n ≥ 3`\n >\n > Sappiamo, allora, che `2n² + 3n + 6 ≤ 6n²`.\n \n #### Espressioni di O grande\n \n Questa tabella rappresenta le espressioni di O grande più comunemente utilizzate, in ordine **dalla più forte alla più debole**.\n \n > Più forte significa che, per ogni riga della tabella, tutte le righe sottostanti sono contenute nell\'espressione.\n >\n > Ad esempio, `O(n) ∈ O(1)`.\n \n | Espressione O() | Nome |\n |-----------------|------|\n | `O(1)` | Costante |\n | `O(log log n)` | loglog |\n | `O(log n)` | Logaritmica |\n | ![LaTeX](https://latex.codecogs.com/png.latex?O(n^{1/c})) (per c ≥ 1) | Sublineare |\n | `O(n)` | Lineare |\n | `O(n log n)` | nlogn |\n | `O(n²)` | Quadratica |\n | `O(n³)` | Cubica |\n | `O(n^k)` (per k ≥ 1) | Polinomiale |\n | `O(a^n)` (per a ≥ 1) | Esponenziale |\n | `O(n!)` | Fattoriale |\n \n #### Polinomiale\n \n Molto spesso, noteremo che il tempo richiesto da una funzione è O grande di un polinomio di grado K, ovvero `f(n) ∈ O(n^k)`.\n \n Notiamo che in questi casi, possiamo semplificare l\'O grande al grado massimo del polinomio.\n \n > Ad esempio, `O(n² + n + 1) = O(n²)`.\n \n ##### Dimostrazione\n \n Per `n > 0 \\and 0 ≤ i ≤ k`: \n ![LaTeX](https://latex.codecogs.com/png.latex?a_k%20n^k%20+%20a_{k-1}%20n^{k-1}%20+%20%E2%80%A6%20+%20a_1%20n%20+%20a_0%20%E2%89%A4%20|a_k|%20n^k%20+%20|a_{k-1}|%20n^k%20+%20%E2%80%A6%20+%20|a_1|%20n^k%20+%20|a_0|%20n^k%20=%20(|a_k|%20+%20|a_{k-1}|%20+%20%E2%80%A6%20+%20|a_1|%20+%20|a_0|)%20n^k)\n \n #### Proprietà di O grande\n \n 1. `f(n) ∈ O(g(n)) -> ∀ a > 0, a * f(n) ∈ O(g(n))`.\n 2. `f(n) ∈ O(g(n)), d(n) ∈ O(h(n)) -> f(n) + d(n) ∈ O(g(n) + h(n)) -> O(max\\{g(n), h(n)\\})`\n 3. `f(n) ∈ O(g(n)), d(n) ∈ O(h(n)) -> f(n) * d(n) ∈ O(g(n) * h(n))`\n \n In pratica, se una funzione è la _somma di più termini_, basta guardare l\'**`O()` più grande** tra tutti i suoi termini; se invece una funzione è un _prodotto di più termini_, si possono **omettere le costanti**, e l\'`O()` finale sarà dato dal **prodotto degli `O()`** dei termini.\n \n ## Lower bound\n \n Possiamo anche stimare il _lower bound_, il limite inferiore: il **numero minimo di operazioni** che viene effettuato **nel caso migliore** con la **massima dimensione dell\'ingresso**.\n \n ### Ω()\n \n > "Omega" \n > Omega di g(n)\n > "big-Omega"\n \n Esiste un equivalente di O grande per il lower bound: è detto _Omega grande_, o più semplicemente _Omega_, e funziona nello stesso identico modo, solo... al contrario.\n \n Diremo che `f(n) ∈ Ω(g(n))` se e solo se `∃ c > 0, n_0 ≥ 0 : ∀ n ≥ n_0 f(n) ≥ c * g(n)`.\n \n #### Espressioni di Ω()\n \n Anche in questa tabella le espressioni sono **dalla più forte alla più debole**.\n \n | Espressione Ω() | Nome |\n |-----------------|------|\n | `Ω(n!)` | Fattoriale |\n | `Ω(a^n)` (per a ≥ 1) | Esponenziale |\n | `Ω(n^k)` (per k ≥ 1) | Polinomiale |\n | `Ω(n³)` | Cubica |\n | `Ω(n²)` | Quadratica |\n | `Ω(n log n)` | nlogn |\n | `Ω(n)` | Lineare |\n | ![LaTeX](https://latex.codecogs.com/png.latex?\\Omega(n^{1/c})) (per c ≥ 1) | Sublineare |\n | `Ω(log n)` | Logaritmica |\n | `Ω(log log n)` | loglog |\n | `Ω(1)` | Costante |\n \n ## Tight bound\n \n Quando **upper e lower bound coincidono**, allora otteniamo un _tight bound_.\n \n ### θ()\n \n > "Theta" \n > Theta di g(n)\n > "big-Theta"\n \n Anche per il tight bound abbiamo una notazione equivalente a O grande e Omega grande: _Theta grande_!\n \n Diciamo che `f(n) ∈ θ(g(n))` se e solo se `∃ c_1, c_2 > 0, n_0 ≥ 0 : ∀ n ≥ n_0, c_1 * g(n) ≤ f(n) ≤ c_2 * g(n)`.\n \n Ha la particolarità che non valgono tutte le proprietà degli altri due: va usata quindi con cautela!\n \n ## Risorse utili\n \n [khanacademy.org](https://www.khanacademy.org/computing/computer-science/algorithms/asymptotic-notation/a/big-big-theta-notation)\n ')),n(r.a,null,n(a.a,null,"\n # Problemi algoritmici\n \n Un _problema algoritmico_ è un problema matematico che si vuole provare a risolvere con un algoritmo.\n \n > Dati 10 numeri, voglio sapere se sono in ordine crescente oppure no.\n \n ## Caterigorizzazione\n \n I problemi algoritmici si dividono in tre categorie: problemi _trattabili_, problemi _intrattabili_ e problemi _irrisolvibili_.\n \n ### Problema trattabile\n \n Perchè un problema algoritmico sia _trattabile_, deve avere **almeno un algoritmo con upper bound polinomiale**.\n \n > Questo significa che il tempo impiegato da un computer per risolvere il problema rimane ragionevole, e che quindi può essere utilizzato in maniera efficiente.\n \n La trattabilità è un campo ancora parecchio aperto: esistono anche tanti problemi di cui non si è ancora dimostrata la trattabilità o intrattabilità.\n \n > La [fattorizzazione](https://it.wikipedia.org/wiki/Fattorizzazione) è uno di questi problemi: l'assenza di una dimostrazione è ciò che la rende uno dei pilastri della sicurezza informatica moderna.\n \n ### Problema intrattabile\n \n Se **un problema non ha nessun algoritmo con upper bound polinomiale**, allora si dice che è **intrattabile**.\n \n ### Problema irrisolvibile\n \n Se **non esistono algoritmi per risolvere un problema**, allora questo si dice **irrisolvibile**.\n \n > [Dato un algoritmo con certi input, riusciamo a capire con un algoritmo se la sua esecuzione termina o no?](https://en.wikipedia.org/wiki/Halting_problem)\n \n ### Upper e lower bound di problemi\n \n Si può anche trovare un _upper bound_ e un _lower bound_ per un problema, ma bisogna generalizzare di più.\n \n L'**upper bound di un problema** è il minimo upper bound di tutti gli algoritmi che lo risolvono; deve esistere almeno un algoritmo che lo risolva che abbia lo stesso _upper bound_. E' praticamente il tempo migliore per risolvere il problema dato.\n \n Il **lower bound di un problema** è il minimo lower bound di tutti gli algoritmi che lo risolvono; non deve esistere nemmeno un algoritmo che abbia un lower bound migliore. E' il numero assolutamente minimo di operazioni richieste, non si può fare meglio di così.\n \n In particolare, abbiamo che l'_upper bound di un algoritmo_ -> l'_upper bound del suo problema_, \n e il _lower bound di un problema_ -> il _lower bound di un suo algoritmo_.\n \n Generalmente, il _lower bound di un problema_ è una rappresentazione abbastanza accurata della sua difficoltà.\n ")),n(r.a,null,n(a.a,null,"\n # Ricerca binaria\n \n Non credo di aver bisogno di studiare la ricerca binaria, quindi non ho preso appunti a riguardo.\n \n Se non siete me, e state cercando informazioni a riguardo, andate a vedere su Wikipedia!\n ")),n(r.a,null,n(a.a,null,"\n # Divide et impera\n \n Un modo efficace per risolvere un problema è di usare il metodo _divide et impera (et combina)_.\n \n - _Divide_: Divido il problema in **tanti sottoproblemi**.\n - _Impera_: **Risolvo indipendentemente dal resto** ciascuno dei sottoproblemi.\n - _Combina_: **Combino** i risultati dei sottoproblemi per **risolvere il problema principale**.\n \n ## Ricorsione\n \n Un algoritmo (o funzione) si dice _ricorsivo_ quando durante l'esecuzione **richiama sè stesso**.\n \n Dato che tutti gli algoritmi devono avere termine entro un tempo finito, se scriviamo una funzione ricorsiva è fondamentale finire con un **caso base**, che non chiami ulteriormente la ricorsione.\n \n Se esiste una funzione ricorsiva, allora esiste _sempre_ una _funzione iterativa_ che darà lo stesso risultato.\n \n > Sul pratico, una funzione ricorsiva tipicamente è **più costosa** del suo equivalente iterativo: se possibile, quindi, la ricorsione andrebbe evitata.\n \n #### Pseudocodice di esempio\n \n ```python\n def fattoriale(n):\n # Caso base; la ricorsione finisce e dà un risultato fisso\n if n <= 1:\n return 1\n # Caso ricorsivo; la funzione restituisce il risultato di sè stessa (ma con parametri diversi)\n else:\n return n * fattoriale(n - 1)\n ```\n ")),n(r.a,null,n(a.a,null,"\n # Master Theorem\n \n Il _Master Theorem_ è uno dei teoremi più importanti dell'algoritmica.\n \n Esso permette di **calcolare l'upper bound di un algoritmo ricorsivo** in modo piuttosto semplice.\n \n ## Ipotesi\n \n Dato un algoritmo:\n - Con uno o più casi base\n - Che richiama la funzione ricorsiva un numero n di volte\n \n ## Tesi\n \n Allora, il suo upper bound avrà la formula:\n \n ![](https://quicklatex.com/cache3/89/ql_08d29a7e55d561a900570bc83b93ff89_l3.png)\n ")),n(r.a,null,n(a.a,null,"\n # Caso particolare del Master Theorem\n \n ## Ipotesi\n \n Se: \n ![](https://quicklatex.com/cache3/57/ql_e34dc27b42831d3c3ff671b0f3861257_l3.png)\n \n Ovvero, se la dimensione dell'input viene divisa ad ogni ciclo da una costante b, è polinomiale e il caso base è costante...\n \n ## Tesi\n \n Allora: \n ![](https://quicklatex.com/cache3/ca/ql_26e3557a6ca2d6ac4b8481e7c5263fca_l3.png)\n \n > In pratica, se il costo dominante è quello della parte \"fissa\" dell'algoritmo, esso sarà `O(n^d)`, mentre se il costo dominante è quello delle chiamate ricorsive, esso sarà `O(n^{log_b e})`. \n > Se nessuno dei due è dominante... si dividono circa in parti uguali, creando un costo di `O(n^d log n)`.\n ")),n(r.a,null,n(a.a,null,"\n # Ordinamento\n \n Un problema molto frequente nell'informatica consiste nell'**ordinare efficientemente grandi quantità di elementi**.\n \n Esistono [tantissimi](https://it.wikipedia.org/wiki/Algoritmo_di_ordinamento) algoritmi per effettuare l'ordinamento. \n L'**efficienza** di ciascuno **varia** di caso in caso: alcuni sono estremamente efficienti se quasi tutti i numeri sono già nell'ordine giusto; altri, invece, potrebbero impiegare tantissimo tempo.\n \n In termini matematici, abbiamo:\n \n - **Input:** A[n]\n - **Output:** B, ∀ i < n, A[i] ≤ A[i+1]\n \n ## Ordinamento tramite confronto\n \n L'ordinamento \"tradizionale\" è detto _ordinamento tramite confronto_: funziona sempre, e **non ha altri modi di ottenere informazioni** se non con l'operazione logica di confronto tra i dati.\n \n ### Limiti\n \n E' un problema risolto: è dimostrabile che il suo **lower bound** è **`Ω(n log n)`**; possiamo quindi dire che qualsiasi algoritmo di ordinamento è in `Ω(n log n)`, e se riusciamo a trovare un algoritmo di ordinamento in `O(n log n)` siamo riusciti a raggiungere il massimo dell'efficienza.\n \n #### Dimostrazione\n \n Consideriamo **tutte le possibili permutazioni** della sequenza da ordinare: sono `n!`.\n \n Per ogni confronto che effettuiamo, **riduciamo la quantità di permutazioni** correttamente ordinate; prima o poi, rimarrà **una sola possibilità**.\n \n **TODO, non trovo la spiegazione corretta!**\n \n ### Esempi\n \n Algoritmi che effettuano l'ordinamento tramite confronto sono:\n - _Bubble sort_\n - _Merge sort_\n - _Insertion sort_\n - _Quick sort_\n - _Heap sort_\n - E tanti, tanti altri!\n \n ## Ordinamento con altri mezzi\n \n Esistono algoritmi che ricavano informazioni in altri modi, diversi dal confronto.\n \n Essi possono avere un lower bound più basso di `O(n log n)`, però hanno spesso limitazioni sul loro utilizzo.\n \n ### Esempi\n \n - _Counting sort_, indicizza i valori da ordinare\n - _Radix sort_, guarda singolarmente le cifre dei valori\n - _Sleep sort_, sfrutta i thread e la funzione sleep per ordinare valori\n - E altri ancora!\n ")),n(r.a,null,n(a.a,null,"\n # Insertion sort\n \n L'_insertion sort_ è una soluzione **iterativa** all'ordinamento per confronto.\n \n ## Funzionamento\n \n Considero la sequenza divisa in **due parti**: una parte **ordinata** e una parte **non ordinata**.\n \n Parto dal primo elemento della lista: è sempre ordinato con sè stesso. \n Poi, aggiungo uno alla volta i numeri della parte non ordinata a quella ordinata; prima trovo in quale posizione dovrò andare a mettere il numero, poi **faccio slittare tutti i numeri dopo quella posizione** avanti di 1, in modo da **creare lo spazio** in cui infine **inserirò** il numero.\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(n²)` | `Ω(n)` | - |\n \n Nel _caso migliore_ (**lista già ordinata**), il numero da inserire è già nella posizione giusta, quindi non devo effettuare altri confronti oltre il primo, rendendo il lower bound dell'algoritmo `Ω(n)`.\n \n Nel _caso peggiore_ (**lista nell'ordine inverso**), dobbiamo confrontare il numero da inserire con tutti gli altri nella parte ordinata: dobbiamo allora eseguire `1+2+3+4+5+… = \\frac{(n-1)(n)}{2}` confronti; ciò significa che l'upper bound è `O(n²)`!\n \n ## Pseudocodice\n \n ```python\n def insertion_sorted(lista):\n # Itero su tutti i numeri della lista, dal primo all'ultimo.\n for divisore_ord in range(len(lista)):\n # Partendo dalla posizione attuale, creo l'indice di divisione numeri ordinati maggiori e minori\n divisore_magg = divisore_ord\n # Faccio slittare avanti i numeri maggiori di quello che stiamo inserendo\n # Se l'indice divisore_magg raggiunge 0, vuol dire che tutti i numeri della lista sono maggiori del numero attuale \n while divisore_magg >= 0 and lista[divisore_magg-1] > lista[divisore_magg]:\n # Scambio la posizione dei due elementi con gli indici specificati\n # Funzione inventata \n lista[divisore_magg], lista[divisore_magg-1] = lista[divisore_magg-1], lista[divisore_magg]\n # Diminuisco il separatore di 1\n divisore_magg -= 1\n ```\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/bn/sorting)\n ")),n(r.a,null,n(a.a,null,"\n # Merge sort\n \n Il _merge sort_ è una soluzione **ricorsiva** all'ordinamento per confronto.\n \n ## Funzionamento\n \n Per questo algoritmo, utilizziamo la tecnica del **divide et impera**.\n \n 1. _Divide_: Divido A in **due parti**.\n 2. _Impera_: Metto **separatamente in ordine** le parti.\n 3. _Unisci_: **Unisco** le due parti.\n \n Consideriamo come **caso base** della ricorsione una parte composta da un numero, che ovviamente è già ordinata con sè stessa.\n \n ### Merge\n \n Per **unire le due parti** usiamo una funzione detta `merge()`.\n \n Costruiamo una nuova sequenza uguale alla sequenza 1, ma **aggiungiamo alla fine un valore sentinella** sempre maggiore di tutti gli elementi contenuti.\n \n > ```\n > | 1 | 3 | 7 | 8 | ∞ |\n > ```\n \n Facciamo **la stessa cosa** per la sequenza due.\n \n > ```\n > | 2 | 4 | 5 | 6 | ∞ |\n > ```\n \n Prendo i primi numeri delle due sequenze e **metto il più piccolo nella sequenza iniziale**.\n \n > ```\n > | 1 | 2 | 3 | | | | | | \n > | | | 7 | 8 | ∞ | \n > | | 4 | 5 | 6 | ∞ | \n > ```\n \n **Continuo** finchè non ho messo tutti i numeri; **grazie alla sentinella non usciremo mai dalla sequenza**, in quanto essa è sempre maggiore di tutti gli altri numeri.\n \n > ```\n > | 1 | 2 | 3 | 4 | 5 | 6 | | | \n > | | | 7 | 8 | ∞ | \n > | | | | | ∞ |\n > ```\n \n Quando **rimangono solo le sentinelle** significa che abbiamo aggiunto tutti gli elementi, e quindi abbiamo finito.\n \n > ```\n > | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | \n > | | | | | ∞ | \n > | | | | | ∞ | \n > ```\n \n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(n log n)` | `Ω(n log n)` | **`θ(n log n)`** |\n \n Il merge sort è un algoritmo ricorsivo con un **caso base in tempo costante** e che **richiama sè stesso 2 volte**.\n \n ```latex\n T(n) =\\\\\n \\\\\n Θ(1) \\qquad n=1\\\\\n 2 T(\\frac{n}{2}) + Θ(n) \\qquad n \\neq 1\n ```\n \n Applicando il **caso particolare del Master Theorem**, otteniamo:\n \n ```latex\n T(n) =\\\\\n \\\\\n Θ(1) \\qquad n=1\\\\\n Θ(n log n) \\qquad n \\neq 1\n ```\n \n ## Pseudocodice\n \n ```python\n def merge_sorted(part):\n # Caso base\n if len(part) == 1:\n return part\n # Divide\n middle = len(part) // 2\n part_a = part[:middle]\n part_b = part[middle:]\n # Impera\n sort_a = merge_sorted(part_a)\n sort_b = merge_sorted(part_b)\n # Combina\n return merge(sort_a, sort_b)\n ```\n \n ## Visualizzazione\n \n [hackerearth.com](https://www.hackerearth.com/practice/algorithms/sorting/merge-sort/visualize/)\n \n [visualgo.net](https://visualgo.net/bn/sorting) (Nota: visualizza solo la fase _Unisci_ del sort)\n ")),n(r.a,null,n(a.a,null,"\n # Quick sort\n \n Il _quick sort_ è un altro approccio **ricorsivo** all'ordinamento per confronto.\n \n ## Funzionamento\n \n Anche qui, applichiamo il **divide et impera**.\n \n 1. _Divide_: Scelgo un **pivot** qualsiasi all'interno della lista. Metto alla sua **sinistra tutti i numeri minori** e alla sua **destra tutti i numeri maggiori**.\n 2. _Impera_: Eseguo un **quick sort su entrambe le sottoliste**.\n \n ### Esempi\n \n #### Iterazione con partizioni bilanciate\n \n Osserviamo come si formi una partizione con tre elementi e una con quattro. \n \n ```\n |¦ [2] 8 7 1 3 5 6 {4}\n 2 |¦ [8] 7 1 3 5 6 {4}\n 2 |8 ¦ [7] 1 3 5 6 {4}\n 2 |8 ¦ [7] 1 3 5 6 {4}\n 2 |8 7 ¦ [1] 3 5 6 {4}\n 2 1 |7 8 ¦ [3] 5 6 {4}\n 2 1 3 |8 7 ¦ [5] 6 {4}\n 2 1 3 |8 7 5 ¦ [6] {4}\n 2 1 3 |8 7 5 6 ¦ [{4}]\n [2 1 3] {4} [8 5 6 7]\n ```\n \n #### Iterazione con partizioni sbilanciate\n \n Osserviamo come si formi una partizione con **zero elementi** e una con tre.\n \n ```\n |¦ [4] 7 3 {1}\n |4 ¦ [7] 3 {1}\n |4 7 |¦ [3] {1}\n |4 7 3 |¦ [{1}]\n [] {1} [4 7 3]\n ```\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(n²)` | `Ω(n log n)` | - |\n \n Il costo della funzione è dato dalla somma del costo per **dividere in due partizioni** con il costo per realizzare il **Quick sort delle due sottopartizioni**\n \n Possiamo applicare allora il **Master Theorem generale**:\n \n ```latex\n T(n)\\\\\n =\\\\\n Θ(1) \\qquad per\\ n = 1\\\\\n T(q) + T(dim_lista - pivot - 1) + Θ(n) \\qquad per\\ n > 1\n ```\n \n ### Il caso migliore\n \n Se il pivot `q` è la **mediana della partizione** che stiamo ordinando, si vengono a creare due _sottopartizioni bilanciate_, e sostituendo otteniamo:\n \n ```latex\n T(n)\\\\\n =\\\\\n Θ(1) \\qquad per\\ n = 1\\\\\n 2 T(\\frac{n}{2}) + Θ(n) \\qquad per\\ n > 1\n ``` \n \n Possiamo allora applicare il **Master Theorem particolare**:\n \n ```latex\n T(n)\\\\\n =\\\\\n Θ(1) \\qquad per\\ n = 1\\\\\n Θ(n log n) \\qquad per\\ n > 1\n ```\n \n ### Il caso peggiore\n \n Se il pivot è uno degli **estremi dell'array**, si creano due _partizioni sbilanciate_: una delle due sottoliste è sempre vuota! \n Allora:\n \n ```latex\n T(n) = T(n-1) + Θ(n)\\\\\n = T(n-2) + Θ(n-1) + Θ(n)\\\\\n = T(n-3) + Θ(n-2) + Θ(n-1) + Θ(n)\\\\\n = …\n ∈ Θ(n^2)\n ```\n \n > \"Non date da mangiare sequenze ordinate al Quicksort, gli sono indigeste.\"\n \n ## Pseudocodice\n \n ```python\n def partition(partizione, inizio, fine):\n \"\"\"Dividi una partizione in due, usando l'ultimo elemento come pivot.\n \n Note utili:\n partizione[fine] è il pivot\n partizione[maggiori] è il primo numero dei maggiori\n partizione[non_iterati] è l'elemento su cui si sta iterando al momento\"\"\"\n # Crea il primo separatore (la | pipe nell'esempio)\n maggiori = inizio\n # Crea il secondo separatore (la ¦ broken pipe nell'esempio)\n non_iterati = inizio\n # Itera su ogni numero tra inizio e fine (escluso!)\n while non_iterati < fine:\n # Se l'elemento su cui stiamo iterando è minore del pivot\n if partizione[non_iterati] <= partizione[fine]:\n # Mettilo nell'insieme dei minori, scambiandolo con il primo numero dei maggiori e incrementando il primo separatore\n partizione[maggiori], partizione[non_iterati] = partizione[non_iterati], partizione[maggiori]\n maggiori += 1\n # Incrementa sempre il secondo separatore\n non_iterati += 1\n # Inserisci il pivot tra le due sottopartizioni create, \n partizione[fine], partizione[non_iterati] = partizione[non_iterati], partizione[fine]\n return maggiori\n ```\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/bn/sorting) (Nota: invece che prendere l'ultimo numero come pivot prende il primo, cambiando leggermente l'algoritmo.)\n \n ## Note per l'esame\n \n > La domanda che fa sempre è **\"Qual è la sequenza di pivot utilizzata?\"**\n \n > Elementi da soli _non_ vengono presi come pivot!\n ")),n(r.a,null,n(a.a,null,'\n # Counting sort\n\n Il _counting sort_ è un approccio diverso all\'ordinamento: **non usa il confronto**!\n \n ## Requisiti\n \n Il counting sort può essere utilizzato solo su **sequenze di numeri interi**, e solo se **siamo a conoscenza del minimo e del massimo** dei numeri contenuti nell\'array, ed essi non sono troppo distanti uno dall\'altro. \n (La memoria occupata dal counting sort aumenta linearmente con la differenza tra minimo e massimo!)\n \n Per semplicità, consideriamo il **minimo `0`**. \n L\'input allora sarà una sequenza di interi `A`, e il valore del **massimo `k`**, tale che `∀ n ∈ A, 0 \\leq n \\leq K`.\n \n ## Funzionamento\n \n Il counting sort **conta le ripetizioni** delle chiavi nella sequenza originale e in seguito **sovrascrive i valori** della sequenza con i valori ordinati ripetuti il numero di volte che sono stati individuati nella sequenza.\n \n > ```\n > 1 4 5 3 4 1 4 2 5 1\n > ```\n >\n > L\'`1` appare 3 volte, il `2` 1 volta, il `3` 1 volta, il `4` tre volte e il `5` due volte.\n >\n > La sequenza viene quindi così sovrascritta:\n > ```\n > 1 1 1 3 4 1 4 2 5 1 # Sovrascriviamo la sequenza con 1 ripetuto 3 volte\n > 1 1 1 2 3 4 4 4 5 1 # Sovrascriviamo la sequenza con 2, 3, 4 ripetuti rispettivamente 1 1 e 3 volte\n > 1 1 1 2 3 4 4 4 5 5 # Sovrascriviamo la sequenza con 5 ripetuto 2 volte: abbiamo finito!\n > ``` \n \n Esiste anche una **versione stabile** del counting sort che, invece che sovrascrivere, **sposta i valori**, mantenendo le informazioni aggiuntive nel caso invece che interi fossero altri tipi di dati.\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(k + n)` | `Ω(k + n)` | **`θ(k + n)`** |\n \n L\'algoritmo è composto da quattro parti:\n - Ricerca del minimo e massimo (in `θ(n)`)\n - Inizializzazione dell\'indice (in `θ(k)`)\n - Conteggio dei numeri (in `θ(n)`)\n - Sovrascrittura dei numeri (in `θ(k + n)`)\n \n `2 + O(k) + O(n) + O(k + n) -> O(k + n)`\n \n Notiamo che `k` è costante, l\'algoritmo è `O(n)`, estremamente efficiente.\n \n ## Pseudocodice\n \n ```python\n def counting_sort(lista: typing.List[int]):\n """Ordina in-place una lista con il counting sort."""\n # Trovo la dimensione della lista\n dim = len(lista)\n # Trovo il massimo e il minimo all\'interno della lista\n minimo = min(lista)\n massimo = max(lista)\n # Creo l\'indice dei numeri, in modo che sia lungo k e pieno di 0\n indice = [0 for _ in range(minimo, massimo+1)]\n # Conto i numeri presenti, scorrendo su lista e aggiungendo 1 al numero corrispondente\n for i in range(dim):\n indice[lista[i]] += 1\n # Sovrascrivo i numeri nella lista\n count = 0\n for pos, val in enumerate(indice):\n for _ in range(val):\n indice[count] = pos\n count += 1\n \n def stable_counting_sorted(lista: typing.List[int], k: int) -> typing.List[int]:\n """Ordina stabilmente una lista con il counting sort stabile, e restituiscila."""\n # Trovo la dimensione della lista\n dim = len(lista)\n # Trovo il massimo e il minimo all\'interno della lista\n minimo = min(lista)\n massimo = max(lista)\n # Creo l\'indice dei numeri, in modo che sia lungo k e pieno di 0\n indice = [0 for _ in range(minimo, massimo+1)]\n # Conto i numeri presenti, scorrendo su lista e aggiungendo 1 al numero corrispondente\n for i in range(dim):\n indice[lista[i]] += 1\n # Faccio diventare l\'indice "il numero di numeri \\leq i"\n for i in range(len(indice)):\n if i == 0:\n continue\n indice[i] += indice[i-1]\n assert indice[-1] == dim\n # Creo una nuova lista, che sarà quella che verrà restituita\n nuova = [None for _ in range(dim)]\n # Inizio a posizionare i numeri, al contrario\n for i in range(0, dim, -1):\n nuova[indice[lista[i]]] = lista[i]\n indice[lista[i]] -= 1\n return nuova\n ```\n ')),n(r.a,null,n(a.a,null,"\n ## Introduzione alle Strutture Dati\n\n Una _struttura dati_ è un modo in cui si possono organizzare i dati di un programma.\n \n Si possono definire in due modi: **elementari** e **astratte**.\n \n ### Strutture dati elementari\n \n Le strutture _elementari_ dipendono strettamente dal modo in cui vengono memorizzati i dati.\n \n > **Array** e **liste** sono strutture dati elementari: sono definite dicendo come sono memorizzati i dati, rispettivamente, in celle contigue di memoria e da una serie di nodi con un valore e che puntano al successivo.\n \n ### Strutture dati astratte\n \n Le strutture _astratte_ sono separate dal modo in cui vengono memorizzati i dati, sono più ad alto livello, e si definiscono descrivendo le **proprietà** della struttura e i **metodi** che su di essa possono essere effettuate.\n \n > Una _classe_ in un qualsiasi linguaggio di programmazione è una struttura dati astratta.\n \n > Una _pila_ astratta:\n > - memorizza dati tutti dello stesso tipo\n > - `pop()`, estrae dalla pila l'ultimo valore inserito\n > - `push(val)`, aggiunge alla pila un valore\n > - `top()`, permette di vedere l'ultimo valore inserito nella pila\n > - `vuota()`, dice se la pila è vuota oppure no.\n ")),n(r.a,null,n(a.a,null,'\n # Array\n\n Un _array_ è sequenza di dati di **lunghezza conosciuta**, tutti dello **stesso tipo** e di una **dimensione fissa**, immagazzinata in **blocchi di memoria contigui**.\n \n ## Proprietà\n \n - E\' possibile accedere a tutti i blocchi di memoria conoscendo la loro **posizione relativa al primo** elemento.\n \n ## Metodi\n \n ```python\n class Array:\n def __init__(self, size, type=int): "Crea un array di dimensione size di elementi di tipo int."\n def __getitem__(self, index): "Restituisci il valore alla posizione index."\n def __setitem__(self, index, value): "Cambia il valore alla posizione index."\n ```\n \n ### Costo computazionale\n \n Tutte le operazioni su un array sono in **accesso immediato `O(1)`**!\n ')),n(r.a,null,n(a.a,null,'\n # Lista\n \n Una _lista_ è una sequenza di dati immagazzinata in **blocchi di memoria qualsiasi**.\n \n ## Proprietà\n \n Ogni dato ha un **riferimento** alla collocazione di memoria **successiva** (un puntatore): insieme, sono detti un _nodo_.\n \n E\' di **natura ricorsiva**: qualsiasi nodo di una lista può essere visto come inizio della lista con sè stesso e i suoi successivi.\n \n ## Metodi\n \n ```python\n class LinkedList:\n def __init__(self, value, next: typing.Optional[Node] = None):\n self.value = value\n self.next: typing.Optional[Node] = next\n \n def is_empty(self) -> bool: "Restituisce se la lista è vuota o no."\n def is_full(self) -> bool: "Restituisce se la lista è piena o no.\n def append(self, value): "Aggiunge un nuovo elemento in testa alla lista."\n def insert(self, value, index): "Inserisce un elemento dopo il nodo in posizione index."\n def insert_node(self, value, node): "Inserisce un nuovo elemento subito dopo un dato nodo."\n def find(self, node) -> int: "Trova l\'indice del nodo."\n def delete(self, value): "Elimina il primo nodo con quel valore dalla lista."\n def delete_node(self, node): "Elimina il nodo dalla lista."\n def forward(self, index) -> Node: "Restituisce il nodo in posizione index."\n ```\n \n ### Costo computazionale\n \n #### `List.forward(index)`\n \n Per raggiungere l\'`n`-esimo elemento, bisogna _scorrere tutti gli elementi prima di esso_: è dunque un **accesso sequenziale** in **`O(n)`**.\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/list)\n ')),n(r.a,null,n(a.a,null,'\n # Coda (Queue)\n\n Una _coda_ è come una pila, ma segue la strategia **First In, First Out** (il primo inserito sarà il primo a essere estratto).\n \n ## Proprietà\n \n - I dati vi possono essere aggiunti solo tramite il **metodo `enqueue()`**\n - I dati possono essere estratti solo tramite il **metodo `dequeue()`**\n - Verranno restituiti i valori inseriti secondo la strategia **First In, First Out** (il primo inserito sarà il primo a essere estratto).\n \n > Hai presente quando fai la fila per pagare al supermercato? Beh, è quello, però non si possono superare le altre persone in nessun modo.\n \n ## Metodi\n \n ```python\n class Queue:\n def __init__(self): "Crea una nuova coda."\n def is_empty(self) -> bool: "Restituisce vero se la coda è vuota."\n def enqueue(self, data): "Aggiunge un dato alla coda."\n def first(self) -> ...: "Restituisce il primo dato della coda."\n def dequeue(self) -> ...: "Restituisce il primo dato della coda e lo rimuove."\n ```\n \n ## Implementazione tramite lista\n \n Posso implementare la coda con una lista, ma per realizzare l\'implementazione più efficiente devo tenere anche un puntatore all\'ultimo elemento della coda, in modo da non doverla scorrere ogni volta che voglio effettuare un\'operazione.\n \n Chiamiamo i due puntatori `head` e `tail` rispettivamente.\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/list)\n ')),n(r.a,null,n(a.a,null,'\n # Pila (Stack)\n\n Una _pila_ è una struttura dati contenente **valori omogenei**.\n \n ## Proprietà\n \n - I dati vi possono essere aggiunti solo tramite il **metodo `push()`**\n - I dati possono essere estratti solo tramite il **metodo `pop()`**\n - Verranno restituiti i valori inseriti secondo la strategia **Last In, First Out** (l\'ultimo inserito sarà il primo a essere estratto).\n \n > Ci si può immaginare una pila di libri, da cui si può solo prendere un libro alla volta, quello più in alto.\n \n ## Metodi\n \n ```python\n class Stack:\n def __init__(self): "Crea una nuova pila."\n def is_empty(self) -> bool: "Restituisce vero se la pila è vuota."\n def push(self, data): "Aggiunge un dato alla pila."\n def top(self) -> ...: "Restituisce il primo dato della pila."\n def pop(self) -> ...: "Restituisce il primo dato della pila e lo rimuove."\n ```\n \n ## Implementazione tramite lista\n \n Utilizzando una lista possiamo realizzare una pila!\n \n La direzione dei puntatori sarà dall\'ultimo al primo, che non punterà più a nessuno.\n \n Il costo di tutti i metodi è `Θ(1)`!\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/list)\n ')),n(r.a,null,n(a.a,null,"\n # Albero radicato\n \n Un _albero radicato_ è una struttura dati di **natura ricorsiva** che organizza i dati in maniera **non-lineare**.\n \n ## Proprietà\n \n - Ogni nodo dell'albero ha un **unico genitore**: `∀ (padre, figlio), (padre' figlio) ∈ E \\implies padre = padre'`\n - Ogni nodo dell'albero può avere **un numero qualsiasi di figli**.\n \x3c!----\x3e\n - I **nodi superiori al padre** vengono chiamati _antenati_.\n - I **nodi inferiori ai figli** vengono chiamati _discendenti_.\n \x3c!----\x3e\n - Nodi **senza padre** sono detti _radice_: `\\notexists (padre, radice) ∈ E`\n - Nodi **con padre e figli** sono detti _rami_ o interni.\n - Nodi **senza figli** sono detti _foglie_.\n \x3c!----\x3e\n - La **distanza** tra il nodo radice e i suoi discendenti è detta _livello_:\n - I figli immediati sono di livello 1.\n - I \"nipoti\" (figli dei figli) sono di livello 2.\n - I figli dei nipoti sono livello 3.\n - E così via.\n - Il **livello massimo** all'interno di un albero è detto _altezza_, _profondità_ oppure _h_, ed è sempre `1 ≤ h ≤ n-1`.\n \x3c!----\x3e\n - Un albero ha sempre `n-1` archi.\n \n ## Alberi particolari\n \n ### Alberi `d`-ari\n \n Un albero _`d`-ario_ è un particolare tipo di albero che **limita il numero massimo di figli di un nodo** a `d`.\n \n > Un albero _binario_ può avere **massimo 2 figli** per ogni nodo; un albero _ternario_ ne può avere **3**; un albero _`17`-ario_ ne potrà avere **17**\n \n #### Alberi completi\n \n Un albero `d`-ario si dice _completo_ se **tutti i nodi hanno 0 o `d` figli**, e mai una numero in mezzo.\n \n #### Alberi bilanciati\n \n Un albero `d`-ario si dice _bilanciato_ se **tutti i livelli eccetto l'ultimo** hanno il numero massimo di figli.\n \n #### Alberi perfettamente bilanciati\n \n Un albero `d`-ario si dice _perfettamente bilanciato_ se **tutti i livelli incluso l'ultimo** hanno il numero massimo di figli.\n \n ##### Particolarità degli alberi binari perfettamente bilanciati\n \n Si può dimostrare per induzione che:\n - Hanno sempre `2^h` foglie.\n - Hanno sempre `2^{h+1}-1` (`\\sum_i=0^n 2^i`) nodi.\n - L'altezza è in `Θ(log n)`.\n \n ## Implementazione degli alberi\n \n Possiamo scegliere se usare una rappresentazione con array o con nodi e puntatori: ognuna ha vantaggi e svantaggi diversi.\n \n ### Implementazione tramite array\n \n E' suggerito se l'albero è regolare; più è simile a un albero d-ario completo, meglio è.\n \n ### Implementazione tramite nodi e puntatori\n \n Più adatta ad alberi irregolari.\n \n Se l'albero è regolare, creiamo il numero esatto di campi:\n \n - Valore\n - Figlio1\n - Figlio2\n - _Opzionale:_ Padre\n \n Se un albero è irregolare, creiamo una specie di lista:\n \n - Valore\n - Primo figlio\n - Prossimo fratello\n - _Opzionale:_ Padre\n ")),n(r.a,null,n(a.a,null,"\n #### Breadth-first search (BFS)\n\n La _breadth-first search_ è un algoritmo che visita **ogni livello** dell'albero in ordine, dal più basso al più alto.\n \n ## Funzionamento\n \n > 1. __Visita radice__\n > 2. __Visita figli__\n > 3. __Visita nipoti__\n > 4. __Visita pronipoti__\n \n Si può implementare con una coda, in cui verranno inseriti i figli del nodo visitato da visitare ed estratti dopo avere completato la visita del livello attuale.\n \n ## Pseudocodice \n \n ```python\n def bfs(radice):\n c = Queue()\n c.enqueue(radice)\n while not c.is_empty():\n nodo = c.dequeue()\n print(nodo)\n for figlio in nodo.figli:\n nodo.enqueue(figlio)\n ```\n ")),n(r.a,null,n(a.a,null,"\n # Depth-First Search\n\n La _depth-first search_ è un algoritmo che visita **tutti i sottoalberi di un figlio** prima di passare ad un altro sfruttando la natura ricorsiva degli alberi.\n \n ## Funzionamento\n \n Ci sono diverse versioni della depth-first search: ognuna visita la radice in un momento diverso.\n \n ### DFS previsita (pre-order)\n \n La _DFS pre-visita_ visita la **radice per prima**, poi tutti i sottoalberi formati dai figli uno dopo l'altro.\n \n > 1. __Visita radice__\n > 2. dfs_pre_order(figlio1)\n > 3. dfs_pre_order(figlio2)\n \n ### Postvisita (post-order)\n \n La _DFS postvisita_ visita prima tutti i sottoalberi dei figli, e **alla fine la radice**.\n \n > 1. dfs_post_order(figlio1)\n > 2. dfs_post_order(figlio2)\n > 3. __Visita radice__\n \n ### Invisita (in-order)\n \n La _DFS invisita_ visita **un certo numero di figli**, poi la radice, e infine i figli restanti.\n \n > 1. dfs_in_order(figlio1, 1)\n > 2. __Visita radice__\n > 3. dfs_in_order(figlio2, 1)\n ")),n(r.a,null,n(a.a,null,"\n # Albero binario di ricerca\n\n ## Proprietà\n \n - Albero **binario**\n - Chiavi appartenenti ad un **insieme totalmente ordinato** (N, Q, R, ma non C)\n \x3c!----\x3e\n - Per ogni nodo con valore `x`, se un valore `v` è nel sottoalbero di sinistra allora `v ≤ x`, mentre se è nel sottoalbero di destra allora `v > x`.\n \n ## Costo computazionale\n \n - Trovare un valore: `O(h)`\n - Ordinare i valori: `O(n)`\n - Trovare il minimo: `O(h)`\n - Trovare il massimo: `O(h)`\n - Inserire un elemento: `O(h)`\n - Cancellare un elemento: `O(h)`\n \n `h` vale `log n` in un albero perfettamente bilanciato, e più l'albero diventa sbilanciato, più si avvicina a `n`, raggiungendola nel caso l'albero sia una lista.\n \n ## Pseudocodice\n \n ### Cancellazione ricorsiva\n \n ```python\n def delete(tree, key):\n if tree is not None:\n # Se ho trovato il nodo che cercavo...\n if tree.key == key:\n # E c'è una sola diramazione...\n # Semplicemente stacca il nodo come in una lista.\n if tree.left is None:\n return tree.right\n if tree.right is None:\n return tree.left\n # Altrimenti, diventa il minimo dell'albero di destra\n tree.key = tree.right.min()\n # Ed eliminalo dal sottoalbero\n tree.right = delete(tree.right, tree.key)\n # Se la chiave attuale è diversa da quella che cerchiamo, continuo a navigare l'albero\n elif tree.key < key:\n tree.left = delete(tree.left, key)\n else:\n tree.right = delete(tree.right, key)\n return tree\n ```\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/bst)\n \n ## Approfondimenti\n \n Esistono alberi più avanzati che mantengono le proprietà degli alberi binari di ricerca, ma che si autobilanciano, come il [Red Black Tree](https://it.wikipedia.org/wiki/RB-Albero).\n ")),n(r.a,null,n(a.a,null,'\n # Heap binario\n \n L\'_heap binario_ è un **albero binario bilanciato a sinistra**.\n \n ## Proprietà\n \n - _Proprietà strutturale_:\n - L\'albero è **perfettamente bilanciato** in tutti i livelli tranne l\'ultimo\n - Nell\'ultimo livello, le foglie occupano le **posizioni più a sinistra** possibili\n - _Proprietà di ordinamento_:\n - La chiave di un qualsiasi nodo è **più piccola** di tutte quelle dei nodi **del suo sottoalbero**\n \n ## Metodi\n \n ```python\n class Heap:\n def __init__(self, H): ...\n def _heapify_ancestors(self, i): "Ripristina le proprietà dell\'heap per il nodo all\'indice specificato e i suoi genitori."\n def minimum(self): "Restituisce la chiave con il valore minimo in H."\n def decrease_value(self, index, new_value): "Diminuisce il valore della chiave all\'indice index a new_value."\n def insert(self, value): "Inserisci un nuovo valore nell\'albero."\n def _heapify_children(self, i): "Ripristina le proprietà dell\'heap per il nodo all\'indice specificato e i suoi figli."\n def pop(self): "Restituisce la chiave con il valore minimo, e la elimina."\n def from_list(l): "Crea un heap da una lista."\n ```\n \n ## Implementazione con un array\n \n Possiamo implementare l\'albero utilizzando un array con le chiavi dell\'albero memorizzate nell\'ordine _breadth-first_.\n \n L\'indice del figlio sinistro può essere trovato a `2i+1`, mentre l\'indice del figlio sinistro può essere trovato a `2i+2`; il genitore è a `i//2-1`.\n \n ### Pseudocodice\n \n ```python\n class Heap:\n def __init__(self, size):\n self.array = Array(size) # Il tipo Array non esiste; consideriamolo pseudocodice\n self.next_value = 0\n \n def _heapify_ancestors(self, index)\n """Ripristina le proprietà dell\'heap per il nodo all\'indice specificato e i suoi genitori.\n \n Costo:\n O(log n)"""\n # Trovo l\'indice del genitore\n parent = index // 2 - 1\n # Controllo se viene mantenuta la proprietà di ordinamento dell\'heap\n if self.array[index] < self.array[parent]:\n # Scambio i valori dei due nodi\n self.array[index], self.array[parent] = self.array[parent], self.array[index]\n # Faccio la stessa cosa con il genitore\n self._heapify(parent)\n \n \n def minimum(self):\n """Restituisce la chiave con il valore minimo in H.\n \n Costo:\n O(1)"""\n return self.array[0]\n \n def decrease_value(self, index, new_value):\n """Diminuisce il valore della chiave all\'indice index a new_value.\n \n Costo:\n O(log n)"""\n # Diminuisco il valore del nodo\n self.array[index] = new_value\n # Aggiorno l\'heap \n self._heapify(index)\n \n def insert(self, value):\n """Inserisci un nuovo valore nell\'albero.\n \n Costo:\n O(log n)"""\n # Trovo l\'indice in cui inserire il valore\n index = self.next_index \n # Aggiungo il valore in fondo\n self.array[index] = value\n # Aggiorno l\'heap\n self._heapify(index)\n \n def _heapify_children(self, index):\n """Ripristina le proprietà dell\'heap per il nodo all\'indice specificato e i suoi figli.\n \n Costo:\n O(log n)"""\n # Trovo l\'indice dei figli\n left = index * 2 + 1\n right = index * 2 + 2\n # Mi assicuro che i figli esistano\n try:\n # Guardo quale dei figli è maggiore\n if self.array[left] > self.array[right]:\n # Scambio i valori\n self.array[left], self.array[index] = self.array[index], self.array[left]\n # Ripeto la procedura sul figlio modificato\n self._heapify_children(left)\n else:\n # Scambio i valori\n self.array[right], self.array[index] = self.array[index], self.array[right]\n # Ripeto la procedura sul figlio modificato\n self._heapify_children(left)\n except IndexError:\n # La foglia non ha figli: ho finito!\n return\n \n def pop(self):\n """Restituisce la chiave con il valore minimo, e la elimina.\n \n Costo:\n O(log n)"""\n # Mi salvo il valore della radice\n value = self.array[0]\n # Sostituisco la radice con l\'ultima foglia a destra\n self.array[0], self.array[self.next_value] = self.array[self.next_value], self.array[0]\n ### Non bisognerebbe eliminare la foglia...?\n # Riordino l\'heap\n self._heapify_children(0)\n return value\n \n @staticmethod\n def from_list(l):\n """Crea un heap da una lista.\n \n Costo:\n O(n log n), ma si può abbassare"""\n heap = Heap(len(l)))\n heap.array = Array.from_list(l) # Pseudocodice\n heap.next_value = len(l)\n # Cominciamo a riordinare l\'heap dalla fine, in modo che rispetti le proprietà\n for index in range(heap.next_value, 0, -1):\n heap._heapify_children(index)\n ```\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/heap)\n ')),n(r.a,null,n(a.a,null,"\n # Coda con priorità\n \n La _coda con priorità_ è una struttura dati dal funzionamento molto simile a quello di una coda, ma invece che restituire il primo elemento inserito, essa restituisce l'**elemento con il valore di priorità minore**.\n \n ## Proprietà\n \n - Ogni elemento è una coppia costituita da **valore** e **priorità** (un numero intero).\n - Nuovi elementi possono essere aggiunti solo tramite il **metodo `insert()`**\n - Gli elementi possono essere estratti solo tramite il **metodo `pop()`**\n - Verranno restituiti i valori inseriti secondo la strategia **Lower Priority** (l'elemento con la priorità minore sarà il primo ad essere restituito).\n - E' possibile diminuire la priorità di un elemento (e quindi anticipare la sua estrazione)\n \n ## Metodi\n \n ```python\n class PriorityQueue:\n def __init__(self): ...\n def insert(self, new_elem: Element): ...\n def minimum(self) -> Element: ...\n def pop(self) -> Element: ...\n def decrease_priority_for(self, elem: Element, priority: int): ...\n ```\n \n ## Implementazione con lista\n \n E' possibile implementare la coda con priorità tramite una **lista**: l'inserimento di nuovi valori diventerà molto efficiente, ma tutte le altre operazioni saranno linearmente lente.\n \n ### Costo computazionale\n \n - *insert()*: `O(1)`\n - *minimum()*: `O(n)`\n - *pop()*: `O(n)`\n - *decrease_priority_for()*: `O(n)`\n \n ## Implementazione con lista ordinata\n \n Implementando la coda con priorità con una **lista ordinata** si avrà un costo di ordinamento elevato negli inserimenti e modifiche alla priorità, ma costi costanti nell'estrazione di un elemento.\n \n ### Costo computazionale\n \n - *insert()*: `O(n)`\n - *minimum()*: `O(1)`\n - *pop()*: `O(1)`\n - *decrease_priority_for()*: `O(n)`\n \n ## Implementazione con heap\n \n La **soluzione migliore** è quella di implementare la coda con priorità tramite un **heap**: tutti i costi saranno logaritmici, eccetto l'inserimento che sarà costante.\n \n - `insert()` costa `O(1)`\n - `minimum()` costa `O(log n)`\n - `pop()` costa `O(log n)`\n - `decrease_priority_for()` costa `O(log n)`\n \n ## Approfondimenti\n \n Esistono code con priorità che restituiscono **l'elemento con priorità maggiore**, invece che quello minore.\n ")),n(r.a,null,n(a.a,null,"\n # Heap sort\n\n L'_heap sort_ è un algoritmo di ordinamento per confronto **iterativo**.\n \n ## Funzionamento\n \n Per effettuare un heap sort, creiamo un **heap massimo** in cui inseriamo tutti i valori che vogliamo ordinare.\n \n Una volta applicate le proprietà dell'heap, chiamiamo una versione particolare di `heap.pop()` che invece che rimuovere dall'array i valori estratti li posiziona nello spazio creatosi in fondo.\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(n log n)` | `Ω(n log n)` | **`θ(n log n)`** |\n ")),n(r.a,null,n(a.a,null,"\n # Grafo\n \n Un _grafo_ è una struttura dati che rappresenta elementi interconnessi tra loro.\n \n Esistono due tipi di grafi: _orientati_ e _non orientati_.\n \n Per semplicità, consideriamo i nostri nodi numerati da 1 a `n`.\n \n ## Proprietà\n \n - Gli elementi sono rappresentati tramite _nodi_.\n - Il loro _grado_ è dato dal **numero degli archi** che vi incidono.\n - Se il grafo è orientato, hanno anche un _in-degree_ (**numero di archi entranti**) e un _out-degree_ (**numero di archi uscenti**).\n - Le connessioni tra elementi sono rappresentate tramite _archi_.\n - Un arco _incide_ esattamente su **due nodi**.\n - Se il grafo è orientato, sono _uscenti_ da uno dei due nodi ed _entranti_ nell'altro.\n - Sono matematicamente meno del **quadrato dei nodi**.\n \n ## Grafi particolari\n \n ### Catena\n \n Una _catena_ è un **grafo non orientato** composto da una **sequenza di nodi** aventi un **grado massimo di 2** tutti collegati tra loro.\n \n ### Cammino\n \n Un _cammino_ è un **grafo orientato** composto da una **sequenza di nodi** aventi un **in-degree** e un **out-degree** **massimo di 1**, collegati tra loro in modo che partendo dal primo e seguendo gli archi sia possibile arrivare all'ultimo.\n \n ### Cricca\n \n Una _cricca_ è un grafo in cui **tutti i nodi sono collegati tra loro**.\n \n Se il grafo è **non orientato**, la cricca ha `((n-1)n)/2` archi.\n \n Se il grafo è **orientato**, ha per ogni coppia un arco in entrambe le direzioni, quindi ha `(n-1)n` archi.\n \n ### Direct Acyclic Graph\n \n Un _DAG_ è un grafo diretto che non contiene nessun ciclo.\n \n Su di esso possiamo effettuare un ordinamento, detto _linearizzazione_, tra i nodi: otteniamo l'_ordine topologico_.\n \n I primi elementi dei DAG sono detti _Source_ (_Sorgente_), mentre gli ultimi sono detti _Sink_ (_Pozzo_).\n \n #### Albero\n \n Un **albero** può essere considerato un DAG con una **sorgente singola** e le **foglie come pozzi**.\n \n ### Grafo fortemente connesso\n \n Un insieme di nodi `V` di un **grafo diretto** `G` si dice una _componente fortemente connessa_ se:\n \n 1. Per ogni coppia di nodi `∀ u, v ∈ V' : ∃ un cammino u->v in G'`\n 2. Massimale (non può diventare più grande)\n \n > Praticamente una componente fortemente connessa è un gruppo di nodi tra i quali si può viaggiare liberamente da e a qualsiasi nodo al suo interno.\n \n Un grafo si dice _fortemente connesso_ se l'insieme `V` coincide con l'insieme dei nodi del grafo `G`.\n \n > Se partendo da qualsiasi nodo di un grafo riesco ad arrivare a qualsiasi altro nodo, allora il grafo è fortemente connesso.\n \n Inoltre, se creiamo un nuovo grafo, in cui **ogni nodo rappresenta una componente fortemente connessa** del nostro grafo iniziale, **otteniamo un DAG**, perchè tutti i cicli sono stati integrati nella componente.\n \n ### Trasposto di un grafo\n \n Il _trasposto_ di un **grafo diretto** `G` è il grafo stesso con gli archi che però vanno nella **direzione opposta**.\n \n ### Grafo pesato\n \n Un _grafo pesato_ è un particolare grafo che associa a ciascun arco un **costo** per attraversarlo.\n \n #### Costi negativi\n \n I costi possono anche essere negativi: rappresenteranno allora un **guadagno** ottenuto attraversando il nodo.\n \n ### Minimum spanning tree\n \n Un _minimum spanning tree_ è il **sottoinsieme degli archi** di un **grafo non diretto** che **connettono tutti i nodi** con il **minor costo possibile**.\n \n I MST hanno [molte proprietà](https://en.wikipedia.org/wiki/Minimum_spanning_tree#Properties); sono troppe da scrivere qui, e probabilmente non ci interesseranno nemmeno.\n \n ## Implementazione tramite matrice di adiacenza\n \n Possiamo implementare un grafo creando una **matrice di `bool` di dimensione `n * n`** in cui le **caselle collegate sono vere** e le caselle non collegate sono false.\n \n > Ad esempio, possiamo implementare un grafo non orientato in questo modo (`█` indica l'esistenza di un collegamento e ` ` indica la sua assenza):\n >\n > | |1|2|3|\n > |-|-|-|-|\n > |1|░|░|░|\n > |2|█|░|░|\n > |3|█| |░|\n >\n > Esistono gli archi `1-2` e `1-3`, ma non esiste un collegamento `2-3`.\n \n > Un grafo orientato invece si può implementare così:\n >\n > | |1|2|3|\n > |-|-|-|-|\n > |1|░|█| |\n > |2|█|░| |\n > |3|█| |░|\n >\n > Esistono gli archi `1->2`, `2->1` e `3->1`, ma non ci sono collegamenti `2->3`, `1->3` e `3->2`.\n \n ### Costo computazionale\n \n #### Tempo\n \n Le matrici di adiacenza portano alla realizzazione di algoritmi molto veloci: verificare l'esistenza di un arco è in `O(1)`!\n \n Abbiamo però penalità significative quando vogliamo effettuare operazioni sugli archi: ad esempio, trovare il trasposto di un grafo implementato con una matrice di adiacenza è in `O(nodi²)`.\n \n #### Memoria\n \n E' poco efficiente in quanto a memoria: l'upper bound è in `O(n^2)`. \n \n ## Implementazione tramite liste di adiacenza\n \n Un'alternativa alla matrice di adiacenza è quella di creare un'**array di liste**, le quali contengono i **vicini di ciascun nodo**.\n \n > |Posizione|Lista|\n > |-|-|\n > |1|[2, 3]|\n > |2|[]|\n > |3|[1]|\n >\n > Esistono gli archi `1->2`, `1->3`, e `3->1`, ma non esistono `2->1`, `2->3` e `3->2`.\n \n ### Costo computazionale\n \n #### Tempo\n \n Utilizzando le liste di adiacenza, il tempo richiesto per verificare l'esistenza di un arco sale a `O(max-out-degree)`.\n \n E' efficace però quando il problema che vogliamo risolvere riguarda operazioni su archi: trovare la trasposta è in `O(archi)`.\n \n #### Memoria \n \n La memoria richiesta dalle liste di adiacenza è minore di quella delle matrici: l'upper bound è in `O(nodi + archi)`.\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/graphds)\n ")),n(r.a,null,n(a.a,null,"\n # Visitare un grafo\n \n Come per gli alberi radicati, esistono due modi per visitare un grafo: _depth-first search_ e _breadth-first search_.\n \n In entrambi i casi, non visito mai due volte lo stesso nodo, e come risultato ottengo **molteplici alberi**, il cui insieme viene detto _foresta di copertura_.\n \n Se il grafo che vogliamo visitare è diretto, allora dobbiamo **considerare come vicini solo gli archi uscenti**\n \n ## Depth-first search\n \n La DFS ci può risultare utile per **identificare le componenti connesse** di un grafo e **identificare eventuali cicli**.\n \n ### Funzionamento\n \n Posso utilizzare la DFS per classificare gli archi di un grafo in quattro categorie:\n \n - _Tree_, archi che ci fanno **scoprire un nuovo nodo**\n - _Forward_, archi che ci portano a un **discendente**\n - _Back_, archi che ci portano ad un **antenato**\n - _Cross_, archi che **connettono due sottoalberi** diversi\n \n Usiamo due array inizializzati a 0 chiamati `pre` e `post`, grandi quanto il numero di archi del grafo, che ci indicano rispettivamente quando un nodo è stato scoperto e quando è terminata la visita. \n Inoltre, creiamo una variabile `clock` che avanza ad ogni evento. \n Alla scoperta di un nuovo nodo, mettiamo il valore attuale di `clock` all'interno di `pre[n]`. \n Alla fine della visita di un nodo invece mettiamo il valore di `clock` in `post[n]`.\n \n **Durante la visita**, gli archi avranno i seguenti valori:\n - _Tree_: `pre[dst] == 0`\n - _Forward_: `pre[src] < pre[dst] && post[dst] > 0`\n - _Back_: `pre[dst] < pre[src] && post[dst] == 0`\n - _Cross_: Tutti gli altri (`post[dst] < pre[src]`)\n \n **A fine visita**, gli archi avranno i seguenti valori:\n - _Tree_: `pre[dst] < pre[dst] < post[dst] < pre[src]`\n - _Forward_: `pre[dst] < pre[dst] < post[dst] < pre[src]`\n - _Back_: `pre[src] < pre[dst] < post[dst] < post[src]`\n - _Cross_: `pre[dst] < post[dst] < pre[src] < post[src]`\n \n Se un **grafo non diretto** contiene degli **archi Back**, allora esso **conterrà un ciclo**.\n \n #### DFS nel grafo trasposto\n \n Se effettuo una DFS sul trasposto di un grafo, posso **scoprire i nodi che hanno un cammino verso l'origine**.\n \n #### DFS nella componente fortemente connessa\n \n Se effettuo una DFS in una componente fortemente connessa e nella sua trasposta, il **`post` della trasposta sarà sempre minore** del `post` della componente originale.\n \n ### Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(nodi + archi)` | `Ω(nodi + archi)` | **`θ(nodi + archi)`** |\n | Memoria | `O(nodi)` | `Ω(nodi)` | **`θ(nodi)`** |\n \n ### Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/dfsbfs)\n \n ## Breadth-first search\n \n La BFS ci può risultare utile per **trovare tutti i nodi a una certa distanza** da un'origine.\n \n ### Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(nodi + archi)` | `Ω(nodi + archi)` | **`θ(nodi + archi)`** |\n | Memoria | `O(nodi + archi)` | `Ω(nodi + archi)` | **`θ(nodi + archi)`** |\n \n ### Pseudocodice\n \n Come per gli alberi, la implementiamo in modo **iterativo**:\n \n ```python\n queue = [starting_node]\n parents = [None for node in graph.nodes]\n distance = [-1 for node in graph.nodes]\n \n # TODO: controllami quando sei più sveglio\n \n while queue:\n node, source, distance = queue.pop(0)\n parents[node.number] = source\n distance[node.number] = distance\n for neighbour in node.neighbours:\n queue.append((neighbour, node, distance+1))\n ```\n \n > Nella coda, la distanza massima tra un nodo e l'altro è 1.\n \n ### Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/dfsbfs)\n ")),n(r.a,null,n(a.a,null,"\n # Algoritmi greedy\n\n Un modo per risolvere problemi algoritmici può essere usare una **tecnica** _greedy_.\n \n Le tecniche greedy consistono nel effettuare tanti piccoli passi, ed effettuare una **scelta** in base ai dati **locali al passo attuale**.\n \n > Scegli il numero di monete più piccole possibili per comporre €1.12.\n >\n > L'algoritmo cerca di scegliere sempre la moneta più grande possibile compatibile con il prezzo in quel momento, quindi:\n > | Moneta scelta | Rimanente |\n > |---------------|-----------|\n > | € 1.00 | € 0.12 |\n > | € 0.10 | € 0.02 |\n > | € 0.02 | € 0.00 |\n \n ## Esempi\n \n Sono algoritmi greedy:\n \n - L'_Algoritmo di Dijkstra_\n - L'_Algoritmo di Kruskal_\n - L'_Algoritmo di Prim_\n ")),n(r.a,null,n(a.a,null,"\n # Percorso più breve\n\n Trovare il _percorso più breve_ (o _cammino minimo_) tra due nodi di un **grafo pesato** è un problema frequente nell'informatica; per questo, sono stati sviluppati [numerosi algoritmi](https://en.wikipedia.org/wiki/Shortest_path_problem) per risolverlo.\n \n > Ad esempio, il pathfinding dei nemici nei videogiochi, oppure Google Maps!\n \n ## Percorso più breve da una sorgente singola\n \n Una sottocategoria del problema del percorso più breve è il caso in cui ci interessa sapere i percorsi più brevi che **partono da uno specifico nodo del grafo**: è detto problema del _percorso più breve da una sorgente singola_, o _single-source shortest path_.\n \n Si può notare che se il grafo contiene **costi negativi** allora è possibile che il percorso più breve non esista, in quanto diventa possibile la comparsa di **cicli di costo infinitamente negativo**.\n \n Possiamo notare che, se il percorso più breve tra `A` e `D` è `A-B-C-D`, allora il cammino minimo tra `B` e `D` passerà obbligatoriamente per `C` (`B-C-D`).\n Diremo più avanti che il percorso più breve ha una **sottostruttura ottimale**.\n \n ### Esempi\n \n Alcuni algoritmi che trovano il percorso più breve sono:\n - L'_Algoritmo di Dijkstra_\n - L'_Algoritmo di Bellman-Ford_\n - La [_ricerca A*_](https://en.wikipedia.org/wiki/A*_search_algorithm)\n ")),n(r.a,null,n(a.a,null,"\n # Algoritmo di Dijkstra\n \n L'_Algoritmo di [Dijkstra](https://upload.wikimedia.org/wikipedia/commons/8/85/Dijkstra.ogg)_ è un algoritmo che risolve il problema del **percorso più breve da una sorgente singola** per grafi con pesi **reali positivi** `\\mathbb{R}^+`.\n \n L'algoritmo trova tutti i percorsi più brevi per raggiungere qualsiasi nodo del grafo partendo da un dato nodo, assieme al costo richiesto per farlo.\n \n ## Funzionamento\n \n 1. Separiamo tutti i nodi del grafo in due gruppi: **visitati** e **non visitati**. \n - Tutti i nodi partono da **non visitati**.\n 2. Per ogni nodo, manteniamo un valore \"**costo richiesto per raggiungerlo**\", che verrà cambiato man mano che l'algoritmo avanza.\n - Il costo di partenza è `+∞`.\n - Il costo sarà **definitivo per i nodi visitati**, e **provvisorio per i non visitati**.\n 3. Creiamo un insieme detto _frontiera_ che conterrà tutti i **nodi non visitati adiacenti** a quelli visitati.\n 4. Prendiamo il nodo iniziale, che avrà un **costo di `0`**, e definiamolo il nodo _attuale_.\n 5. Finchè ci sono dei nodi non sono stati visitati, ripetiamo il seguente ciclo:\n 1. Aggiungiamo i nodi adiacenti al nodo attuale alla frontiera.\n - Il costo per raggiungerli sarà il **costo per il nodo attuale sommato al costo dell'arco** che li connette al nodo attuale. \n Se questo **costo** risulta essere **minore del costo provvisorio** precedente, esso **diventerà il nuovo costo**.\n - Questa operazione è detta _rilassamento dell'arco_.\n 2. Facciamo diventare **visitato** il nodo attuale.\n - Il percorso che abbiamo fatto per raggiungerlo è obbligatoriamente il più breve.\n 3. Il prossimo nodo attuale sarà il nodo di frontiera con un costo più basso.\n - Per questo, è possibile definire l'algoritmo di Dijkstra come un **algoritmo greedy**.\n \n ### Non funziona se...\n \n L'algoritmo smette di funzionare nel caso in cui siano presenti **costi negativi** e il grafo non sia **aciclico**, in quanto non saremmo mai in grado di rendere visitato un nodo.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | `O(nodi + archi) log nodi)` |\n \n ### Scomposizione\n \n - Inizializzazione: `O(nodi)`\n - Creazione coda priorità: `O(nodi log nodi)`\n - Ciclo: `O((nodi + archi) log nodi)`\n \n ## Pseudocodice\n \n ```python\n import math\n \n class Info:\n def __init__(self, distance=math.inf, previous=None):\n self.distance = distance\n self.previous = previous\n \n def dijkstra(graph, start):\n data = [Info() for node in graph.nodes]\n queue = PriorityQueue([start])\n while queue:\n node = queue.pop()\n for arc in node.connections:\n other = arc.other(node)\n if data[node.number].distance + arc.cost < data[other].distance:\n data[other].distance = data[node.number].distance + arc.cost\n queue.decrease_priority_for(other, data[other].distance)\n data[v].previous = node\n return data\n ```\n \n ## Visualizzazione\n \n [Visualgo](https://visualgo.net/en/sssp)\n ")),n(r.a,null,n(a.a,null,"\n # Algoritmo di Bellman-Ford\n\n L'_Algoritmo di Bellman-Ford_ è un algoritmo che, come l'Algoritmo di Dijkstra, risolve il problema del **percorso più breve da una sorgente singola**, però, a differenza da quest'ultimo, l'Algoritmo di Bellman-Ford accetta in input anche grafi con pesi **reali** `\\mathbb{R}` (sia positivi, sia negativi).\n \n ## Funzionamento\n \n L'approccio dell'algoritmo è simile a quello di Dijkstra: entrambi usano il **rilassamento** degli archi per ottenere un costo provvisorio per il raggiungimento di un nodo, ma invece che rilassare solo l'arco con costo inferiore, questo algoritmo **rilassa tutti gli archi** ripetutamente, eliminando la frontiera e il problema dei nodi negativi.\n \n L'operazione di rilassamento è ripetuta `nodi - 1` volte, ovvero la **lunghezza massima** di un cammino aciclico all'interno di un grafo.\n \n Possiamo individuare dopo i rilassamenti se è presente un nodo con un **ciclo negativo**: ci basta controllare se esiste un arco che connette due nodi con una distanza incompatibile: se `a.distanza + arco.costo < b.distanza`, allora è presente un ciclo negativo.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | `O(nodi * archi)` |\n \n ## Pseudocodice\n \n > TODO\n \n ## Visualizzazione\n \n [Visualgo](https://visualgo.net/en/sssp)\n ")),n(r.a,null,n(a.a,null,'\n # Disjoint set\n \n Il _disjoint set_ è una struttura dati che rappresenta elementi di un insieme raggruppati in **sottoinsiemi disgiunti**.\n \n ## Metodi\n \n ```python\n class DisjointNode:\n def __init__(self): ...\n def find_set(self): "Trova il rappresentante dell\'elemento."\n def union(self, other): "Unisce i sottoinsiemi che contengono questo nodo e `other`."\n ```\n \n ## Implementazione tramite array\n \n Possiamo implementare il disjoint set con due array: uno per l\'**indice del rappresentante** e uno per il **rango dell\'insieme**.\n \n Un singoletto avrà **sè stesso come rappresentante** e **rango `0`**.\n \n ### Costo computazionale\n \n - *create_set()*: `O(1)`\n - *find_set()*: `O(h)`\n - *union()*: `O(h)`\n \n ### Pseudocodice\n \n ```python\n class DisjointNode:\n def __init__(self):\n self.parent = self\n self.rank = 0\n \n def find_set(self):\n element = self\n while self.parent != element:\n element = self.parent\n return element\n \n def union(self, other):\n repres_self = self.find_set()\n repres_other = other.find_set()\n if repres_self == repres_other:\n return\n if repres_self.rank < repres_other.rank:\n repres_greater = repres_other\n repres_lesser = repres_self\n else:\n repres_greater = repres_self\n repres_lesser = repres_other\n repres_lesser.parent = repres_greater\n if repres_greater.rank == repres_lesser.rank:\n repres_greater.rank += 1\n ```\n \n ### Visualizzazione\n \n [cs.usfca.edu](https://www.cs.usfca.edu/~galles/JavascriptVisual/DisjointSets.html)\n ')),n(r.a,null,n(a.a,null,"\n # Trovare il minimum spanning tree\n\n Un altro problema ricorrente riguardante i grafi è trovare il _minimum spanning tree_ di un dato grafo non diretto.\n \n > E' utile per trovare il modo più efficiente per connettere le cose: ad esempio, per decidere la struttura di una rete internet!\n \n ## Esempi\n \n Gli algoritmi principali che risolvono il problema sono due, ed entrambi sono **algoritmi greedy**:\n \n - L'_Algoritmo di Kruskal_\n - L'_Algoritmo di Prim_\n ")),n(r.a,null,n(a.a,null,"\n # Algoritmo di Kruskal\n \n L'_Algoritmo di Kruskal_ è un algoritmo **greedy** che **trova il minimum spanning tree** di un grafo.\n \n ## Funzionamento\n \n 1. Ripetiamo questa procedura finchè tutti i nodi non sono connessi:\n 1. Prendiamo ad ogni passo **l'arco meno costoso** del grafo non ancora aggiunto all'insieme.\n 2. Assicuriamoci che **non si creino cicli**: se non se ne verrebbero a creare, possiamo **aggiungere l'arco all'insieme**.\n - Gli archi devono quindi connettere nodi in **componenti connesse diverse**.\n - Possiamo rappresentare le componenti connesse con un **Disjoint Set**.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | `O(archi²)` |\n \n ### Scomposizione\n \n - DisjointSet.__init__(): `O(archi)`\n - Per ogni ciclo: `O(archi²)`\n - DisjointSet.find_set(): `O(1)`\n - DisjointSet.union(): `O(archi)`\n \n ## Pseudocodice\n \n ```python\n def minimum_spanning_tree_kruskal(graph):\n ds = DisjointSet()\n for node in graph.nodes:\n ds.create_set(node)\n arcs = []\n sorted_arcs = sorted(graph.arcs, key=lambda arc: arc.cost)\n for arc in sorted_arcs:\n if ds.find_set(node.start) != ds.find_set(node.end):\n arcs.append(arc)\n ds.union(node.start, node.end)\n return arcs\n ```\n ")),n(r.a,null,n(a.a,null,"\n # Algoritmo di Prim\n \n L'_Algoritmo di Prim_ è un altro algoritmo **greedy** che **trova il minimum spanning tree** di un grafo.\n \n ## Funzionamento\n \n Creo una **coda con priorità** in cui inserisco tutti gli archi visibili dal mio albero, in cui la chiave è il **costo dell'arco**.\n \n Per trovare l'arco con costo più piccolo posso **estrarre un arco** dalla coda: la priorità ci garantisce che esso è l'**arco meno costoso**.\n \n Aggiungo allora un nuovo nodo all'albero, e con esso, **aggiungo alla coda** tutti gli **archi che scoprono un nuovo nodo**.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | `O(archi + nodi log nodi)` |\n \n ## Pseudocodice\n \n ```python\n import math\n \n def minimum_spanning_tree_prim(graph, cost_array, start_node):\n # E' un Array di bool: se l'indice corrispondente al nodo è uguale a true, vuol dire che il (nodo è contenuto nell'albero.\n contains = [False for _ in range(len(graph))]\n # Contiene il precedente di ogni nodo \n prev = [None for _ in range(len(graph))]\n # Contiene il costo per arrivare a quel nodo\n cost = [math.inf for _ in range(len(graph))]\n # Creo la priority queue\n pq = PriorityQueue(graph.arcs, key=lambda arc: arc.cost)\n # Parto dal nodo `start_index`\n # Il costo dell'origine è 0.\n cost[start_node.index] = 0\n contains[start_node.index] = True\n \n while not pq.is_empty():\n new_node = pq.pop()\n contains[new_node.index] = True\n for arc in new_node.connections:\n other_node = arc.other(new_node)\n if not contains[other_node.index] and cost[other_node.index] > arc.cost:\n cost[other_node.index] = arc.cost\n prev[other_node.index] = new_node\n pq.decrease_priority_for(other_node, arc.cost)\n # L'array di prev rappresenta un albero.\n return prev\n ```_\n ")),n(r.a,null,n(a.a,null,"\n # Compressione\n\n _Comprimere_ un file significa **ridurne le dimensioni** senza modificarne il significato.\n \n ## Categorie\n \n ### Compressione lossless\n \n Nella _compressione lossless_, i dati possono essere decompressi riottenendo una copia identica dell'originale.\n \n > Immaginiamo un file che contiene solo le lettere `a, b, c, d, e, f`.\n >\n > Le lettere compaiono con questa frequenza:\n > |a|b|c|d|e|f|\n > |45%|13%|12%|16%|9%|5%|\n >\n > Possiamo codificare le lettere nel seguente modo:\n > |a|b|c|d|e|f|\n > |`0b0`|`0b100`|`0b101`|`0b111`|`0b1100`|`0b1101`|\n >\n > Scrivere `abacadae` richiederebbe 64 bits con la codifica ASCII estesa, ma in questo modo riusciamo a scriverlo con soli 17 bits!\n \n Le codifiche di un file compresso devono rispettare la proprietà del _Codice a prefisso_, che dice che **nessun codice deve essere il prefisso di un altro codice**; altrimenti, si avrebbero ambiguità nella decodifica.\n \n > a = `1`\n > b = `11`\n >\n > `111` è `ab`, `ba` oppure `aaa`?\n \n Creiamo allora un _albero di decodifica_: un **albero binario** che, leggendo uno ad uno i bit codificati, ci permette di arrivare al **valore del codice presente sulle foglie** dell'albero.\n \n Gli alberi di decodifica sono sempre **completi**.\n \n > Un albero di decodifica incompleto sarebbe non ottimizzato!\n \n #### Esempi\n \n - .png\n - .flac\n - .zip\n - ...\n \n ### Compressione lossy\n \n Nella _compressione lossy_, alcuni dati [solitamente](http://needsmorejpeg.com/) irrilevanti vengono perduti: non si può, dunque, ricostruire l'originale.\n \n #### Esempi\n \n - .jpeg\n - .mp3\n - ...\n ")),n(r.a,null,n(a.a,null,"\n # Algoritmo di Huffman\n\n L'_Algoritmo di Huffman_ è un **algoritmo greedy** per la **costruzione di un albero di decodifica**.\n \n ## Funzionamento\n \n 1. Costruisco **un albero** (con un solo nodo) **per ogni elemento dell'alfabeto**.\n 2. Associo ad **ogni albero la frequenza dell'elemento** da cui è stato creato, per poi inserire tutti gli elementi in una coda con priorità.\n 3. Finchè non ho **un albero solo**:\n 1. Estraggo dalla coda i **due alberi con frequenza minore**.\n 2. **Li rendo fratelli**, creando un nuovo nodo in cui sono uno figlio destro e uno figlio sinistro.\n 3. Associo al nuovo nodo la **somma delle frequenze dei due alberi**, e inserisco il nuovo albero nella coda.\n \n > È molto raro che venga un albero \"dritto\"; se succede, probabilmente c'è qualcosa che non va.\n ")),n(r.a,null,n(a.a,null,"\n # Dizionario\n \n Un _dizionario_ è una struttura dati che **associa dei valori a delle chiavi**.\n \n ## Proprietà\n \n - Ogni elemento del dizionario è un **valore** che è stato **associato a una chiave**.\n - Possiamo aggiungere nuovi elementi con il **metodo `add(chiave, valore)`**.\n - Posiamo estrarre elementi con il **metodo `get(chiave)`**, che restituirà il valore associato a `chiave`.\n - E' possibile rimuovere elementi con il **metodo `delete(chiave)`**.\n - Due elementi con **chiavi diverse** non devono **mai restituire lo stesso valore**.\n \n ## Metodi\n \n Beh... Non ha molto senso in questo caso...\n \n ```python\n dict()\n ```\n \n ## Implementazione con tabella hash\n \n Una _tabella hash_ è un'array di coppie **chiave-valore**, che formano l'insieme _universo_.\n \n Per determinare l'**indice dell'array** in cui inserire una coppia, usiamo una [funzione _hash_](https://it.wikipedia.org/wiki/Hash#Algoritmo_di_hash) sulla chiave, che restituirà **numeri da `0` a `len(hash_table)`**.\n \n ### Risoluzione collisioni\n \n Potrebbe capitare però che **due chiavi diverse abbiano lo stesso indice**. Dobbiamo allora usare un metodo di _risoluzione collisioni_, che mi permetta di distinguere tra chiavi diverse.\n \n #### Lista di trabocco\n \n Possiamo salvare nell'array **liste di coppie** chiave-valore; in caso di collisione, **aggiungo un nuovo elemento alla lista**.\n \n In media, ciascuna di queste liste conterrà `elementi_inseriti / dimensione_tabella` elementi.\n \n #### Indirizzamento aperto\n \n Possiamo decidere di mettere le coppie che non trovano posto nel loro indice in **un altro indirizzo vuoto** dell'array.\n \n Ci sono diversi modi in cui decidere il nuovo indirizzo, ognuno con vantaggi e svantaggi: si può scegliere quello successivo, oppure il primo vuoto dell'array, oppure un indirizzo casuale.\n \n > Python, nei `dict`, usa indirizzamento aperto pseudorandom.\n \n ### Costo computazionale\n \n - Aggiungere una chiave: `O(n)`\n - Trovare una chiave: `O(n)`\n - Eliminare una chiave: `O(n)`\n ")),n(r.a,null,n(a.a,null,"\n # Programmazione dinamica\n \n La _programmazione dinamica_ è una **tecnica** di programmazione che prevede l'**estensione di una soluzione ottima precedente**.\n \n Tutti i problemi in cui si può applicare si possono risolvere anche con la **ricorsione**, ma a differenza della ricorsione, questa tecnica riesce ad evitare di ricalcolare la soluzione per ogni chiamata ricorsiva, ottenendo quindi tempi molto migliori.\n \n Si può applicare solo se un problema ha una **sottostruttura ottimale**, ovvero se la soluzione ottima di un sottoproblema è inclusa nella soluzione ottima del problema. \n \n ## Esempi\n \n - _Problema dello zaino_\n - ...\n \n > Il cammino minimo per raggiungere un nodo in un DAG è dato da `arco.costo + arco.primo_nodo.costo_cammino_minimo()`.\n >\n > ```python\n > def SPD_PD(graph, start):\n > distance = [float(inf) for node in graph.nodes]:\n > distance[start] = 0\n > # I nodi devono essere in ordine di linearizzazione\n > for node in graph.nodes:\n > distance[node] = min([(arc.cost + distance[arc.other(node)] for arc in node.connections])\n > ```\n \n > Ho una sequenza di interi da `a_1` a `a_n`. Voglio trovare la sottosequenza crescente più lunga.\n >\n > 5 2 3 4 7 3 6 3 1 6\n >\n > Trovo tutte le sequenze lunghe 1, e le rendo nodi di un grafo diretto.\n >\n > Da ogni nodo, creo una connessione verso i suoi maggiori.\n >\n > Infine, cerco i cammini massimi del grafo. \n > \n > Essi saranno la soluzione del problema.\n \n > Trova la lunghezza della sottosequenza più lunga che termina con `j`.\n >\n > `L[j]` = lunghezza della sottosequenza più lunga che termina in `j`\n > \n > ```python\n > L[j] = max([1 + L[node] for arc in node.connections)]\n > ```\n >\n > Esempio:\n > ```python\n > L[9] = max([1+L[8], 1+L[3], 1+L[6]])\n > ```\n ")),n(r.a,null,n(a.a,null,"\n # Problema dello zaino\n \n Il problema dello zaino è un problema _pseudo-trattabile_: non abbiamo dimostrazioni di se sia trattabile o intrattabile.\n \n ## Descrizione\n \n > Sei un ladro, e devi mettere **più refurtiva possibile** nello zaino per scappare. \n > Lo zaino può portare **al massimo `dim` kili**.\n >\n > **Quali** (e quanti) oggetti scegli?\n \n | Input | Output |\n |-------|--------|\n | `dim`ensione_zaino, `n`umero_oggetti, `oggetto.peso`, `oggetto.valore` | `profitto_massimo` |\n \n ## Categorie\n \n ### Problema con ripetizione\n \n Puoi prendere **tutte le copie che vuoi** di un oggetto.\n \n #### Soluzione\n \n `K(dim)` è il valore massimo ottenibile con uno zaino di capacità `dim`.\n \n > Se `i` appartenesse alla soluzione ottima, allora `K(dim) = i.valore + K(dim - i.peso)`...\n \n Possiamo dire che `K(dim) = max(i.valore + K(dim - i.peso))`.\n \n Inoltre, `K(0) = 0`.\n \n Ci salviamo tutte le soluzioni da `K(0)` a `K(dim)`, e le usiamo per calcolare il massimo in seguito.\n \n Calcolare `K(dim)` avrà allora un costo di `O(n * dim)`:\n - `n`, perchè trovare il massimo è un'operazione lineare\n - `dim`, perchè `dim` sono tutti i casi tra i quali devo andare a provare\n \n Il costo computazionale, allora, è in `O(n * dim)`. \n \n Però, il **tempo richiesto** dal nostro algoritmo dipende non dalla lunghezza dell'input, bensì dal **valore numerico** di `dim`, che corrisponde alla dimensione dell'array delle soluzioni. \n Allora, si dice che l'algoritmo è in **tempo _pseudo-polinomiale_**.\n \n ### Problema senza ripetizione\n \n Si può prendere **ogni oggetto una volta sola**.\n \n #### Soluzione _bruteforce_\n \n Scelgo se prendere o no l'item 1.\n \n Si creano due percorsi:\n - Non prendo l'oggetto: `valore = 0, peso = 0`\n - Prendo l'oggetto: `valore = oggetto.valore, peso = oggetto.peso`\n \n Continuo a creare percorsi, creando una specie di albero binario.\n \n Se a un certo punto vedo che `valore = x, peso = K` e `valore < x, peso = K`, allora posso escludere automaticamente tutto il sottoalbero destro, perchè non può essere migliore del sinistro: allora, sarò riuscito a ridurre il numero dei casi rispetto alla ricorsione.\n \n ### Problema in due variabili\n \n `K(j, w)` = massimo valore ottenibile con uno zaino di capacità `w` scegliendo gli item da `1` a `j`.\n \n Non possiamo più applicare la soluzione bruteforce, perchè abbiamo due variabili, `j` e `w`.\n \n Allora, prendo l'elemento `j`. Esso può essere o non essere nella soluzione: mi calcolo entrambe le alternative, e mi tengo l'alternativa dal valore più alto.\n \n Se `j` non è nella soluzione, il risultato diventerà `K(j-1, w)`; se invece è nella soluzione, il risultato sarà `j.valore + K(j-1, w-j.peso)`.\n \n In pratica, prendiamo\n \n ```latex\n K(j, w) = max\n \\begin{cases}\n V_j + K(j-1, w-w_j)\n K(j-1, w)\n \\end{cases}\n ```\n \n Costruisco allora una matrice con `j` su un asse e `w` sull'altro. \n Riempio le caselle con il valore di `K(j, w)`. \n Nella casella con `K(j, w)` avremo la soluzione ottima.\n \n Il tempo necessario per riempire tutte le caselle è nuovamente `O(n * w)`, ancora **pseudopolinomiale**.\n \n Per sapere che oggetti ho messo o no devo tenere traccia in qualche modo della catena del calcolo, usando, ad esempio, una pila.\n ")),n(r.a,null,n(a.a,null,"\n # Problemi intrattabili\n \n ## Problema di Set-Cover\n \n ### Input\n \n `U`niverso di `e`lementi\n \n `S`ottoinsieme di `s`ottoinsiemi di elementi di `U`\n \n ### Output\n \n Il minimo `S'`ottoinsieme di `s`ottoinsiemi che copra completamente `U`.\n \n ### Soluzione in `O(n^d)`\n \n Non c'è.\n \n ### Non-soluzione alternativa\n \n Faccio una scelta greedy, ma non posso dimostrare in alcun modo che la soluzione ottenuta sia quella ottima. \n Infatti, l'algoritmo non dà sempre la soluzione ottima, ma dà una soluzione accettabile in tempo polinomiale.\n \n Seleziono sempre il sottoinsieme che copre più elementi mancanti possibili.\n \n #### Costo computazionale\n \n `Costo greedy <= log(numero_elementi) * Costo ottimo`\n ")))}}.call(this,i("hosL").h)}}]); +//# sourceMappingURL=route-AlgoritmiEStruttureDati.chunk.65c03.js.map \ No newline at end of file diff --git a/docs/route-AlgoritmiEStruttureDati.chunk.59c45.js.map b/docs/route-AlgoritmiEStruttureDati.chunk.65c03.js.map similarity index 99% rename from docs/route-AlgoritmiEStruttureDati.chunk.59c45.js.map rename to docs/route-AlgoritmiEStruttureDati.chunk.65c03.js.map 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\n \n {r`\n # Algoritmi e Strutture Dati\n\n Docente: [**Manuela Montangero**](mailto:manuela.montangero@unimore.it)\n\n Crediti: **9 CFU** (72 ore di lezione)\n\n Orario di ricevimento: **Giovedì dalle 14:30 alle 16:30**\n _Mandare una mail prima, altrimenti potrebbe andarsene_\n\n\n #### Regole particolari per le email\n\n - Oggetto \"ASD\"\n - Mail **firmata** con **nome e cognome**\n - Mail spedita dall'**account Unimore**\n\n ### Materiale\n\n Libri:\n - **Introduzione agli Algoritmi e Strutture Dati** di _T.H. Cormen, C. E. Leiserson, R. L. Rivest, C. Stein_\n\n **[Dolly (FIM)](https://dolly.fim.unimore.it/2018/course/view.php?id=26)**\n\n ### Tutorato\n\n Tutor: [**Gianluca d'Addese**](mailto:tutoratoalgoritmi@gmail.com)\n\n Cosa: **Esercizi sugli argomenti visti a lezione** e **preparatori all'esame**\n\n Quando: **Mercoledì dalle 09:00 alle 11:00**...?\n\n ### Esame\n\n Per iscriversi all'esame, bisogna aver passato:\n\n - Analisi matematica (propedeutica)\n - Programmazione I\n\n Formato:\n\n - Prima prova scritta\n - Risolvere problemi con algoritmi proposti a lezione\n - E' un test sulla preparazione\n - Dura 1h30m\n - Non si può usare nessun tipo di materiale\n - Seconda prova scritta\n - Proponi soluzioni per nuovi problemi non studiati a lezione\n - Domande teoriche sugli argomenti studiati\n - Dura 2h\n - E' il giorno dopo la prima prova\n - Si può utilizzare qualsiasi materiale, ma non deve permettere di comunicare\n - Orale facoltativo\n - Solo per chi supera entrambi gli scritti\n - Domande su quello che abbiamo visto a lezione (\"perchè gli algoritmi funzionano?\")\n - Informare via email entro 3 giorni dalla pubblicazione degli esiti della seconda prova\n - L'orale potrebbe migliorare o peggiorare il voto (anche \"molto\")\n\n **Attenzione:** Vengono verbalizzati anche i voti insufficienti; ricordarsi di rifiutarli!\n\n Ci sono i seguenti appelli:\n\n - 3 appelli tra Giugno e Luglio\n - 1 appello a Settembre\n - 2 appelli a Gennaio e Febbraio\n\n Vale il salto di appello se:\n\n - Uno studente regolarmente iscritto **non si presenta** all'appello e non ha avvisato via email almeno il giorno prima.\n - Uno studente ha riportato una **grave insufficienza** in uno dei due scritti, e l'appello successivo è nella stessa sessione\n\n\n ### Note\n\n Il corso è ben collegato con quello di Programmazione 2.\n\n Dormire non fa bene!\n `}\n \n \n {`\n # Il nome del corso\n\n ## Cosa sono gli algoritmi?\n\n Gli algoritmi sono modi sistematici per risolvere problemi.\n\n Sono fondamentali per sviluppare software, in quanto i computer sono eccellenti esecutori di algoritmi.\n\n ## Come si sviluppa un algoritmo?\n\n Innanzitutto, bisogna conoscere gli _input_ e gli _output_ del problema, rispettivamente i dati di partenza e i dati di arrivo di esso; si ha quindi una fase di **ricerca**.\n\n Poi, si deve trovare un procedimento che ci faccia risolvere il nostro problema: è quello che faremo in questa materia!\n\n Infine, bisogna scrivere la soluzione in un modo che possa essere eseguita da un computer: questa è la **programmazione**.\n\n ## Che tipo di problemi possiamo risolvere?\n\n Un algoritmo risolve problemi di tipo generale, non ci interessa sapere _il risultato di 123+456_, ma vogliamo sapere _il risultato di x+y_, dove x e y sono due numeri naturali qualsiasi.\n\n Un problema può essere quindi considerato circa come una **funzione matematica**, che connette ogni input a un output corrispondente.\n\n ## Che caratteristiche ha un algoritmo?\n\n Per prima cosa, ripetendo l'algoritmo più volte con lo stesso ingresso deve dare sempre la stessa uscita come **risultato**, finendo in un **tempo finito**.\n\n Deve essere **ben ordinato**: cambiando l'ordine in cui vengono effettuate le operazioni, è probabile che anche il risultato cambi!\n\n Le sue istruzioni devono essere **non ambigue**, cioè che non possano essere interpretate in più modi, e **effettivamente realizzabili**, cioè realizzabili con l'esecutore che vogliamo usare per eseguire l'algoritmo.\n\n ## Esistono algoritmi equivalenti?\n\n **Sì!** Possono esserci due algoritmi che dati gli stessi input, hanno gli stessi output, e quindi risolvono lo stesso problema.\n\n In compenso, possono avere un numero di operazioni diverse, e quindi essere **uno più veloce** (da eseguire) dell'altro.\n\n ## Come si verifica la correttezza di un algoritmo?\n\n L'algoritmo deve essere **valido per tutti gli input**, anche se questi sono infiniti.\n\n Possiamo effettuare prove matematiche per verificarne la correttezza; il **principio di induzione** è dunque una dei teoremi fondamentali dell'algoritmica.\n\n Possiamo però verificare la _non correttezza_ di un algoritmo trovando un singolo controesempio.\n `}\n \n \n {`\n # Efficienza degli algoritmi\n \n Un buon algoritmo deve essere **efficiente**, ovvero deve usare il minimo delle risorse necessarie, come _usare il minimo di tempo possibile_.\n \n ## Come misuriamo il tempo necessario?\n \n Cerchiamo di astrarre il tempo dal particolare esecutore, e andiamo a contare il numero di operazioni elementari richieste per eseguire il nostro algoritmo nel caso peggiore.\n \n Un algoritmo efficiente, infatti, all'aumentare dei dati in ingresso, diventerà sempre più veloce rispetto a uno non efficiente, anche su computer più lenti!\n \n > Il [Bubble Sort](https://en.wikipedia.org/wiki/Bubble_sort) è sempre più lento di un [Tree Sort](https://en.wikipedia.org/wiki/Tree_sort), anche su computer più lenti, perchè, dovendo ordinare liste sempre più lunghe, prima o poi si raggiunge un punto in cui il primo è più veloce (in termini di tempo) dell'altro.\n \n Dobbiamo andare a vedere, quindi, _il numero di operazioni richieste per ottenere il risultato nel caso peggiore_.\n \n Consideriamo operazioni sia operazioni aritmetiche sia operazioni logiche, e diciamo che ciascuna costa 1.\n \n > L'[algoritmo di Euclide](https://it.wikipedia.org/wiki/Algoritmo_di_Euclide) per l'MCD costa \\`3\\` per ogni iterazione (un giro del ciclo \\`while\\`). Diciamo, allora, che costa \\`3n\\`, dove \\`n\\` è il numero più alto dei due, perchè nel caso peggiore (uno dei due numeri è 1) l'algoritmo compie \\`n\\` iterazioni.\n \n ## Altri parametri ottimizzabili\n \n È possibile che alcuni algoritmi per vari motivi cerchino di ottimizzare altri parametri diversi dal tempo, come ad esempio _la dimensione dell'input_ o la _memoria utilizzata_. \n \n > Generalmente, questo viene fatto sui dispositivi embedded, con memoria molto limitata.\n \n ### Criteri di costo di memoria\n \n Ci sono vari criteri con cui stimare la memoria richiesta da un dato: è possibile che il costo risultante vari in base al criterio scelto!\n \n #### Criterio di costo logaritmico\n \n Un dato costa il numero di bit necessari per rappresentarlo.\n \n > Un int che contiene il numero \\`n\\` costa \\`log_2(n)\\`. \n > Un array di \\`[n]\\` numeri tutti uguali costa \\`n log_2(n)\\`.\n \n #### Criterio di costo uniforme\n \n Un dato costa il numero di elementi che lo costituiscono.\n \n > Un int che contiene il numero \\`n\\` costa \\`1\\`. \n > Un array di \\`[n]\\` numeri costa \\`n\\`. \n > Una matrice \\`[m][n]\\` costa \\`m*n\\`.\n `}\n \n \n {`\n # Modelli algoritmici\n\n Per progettare un algoritmo, abbiamo bisogno di sapere le proprietà del nostro esecutore, ovvero il suo _modello algoritmico_.\n \n > Ad esempio, dobbiamo sapere quali istruzioni è in grado di eseguire, e quanto tempo queste istruzioni richiedono.\n \n ## Il modello RAM\n \n Il modello in uso su tutti i computer attuali è il _modello RAM_: \n \n - In ogni cella di memoria può essere archiviato un dato.\n - Il **tempo di accesso** alle celle è **costante** per tutte le celle.\n - La **memoria** principale è **infinita**.\n - Si ha **un solo processore**.\n `}\n \n \n {`\n # Notazione asintotica\n \n La _notazione asintotica_ è un sistema per **stimare** velocemente il costo di un algoritmo complesso.\n \n Ci permette di **confrontare velocemente il caso peggiore** degli algoritmi.\n \n In particolare, consideriamo il _rapporto tra il numero di operazioni nel caso peggiore e la dimensione dell'input_.\n \n ## Limiti\n \n Possiamo dare a questa stima dei limiti, superiore e inferiore, che rappresenteranno rispettivamente un costo che non sarà **mai superato** e un costo che verrà **sempre superato**.\n \n Chiameremo questi limiti _upper bound_ e _lower bound_; la loro combinazione darà un _tight bound_.\n \n L'obiettivo sarà di _ricavare i bound più precisi possibile_ per un dato algoritmo, ovvero l'**upper bound più basso** e il **lower bound più alto**.\n \n ### O grande\n \n > \"O grande\" \n > O di g(n)\n > \"big-O\"\n \n Per rappresentare la stima, useremo una notazione particolare, detta _O grande_, con la seguente proprietà:\n - Date due funzioni \\`f(n) : N -> R\\` e \\`g(n) : N -> R\\`, diremo che \\`f(n) ∈ O(g(n))\\` se e soltanto se \\`∃ c > 0, n ≥ n_0\\` tali che \\`∀ n ≥ 0, f(n) ≤ c * g(n)\\`\n \n Quando una funzione è O grande di un altra, significa che **asintoticamente, la funzione in O grande è sempre maggiore di quella che sta venendo stimata**.\n \n > **Ipotesi** \n > - \\`f(n) = 2n² + 3n + 6\\` \n > - \\`g(n) = n²\\`\n >\n > **Tesi** \n > - \\`f(n) ∈ O(n²)\\`.\n >\n > **Svolgimento** \n > Scrivo una disequazione, lasciando intatto il termine noto: \n > 1. \\`2n² + 3n + 6 ≤ 2n² + 3n² + 6\\` \n > 2. \\`n² ≤ 2n² + 3n² + n² = 6n²\\` per \\`n ≥ 3\\`\n >\n > Sappiamo, allora, che \\`2n² + 3n + 6 ≤ 6n²\\`.\n \n #### Espressioni di O grande\n \n Questa tabella rappresenta le espressioni di O grande più comunemente utilizzate, in ordine **dalla più forte alla più debole**.\n \n > Più forte significa che, per ogni riga della tabella, tutte le righe sottostanti sono contenute nell'espressione.\n >\n > Ad esempio, \\`O(n) ∈ O(1)\\`.\n \n | Espressione O() | Nome |\n |-----------------|------|\n | \\`O(1)\\` | Costante |\n | \\`O(log log n)\\` | loglog |\n | \\`O(log n)\\` | Logaritmica |\n | ![LaTeX](https://latex.codecogs.com/png.latex?O(n^{1/c})) (per c ≥ 1) | Sublineare |\n | \\`O(n)\\` | Lineare |\n | \\`O(n log n)\\` | nlogn |\n | \\`O(n²)\\` | Quadratica |\n | \\`O(n³)\\` | Cubica |\n | \\`O(n^k)\\` (per k ≥ 1) | Polinomiale |\n | \\`O(a^n)\\` (per a ≥ 1) | Esponenziale |\n | \\`O(n!)\\` | Fattoriale |\n \n #### Polinomiale\n \n Molto spesso, noteremo che il tempo richiesto da una funzione è O grande di un polinomio di grado K, ovvero \\`f(n) ∈ O(n^k)\\`.\n \n Notiamo che in questi casi, possiamo semplificare l'O grande al grado massimo del polinomio.\n \n > Ad esempio, \\`O(n² + n + 1) = O(n²)\\`.\n \n ##### Dimostrazione\n \n Per \\`n > 0 \\\\and 0 ≤ i ≤ k\\`: \n ![LaTeX](https://latex.codecogs.com/png.latex?a_k%20n^k%20+%20a_{k-1}%20n^{k-1}%20+%20%E2%80%A6%20+%20a_1%20n%20+%20a_0%20%E2%89%A4%20|a_k|%20n^k%20+%20|a_{k-1}|%20n^k%20+%20%E2%80%A6%20+%20|a_1|%20n^k%20+%20|a_0|%20n^k%20=%20(|a_k|%20+%20|a_{k-1}|%20+%20%E2%80%A6%20+%20|a_1|%20+%20|a_0|)%20n^k)\n \n #### Proprietà di O grande\n \n 1. \\`f(n) ∈ O(g(n)) -> ∀ a > 0, a * f(n) ∈ O(g(n))\\`.\n 2. \\`f(n) ∈ O(g(n)), d(n) ∈ O(h(n)) -> f(n) + d(n) ∈ O(g(n) + h(n)) -> O(max\\\\{g(n), h(n)\\\\})\\`\n 3. \\`f(n) ∈ O(g(n)), d(n) ∈ O(h(n)) -> f(n) * d(n) ∈ O(g(n) * h(n))\\`\n \n In pratica, se una funzione è la _somma di più termini_, basta guardare l'**\\`O()\\` più grande** tra tutti i suoi termini; se invece una funzione è un _prodotto di più termini_, si possono **omettere le costanti**, e l'\\`O()\\` finale sarà dato dal **prodotto degli \\`O()\\`** dei termini.\n \n ## Lower bound\n \n Possiamo anche stimare il _lower bound_, il limite inferiore: il **numero minimo di operazioni** che viene effettuato **nel caso migliore** con la **massima dimensione dell'ingresso**.\n \n ### Ω()\n \n > \"Omega\" \n > Omega di g(n)\n > \"big-Omega\"\n \n Esiste un equivalente di O grande per il lower bound: è detto _Omega grande_, o più semplicemente _Omega_, e funziona nello stesso identico modo, solo... al contrario.\n \n Diremo che \\`f(n) ∈ Ω(g(n))\\` se e solo se \\`∃ c > 0, n_0 ≥ 0 : ∀ n ≥ n_0 f(n) ≥ c * g(n)\\`.\n \n #### Espressioni di Ω()\n \n Anche in questa tabella le espressioni sono **dalla più forte alla più debole**.\n \n | Espressione Ω() | Nome |\n |-----------------|------|\n | \\`Ω(n!)\\` | Fattoriale |\n | \\`Ω(a^n)\\` (per a ≥ 1) | Esponenziale |\n | \\`Ω(n^k)\\` (per k ≥ 1) | Polinomiale |\n | \\`Ω(n³)\\` | Cubica |\n | \\`Ω(n²)\\` | Quadratica |\n | \\`Ω(n log n)\\` | nlogn |\n | \\`Ω(n)\\` | Lineare |\n | ![LaTeX](https://latex.codecogs.com/png.latex?\\\\Omega(n^{1/c})) (per c ≥ 1) | Sublineare |\n | \\`Ω(log n)\\` | Logaritmica |\n | \\`Ω(log log n)\\` | loglog |\n | \\`Ω(1)\\` | Costante |\n \n ## Tight bound\n \n Quando **upper e lower bound coincidono**, allora otteniamo un _tight bound_.\n \n ### θ()\n \n > \"Theta\" \n > Theta di g(n)\n > \"big-Theta\"\n \n Anche per il tight bound abbiamo una notazione equivalente a O grande e Omega grande: _Theta grande_!\n \n Diciamo che \\`f(n) ∈ θ(g(n))\\` se e solo se \\`∃ c_1, c_2 > 0, n_0 ≥ 0 : ∀ n ≥ n_0, c_1 * g(n) ≤ f(n) ≤ c_2 * g(n)\\`.\n \n Ha la particolarità che non valgono tutte le proprietà degli altri due: va usata quindi con cautela!\n \n ## Risorse utili\n \n [khanacademy.org](https://www.khanacademy.org/computing/computer-science/algorithms/asymptotic-notation/a/big-big-theta-notation)\n `}\n \n \n {`\n # Problemi algoritmici\n \n Un _problema algoritmico_ è un problema matematico che si vuole provare a risolvere con un algoritmo.\n \n > Dati 10 numeri, voglio sapere se sono in ordine crescente oppure no.\n \n ## Caterigorizzazione\n \n I problemi algoritmici si dividono in tre categorie: problemi _trattabili_, problemi _intrattabili_ e problemi _irrisolvibili_.\n \n ### Problema trattabile\n \n Perchè un problema algoritmico sia _trattabile_, deve avere **almeno un algoritmo con upper bound polinomiale**.\n \n > Questo significa che il tempo impiegato da un computer per risolvere il problema rimane ragionevole, e che quindi può essere utilizzato in maniera efficiente.\n \n La trattabilità è un campo ancora parecchio aperto: esistono anche tanti problemi di cui non si è ancora dimostrata la trattabilità o intrattabilità.\n \n > La [fattorizzazione](https://it.wikipedia.org/wiki/Fattorizzazione) è uno di questi problemi: l'assenza di una dimostrazione è ciò che la rende uno dei pilastri della sicurezza informatica moderna.\n \n ### Problema intrattabile\n \n Se **un problema non ha nessun algoritmo con upper bound polinomiale**, allora si dice che è **intrattabile**.\n \n ### Problema irrisolvibile\n \n Se **non esistono algoritmi per risolvere un problema**, allora questo si dice **irrisolvibile**.\n \n > [Dato un algoritmo con certi input, riusciamo a capire con un algoritmo se la sua esecuzione termina o no?](https://en.wikipedia.org/wiki/Halting_problem)\n \n ### Upper e lower bound di problemi\n \n Si può anche trovare un _upper bound_ e un _lower bound_ per un problema, ma bisogna generalizzare di più.\n \n L'**upper bound di un problema** è il minimo upper bound di tutti gli algoritmi che lo risolvono; deve esistere almeno un algoritmo che lo risolva che abbia lo stesso _upper bound_. E' praticamente il tempo migliore per risolvere il problema dato.\n \n Il **lower bound di un problema** è il minimo lower bound di tutti gli algoritmi che lo risolvono; non deve esistere nemmeno un algoritmo che abbia un lower bound migliore. E' il numero assolutamente minimo di operazioni richieste, non si può fare meglio di così.\n \n In particolare, abbiamo che l'_upper bound di un algoritmo_ -> l'_upper bound del suo problema_, \n e il _lower bound di un problema_ -> il _lower bound di un suo algoritmo_.\n \n Generalmente, il _lower bound di un problema_ è una rappresentazione abbastanza accurata della sua difficoltà.\n `}\n \n \n {`\n # Ricerca binaria\n \n Non credo di aver bisogno di studiare la ricerca binaria, quindi non ho preso appunti a riguardo.\n \n Se non siete me, e state cercando informazioni a riguardo, andate a vedere su Wikipedia!\n `}\n \n \n {`\n # Divide et impera\n \n Un modo efficace per risolvere un problema è di usare il metodo _divide et impera (et combina)_.\n \n - _Divide_: Divido il problema in **tanti sottoproblemi**.\n - _Impera_: **Risolvo indipendentemente dal resto** ciascuno dei sottoproblemi.\n - _Combina_: **Combino** i risultati dei sottoproblemi per **risolvere il problema principale**.\n \n ## Ricorsione\n \n Un algoritmo (o funzione) si dice _ricorsivo_ quando durante l'esecuzione **richiama sè stesso**.\n \n Dato che tutti gli algoritmi devono avere termine entro un tempo finito, se scriviamo una funzione ricorsiva è fondamentale finire con un **caso base**, che non chiami ulteriormente la ricorsione.\n \n Se esiste una funzione ricorsiva, allora esiste _sempre_ una _funzione iterativa_ che darà lo stesso risultato.\n \n > Sul pratico, una funzione ricorsiva tipicamente è **più costosa** del suo equivalente iterativo: se possibile, quindi, la ricorsione andrebbe evitata.\n \n #### Pseudocodice di esempio\n \n \\`\\`\\`python\n def fattoriale(n):\n # Caso base; la ricorsione finisce e dà un risultato fisso\n if n <= 1:\n return 1\n # Caso ricorsivo; la funzione restituisce il risultato di sè stessa (ma con parametri diversi)\n else:\n return n * fattoriale(n - 1)\n \\`\\`\\`\n `}\n \n \n {`\n # Master Theorem\n \n Il _Master Theorem_ è uno dei teoremi più importanti dell'algoritmica.\n \n Esso permette di **calcolare l'upper bound di un algoritmo ricorsivo** in modo piuttosto semplice.\n \n ## Ipotesi\n \n Dato un algoritmo:\n - Con uno o più casi base\n - Che richiama la funzione ricorsiva un numero n di volte\n \n ## Tesi\n \n Allora, il suo upper bound avrà la formula:\n \n ![](https://quicklatex.com/cache3/89/ql_08d29a7e55d561a900570bc83b93ff89_l3.png)\n `}\n \n \n {`\n # Caso particolare del Master Theorem\n \n ## Ipotesi\n \n Se: \n ![](https://quicklatex.com/cache3/57/ql_e34dc27b42831d3c3ff671b0f3861257_l3.png)\n \n Ovvero, se la dimensione dell'input viene divisa ad ogni ciclo da una costante b, è polinomiale e il caso base è costante...\n \n ## Tesi\n \n Allora: \n ![](https://quicklatex.com/cache3/ca/ql_26e3557a6ca2d6ac4b8481e7c5263fca_l3.png)\n \n > In pratica, se il costo dominante è quello della parte \"fissa\" dell'algoritmo, esso sarà \\`O(n^d)\\`, mentre se il costo dominante è quello delle chiamate ricorsive, esso sarà \\`O(n^{log_b e})\\`. \n > Se nessuno dei due è dominante... si dividono circa in parti uguali, creando un costo di \\`O(n^d log n)\\`.\n `}\n \n \n {`\n # Ordinamento\n \n Un problema molto frequente nell'informatica consiste nell'**ordinare efficientemente grandi quantità di elementi**.\n \n Esistono [tantissimi](https://it.wikipedia.org/wiki/Algoritmo_di_ordinamento) algoritmi per effettuare l'ordinamento. \n L'**efficienza** di ciascuno **varia** di caso in caso: alcuni sono estremamente efficienti se quasi tutti i numeri sono già nell'ordine giusto; altri, invece, potrebbero impiegare tantissimo tempo.\n \n In termini matematici, abbiamo:\n \n - **Input:** A[n]\n - **Output:** B, ∀ i < n, A[i] ≤ A[i+1]\n \n ## Ordinamento tramite confronto\n \n L'ordinamento \"tradizionale\" è detto _ordinamento tramite confronto_: funziona sempre, e **non ha altri modi di ottenere informazioni** se non con l'operazione logica di confronto tra i dati.\n \n ### Limiti\n \n E' un problema risolto: è dimostrabile che il suo **lower bound** è **\\`Ω(n log n)\\`**; possiamo quindi dire che qualsiasi algoritmo di ordinamento è in \\`Ω(n log n)\\`, e se riusciamo a trovare un algoritmo di ordinamento in \\`O(n log n)\\` siamo riusciti a raggiungere il massimo dell'efficienza.\n \n #### Dimostrazione\n \n Consideriamo **tutte le possibili permutazioni** della sequenza da ordinare: sono \\`n!\\`.\n \n Per ogni confronto che effettuiamo, **riduciamo la quantità di permutazioni** correttamente ordinate; prima o poi, rimarrà **una sola possibilità**.\n \n **TODO, non trovo la spiegazione corretta!**\n \n ### Esempi\n \n Algoritmi che effettuano l'ordinamento tramite confronto sono:\n - _Bubble sort_\n - _Merge sort_\n - _Insertion sort_\n - _Quick sort_\n - _Heap sort_\n - E tanti, tanti altri!\n \n ## Ordinamento con altri mezzi\n \n Esistono algoritmi che ricavano informazioni in altri modi, diversi dal confronto.\n \n Essi possono avere un lower bound più basso di \\`O(n log n)\\`, però hanno spesso limitazioni sul loro utilizzo.\n \n ### Esempi\n \n - _Counting sort_, indicizza i valori da ordinare\n - _Radix sort_, guarda singolarmente le cifre dei valori\n - _Sleep sort_, sfrutta i thread e la funzione sleep per ordinare valori\n - E altri ancora!\n `}\n \n \n {`\n # Insertion sort\n \n L'_insertion sort_ è una soluzione **iterativa** all'ordinamento per confronto.\n \n ## Funzionamento\n \n Considero la sequenza divisa in **due parti**: una parte **ordinata** e una parte **non ordinata**.\n \n Parto dal primo elemento della lista: è sempre ordinato con sè stesso. \n Poi, aggiungo uno alla volta i numeri della parte non ordinata a quella ordinata; prima trovo in quale posizione dovrò andare a mettere il numero, poi **faccio slittare tutti i numeri dopo quella posizione** avanti di 1, in modo da **creare lo spazio** in cui infine **inserirò** il numero.\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | \\`O(n²)\\` | \\`Ω(n)\\` | - |\n \n Nel _caso migliore_ (**lista già ordinata**), il numero da inserire è già nella posizione giusta, quindi non devo effettuare altri confronti oltre il primo, rendendo il lower bound dell'algoritmo \\`Ω(n)\\`.\n \n Nel _caso peggiore_ (**lista nell'ordine inverso**), dobbiamo confrontare il numero da inserire con tutti gli altri nella parte ordinata: dobbiamo allora eseguire \\`1+2+3+4+5+… = \\\\frac{(n-1)(n)}{2}\\` confronti; ciò significa che l'upper bound è \\`O(n²)\\`!\n \n ## Pseudocodice\n \n \\`\\`\\`python\n def insertion_sorted(lista):\n # Itero su tutti i numeri della lista, dal primo all'ultimo.\n for divisore_ord in range(len(lista)):\n # Partendo dalla posizione attuale, creo l'indice di divisione numeri ordinati maggiori e minori\n divisore_magg = divisore_ord\n # Faccio slittare avanti i numeri maggiori di quello che stiamo inserendo\n # Se l'indice divisore_magg raggiunge 0, vuol dire che tutti i numeri della lista sono maggiori del numero attuale \n while divisore_magg >= 0 and lista[divisore_magg-1] > lista[divisore_magg]:\n # Scambio la posizione dei due elementi con gli indici specificati\n # Funzione inventata \n lista[divisore_magg], lista[divisore_magg-1] = lista[divisore_magg-1], lista[divisore_magg]\n # Diminuisco il separatore di 1\n divisore_magg -= 1\n \\`\\`\\`\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/bn/sorting)\n `}\n \n \n {`\n # Merge sort\n \n Il _merge sort_ è una soluzione **ricorsiva** all'ordinamento per confronto.\n \n ## Funzionamento\n \n Per questo algoritmo, utilizziamo la tecnica del **divide et impera**.\n \n 1. _Divide_: Divido A in **due parti**.\n 2. _Impera_: Metto **separatamente in ordine** le parti.\n 3. _Unisci_: **Unisco** le due parti.\n \n Consideriamo come **caso base** della ricorsione una parte composta da un numero, che ovviamente è già ordinata con sè stessa.\n \n ### Merge\n \n Per **unire le due parti** usiamo una funzione detta \\`merge()\\`.\n \n Costruiamo una nuova sequenza uguale alla sequenza 1, ma **aggiungiamo alla fine un valore sentinella** sempre maggiore di tutti gli elementi contenuti.\n \n > \\`\\`\\`\n > | 1 | 3 | 7 | 8 | ∞ |\n > \\`\\`\\`\n \n Facciamo **la stessa cosa** per la sequenza due.\n \n > \\`\\`\\`\n > | 2 | 4 | 5 | 6 | ∞ |\n > \\`\\`\\`\n \n Prendo i primi numeri delle due sequenze e **metto il più piccolo nella sequenza iniziale**.\n \n > \\`\\`\\`\n > | 1 | 2 | 3 | | | | | | \n > | | | 7 | 8 | ∞ | \n > | | 4 | 5 | 6 | ∞ | \n > \\`\\`\\`\n \n **Continuo** finchè non ho messo tutti i numeri; **grazie alla sentinella non usciremo mai dalla sequenza**, in quanto essa è sempre maggiore di tutti gli altri numeri.\n \n > \\`\\`\\`\n > | 1 | 2 | 3 | 4 | 5 | 6 | | | \n > | | | 7 | 8 | ∞ | \n > | | | | | ∞ |\n > \\`\\`\\`\n \n Quando **rimangono solo le sentinelle** significa che abbiamo aggiunto tutti gli elementi, e quindi abbiamo finito.\n \n > \\`\\`\\`\n > | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | \n > | | | | | ∞ | \n > | | | | | ∞ | \n > \\`\\`\\`\n \n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | \\`O(n log n)\\` | \\`Ω(n log n)\\` | **\\`θ(n log n)\\`** |\n \n Il merge sort è un algoritmo ricorsivo con un **caso base in tempo costante** e che **richiama sè stesso 2 volte**.\n \n \\`\\`\\`latex\n T(n) =\\\\\\\\\n \\\\\\\\\n Θ(1) \\\\qquad n=1\\\\\\\\\n 2 T(\\\\frac{n}{2}) + Θ(n) \\\\qquad n \\\\neq 1\n \\`\\`\\`\n \n Applicando il **caso particolare del Master Theorem**, otteniamo:\n \n \\`\\`\\`latex\n T(n) =\\\\\\\\\n \\\\\\\\\n Θ(1) \\\\qquad n=1\\\\\\\\\n Θ(n log n) \\\\qquad n \\\\neq 1\n \\`\\`\\`\n \n ## Pseudocodice\n \n \\`\\`\\`python\n def merge_sorted(part):\n # Caso base\n if len(part) == 1:\n return part\n # Divide\n middle = len(part) // 2\n part_a = part[:middle]\n part_b = part[middle:]\n # Impera\n sort_a = merge_sorted(part_a)\n sort_b = merge_sorted(part_b)\n # Combina\n return merge(sort_a, sort_b)\n \\`\\`\\`\n \n ## Visualizzazione\n \n [hackerearth.com](https://www.hackerearth.com/practice/algorithms/sorting/merge-sort/visualize/)\n \n [visualgo.net](https://visualgo.net/bn/sorting) (Nota: visualizza solo la fase _Unisci_ del sort)\n `}\n \n \n {`\n # Quick sort\n \n Il _quick sort_ è un altro approccio **ricorsivo** all'ordinamento per confronto.\n \n ## Funzionamento\n \n Anche qui, applichiamo il **divide et impera**.\n \n 1. _Divide_: Scelgo un **pivot** qualsiasi all'interno della lista. Metto alla sua **sinistra tutti i numeri minori** e alla sua **destra tutti i numeri maggiori**.\n 2. _Impera_: Eseguo un **quick sort su entrambe le sottoliste**.\n \n ### Esempi\n \n #### Iterazione con partizioni bilanciate\n \n Osserviamo come si formi una partizione con tre elementi e una con quattro. \n \n \\`\\`\\`\n |¦ [2] 8 7 1 3 5 6 {4}\n 2 |¦ [8] 7 1 3 5 6 {4}\n 2 |8 ¦ [7] 1 3 5 6 {4}\n 2 |8 ¦ [7] 1 3 5 6 {4}\n 2 |8 7 ¦ [1] 3 5 6 {4}\n 2 1 |7 8 ¦ [3] 5 6 {4}\n 2 1 3 |8 7 ¦ [5] 6 {4}\n 2 1 3 |8 7 5 ¦ [6] {4}\n 2 1 3 |8 7 5 6 ¦ [{4}]\n [2 1 3] {4} [8 5 6 7]\n \\`\\`\\`\n \n #### Iterazione con partizioni sbilanciate\n \n Osserviamo come si formi una partizione con **zero elementi** e una con tre.\n \n \\`\\`\\`\n |¦ [4] 7 3 {1}\n |4 ¦ [7] 3 {1}\n |4 7 |¦ [3] {1}\n |4 7 3 |¦ [{1}]\n [] {1} [4 7 3]\n \\`\\`\\`\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | \\`O(n²)\\` | \\`Ω(n log n)\\` | - |\n \n Il costo della funzione è dato dalla somma del costo per **dividere in due partizioni** con il costo per realizzare il **Quick sort delle due sottopartizioni**\n \n Possiamo applicare allora il **Master Theorem generale**:\n \n \\`\\`\\`latex\n T(n)\\\\\\\\\n =\\\\\\\\\n Θ(1) \\\\qquad per\\\\ n = 1\\\\\\\\\n T(q) + T(dim_lista - pivot - 1) + Θ(n) \\\\qquad per\\\\ n > 1\n \\`\\`\\`\n \n ### Il caso migliore\n \n Se il pivot \\`q\\` è la **mediana della partizione** che stiamo ordinando, si vengono a creare due _sottopartizioni bilanciate_, e sostituendo otteniamo:\n \n \\`\\`\\`latex\n T(n)\\\\\\\\\n =\\\\\\\\\n Θ(1) \\\\qquad per\\\\ n = 1\\\\\\\\\n 2 T(\\\\frac{n}{2}) + Θ(n) \\\\qquad per\\\\ n > 1\n \\`\\`\\` \n \n Possiamo allora applicare il **Master Theorem particolare**:\n \n \\`\\`\\`latex\n T(n)\\\\\\\\\n =\\\\\\\\\n Θ(1) \\\\qquad per\\\\ n = 1\\\\\\\\\n Θ(n log n) \\\\qquad per\\\\ n > 1\n \\`\\`\\`\n \n ### Il caso peggiore\n \n Se il pivot è uno degli **estremi dell'array**, si creano due _partizioni sbilanciate_: una delle due sottoliste è sempre vuota! \n Allora:\n \n \\`\\`\\`latex\n T(n) = T(n-1) + Θ(n)\\\\\\\\\n = T(n-2) + Θ(n-1) + Θ(n)\\\\\\\\\n = T(n-3) + Θ(n-2) + Θ(n-1) + Θ(n)\\\\\\\\\n = …\n ∈ Θ(n^2)\n \\`\\`\\`\n \n > \"Non date da mangiare sequenze ordinate al Quicksort, gli sono indigeste.\"\n \n ## Pseudocodice\n \n \\`\\`\\`python\n def partition(partizione, inizio, fine):\n \"\"\"Dividi una partizione in due, usando l'ultimo elemento come pivot.\n \n Note utili:\n partizione[fine] è il pivot\n partizione[maggiori] è il primo numero dei maggiori\n partizione[non_iterati] è l'elemento su cui si sta iterando al momento\"\"\"\n # Crea il primo separatore (la | pipe nell'esempio)\n maggiori = inizio\n # Crea il secondo separatore (la ¦ broken pipe nell'esempio)\n non_iterati = inizio\n # Itera su ogni numero tra inizio e fine (escluso!)\n while non_iterati < fine:\n # Se l'elemento su cui stiamo iterando è minore del pivot\n if partizione[non_iterati] <= partizione[fine]:\n # Mettilo nell'insieme dei minori, scambiandolo con il primo numero dei maggiori e incrementando il primo separatore\n partizione[maggiori], partizione[non_iterati] = partizione[non_iterati], partizione[maggiori]\n maggiori += 1\n # Incrementa sempre il secondo separatore\n non_iterati += 1\n # Inserisci il pivot tra le due sottopartizioni create, \n partizione[fine], partizione[non_iterati] = partizione[non_iterati], partizione[fine]\n return maggiori\n \\`\\`\\`\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/bn/sorting) (Nota: invece che prendere l'ultimo numero come pivot prende il primo, cambiando leggermente l'algoritmo.)\n \n ## Note per l'esame\n \n > La domanda che fa sempre è **\"Qual è la sequenza di pivot utilizzata?\"**\n \n > Elementi da soli _non_ vengono presi come pivot!\n `}\n \n \n {`\n # Counting sort\n\n Il _counting sort_ è un approccio diverso all'ordinamento: **non usa il confronto**!\n \n ## Requisiti\n \n Il counting sort può essere utilizzato solo su **sequenze di numeri interi**, e solo se **siamo a conoscenza del minimo e del massimo** dei numeri contenuti nell'array, ed essi non sono troppo distanti uno dall'altro. \n (La memoria occupata dal counting sort aumenta linearmente con la differenza tra minimo e massimo!)\n \n Per semplicità, consideriamo il **minimo \\`0\\`**. \n L'input allora sarà una sequenza di interi \\`A\\`, e il valore del **massimo \\`k\\`**, tale che \\`∀ n ∈ A, 0 \\\\leq n \\\\leq K\\`.\n \n ## Funzionamento\n \n Il counting sort **conta le ripetizioni** delle chiavi nella sequenza originale e in seguito **sovrascrive i valori** della sequenza con i valori ordinati ripetuti il numero di volte che sono stati individuati nella sequenza.\n \n > \\`\\`\\`\n > 1 4 5 3 4 1 4 2 5 1\n > \\`\\`\\`\n >\n > L'\\`1\\` appare 3 volte, il \\`2\\` 1 volta, il \\`3\\` 1 volta, il \\`4\\` tre volte e il \\`5\\` due volte.\n >\n > La sequenza viene quindi così sovrascritta:\n > \\`\\`\\`\n > 1 1 1 3 4 1 4 2 5 1 # Sovrascriviamo la sequenza con 1 ripetuto 3 volte\n > 1 1 1 2 3 4 4 4 5 1 # Sovrascriviamo la sequenza con 2, 3, 4 ripetuti rispettivamente 1 1 e 3 volte\n > 1 1 1 2 3 4 4 4 5 5 # Sovrascriviamo la sequenza con 5 ripetuto 2 volte: abbiamo finito!\n > \\`\\`\\` \n \n Esiste anche una **versione stabile** del counting sort che, invece che sovrascrivere, **sposta i valori**, mantenendo le informazioni aggiuntive nel caso invece che interi fossero altri tipi di dati.\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | \\`O(k + n)\\` | \\`Ω(k + n)\\` | **\\`θ(k + n)\\`** |\n \n L'algoritmo è composto da quattro parti:\n - Ricerca del minimo e massimo (in \\`θ(n)\\`)\n - Inizializzazione dell'indice (in \\`θ(k)\\`)\n - Conteggio dei numeri (in \\`θ(n)\\`)\n - Sovrascrittura dei numeri (in \\`θ(k + n)\\`)\n \n \\`2 + O(k) + O(n) + O(k + n) -> O(k + n)\\`\n \n Notiamo che \\`k\\` è costante, l'algoritmo è \\`O(n)\\`, estremamente efficiente.\n \n ## Pseudocodice\n \n \\`\\`\\`python\n def counting_sort(lista: typing.List[int]):\n \"\"\"Ordina in-place una lista con il counting sort.\"\"\"\n # Trovo la dimensione della lista\n dim = len(lista)\n # Trovo il massimo e il minimo all'interno della lista\n minimo = min(lista)\n massimo = max(lista)\n # Creo l'indice dei numeri, in modo che sia lungo k e pieno di 0\n indice = [0 for _ in range(minimo, massimo+1)]\n # Conto i numeri presenti, scorrendo su lista e aggiungendo 1 al numero corrispondente\n for i in range(dim):\n indice[lista[i]] += 1\n # Sovrascrivo i numeri nella lista\n count = 0\n for pos, val in enumerate(indice):\n for _ in range(val):\n indice[count] = pos\n count += 1\n \n def stable_counting_sorted(lista: typing.List[int], k: int) -> typing.List[int]:\n \"\"\"Ordina stabilmente una lista con il counting sort stabile, e restituiscila.\"\"\"\n # Trovo la dimensione della lista\n dim = len(lista)\n # Trovo il massimo e il minimo all'interno della lista\n minimo = min(lista)\n massimo = max(lista)\n # Creo l'indice dei numeri, in modo che sia lungo k e pieno di 0\n indice = [0 for _ in range(minimo, massimo+1)]\n # Conto i numeri presenti, scorrendo su lista e aggiungendo 1 al numero corrispondente\n for i in range(dim):\n indice[lista[i]] += 1\n # Faccio diventare l'indice \"il numero di numeri \\\\leq i\"\n for i in range(len(indice)):\n if i == 0:\n continue\n indice[i] += indice[i-1]\n assert indice[-1] == dim\n # Creo una nuova lista, che sarà quella che verrà restituita\n nuova = [None for _ in range(dim)]\n # Inizio a posizionare i numeri, al contrario\n for i in range(0, dim, -1):\n nuova[indice[lista[i]]] = lista[i]\n indice[lista[i]] -= 1\n return nuova\n \\`\\`\\`\n `}\n \n \n {`\n ## Introduzione alle Strutture Dati\n\n Una _struttura dati_ è un modo in cui si possono organizzare i dati di un programma.\n \n Si possono definire in due modi: **elementari** e **astratte**.\n \n ### Strutture dati elementari\n \n Le strutture _elementari_ dipendono strettamente dal modo in cui vengono memorizzati i dati.\n \n > **Array** e **liste** sono strutture dati elementari: sono definite dicendo come sono memorizzati i dati, rispettivamente, in celle contigue di memoria e da una serie di nodi con un valore e che puntano al successivo.\n \n ### Strutture dati astratte\n \n Le strutture _astratte_ sono separate dal modo in cui vengono memorizzati i dati, sono più ad alto livello, e si definiscono descrivendo le **proprietà** della struttura e i **metodi** che su di essa possono essere effettuate.\n \n > Una _classe_ in un qualsiasi linguaggio di programmazione è una struttura dati astratta.\n \n > Una _pila_ astratta:\n > - memorizza dati tutti dello stesso tipo\n > - \\`pop()\\`, estrae dalla pila l'ultimo valore inserito\n > - \\`push(val)\\`, aggiunge alla pila un valore\n > - \\`top()\\`, permette di vedere l'ultimo valore inserito nella pila\n > - \\`vuota()\\`, dice se la pila è vuota oppure no.\n `}\n \n \n {`\n # Array\n\n Un _array_ è sequenza di dati di **lunghezza conosciuta**, tutti dello **stesso tipo** e di una **dimensione fissa**, immagazzinata in **blocchi di memoria contigui**.\n \n ## Proprietà\n \n - E' possibile accedere a tutti i blocchi di memoria conoscendo la loro **posizione relativa al primo** elemento.\n \n ## Metodi\n \n \\`\\`\\`python\n class Array:\n def __init__(self, size, type=int): \"Crea un array di dimensione size di elementi di tipo int.\"\n def __getitem__(self, index): \"Restituisci il valore alla posizione index.\"\n def __setitem__(self, index, value): \"Cambia il valore alla posizione index.\"\n \\`\\`\\`\n \n ### Costo computazionale\n \n Tutte le operazioni su un array sono in **accesso immediato \\`O(1)\\`**!\n `}\n \n \n {`\n # Lista\n \n Una _lista_ è una sequenza di dati immagazzinata in **blocchi di memoria qualsiasi**.\n \n ## Proprietà\n \n Ogni dato ha un **riferimento** alla collocazione di memoria **successiva** (un puntatore): insieme, sono detti un _nodo_.\n \n E' di **natura ricorsiva**: qualsiasi nodo di una lista può essere visto come inizio della lista con sè stesso e i suoi successivi.\n \n ## Metodi\n \n \\`\\`\\`python\n class LinkedList:\n def __init__(self, value, next: typing.Optional[Node] = None):\n self.value = value\n self.next: typing.Optional[Node] = next\n \n def is_empty(self) -> bool: \"Restituisce se la lista è vuota o no.\"\n def is_full(self) -> bool: \"Restituisce se la lista è piena o no.\n def append(self, value): \"Aggiunge un nuovo elemento in testa alla lista.\"\n def insert(self, value, index): \"Inserisce un elemento dopo il nodo in posizione index.\"\n def insert_node(self, value, node): \"Inserisce un nuovo elemento subito dopo un dato nodo.\"\n def find(self, node) -> int: \"Trova l'indice del nodo.\"\n def delete(self, value): \"Elimina il primo nodo con quel valore dalla lista.\"\n def delete_node(self, node): \"Elimina il nodo dalla lista.\"\n def forward(self, index) -> Node: \"Restituisce il nodo in posizione index.\"\n \\`\\`\\`\n \n ### Costo computazionale\n \n #### \\`List.forward(index)\\`\n \n Per raggiungere l'\\`n\\`-esimo elemento, bisogna _scorrere tutti gli elementi prima di esso_: è dunque un **accesso sequenziale** in **\\`O(n)\\`**.\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/list)\n `}\n \n \n {`\n # Coda (Queue)\n\n Una _coda_ è come una pila, ma segue la strategia **First In, First Out** (il primo inserito sarà il primo a essere estratto).\n \n ## Proprietà\n \n - I dati vi possono essere aggiunti solo tramite il **metodo \\`enqueue()\\`**\n - I dati possono essere estratti solo tramite il **metodo \\`dequeue()\\`**\n - Verranno restituiti i valori inseriti secondo la strategia **First In, First Out** (il primo inserito sarà il primo a essere estratto).\n \n > Hai presente quando fai la fila per pagare al supermercato? Beh, è quello, però non si possono superare le altre persone in nessun modo.\n \n ## Metodi\n \n \\`\\`\\`python\n class Queue:\n def __init__(self): \"Crea una nuova coda.\"\n def is_empty(self) -> bool: \"Restituisce vero se la coda è vuota.\"\n def enqueue(self, data): \"Aggiunge un dato alla coda.\"\n def first(self) -> ...: \"Restituisce il primo dato della coda.\"\n def dequeue(self) -> ...: \"Restituisce il primo dato della coda e lo rimuove.\"\n \\`\\`\\`\n \n ## Implementazione tramite lista\n \n Posso implementare la coda con una lista, ma per realizzare l'implementazione più efficiente devo tenere anche un puntatore all'ultimo elemento della coda, in modo da non doverla scorrere ogni volta che voglio effettuare un'operazione.\n \n Chiamiamo i due puntatori \\`head\\` e \\`tail\\` rispettivamente.\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/list)\n `}\n \n \n {`\n # Pila (Stack)\n\n Una _pila_ è una struttura dati contenente **valori omogenei**.\n \n ## Proprietà\n \n - I dati vi possono essere aggiunti solo tramite il **metodo \\`push()\\`**\n - I dati possono essere estratti solo tramite il **metodo \\`pop()\\`**\n - Verranno restituiti i valori inseriti secondo la strategia **Last In, First Out** (l'ultimo inserito sarà il primo a essere estratto).\n \n > Ci si può immaginare una pila di libri, da cui si può solo prendere un libro alla volta, quello più in alto.\n \n ## Metodi\n \n \\`\\`\\`python\n class Stack:\n def __init__(self): \"Crea una nuova pila.\"\n def is_empty(self) -> bool: \"Restituisce vero se la pila è vuota.\"\n def push(self, data): \"Aggiunge un dato alla pila.\"\n def top(self) -> ...: \"Restituisce il primo dato della pila.\"\n def pop(self) -> ...: \"Restituisce il primo dato della pila e lo rimuove.\"\n \\`\\`\\`\n \n ## Implementazione tramite lista\n \n Utilizzando una lista possiamo realizzare una pila!\n \n La direzione dei puntatori sarà dall'ultimo al primo, che non punterà più a nessuno.\n \n Il costo di tutti i metodi è \\`Θ(1)\\`!\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/list)\n `}\n \n \n {`\n # Albero radicato\n \n Un _albero radicato_ è una struttura dati di **natura ricorsiva** che organizza i dati in maniera **non-lineare**.\n \n ## Proprietà\n \n - Ogni nodo dell'albero ha un **unico genitore**: \\`∀ (padre, figlio), (padre' figlio) ∈ E \\\\implies padre = padre'\\`\n - Ogni nodo dell'albero può avere **un numero qualsiasi di figli**.\n \n - I **nodi superiori al padre** vengono chiamati _antenati_.\n - I **nodi inferiori ai figli** vengono chiamati _discendenti_.\n \n - Nodi **senza padre** sono detti _radice_: \\`\\\\notexists (padre, radice) ∈ E\\`\n - Nodi **con padre e figli** sono detti _rami_ o interni.\n - Nodi **senza figli** sono detti _foglie_.\n \n - La **distanza** tra il nodo radice e i suoi discendenti è detta _livello_:\n - I figli immediati sono di livello 1.\n - I \"nipoti\" (figli dei figli) sono di livello 2.\n - I figli dei nipoti sono livello 3.\n - E così via.\n - Il **livello massimo** all'interno di un albero è detto _altezza_, _profondità_ oppure _h_, ed è sempre \\`1 ≤ h ≤ n-1\\`.\n \n - Un albero ha sempre \\`n-1\\` archi.\n \n ## Alberi particolari\n \n ### Alberi \\`d\\`-ari\n \n Un albero _\\`d\\`-ario_ è un particolare tipo di albero che **limita il numero massimo di figli di un nodo** a \\`d\\`.\n \n > Un albero _binario_ può avere **massimo 2 figli** per ogni nodo; un albero _ternario_ ne può avere **3**; un albero _\\`17\\`-ario_ ne potrà avere **17**\n \n #### Alberi completi\n \n Un albero \\`d\\`-ario si dice _completo_ se **tutti i nodi hanno 0 o \\`d\\` figli**, e mai una numero in mezzo.\n \n #### Alberi bilanciati\n \n Un albero \\`d\\`-ario si dice _bilanciato_ se **tutti i livelli eccetto l'ultimo** hanno il numero massimo di figli.\n \n #### Alberi perfettamente bilanciati\n \n Un albero \\`d\\`-ario si dice _perfettamente bilanciato_ se **tutti i livelli incluso l'ultimo** hanno il numero massimo di figli.\n \n ##### Particolarità degli alberi binari perfettamente bilanciati\n \n Si può dimostrare per induzione che:\n - Hanno sempre \\`2^h\\` foglie.\n - Hanno sempre \\`2^{h+1}-1\\` (\\`\\\\sum_i=0^n 2^i\\`) nodi.\n - L'altezza è in \\`Θ(log n)\\`.\n \n ## Implementazione degli alberi\n \n Possiamo scegliere se usare una rappresentazione con array o con nodi e puntatori: ognuna ha vantaggi e svantaggi diversi.\n \n ### Implementazione tramite array\n \n E' suggerito se l'albero è regolare; più è simile a un albero d-ario completo, meglio è.\n \n ### Implementazione tramite nodi e puntatori\n \n Più adatta ad alberi irregolari.\n \n Se l'albero è regolare, creiamo il numero esatto di campi:\n \n - Valore\n - Figlio1\n - Figlio2\n - _Opzionale:_ Padre\n \n Se un albero è irregolare, creiamo una specie di lista:\n \n - Valore\n - Primo figlio\n - Prossimo fratello\n - _Opzionale:_ Padre\n `}\n \n \n {`\n #### Breadth-first search (BFS)\n\n La _breadth-first search_ è un algoritmo che visita **ogni livello** dell'albero in ordine, dal più basso al più alto.\n \n ## Funzionamento\n \n > 1. __Visita radice__\n > 2. __Visita figli__\n > 3. __Visita nipoti__\n > 4. __Visita pronipoti__\n \n Si può implementare con una coda, in cui verranno inseriti i figli del nodo visitato da visitare ed estratti dopo avere completato la visita del livello attuale.\n \n ## Pseudocodice \n \n \\`\\`\\`python\n def bfs(radice):\n c = Queue()\n c.enqueue(radice)\n while not c.is_empty():\n nodo = c.dequeue()\n print(nodo)\n for figlio in nodo.figli:\n nodo.enqueue(figlio)\n \\`\\`\\`\n `}\n \n \n {`\n # Depth-First Search\n\n La _depth-first search_ è un algoritmo che visita **tutti i sottoalberi di un figlio** prima di passare ad un altro sfruttando la natura ricorsiva degli alberi.\n \n ## Funzionamento\n \n Ci sono diverse versioni della depth-first search: ognuna visita la radice in un momento diverso.\n \n ### DFS previsita (pre-order)\n \n La _DFS pre-visita_ visita la **radice per prima**, poi tutti i sottoalberi formati dai figli uno dopo l'altro.\n \n > 1. __Visita radice__\n > 2. dfs_pre_order(figlio1)\n > 3. dfs_pre_order(figlio2)\n \n ### Postvisita (post-order)\n \n La _DFS postvisita_ visita prima tutti i sottoalberi dei figli, e **alla fine la radice**.\n \n > 1. dfs_post_order(figlio1)\n > 2. dfs_post_order(figlio2)\n > 3. __Visita radice__\n \n ### Invisita (in-order)\n \n La _DFS invisita_ visita **un certo numero di figli**, poi la radice, e infine i figli restanti.\n \n > 1. dfs_in_order(figlio1, 1)\n > 2. __Visita radice__\n > 3. dfs_in_order(figlio2, 1)\n `}\n \n \n {`\n # Albero binario di ricerca\n\n ## Proprietà\n \n - Albero **binario**\n - Chiavi appartenenti ad un **insieme totalmente ordinato** (N, Q, R, ma non C)\n \n - Per ogni nodo con valore \\`x\\`, se un valore \\`v\\` è nel sottoalbero di sinistra allora \\`v ≤ x\\`, mentre se è nel sottoalbero di destra allora \\`v > x\\`.\n \n ## Costo computazionale\n \n - Trovare un valore: \\`O(h)\\`\n - Ordinare i valori: \\`O(n)\\`\n - Trovare il minimo: \\`O(h)\\`\n - Trovare il massimo: \\`O(h)\\`\n - Inserire un elemento: \\`O(h)\\`\n - Cancellare un elemento: \\`O(h)\\`\n \n \\`h\\` vale \\`log n\\` in un albero perfettamente bilanciato, e più l'albero diventa sbilanciato, più si avvicina a \\`n\\`, raggiungendola nel caso l'albero sia una lista.\n \n ## Pseudocodice\n \n ### Cancellazione ricorsiva\n \n \\`\\`\\`python\n def delete(tree, key):\n if tree is not None:\n # Se ho trovato il nodo che cercavo...\n if tree.key == key:\n # E c'è una sola diramazione...\n # Semplicemente stacca il nodo come in una lista.\n if tree.left is None:\n return tree.right\n if tree.right is None:\n return tree.left\n # Altrimenti, diventa il minimo dell'albero di destra\n tree.key = tree.right.min()\n # Ed eliminalo dal sottoalbero\n tree.right = delete(tree.right, tree.key)\n # Se la chiave attuale è diversa da quella che cerchiamo, continuo a navigare l'albero\n elif tree.key < key:\n tree.left = delete(tree.left, key)\n else:\n tree.right = delete(tree.right, key)\n return tree\n \\`\\`\\`\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/bst)\n \n ## Approfondimenti\n \n Esistono alberi più avanzati che mantengono le proprietà degli alberi binari di ricerca, ma che si autobilanciano, come il [Red Black Tree](https://it.wikipedia.org/wiki/RB-Albero).\n `}\n \n \n {`\n # Heap binario\n \n L'_heap binario_ è un **albero binario bilanciato a sinistra**.\n \n ## Proprietà\n \n - _Proprietà strutturale_:\n - L'albero è **perfettamente bilanciato** in tutti i livelli tranne l'ultimo\n - Nell'ultimo livello, le foglie occupano le **posizioni più a sinistra** possibili\n - _Proprietà di ordinamento_:\n - La chiave di un qualsiasi nodo è **più piccola** di tutte quelle dei nodi **del suo sottoalbero**\n \n ## Metodi\n \n \\`\\`\\`python\n class Heap:\n def __init__(self, H): ...\n def _heapify_ancestors(self, i): \"Ripristina le proprietà dell'heap per il nodo all'indice specificato e i suoi genitori.\"\n def minimum(self): \"Restituisce la chiave con il valore minimo in H.\"\n def decrease_value(self, index, new_value): \"Diminuisce il valore della chiave all'indice index a new_value.\"\n def insert(self, value): \"Inserisci un nuovo valore nell'albero.\"\n def _heapify_children(self, i): \"Ripristina le proprietà dell'heap per il nodo all'indice specificato e i suoi figli.\"\n def pop(self): \"Restituisce la chiave con il valore minimo, e la elimina.\"\n def from_list(l): \"Crea un heap da una lista.\"\n \\`\\`\\`\n \n ## Implementazione con un array\n \n Possiamo implementare l'albero utilizzando un array con le chiavi dell'albero memorizzate nell'ordine _breadth-first_.\n \n L'indice del figlio sinistro può essere trovato a \\`2i+1\\`, mentre l'indice del figlio sinistro può essere trovato a \\`2i+2\\`; il genitore è a \\`i//2-1\\`.\n \n ### Pseudocodice\n \n \\`\\`\\`python\n class Heap:\n def __init__(self, size):\n self.array = Array(size) # Il tipo Array non esiste; consideriamolo pseudocodice\n self.next_value = 0\n \n def _heapify_ancestors(self, index)\n \"\"\"Ripristina le proprietà dell'heap per il nodo all'indice specificato e i suoi genitori.\n \n Costo:\n O(log n)\"\"\"\n # Trovo l'indice del genitore\n parent = index // 2 - 1\n # Controllo se viene mantenuta la proprietà di ordinamento dell'heap\n if self.array[index] < self.array[parent]:\n # Scambio i valori dei due nodi\n self.array[index], self.array[parent] = self.array[parent], self.array[index]\n # Faccio la stessa cosa con il genitore\n self._heapify(parent)\n \n \n def minimum(self):\n \"\"\"Restituisce la chiave con il valore minimo in H.\n \n Costo:\n O(1)\"\"\"\n return self.array[0]\n \n def decrease_value(self, index, new_value):\n \"\"\"Diminuisce il valore della chiave all'indice index a new_value.\n \n Costo:\n O(log n)\"\"\"\n # Diminuisco il valore del nodo\n self.array[index] = new_value\n # Aggiorno l'heap \n self._heapify(index)\n \n def insert(self, value):\n \"\"\"Inserisci un nuovo valore nell'albero.\n \n Costo:\n O(log n)\"\"\"\n # Trovo l'indice in cui inserire il valore\n index = self.next_index \n # Aggiungo il valore in fondo\n self.array[index] = value\n # Aggiorno l'heap\n self._heapify(index)\n \n def _heapify_children(self, index):\n \"\"\"Ripristina le proprietà dell'heap per il nodo all'indice specificato e i suoi figli.\n \n Costo:\n O(log n)\"\"\"\n # Trovo l'indice dei figli\n left = index * 2 + 1\n right = index * 2 + 2\n # Mi assicuro che i figli esistano\n try:\n # Guardo quale dei figli è maggiore\n if self.array[left] > self.array[right]:\n # Scambio i valori\n self.array[left], self.array[index] = self.array[index], self.array[left]\n # Ripeto la procedura sul figlio modificato\n self._heapify_children(left)\n else:\n # Scambio i valori\n self.array[right], self.array[index] = self.array[index], self.array[right]\n # Ripeto la procedura sul figlio modificato\n self._heapify_children(left)\n except IndexError:\n # La foglia non ha figli: ho finito!\n return\n \n def pop(self):\n \"\"\"Restituisce la chiave con il valore minimo, e la elimina.\n \n Costo:\n O(log n)\"\"\"\n # Mi salvo il valore della radice\n value = self.array[0]\n # Sostituisco la radice con l'ultima foglia a destra\n self.array[0], self.array[self.next_value] = self.array[self.next_value], self.array[0]\n ### Non bisognerebbe eliminare la foglia...?\n # Riordino l'heap\n self._heapify_children(0)\n return value\n \n @staticmethod\n def from_list(l):\n \"\"\"Crea un heap da una lista.\n \n Costo:\n O(n log n), ma si può abbassare\"\"\"\n heap = Heap(len(l)))\n heap.array = Array.from_list(l) # Pseudocodice\n heap.next_value = len(l)\n # Cominciamo a riordinare l'heap dalla fine, in modo che rispetti le proprietà\n for index in range(heap.next_value, 0, -1):\n heap._heapify_children(index)\n \\`\\`\\`\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/heap)\n `}\n \n \n {`\n # Coda con priorità\n \n La _coda con priorità_ è una struttura dati dal funzionamento molto simile a quello di una coda, ma invece che restituire il primo elemento inserito, essa restituisce l'**elemento con il valore di priorità minore**.\n \n ## Proprietà\n \n - Ogni elemento è una coppia costituita da **valore** e **priorità** (un numero intero).\n - Nuovi elementi possono essere aggiunti solo tramite il **metodo \\`insert()\\`**\n - Gli elementi possono essere estratti solo tramite il **metodo \\`pop()\\`**\n - Verranno restituiti i valori inseriti secondo la strategia **Lower Priority** (l'elemento con la priorità minore sarà il primo ad essere restituito).\n - E' possibile diminuire la priorità di un elemento (e quindi anticipare la sua estrazione)\n \n ## Metodi\n \n \\`\\`\\`python\n class PriorityQueue:\n def __init__(self): ...\n def insert(self, new_elem: Element): ...\n def minimum(self) -> Element: ...\n def pop(self) -> Element: ...\n def decrease_priority_for(self, elem: Element, priority: int): ...\n \\`\\`\\`\n \n ## Implementazione con lista\n \n E' possibile implementare la coda con priorità tramite una **lista**: l'inserimento di nuovi valori diventerà molto efficiente, ma tutte le altre operazioni saranno linearmente lente.\n \n ### Costo computazionale\n \n - *insert()*: \\`O(1)\\`\n - *minimum()*: \\`O(n)\\`\n - *pop()*: \\`O(n)\\`\n - *decrease_priority_for()*: \\`O(n)\\`\n \n ## Implementazione con lista ordinata\n \n Implementando la coda con priorità con una **lista ordinata** si avrà un costo di ordinamento elevato negli inserimenti e modifiche alla priorità, ma costi costanti nell'estrazione di un elemento.\n \n ### Costo computazionale\n \n - *insert()*: \\`O(n)\\`\n - *minimum()*: \\`O(1)\\`\n - *pop()*: \\`O(1)\\`\n - *decrease_priority_for()*: \\`O(n)\\`\n \n ## Implementazione con heap\n \n La **soluzione migliore** è quella di implementare la coda con priorità tramite un **heap**: tutti i costi saranno logaritmici, eccetto l'inserimento che sarà costante.\n \n - \\`insert()\\` costa \\`O(1)\\`\n - \\`minimum()\\` costa \\`O(log n)\\`\n - \\`pop()\\` costa \\`O(log n)\\`\n - \\`decrease_priority_for()\\` costa \\`O(log n)\\`\n \n ## Approfondimenti\n \n Esistono code con priorità che restituiscono **l'elemento con priorità maggiore**, invece che quello minore.\n `}\n \n \n {`\n # Heap sort\n\n L'_heap sort_ è un algoritmo di ordinamento per confronto **iterativo**.\n \n ## Funzionamento\n \n Per effettuare un heap sort, creiamo un **heap massimo** in cui inseriamo tutti i valori che vogliamo ordinare.\n \n Una volta applicate le proprietà dell'heap, chiamiamo una versione particolare di \\`heap.pop()\\` che invece che rimuovere dall'array i valori estratti li posiziona nello spazio creatosi in fondo.\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | \\`O(n log n)\\` | \\`Ω(n log n)\\` | **\\`θ(n log n)\\`** |\n `}\n \n \n {`\n # Grafo\n \n Un _grafo_ è una struttura dati che rappresenta elementi interconnessi tra loro.\n \n Esistono due tipi di grafi: _orientati_ e _non orientati_.\n \n Per semplicità, consideriamo i nostri nodi numerati da 1 a \\`n\\`.\n \n ## Proprietà\n \n - Gli elementi sono rappresentati tramite _nodi_.\n - Il loro _grado_ è dato dal **numero degli archi** che vi incidono.\n - Se il grafo è orientato, hanno anche un _in-degree_ (**numero di archi entranti**) e un _out-degree_ (**numero di archi uscenti**).\n - Le connessioni tra elementi sono rappresentate tramite _archi_.\n - Un arco _incide_ esattamente su **due nodi**.\n - Se il grafo è orientato, sono _uscenti_ da uno dei due nodi ed _entranti_ nell'altro.\n - Sono matematicamente meno del **quadrato dei nodi**.\n \n ## Grafi particolari\n \n ### Catena\n \n Una _catena_ è un **grafo non orientato** composto da una **sequenza di nodi** aventi un **grado massimo di 2** tutti collegati tra loro.\n \n ### Cammino\n \n Un _cammino_ è un **grafo orientato** composto da una **sequenza di nodi** aventi un **in-degree** e un **out-degree** **massimo di 1**, collegati tra loro in modo che partendo dal primo e seguendo gli archi sia possibile arrivare all'ultimo.\n \n ### Cricca\n \n Una _cricca_ è un grafo in cui **tutti i nodi sono collegati tra loro**.\n \n Se il grafo è **non orientato**, la cricca ha \\`((n-1)n)/2\\` archi.\n \n Se il grafo è **orientato**, ha per ogni coppia un arco in entrambe le direzioni, quindi ha \\`(n-1)n\\` archi.\n \n ### Direct Acyclic Graph\n \n Un _DAG_ è un grafo diretto che non contiene nessun ciclo.\n \n Su di esso possiamo effettuare un ordinamento, detto _linearizzazione_, tra i nodi: otteniamo l'_ordine topologico_.\n \n I primi elementi dei DAG sono detti _Source_ (_Sorgente_), mentre gli ultimi sono detti _Sink_ (_Pozzo_).\n \n #### Albero\n \n Un **albero** può essere considerato un DAG con una **sorgente singola** e le **foglie come pozzi**.\n \n ### Grafo fortemente connesso\n \n Un insieme di nodi \\`V\\` di un **grafo diretto** \\`G\\` si dice una _componente fortemente connessa_ se:\n \n 1. Per ogni coppia di nodi \\`∀ u, v ∈ V' : ∃ un cammino u->v in G'\\`\n 2. Massimale (non può diventare più grande)\n \n > Praticamente una componente fortemente connessa è un gruppo di nodi tra i quali si può viaggiare liberamente da e a qualsiasi nodo al suo interno.\n \n Un grafo si dice _fortemente connesso_ se l'insieme \\`V\\` coincide con l'insieme dei nodi del grafo \\`G\\`.\n \n > Se partendo da qualsiasi nodo di un grafo riesco ad arrivare a qualsiasi altro nodo, allora il grafo è fortemente connesso.\n \n Inoltre, se creiamo un nuovo grafo, in cui **ogni nodo rappresenta una componente fortemente connessa** del nostro grafo iniziale, **otteniamo un DAG**, perchè tutti i cicli sono stati integrati nella componente.\n \n ### Trasposto di un grafo\n \n Il _trasposto_ di un **grafo diretto** \\`G\\` è il grafo stesso con gli archi che però vanno nella **direzione opposta**.\n \n ### Grafo pesato\n \n Un _grafo pesato_ è un particolare grafo che associa a ciascun arco un **costo** per attraversarlo.\n \n #### Costi negativi\n \n I costi possono anche essere negativi: rappresenteranno allora un **guadagno** ottenuto attraversando il nodo.\n \n ### Minimum spanning tree\n \n Un _minimum spanning tree_ è il **sottoinsieme degli archi** di un **grafo non diretto** che **connettono tutti i nodi** con il **minor costo possibile**.\n \n I MST hanno [molte proprietà](https://en.wikipedia.org/wiki/Minimum_spanning_tree#Properties); sono troppe da scrivere qui, e probabilmente non ci interesseranno nemmeno.\n \n ## Implementazione tramite matrice di adiacenza\n \n Possiamo implementare un grafo creando una **matrice di \\`bool\\` di dimensione \\`n * n\\`** in cui le **caselle collegate sono vere** e le caselle non collegate sono false.\n \n > Ad esempio, possiamo implementare un grafo non orientato in questo modo (\\`█\\` indica l'esistenza di un collegamento e \\` \\` indica la sua assenza):\n >\n > | |1|2|3|\n > |-|-|-|-|\n > |1|░|░|░|\n > |2|█|░|░|\n > |3|█| |░|\n >\n > Esistono gli archi \\`1-2\\` e \\`1-3\\`, ma non esiste un collegamento \\`2-3\\`.\n \n > Un grafo orientato invece si può implementare così:\n >\n > | |1|2|3|\n > |-|-|-|-|\n > |1|░|█| |\n > |2|█|░| |\n > |3|█| |░|\n >\n > Esistono gli archi \\`1->2\\`, \\`2->1\\` e \\`3->1\\`, ma non ci sono collegamenti \\`2->3\\`, \\`1->3\\` e \\`3->2\\`.\n \n ### Costo computazionale\n \n #### Tempo\n \n Le matrici di adiacenza portano alla realizzazione di algoritmi molto veloci: verificare l'esistenza di un arco è in \\`O(1)\\`!\n \n Abbiamo però penalità significative quando vogliamo effettuare operazioni sugli archi: ad esempio, trovare il trasposto di un grafo implementato con una matrice di adiacenza è in \\`O(nodi²)\\`.\n \n #### Memoria\n \n E' poco efficiente in quanto a memoria: l'upper bound è in \\`O(n^2)\\`. \n \n ## Implementazione tramite liste di adiacenza\n \n Un'alternativa alla matrice di adiacenza è quella di creare un'**array di liste**, le quali contengono i **vicini di ciascun nodo**.\n \n > |Posizione|Lista|\n > |-|-|\n > |1|[2, 3]|\n > |2|[]|\n > |3|[1]|\n >\n > Esistono gli archi \\`1->2\\`, \\`1->3\\`, e \\`3->1\\`, ma non esistono \\`2->1\\`, \\`2->3\\` e \\`3->2\\`.\n \n ### Costo computazionale\n \n #### Tempo\n \n Utilizzando le liste di adiacenza, il tempo richiesto per verificare l'esistenza di un arco sale a \\`O(max-out-degree)\\`.\n \n E' efficace però quando il problema che vogliamo risolvere riguarda operazioni su archi: trovare la trasposta è in \\`O(archi)\\`.\n \n #### Memoria \n \n La memoria richiesta dalle liste di adiacenza è minore di quella delle matrici: l'upper bound è in \\`O(nodi + archi)\\`.\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/graphds)\n `}\n \n \n {`\n # Visitare un grafo\n \n Come per gli alberi radicati, esistono due modi per visitare un grafo: _depth-first search_ e _breadth-first search_.\n \n In entrambi i casi, non visito mai due volte lo stesso nodo, e come risultato ottengo **molteplici alberi**, il cui insieme viene detto _foresta di copertura_.\n \n Se il grafo che vogliamo visitare è diretto, allora dobbiamo **considerare come vicini solo gli archi uscenti**\n \n ## Depth-first search\n \n La DFS ci può risultare utile per **identificare le componenti connesse** di un grafo e **identificare eventuali cicli**.\n \n ### Funzionamento\n \n Posso utilizzare la DFS per classificare gli archi di un grafo in quattro categorie:\n \n - _Tree_, archi che ci fanno **scoprire un nuovo nodo**\n - _Forward_, archi che ci portano a un **discendente**\n - _Back_, archi che ci portano ad un **antenato**\n - _Cross_, archi che **connettono due sottoalberi** diversi\n \n Usiamo due array inizializzati a 0 chiamati \\`pre\\` e \\`post\\`, grandi quanto il numero di archi del grafo, che ci indicano rispettivamente quando un nodo è stato scoperto e quando è terminata la visita. \n Inoltre, creiamo una variabile \\`clock\\` che avanza ad ogni evento. \n Alla scoperta di un nuovo nodo, mettiamo il valore attuale di \\`clock\\` all'interno di \\`pre[n]\\`. \n Alla fine della visita di un nodo invece mettiamo il valore di \\`clock\\` in \\`post[n]\\`.\n \n **Durante la visita**, gli archi avranno i seguenti valori:\n - _Tree_: \\`pre[dst] == 0\\`\n - _Forward_: \\`pre[src] < pre[dst] && post[dst] > 0\\`\n - _Back_: \\`pre[dst] < pre[src] && post[dst] == 0\\`\n - _Cross_: Tutti gli altri (\\`post[dst] < pre[src]\\`)\n \n **A fine visita**, gli archi avranno i seguenti valori:\n - _Tree_: \\`pre[dst] < pre[dst] < post[dst] < pre[src]\\`\n - _Forward_: \\`pre[dst] < pre[dst] < post[dst] < pre[src]\\`\n - _Back_: \\`pre[src] < pre[dst] < post[dst] < post[src]\\`\n - _Cross_: \\`pre[dst] < post[dst] < pre[src] < post[src]\\`\n \n Se un **grafo non diretto** contiene degli **archi Back**, allora esso **conterrà un ciclo**.\n \n #### DFS nel grafo trasposto\n \n Se effettuo una DFS sul trasposto di un grafo, posso **scoprire i nodi che hanno un cammino verso l'origine**.\n \n #### DFS nella componente fortemente connessa\n \n Se effettuo una DFS in una componente fortemente connessa e nella sua trasposta, il **\\`post\\` della trasposta sarà sempre minore** del \\`post\\` della componente originale.\n \n ### Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | \\`O(nodi + archi)\\` | \\`Ω(nodi + archi)\\` | **\\`θ(nodi + archi)\\`** |\n | Memoria | \\`O(nodi)\\` | \\`Ω(nodi)\\` | **\\`θ(nodi)\\`** |\n \n ### Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/dfsbfs)\n \n ## Breadth-first search\n \n La BFS ci può risultare utile per **trovare tutti i nodi a una certa distanza** da un'origine.\n \n ### Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | \\`O(nodi + archi)\\` | \\`Ω(nodi + archi)\\` | **\\`θ(nodi + archi)\\`** |\n | Memoria | \\`O(nodi + archi)\\` | \\`Ω(nodi + archi)\\` | **\\`θ(nodi + archi)\\`** |\n \n ### Pseudocodice\n \n Come per gli alberi, la implementiamo in modo **iterativo**:\n \n \\`\\`\\`python\n queue = [starting_node]\n parents = [None for node in graph.nodes]\n distance = [-1 for node in graph.nodes]\n \n # TODO: controllami quando sei più sveglio\n \n while queue:\n node, source, distance = queue.pop(0)\n parents[node.number] = source\n distance[node.number] = distance\n for neighbour in node.neighbours:\n queue.append((neighbour, node, distance+1))\n \\`\\`\\`\n \n > Nella coda, la distanza massima tra un nodo e l'altro è 1.\n \n ### Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/dfsbfs)\n `}\n \n \n {`\n # Algoritmi greedy\n\n Un modo per risolvere problemi algoritmici può essere usare una **tecnica** _greedy_.\n \n Le tecniche greedy consistono nel effettuare tanti piccoli passi, ed effettuare una **scelta** in base ai dati **locali al passo attuale**.\n \n > Scegli il numero di monete più piccole possibili per comporre €1.12.\n >\n > L'algoritmo cerca di scegliere sempre la moneta più grande possibile compatibile con il prezzo in quel momento, quindi:\n > | Moneta scelta | Rimanente |\n > |---------------|-----------|\n > | € 1.00 | € 0.12 |\n > | € 0.10 | € 0.02 |\n > | € 0.02 | € 0.00 |\n \n ## Esempi\n \n Sono algoritmi greedy:\n \n - L'_Algoritmo di Dijkstra_\n - L'_Algoritmo di Kruskal_\n - L'_Algoritmo di Prim_\n `}\n \n \n {`\n # Percorso più breve\n\n Trovare il _percorso più breve_ (o _cammino minimo_) tra due nodi di un **grafo pesato** è un problema frequente nell'informatica; per questo, sono stati sviluppati [numerosi algoritmi](https://en.wikipedia.org/wiki/Shortest_path_problem) per risolverlo.\n \n > Ad esempio, il pathfinding dei nemici nei videogiochi, oppure Google Maps!\n \n ## Percorso più breve da una sorgente singola\n \n Una sottocategoria del problema del percorso più breve è il caso in cui ci interessa sapere i percorsi più brevi che **partono da uno specifico nodo del grafo**: è detto problema del _percorso più breve da una sorgente singola_, o _single-source shortest path_.\n \n Si può notare che se il grafo contiene **costi negativi** allora è possibile che il percorso più breve non esista, in quanto diventa possibile la comparsa di **cicli di costo infinitamente negativo**.\n \n Possiamo notare che, se il percorso più breve tra \\`A\\` e \\`D\\` è \\`A-B-C-D\\`, allora il cammino minimo tra \\`B\\` e \\`D\\` passerà obbligatoriamente per \\`C\\` (\\`B-C-D\\`).\n Diremo più avanti che il percorso più breve ha una **sottostruttura ottimale**.\n \n ### Esempi\n \n Alcuni algoritmi che trovano il percorso più breve sono:\n - L'_Algoritmo di Dijkstra_\n - L'_Algoritmo di Bellman-Ford_\n - La [_ricerca A*_](https://en.wikipedia.org/wiki/A*_search_algorithm)\n `}\n \n \n {`\n # Algoritmo di Dijkstra\n \n L'_Algoritmo di [Dijkstra](https://upload.wikimedia.org/wikipedia/commons/8/85/Dijkstra.ogg)_ è un algoritmo che risolve il problema del **percorso più breve da una sorgente singola** per grafi con pesi **reali positivi** \\`\\\\mathbb{R}^+\\`.\n \n L'algoritmo trova tutti i percorsi più brevi per raggiungere qualsiasi nodo del grafo partendo da un dato nodo, assieme al costo richiesto per farlo.\n \n ## Funzionamento\n \n 1. Separiamo tutti i nodi del grafo in due gruppi: **visitati** e **non visitati**. \n - Tutti i nodi partono da **non visitati**.\n 2. Per ogni nodo, manteniamo un valore \"**costo richiesto per raggiungerlo**\", che verrà cambiato man mano che l'algoritmo avanza.\n - Il costo di partenza è \\`+∞\\`.\n - Il costo sarà **definitivo per i nodi visitati**, e **provvisorio per i non visitati**.\n 3. Creiamo un insieme detto _frontiera_ che conterrà tutti i **nodi non visitati adiacenti** a quelli visitati.\n 4. Prendiamo il nodo iniziale, che avrà un **costo di \\`0\\`**, e definiamolo il nodo _attuale_.\n 5. Finchè ci sono dei nodi non sono stati visitati, ripetiamo il seguente ciclo:\n 1. Aggiungiamo i nodi adiacenti al nodo attuale alla frontiera.\n - Il costo per raggiungerli sarà il **costo per il nodo attuale sommato al costo dell'arco** che li connette al nodo attuale. \n Se questo **costo** risulta essere **minore del costo provvisorio** precedente, esso **diventerà il nuovo costo**.\n - Questa operazione è detta _rilassamento dell'arco_.\n 2. Facciamo diventare **visitato** il nodo attuale.\n - Il percorso che abbiamo fatto per raggiungerlo è obbligatoriamente il più breve.\n 3. Il prossimo nodo attuale sarà il nodo di frontiera con un costo più basso.\n - Per questo, è possibile definire l'algoritmo di Dijkstra come un **algoritmo greedy**.\n \n ### Non funziona se...\n \n L'algoritmo smette di funzionare nel caso in cui siano presenti **costi negativi** e il grafo non sia **aciclico**, in quanto non saremmo mai in grado di rendere visitato un nodo.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | \\`O(nodi + archi) log nodi)\\` |\n \n ### Scomposizione\n \n - Inizializzazione: \\`O(nodi)\\`\n - Creazione coda priorità: \\`O(nodi log nodi)\\`\n - Ciclo: \\`O((nodi + archi) log nodi)\\`\n \n ## Pseudocodice\n \n \\`\\`\\`python\n import math\n \n class Info:\n def __init__(self, distance=math.inf, previous=None):\n self.distance = distance\n self.previous = previous\n \n def dijkstra(graph, start):\n data = [Info() for node in graph.nodes]\n queue = PriorityQueue([start])\n while queue:\n node = queue.pop()\n for arc in node.connections:\n other = arc.other(node)\n if data[node.number].distance + arc.cost < data[other].distance:\n data[other].distance = data[node.number].distance + arc.cost\n queue.decrease_priority_for(other, data[other].distance)\n data[v].previous = node\n return data\n \\`\\`\\`\n \n ## Visualizzazione\n \n [Visualgo](https://visualgo.net/en/sssp)\n `}\n \n \n {`\n # Algoritmo di Bellman-Ford\n\n L'_Algoritmo di Bellman-Ford_ è un algoritmo che, come l'Algoritmo di Dijkstra, risolve il problema del **percorso più breve da una sorgente singola**, però, a differenza da quest'ultimo, l'Algoritmo di Bellman-Ford accetta in input anche grafi con pesi **reali** \\`\\\\mathbb{R}\\` (sia positivi, sia negativi).\n \n ## Funzionamento\n \n L'approccio dell'algoritmo è simile a quello di Dijkstra: entrambi usano il **rilassamento** degli archi per ottenere un costo provvisorio per il raggiungimento di un nodo, ma invece che rilassare solo l'arco con costo inferiore, questo algoritmo **rilassa tutti gli archi** ripetutamente, eliminando la frontiera e il problema dei nodi negativi.\n \n L'operazione di rilassamento è ripetuta \\`nodi - 1\\` volte, ovvero la **lunghezza massima** di un cammino aciclico all'interno di un grafo.\n \n Possiamo individuare dopo i rilassamenti se è presente un nodo con un **ciclo negativo**: ci basta controllare se esiste un arco che connette due nodi con una distanza incompatibile: se \\`a.distanza + arco.costo < b.distanza\\`, allora è presente un ciclo negativo.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | \\`O(nodi * archi)\\` |\n \n ## Pseudocodice\n \n > TODO\n \n ## Visualizzazione\n \n [Visualgo](https://visualgo.net/en/sssp)\n `}\n \n \n {`\n # Disjoint set\n \n Il _disjoint set_ è una struttura dati che rappresenta elementi di un insieme raggruppati in **sottoinsiemi disgiunti**.\n \n ## Metodi\n \n \\`\\`\\`python\n class DisjointNode:\n def __init__(self): ...\n def find_set(self): \"Trova il rappresentante dell'elemento.\"\n def union(self, other): \"Unisce i sottoinsiemi che contengono questo nodo e \\`other\\`.\"\n \\`\\`\\`\n \n ## Implementazione tramite array\n \n Possiamo implementare il disjoint set con due array: uno per l'**indice del rappresentante** e uno per il **rango dell'insieme**.\n \n Un singoletto avrà **sè stesso come rappresentante** e **rango \\`0\\`**.\n \n ### Costo computazionale\n \n - *create_set()*: \\`O(1)\\`\n - *find_set()*: \\`O(h)\\`\n - *union()*: \\`O(h)\\`\n \n ### Pseudocodice\n \n \\`\\`\\`python\n class DisjointNode:\n def __init__(self):\n self.parent = self\n self.rank = 0\n \n def find_set(self):\n element = self\n while self.parent != element:\n element = self.parent\n return element\n \n def union(self, other):\n repres_self = self.find_set()\n repres_other = other.find_set()\n if repres_self == repres_other:\n return\n if repres_self.rank < repres_other.rank:\n repres_greater = repres_other\n repres_lesser = repres_self\n else:\n repres_greater = repres_self\n repres_lesser = repres_other\n repres_lesser.parent = repres_greater\n if repres_greater.rank == repres_lesser.rank:\n repres_greater.rank += 1\n \\`\\`\\`\n \n ### Visualizzazione\n \n [cs.usfca.edu](https://www.cs.usfca.edu/~galles/JavascriptVisual/DisjointSets.html)\n `}\n \n \n {`\n # Trovare il minimum spanning tree\n\n Un altro problema ricorrente riguardante i grafi è trovare il _minimum spanning tree_ di un dato grafo non diretto.\n \n > E' utile per trovare il modo più efficiente per connettere le cose: ad esempio, per decidere la struttura di una rete internet!\n \n ## Esempi\n \n Gli algoritmi principali che risolvono il problema sono due, ed entrambi sono **algoritmi greedy**:\n \n - L'_Algoritmo di Kruskal_\n - L'_Algoritmo di Prim_\n `}\n \n \n {`\n # Algoritmo di Kruskal\n \n L'_Algoritmo di Kruskal_ è un algoritmo **greedy** che **trova il minimum spanning tree** di un grafo.\n \n ## Funzionamento\n \n 1. Ripetiamo questa procedura finchè tutti i nodi non sono connessi:\n 1. Prendiamo ad ogni passo **l'arco meno costoso** del grafo non ancora aggiunto all'insieme.\n 2. Assicuriamoci che **non si creino cicli**: se non se ne verrebbero a creare, possiamo **aggiungere l'arco all'insieme**.\n - Gli archi devono quindi connettere nodi in **componenti connesse diverse**.\n - Possiamo rappresentare le componenti connesse con un **Disjoint Set**.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | \\`O(archi²)\\` |\n \n ### Scomposizione\n \n - DisjointSet.__init__(): \\`O(archi)\\`\n - Per ogni ciclo: \\`O(archi²)\\`\n - DisjointSet.find_set(): \\`O(1)\\`\n - DisjointSet.union(): \\`O(archi)\\`\n \n ## Pseudocodice\n \n \\`\\`\\`python\n def minimum_spanning_tree_kruskal(graph):\n ds = DisjointSet()\n for node in graph.nodes:\n ds.create_set(node)\n arcs = []\n sorted_arcs = sorted(graph.arcs, key=lambda arc: arc.cost)\n for arc in sorted_arcs:\n if ds.find_set(node.start) != ds.find_set(node.end):\n arcs.append(arc)\n ds.union(node.start, node.end)\n return arcs\n \\`\\`\\`\n `}\n \n \n {`\n # Algoritmo di Prim\n \n L'_Algoritmo di Prim_ è un altro algoritmo **greedy** che **trova il minimum spanning tree** di un grafo.\n \n ## Funzionamento\n \n Creo una **coda con priorità** in cui inserisco tutti gli archi visibili dal mio albero, in cui la chiave è il **costo dell'arco**.\n \n Per trovare l'arco con costo più piccolo posso **estrarre un arco** dalla coda: la priorità ci garantisce che esso è l'**arco meno costoso**.\n \n Aggiungo allora un nuovo nodo all'albero, e con esso, **aggiungo alla coda** tutti gli **archi che scoprono un nuovo nodo**.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | \\`O(archi + nodi log nodi)\\` |\n \n ## Pseudocodice\n \n \\`\\`\\`python\n import math\n \n def minimum_spanning_tree_prim(graph, cost_array, start_node):\n # E' un Array di bool: se l'indice corrispondente al nodo è uguale a true, vuol dire che il (nodo è contenuto nell'albero.\n contains = [False for _ in range(len(graph))]\n # Contiene il precedente di ogni nodo \n prev = [None for _ in range(len(graph))]\n # Contiene il costo per arrivare a quel nodo\n cost = [math.inf for _ in range(len(graph))]\n # Creo la priority queue\n pq = PriorityQueue(graph.arcs, key=lambda arc: arc.cost)\n # Parto dal nodo \\`start_index\\`\n # Il costo dell'origine è 0.\n cost[start_node.index] = 0\n contains[start_node.index] = True\n \n while not pq.is_empty():\n new_node = pq.pop()\n contains[new_node.index] = True\n for arc in new_node.connections:\n other_node = arc.other(new_node)\n if not contains[other_node.index] and cost[other_node.index] > arc.cost:\n cost[other_node.index] = arc.cost\n prev[other_node.index] = new_node\n pq.decrease_priority_for(other_node, arc.cost)\n # L'array di prev rappresenta un albero.\n return prev\n \\`\\`\\`_\n `}\n \n \n {`\n # Compressione\n\n _Comprimere_ un file significa **ridurne le dimensioni** senza modificarne il significato.\n \n ## Categorie\n \n ### Compressione lossless\n \n Nella _compressione lossless_, i dati possono essere decompressi riottenendo una copia identica dell'originale.\n \n > Immaginiamo un file che contiene solo le lettere \\`a, b, c, d, e, f\\`.\n >\n > Le lettere compaiono con questa frequenza:\n > |a|b|c|d|e|f|\n > |45%|13%|12%|16%|9%|5%|\n >\n > Possiamo codificare le lettere nel seguente modo:\n > |a|b|c|d|e|f|\n > |\\`0b0\\`|\\`0b100\\`|\\`0b101\\`|\\`0b111\\`|\\`0b1100\\`|\\`0b1101\\`|\n >\n > Scrivere \\`abacadae\\` richiederebbe 64 bits con la codifica ASCII estesa, ma in questo modo riusciamo a scriverlo con soli 17 bits!\n \n Le codifiche di un file compresso devono rispettare la proprietà del _Codice a prefisso_, che dice che **nessun codice deve essere il prefisso di un altro codice**; altrimenti, si avrebbero ambiguità nella decodifica.\n \n > a = \\`1\\`\n > b = \\`11\\`\n >\n > \\`111\\` è \\`ab\\`, \\`ba\\` oppure \\`aaa\\`?\n \n Creiamo allora un _albero di decodifica_: un **albero binario** che, leggendo uno ad uno i bit codificati, ci permette di arrivare al **valore del codice presente sulle foglie** dell'albero.\n \n Gli alberi di decodifica sono sempre **completi**.\n \n > Un albero di decodifica incompleto sarebbe non ottimizzato!\n \n #### Esempi\n \n - .png\n - .flac\n - .zip\n - ...\n \n ### Compressione lossy\n \n Nella _compressione lossy_, alcuni dati [solitamente](http://needsmorejpeg.com/) irrilevanti vengono perduti: non si può, dunque, ricostruire l'originale.\n \n #### Esempi\n \n - .jpeg\n - .mp3\n - ...\n `}\n \n \n {`\n # Algoritmo di Huffman\n\n L'_Algoritmo di Huffman_ è un **algoritmo greedy** per la **costruzione di un albero di decodifica**.\n \n ## Funzionamento\n \n 1. Costruisco **un albero** (con un solo nodo) **per ogni elemento dell'alfabeto**.\n 2. Associo ad **ogni albero la frequenza dell'elemento** da cui è stato creato, per poi inserire tutti gli elementi in una coda con priorità.\n 3. Finchè non ho **un albero solo**:\n 1. Estraggo dalla coda i **due alberi con frequenza minore**.\n 2. **Li rendo fratelli**, creando un nuovo nodo in cui sono uno figlio destro e uno figlio sinistro.\n 3. Associo al nuovo nodo la **somma delle frequenze dei due alberi**, e inserisco il nuovo albero nella coda.\n \n > È molto raro che venga un albero \"dritto\"; se succede, probabilmente c'è qualcosa che non va.\n `}\n \n \n {`\n # Dizionario\n \n Un _dizionario_ è una struttura dati che **associa dei valori a delle chiavi**.\n \n ## Proprietà\n \n - Ogni elemento del dizionario è un **valore** che è stato **associato a una chiave**.\n - Possiamo aggiungere nuovi elementi con il **metodo \\`add(chiave, valore)\\`**.\n - Posiamo estrarre elementi con il **metodo \\`get(chiave)\\`**, che restituirà il valore associato a \\`chiave\\`.\n - E' possibile rimuovere elementi con il **metodo \\`delete(chiave)\\`**.\n - Due elementi con **chiavi diverse** non devono **mai restituire lo stesso valore**.\n \n ## Metodi\n \n Beh... Non ha molto senso in questo caso...\n \n \\`\\`\\`python\n dict()\n \\`\\`\\`\n \n ## Implementazione con tabella hash\n \n Una _tabella hash_ è un'array di coppie **chiave-valore**, che formano l'insieme _universo_.\n \n Per determinare l'**indice dell'array** in cui inserire una coppia, usiamo una [funzione _hash_](https://it.wikipedia.org/wiki/Hash#Algoritmo_di_hash) sulla chiave, che restituirà **numeri da \\`0\\` a \\`len(hash_table)\\`**.\n \n ### Risoluzione collisioni\n \n Potrebbe capitare però che **due chiavi diverse abbiano lo stesso indice**. Dobbiamo allora usare un metodo di _risoluzione collisioni_, che mi permetta di distinguere tra chiavi diverse.\n \n #### Lista di trabocco\n \n Possiamo salvare nell'array **liste di coppie** chiave-valore; in caso di collisione, **aggiungo un nuovo elemento alla lista**.\n \n In media, ciascuna di queste liste conterrà \\`elementi_inseriti / dimensione_tabella\\` elementi.\n \n #### Indirizzamento aperto\n \n Possiamo decidere di mettere le coppie che non trovano posto nel loro indice in **un altro indirizzo vuoto** dell'array.\n \n Ci sono diversi modi in cui decidere il nuovo indirizzo, ognuno con vantaggi e svantaggi: si può scegliere quello successivo, oppure il primo vuoto dell'array, oppure un indirizzo casuale.\n \n > Python, nei \\`dict\\`, usa indirizzamento aperto pseudorandom.\n \n ### Costo computazionale\n \n - Aggiungere una chiave: \\`O(n)\\`\n - Trovare una chiave: \\`O(n)\\`\n - Eliminare una chiave: \\`O(n)\\`\n `}\n \n \n {`\n # Programmazione dinamica\n \n La _programmazione dinamica_ è una **tecnica** di programmazione che prevede l'**estensione di una soluzione ottima precedente**.\n \n Tutti i problemi in cui si può applicare si possono risolvere anche con la **ricorsione**, ma a differenza della ricorsione, questa tecnica riesce ad evitare di ricalcolare la soluzione per ogni chiamata ricorsiva, ottenendo quindi tempi molto migliori.\n \n Si può applicare solo se un problema ha una **sottostruttura ottimale**, ovvero se la soluzione ottima di un sottoproblema è inclusa nella soluzione ottima del problema. \n \n ## Esempi\n \n - _Problema dello zaino_\n - ...\n \n > Il cammino minimo per raggiungere un nodo in un DAG è dato da \\`arco.costo + arco.primo_nodo.costo_cammino_minimo()\\`.\n >\n > \\`\\`\\`python\n > def SPD_PD(graph, start):\n > distance = [float(inf) for node in graph.nodes]:\n > distance[start] = 0\n > # I nodi devono essere in ordine di linearizzazione\n > for node in graph.nodes:\n > distance[node] = min([(arc.cost + distance[arc.other(node)] for arc in node.connections])\n > \\`\\`\\`\n \n > Ho una sequenza di interi da \\`a_1\\` a \\`a_n\\`. Voglio trovare la sottosequenza crescente più lunga.\n >\n > 5 2 3 4 7 3 6 3 1 6\n >\n > Trovo tutte le sequenze lunghe 1, e le rendo nodi di un grafo diretto.\n >\n > Da ogni nodo, creo una connessione verso i suoi maggiori.\n >\n > Infine, cerco i cammini massimi del grafo. \n > \n > Essi saranno la soluzione del problema.\n \n > Trova la lunghezza della sottosequenza più lunga che termina con \\`j\\`.\n >\n > \\`L[j]\\` = lunghezza della sottosequenza più lunga che termina in \\`j\\`\n > \n > \\`\\`\\`python\n > L[j] = max([1 + L[node] for arc in node.connections)]\n > \\`\\`\\`\n >\n > Esempio:\n > \\`\\`\\`python\n > L[9] = max([1+L[8], 1+L[3], 1+L[6]])\n > \\`\\`\\`\n `}\n \n \n {`\n # Problema dello zaino\n \n Il problema dello zaino è un problema _pseudo-trattabile_: non abbiamo dimostrazioni di se sia trattabile o intrattabile.\n \n ## Descrizione\n \n > Sei un ladro, e devi mettere **più refurtiva possibile** nello zaino per scappare. \n > Lo zaino può portare **al massimo \\`dim\\` kili**.\n >\n > **Quali** (e quanti) oggetti scegli?\n \n | Input | Output |\n |-------|--------|\n | \\`dim\\`ensione_zaino, \\`n\\`umero_oggetti, \\`oggetto.peso\\`, \\`oggetto.valore\\` | \\`profitto_massimo\\` |\n \n ## Categorie\n \n ### Problema con ripetizione\n \n Puoi prendere **tutte le copie che vuoi** di un oggetto.\n \n #### Soluzione\n \n \\`K(dim)\\` è il valore massimo ottenibile con uno zaino di capacità \\`dim\\`.\n \n > Se \\`i\\` appartenesse alla soluzione ottima, allora \\`K(dim) = i.valore + K(dim - i.peso)\\`...\n \n Possiamo dire che \\`K(dim) = max(i.valore + K(dim - i.peso))\\`.\n \n Inoltre, \\`K(0) = 0\\`.\n \n Ci salviamo tutte le soluzioni da \\`K(0)\\` a \\`K(dim)\\`, e le usiamo per calcolare il massimo in seguito.\n \n Calcolare \\`K(dim)\\` avrà allora un costo di \\`O(n * dim)\\`:\n - \\`n\\`, perchè trovare il massimo è un'operazione lineare\n - \\`dim\\`, perchè \\`dim\\` sono tutti i casi tra i quali devo andare a provare\n \n Il costo computazionale, allora, è in \\`O(n * dim)\\`. \n \n Però, il **tempo richiesto** dal nostro algoritmo dipende non dalla lunghezza dell'input, bensì dal **valore numerico** di \\`dim\\`, che corrisponde alla dimensione dell'array delle soluzioni. \n Allora, si dice che l'algoritmo è in **tempo _pseudo-polinomiale_**.\n \n ### Problema senza ripetizione\n \n Si può prendere **ogni oggetto una volta sola**.\n \n #### Soluzione _bruteforce_\n \n Scelgo se prendere o no l'item 1.\n \n Si creano due percorsi:\n - Non prendo l'oggetto: \\`valore = 0, peso = 0\\`\n - Prendo l'oggetto: \\`valore = oggetto.valore, peso = oggetto.peso\\`\n \n Continuo a creare percorsi, creando una specie di albero binario.\n \n Se a un certo punto vedo che \\`valore = x, peso = K\\` e \\`valore < x, peso = K\\`, allora posso escludere automaticamente tutto il sottoalbero destro, perchè non può essere migliore del sinistro: allora, sarò riuscito a ridurre il numero dei casi rispetto alla ricorsione.\n \n ### Problema in due variabili\n \n \\`K(j, w)\\` = massimo valore ottenibile con uno zaino di capacità \\`w\\` scegliendo gli item da \\`1\\` a \\`j\\`.\n \n Non possiamo più applicare la soluzione bruteforce, perchè abbiamo due variabili, \\`j\\` e \\`w\\`.\n \n Allora, prendo l'elemento \\`j\\`. Esso può essere o non essere nella soluzione: mi calcolo entrambe le alternative, e mi tengo l'alternativa dal valore più alto.\n \n Se \\`j\\` non è nella soluzione, il risultato diventerà \\`K(j-1, w)\\`; se invece è nella soluzione, il risultato sarà \\`j.valore + K(j-1, w-j.peso)\\`.\n \n In pratica, prendiamo\n \n \\`\\`\\`latex\n K(j, w) = max\n \\\\begin{cases}\n V_j + K(j-1, w-w_j)\n K(j-1, w)\n \\\\end{cases}\n \\`\\`\\`\n \n Costruisco allora una matrice con \\`j\\` su un asse e \\`w\\` sull'altro. \n Riempio le caselle con il valore di \\`K(j, w)\\`. \n Nella casella con \\`K(j, w)\\` avremo la soluzione ottima.\n \n Il tempo necessario per riempire tutte le caselle è nuovamente \\`O(n * w)\\`, ancora **pseudopolinomiale**.\n \n Per sapere che oggetti ho messo o no devo tenere traccia in qualche modo della catena del calcolo, usando, ad esempio, una pila.\n `}\n \n \n {`\n # Problemi intrattabili\n \n ## Problema di Set-Cover\n \n ### Input\n \n \\`U\\`niverso di \\`e\\`lementi\n \n \\`S\\`ottoinsieme di \\`s\\`ottoinsiemi di elementi di \\`U\\`\n \n ### Output\n \n Il minimo \\`S'\\`ottoinsieme di \\`s\\`ottoinsiemi che copra completamente \\`U\\`.\n \n ### Soluzione in \\`O(n^d)\\`\n \n Non c'è.\n \n ### Non-soluzione alternativa\n \n Faccio una scelta greedy, ma non posso dimostrare in alcun modo che la soluzione ottenuta sia quella ottima. \n Infatti, l'algoritmo non dà sempre la soluzione ottima, ma dà una soluzione accettabile in tempo polinomiale.\n \n Seleziono sempre il sottoinsieme che copre più elementi mancanti possibili.\n \n #### Costo computazionale\n \n \\`Costo greedy <= log(numero_elementi) * Costo ottimo\\`\n `}\n \n
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\n \n {r`\n # Algoritmi e Strutture Dati\n\n Docente: [**Manuela Montangero**](mailto:manuela.montangero@unimore.it)\n\n Crediti: **9 CFU** (72 ore di lezione)\n\n Orario di ricevimento: **Giovedì dalle 14:30 alle 16:30**\n _Mandare una mail prima, altrimenti potrebbe andarsene_\n\n\n #### Regole particolari per le email\n\n - Oggetto \"ASD\"\n - Mail **firmata** con **nome e cognome**\n - Mail spedita dall'**account Unimore**\n\n ### Materiale\n\n Libri:\n - **Introduzione agli Algoritmi e Strutture Dati** di _T.H. Cormen, C. E. Leiserson, R. L. Rivest, C. Stein_\n\n **[Dolly (FIM)](https://dolly.fim.unimore.it/2018/course/view.php?id=26)**\n\n ### Tutorato\n\n Tutor: [**Gianluca d'Addese**](mailto:tutoratoalgoritmi@gmail.com)\n\n Cosa: **Esercizi sugli argomenti visti a lezione** e **preparatori all'esame**\n\n Quando: **Mercoledì dalle 09:00 alle 11:00**...?\n\n ### Esame\n\n Per iscriversi all'esame, bisogna aver passato:\n\n - Analisi matematica (propedeutica)\n - Programmazione I\n\n Formato:\n\n - Prima prova scritta\n - Risolvere problemi con algoritmi proposti a lezione\n - E' un test sulla preparazione\n - Dura 1h30m\n - Non si può usare nessun tipo di materiale\n - Seconda prova scritta\n - Proponi soluzioni per nuovi problemi non studiati a lezione\n - Domande teoriche sugli argomenti studiati\n - Dura 2h\n - E' il giorno dopo la prima prova\n - Si può utilizzare qualsiasi materiale, ma non deve permettere di comunicare\n - Orale facoltativo\n - Solo per chi supera entrambi gli scritti\n - Domande su quello che abbiamo visto a lezione (\"perchè gli algoritmi funzionano?\")\n - Informare via email entro 3 giorni dalla pubblicazione degli esiti della seconda prova\n - L'orale potrebbe migliorare o peggiorare il voto (anche \"molto\")\n\n **Attenzione:** Vengono verbalizzati anche i voti insufficienti; ricordarsi di rifiutarli!\n\n Ci sono i seguenti appelli:\n\n - 3 appelli tra Giugno e Luglio\n - 1 appello a Settembre\n - 2 appelli a Gennaio e Febbraio\n\n Vale il salto di appello se:\n\n - Uno studente regolarmente iscritto **non si presenta** all'appello e non ha avvisato via email almeno il giorno prima.\n - Uno studente ha riportato una **grave insufficienza** in uno dei due scritti, e l'appello successivo è nella stessa sessione\n\n\n ### Note\n\n Il corso è ben collegato con quello di Programmazione 2.\n\n Dormire non fa bene!\n `}\n \n \n {`\n # Il nome del corso\n\n ## Cosa sono gli algoritmi?\n\n Gli algoritmi sono modi sistematici per risolvere problemi.\n\n Sono fondamentali per sviluppare software, in quanto i computer sono eccellenti esecutori di algoritmi.\n\n ## Come si sviluppa un algoritmo?\n\n Innanzitutto, bisogna conoscere gli _input_ e gli _output_ del problema, rispettivamente i dati di partenza e i dati di arrivo di esso; si ha quindi una fase di **ricerca**.\n\n Poi, si deve trovare un procedimento che ci faccia risolvere il nostro problema: è quello che faremo in questa materia!\n\n Infine, bisogna scrivere la soluzione in un modo che possa essere eseguita da un computer: questa è la **programmazione**.\n\n ## Che tipo di problemi possiamo risolvere?\n\n Un algoritmo risolve problemi di tipo generale, non ci interessa sapere _il risultato di 123+456_, ma vogliamo sapere _il risultato di x+y_, dove x e y sono due numeri naturali qualsiasi.\n\n Un problema può essere quindi considerato circa come una **funzione matematica**, che connette ogni input a un output corrispondente.\n\n ## Che caratteristiche ha un algoritmo?\n\n Per prima cosa, ripetendo l'algoritmo più volte con lo stesso ingresso deve dare sempre la stessa uscita come **risultato**, finendo in un **tempo finito**.\n\n Deve essere **ben ordinato**: cambiando l'ordine in cui vengono effettuate le operazioni, è probabile che anche il risultato cambi!\n\n Le sue istruzioni devono essere **non ambigue**, cioè che non possano essere interpretate in più modi, e **effettivamente realizzabili**, cioè realizzabili con l'esecutore che vogliamo usare per eseguire l'algoritmo.\n\n ## Esistono algoritmi equivalenti?\n\n **Sì!** Possono esserci due algoritmi che dati gli stessi input, hanno gli stessi output, e quindi risolvono lo stesso problema.\n\n In compenso, possono avere un numero di operazioni diverse, e quindi essere **uno più veloce** (da eseguire) dell'altro.\n\n ## Come si verifica la correttezza di un algoritmo?\n\n L'algoritmo deve essere **valido per tutti gli input**, anche se questi sono infiniti.\n\n Possiamo effettuare prove matematiche per verificarne la correttezza; il **principio di induzione** è dunque una dei teoremi fondamentali dell'algoritmica.\n\n Possiamo però verificare la _non correttezza_ di un algoritmo trovando un singolo controesempio.\n `}\n \n \n {`\n # Efficienza degli algoritmi\n \n Un buon algoritmo deve essere **efficiente**, ovvero deve usare il minimo delle risorse necessarie, come _usare il minimo di tempo possibile_.\n \n ## Come misuriamo il tempo necessario?\n \n Cerchiamo di astrarre il tempo dal particolare esecutore, e andiamo a contare il numero di operazioni elementari richieste per eseguire il nostro algoritmo nel caso peggiore.\n \n Un algoritmo efficiente, infatti, all'aumentare dei dati in ingresso, diventerà sempre più veloce rispetto a uno non efficiente, anche su computer più lenti!\n \n > Il [Bubble Sort](https://en.wikipedia.org/wiki/Bubble_sort) è sempre più lento di un [Tree Sort](https://en.wikipedia.org/wiki/Tree_sort), anche su computer più lenti, perchè, dovendo ordinare liste sempre più lunghe, prima o poi si raggiunge un punto in cui il primo è più veloce (in termini di tempo) dell'altro.\n \n Dobbiamo andare a vedere, quindi, _il numero di operazioni richieste per ottenere il risultato nel caso peggiore_.\n \n Consideriamo operazioni sia operazioni aritmetiche sia operazioni logiche, e diciamo che ciascuna costa 1.\n \n > L'[algoritmo di Euclide](https://it.wikipedia.org/wiki/Algoritmo_di_Euclide) per l'MCD costa \\`3\\` per ogni iterazione (un giro del ciclo \\`while\\`). Diciamo, allora, che costa \\`3n\\`, dove \\`n\\` è il numero più alto dei due, perchè nel caso peggiore (uno dei due numeri è 1) l'algoritmo compie \\`n\\` iterazioni.\n \n ## Altri parametri ottimizzabili\n \n È possibile che alcuni algoritmi per vari motivi cerchino di ottimizzare altri parametri diversi dal tempo, come ad esempio _la dimensione dell'input_ o la _memoria utilizzata_. \n \n > Generalmente, questo viene fatto sui dispositivi embedded, con memoria molto limitata.\n \n ### Criteri di costo di memoria\n \n Ci sono vari criteri con cui stimare la memoria richiesta da un dato: è possibile che il costo risultante vari in base al criterio scelto!\n \n #### Criterio di costo logaritmico\n \n Un dato costa il numero di bit necessari per rappresentarlo.\n \n > Un int che contiene il numero \\`n\\` costa \\`log_2(n)\\`. \n > Un array di \\`[n]\\` numeri tutti uguali costa \\`n log_2(n)\\`.\n \n #### Criterio di costo uniforme\n \n Un dato costa il numero di elementi che lo costituiscono.\n \n > Un int che contiene il numero \\`n\\` costa \\`1\\`. \n > Un array di \\`[n]\\` numeri costa \\`n\\`. \n > Una matrice \\`[m][n]\\` costa \\`m*n\\`.\n `}\n \n \n {`\n # Modelli algoritmici\n\n Per progettare un algoritmo, abbiamo bisogno di sapere le proprietà del nostro esecutore, ovvero il suo _modello algoritmico_.\n \n > Ad esempio, dobbiamo sapere quali istruzioni è in grado di eseguire, e quanto tempo queste istruzioni richiedono.\n \n ## Il modello RAM\n \n Il modello in uso su tutti i computer attuali è il _modello RAM_: \n \n - In ogni cella di memoria può essere archiviato un dato.\n - Il **tempo di accesso** alle celle è **costante** per tutte le celle.\n - La **memoria** principale è **infinita**.\n - Si ha **un solo processore**.\n `}\n \n \n {`\n # Notazione asintotica\n \n La _notazione asintotica_ è un sistema per **stimare** velocemente il costo di un algoritmo complesso.\n \n Ci permette di **confrontare velocemente il caso peggiore** degli algoritmi.\n \n In particolare, consideriamo il _rapporto tra il numero di operazioni nel caso peggiore e la dimensione dell'input_.\n \n ## Limiti\n \n Possiamo dare a questa stima dei limiti, superiore e inferiore, che rappresenteranno rispettivamente un costo che non sarà **mai superato** e un costo che verrà **sempre superato**.\n \n Chiameremo questi limiti _upper bound_ e _lower bound_; la loro combinazione darà un _tight bound_.\n \n L'obiettivo sarà di _ricavare i bound più precisi possibile_ per un dato algoritmo, ovvero l'**upper bound più basso** e il **lower bound più alto**.\n \n ### O grande\n \n > \"O grande\" \n > O di g(n)\n > \"big-O\"\n \n Per rappresentare la stima, useremo una notazione particolare, detta _O grande_, con la seguente proprietà:\n - Date due funzioni \\`f(n) : N -> R\\` e \\`g(n) : N -> R\\`, diremo che \\`f(n) ∈ O(g(n))\\` se e soltanto se \\`∃ c > 0, n ≥ n_0\\` tali che \\`∀ n ≥ 0, f(n) ≤ c * g(n)\\`\n \n Quando una funzione è O grande di un altra, significa che **asintoticamente, la funzione in O grande è sempre maggiore di quella che sta venendo stimata**.\n \n > **Ipotesi** \n > - \\`f(n) = 2n² + 3n + 6\\` \n > - \\`g(n) = n²\\`\n >\n > **Tesi** \n > - \\`f(n) ∈ O(n²)\\`.\n >\n > **Svolgimento** \n > Scrivo una disequazione, lasciando intatto il termine noto: \n > 1. \\`2n² + 3n + 6 ≤ 2n² + 3n² + 6\\` \n > 2. \\`n² ≤ 2n² + 3n² + n² = 6n²\\` per \\`n ≥ 3\\`\n >\n > Sappiamo, allora, che \\`2n² + 3n + 6 ≤ 6n²\\`.\n \n #### Espressioni di O grande\n \n Questa tabella rappresenta le espressioni di O grande più comunemente utilizzate, in ordine **dalla più forte alla più debole**.\n \n > Più forte significa che, per ogni riga della tabella, tutte le righe sottostanti sono contenute nell'espressione.\n >\n > Ad esempio, \\`O(n) ∈ O(1)\\`.\n \n | Espressione O() | Nome |\n |-----------------|------|\n | \\`O(1)\\` | Costante |\n | \\`O(log log n)\\` | loglog |\n | \\`O(log n)\\` | Logaritmica |\n | ![LaTeX](https://latex.codecogs.com/png.latex?O(n^{1/c})) (per c ≥ 1) | Sublineare |\n | \\`O(n)\\` | Lineare |\n | \\`O(n log n)\\` | nlogn |\n | \\`O(n²)\\` | Quadratica |\n | \\`O(n³)\\` | Cubica |\n | \\`O(n^k)\\` (per k ≥ 1) | Polinomiale |\n | \\`O(a^n)\\` (per a ≥ 1) | Esponenziale |\n | \\`O(n!)\\` | Fattoriale |\n \n #### Polinomiale\n \n Molto spesso, noteremo che il tempo richiesto da una funzione è O grande di un polinomio di grado K, ovvero \\`f(n) ∈ O(n^k)\\`.\n \n Notiamo che in questi casi, possiamo semplificare l'O grande al grado massimo del polinomio.\n \n > Ad esempio, \\`O(n² + n + 1) = O(n²)\\`.\n \n ##### Dimostrazione\n \n Per \\`n > 0 \\\\and 0 ≤ i ≤ k\\`: \n ![LaTeX](https://latex.codecogs.com/png.latex?a_k%20n^k%20+%20a_{k-1}%20n^{k-1}%20+%20%E2%80%A6%20+%20a_1%20n%20+%20a_0%20%E2%89%A4%20|a_k|%20n^k%20+%20|a_{k-1}|%20n^k%20+%20%E2%80%A6%20+%20|a_1|%20n^k%20+%20|a_0|%20n^k%20=%20(|a_k|%20+%20|a_{k-1}|%20+%20%E2%80%A6%20+%20|a_1|%20+%20|a_0|)%20n^k)\n \n #### Proprietà di O grande\n \n 1. \\`f(n) ∈ O(g(n)) -> ∀ a > 0, a * f(n) ∈ O(g(n))\\`.\n 2. \\`f(n) ∈ O(g(n)), d(n) ∈ O(h(n)) -> f(n) + d(n) ∈ O(g(n) + h(n)) -> O(max\\\\{g(n), h(n)\\\\})\\`\n 3. \\`f(n) ∈ O(g(n)), d(n) ∈ O(h(n)) -> f(n) * d(n) ∈ O(g(n) * h(n))\\`\n \n In pratica, se una funzione è la _somma di più termini_, basta guardare l'**\\`O()\\` più grande** tra tutti i suoi termini; se invece una funzione è un _prodotto di più termini_, si possono **omettere le costanti**, e l'\\`O()\\` finale sarà dato dal **prodotto degli \\`O()\\`** dei termini.\n \n ## Lower bound\n \n Possiamo anche stimare il _lower bound_, il limite inferiore: il **numero minimo di operazioni** che viene effettuato **nel caso migliore** con la **massima dimensione dell'ingresso**.\n \n ### Ω()\n \n > \"Omega\" \n > Omega di g(n)\n > \"big-Omega\"\n \n Esiste un equivalente di O grande per il lower bound: è detto _Omega grande_, o più semplicemente _Omega_, e funziona nello stesso identico modo, solo... al contrario.\n \n Diremo che \\`f(n) ∈ Ω(g(n))\\` se e solo se \\`∃ c > 0, n_0 ≥ 0 : ∀ n ≥ n_0 f(n) ≥ c * g(n)\\`.\n \n #### Espressioni di Ω()\n \n Anche in questa tabella le espressioni sono **dalla più forte alla più debole**.\n \n | Espressione Ω() | Nome |\n |-----------------|------|\n | \\`Ω(n!)\\` | Fattoriale |\n | \\`Ω(a^n)\\` (per a ≥ 1) | Esponenziale |\n | \\`Ω(n^k)\\` (per k ≥ 1) | Polinomiale |\n | \\`Ω(n³)\\` | Cubica |\n | \\`Ω(n²)\\` | Quadratica |\n | \\`Ω(n log n)\\` | nlogn |\n | \\`Ω(n)\\` | Lineare |\n | ![LaTeX](https://latex.codecogs.com/png.latex?\\\\Omega(n^{1/c})) (per c ≥ 1) | Sublineare |\n | \\`Ω(log n)\\` | Logaritmica |\n | \\`Ω(log log n)\\` | loglog |\n | \\`Ω(1)\\` | Costante |\n \n ## Tight bound\n \n Quando **upper e lower bound coincidono**, allora otteniamo un _tight bound_.\n \n ### θ()\n \n > \"Theta\" \n > Theta di g(n)\n > \"big-Theta\"\n \n Anche per il tight bound abbiamo una notazione equivalente a O grande e Omega grande: _Theta grande_!\n \n Diciamo che \\`f(n) ∈ θ(g(n))\\` se e solo se \\`∃ c_1, c_2 > 0, n_0 ≥ 0 : ∀ n ≥ n_0, c_1 * g(n) ≤ f(n) ≤ c_2 * g(n)\\`.\n \n Ha la particolarità che non valgono tutte le proprietà degli altri due: va usata quindi con cautela!\n \n ## Risorse utili\n \n [khanacademy.org](https://www.khanacademy.org/computing/computer-science/algorithms/asymptotic-notation/a/big-big-theta-notation)\n `}\n \n \n {`\n # Problemi algoritmici\n \n Un _problema algoritmico_ è un problema matematico che si vuole provare a risolvere con un algoritmo.\n \n > Dati 10 numeri, voglio sapere se sono in ordine crescente oppure no.\n \n ## Caterigorizzazione\n \n I problemi algoritmici si dividono in tre categorie: problemi _trattabili_, problemi _intrattabili_ e problemi _irrisolvibili_.\n \n ### Problema trattabile\n \n Perchè un problema algoritmico sia _trattabile_, deve avere **almeno un algoritmo con upper bound polinomiale**.\n \n > Questo significa che il tempo impiegato da un computer per risolvere il problema rimane ragionevole, e che quindi può essere utilizzato in maniera efficiente.\n \n La trattabilità è un campo ancora parecchio aperto: esistono anche tanti problemi di cui non si è ancora dimostrata la trattabilità o intrattabilità.\n \n > La [fattorizzazione](https://it.wikipedia.org/wiki/Fattorizzazione) è uno di questi problemi: l'assenza di una dimostrazione è ciò che la rende uno dei pilastri della sicurezza informatica moderna.\n \n ### Problema intrattabile\n \n Se **un problema non ha nessun algoritmo con upper bound polinomiale**, allora si dice che è **intrattabile**.\n \n ### Problema irrisolvibile\n \n Se **non esistono algoritmi per risolvere un problema**, allora questo si dice **irrisolvibile**.\n \n > [Dato un algoritmo con certi input, riusciamo a capire con un algoritmo se la sua esecuzione termina o no?](https://en.wikipedia.org/wiki/Halting_problem)\n \n ### Upper e lower bound di problemi\n \n Si può anche trovare un _upper bound_ e un _lower bound_ per un problema, ma bisogna generalizzare di più.\n \n L'**upper bound di un problema** è il minimo upper bound di tutti gli algoritmi che lo risolvono; deve esistere almeno un algoritmo che lo risolva che abbia lo stesso _upper bound_. E' praticamente il tempo migliore per risolvere il problema dato.\n \n Il **lower bound di un problema** è il minimo lower bound di tutti gli algoritmi che lo risolvono; non deve esistere nemmeno un algoritmo che abbia un lower bound migliore. E' il numero assolutamente minimo di operazioni richieste, non si può fare meglio di così.\n \n In particolare, abbiamo che l'_upper bound di un algoritmo_ -> l'_upper bound del suo problema_, \n e il _lower bound di un problema_ -> il _lower bound di un suo algoritmo_.\n \n Generalmente, il _lower bound di un problema_ è una rappresentazione abbastanza accurata della sua difficoltà.\n `}\n \n \n {`\n # Ricerca binaria\n \n Non credo di aver bisogno di studiare la ricerca binaria, quindi non ho preso appunti a riguardo.\n \n Se non siete me, e state cercando informazioni a riguardo, andate a vedere su Wikipedia!\n `}\n \n \n {`\n # Divide et impera\n \n Un modo efficace per risolvere un problema è di usare il metodo _divide et impera (et combina)_.\n \n - _Divide_: Divido il problema in **tanti sottoproblemi**.\n - _Impera_: **Risolvo indipendentemente dal resto** ciascuno dei sottoproblemi.\n - _Combina_: **Combino** i risultati dei sottoproblemi per **risolvere il problema principale**.\n \n ## Ricorsione\n \n Un algoritmo (o funzione) si dice _ricorsivo_ quando durante l'esecuzione **richiama sè stesso**.\n \n Dato che tutti gli algoritmi devono avere termine entro un tempo finito, se scriviamo una funzione ricorsiva è fondamentale finire con un **caso base**, che non chiami ulteriormente la ricorsione.\n \n Se esiste una funzione ricorsiva, allora esiste _sempre_ una _funzione iterativa_ che darà lo stesso risultato.\n \n > Sul pratico, una funzione ricorsiva tipicamente è **più costosa** del suo equivalente iterativo: se possibile, quindi, la ricorsione andrebbe evitata.\n \n #### Pseudocodice di esempio\n \n \\`\\`\\`python\n def fattoriale(n):\n # Caso base; la ricorsione finisce e dà un risultato fisso\n if n <= 1:\n return 1\n # Caso ricorsivo; la funzione restituisce il risultato di sè stessa (ma con parametri diversi)\n else:\n return n * fattoriale(n - 1)\n \\`\\`\\`\n `}\n \n \n {`\n # Master Theorem\n \n Il _Master Theorem_ è uno dei teoremi più importanti dell'algoritmica.\n \n Esso permette di **calcolare l'upper bound di un algoritmo ricorsivo** in modo piuttosto semplice.\n \n ## Ipotesi\n \n Dato un algoritmo:\n - Con uno o più casi base\n - Che richiama la funzione ricorsiva un numero n di volte\n \n ## Tesi\n \n Allora, il suo upper bound avrà la formula:\n \n ![](https://quicklatex.com/cache3/89/ql_08d29a7e55d561a900570bc83b93ff89_l3.png)\n `}\n \n \n {`\n # Caso particolare del Master Theorem\n \n ## Ipotesi\n \n Se: \n ![](https://quicklatex.com/cache3/57/ql_e34dc27b42831d3c3ff671b0f3861257_l3.png)\n \n Ovvero, se la dimensione dell'input viene divisa ad ogni ciclo da una costante b, è polinomiale e il caso base è costante...\n \n ## Tesi\n \n Allora: \n ![](https://quicklatex.com/cache3/ca/ql_26e3557a6ca2d6ac4b8481e7c5263fca_l3.png)\n \n > In pratica, se il costo dominante è quello della parte \"fissa\" dell'algoritmo, esso sarà \\`O(n^d)\\`, mentre se il costo dominante è quello delle chiamate ricorsive, esso sarà \\`O(n^{log_b e})\\`. \n > Se nessuno dei due è dominante... si dividono circa in parti uguali, creando un costo di \\`O(n^d log n)\\`.\n `}\n \n \n {`\n # Ordinamento\n \n Un problema molto frequente nell'informatica consiste nell'**ordinare efficientemente grandi quantità di elementi**.\n \n Esistono [tantissimi](https://it.wikipedia.org/wiki/Algoritmo_di_ordinamento) algoritmi per effettuare l'ordinamento. \n L'**efficienza** di ciascuno **varia** di caso in caso: alcuni sono estremamente efficienti se quasi tutti i numeri sono già nell'ordine giusto; altri, invece, potrebbero impiegare tantissimo tempo.\n \n In termini matematici, abbiamo:\n \n - **Input:** A[n]\n - **Output:** B, ∀ i < n, A[i] ≤ A[i+1]\n \n ## Ordinamento tramite confronto\n \n L'ordinamento \"tradizionale\" è detto _ordinamento tramite confronto_: funziona sempre, e **non ha altri modi di ottenere informazioni** se non con l'operazione logica di confronto tra i dati.\n \n ### Limiti\n \n E' un problema risolto: è dimostrabile che il suo **lower bound** è **\\`Ω(n log n)\\`**; possiamo quindi dire che qualsiasi algoritmo di ordinamento è in \\`Ω(n log n)\\`, e se riusciamo a trovare un algoritmo di ordinamento in \\`O(n log n)\\` siamo riusciti a raggiungere il massimo dell'efficienza.\n \n #### Dimostrazione\n \n Consideriamo **tutte le possibili permutazioni** della sequenza da ordinare: sono \\`n!\\`.\n \n Per ogni confronto che effettuiamo, **riduciamo la quantità di permutazioni** correttamente ordinate; prima o poi, rimarrà **una sola possibilità**.\n \n **TODO, non trovo la spiegazione corretta!**\n \n ### Esempi\n \n Algoritmi che effettuano l'ordinamento tramite confronto sono:\n - _Bubble sort_\n - _Merge sort_\n - _Insertion sort_\n - _Quick sort_\n - _Heap sort_\n - E tanti, tanti altri!\n \n ## Ordinamento con altri mezzi\n \n Esistono algoritmi che ricavano informazioni in altri modi, diversi dal confronto.\n \n Essi possono avere un lower bound più basso di \\`O(n log n)\\`, però hanno spesso limitazioni sul loro utilizzo.\n \n ### Esempi\n \n - _Counting sort_, indicizza i valori da ordinare\n - _Radix sort_, guarda singolarmente le cifre dei valori\n - _Sleep sort_, sfrutta i thread e la funzione sleep per ordinare valori\n - E altri ancora!\n `}\n \n \n {`\n # Insertion sort\n \n L'_insertion sort_ è una soluzione **iterativa** all'ordinamento per confronto.\n \n ## Funzionamento\n \n Considero la sequenza divisa in **due parti**: una parte **ordinata** e una parte **non ordinata**.\n \n Parto dal primo elemento della lista: è sempre ordinato con sè stesso. \n Poi, aggiungo uno alla volta i numeri della parte non ordinata a quella ordinata; prima trovo in quale posizione dovrò andare a mettere il numero, poi **faccio slittare tutti i numeri dopo quella posizione** avanti di 1, in modo da **creare lo spazio** in cui infine **inserirò** il numero.\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | \\`O(n²)\\` | \\`Ω(n)\\` | - |\n \n Nel _caso migliore_ (**lista già ordinata**), il numero da inserire è già nella posizione giusta, quindi non devo effettuare altri confronti oltre il primo, rendendo il lower bound dell'algoritmo \\`Ω(n)\\`.\n \n Nel _caso peggiore_ (**lista nell'ordine inverso**), dobbiamo confrontare il numero da inserire con tutti gli altri nella parte ordinata: dobbiamo allora eseguire \\`1+2+3+4+5+… = \\\\frac{(n-1)(n)}{2}\\` confronti; ciò significa che l'upper bound è \\`O(n²)\\`!\n \n ## Pseudocodice\n \n \\`\\`\\`python\n def insertion_sorted(lista):\n # Itero su tutti i numeri della lista, dal primo all'ultimo.\n for divisore_ord in range(len(lista)):\n # Partendo dalla posizione attuale, creo l'indice di divisione numeri ordinati maggiori e minori\n divisore_magg = divisore_ord\n # Faccio slittare avanti i numeri maggiori di quello che stiamo inserendo\n # Se l'indice divisore_magg raggiunge 0, vuol dire che tutti i numeri della lista sono maggiori del numero attuale \n while divisore_magg >= 0 and lista[divisore_magg-1] > lista[divisore_magg]:\n # Scambio la posizione dei due elementi con gli indici specificati\n # Funzione inventata \n lista[divisore_magg], lista[divisore_magg-1] = lista[divisore_magg-1], lista[divisore_magg]\n # Diminuisco il separatore di 1\n divisore_magg -= 1\n \\`\\`\\`\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/bn/sorting)\n `}\n \n \n {`\n # Merge sort\n \n Il _merge sort_ è una soluzione **ricorsiva** all'ordinamento per confronto.\n \n ## Funzionamento\n \n Per questo algoritmo, utilizziamo la tecnica del **divide et impera**.\n \n 1. _Divide_: Divido A in **due parti**.\n 2. _Impera_: Metto **separatamente in ordine** le parti.\n 3. _Unisci_: **Unisco** le due parti.\n \n Consideriamo come **caso base** della ricorsione una parte composta da un numero, che ovviamente è già ordinata con sè stessa.\n \n ### Merge\n \n Per **unire le due parti** usiamo una funzione detta \\`merge()\\`.\n \n Costruiamo una nuova sequenza uguale alla sequenza 1, ma **aggiungiamo alla fine un valore sentinella** sempre maggiore di tutti gli elementi contenuti.\n \n > \\`\\`\\`\n > | 1 | 3 | 7 | 8 | ∞ |\n > \\`\\`\\`\n \n Facciamo **la stessa cosa** per la sequenza due.\n \n > \\`\\`\\`\n > | 2 | 4 | 5 | 6 | ∞ |\n > \\`\\`\\`\n \n Prendo i primi numeri delle due sequenze e **metto il più piccolo nella sequenza iniziale**.\n \n > \\`\\`\\`\n > | 1 | 2 | 3 | | | | | | \n > | | | 7 | 8 | ∞ | \n > | | 4 | 5 | 6 | ∞ | \n > \\`\\`\\`\n \n **Continuo** finchè non ho messo tutti i numeri; **grazie alla sentinella non usciremo mai dalla sequenza**, in quanto essa è sempre maggiore di tutti gli altri numeri.\n \n > \\`\\`\\`\n > | 1 | 2 | 3 | 4 | 5 | 6 | | | \n > | | | 7 | 8 | ∞ | \n > | | | | | ∞ |\n > \\`\\`\\`\n \n Quando **rimangono solo le sentinelle** significa che abbiamo aggiunto tutti gli elementi, e quindi abbiamo finito.\n \n > \\`\\`\\`\n > | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | \n > | | | | | ∞ | \n > | | | | | ∞ | \n > \\`\\`\\`\n \n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | \\`O(n log n)\\` | \\`Ω(n log n)\\` | **\\`θ(n log n)\\`** |\n \n Il merge sort è un algoritmo ricorsivo con un **caso base in tempo costante** e che **richiama sè stesso 2 volte**.\n \n \\`\\`\\`latex\n T(n) =\\\\\\\\\n \\\\\\\\\n Θ(1) \\\\qquad n=1\\\\\\\\\n 2 T(\\\\frac{n}{2}) + Θ(n) \\\\qquad n \\\\neq 1\n \\`\\`\\`\n \n Applicando il **caso particolare del Master Theorem**, otteniamo:\n \n \\`\\`\\`latex\n T(n) =\\\\\\\\\n \\\\\\\\\n Θ(1) \\\\qquad n=1\\\\\\\\\n Θ(n log n) \\\\qquad n \\\\neq 1\n \\`\\`\\`\n \n ## Pseudocodice\n \n \\`\\`\\`python\n def merge_sorted(part):\n # Caso base\n if len(part) == 1:\n return part\n # Divide\n middle = len(part) // 2\n part_a = part[:middle]\n part_b = part[middle:]\n # Impera\n sort_a = merge_sorted(part_a)\n sort_b = merge_sorted(part_b)\n # Combina\n return merge(sort_a, sort_b)\n \\`\\`\\`\n \n ## Visualizzazione\n \n [hackerearth.com](https://www.hackerearth.com/practice/algorithms/sorting/merge-sort/visualize/)\n \n [visualgo.net](https://visualgo.net/bn/sorting) (Nota: visualizza solo la fase _Unisci_ del sort)\n `}\n \n \n {`\n # Quick sort\n \n Il _quick sort_ è un altro approccio **ricorsivo** all'ordinamento per confronto.\n \n ## Funzionamento\n \n Anche qui, applichiamo il **divide et impera**.\n \n 1. _Divide_: Scelgo un **pivot** qualsiasi all'interno della lista. Metto alla sua **sinistra tutti i numeri minori** e alla sua **destra tutti i numeri maggiori**.\n 2. _Impera_: Eseguo un **quick sort su entrambe le sottoliste**.\n \n ### Esempi\n \n #### Iterazione con partizioni bilanciate\n \n Osserviamo come si formi una partizione con tre elementi e una con quattro. \n \n \\`\\`\\`\n |¦ [2] 8 7 1 3 5 6 {4}\n 2 |¦ [8] 7 1 3 5 6 {4}\n 2 |8 ¦ [7] 1 3 5 6 {4}\n 2 |8 ¦ [7] 1 3 5 6 {4}\n 2 |8 7 ¦ [1] 3 5 6 {4}\n 2 1 |7 8 ¦ [3] 5 6 {4}\n 2 1 3 |8 7 ¦ [5] 6 {4}\n 2 1 3 |8 7 5 ¦ [6] {4}\n 2 1 3 |8 7 5 6 ¦ [{4}]\n [2 1 3] {4} [8 5 6 7]\n \\`\\`\\`\n \n #### Iterazione con partizioni sbilanciate\n \n Osserviamo come si formi una partizione con **zero elementi** e una con tre.\n \n \\`\\`\\`\n |¦ [4] 7 3 {1}\n |4 ¦ [7] 3 {1}\n |4 7 |¦ [3] {1}\n |4 7 3 |¦ [{1}]\n [] {1} [4 7 3]\n \\`\\`\\`\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | \\`O(n²)\\` | \\`Ω(n log n)\\` | - |\n \n Il costo della funzione è dato dalla somma del costo per **dividere in due partizioni** con il costo per realizzare il **Quick sort delle due sottopartizioni**\n \n Possiamo applicare allora il **Master Theorem generale**:\n \n \\`\\`\\`latex\n T(n)\\\\\\\\\n =\\\\\\\\\n Θ(1) \\\\qquad per\\\\ n = 1\\\\\\\\\n T(q) + T(dim_lista - pivot - 1) + Θ(n) \\\\qquad per\\\\ n > 1\n \\`\\`\\`\n \n ### Il caso migliore\n \n Se il pivot \\`q\\` è la **mediana della partizione** che stiamo ordinando, si vengono a creare due _sottopartizioni bilanciate_, e sostituendo otteniamo:\n \n \\`\\`\\`latex\n T(n)\\\\\\\\\n =\\\\\\\\\n Θ(1) \\\\qquad per\\\\ n = 1\\\\\\\\\n 2 T(\\\\frac{n}{2}) + Θ(n) \\\\qquad per\\\\ n > 1\n \\`\\`\\` \n \n Possiamo allora applicare il **Master Theorem particolare**:\n \n \\`\\`\\`latex\n T(n)\\\\\\\\\n =\\\\\\\\\n Θ(1) \\\\qquad per\\\\ n = 1\\\\\\\\\n Θ(n log n) \\\\qquad per\\\\ n > 1\n \\`\\`\\`\n \n ### Il caso peggiore\n \n Se il pivot è uno degli **estremi dell'array**, si creano due _partizioni sbilanciate_: una delle due sottoliste è sempre vuota! \n Allora:\n \n \\`\\`\\`latex\n T(n) = T(n-1) + Θ(n)\\\\\\\\\n = T(n-2) + Θ(n-1) + Θ(n)\\\\\\\\\n = T(n-3) + Θ(n-2) + Θ(n-1) + Θ(n)\\\\\\\\\n = …\n ∈ Θ(n^2)\n \\`\\`\\`\n \n > \"Non date da mangiare sequenze ordinate al Quicksort, gli sono indigeste.\"\n \n ## Pseudocodice\n \n \\`\\`\\`python\n def partition(partizione, inizio, fine):\n \"\"\"Dividi una partizione in due, usando l'ultimo elemento come pivot.\n \n Note utili:\n partizione[fine] è il pivot\n partizione[maggiori] è il primo numero dei maggiori\n partizione[non_iterati] è l'elemento su cui si sta iterando al momento\"\"\"\n # Crea il primo separatore (la | pipe nell'esempio)\n maggiori = inizio\n # Crea il secondo separatore (la ¦ broken pipe nell'esempio)\n non_iterati = inizio\n # Itera su ogni numero tra inizio e fine (escluso!)\n while non_iterati < fine:\n # Se l'elemento su cui stiamo iterando è minore del pivot\n if partizione[non_iterati] <= partizione[fine]:\n # Mettilo nell'insieme dei minori, scambiandolo con il primo numero dei maggiori e incrementando il primo separatore\n partizione[maggiori], partizione[non_iterati] = partizione[non_iterati], partizione[maggiori]\n maggiori += 1\n # Incrementa sempre il secondo separatore\n non_iterati += 1\n # Inserisci il pivot tra le due sottopartizioni create, \n partizione[fine], partizione[non_iterati] = partizione[non_iterati], partizione[fine]\n return maggiori\n \\`\\`\\`\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/bn/sorting) (Nota: invece che prendere l'ultimo numero come pivot prende il primo, cambiando leggermente l'algoritmo.)\n \n ## Note per l'esame\n \n > La domanda che fa sempre è **\"Qual è la sequenza di pivot utilizzata?\"**\n \n > Elementi da soli _non_ vengono presi come pivot!\n `}\n \n \n {`\n # Counting sort\n\n Il _counting sort_ è un approccio diverso all'ordinamento: **non usa il confronto**!\n \n ## Requisiti\n \n Il counting sort può essere utilizzato solo su **sequenze di numeri interi**, e solo se **siamo a conoscenza del minimo e del massimo** dei numeri contenuti nell'array, ed essi non sono troppo distanti uno dall'altro. \n (La memoria occupata dal counting sort aumenta linearmente con la differenza tra minimo e massimo!)\n \n Per semplicità, consideriamo il **minimo \\`0\\`**. \n L'input allora sarà una sequenza di interi \\`A\\`, e il valore del **massimo \\`k\\`**, tale che \\`∀ n ∈ A, 0 \\\\leq n \\\\leq K\\`.\n \n ## Funzionamento\n \n Il counting sort **conta le ripetizioni** delle chiavi nella sequenza originale e in seguito **sovrascrive i valori** della sequenza con i valori ordinati ripetuti il numero di volte che sono stati individuati nella sequenza.\n \n > \\`\\`\\`\n > 1 4 5 3 4 1 4 2 5 1\n > \\`\\`\\`\n >\n > L'\\`1\\` appare 3 volte, il \\`2\\` 1 volta, il \\`3\\` 1 volta, il \\`4\\` tre volte e il \\`5\\` due volte.\n >\n > La sequenza viene quindi così sovrascritta:\n > \\`\\`\\`\n > 1 1 1 3 4 1 4 2 5 1 # Sovrascriviamo la sequenza con 1 ripetuto 3 volte\n > 1 1 1 2 3 4 4 4 5 1 # Sovrascriviamo la sequenza con 2, 3, 4 ripetuti rispettivamente 1 1 e 3 volte\n > 1 1 1 2 3 4 4 4 5 5 # Sovrascriviamo la sequenza con 5 ripetuto 2 volte: abbiamo finito!\n > \\`\\`\\` \n \n Esiste anche una **versione stabile** del counting sort che, invece che sovrascrivere, **sposta i valori**, mantenendo le informazioni aggiuntive nel caso invece che interi fossero altri tipi di dati.\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | \\`O(k + n)\\` | \\`Ω(k + n)\\` | **\\`θ(k + n)\\`** |\n \n L'algoritmo è composto da quattro parti:\n - Ricerca del minimo e massimo (in \\`θ(n)\\`)\n - Inizializzazione dell'indice (in \\`θ(k)\\`)\n - Conteggio dei numeri (in \\`θ(n)\\`)\n - Sovrascrittura dei numeri (in \\`θ(k + n)\\`)\n \n \\`2 + O(k) + O(n) + O(k + n) -> O(k + n)\\`\n \n Notiamo che \\`k\\` è costante, l'algoritmo è \\`O(n)\\`, estremamente efficiente.\n \n ## Pseudocodice\n \n \\`\\`\\`python\n def counting_sort(lista: typing.List[int]):\n \"\"\"Ordina in-place una lista con il counting sort.\"\"\"\n # Trovo la dimensione della lista\n dim = len(lista)\n # Trovo il massimo e il minimo all'interno della lista\n minimo = min(lista)\n massimo = max(lista)\n # Creo l'indice dei numeri, in modo che sia lungo k e pieno di 0\n indice = [0 for _ in range(minimo, massimo+1)]\n # Conto i numeri presenti, scorrendo su lista e aggiungendo 1 al numero corrispondente\n for i in range(dim):\n indice[lista[i]] += 1\n # Sovrascrivo i numeri nella lista\n count = 0\n for pos, val in enumerate(indice):\n for _ in range(val):\n indice[count] = pos\n count += 1\n \n def stable_counting_sorted(lista: typing.List[int], k: int) -> typing.List[int]:\n \"\"\"Ordina stabilmente una lista con il counting sort stabile, e restituiscila.\"\"\"\n # Trovo la dimensione della lista\n dim = len(lista)\n # Trovo il massimo e il minimo all'interno della lista\n minimo = min(lista)\n massimo = max(lista)\n # Creo l'indice dei numeri, in modo che sia lungo k e pieno di 0\n indice = [0 for _ in range(minimo, massimo+1)]\n # Conto i numeri presenti, scorrendo su lista e aggiungendo 1 al numero corrispondente\n for i in range(dim):\n indice[lista[i]] += 1\n # Faccio diventare l'indice \"il numero di numeri \\\\leq i\"\n for i in range(len(indice)):\n if i == 0:\n continue\n indice[i] += indice[i-1]\n assert indice[-1] == dim\n # Creo una nuova lista, che sarà quella che verrà restituita\n nuova = [None for _ in range(dim)]\n # Inizio a posizionare i numeri, al contrario\n for i in range(0, dim, -1):\n nuova[indice[lista[i]]] = lista[i]\n indice[lista[i]] -= 1\n return nuova\n \\`\\`\\`\n `}\n \n \n {`\n ## Introduzione alle Strutture Dati\n\n Una _struttura dati_ è un modo in cui si possono organizzare i dati di un programma.\n \n Si possono definire in due modi: **elementari** e **astratte**.\n \n ### Strutture dati elementari\n \n Le strutture _elementari_ dipendono strettamente dal modo in cui vengono memorizzati i dati.\n \n > **Array** e **liste** sono strutture dati elementari: sono definite dicendo come sono memorizzati i dati, rispettivamente, in celle contigue di memoria e da una serie di nodi con un valore e che puntano al successivo.\n \n ### Strutture dati astratte\n \n Le strutture _astratte_ sono separate dal modo in cui vengono memorizzati i dati, sono più ad alto livello, e si definiscono descrivendo le **proprietà** della struttura e i **metodi** che su di essa possono essere effettuate.\n \n > Una _classe_ in un qualsiasi linguaggio di programmazione è una struttura dati astratta.\n \n > Una _pila_ astratta:\n > - memorizza dati tutti dello stesso tipo\n > - \\`pop()\\`, estrae dalla pila l'ultimo valore inserito\n > - \\`push(val)\\`, aggiunge alla pila un valore\n > - \\`top()\\`, permette di vedere l'ultimo valore inserito nella pila\n > - \\`vuota()\\`, dice se la pila è vuota oppure no.\n `}\n \n \n {`\n # Array\n\n Un _array_ è sequenza di dati di **lunghezza conosciuta**, tutti dello **stesso tipo** e di una **dimensione fissa**, immagazzinata in **blocchi di memoria contigui**.\n \n ## Proprietà\n \n - E' possibile accedere a tutti i blocchi di memoria conoscendo la loro **posizione relativa al primo** elemento.\n \n ## Metodi\n \n \\`\\`\\`python\n class Array:\n def __init__(self, size, type=int): \"Crea un array di dimensione size di elementi di tipo int.\"\n def __getitem__(self, index): \"Restituisci il valore alla posizione index.\"\n def __setitem__(self, index, value): \"Cambia il valore alla posizione index.\"\n \\`\\`\\`\n \n ### Costo computazionale\n \n Tutte le operazioni su un array sono in **accesso immediato \\`O(1)\\`**!\n `}\n \n \n {`\n # Lista\n \n Una _lista_ è una sequenza di dati immagazzinata in **blocchi di memoria qualsiasi**.\n \n ## Proprietà\n \n Ogni dato ha un **riferimento** alla collocazione di memoria **successiva** (un puntatore): insieme, sono detti un _nodo_.\n \n E' di **natura ricorsiva**: qualsiasi nodo di una lista può essere visto come inizio della lista con sè stesso e i suoi successivi.\n \n ## Metodi\n \n \\`\\`\\`python\n class LinkedList:\n def __init__(self, value, next: typing.Optional[Node] = None):\n self.value = value\n self.next: typing.Optional[Node] = next\n \n def is_empty(self) -> bool: \"Restituisce se la lista è vuota o no.\"\n def is_full(self) -> bool: \"Restituisce se la lista è piena o no.\n def append(self, value): \"Aggiunge un nuovo elemento in testa alla lista.\"\n def insert(self, value, index): \"Inserisce un elemento dopo il nodo in posizione index.\"\n def insert_node(self, value, node): \"Inserisce un nuovo elemento subito dopo un dato nodo.\"\n def find(self, node) -> int: \"Trova l'indice del nodo.\"\n def delete(self, value): \"Elimina il primo nodo con quel valore dalla lista.\"\n def delete_node(self, node): \"Elimina il nodo dalla lista.\"\n def forward(self, index) -> Node: \"Restituisce il nodo in posizione index.\"\n \\`\\`\\`\n \n ### Costo computazionale\n \n #### \\`List.forward(index)\\`\n \n Per raggiungere l'\\`n\\`-esimo elemento, bisogna _scorrere tutti gli elementi prima di esso_: è dunque un **accesso sequenziale** in **\\`O(n)\\`**.\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/list)\n `}\n \n \n {`\n # Coda (Queue)\n\n Una _coda_ è come una pila, ma segue la strategia **First In, First Out** (il primo inserito sarà il primo a essere estratto).\n \n ## Proprietà\n \n - I dati vi possono essere aggiunti solo tramite il **metodo \\`enqueue()\\`**\n - I dati possono essere estratti solo tramite il **metodo \\`dequeue()\\`**\n - Verranno restituiti i valori inseriti secondo la strategia **First In, First Out** (il primo inserito sarà il primo a essere estratto).\n \n > Hai presente quando fai la fila per pagare al supermercato? Beh, è quello, però non si possono superare le altre persone in nessun modo.\n \n ## Metodi\n \n \\`\\`\\`python\n class Queue:\n def __init__(self): \"Crea una nuova coda.\"\n def is_empty(self) -> bool: \"Restituisce vero se la coda è vuota.\"\n def enqueue(self, data): \"Aggiunge un dato alla coda.\"\n def first(self) -> ...: \"Restituisce il primo dato della coda.\"\n def dequeue(self) -> ...: \"Restituisce il primo dato della coda e lo rimuove.\"\n \\`\\`\\`\n \n ## Implementazione tramite lista\n \n Posso implementare la coda con una lista, ma per realizzare l'implementazione più efficiente devo tenere anche un puntatore all'ultimo elemento della coda, in modo da non doverla scorrere ogni volta che voglio effettuare un'operazione.\n \n Chiamiamo i due puntatori \\`head\\` e \\`tail\\` rispettivamente.\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/list)\n `}\n \n \n {`\n # Pila (Stack)\n\n Una _pila_ è una struttura dati contenente **valori omogenei**.\n \n ## Proprietà\n \n - I dati vi possono essere aggiunti solo tramite il **metodo \\`push()\\`**\n - I dati possono essere estratti solo tramite il **metodo \\`pop()\\`**\n - Verranno restituiti i valori inseriti secondo la strategia **Last In, First Out** (l'ultimo inserito sarà il primo a essere estratto).\n \n > Ci si può immaginare una pila di libri, da cui si può solo prendere un libro alla volta, quello più in alto.\n \n ## Metodi\n \n \\`\\`\\`python\n class Stack:\n def __init__(self): \"Crea una nuova pila.\"\n def is_empty(self) -> bool: \"Restituisce vero se la pila è vuota.\"\n def push(self, data): \"Aggiunge un dato alla pila.\"\n def top(self) -> ...: \"Restituisce il primo dato della pila.\"\n def pop(self) -> ...: \"Restituisce il primo dato della pila e lo rimuove.\"\n \\`\\`\\`\n \n ## Implementazione tramite lista\n \n Utilizzando una lista possiamo realizzare una pila!\n \n La direzione dei puntatori sarà dall'ultimo al primo, che non punterà più a nessuno.\n \n Il costo di tutti i metodi è \\`Θ(1)\\`!\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/list)\n `}\n \n \n {`\n # Albero radicato\n \n Un _albero radicato_ è una struttura dati di **natura ricorsiva** che organizza i dati in maniera **non-lineare**.\n \n ## Proprietà\n \n - Ogni nodo dell'albero ha un **unico genitore**: \\`∀ (padre, figlio), (padre' figlio) ∈ E \\\\implies padre = padre'\\`\n - Ogni nodo dell'albero può avere **un numero qualsiasi di figli**.\n \n - I **nodi superiori al padre** vengono chiamati _antenati_.\n - I **nodi inferiori ai figli** vengono chiamati _discendenti_.\n \n - Nodi **senza padre** sono detti _radice_: \\`\\\\notexists (padre, radice) ∈ E\\`\n - Nodi **con padre e figli** sono detti _rami_ o interni.\n - Nodi **senza figli** sono detti _foglie_.\n \n - La **distanza** tra il nodo radice e i suoi discendenti è detta _livello_:\n - I figli immediati sono di livello 1.\n - I \"nipoti\" (figli dei figli) sono di livello 2.\n - I figli dei nipoti sono livello 3.\n - E così via.\n - Il **livello massimo** all'interno di un albero è detto _altezza_, _profondità_ oppure _h_, ed è sempre \\`1 ≤ h ≤ n-1\\`.\n \n - Un albero ha sempre \\`n-1\\` archi.\n \n ## Alberi particolari\n \n ### Alberi \\`d\\`-ari\n \n Un albero _\\`d\\`-ario_ è un particolare tipo di albero che **limita il numero massimo di figli di un nodo** a \\`d\\`.\n \n > Un albero _binario_ può avere **massimo 2 figli** per ogni nodo; un albero _ternario_ ne può avere **3**; un albero _\\`17\\`-ario_ ne potrà avere **17**\n \n #### Alberi completi\n \n Un albero \\`d\\`-ario si dice _completo_ se **tutti i nodi hanno 0 o \\`d\\` figli**, e mai una numero in mezzo.\n \n #### Alberi bilanciati\n \n Un albero \\`d\\`-ario si dice _bilanciato_ se **tutti i livelli eccetto l'ultimo** hanno il numero massimo di figli.\n \n #### Alberi perfettamente bilanciati\n \n Un albero \\`d\\`-ario si dice _perfettamente bilanciato_ se **tutti i livelli incluso l'ultimo** hanno il numero massimo di figli.\n \n ##### Particolarità degli alberi binari perfettamente bilanciati\n \n Si può dimostrare per induzione che:\n - Hanno sempre \\`2^h\\` foglie.\n - Hanno sempre \\`2^{h+1}-1\\` (\\`\\\\sum_i=0^n 2^i\\`) nodi.\n - L'altezza è in \\`Θ(log n)\\`.\n \n ## Implementazione degli alberi\n \n Possiamo scegliere se usare una rappresentazione con array o con nodi e puntatori: ognuna ha vantaggi e svantaggi diversi.\n \n ### Implementazione tramite array\n \n E' suggerito se l'albero è regolare; più è simile a un albero d-ario completo, meglio è.\n \n ### Implementazione tramite nodi e puntatori\n \n Più adatta ad alberi irregolari.\n \n Se l'albero è regolare, creiamo il numero esatto di campi:\n \n - Valore\n - Figlio1\n - Figlio2\n - _Opzionale:_ Padre\n \n Se un albero è irregolare, creiamo una specie di lista:\n \n - Valore\n - Primo figlio\n - Prossimo fratello\n - _Opzionale:_ Padre\n `}\n \n \n {`\n #### Breadth-first search (BFS)\n\n La _breadth-first search_ è un algoritmo che visita **ogni livello** dell'albero in ordine, dal più basso al più alto.\n \n ## Funzionamento\n \n > 1. __Visita radice__\n > 2. __Visita figli__\n > 3. __Visita nipoti__\n > 4. __Visita pronipoti__\n \n Si può implementare con una coda, in cui verranno inseriti i figli del nodo visitato da visitare ed estratti dopo avere completato la visita del livello attuale.\n \n ## Pseudocodice \n \n \\`\\`\\`python\n def bfs(radice):\n c = Queue()\n c.enqueue(radice)\n while not c.is_empty():\n nodo = c.dequeue()\n print(nodo)\n for figlio in nodo.figli:\n nodo.enqueue(figlio)\n \\`\\`\\`\n `}\n \n \n {`\n # Depth-First Search\n\n La _depth-first search_ è un algoritmo che visita **tutti i sottoalberi di un figlio** prima di passare ad un altro sfruttando la natura ricorsiva degli alberi.\n \n ## Funzionamento\n \n Ci sono diverse versioni della depth-first search: ognuna visita la radice in un momento diverso.\n \n ### DFS previsita (pre-order)\n \n La _DFS pre-visita_ visita la **radice per prima**, poi tutti i sottoalberi formati dai figli uno dopo l'altro.\n \n > 1. __Visita radice__\n > 2. dfs_pre_order(figlio1)\n > 3. dfs_pre_order(figlio2)\n \n ### Postvisita (post-order)\n \n La _DFS postvisita_ visita prima tutti i sottoalberi dei figli, e **alla fine la radice**.\n \n > 1. dfs_post_order(figlio1)\n > 2. dfs_post_order(figlio2)\n > 3. __Visita radice__\n \n ### Invisita (in-order)\n \n La _DFS invisita_ visita **un certo numero di figli**, poi la radice, e infine i figli restanti.\n \n > 1. dfs_in_order(figlio1, 1)\n > 2. __Visita radice__\n > 3. dfs_in_order(figlio2, 1)\n `}\n \n \n {`\n # Albero binario di ricerca\n\n ## Proprietà\n \n - Albero **binario**\n - Chiavi appartenenti ad un **insieme totalmente ordinato** (N, Q, R, ma non C)\n \n - Per ogni nodo con valore \\`x\\`, se un valore \\`v\\` è nel sottoalbero di sinistra allora \\`v ≤ x\\`, mentre se è nel sottoalbero di destra allora \\`v > x\\`.\n \n ## Costo computazionale\n \n - Trovare un valore: \\`O(h)\\`\n - Ordinare i valori: \\`O(n)\\`\n - Trovare il minimo: \\`O(h)\\`\n - Trovare il massimo: \\`O(h)\\`\n - Inserire un elemento: \\`O(h)\\`\n - Cancellare un elemento: \\`O(h)\\`\n \n \\`h\\` vale \\`log n\\` in un albero perfettamente bilanciato, e più l'albero diventa sbilanciato, più si avvicina a \\`n\\`, raggiungendola nel caso l'albero sia una lista.\n \n ## Pseudocodice\n \n ### Cancellazione ricorsiva\n \n \\`\\`\\`python\n def delete(tree, key):\n if tree is not None:\n # Se ho trovato il nodo che cercavo...\n if tree.key == key:\n # E c'è una sola diramazione...\n # Semplicemente stacca il nodo come in una lista.\n if tree.left is None:\n return tree.right\n if tree.right is None:\n return tree.left\n # Altrimenti, diventa il minimo dell'albero di destra\n tree.key = tree.right.min()\n # Ed eliminalo dal sottoalbero\n tree.right = delete(tree.right, tree.key)\n # Se la chiave attuale è diversa da quella che cerchiamo, continuo a navigare l'albero\n elif tree.key < key:\n tree.left = delete(tree.left, key)\n else:\n tree.right = delete(tree.right, key)\n return tree\n \\`\\`\\`\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/bst)\n \n ## Approfondimenti\n \n Esistono alberi più avanzati che mantengono le proprietà degli alberi binari di ricerca, ma che si autobilanciano, come il [Red Black Tree](https://it.wikipedia.org/wiki/RB-Albero).\n `}\n \n \n {`\n # Heap binario\n \n L'_heap binario_ è un **albero binario bilanciato a sinistra**.\n \n ## Proprietà\n \n - _Proprietà strutturale_:\n - L'albero è **perfettamente bilanciato** in tutti i livelli tranne l'ultimo\n - Nell'ultimo livello, le foglie occupano le **posizioni più a sinistra** possibili\n - _Proprietà di ordinamento_:\n - La chiave di un qualsiasi nodo è **più piccola** di tutte quelle dei nodi **del suo sottoalbero**\n \n ## Metodi\n \n \\`\\`\\`python\n class Heap:\n def __init__(self, H): ...\n def _heapify_ancestors(self, i): \"Ripristina le proprietà dell'heap per il nodo all'indice specificato e i suoi genitori.\"\n def minimum(self): \"Restituisce la chiave con il valore minimo in H.\"\n def decrease_value(self, index, new_value): \"Diminuisce il valore della chiave all'indice index a new_value.\"\n def insert(self, value): \"Inserisci un nuovo valore nell'albero.\"\n def _heapify_children(self, i): \"Ripristina le proprietà dell'heap per il nodo all'indice specificato e i suoi figli.\"\n def pop(self): \"Restituisce la chiave con il valore minimo, e la elimina.\"\n def from_list(l): \"Crea un heap da una lista.\"\n \\`\\`\\`\n \n ## Implementazione con un array\n \n Possiamo implementare l'albero utilizzando un array con le chiavi dell'albero memorizzate nell'ordine _breadth-first_.\n \n L'indice del figlio sinistro può essere trovato a \\`2i+1\\`, mentre l'indice del figlio sinistro può essere trovato a \\`2i+2\\`; il genitore è a \\`i//2-1\\`.\n \n ### Pseudocodice\n \n \\`\\`\\`python\n class Heap:\n def __init__(self, size):\n self.array = Array(size) # Il tipo Array non esiste; consideriamolo pseudocodice\n self.next_value = 0\n \n def _heapify_ancestors(self, index)\n \"\"\"Ripristina le proprietà dell'heap per il nodo all'indice specificato e i suoi genitori.\n \n Costo:\n O(log n)\"\"\"\n # Trovo l'indice del genitore\n parent = index // 2 - 1\n # Controllo se viene mantenuta la proprietà di ordinamento dell'heap\n if self.array[index] < self.array[parent]:\n # Scambio i valori dei due nodi\n self.array[index], self.array[parent] = self.array[parent], self.array[index]\n # Faccio la stessa cosa con il genitore\n self._heapify(parent)\n \n \n def minimum(self):\n \"\"\"Restituisce la chiave con il valore minimo in H.\n \n Costo:\n O(1)\"\"\"\n return self.array[0]\n \n def decrease_value(self, index, new_value):\n \"\"\"Diminuisce il valore della chiave all'indice index a new_value.\n \n Costo:\n O(log n)\"\"\"\n # Diminuisco il valore del nodo\n self.array[index] = new_value\n # Aggiorno l'heap \n self._heapify(index)\n \n def insert(self, value):\n \"\"\"Inserisci un nuovo valore nell'albero.\n \n Costo:\n O(log n)\"\"\"\n # Trovo l'indice in cui inserire il valore\n index = self.next_index \n # Aggiungo il valore in fondo\n self.array[index] = value\n # Aggiorno l'heap\n self._heapify(index)\n \n def _heapify_children(self, index):\n \"\"\"Ripristina le proprietà dell'heap per il nodo all'indice specificato e i suoi figli.\n \n Costo:\n O(log n)\"\"\"\n # Trovo l'indice dei figli\n left = index * 2 + 1\n right = index * 2 + 2\n # Mi assicuro che i figli esistano\n try:\n # Guardo quale dei figli è maggiore\n if self.array[left] > self.array[right]:\n # Scambio i valori\n self.array[left], self.array[index] = self.array[index], self.array[left]\n # Ripeto la procedura sul figlio modificato\n self._heapify_children(left)\n else:\n # Scambio i valori\n self.array[right], self.array[index] = self.array[index], self.array[right]\n # Ripeto la procedura sul figlio modificato\n self._heapify_children(left)\n except IndexError:\n # La foglia non ha figli: ho finito!\n return\n \n def pop(self):\n \"\"\"Restituisce la chiave con il valore minimo, e la elimina.\n \n Costo:\n O(log n)\"\"\"\n # Mi salvo il valore della radice\n value = self.array[0]\n # Sostituisco la radice con l'ultima foglia a destra\n self.array[0], self.array[self.next_value] = self.array[self.next_value], self.array[0]\n ### Non bisognerebbe eliminare la foglia...?\n # Riordino l'heap\n self._heapify_children(0)\n return value\n \n @staticmethod\n def from_list(l):\n \"\"\"Crea un heap da una lista.\n \n Costo:\n O(n log n), ma si può abbassare\"\"\"\n heap = Heap(len(l)))\n heap.array = Array.from_list(l) # Pseudocodice\n heap.next_value = len(l)\n # Cominciamo a riordinare l'heap dalla fine, in modo che rispetti le proprietà\n for index in range(heap.next_value, 0, -1):\n heap._heapify_children(index)\n \\`\\`\\`\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/heap)\n `}\n \n \n {`\n # Coda con priorità\n \n La _coda con priorità_ è una struttura dati dal funzionamento molto simile a quello di una coda, ma invece che restituire il primo elemento inserito, essa restituisce l'**elemento con il valore di priorità minore**.\n \n ## Proprietà\n \n - Ogni elemento è una coppia costituita da **valore** e **priorità** (un numero intero).\n - Nuovi elementi possono essere aggiunti solo tramite il **metodo \\`insert()\\`**\n - Gli elementi possono essere estratti solo tramite il **metodo \\`pop()\\`**\n - Verranno restituiti i valori inseriti secondo la strategia **Lower Priority** (l'elemento con la priorità minore sarà il primo ad essere restituito).\n - E' possibile diminuire la priorità di un elemento (e quindi anticipare la sua estrazione)\n \n ## Metodi\n \n \\`\\`\\`python\n class PriorityQueue:\n def __init__(self): ...\n def insert(self, new_elem: Element): ...\n def minimum(self) -> Element: ...\n def pop(self) -> Element: ...\n def decrease_priority_for(self, elem: Element, priority: int): ...\n \\`\\`\\`\n \n ## Implementazione con lista\n \n E' possibile implementare la coda con priorità tramite una **lista**: l'inserimento di nuovi valori diventerà molto efficiente, ma tutte le altre operazioni saranno linearmente lente.\n \n ### Costo computazionale\n \n - *insert()*: \\`O(1)\\`\n - *minimum()*: \\`O(n)\\`\n - *pop()*: \\`O(n)\\`\n - *decrease_priority_for()*: \\`O(n)\\`\n \n ## Implementazione con lista ordinata\n \n Implementando la coda con priorità con una **lista ordinata** si avrà un costo di ordinamento elevato negli inserimenti e modifiche alla priorità, ma costi costanti nell'estrazione di un elemento.\n \n ### Costo computazionale\n \n - *insert()*: \\`O(n)\\`\n - *minimum()*: \\`O(1)\\`\n - *pop()*: \\`O(1)\\`\n - *decrease_priority_for()*: \\`O(n)\\`\n \n ## Implementazione con heap\n \n La **soluzione migliore** è quella di implementare la coda con priorità tramite un **heap**: tutti i costi saranno logaritmici, eccetto l'inserimento che sarà costante.\n \n - \\`insert()\\` costa \\`O(1)\\`\n - \\`minimum()\\` costa \\`O(log n)\\`\n - \\`pop()\\` costa \\`O(log n)\\`\n - \\`decrease_priority_for()\\` costa \\`O(log n)\\`\n \n ## Approfondimenti\n \n Esistono code con priorità che restituiscono **l'elemento con priorità maggiore**, invece che quello minore.\n `}\n \n \n {`\n # Heap sort\n\n L'_heap sort_ è un algoritmo di ordinamento per confronto **iterativo**.\n \n ## Funzionamento\n \n Per effettuare un heap sort, creiamo un **heap massimo** in cui inseriamo tutti i valori che vogliamo ordinare.\n \n Una volta applicate le proprietà dell'heap, chiamiamo una versione particolare di \\`heap.pop()\\` che invece che rimuovere dall'array i valori estratti li posiziona nello spazio creatosi in fondo.\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | \\`O(n log n)\\` | \\`Ω(n log n)\\` | **\\`θ(n log n)\\`** |\n `}\n \n \n {`\n # Grafo\n \n Un _grafo_ è una struttura dati che rappresenta elementi interconnessi tra loro.\n \n Esistono due tipi di grafi: _orientati_ e _non orientati_.\n \n Per semplicità, consideriamo i nostri nodi numerati da 1 a \\`n\\`.\n \n ## Proprietà\n \n - Gli elementi sono rappresentati tramite _nodi_.\n - Il loro _grado_ è dato dal **numero degli archi** che vi incidono.\n - Se il grafo è orientato, hanno anche un _in-degree_ (**numero di archi entranti**) e un _out-degree_ (**numero di archi uscenti**).\n - Le connessioni tra elementi sono rappresentate tramite _archi_.\n - Un arco _incide_ esattamente su **due nodi**.\n - Se il grafo è orientato, sono _uscenti_ da uno dei due nodi ed _entranti_ nell'altro.\n - Sono matematicamente meno del **quadrato dei nodi**.\n \n ## Grafi particolari\n \n ### Catena\n \n Una _catena_ è un **grafo non orientato** composto da una **sequenza di nodi** aventi un **grado massimo di 2** tutti collegati tra loro.\n \n ### Cammino\n \n Un _cammino_ è un **grafo orientato** composto da una **sequenza di nodi** aventi un **in-degree** e un **out-degree** **massimo di 1**, collegati tra loro in modo che partendo dal primo e seguendo gli archi sia possibile arrivare all'ultimo.\n \n ### Cricca\n \n Una _cricca_ è un grafo in cui **tutti i nodi sono collegati tra loro**.\n \n Se il grafo è **non orientato**, la cricca ha \\`((n-1)n)/2\\` archi.\n \n Se il grafo è **orientato**, ha per ogni coppia un arco in entrambe le direzioni, quindi ha \\`(n-1)n\\` archi.\n \n ### Direct Acyclic Graph\n \n Un _DAG_ è un grafo diretto che non contiene nessun ciclo.\n \n Su di esso possiamo effettuare un ordinamento, detto _linearizzazione_, tra i nodi: otteniamo l'_ordine topologico_.\n \n I primi elementi dei DAG sono detti _Source_ (_Sorgente_), mentre gli ultimi sono detti _Sink_ (_Pozzo_).\n \n #### Albero\n \n Un **albero** può essere considerato un DAG con una **sorgente singola** e le **foglie come pozzi**.\n \n ### Grafo fortemente connesso\n \n Un insieme di nodi \\`V\\` di un **grafo diretto** \\`G\\` si dice una _componente fortemente connessa_ se:\n \n 1. Per ogni coppia di nodi \\`∀ u, v ∈ V' : ∃ un cammino u->v in G'\\`\n 2. Massimale (non può diventare più grande)\n \n > Praticamente una componente fortemente connessa è un gruppo di nodi tra i quali si può viaggiare liberamente da e a qualsiasi nodo al suo interno.\n \n Un grafo si dice _fortemente connesso_ se l'insieme \\`V\\` coincide con l'insieme dei nodi del grafo \\`G\\`.\n \n > Se partendo da qualsiasi nodo di un grafo riesco ad arrivare a qualsiasi altro nodo, allora il grafo è fortemente connesso.\n \n Inoltre, se creiamo un nuovo grafo, in cui **ogni nodo rappresenta una componente fortemente connessa** del nostro grafo iniziale, **otteniamo un DAG**, perchè tutti i cicli sono stati integrati nella componente.\n \n ### Trasposto di un grafo\n \n Il _trasposto_ di un **grafo diretto** \\`G\\` è il grafo stesso con gli archi che però vanno nella **direzione opposta**.\n \n ### Grafo pesato\n \n Un _grafo pesato_ è un particolare grafo che associa a ciascun arco un **costo** per attraversarlo.\n \n #### Costi negativi\n \n I costi possono anche essere negativi: rappresenteranno allora un **guadagno** ottenuto attraversando il nodo.\n \n ### Minimum spanning tree\n \n Un _minimum spanning tree_ è il **sottoinsieme degli archi** di un **grafo non diretto** che **connettono tutti i nodi** con il **minor costo possibile**.\n \n I MST hanno [molte proprietà](https://en.wikipedia.org/wiki/Minimum_spanning_tree#Properties); sono troppe da scrivere qui, e probabilmente non ci interesseranno nemmeno.\n \n ## Implementazione tramite matrice di adiacenza\n \n Possiamo implementare un grafo creando una **matrice di \\`bool\\` di dimensione \\`n * n\\`** in cui le **caselle collegate sono vere** e le caselle non collegate sono false.\n \n > Ad esempio, possiamo implementare un grafo non orientato in questo modo (\\`█\\` indica l'esistenza di un collegamento e \\` \\` indica la sua assenza):\n >\n > | |1|2|3|\n > |-|-|-|-|\n > |1|░|░|░|\n > |2|█|░|░|\n > |3|█| |░|\n >\n > Esistono gli archi \\`1-2\\` e \\`1-3\\`, ma non esiste un collegamento \\`2-3\\`.\n \n > Un grafo orientato invece si può implementare così:\n >\n > | |1|2|3|\n > |-|-|-|-|\n > |1|░|█| |\n > |2|█|░| |\n > |3|█| |░|\n >\n > Esistono gli archi \\`1->2\\`, \\`2->1\\` e \\`3->1\\`, ma non ci sono collegamenti \\`2->3\\`, \\`1->3\\` e \\`3->2\\`.\n \n ### Costo computazionale\n \n #### Tempo\n \n Le matrici di adiacenza portano alla realizzazione di algoritmi molto veloci: verificare l'esistenza di un arco è in \\`O(1)\\`!\n \n Abbiamo però penalità significative quando vogliamo effettuare operazioni sugli archi: ad esempio, trovare il trasposto di un grafo implementato con una matrice di adiacenza è in \\`O(nodi²)\\`.\n \n #### Memoria\n \n E' poco efficiente in quanto a memoria: l'upper bound è in \\`O(n^2)\\`. \n \n ## Implementazione tramite liste di adiacenza\n \n Un'alternativa alla matrice di adiacenza è quella di creare un'**array di liste**, le quali contengono i **vicini di ciascun nodo**.\n \n > |Posizione|Lista|\n > |-|-|\n > |1|[2, 3]|\n > |2|[]|\n > |3|[1]|\n >\n > Esistono gli archi \\`1->2\\`, \\`1->3\\`, e \\`3->1\\`, ma non esistono \\`2->1\\`, \\`2->3\\` e \\`3->2\\`.\n \n ### Costo computazionale\n \n #### Tempo\n \n Utilizzando le liste di adiacenza, il tempo richiesto per verificare l'esistenza di un arco sale a \\`O(max-out-degree)\\`.\n \n E' efficace però quando il problema che vogliamo risolvere riguarda operazioni su archi: trovare la trasposta è in \\`O(archi)\\`.\n \n #### Memoria \n \n La memoria richiesta dalle liste di adiacenza è minore di quella delle matrici: l'upper bound è in \\`O(nodi + archi)\\`.\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/graphds)\n `}\n \n \n {`\n # Visitare un grafo\n \n Come per gli alberi radicati, esistono due modi per visitare un grafo: _depth-first search_ e _breadth-first search_.\n \n In entrambi i casi, non visito mai due volte lo stesso nodo, e come risultato ottengo **molteplici alberi**, il cui insieme viene detto _foresta di copertura_.\n \n Se il grafo che vogliamo visitare è diretto, allora dobbiamo **considerare come vicini solo gli archi uscenti**\n \n ## Depth-first search\n \n La DFS ci può risultare utile per **identificare le componenti connesse** di un grafo e **identificare eventuali cicli**.\n \n ### Funzionamento\n \n Posso utilizzare la DFS per classificare gli archi di un grafo in quattro categorie:\n \n - _Tree_, archi che ci fanno **scoprire un nuovo nodo**\n - _Forward_, archi che ci portano a un **discendente**\n - _Back_, archi che ci portano ad un **antenato**\n - _Cross_, archi che **connettono due sottoalberi** diversi\n \n Usiamo due array inizializzati a 0 chiamati \\`pre\\` e \\`post\\`, grandi quanto il numero di archi del grafo, che ci indicano rispettivamente quando un nodo è stato scoperto e quando è terminata la visita. \n Inoltre, creiamo una variabile \\`clock\\` che avanza ad ogni evento. \n Alla scoperta di un nuovo nodo, mettiamo il valore attuale di \\`clock\\` all'interno di \\`pre[n]\\`. \n Alla fine della visita di un nodo invece mettiamo il valore di \\`clock\\` in \\`post[n]\\`.\n \n **Durante la visita**, gli archi avranno i seguenti valori:\n - _Tree_: \\`pre[dst] == 0\\`\n - _Forward_: \\`pre[src] < pre[dst] && post[dst] > 0\\`\n - _Back_: \\`pre[dst] < pre[src] && post[dst] == 0\\`\n - _Cross_: Tutti gli altri (\\`post[dst] < pre[src]\\`)\n \n **A fine visita**, gli archi avranno i seguenti valori:\n - _Tree_: \\`pre[dst] < pre[dst] < post[dst] < pre[src]\\`\n - _Forward_: \\`pre[dst] < pre[dst] < post[dst] < pre[src]\\`\n - _Back_: \\`pre[src] < pre[dst] < post[dst] < post[src]\\`\n - _Cross_: \\`pre[dst] < post[dst] < pre[src] < post[src]\\`\n \n Se un **grafo non diretto** contiene degli **archi Back**, allora esso **conterrà un ciclo**.\n \n #### DFS nel grafo trasposto\n \n Se effettuo una DFS sul trasposto di un grafo, posso **scoprire i nodi che hanno un cammino verso l'origine**.\n \n #### DFS nella componente fortemente connessa\n \n Se effettuo una DFS in una componente fortemente connessa e nella sua trasposta, il **\\`post\\` della trasposta sarà sempre minore** del \\`post\\` della componente originale.\n \n ### Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | \\`O(nodi + archi)\\` | \\`Ω(nodi + archi)\\` | **\\`θ(nodi + archi)\\`** |\n | Memoria | \\`O(nodi)\\` | \\`Ω(nodi)\\` | **\\`θ(nodi)\\`** |\n \n ### Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/dfsbfs)\n \n ## Breadth-first search\n \n La BFS ci può risultare utile per **trovare tutti i nodi a una certa distanza** da un'origine.\n \n ### Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | \\`O(nodi + archi)\\` | \\`Ω(nodi + archi)\\` | **\\`θ(nodi + archi)\\`** |\n | Memoria | \\`O(nodi + archi)\\` | \\`Ω(nodi + archi)\\` | **\\`θ(nodi + archi)\\`** |\n \n ### Pseudocodice\n \n Come per gli alberi, la implementiamo in modo **iterativo**:\n \n \\`\\`\\`python\n queue = [starting_node]\n parents = [None for node in graph.nodes]\n distance = [-1 for node in graph.nodes]\n \n # TODO: controllami quando sei più sveglio\n \n while queue:\n node, source, distance = queue.pop(0)\n parents[node.number] = source\n distance[node.number] = distance\n for neighbour in node.neighbours:\n queue.append((neighbour, node, distance+1))\n \\`\\`\\`\n \n > Nella coda, la distanza massima tra un nodo e l'altro è 1.\n \n ### Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/dfsbfs)\n `}\n \n \n {`\n # Algoritmi greedy\n\n Un modo per risolvere problemi algoritmici può essere usare una **tecnica** _greedy_.\n \n Le tecniche greedy consistono nel effettuare tanti piccoli passi, ed effettuare una **scelta** in base ai dati **locali al passo attuale**.\n \n > Scegli il numero di monete più piccole possibili per comporre €1.12.\n >\n > L'algoritmo cerca di scegliere sempre la moneta più grande possibile compatibile con il prezzo in quel momento, quindi:\n > | Moneta scelta | Rimanente |\n > |---------------|-----------|\n > | € 1.00 | € 0.12 |\n > | € 0.10 | € 0.02 |\n > | € 0.02 | € 0.00 |\n \n ## Esempi\n \n Sono algoritmi greedy:\n \n - L'_Algoritmo di Dijkstra_\n - L'_Algoritmo di Kruskal_\n - L'_Algoritmo di Prim_\n `}\n \n \n {`\n # Percorso più breve\n\n Trovare il _percorso più breve_ (o _cammino minimo_) tra due nodi di un **grafo pesato** è un problema frequente nell'informatica; per questo, sono stati sviluppati [numerosi algoritmi](https://en.wikipedia.org/wiki/Shortest_path_problem) per risolverlo.\n \n > Ad esempio, il pathfinding dei nemici nei videogiochi, oppure Google Maps!\n \n ## Percorso più breve da una sorgente singola\n \n Una sottocategoria del problema del percorso più breve è il caso in cui ci interessa sapere i percorsi più brevi che **partono da uno specifico nodo del grafo**: è detto problema del _percorso più breve da una sorgente singola_, o _single-source shortest path_.\n \n Si può notare che se il grafo contiene **costi negativi** allora è possibile che il percorso più breve non esista, in quanto diventa possibile la comparsa di **cicli di costo infinitamente negativo**.\n \n Possiamo notare che, se il percorso più breve tra \\`A\\` e \\`D\\` è \\`A-B-C-D\\`, allora il cammino minimo tra \\`B\\` e \\`D\\` passerà obbligatoriamente per \\`C\\` (\\`B-C-D\\`).\n Diremo più avanti che il percorso più breve ha una **sottostruttura ottimale**.\n \n ### Esempi\n \n Alcuni algoritmi che trovano il percorso più breve sono:\n - L'_Algoritmo di Dijkstra_\n - L'_Algoritmo di Bellman-Ford_\n - La [_ricerca A*_](https://en.wikipedia.org/wiki/A*_search_algorithm)\n `}\n \n \n {`\n # Algoritmo di Dijkstra\n \n L'_Algoritmo di [Dijkstra](https://upload.wikimedia.org/wikipedia/commons/8/85/Dijkstra.ogg)_ è un algoritmo che risolve il problema del **percorso più breve da una sorgente singola** per grafi con pesi **reali positivi** \\`\\\\mathbb{R}^+\\`.\n \n L'algoritmo trova tutti i percorsi più brevi per raggiungere qualsiasi nodo del grafo partendo da un dato nodo, assieme al costo richiesto per farlo.\n \n ## Funzionamento\n \n 1. Separiamo tutti i nodi del grafo in due gruppi: **visitati** e **non visitati**. \n - Tutti i nodi partono da **non visitati**.\n 2. Per ogni nodo, manteniamo un valore \"**costo richiesto per raggiungerlo**\", che verrà cambiato man mano che l'algoritmo avanza.\n - Il costo di partenza è \\`+∞\\`.\n - Il costo sarà **definitivo per i nodi visitati**, e **provvisorio per i non visitati**.\n 3. Creiamo un insieme detto _frontiera_ che conterrà tutti i **nodi non visitati adiacenti** a quelli visitati.\n 4. Prendiamo il nodo iniziale, che avrà un **costo di \\`0\\`**, e definiamolo il nodo _attuale_.\n 5. Finchè ci sono dei nodi non sono stati visitati, ripetiamo il seguente ciclo:\n 1. Aggiungiamo i nodi adiacenti al nodo attuale alla frontiera.\n - Il costo per raggiungerli sarà il **costo per il nodo attuale sommato al costo dell'arco** che li connette al nodo attuale. \n Se questo **costo** risulta essere **minore del costo provvisorio** precedente, esso **diventerà il nuovo costo**.\n - Questa operazione è detta _rilassamento dell'arco_.\n 2. Facciamo diventare **visitato** il nodo attuale.\n - Il percorso che abbiamo fatto per raggiungerlo è obbligatoriamente il più breve.\n 3. Il prossimo nodo attuale sarà il nodo di frontiera con un costo più basso.\n - Per questo, è possibile definire l'algoritmo di Dijkstra come un **algoritmo greedy**.\n \n ### Non funziona se...\n \n L'algoritmo smette di funzionare nel caso in cui siano presenti **costi negativi** e il grafo non sia **aciclico**, in quanto non saremmo mai in grado di rendere visitato un nodo.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | \\`O(nodi + archi) log nodi)\\` |\n \n ### Scomposizione\n \n - Inizializzazione: \\`O(nodi)\\`\n - Creazione coda priorità: \\`O(nodi log nodi)\\`\n - Ciclo: \\`O((nodi + archi) log nodi)\\`\n \n ## Pseudocodice\n \n \\`\\`\\`python\n import math\n \n class Info:\n def __init__(self, distance=math.inf, previous=None):\n self.distance = distance\n self.previous = previous\n \n def dijkstra(graph, start):\n data = [Info() for node in graph.nodes]\n queue = PriorityQueue([start])\n while queue:\n node = queue.pop()\n for arc in node.connections:\n other = arc.other(node)\n if data[node.number].distance + arc.cost < data[other].distance:\n data[other].distance = data[node.number].distance + arc.cost\n queue.decrease_priority_for(other, data[other].distance)\n data[v].previous = node\n return data\n \\`\\`\\`\n \n ## Visualizzazione\n \n [Visualgo](https://visualgo.net/en/sssp)\n `}\n \n \n {`\n # Algoritmo di Bellman-Ford\n\n L'_Algoritmo di Bellman-Ford_ è un algoritmo che, come l'Algoritmo di Dijkstra, risolve il problema del **percorso più breve da una sorgente singola**, però, a differenza da quest'ultimo, l'Algoritmo di Bellman-Ford accetta in input anche grafi con pesi **reali** \\`\\\\mathbb{R}\\` (sia positivi, sia negativi).\n \n ## Funzionamento\n \n L'approccio dell'algoritmo è simile a quello di Dijkstra: entrambi usano il **rilassamento** degli archi per ottenere un costo provvisorio per il raggiungimento di un nodo, ma invece che rilassare solo l'arco con costo inferiore, questo algoritmo **rilassa tutti gli archi** ripetutamente, eliminando la frontiera e il problema dei nodi negativi.\n \n L'operazione di rilassamento è ripetuta \\`nodi - 1\\` volte, ovvero la **lunghezza massima** di un cammino aciclico all'interno di un grafo.\n \n Possiamo individuare dopo i rilassamenti se è presente un nodo con un **ciclo negativo**: ci basta controllare se esiste un arco che connette due nodi con una distanza incompatibile: se \\`a.distanza + arco.costo < b.distanza\\`, allora è presente un ciclo negativo.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | \\`O(nodi * archi)\\` |\n \n ## Pseudocodice\n \n > TODO\n \n ## Visualizzazione\n \n [Visualgo](https://visualgo.net/en/sssp)\n `}\n \n \n {`\n # Disjoint set\n \n Il _disjoint set_ è una struttura dati che rappresenta elementi di un insieme raggruppati in **sottoinsiemi disgiunti**.\n \n ## Metodi\n \n \\`\\`\\`python\n class DisjointNode:\n def __init__(self): ...\n def find_set(self): \"Trova il rappresentante dell'elemento.\"\n def union(self, other): \"Unisce i sottoinsiemi che contengono questo nodo e \\`other\\`.\"\n \\`\\`\\`\n \n ## Implementazione tramite array\n \n Possiamo implementare il disjoint set con due array: uno per l'**indice del rappresentante** e uno per il **rango dell'insieme**.\n \n Un singoletto avrà **sè stesso come rappresentante** e **rango \\`0\\`**.\n \n ### Costo computazionale\n \n - *create_set()*: \\`O(1)\\`\n - *find_set()*: \\`O(h)\\`\n - *union()*: \\`O(h)\\`\n \n ### Pseudocodice\n \n \\`\\`\\`python\n class DisjointNode:\n def __init__(self):\n self.parent = self\n self.rank = 0\n \n def find_set(self):\n element = self\n while self.parent != element:\n element = self.parent\n return element\n \n def union(self, other):\n repres_self = self.find_set()\n repres_other = other.find_set()\n if repres_self == repres_other:\n return\n if repres_self.rank < repres_other.rank:\n repres_greater = repres_other\n repres_lesser = repres_self\n else:\n repres_greater = repres_self\n repres_lesser = repres_other\n repres_lesser.parent = repres_greater\n if repres_greater.rank == repres_lesser.rank:\n repres_greater.rank += 1\n \\`\\`\\`\n \n ### Visualizzazione\n \n [cs.usfca.edu](https://www.cs.usfca.edu/~galles/JavascriptVisual/DisjointSets.html)\n `}\n \n \n {`\n # Trovare il minimum spanning tree\n\n Un altro problema ricorrente riguardante i grafi è trovare il _minimum spanning tree_ di un dato grafo non diretto.\n \n > E' utile per trovare il modo più efficiente per connettere le cose: ad esempio, per decidere la struttura di una rete internet!\n \n ## Esempi\n \n Gli algoritmi principali che risolvono il problema sono due, ed entrambi sono **algoritmi greedy**:\n \n - L'_Algoritmo di Kruskal_\n - L'_Algoritmo di Prim_\n `}\n \n \n {`\n # Algoritmo di Kruskal\n \n L'_Algoritmo di Kruskal_ è un algoritmo **greedy** che **trova il minimum spanning tree** di un grafo.\n \n ## Funzionamento\n \n 1. Ripetiamo questa procedura finchè tutti i nodi non sono connessi:\n 1. Prendiamo ad ogni passo **l'arco meno costoso** del grafo non ancora aggiunto all'insieme.\n 2. Assicuriamoci che **non si creino cicli**: se non se ne verrebbero a creare, possiamo **aggiungere l'arco all'insieme**.\n - Gli archi devono quindi connettere nodi in **componenti connesse diverse**.\n - Possiamo rappresentare le componenti connesse con un **Disjoint Set**.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | \\`O(archi²)\\` |\n \n ### Scomposizione\n \n - DisjointSet.__init__(): \\`O(archi)\\`\n - Per ogni ciclo: \\`O(archi²)\\`\n - DisjointSet.find_set(): \\`O(1)\\`\n - DisjointSet.union(): \\`O(archi)\\`\n \n ## Pseudocodice\n \n \\`\\`\\`python\n def minimum_spanning_tree_kruskal(graph):\n ds = DisjointSet()\n for node in graph.nodes:\n ds.create_set(node)\n arcs = []\n sorted_arcs = sorted(graph.arcs, key=lambda arc: arc.cost)\n for arc in sorted_arcs:\n if ds.find_set(node.start) != ds.find_set(node.end):\n arcs.append(arc)\n ds.union(node.start, node.end)\n return arcs\n \\`\\`\\`\n `}\n \n \n {`\n # Algoritmo di Prim\n \n L'_Algoritmo di Prim_ è un altro algoritmo **greedy** che **trova il minimum spanning tree** di un grafo.\n \n ## Funzionamento\n \n Creo una **coda con priorità** in cui inserisco tutti gli archi visibili dal mio albero, in cui la chiave è il **costo dell'arco**.\n \n Per trovare l'arco con costo più piccolo posso **estrarre un arco** dalla coda: la priorità ci garantisce che esso è l'**arco meno costoso**.\n \n Aggiungo allora un nuovo nodo all'albero, e con esso, **aggiungo alla coda** tutti gli **archi che scoprono un nuovo nodo**.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | \\`O(archi + nodi log nodi)\\` |\n \n ## Pseudocodice\n \n \\`\\`\\`python\n import math\n \n def minimum_spanning_tree_prim(graph, cost_array, start_node):\n # E' un Array di bool: se l'indice corrispondente al nodo è uguale a true, vuol dire che il (nodo è contenuto nell'albero.\n contains = [False for _ in range(len(graph))]\n # Contiene il precedente di ogni nodo \n prev = [None for _ in range(len(graph))]\n # Contiene il costo per arrivare a quel nodo\n cost = [math.inf for _ in range(len(graph))]\n # Creo la priority queue\n pq = PriorityQueue(graph.arcs, key=lambda arc: arc.cost)\n # Parto dal nodo \\`start_index\\`\n # Il costo dell'origine è 0.\n cost[start_node.index] = 0\n contains[start_node.index] = True\n \n while not pq.is_empty():\n new_node = pq.pop()\n contains[new_node.index] = True\n for arc in new_node.connections:\n other_node = arc.other(new_node)\n if not contains[other_node.index] and cost[other_node.index] > arc.cost:\n cost[other_node.index] = arc.cost\n prev[other_node.index] = new_node\n pq.decrease_priority_for(other_node, arc.cost)\n # L'array di prev rappresenta un albero.\n return prev\n \\`\\`\\`_\n `}\n \n \n {`\n # Compressione\n\n _Comprimere_ un file significa **ridurne le dimensioni** senza modificarne il significato.\n \n ## Categorie\n \n ### Compressione lossless\n \n Nella _compressione lossless_, i dati possono essere decompressi riottenendo una copia identica dell'originale.\n \n > Immaginiamo un file che contiene solo le lettere \\`a, b, c, d, e, f\\`.\n >\n > Le lettere compaiono con questa frequenza:\n > |a|b|c|d|e|f|\n > |45%|13%|12%|16%|9%|5%|\n >\n > Possiamo codificare le lettere nel seguente modo:\n > |a|b|c|d|e|f|\n > |\\`0b0\\`|\\`0b100\\`|\\`0b101\\`|\\`0b111\\`|\\`0b1100\\`|\\`0b1101\\`|\n >\n > Scrivere \\`abacadae\\` richiederebbe 64 bits con la codifica ASCII estesa, ma in questo modo riusciamo a scriverlo con soli 17 bits!\n \n Le codifiche di un file compresso devono rispettare la proprietà del _Codice a prefisso_, che dice che **nessun codice deve essere il prefisso di un altro codice**; altrimenti, si avrebbero ambiguità nella decodifica.\n \n > a = \\`1\\`\n > b = \\`11\\`\n >\n > \\`111\\` è \\`ab\\`, \\`ba\\` oppure \\`aaa\\`?\n \n Creiamo allora un _albero di decodifica_: un **albero binario** che, leggendo uno ad uno i bit codificati, ci permette di arrivare al **valore del codice presente sulle foglie** dell'albero.\n \n Gli alberi di decodifica sono sempre **completi**.\n \n > Un albero di decodifica incompleto sarebbe non ottimizzato!\n \n #### Esempi\n \n - .png\n - .flac\n - .zip\n - ...\n \n ### Compressione lossy\n \n Nella _compressione lossy_, alcuni dati [solitamente](http://needsmorejpeg.com/) irrilevanti vengono perduti: non si può, dunque, ricostruire l'originale.\n \n #### Esempi\n \n - .jpeg\n - .mp3\n - ...\n `}\n \n \n {`\n # Algoritmo di Huffman\n\n L'_Algoritmo di Huffman_ è un **algoritmo greedy** per la **costruzione di un albero di decodifica**.\n \n ## Funzionamento\n \n 1. Costruisco **un albero** (con un solo nodo) **per ogni elemento dell'alfabeto**.\n 2. Associo ad **ogni albero la frequenza dell'elemento** da cui è stato creato, per poi inserire tutti gli elementi in una coda con priorità.\n 3. Finchè non ho **un albero solo**:\n 1. Estraggo dalla coda i **due alberi con frequenza minore**.\n 2. **Li rendo fratelli**, creando un nuovo nodo in cui sono uno figlio destro e uno figlio sinistro.\n 3. Associo al nuovo nodo la **somma delle frequenze dei due alberi**, e inserisco il nuovo albero nella coda.\n \n > È molto raro che venga un albero \"dritto\"; se succede, probabilmente c'è qualcosa che non va.\n `}\n \n \n {`\n # Dizionario\n \n Un _dizionario_ è una struttura dati che **associa dei valori a delle chiavi**.\n \n ## Proprietà\n \n - Ogni elemento del dizionario è un **valore** che è stato **associato a una chiave**.\n - Possiamo aggiungere nuovi elementi con il **metodo \\`add(chiave, valore)\\`**.\n - Posiamo estrarre elementi con il **metodo \\`get(chiave)\\`**, che restituirà il valore associato a \\`chiave\\`.\n - E' possibile rimuovere elementi con il **metodo \\`delete(chiave)\\`**.\n - Due elementi con **chiavi diverse** non devono **mai restituire lo stesso valore**.\n \n ## Metodi\n \n Beh... Non ha molto senso in questo caso...\n \n \\`\\`\\`python\n dict()\n \\`\\`\\`\n \n ## Implementazione con tabella hash\n \n Una _tabella hash_ è un'array di coppie **chiave-valore**, che formano l'insieme _universo_.\n \n Per determinare l'**indice dell'array** in cui inserire una coppia, usiamo una [funzione _hash_](https://it.wikipedia.org/wiki/Hash#Algoritmo_di_hash) sulla chiave, che restituirà **numeri da \\`0\\` a \\`len(hash_table)\\`**.\n \n ### Risoluzione collisioni\n \n Potrebbe capitare però che **due chiavi diverse abbiano lo stesso indice**. Dobbiamo allora usare un metodo di _risoluzione collisioni_, che mi permetta di distinguere tra chiavi diverse.\n \n #### Lista di trabocco\n \n Possiamo salvare nell'array **liste di coppie** chiave-valore; in caso di collisione, **aggiungo un nuovo elemento alla lista**.\n \n In media, ciascuna di queste liste conterrà \\`elementi_inseriti / dimensione_tabella\\` elementi.\n \n #### Indirizzamento aperto\n \n Possiamo decidere di mettere le coppie che non trovano posto nel loro indice in **un altro indirizzo vuoto** dell'array.\n \n Ci sono diversi modi in cui decidere il nuovo indirizzo, ognuno con vantaggi e svantaggi: si può scegliere quello successivo, oppure il primo vuoto dell'array, oppure un indirizzo casuale.\n \n > Python, nei \\`dict\\`, usa indirizzamento aperto pseudorandom.\n \n ### Costo computazionale\n \n - Aggiungere una chiave: \\`O(n)\\`\n - Trovare una chiave: \\`O(n)\\`\n - Eliminare una chiave: \\`O(n)\\`\n `}\n \n \n {`\n # Programmazione dinamica\n \n La _programmazione dinamica_ è una **tecnica** di programmazione che prevede l'**estensione di una soluzione ottima precedente**.\n \n Tutti i problemi in cui si può applicare si possono risolvere anche con la **ricorsione**, ma a differenza della ricorsione, questa tecnica riesce ad evitare di ricalcolare la soluzione per ogni chiamata ricorsiva, ottenendo quindi tempi molto migliori.\n \n Si può applicare solo se un problema ha una **sottostruttura ottimale**, ovvero se la soluzione ottima di un sottoproblema è inclusa nella soluzione ottima del problema. \n \n ## Esempi\n \n - _Problema dello zaino_\n - ...\n \n > Il cammino minimo per raggiungere un nodo in un DAG è dato da \\`arco.costo + arco.primo_nodo.costo_cammino_minimo()\\`.\n >\n > \\`\\`\\`python\n > def SPD_PD(graph, start):\n > distance = [float(inf) for node in graph.nodes]:\n > distance[start] = 0\n > # I nodi devono essere in ordine di linearizzazione\n > for node in graph.nodes:\n > distance[node] = min([(arc.cost + distance[arc.other(node)] for arc in node.connections])\n > \\`\\`\\`\n \n > Ho una sequenza di interi da \\`a_1\\` a \\`a_n\\`. Voglio trovare la sottosequenza crescente più lunga.\n >\n > 5 2 3 4 7 3 6 3 1 6\n >\n > Trovo tutte le sequenze lunghe 1, e le rendo nodi di un grafo diretto.\n >\n > Da ogni nodo, creo una connessione verso i suoi maggiori.\n >\n > Infine, cerco i cammini massimi del grafo. \n > \n > Essi saranno la soluzione del problema.\n \n > Trova la lunghezza della sottosequenza più lunga che termina con \\`j\\`.\n >\n > \\`L[j]\\` = lunghezza della sottosequenza più lunga che termina in \\`j\\`\n > \n > \\`\\`\\`python\n > L[j] = max([1 + L[node] for arc in node.connections)]\n > \\`\\`\\`\n >\n > Esempio:\n > \\`\\`\\`python\n > L[9] = max([1+L[8], 1+L[3], 1+L[6]])\n > \\`\\`\\`\n `}\n \n \n {`\n # Problema dello zaino\n \n Il problema dello zaino è un problema _pseudo-trattabile_: non abbiamo dimostrazioni di se sia trattabile o intrattabile.\n \n ## Descrizione\n \n > Sei un ladro, e devi mettere **più refurtiva possibile** nello zaino per scappare. \n > Lo zaino può portare **al massimo \\`dim\\` kili**.\n >\n > **Quali** (e quanti) oggetti scegli?\n \n | Input | Output |\n |-------|--------|\n | \\`dim\\`ensione_zaino, \\`n\\`umero_oggetti, \\`oggetto.peso\\`, \\`oggetto.valore\\` | \\`profitto_massimo\\` |\n \n ## Categorie\n \n ### Problema con ripetizione\n \n Puoi prendere **tutte le copie che vuoi** di un oggetto.\n \n #### Soluzione\n \n \\`K(dim)\\` è il valore massimo ottenibile con uno zaino di capacità \\`dim\\`.\n \n > Se \\`i\\` appartenesse alla soluzione ottima, allora \\`K(dim) = i.valore + K(dim - i.peso)\\`...\n \n Possiamo dire che \\`K(dim) = max(i.valore + K(dim - i.peso))\\`.\n \n Inoltre, \\`K(0) = 0\\`.\n \n Ci salviamo tutte le soluzioni da \\`K(0)\\` a \\`K(dim)\\`, e le usiamo per calcolare il massimo in seguito.\n \n Calcolare \\`K(dim)\\` avrà allora un costo di \\`O(n * dim)\\`:\n - \\`n\\`, perchè trovare il massimo è un'operazione lineare\n - \\`dim\\`, perchè \\`dim\\` sono tutti i casi tra i quali devo andare a provare\n \n Il costo computazionale, allora, è in \\`O(n * dim)\\`. \n \n Però, il **tempo richiesto** dal nostro algoritmo dipende non dalla lunghezza dell'input, bensì dal **valore numerico** di \\`dim\\`, che corrisponde alla dimensione dell'array delle soluzioni. \n Allora, si dice che l'algoritmo è in **tempo _pseudo-polinomiale_**.\n \n ### Problema senza ripetizione\n \n Si può prendere **ogni oggetto una volta sola**.\n \n #### Soluzione _bruteforce_\n \n Scelgo se prendere o no l'item 1.\n \n Si creano due percorsi:\n - Non prendo l'oggetto: \\`valore = 0, peso = 0\\`\n - Prendo l'oggetto: \\`valore = oggetto.valore, peso = oggetto.peso\\`\n \n Continuo a creare percorsi, creando una specie di albero binario.\n \n Se a un certo punto vedo che \\`valore = x, peso = K\\` e \\`valore < x, peso = K\\`, allora posso escludere automaticamente tutto il sottoalbero destro, perchè non può essere migliore del sinistro: allora, sarò riuscito a ridurre il numero dei casi rispetto alla ricorsione.\n \n ### Problema in due variabili\n \n \\`K(j, w)\\` = massimo valore ottenibile con uno zaino di capacità \\`w\\` scegliendo gli item da \\`1\\` a \\`j\\`.\n \n Non possiamo più applicare la soluzione bruteforce, perchè abbiamo due variabili, \\`j\\` e \\`w\\`.\n \n Allora, prendo l'elemento \\`j\\`. Esso può essere o non essere nella soluzione: mi calcolo entrambe le alternative, e mi tengo l'alternativa dal valore più alto.\n \n Se \\`j\\` non è nella soluzione, il risultato diventerà \\`K(j-1, w)\\`; se invece è nella soluzione, il risultato sarà \\`j.valore + K(j-1, w-j.peso)\\`.\n \n In pratica, prendiamo\n \n \\`\\`\\`latex\n K(j, w) = max\n \\\\begin{cases}\n V_j + K(j-1, w-w_j)\n K(j-1, w)\n \\\\end{cases}\n \\`\\`\\`\n \n Costruisco allora una matrice con \\`j\\` su un asse e \\`w\\` sull'altro. \n Riempio le caselle con il valore di \\`K(j, w)\\`. \n Nella casella con \\`K(j, w)\\` avremo la soluzione ottima.\n \n Il tempo necessario per riempire tutte le caselle è nuovamente \\`O(n * w)\\`, ancora **pseudopolinomiale**.\n \n Per sapere che oggetti ho messo o no devo tenere traccia in qualche modo della catena del calcolo, usando, ad esempio, una pila.\n `}\n \n \n {`\n # Problemi intrattabili\n \n ## Problema di Set-Cover\n \n ### Input\n \n \\`U\\`niverso di \\`e\\`lementi\n \n \\`S\\`ottoinsieme di \\`s\\`ottoinsiemi di elementi di \\`U\\`\n \n ### Output\n \n Il minimo \\`S'\\`ottoinsieme di \\`s\\`ottoinsiemi che copra completamente \\`U\\`.\n \n ### Soluzione in \\`O(n^d)\\`\n \n Non c'è.\n \n ### Non-soluzione alternativa\n \n Faccio una scelta greedy, ma non posso dimostrare in alcun modo che la soluzione ottenuta sia quella ottima. \n Infatti, l'algoritmo non dà sempre la soluzione ottima, ma dà una soluzione accettabile in tempo polinomiale.\n \n Seleziono sempre il sottoinsieme che copre più elementi mancanti possibili.\n \n #### Costo computazionale\n \n \\`Costo greedy <= log(numero_elementi) * Costo ottimo\\`\n `}\n \n
\n );\n}\n"],"sourceRoot":""} \ No newline at end of file diff --git a/docs/route-AlgoritmiEStruttureDati.chunk.02d3a.esm.js b/docs/route-AlgoritmiEStruttureDati.chunk.92b93.esm.js similarity index 99% rename from docs/route-AlgoritmiEStruttureDati.chunk.02d3a.esm.js rename to docs/route-AlgoritmiEStruttureDati.chunk.92b93.esm.js index e278226..6e0d8eb 100644 --- a/docs/route-AlgoritmiEStruttureDati.chunk.02d3a.esm.js +++ b/docs/route-AlgoritmiEStruttureDati.chunk.92b93.esm.js @@ -1,4 +1,4 @@ -(window.webpackJsonp=window.webpackJsonp||[]).push([[3],{"ox/y":function(n,e,i){"use strict";function o(n,e){if(!n)throw new ReferenceError("this hasn't been initialised - super() hasn't been called");return!e||"object"!=typeof e&&"function"!=typeof e?n:e}Object.defineProperty(e,"__esModule",{value:!0}),e.Link=e.Match=void 0;var a=Object.assign||function(n){for(var e=1;e>>0,1)},e.prototype.render=function(n){var e=this.nextUrl||(0,t.getCurrentUrl)(),i=e.replace(/\?.+$/,"");return this.nextUrl=null,n.children({url:e,path:i,matches:!1!==(0,t.exec)(i,n.path,{})})},e}(r.Component),s=function(n){var e=n.activeClassName,i=n.path,o=function(n,e){var i={};for(var o in n)e.indexOf(o)>=0||Object.prototype.hasOwnProperty.call(n,o)&&(i[o]=n[o]);return i}(n,["activeClassName","path"]);return(0,r.h)(l,{path:i||o.href},(function(n){return(0,r.h)(t.Link,a({},o,{class:[o.class||o.className,n.matches&&e].filter(Boolean).join(" ")}))}))};e.Link=s,e.default=l,l.Link=s},w9qZ:function(n,e,i){"use strict";i.r(e),function(n){var o=i("sJH0"),a=i("imVn");i("ox/y");let r,t=n=>n;const l=String.raw;e.default=function(){return n("div",null,n(a.a,null,n(o.a,null,l(r||(r=t` +(window.webpackJsonp=window.webpackJsonp||[]).push([[4],{"ox/y":function(n,e,i){"use strict";function o(n,e){if(!n)throw new ReferenceError("this hasn't been initialised - super() hasn't been called");return!e||"object"!=typeof e&&"function"!=typeof e?n:e}Object.defineProperty(e,"__esModule",{value:!0}),e.Link=e.Match=void 0;var a=Object.assign||function(n){for(var e=1;e>>0,1)},e.prototype.render=function(n){var e=this.nextUrl||(0,t.getCurrentUrl)(),i=e.replace(/\?.+$/,"");return this.nextUrl=null,n.children({url:e,path:i,matches:!1!==(0,t.exec)(i,n.path,{})})},e}(r.Component),s=function(n){var e=n.activeClassName,i=n.path,o=function(n,e){var i={};for(var o in n)e.indexOf(o)>=0||Object.prototype.hasOwnProperty.call(n,o)&&(i[o]=n[o]);return i}(n,["activeClassName","path"]);return(0,r.h)(l,{path:i||o.href},(function(n){return(0,r.h)(t.Link,a({},o,{class:[o.class||o.className,n.matches&&e].filter(Boolean).join(" ")}))}))};e.Link=s,e.default=l,l.Link=s},w9qZ:function(n,e,i){"use strict";i.r(e),function(n){var o=i("sJH0"),a=i("imVn");i("ox/y");let r,t=n=>n;const l=String.raw;e.default=function(){return n("div",null,n(a.a,null,n(o.a,null,l(r||(r=t` # Algoritmi e Strutture Dati Docente: [**Manuela Montangero**](mailto:manuela.montangero@unimore.it) @@ -76,4 +76,4 @@ Dormire non fa bene! `)))),n(a.a,null,n(o.a,null,"\n # Il nome del corso\n\n ## Cosa sono gli algoritmi?\n\n Gli algoritmi sono modi sistematici per risolvere problemi.\n\n Sono fondamentali per sviluppare software, in quanto i computer sono eccellenti esecutori di algoritmi.\n\n ## Come si sviluppa un algoritmo?\n\n Innanzitutto, bisogna conoscere gli _input_ e gli _output_ del problema, rispettivamente i dati di partenza e i dati di arrivo di esso; si ha quindi una fase di **ricerca**.\n\n Poi, si deve trovare un procedimento che ci faccia risolvere il nostro problema: è quello che faremo in questa materia!\n\n Infine, bisogna scrivere la soluzione in un modo che possa essere eseguita da un computer: questa è la **programmazione**.\n\n ## Che tipo di problemi possiamo risolvere?\n\n Un algoritmo risolve problemi di tipo generale, non ci interessa sapere _il risultato di 123+456_, ma vogliamo sapere _il risultato di x+y_, dove x e y sono due numeri naturali qualsiasi.\n\n Un problema può essere quindi considerato circa come una **funzione matematica**, che connette ogni input a un output corrispondente.\n\n ## Che caratteristiche ha un algoritmo?\n\n Per prima cosa, ripetendo l'algoritmo più volte con lo stesso ingresso deve dare sempre la stessa uscita come **risultato**, finendo in un **tempo finito**.\n\n Deve essere **ben ordinato**: cambiando l'ordine in cui vengono effettuate le operazioni, è probabile che anche il risultato cambi!\n\n Le sue istruzioni devono essere **non ambigue**, cioè che non possano essere interpretate in più modi, e **effettivamente realizzabili**, cioè realizzabili con l'esecutore che vogliamo usare per eseguire l'algoritmo.\n\n ## Esistono algoritmi equivalenti?\n\n **Sì!** Possono esserci due algoritmi che dati gli stessi input, hanno gli stessi output, e quindi risolvono lo stesso problema.\n\n In compenso, possono avere un numero di operazioni diverse, e quindi essere **uno più veloce** (da eseguire) dell'altro.\n\n ## Come si verifica la correttezza di un algoritmo?\n\n L'algoritmo deve essere **valido per tutti gli input**, anche se questi sono infiniti.\n\n Possiamo effettuare prove matematiche per verificarne la correttezza; il **principio di induzione** è dunque una dei teoremi fondamentali dell'algoritmica.\n\n Possiamo però verificare la _non correttezza_ di un algoritmo trovando un singolo controesempio.\n ")),n(a.a,null,n(o.a,null,"\n # Efficienza degli algoritmi\n \n Un buon algoritmo deve essere **efficiente**, ovvero deve usare il minimo delle risorse necessarie, come _usare il minimo di tempo possibile_.\n \n ## Come misuriamo il tempo necessario?\n \n Cerchiamo di astrarre il tempo dal particolare esecutore, e andiamo a contare il numero di operazioni elementari richieste per eseguire il nostro algoritmo nel caso peggiore.\n \n Un algoritmo efficiente, infatti, all'aumentare dei dati in ingresso, diventerà sempre più veloce rispetto a uno non efficiente, anche su computer più lenti!\n \n > Il [Bubble Sort](https://en.wikipedia.org/wiki/Bubble_sort) è sempre più lento di un [Tree Sort](https://en.wikipedia.org/wiki/Tree_sort), anche su computer più lenti, perchè, dovendo ordinare liste sempre più lunghe, prima o poi si raggiunge un punto in cui il primo è più veloce (in termini di tempo) dell'altro.\n \n Dobbiamo andare a vedere, quindi, _il numero di operazioni richieste per ottenere il risultato nel caso peggiore_.\n \n Consideriamo operazioni sia operazioni aritmetiche sia operazioni logiche, e diciamo che ciascuna costa 1.\n \n > L'[algoritmo di Euclide](https://it.wikipedia.org/wiki/Algoritmo_di_Euclide) per l'MCD costa `3` per ogni iterazione (un giro del ciclo `while`). Diciamo, allora, che costa `3n`, dove `n` è il numero più alto dei due, perchè nel caso peggiore (uno dei due numeri è 1) l'algoritmo compie `n` iterazioni.\n \n ## Altri parametri ottimizzabili\n \n È possibile che alcuni algoritmi per vari motivi cerchino di ottimizzare altri parametri diversi dal tempo, come ad esempio _la dimensione dell'input_ o la _memoria utilizzata_. \n \n > Generalmente, questo viene fatto sui dispositivi embedded, con memoria molto limitata.\n \n ### Criteri di costo di memoria\n \n Ci sono vari criteri con cui stimare la memoria richiesta da un dato: è possibile che il costo risultante vari in base al criterio scelto!\n \n #### Criterio di costo logaritmico\n \n Un dato costa il numero di bit necessari per rappresentarlo.\n \n > Un int che contiene il numero `n` costa `log_2(n)`. \n > Un array di `[n]` numeri tutti uguali costa `n log_2(n)`.\n \n #### Criterio di costo uniforme\n \n Un dato costa il numero di elementi che lo costituiscono.\n \n > Un int che contiene il numero `n` costa `1`. \n > Un array di `[n]` numeri costa `n`. \n > Una matrice `[m][n]` costa `m*n`.\n ")),n(a.a,null,n(o.a,null,"\n # Modelli algoritmici\n\n Per progettare un algoritmo, abbiamo bisogno di sapere le proprietà del nostro esecutore, ovvero il suo _modello algoritmico_.\n \n > Ad esempio, dobbiamo sapere quali istruzioni è in grado di eseguire, e quanto tempo queste istruzioni richiedono.\n \n ## Il modello RAM\n \n Il modello in uso su tutti i computer attuali è il _modello RAM_: \n \n - In ogni cella di memoria può essere archiviato un dato.\n - Il **tempo di accesso** alle celle è **costante** per tutte le celle.\n - La **memoria** principale è **infinita**.\n - Si ha **un solo processore**.\n ")),n(a.a,null,n(o.a,null,'\n # Notazione asintotica\n \n La _notazione asintotica_ è un sistema per **stimare** velocemente il costo di un algoritmo complesso.\n \n Ci permette di **confrontare velocemente il caso peggiore** degli algoritmi.\n \n In particolare, consideriamo il _rapporto tra il numero di operazioni nel caso peggiore e la dimensione dell\'input_.\n \n ## Limiti\n \n Possiamo dare a questa stima dei limiti, superiore e inferiore, che rappresenteranno rispettivamente un costo che non sarà **mai superato** e un costo che verrà **sempre superato**.\n \n Chiameremo questi limiti _upper bound_ e _lower bound_; la loro combinazione darà un _tight bound_.\n \n L\'obiettivo sarà di _ricavare i bound più precisi possibile_ per un dato algoritmo, ovvero l\'**upper bound più basso** e il **lower bound più alto**.\n \n ### O grande\n \n > "O grande" \n > O di g(n)\n > "big-O"\n \n Per rappresentare la stima, useremo una notazione particolare, detta _O grande_, con la seguente proprietà:\n - Date due funzioni `f(n) : N -> R` e `g(n) : N -> R`, diremo che `f(n) ∈ O(g(n))` se e soltanto se `∃ c > 0, n ≥ n_0` tali che `∀ n ≥ 0, f(n) ≤ c * g(n)`\n \n Quando una funzione è O grande di un altra, significa che **asintoticamente, la funzione in O grande è sempre maggiore di quella che sta venendo stimata**.\n \n > **Ipotesi** \n > - `f(n) = 2n² + 3n + 6` \n > - `g(n) = n²`\n >\n > **Tesi** \n > - `f(n) ∈ O(n²)`.\n >\n > **Svolgimento** \n > Scrivo una disequazione, lasciando intatto il termine noto: \n > 1. `2n² + 3n + 6 ≤ 2n² + 3n² + 6` \n > 2. `n² ≤ 2n² + 3n² + n² = 6n²` per `n ≥ 3`\n >\n > Sappiamo, allora, che `2n² + 3n + 6 ≤ 6n²`.\n \n #### Espressioni di O grande\n \n Questa tabella rappresenta le espressioni di O grande più comunemente utilizzate, in ordine **dalla più forte alla più debole**.\n \n > Più forte significa che, per ogni riga della tabella, tutte le righe sottostanti sono contenute nell\'espressione.\n >\n > Ad esempio, `O(n) ∈ O(1)`.\n \n | Espressione O() | Nome |\n |-----------------|------|\n | `O(1)` | Costante |\n | `O(log log n)` | loglog |\n | `O(log n)` | Logaritmica |\n | ![LaTeX](https://latex.codecogs.com/png.latex?O(n^{1/c})) (per c ≥ 1) | Sublineare |\n | `O(n)` | Lineare |\n | `O(n log n)` | nlogn |\n | `O(n²)` | Quadratica |\n | `O(n³)` | Cubica |\n | `O(n^k)` (per k ≥ 1) | Polinomiale |\n | `O(a^n)` (per a ≥ 1) | Esponenziale |\n | `O(n!)` | Fattoriale |\n \n #### Polinomiale\n \n Molto spesso, noteremo che il tempo richiesto da una funzione è O grande di un polinomio di grado K, ovvero `f(n) ∈ O(n^k)`.\n \n Notiamo che in questi casi, possiamo semplificare l\'O grande al grado massimo del polinomio.\n \n > Ad esempio, `O(n² + n + 1) = O(n²)`.\n \n ##### Dimostrazione\n \n Per `n > 0 \\and 0 ≤ i ≤ k`: \n ![LaTeX](https://latex.codecogs.com/png.latex?a_k%20n^k%20+%20a_{k-1}%20n^{k-1}%20+%20%E2%80%A6%20+%20a_1%20n%20+%20a_0%20%E2%89%A4%20|a_k|%20n^k%20+%20|a_{k-1}|%20n^k%20+%20%E2%80%A6%20+%20|a_1|%20n^k%20+%20|a_0|%20n^k%20=%20(|a_k|%20+%20|a_{k-1}|%20+%20%E2%80%A6%20+%20|a_1|%20+%20|a_0|)%20n^k)\n \n #### Proprietà di O grande\n \n 1. `f(n) ∈ O(g(n)) -> ∀ a > 0, a * f(n) ∈ O(g(n))`.\n 2. `f(n) ∈ O(g(n)), d(n) ∈ O(h(n)) -> f(n) + d(n) ∈ O(g(n) + h(n)) -> O(max\\{g(n), h(n)\\})`\n 3. `f(n) ∈ O(g(n)), d(n) ∈ O(h(n)) -> f(n) * d(n) ∈ O(g(n) * h(n))`\n \n In pratica, se una funzione è la _somma di più termini_, basta guardare l\'**`O()` più grande** tra tutti i suoi termini; se invece una funzione è un _prodotto di più termini_, si possono **omettere le costanti**, e l\'`O()` finale sarà dato dal **prodotto degli `O()`** dei termini.\n \n ## Lower bound\n \n Possiamo anche stimare il _lower bound_, il limite inferiore: il **numero minimo di operazioni** che viene effettuato **nel caso migliore** con la **massima dimensione dell\'ingresso**.\n \n ### Ω()\n \n > "Omega" \n > Omega di g(n)\n > "big-Omega"\n \n Esiste un equivalente di O grande per il lower bound: è detto _Omega grande_, o più semplicemente _Omega_, e funziona nello stesso identico modo, solo... al contrario.\n \n Diremo che `f(n) ∈ Ω(g(n))` se e solo se `∃ c > 0, n_0 ≥ 0 : ∀ n ≥ n_0 f(n) ≥ c * g(n)`.\n \n #### Espressioni di Ω()\n \n Anche in questa tabella le espressioni sono **dalla più forte alla più debole**.\n \n | Espressione Ω() | Nome |\n |-----------------|------|\n | `Ω(n!)` | Fattoriale |\n | `Ω(a^n)` (per a ≥ 1) | Esponenziale |\n | `Ω(n^k)` (per k ≥ 1) | Polinomiale |\n | `Ω(n³)` | Cubica |\n | `Ω(n²)` | Quadratica |\n | `Ω(n log n)` | nlogn |\n | `Ω(n)` | Lineare |\n | ![LaTeX](https://latex.codecogs.com/png.latex?\\Omega(n^{1/c})) (per c ≥ 1) | Sublineare |\n | `Ω(log n)` | Logaritmica |\n | `Ω(log log n)` | loglog |\n | `Ω(1)` | Costante |\n \n ## Tight bound\n \n Quando **upper e lower bound coincidono**, allora otteniamo un _tight bound_.\n \n ### θ()\n \n > "Theta" \n > Theta di g(n)\n > "big-Theta"\n \n Anche per il tight bound abbiamo una notazione equivalente a O grande e Omega grande: _Theta grande_!\n \n Diciamo che `f(n) ∈ θ(g(n))` se e solo se `∃ c_1, c_2 > 0, n_0 ≥ 0 : ∀ n ≥ n_0, c_1 * g(n) ≤ f(n) ≤ c_2 * g(n)`.\n \n Ha la particolarità che non valgono tutte le proprietà degli altri due: va usata quindi con cautela!\n \n ## Risorse utili\n \n [khanacademy.org](https://www.khanacademy.org/computing/computer-science/algorithms/asymptotic-notation/a/big-big-theta-notation)\n ')),n(a.a,null,n(o.a,null,"\n # Problemi algoritmici\n \n Un _problema algoritmico_ è un problema matematico che si vuole provare a risolvere con un algoritmo.\n \n > Dati 10 numeri, voglio sapere se sono in ordine crescente oppure no.\n \n ## Caterigorizzazione\n \n I problemi algoritmici si dividono in tre categorie: problemi _trattabili_, problemi _intrattabili_ e problemi _irrisolvibili_.\n \n ### Problema trattabile\n \n Perchè un problema algoritmico sia _trattabile_, deve avere **almeno un algoritmo con upper bound polinomiale**.\n \n > Questo significa che il tempo impiegato da un computer per risolvere il problema rimane ragionevole, e che quindi può essere utilizzato in maniera efficiente.\n \n La trattabilità è un campo ancora parecchio aperto: esistono anche tanti problemi di cui non si è ancora dimostrata la trattabilità o intrattabilità.\n \n > La [fattorizzazione](https://it.wikipedia.org/wiki/Fattorizzazione) è uno di questi problemi: l'assenza di una dimostrazione è ciò che la rende uno dei pilastri della sicurezza informatica moderna.\n \n ### Problema intrattabile\n \n Se **un problema non ha nessun algoritmo con upper bound polinomiale**, allora si dice che è **intrattabile**.\n \n ### Problema irrisolvibile\n \n Se **non esistono algoritmi per risolvere un problema**, allora questo si dice **irrisolvibile**.\n \n > [Dato un algoritmo con certi input, riusciamo a capire con un algoritmo se la sua esecuzione termina o no?](https://en.wikipedia.org/wiki/Halting_problem)\n \n ### Upper e lower bound di problemi\n \n Si può anche trovare un _upper bound_ e un _lower bound_ per un problema, ma bisogna generalizzare di più.\n \n L'**upper bound di un problema** è il minimo upper bound di tutti gli algoritmi che lo risolvono; deve esistere almeno un algoritmo che lo risolva che abbia lo stesso _upper bound_. E' praticamente il tempo migliore per risolvere il problema dato.\n \n Il **lower bound di un problema** è il minimo lower bound di tutti gli algoritmi che lo risolvono; non deve esistere nemmeno un algoritmo che abbia un lower bound migliore. E' il numero assolutamente minimo di operazioni richieste, non si può fare meglio di così.\n \n In particolare, abbiamo che l'_upper bound di un algoritmo_ -> l'_upper bound del suo problema_, \n e il _lower bound di un problema_ -> il _lower bound di un suo algoritmo_.\n \n Generalmente, il _lower bound di un problema_ è una rappresentazione abbastanza accurata della sua difficoltà.\n ")),n(a.a,null,n(o.a,null,"\n # Ricerca binaria\n \n Non credo di aver bisogno di studiare la ricerca binaria, quindi non ho preso appunti a riguardo.\n \n Se non siete me, e state cercando informazioni a riguardo, andate a vedere su Wikipedia!\n ")),n(a.a,null,n(o.a,null,"\n # Divide et impera\n \n Un modo efficace per risolvere un problema è di usare il metodo _divide et impera (et combina)_.\n \n - _Divide_: Divido il problema in **tanti sottoproblemi**.\n - _Impera_: **Risolvo indipendentemente dal resto** ciascuno dei sottoproblemi.\n - _Combina_: **Combino** i risultati dei sottoproblemi per **risolvere il problema principale**.\n \n ## Ricorsione\n \n Un algoritmo (o funzione) si dice _ricorsivo_ quando durante l'esecuzione **richiama sè stesso**.\n \n Dato che tutti gli algoritmi devono avere termine entro un tempo finito, se scriviamo una funzione ricorsiva è fondamentale finire con un **caso base**, che non chiami ulteriormente la ricorsione.\n \n Se esiste una funzione ricorsiva, allora esiste _sempre_ una _funzione iterativa_ che darà lo stesso risultato.\n \n > Sul pratico, una funzione ricorsiva tipicamente è **più costosa** del suo equivalente iterativo: se possibile, quindi, la ricorsione andrebbe evitata.\n \n #### Pseudocodice di esempio\n \n ```python\n def fattoriale(n):\n # Caso base; la ricorsione finisce e dà un risultato fisso\n if n <= 1:\n return 1\n # Caso ricorsivo; la funzione restituisce il risultato di sè stessa (ma con parametri diversi)\n else:\n return n * fattoriale(n - 1)\n ```\n ")),n(a.a,null,n(o.a,null,"\n # Master Theorem\n \n Il _Master Theorem_ è uno dei teoremi più importanti dell'algoritmica.\n \n Esso permette di **calcolare l'upper bound di un algoritmo ricorsivo** in modo piuttosto semplice.\n \n ## Ipotesi\n \n Dato un algoritmo:\n - Con uno o più casi base\n - Che richiama la funzione ricorsiva un numero n di volte\n \n ## Tesi\n \n Allora, il suo upper bound avrà la formula:\n \n ![](https://quicklatex.com/cache3/89/ql_08d29a7e55d561a900570bc83b93ff89_l3.png)\n ")),n(a.a,null,n(o.a,null,"\n # Caso particolare del Master Theorem\n \n ## Ipotesi\n \n Se: \n ![](https://quicklatex.com/cache3/57/ql_e34dc27b42831d3c3ff671b0f3861257_l3.png)\n \n Ovvero, se la dimensione dell'input viene divisa ad ogni ciclo da una costante b, è polinomiale e il caso base è costante...\n \n ## Tesi\n \n Allora: \n ![](https://quicklatex.com/cache3/ca/ql_26e3557a6ca2d6ac4b8481e7c5263fca_l3.png)\n \n > In pratica, se il costo dominante è quello della parte \"fissa\" dell'algoritmo, esso sarà `O(n^d)`, mentre se il costo dominante è quello delle chiamate ricorsive, esso sarà `O(n^{log_b e})`. \n > Se nessuno dei due è dominante... si dividono circa in parti uguali, creando un costo di `O(n^d log n)`.\n ")),n(a.a,null,n(o.a,null,"\n # Ordinamento\n \n Un problema molto frequente nell'informatica consiste nell'**ordinare efficientemente grandi quantità di elementi**.\n \n Esistono [tantissimi](https://it.wikipedia.org/wiki/Algoritmo_di_ordinamento) algoritmi per effettuare l'ordinamento. \n L'**efficienza** di ciascuno **varia** di caso in caso: alcuni sono estremamente efficienti se quasi tutti i numeri sono già nell'ordine giusto; altri, invece, potrebbero impiegare tantissimo tempo.\n \n In termini matematici, abbiamo:\n \n - **Input:** A[n]\n - **Output:** B, ∀ i < n, A[i] ≤ A[i+1]\n \n ## Ordinamento tramite confronto\n \n L'ordinamento \"tradizionale\" è detto _ordinamento tramite confronto_: funziona sempre, e **non ha altri modi di ottenere informazioni** se non con l'operazione logica di confronto tra i dati.\n \n ### Limiti\n \n E' un problema risolto: è dimostrabile che il suo **lower bound** è **`Ω(n log n)`**; possiamo quindi dire che qualsiasi algoritmo di ordinamento è in `Ω(n log n)`, e se riusciamo a trovare un algoritmo di ordinamento in `O(n log n)` siamo riusciti a raggiungere il massimo dell'efficienza.\n \n #### Dimostrazione\n \n Consideriamo **tutte le possibili permutazioni** della sequenza da ordinare: sono `n!`.\n \n Per ogni confronto che effettuiamo, **riduciamo la quantità di permutazioni** correttamente ordinate; prima o poi, rimarrà **una sola possibilità**.\n \n **TODO, non trovo la spiegazione corretta!**\n \n ### Esempi\n \n Algoritmi che effettuano l'ordinamento tramite confronto sono:\n - _Bubble sort_\n - _Merge sort_\n - _Insertion sort_\n - _Quick sort_\n - _Heap sort_\n - E tanti, tanti altri!\n \n ## Ordinamento con altri mezzi\n \n Esistono algoritmi che ricavano informazioni in altri modi, diversi dal confronto.\n \n Essi possono avere un lower bound più basso di `O(n log n)`, però hanno spesso limitazioni sul loro utilizzo.\n \n ### Esempi\n \n - _Counting sort_, indicizza i valori da ordinare\n - _Radix sort_, guarda singolarmente le cifre dei valori\n - _Sleep sort_, sfrutta i thread e la funzione sleep per ordinare valori\n - E altri ancora!\n ")),n(a.a,null,n(o.a,null,"\n # Insertion sort\n \n L'_insertion sort_ è una soluzione **iterativa** all'ordinamento per confronto.\n \n ## Funzionamento\n \n Considero la sequenza divisa in **due parti**: una parte **ordinata** e una parte **non ordinata**.\n \n Parto dal primo elemento della lista: è sempre ordinato con sè stesso. \n Poi, aggiungo uno alla volta i numeri della parte non ordinata a quella ordinata; prima trovo in quale posizione dovrò andare a mettere il numero, poi **faccio slittare tutti i numeri dopo quella posizione** avanti di 1, in modo da **creare lo spazio** in cui infine **inserirò** il numero.\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(n²)` | `Ω(n)` | - |\n \n Nel _caso migliore_ (**lista già ordinata**), il numero da inserire è già nella posizione giusta, quindi non devo effettuare altri confronti oltre il primo, rendendo il lower bound dell'algoritmo `Ω(n)`.\n \n Nel _caso peggiore_ (**lista nell'ordine inverso**), dobbiamo confrontare il numero da inserire con tutti gli altri nella parte ordinata: dobbiamo allora eseguire `1+2+3+4+5+… = \\frac{(n-1)(n)}{2}` confronti; ciò significa che l'upper bound è `O(n²)`!\n \n ## Pseudocodice\n \n ```python\n def insertion_sorted(lista):\n # Itero su tutti i numeri della lista, dal primo all'ultimo.\n for divisore_ord in range(len(lista)):\n # Partendo dalla posizione attuale, creo l'indice di divisione numeri ordinati maggiori e minori\n divisore_magg = divisore_ord\n # Faccio slittare avanti i numeri maggiori di quello che stiamo inserendo\n # Se l'indice divisore_magg raggiunge 0, vuol dire che tutti i numeri della lista sono maggiori del numero attuale \n while divisore_magg >= 0 and lista[divisore_magg-1] > lista[divisore_magg]:\n # Scambio la posizione dei due elementi con gli indici specificati\n # Funzione inventata \n lista[divisore_magg], lista[divisore_magg-1] = lista[divisore_magg-1], lista[divisore_magg]\n # Diminuisco il separatore di 1\n divisore_magg -= 1\n ```\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/bn/sorting)\n ")),n(a.a,null,n(o.a,null,"\n # Merge sort\n \n Il _merge sort_ è una soluzione **ricorsiva** all'ordinamento per confronto.\n \n ## Funzionamento\n \n Per questo algoritmo, utilizziamo la tecnica del **divide et impera**.\n \n 1. _Divide_: Divido A in **due parti**.\n 2. _Impera_: Metto **separatamente in ordine** le parti.\n 3. _Unisci_: **Unisco** le due parti.\n \n Consideriamo come **caso base** della ricorsione una parte composta da un numero, che ovviamente è già ordinata con sè stessa.\n \n ### Merge\n \n Per **unire le due parti** usiamo una funzione detta `merge()`.\n \n Costruiamo una nuova sequenza uguale alla sequenza 1, ma **aggiungiamo alla fine un valore sentinella** sempre maggiore di tutti gli elementi contenuti.\n \n > ```\n > | 1 | 3 | 7 | 8 | ∞ |\n > ```\n \n Facciamo **la stessa cosa** per la sequenza due.\n \n > ```\n > | 2 | 4 | 5 | 6 | ∞ |\n > ```\n \n Prendo i primi numeri delle due sequenze e **metto il più piccolo nella sequenza iniziale**.\n \n > ```\n > | 1 | 2 | 3 | | | | | | \n > | | | 7 | 8 | ∞ | \n > | | 4 | 5 | 6 | ∞ | \n > ```\n \n **Continuo** finchè non ho messo tutti i numeri; **grazie alla sentinella non usciremo mai dalla sequenza**, in quanto essa è sempre maggiore di tutti gli altri numeri.\n \n > ```\n > | 1 | 2 | 3 | 4 | 5 | 6 | | | \n > | | | 7 | 8 | ∞ | \n > | | | | | ∞ |\n > ```\n \n Quando **rimangono solo le sentinelle** significa che abbiamo aggiunto tutti gli elementi, e quindi abbiamo finito.\n \n > ```\n > | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | \n > | | | | | ∞ | \n > | | | | | ∞ | \n > ```\n \n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(n log n)` | `Ω(n log n)` | **`θ(n log n)`** |\n \n Il merge sort è un algoritmo ricorsivo con un **caso base in tempo costante** e che **richiama sè stesso 2 volte**.\n \n ```latex\n T(n) =\\\\\n \\\\\n Θ(1) \\qquad n=1\\\\\n 2 T(\\frac{n}{2}) + Θ(n) \\qquad n \\neq 1\n ```\n \n Applicando il **caso particolare del Master Theorem**, otteniamo:\n \n ```latex\n T(n) =\\\\\n \\\\\n Θ(1) \\qquad n=1\\\\\n Θ(n log n) \\qquad n \\neq 1\n ```\n \n ## Pseudocodice\n \n ```python\n def merge_sorted(part):\n # Caso base\n if len(part) == 1:\n return part\n # Divide\n middle = len(part) // 2\n part_a = part[:middle]\n part_b = part[middle:]\n # Impera\n sort_a = merge_sorted(part_a)\n sort_b = merge_sorted(part_b)\n # Combina\n return merge(sort_a, sort_b)\n ```\n \n ## Visualizzazione\n \n [hackerearth.com](https://www.hackerearth.com/practice/algorithms/sorting/merge-sort/visualize/)\n \n [visualgo.net](https://visualgo.net/bn/sorting) (Nota: visualizza solo la fase _Unisci_ del sort)\n ")),n(a.a,null,n(o.a,null,"\n # Quick sort\n \n Il _quick sort_ è un altro approccio **ricorsivo** all'ordinamento per confronto.\n \n ## Funzionamento\n \n Anche qui, applichiamo il **divide et impera**.\n \n 1. _Divide_: Scelgo un **pivot** qualsiasi all'interno della lista. Metto alla sua **sinistra tutti i numeri minori** e alla sua **destra tutti i numeri maggiori**.\n 2. _Impera_: Eseguo un **quick sort su entrambe le sottoliste**.\n \n ### Esempi\n \n #### Iterazione con partizioni bilanciate\n \n Osserviamo come si formi una partizione con tre elementi e una con quattro. \n \n ```\n |¦ [2] 8 7 1 3 5 6 {4}\n 2 |¦ [8] 7 1 3 5 6 {4}\n 2 |8 ¦ [7] 1 3 5 6 {4}\n 2 |8 ¦ [7] 1 3 5 6 {4}\n 2 |8 7 ¦ [1] 3 5 6 {4}\n 2 1 |7 8 ¦ [3] 5 6 {4}\n 2 1 3 |8 7 ¦ [5] 6 {4}\n 2 1 3 |8 7 5 ¦ [6] {4}\n 2 1 3 |8 7 5 6 ¦ [{4}]\n [2 1 3] {4} [8 5 6 7]\n ```\n \n #### Iterazione con partizioni sbilanciate\n \n Osserviamo come si formi una partizione con **zero elementi** e una con tre.\n \n ```\n |¦ [4] 7 3 {1}\n |4 ¦ [7] 3 {1}\n |4 7 |¦ [3] {1}\n |4 7 3 |¦ [{1}]\n [] {1} [4 7 3]\n ```\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(n²)` | `Ω(n log n)` | - |\n \n Il costo della funzione è dato dalla somma del costo per **dividere in due partizioni** con il costo per realizzare il **Quick sort delle due sottopartizioni**\n \n Possiamo applicare allora il **Master Theorem generale**:\n \n ```latex\n T(n)\\\\\n =\\\\\n Θ(1) \\qquad per\\ n = 1\\\\\n T(q) + T(dim_lista - pivot - 1) + Θ(n) \\qquad per\\ n > 1\n ```\n \n ### Il caso migliore\n \n Se il pivot `q` è la **mediana della partizione** che stiamo ordinando, si vengono a creare due _sottopartizioni bilanciate_, e sostituendo otteniamo:\n \n ```latex\n T(n)\\\\\n =\\\\\n Θ(1) \\qquad per\\ n = 1\\\\\n 2 T(\\frac{n}{2}) + Θ(n) \\qquad per\\ n > 1\n ``` \n \n Possiamo allora applicare il **Master Theorem particolare**:\n \n ```latex\n T(n)\\\\\n =\\\\\n Θ(1) \\qquad per\\ n = 1\\\\\n Θ(n log n) \\qquad per\\ n > 1\n ```\n \n ### Il caso peggiore\n \n Se il pivot è uno degli **estremi dell'array**, si creano due _partizioni sbilanciate_: una delle due sottoliste è sempre vuota! \n Allora:\n \n ```latex\n T(n) = T(n-1) + Θ(n)\\\\\n = T(n-2) + Θ(n-1) + Θ(n)\\\\\n = T(n-3) + Θ(n-2) + Θ(n-1) + Θ(n)\\\\\n = …\n ∈ Θ(n^2)\n ```\n \n > \"Non date da mangiare sequenze ordinate al Quicksort, gli sono indigeste.\"\n \n ## Pseudocodice\n \n ```python\n def partition(partizione, inizio, fine):\n \"\"\"Dividi una partizione in due, usando l'ultimo elemento come pivot.\n \n Note utili:\n partizione[fine] è il pivot\n partizione[maggiori] è il primo numero dei maggiori\n partizione[non_iterati] è l'elemento su cui si sta iterando al momento\"\"\"\n # Crea il primo separatore (la | pipe nell'esempio)\n maggiori = inizio\n # Crea il secondo separatore (la ¦ broken pipe nell'esempio)\n non_iterati = inizio\n # Itera su ogni numero tra inizio e fine (escluso!)\n while non_iterati < fine:\n # Se l'elemento su cui stiamo iterando è minore del pivot\n if partizione[non_iterati] <= partizione[fine]:\n # Mettilo nell'insieme dei minori, scambiandolo con il primo numero dei maggiori e incrementando il primo separatore\n partizione[maggiori], partizione[non_iterati] = partizione[non_iterati], partizione[maggiori]\n maggiori += 1\n # Incrementa sempre il secondo separatore\n non_iterati += 1\n # Inserisci il pivot tra le due sottopartizioni create, \n partizione[fine], partizione[non_iterati] = partizione[non_iterati], partizione[fine]\n return maggiori\n ```\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/bn/sorting) (Nota: invece che prendere l'ultimo numero come pivot prende il primo, cambiando leggermente l'algoritmo.)\n \n ## Note per l'esame\n \n > La domanda che fa sempre è **\"Qual è la sequenza di pivot utilizzata?\"**\n \n > Elementi da soli _non_ vengono presi come pivot!\n ")),n(a.a,null,n(o.a,null,'\n # Counting sort\n\n Il _counting sort_ è un approccio diverso all\'ordinamento: **non usa il confronto**!\n \n ## Requisiti\n \n Il counting sort può essere utilizzato solo su **sequenze di numeri interi**, e solo se **siamo a conoscenza del minimo e del massimo** dei numeri contenuti nell\'array, ed essi non sono troppo distanti uno dall\'altro. \n (La memoria occupata dal counting sort aumenta linearmente con la differenza tra minimo e massimo!)\n \n Per semplicità, consideriamo il **minimo `0`**. \n L\'input allora sarà una sequenza di interi `A`, e il valore del **massimo `k`**, tale che `∀ n ∈ A, 0 \\leq n \\leq K`.\n \n ## Funzionamento\n \n Il counting sort **conta le ripetizioni** delle chiavi nella sequenza originale e in seguito **sovrascrive i valori** della sequenza con i valori ordinati ripetuti il numero di volte che sono stati individuati nella sequenza.\n \n > ```\n > 1 4 5 3 4 1 4 2 5 1\n > ```\n >\n > L\'`1` appare 3 volte, il `2` 1 volta, il `3` 1 volta, il `4` tre volte e il `5` due volte.\n >\n > La sequenza viene quindi così sovrascritta:\n > ```\n > 1 1 1 3 4 1 4 2 5 1 # Sovrascriviamo la sequenza con 1 ripetuto 3 volte\n > 1 1 1 2 3 4 4 4 5 1 # Sovrascriviamo la sequenza con 2, 3, 4 ripetuti rispettivamente 1 1 e 3 volte\n > 1 1 1 2 3 4 4 4 5 5 # Sovrascriviamo la sequenza con 5 ripetuto 2 volte: abbiamo finito!\n > ``` \n \n Esiste anche una **versione stabile** del counting sort che, invece che sovrascrivere, **sposta i valori**, mantenendo le informazioni aggiuntive nel caso invece che interi fossero altri tipi di dati.\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(k + n)` | `Ω(k + n)` | **`θ(k + n)`** |\n \n L\'algoritmo è composto da quattro parti:\n - Ricerca del minimo e massimo (in `θ(n)`)\n - Inizializzazione dell\'indice (in `θ(k)`)\n - Conteggio dei numeri (in `θ(n)`)\n - Sovrascrittura dei numeri (in `θ(k + n)`)\n \n `2 + O(k) + O(n) + O(k + n) -> O(k + n)`\n \n Notiamo che `k` è costante, l\'algoritmo è `O(n)`, estremamente efficiente.\n \n ## Pseudocodice\n \n ```python\n def counting_sort(lista: typing.List[int]):\n """Ordina in-place una lista con il counting sort."""\n # Trovo la dimensione della lista\n dim = len(lista)\n # Trovo il massimo e il minimo all\'interno della lista\n minimo = min(lista)\n massimo = max(lista)\n # Creo l\'indice dei numeri, in modo che sia lungo k e pieno di 0\n indice = [0 for _ in range(minimo, massimo+1)]\n # Conto i numeri presenti, scorrendo su lista e aggiungendo 1 al numero corrispondente\n for i in range(dim):\n indice[lista[i]] += 1\n # Sovrascrivo i numeri nella lista\n count = 0\n for pos, val in enumerate(indice):\n for _ in range(val):\n indice[count] = pos\n count += 1\n \n def stable_counting_sorted(lista: typing.List[int], k: int) -> typing.List[int]:\n """Ordina stabilmente una lista con il counting sort stabile, e restituiscila."""\n # Trovo la dimensione della lista\n dim = len(lista)\n # Trovo il massimo e il minimo all\'interno della lista\n minimo = min(lista)\n massimo = max(lista)\n # Creo l\'indice dei numeri, in modo che sia lungo k e pieno di 0\n indice = [0 for _ in range(minimo, massimo+1)]\n # Conto i numeri presenti, scorrendo su lista e aggiungendo 1 al numero corrispondente\n for i in range(dim):\n indice[lista[i]] += 1\n # Faccio diventare l\'indice "il numero di numeri \\leq i"\n for i in range(len(indice)):\n if i == 0:\n continue\n indice[i] += indice[i-1]\n assert indice[-1] == dim\n # Creo una nuova lista, che sarà quella che verrà restituita\n nuova = [None for _ in range(dim)]\n # Inizio a posizionare i numeri, al contrario\n for i in range(0, dim, -1):\n nuova[indice[lista[i]]] = lista[i]\n indice[lista[i]] -= 1\n return nuova\n ```\n ')),n(a.a,null,n(o.a,null,"\n ## Introduzione alle Strutture Dati\n\n Una _struttura dati_ è un modo in cui si possono organizzare i dati di un programma.\n \n Si possono definire in due modi: **elementari** e **astratte**.\n \n ### Strutture dati elementari\n \n Le strutture _elementari_ dipendono strettamente dal modo in cui vengono memorizzati i dati.\n \n > **Array** e **liste** sono strutture dati elementari: sono definite dicendo come sono memorizzati i dati, rispettivamente, in celle contigue di memoria e da una serie di nodi con un valore e che puntano al successivo.\n \n ### Strutture dati astratte\n \n Le strutture _astratte_ sono separate dal modo in cui vengono memorizzati i dati, sono più ad alto livello, e si definiscono descrivendo le **proprietà** della struttura e i **metodi** che su di essa possono essere effettuate.\n \n > Una _classe_ in un qualsiasi linguaggio di programmazione è una struttura dati astratta.\n \n > Una _pila_ astratta:\n > - memorizza dati tutti dello stesso tipo\n > - `pop()`, estrae dalla pila l'ultimo valore inserito\n > - `push(val)`, aggiunge alla pila un valore\n > - `top()`, permette di vedere l'ultimo valore inserito nella pila\n > - `vuota()`, dice se la pila è vuota oppure no.\n ")),n(a.a,null,n(o.a,null,'\n # Array\n\n Un _array_ è sequenza di dati di **lunghezza conosciuta**, tutti dello **stesso tipo** e di una **dimensione fissa**, immagazzinata in **blocchi di memoria contigui**.\n \n ## Proprietà\n \n - E\' possibile accedere a tutti i blocchi di memoria conoscendo la loro **posizione relativa al primo** elemento.\n \n ## Metodi\n \n ```python\n class Array:\n def __init__(self, size, type=int): "Crea un array di dimensione size di elementi di tipo int."\n def __getitem__(self, index): "Restituisci il valore alla posizione index."\n def __setitem__(self, index, value): "Cambia il valore alla posizione index."\n ```\n \n ### Costo computazionale\n \n Tutte le operazioni su un array sono in **accesso immediato `O(1)`**!\n ')),n(a.a,null,n(o.a,null,'\n # Lista\n \n Una _lista_ è una sequenza di dati immagazzinata in **blocchi di memoria qualsiasi**.\n \n ## Proprietà\n \n Ogni dato ha un **riferimento** alla collocazione di memoria **successiva** (un puntatore): insieme, sono detti un _nodo_.\n \n E\' di **natura ricorsiva**: qualsiasi nodo di una lista può essere visto come inizio della lista con sè stesso e i suoi successivi.\n \n ## Metodi\n \n ```python\n class LinkedList:\n def __init__(self, value, next: typing.Optional[Node] = None):\n self.value = value\n self.next: typing.Optional[Node] = next\n \n def is_empty(self) -> bool: "Restituisce se la lista è vuota o no."\n def is_full(self) -> bool: "Restituisce se la lista è piena o no.\n def append(self, value): "Aggiunge un nuovo elemento in testa alla lista."\n def insert(self, value, index): "Inserisce un elemento dopo il nodo in posizione index."\n def insert_node(self, value, node): "Inserisce un nuovo elemento subito dopo un dato nodo."\n def find(self, node) -> int: "Trova l\'indice del nodo."\n def delete(self, value): "Elimina il primo nodo con quel valore dalla lista."\n def delete_node(self, node): "Elimina il nodo dalla lista."\n def forward(self, index) -> Node: "Restituisce il nodo in posizione index."\n ```\n \n ### Costo computazionale\n \n #### `List.forward(index)`\n \n Per raggiungere l\'`n`-esimo elemento, bisogna _scorrere tutti gli elementi prima di esso_: è dunque un **accesso sequenziale** in **`O(n)`**.\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/list)\n ')),n(a.a,null,n(o.a,null,'\n # Coda (Queue)\n\n Una _coda_ è come una pila, ma segue la strategia **First In, First Out** (il primo inserito sarà il primo a essere estratto).\n \n ## Proprietà\n \n - I dati vi possono essere aggiunti solo tramite il **metodo `enqueue()`**\n - I dati possono essere estratti solo tramite il **metodo `dequeue()`**\n - Verranno restituiti i valori inseriti secondo la strategia **First In, First Out** (il primo inserito sarà il primo a essere estratto).\n \n > Hai presente quando fai la fila per pagare al supermercato? Beh, è quello, però non si possono superare le altre persone in nessun modo.\n \n ## Metodi\n \n ```python\n class Queue:\n def __init__(self): "Crea una nuova coda."\n def is_empty(self) -> bool: "Restituisce vero se la coda è vuota."\n def enqueue(self, data): "Aggiunge un dato alla coda."\n def first(self) -> ...: "Restituisce il primo dato della coda."\n def dequeue(self) -> ...: "Restituisce il primo dato della coda e lo rimuove."\n ```\n \n ## Implementazione tramite lista\n \n Posso implementare la coda con una lista, ma per realizzare l\'implementazione più efficiente devo tenere anche un puntatore all\'ultimo elemento della coda, in modo da non doverla scorrere ogni volta che voglio effettuare un\'operazione.\n \n Chiamiamo i due puntatori `head` e `tail` rispettivamente.\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/list)\n ')),n(a.a,null,n(o.a,null,'\n # Pila (Stack)\n\n Una _pila_ è una struttura dati contenente **valori omogenei**.\n \n ## Proprietà\n \n - I dati vi possono essere aggiunti solo tramite il **metodo `push()`**\n - I dati possono essere estratti solo tramite il **metodo `pop()`**\n - Verranno restituiti i valori inseriti secondo la strategia **Last In, First Out** (l\'ultimo inserito sarà il primo a essere estratto).\n \n > Ci si può immaginare una pila di libri, da cui si può solo prendere un libro alla volta, quello più in alto.\n \n ## Metodi\n \n ```python\n class Stack:\n def __init__(self): "Crea una nuova pila."\n def is_empty(self) -> bool: "Restituisce vero se la pila è vuota."\n def push(self, data): "Aggiunge un dato alla pila."\n def top(self) -> ...: "Restituisce il primo dato della pila."\n def pop(self) -> ...: "Restituisce il primo dato della pila e lo rimuove."\n ```\n \n ## Implementazione tramite lista\n \n Utilizzando una lista possiamo realizzare una pila!\n \n La direzione dei puntatori sarà dall\'ultimo al primo, che non punterà più a nessuno.\n \n Il costo di tutti i metodi è `Θ(1)`!\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/list)\n ')),n(a.a,null,n(o.a,null,"\n # Albero radicato\n \n Un _albero radicato_ è una struttura dati di **natura ricorsiva** che organizza i dati in maniera **non-lineare**.\n \n ## Proprietà\n \n - Ogni nodo dell'albero ha un **unico genitore**: `∀ (padre, figlio), (padre' figlio) ∈ E \\implies padre = padre'`\n - Ogni nodo dell'albero può avere **un numero qualsiasi di figli**.\n \x3c!----\x3e\n - I **nodi superiori al padre** vengono chiamati _antenati_.\n - I **nodi inferiori ai figli** vengono chiamati _discendenti_.\n \x3c!----\x3e\n - Nodi **senza padre** sono detti _radice_: `\\notexists (padre, radice) ∈ E`\n - Nodi **con padre e figli** sono detti _rami_ o interni.\n - Nodi **senza figli** sono detti _foglie_.\n \x3c!----\x3e\n - La **distanza** tra il nodo radice e i suoi discendenti è detta _livello_:\n - I figli immediati sono di livello 1.\n - I \"nipoti\" (figli dei figli) sono di livello 2.\n - I figli dei nipoti sono livello 3.\n - E così via.\n - Il **livello massimo** all'interno di un albero è detto _altezza_, _profondità_ oppure _h_, ed è sempre `1 ≤ h ≤ n-1`.\n \x3c!----\x3e\n - Un albero ha sempre `n-1` archi.\n \n ## Alberi particolari\n \n ### Alberi `d`-ari\n \n Un albero _`d`-ario_ è un particolare tipo di albero che **limita il numero massimo di figli di un nodo** a `d`.\n \n > Un albero _binario_ può avere **massimo 2 figli** per ogni nodo; un albero _ternario_ ne può avere **3**; un albero _`17`-ario_ ne potrà avere **17**\n \n #### Alberi completi\n \n Un albero `d`-ario si dice _completo_ se **tutti i nodi hanno 0 o `d` figli**, e mai una numero in mezzo.\n \n #### Alberi bilanciati\n \n Un albero `d`-ario si dice _bilanciato_ se **tutti i livelli eccetto l'ultimo** hanno il numero massimo di figli.\n \n #### Alberi perfettamente bilanciati\n \n Un albero `d`-ario si dice _perfettamente bilanciato_ se **tutti i livelli incluso l'ultimo** hanno il numero massimo di figli.\n \n ##### Particolarità degli alberi binari perfettamente bilanciati\n \n Si può dimostrare per induzione che:\n - Hanno sempre `2^h` foglie.\n - Hanno sempre `2^{h+1}-1` (`\\sum_i=0^n 2^i`) nodi.\n - L'altezza è in `Θ(log n)`.\n \n ## Implementazione degli alberi\n \n Possiamo scegliere se usare una rappresentazione con array o con nodi e puntatori: ognuna ha vantaggi e svantaggi diversi.\n \n ### Implementazione tramite array\n \n E' suggerito se l'albero è regolare; più è simile a un albero d-ario completo, meglio è.\n \n ### Implementazione tramite nodi e puntatori\n \n Più adatta ad alberi irregolari.\n \n Se l'albero è regolare, creiamo il numero esatto di campi:\n \n - Valore\n - Figlio1\n - Figlio2\n - _Opzionale:_ Padre\n \n Se un albero è irregolare, creiamo una specie di lista:\n \n - Valore\n - Primo figlio\n - Prossimo fratello\n - _Opzionale:_ Padre\n ")),n(a.a,null,n(o.a,null,"\n #### Breadth-first search (BFS)\n\n La _breadth-first search_ è un algoritmo che visita **ogni livello** dell'albero in ordine, dal più basso al più alto.\n \n ## Funzionamento\n \n > 1. __Visita radice__\n > 2. __Visita figli__\n > 3. __Visita nipoti__\n > 4. __Visita pronipoti__\n \n Si può implementare con una coda, in cui verranno inseriti i figli del nodo visitato da visitare ed estratti dopo avere completato la visita del livello attuale.\n \n ## Pseudocodice \n \n ```python\n def bfs(radice):\n c = Queue()\n c.enqueue(radice)\n while not c.is_empty():\n nodo = c.dequeue()\n print(nodo)\n for figlio in nodo.figli:\n nodo.enqueue(figlio)\n ```\n ")),n(a.a,null,n(o.a,null,"\n # Depth-First Search\n\n La _depth-first search_ è un algoritmo che visita **tutti i sottoalberi di un figlio** prima di passare ad un altro sfruttando la natura ricorsiva degli alberi.\n \n ## Funzionamento\n \n Ci sono diverse versioni della depth-first search: ognuna visita la radice in un momento diverso.\n \n ### DFS previsita (pre-order)\n \n La _DFS pre-visita_ visita la **radice per prima**, poi tutti i sottoalberi formati dai figli uno dopo l'altro.\n \n > 1. __Visita radice__\n > 2. dfs_pre_order(figlio1)\n > 3. dfs_pre_order(figlio2)\n \n ### Postvisita (post-order)\n \n La _DFS postvisita_ visita prima tutti i sottoalberi dei figli, e **alla fine la radice**.\n \n > 1. dfs_post_order(figlio1)\n > 2. dfs_post_order(figlio2)\n > 3. __Visita radice__\n \n ### Invisita (in-order)\n \n La _DFS invisita_ visita **un certo numero di figli**, poi la radice, e infine i figli restanti.\n \n > 1. dfs_in_order(figlio1, 1)\n > 2. __Visita radice__\n > 3. dfs_in_order(figlio2, 1)\n ")),n(a.a,null,n(o.a,null,"\n # Albero binario di ricerca\n\n ## Proprietà\n \n - Albero **binario**\n - Chiavi appartenenti ad un **insieme totalmente ordinato** (N, Q, R, ma non C)\n \x3c!----\x3e\n - Per ogni nodo con valore `x`, se un valore `v` è nel sottoalbero di sinistra allora `v ≤ x`, mentre se è nel sottoalbero di destra allora `v > x`.\n \n ## Costo computazionale\n \n - Trovare un valore: `O(h)`\n - Ordinare i valori: `O(n)`\n - Trovare il minimo: `O(h)`\n - Trovare il massimo: `O(h)`\n - Inserire un elemento: `O(h)`\n - Cancellare un elemento: `O(h)`\n \n `h` vale `log n` in un albero perfettamente bilanciato, e più l'albero diventa sbilanciato, più si avvicina a `n`, raggiungendola nel caso l'albero sia una lista.\n \n ## Pseudocodice\n \n ### Cancellazione ricorsiva\n \n ```python\n def delete(tree, key):\n if tree is not None:\n # Se ho trovato il nodo che cercavo...\n if tree.key == key:\n # E c'è una sola diramazione...\n # Semplicemente stacca il nodo come in una lista.\n if tree.left is None:\n return tree.right\n if tree.right is None:\n return tree.left\n # Altrimenti, diventa il minimo dell'albero di destra\n tree.key = tree.right.min()\n # Ed eliminalo dal sottoalbero\n tree.right = delete(tree.right, tree.key)\n # Se la chiave attuale è diversa da quella che cerchiamo, continuo a navigare l'albero\n elif tree.key < key:\n tree.left = delete(tree.left, key)\n else:\n tree.right = delete(tree.right, key)\n return tree\n ```\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/bst)\n \n ## Approfondimenti\n \n Esistono alberi più avanzati che mantengono le proprietà degli alberi binari di ricerca, ma che si autobilanciano, come il [Red Black Tree](https://it.wikipedia.org/wiki/RB-Albero).\n ")),n(a.a,null,n(o.a,null,'\n # Heap binario\n \n L\'_heap binario_ è un **albero binario bilanciato a sinistra**.\n \n ## Proprietà\n \n - _Proprietà strutturale_:\n - L\'albero è **perfettamente bilanciato** in tutti i livelli tranne l\'ultimo\n - Nell\'ultimo livello, le foglie occupano le **posizioni più a sinistra** possibili\n - _Proprietà di ordinamento_:\n - La chiave di un qualsiasi nodo è **più piccola** di tutte quelle dei nodi **del suo sottoalbero**\n \n ## Metodi\n \n ```python\n class Heap:\n def __init__(self, H): ...\n def _heapify_ancestors(self, i): "Ripristina le proprietà dell\'heap per il nodo all\'indice specificato e i suoi genitori."\n def minimum(self): "Restituisce la chiave con il valore minimo in H."\n def decrease_value(self, index, new_value): "Diminuisce il valore della chiave all\'indice index a new_value."\n def insert(self, value): "Inserisci un nuovo valore nell\'albero."\n def _heapify_children(self, i): "Ripristina le proprietà dell\'heap per il nodo all\'indice specificato e i suoi figli."\n def pop(self): "Restituisce la chiave con il valore minimo, e la elimina."\n def from_list(l): "Crea un heap da una lista."\n ```\n \n ## Implementazione con un array\n \n Possiamo implementare l\'albero utilizzando un array con le chiavi dell\'albero memorizzate nell\'ordine _breadth-first_.\n \n L\'indice del figlio sinistro può essere trovato a `2i+1`, mentre l\'indice del figlio sinistro può essere trovato a `2i+2`; il genitore è a `i//2-1`.\n \n ### Pseudocodice\n \n ```python\n class Heap:\n def __init__(self, size):\n self.array = Array(size) # Il tipo Array non esiste; consideriamolo pseudocodice\n self.next_value = 0\n \n def _heapify_ancestors(self, index)\n """Ripristina le proprietà dell\'heap per il nodo all\'indice specificato e i suoi genitori.\n \n Costo:\n O(log n)"""\n # Trovo l\'indice del genitore\n parent = index // 2 - 1\n # Controllo se viene mantenuta la proprietà di ordinamento dell\'heap\n if self.array[index] < self.array[parent]:\n # Scambio i valori dei due nodi\n self.array[index], self.array[parent] = self.array[parent], self.array[index]\n # Faccio la stessa cosa con il genitore\n self._heapify(parent)\n \n \n def minimum(self):\n """Restituisce la chiave con il valore minimo in H.\n \n Costo:\n O(1)"""\n return self.array[0]\n \n def decrease_value(self, index, new_value):\n """Diminuisce il valore della chiave all\'indice index a new_value.\n \n Costo:\n O(log n)"""\n # Diminuisco il valore del nodo\n self.array[index] = new_value\n # Aggiorno l\'heap \n self._heapify(index)\n \n def insert(self, value):\n """Inserisci un nuovo valore nell\'albero.\n \n Costo:\n O(log n)"""\n # Trovo l\'indice in cui inserire il valore\n index = self.next_index \n # Aggiungo il valore in fondo\n self.array[index] = value\n # Aggiorno l\'heap\n self._heapify(index)\n \n def _heapify_children(self, index):\n """Ripristina le proprietà dell\'heap per il nodo all\'indice specificato e i suoi figli.\n \n Costo:\n O(log n)"""\n # Trovo l\'indice dei figli\n left = index * 2 + 1\n right = index * 2 + 2\n # Mi assicuro che i figli esistano\n try:\n # Guardo quale dei figli è maggiore\n if self.array[left] > self.array[right]:\n # Scambio i valori\n self.array[left], self.array[index] = self.array[index], self.array[left]\n # Ripeto la procedura sul figlio modificato\n self._heapify_children(left)\n else:\n # Scambio i valori\n self.array[right], self.array[index] = self.array[index], self.array[right]\n # Ripeto la procedura sul figlio modificato\n self._heapify_children(left)\n except IndexError:\n # La foglia non ha figli: ho finito!\n return\n \n def pop(self):\n """Restituisce la chiave con il valore minimo, e la elimina.\n \n Costo:\n O(log n)"""\n # Mi salvo il valore della radice\n value = self.array[0]\n # Sostituisco la radice con l\'ultima foglia a destra\n self.array[0], self.array[self.next_value] = self.array[self.next_value], self.array[0]\n ### Non bisognerebbe eliminare la foglia...?\n # Riordino l\'heap\n self._heapify_children(0)\n return value\n \n @staticmethod\n def from_list(l):\n """Crea un heap da una lista.\n \n Costo:\n O(n log n), ma si può abbassare"""\n heap = Heap(len(l)))\n heap.array = Array.from_list(l) # Pseudocodice\n heap.next_value = len(l)\n # Cominciamo a riordinare l\'heap dalla fine, in modo che rispetti le proprietà\n for index in range(heap.next_value, 0, -1):\n heap._heapify_children(index)\n ```\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/heap)\n ')),n(a.a,null,n(o.a,null,"\n # Coda con priorità\n \n La _coda con priorità_ è una struttura dati dal funzionamento molto simile a quello di una coda, ma invece che restituire il primo elemento inserito, essa restituisce l'**elemento con il valore di priorità minore**.\n \n ## Proprietà\n \n - Ogni elemento è una coppia costituita da **valore** e **priorità** (un numero intero).\n - Nuovi elementi possono essere aggiunti solo tramite il **metodo `insert()`**\n - Gli elementi possono essere estratti solo tramite il **metodo `pop()`**\n - Verranno restituiti i valori inseriti secondo la strategia **Lower Priority** (l'elemento con la priorità minore sarà il primo ad essere restituito).\n - E' possibile diminuire la priorità di un elemento (e quindi anticipare la sua estrazione)\n \n ## Metodi\n \n ```python\n class PriorityQueue:\n def __init__(self): ...\n def insert(self, new_elem: Element): ...\n def minimum(self) -> Element: ...\n def pop(self) -> Element: ...\n def decrease_priority_for(self, elem: Element, priority: int): ...\n ```\n \n ## Implementazione con lista\n \n E' possibile implementare la coda con priorità tramite una **lista**: l'inserimento di nuovi valori diventerà molto efficiente, ma tutte le altre operazioni saranno linearmente lente.\n \n ### Costo computazionale\n \n - *insert()*: `O(1)`\n - *minimum()*: `O(n)`\n - *pop()*: `O(n)`\n - *decrease_priority_for()*: `O(n)`\n \n ## Implementazione con lista ordinata\n \n Implementando la coda con priorità con una **lista ordinata** si avrà un costo di ordinamento elevato negli inserimenti e modifiche alla priorità, ma costi costanti nell'estrazione di un elemento.\n \n ### Costo computazionale\n \n - *insert()*: `O(n)`\n - *minimum()*: `O(1)`\n - *pop()*: `O(1)`\n - *decrease_priority_for()*: `O(n)`\n \n ## Implementazione con heap\n \n La **soluzione migliore** è quella di implementare la coda con priorità tramite un **heap**: tutti i costi saranno logaritmici, eccetto l'inserimento che sarà costante.\n \n - `insert()` costa `O(1)`\n - `minimum()` costa `O(log n)`\n - `pop()` costa `O(log n)`\n - `decrease_priority_for()` costa `O(log n)`\n \n ## Approfondimenti\n \n Esistono code con priorità che restituiscono **l'elemento con priorità maggiore**, invece che quello minore.\n ")),n(a.a,null,n(o.a,null,"\n # Heap sort\n\n L'_heap sort_ è un algoritmo di ordinamento per confronto **iterativo**.\n \n ## Funzionamento\n \n Per effettuare un heap sort, creiamo un **heap massimo** in cui inseriamo tutti i valori che vogliamo ordinare.\n \n Una volta applicate le proprietà dell'heap, chiamiamo una versione particolare di `heap.pop()` che invece che rimuovere dall'array i valori estratti li posiziona nello spazio creatosi in fondo.\n \n ## Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(n log n)` | `Ω(n log n)` | **`θ(n log n)`** |\n ")),n(a.a,null,n(o.a,null,"\n # Grafo\n \n Un _grafo_ è una struttura dati che rappresenta elementi interconnessi tra loro.\n \n Esistono due tipi di grafi: _orientati_ e _non orientati_.\n \n Per semplicità, consideriamo i nostri nodi numerati da 1 a `n`.\n \n ## Proprietà\n \n - Gli elementi sono rappresentati tramite _nodi_.\n - Il loro _grado_ è dato dal **numero degli archi** che vi incidono.\n - Se il grafo è orientato, hanno anche un _in-degree_ (**numero di archi entranti**) e un _out-degree_ (**numero di archi uscenti**).\n - Le connessioni tra elementi sono rappresentate tramite _archi_.\n - Un arco _incide_ esattamente su **due nodi**.\n - Se il grafo è orientato, sono _uscenti_ da uno dei due nodi ed _entranti_ nell'altro.\n - Sono matematicamente meno del **quadrato dei nodi**.\n \n ## Grafi particolari\n \n ### Catena\n \n Una _catena_ è un **grafo non orientato** composto da una **sequenza di nodi** aventi un **grado massimo di 2** tutti collegati tra loro.\n \n ### Cammino\n \n Un _cammino_ è un **grafo orientato** composto da una **sequenza di nodi** aventi un **in-degree** e un **out-degree** **massimo di 1**, collegati tra loro in modo che partendo dal primo e seguendo gli archi sia possibile arrivare all'ultimo.\n \n ### Cricca\n \n Una _cricca_ è un grafo in cui **tutti i nodi sono collegati tra loro**.\n \n Se il grafo è **non orientato**, la cricca ha `((n-1)n)/2` archi.\n \n Se il grafo è **orientato**, ha per ogni coppia un arco in entrambe le direzioni, quindi ha `(n-1)n` archi.\n \n ### Direct Acyclic Graph\n \n Un _DAG_ è un grafo diretto che non contiene nessun ciclo.\n \n Su di esso possiamo effettuare un ordinamento, detto _linearizzazione_, tra i nodi: otteniamo l'_ordine topologico_.\n \n I primi elementi dei DAG sono detti _Source_ (_Sorgente_), mentre gli ultimi sono detti _Sink_ (_Pozzo_).\n \n #### Albero\n \n Un **albero** può essere considerato un DAG con una **sorgente singola** e le **foglie come pozzi**.\n \n ### Grafo fortemente connesso\n \n Un insieme di nodi `V` di un **grafo diretto** `G` si dice una _componente fortemente connessa_ se:\n \n 1. Per ogni coppia di nodi `∀ u, v ∈ V' : ∃ un cammino u->v in G'`\n 2. Massimale (non può diventare più grande)\n \n > Praticamente una componente fortemente connessa è un gruppo di nodi tra i quali si può viaggiare liberamente da e a qualsiasi nodo al suo interno.\n \n Un grafo si dice _fortemente connesso_ se l'insieme `V` coincide con l'insieme dei nodi del grafo `G`.\n \n > Se partendo da qualsiasi nodo di un grafo riesco ad arrivare a qualsiasi altro nodo, allora il grafo è fortemente connesso.\n \n Inoltre, se creiamo un nuovo grafo, in cui **ogni nodo rappresenta una componente fortemente connessa** del nostro grafo iniziale, **otteniamo un DAG**, perchè tutti i cicli sono stati integrati nella componente.\n \n ### Trasposto di un grafo\n \n Il _trasposto_ di un **grafo diretto** `G` è il grafo stesso con gli archi che però vanno nella **direzione opposta**.\n \n ### Grafo pesato\n \n Un _grafo pesato_ è un particolare grafo che associa a ciascun arco un **costo** per attraversarlo.\n \n #### Costi negativi\n \n I costi possono anche essere negativi: rappresenteranno allora un **guadagno** ottenuto attraversando il nodo.\n \n ### Minimum spanning tree\n \n Un _minimum spanning tree_ è il **sottoinsieme degli archi** di un **grafo non diretto** che **connettono tutti i nodi** con il **minor costo possibile**.\n \n I MST hanno [molte proprietà](https://en.wikipedia.org/wiki/Minimum_spanning_tree#Properties); sono troppe da scrivere qui, e probabilmente non ci interesseranno nemmeno.\n \n ## Implementazione tramite matrice di adiacenza\n \n Possiamo implementare un grafo creando una **matrice di `bool` di dimensione `n * n`** in cui le **caselle collegate sono vere** e le caselle non collegate sono false.\n \n > Ad esempio, possiamo implementare un grafo non orientato in questo modo (`█` indica l'esistenza di un collegamento e ` ` indica la sua assenza):\n >\n > | |1|2|3|\n > |-|-|-|-|\n > |1|░|░|░|\n > |2|█|░|░|\n > |3|█| |░|\n >\n > Esistono gli archi `1-2` e `1-3`, ma non esiste un collegamento `2-3`.\n \n > Un grafo orientato invece si può implementare così:\n >\n > | |1|2|3|\n > |-|-|-|-|\n > |1|░|█| |\n > |2|█|░| |\n > |3|█| |░|\n >\n > Esistono gli archi `1->2`, `2->1` e `3->1`, ma non ci sono collegamenti `2->3`, `1->3` e `3->2`.\n \n ### Costo computazionale\n \n #### Tempo\n \n Le matrici di adiacenza portano alla realizzazione di algoritmi molto veloci: verificare l'esistenza di un arco è in `O(1)`!\n \n Abbiamo però penalità significative quando vogliamo effettuare operazioni sugli archi: ad esempio, trovare il trasposto di un grafo implementato con una matrice di adiacenza è in `O(nodi²)`.\n \n #### Memoria\n \n E' poco efficiente in quanto a memoria: l'upper bound è in `O(n^2)`. \n \n ## Implementazione tramite liste di adiacenza\n \n Un'alternativa alla matrice di adiacenza è quella di creare un'**array di liste**, le quali contengono i **vicini di ciascun nodo**.\n \n > |Posizione|Lista|\n > |-|-|\n > |1|[2, 3]|\n > |2|[]|\n > |3|[1]|\n >\n > Esistono gli archi `1->2`, `1->3`, e `3->1`, ma non esistono `2->1`, `2->3` e `3->2`.\n \n ### Costo computazionale\n \n #### Tempo\n \n Utilizzando le liste di adiacenza, il tempo richiesto per verificare l'esistenza di un arco sale a `O(max-out-degree)`.\n \n E' efficace però quando il problema che vogliamo risolvere riguarda operazioni su archi: trovare la trasposta è in `O(archi)`.\n \n #### Memoria \n \n La memoria richiesta dalle liste di adiacenza è minore di quella delle matrici: l'upper bound è in `O(nodi + archi)`.\n \n ## Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/graphds)\n ")),n(a.a,null,n(o.a,null,"\n # Visitare un grafo\n \n Come per gli alberi radicati, esistono due modi per visitare un grafo: _depth-first search_ e _breadth-first search_.\n \n In entrambi i casi, non visito mai due volte lo stesso nodo, e come risultato ottengo **molteplici alberi**, il cui insieme viene detto _foresta di copertura_.\n \n Se il grafo che vogliamo visitare è diretto, allora dobbiamo **considerare come vicini solo gli archi uscenti**\n \n ## Depth-first search\n \n La DFS ci può risultare utile per **identificare le componenti connesse** di un grafo e **identificare eventuali cicli**.\n \n ### Funzionamento\n \n Posso utilizzare la DFS per classificare gli archi di un grafo in quattro categorie:\n \n - _Tree_, archi che ci fanno **scoprire un nuovo nodo**\n - _Forward_, archi che ci portano a un **discendente**\n - _Back_, archi che ci portano ad un **antenato**\n - _Cross_, archi che **connettono due sottoalberi** diversi\n \n Usiamo due array inizializzati a 0 chiamati `pre` e `post`, grandi quanto il numero di archi del grafo, che ci indicano rispettivamente quando un nodo è stato scoperto e quando è terminata la visita. \n Inoltre, creiamo una variabile `clock` che avanza ad ogni evento. \n Alla scoperta di un nuovo nodo, mettiamo il valore attuale di `clock` all'interno di `pre[n]`. \n Alla fine della visita di un nodo invece mettiamo il valore di `clock` in `post[n]`.\n \n **Durante la visita**, gli archi avranno i seguenti valori:\n - _Tree_: `pre[dst] == 0`\n - _Forward_: `pre[src] < pre[dst] && post[dst] > 0`\n - _Back_: `pre[dst] < pre[src] && post[dst] == 0`\n - _Cross_: Tutti gli altri (`post[dst] < pre[src]`)\n \n **A fine visita**, gli archi avranno i seguenti valori:\n - _Tree_: `pre[dst] < pre[dst] < post[dst] < pre[src]`\n - _Forward_: `pre[dst] < pre[dst] < post[dst] < pre[src]`\n - _Back_: `pre[src] < pre[dst] < post[dst] < post[src]`\n - _Cross_: `pre[dst] < post[dst] < pre[src] < post[src]`\n \n Se un **grafo non diretto** contiene degli **archi Back**, allora esso **conterrà un ciclo**.\n \n #### DFS nel grafo trasposto\n \n Se effettuo una DFS sul trasposto di un grafo, posso **scoprire i nodi che hanno un cammino verso l'origine**.\n \n #### DFS nella componente fortemente connessa\n \n Se effettuo una DFS in una componente fortemente connessa e nella sua trasposta, il **`post` della trasposta sarà sempre minore** del `post` della componente originale.\n \n ### Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(nodi + archi)` | `Ω(nodi + archi)` | **`θ(nodi + archi)`** |\n | Memoria | `O(nodi)` | `Ω(nodi)` | **`θ(nodi)`** |\n \n ### Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/dfsbfs)\n \n ## Breadth-first search\n \n La BFS ci può risultare utile per **trovare tutti i nodi a una certa distanza** da un'origine.\n \n ### Costo computazionale\n \n | Categoria | Upper bound | Lower bound | Tight bound |\n |-----------|-------------|-------------|-------------|\n | Tempo | `O(nodi + archi)` | `Ω(nodi + archi)` | **`θ(nodi + archi)`** |\n | Memoria | `O(nodi + archi)` | `Ω(nodi + archi)` | **`θ(nodi + archi)`** |\n \n ### Pseudocodice\n \n Come per gli alberi, la implementiamo in modo **iterativo**:\n \n ```python\n queue = [starting_node]\n parents = [None for node in graph.nodes]\n distance = [-1 for node in graph.nodes]\n \n # TODO: controllami quando sei più sveglio\n \n while queue:\n node, source, distance = queue.pop(0)\n parents[node.number] = source\n distance[node.number] = distance\n for neighbour in node.neighbours:\n queue.append((neighbour, node, distance+1))\n ```\n \n > Nella coda, la distanza massima tra un nodo e l'altro è 1.\n \n ### Visualizzazione\n \n [visualgo.net](https://visualgo.net/en/dfsbfs)\n ")),n(a.a,null,n(o.a,null,"\n # Algoritmi greedy\n\n Un modo per risolvere problemi algoritmici può essere usare una **tecnica** _greedy_.\n \n Le tecniche greedy consistono nel effettuare tanti piccoli passi, ed effettuare una **scelta** in base ai dati **locali al passo attuale**.\n \n > Scegli il numero di monete più piccole possibili per comporre €1.12.\n >\n > L'algoritmo cerca di scegliere sempre la moneta più grande possibile compatibile con il prezzo in quel momento, quindi:\n > | Moneta scelta | Rimanente |\n > |---------------|-----------|\n > | € 1.00 | € 0.12 |\n > | € 0.10 | € 0.02 |\n > | € 0.02 | € 0.00 |\n \n ## Esempi\n \n Sono algoritmi greedy:\n \n - L'_Algoritmo di Dijkstra_\n - L'_Algoritmo di Kruskal_\n - L'_Algoritmo di Prim_\n ")),n(a.a,null,n(o.a,null,"\n # Percorso più breve\n\n Trovare il _percorso più breve_ (o _cammino minimo_) tra due nodi di un **grafo pesato** è un problema frequente nell'informatica; per questo, sono stati sviluppati [numerosi algoritmi](https://en.wikipedia.org/wiki/Shortest_path_problem) per risolverlo.\n \n > Ad esempio, il pathfinding dei nemici nei videogiochi, oppure Google Maps!\n \n ## Percorso più breve da una sorgente singola\n \n Una sottocategoria del problema del percorso più breve è il caso in cui ci interessa sapere i percorsi più brevi che **partono da uno specifico nodo del grafo**: è detto problema del _percorso più breve da una sorgente singola_, o _single-source shortest path_.\n \n Si può notare che se il grafo contiene **costi negativi** allora è possibile che il percorso più breve non esista, in quanto diventa possibile la comparsa di **cicli di costo infinitamente negativo**.\n \n Possiamo notare che, se il percorso più breve tra `A` e `D` è `A-B-C-D`, allora il cammino minimo tra `B` e `D` passerà obbligatoriamente per `C` (`B-C-D`).\n Diremo più avanti che il percorso più breve ha una **sottostruttura ottimale**.\n \n ### Esempi\n \n Alcuni algoritmi che trovano il percorso più breve sono:\n - L'_Algoritmo di Dijkstra_\n - L'_Algoritmo di Bellman-Ford_\n - La [_ricerca A*_](https://en.wikipedia.org/wiki/A*_search_algorithm)\n ")),n(a.a,null,n(o.a,null,"\n # Algoritmo di Dijkstra\n \n L'_Algoritmo di [Dijkstra](https://upload.wikimedia.org/wikipedia/commons/8/85/Dijkstra.ogg)_ è un algoritmo che risolve il problema del **percorso più breve da una sorgente singola** per grafi con pesi **reali positivi** `\\mathbb{R}^+`.\n \n L'algoritmo trova tutti i percorsi più brevi per raggiungere qualsiasi nodo del grafo partendo da un dato nodo, assieme al costo richiesto per farlo.\n \n ## Funzionamento\n \n 1. Separiamo tutti i nodi del grafo in due gruppi: **visitati** e **non visitati**. \n - Tutti i nodi partono da **non visitati**.\n 2. Per ogni nodo, manteniamo un valore \"**costo richiesto per raggiungerlo**\", che verrà cambiato man mano che l'algoritmo avanza.\n - Il costo di partenza è `+∞`.\n - Il costo sarà **definitivo per i nodi visitati**, e **provvisorio per i non visitati**.\n 3. Creiamo un insieme detto _frontiera_ che conterrà tutti i **nodi non visitati adiacenti** a quelli visitati.\n 4. Prendiamo il nodo iniziale, che avrà un **costo di `0`**, e definiamolo il nodo _attuale_.\n 5. Finchè ci sono dei nodi non sono stati visitati, ripetiamo il seguente ciclo:\n 1. Aggiungiamo i nodi adiacenti al nodo attuale alla frontiera.\n - Il costo per raggiungerli sarà il **costo per il nodo attuale sommato al costo dell'arco** che li connette al nodo attuale. \n Se questo **costo** risulta essere **minore del costo provvisorio** precedente, esso **diventerà il nuovo costo**.\n - Questa operazione è detta _rilassamento dell'arco_.\n 2. Facciamo diventare **visitato** il nodo attuale.\n - Il percorso che abbiamo fatto per raggiungerlo è obbligatoriamente il più breve.\n 3. Il prossimo nodo attuale sarà il nodo di frontiera con un costo più basso.\n - Per questo, è possibile definire l'algoritmo di Dijkstra come un **algoritmo greedy**.\n \n ### Non funziona se...\n \n L'algoritmo smette di funzionare nel caso in cui siano presenti **costi negativi** e il grafo non sia **aciclico**, in quanto non saremmo mai in grado di rendere visitato un nodo.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | `O(nodi + archi) log nodi)` |\n \n ### Scomposizione\n \n - Inizializzazione: `O(nodi)`\n - Creazione coda priorità: `O(nodi log nodi)`\n - Ciclo: `O((nodi + archi) log nodi)`\n \n ## Pseudocodice\n \n ```python\n import math\n \n class Info:\n def __init__(self, distance=math.inf, previous=None):\n self.distance = distance\n self.previous = previous\n \n def dijkstra(graph, start):\n data = [Info() for node in graph.nodes]\n queue = PriorityQueue([start])\n while queue:\n node = queue.pop()\n for arc in node.connections:\n other = arc.other(node)\n if data[node.number].distance + arc.cost < data[other].distance:\n data[other].distance = data[node.number].distance + arc.cost\n queue.decrease_priority_for(other, data[other].distance)\n data[v].previous = node\n return data\n ```\n \n ## Visualizzazione\n \n [Visualgo](https://visualgo.net/en/sssp)\n ")),n(a.a,null,n(o.a,null,"\n # Algoritmo di Bellman-Ford\n\n L'_Algoritmo di Bellman-Ford_ è un algoritmo che, come l'Algoritmo di Dijkstra, risolve il problema del **percorso più breve da una sorgente singola**, però, a differenza da quest'ultimo, l'Algoritmo di Bellman-Ford accetta in input anche grafi con pesi **reali** `\\mathbb{R}` (sia positivi, sia negativi).\n \n ## Funzionamento\n \n L'approccio dell'algoritmo è simile a quello di Dijkstra: entrambi usano il **rilassamento** degli archi per ottenere un costo provvisorio per il raggiungimento di un nodo, ma invece che rilassare solo l'arco con costo inferiore, questo algoritmo **rilassa tutti gli archi** ripetutamente, eliminando la frontiera e il problema dei nodi negativi.\n \n L'operazione di rilassamento è ripetuta `nodi - 1` volte, ovvero la **lunghezza massima** di un cammino aciclico all'interno di un grafo.\n \n Possiamo individuare dopo i rilassamenti se è presente un nodo con un **ciclo negativo**: ci basta controllare se esiste un arco che connette due nodi con una distanza incompatibile: se `a.distanza + arco.costo < b.distanza`, allora è presente un ciclo negativo.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | `O(nodi * archi)` |\n \n ## Pseudocodice\n \n > TODO\n \n ## Visualizzazione\n \n [Visualgo](https://visualgo.net/en/sssp)\n ")),n(a.a,null,n(o.a,null,'\n # Disjoint set\n \n Il _disjoint set_ è una struttura dati che rappresenta elementi di un insieme raggruppati in **sottoinsiemi disgiunti**.\n \n ## Metodi\n \n ```python\n class DisjointNode:\n def __init__(self): ...\n def find_set(self): "Trova il rappresentante dell\'elemento."\n def union(self, other): "Unisce i sottoinsiemi che contengono questo nodo e `other`."\n ```\n \n ## Implementazione tramite array\n \n Possiamo implementare il disjoint set con due array: uno per l\'**indice del rappresentante** e uno per il **rango dell\'insieme**.\n \n Un singoletto avrà **sè stesso come rappresentante** e **rango `0`**.\n \n ### Costo computazionale\n \n - *create_set()*: `O(1)`\n - *find_set()*: `O(h)`\n - *union()*: `O(h)`\n \n ### Pseudocodice\n \n ```python\n class DisjointNode:\n def __init__(self):\n self.parent = self\n self.rank = 0\n \n def find_set(self):\n element = self\n while self.parent != element:\n element = self.parent\n return element\n \n def union(self, other):\n repres_self = self.find_set()\n repres_other = other.find_set()\n if repres_self == repres_other:\n return\n if repres_self.rank < repres_other.rank:\n repres_greater = repres_other\n repres_lesser = repres_self\n else:\n repres_greater = repres_self\n repres_lesser = repres_other\n repres_lesser.parent = repres_greater\n if repres_greater.rank == repres_lesser.rank:\n repres_greater.rank += 1\n ```\n \n ### Visualizzazione\n \n [cs.usfca.edu](https://www.cs.usfca.edu/~galles/JavascriptVisual/DisjointSets.html)\n ')),n(a.a,null,n(o.a,null,"\n # Trovare il minimum spanning tree\n\n Un altro problema ricorrente riguardante i grafi è trovare il _minimum spanning tree_ di un dato grafo non diretto.\n \n > E' utile per trovare il modo più efficiente per connettere le cose: ad esempio, per decidere la struttura di una rete internet!\n \n ## Esempi\n \n Gli algoritmi principali che risolvono il problema sono due, ed entrambi sono **algoritmi greedy**:\n \n - L'_Algoritmo di Kruskal_\n - L'_Algoritmo di Prim_\n ")),n(a.a,null,n(o.a,null,"\n # Algoritmo di Kruskal\n \n L'_Algoritmo di Kruskal_ è un algoritmo **greedy** che **trova il minimum spanning tree** di un grafo.\n \n ## Funzionamento\n \n 1. Ripetiamo questa procedura finchè tutti i nodi non sono connessi:\n 1. Prendiamo ad ogni passo **l'arco meno costoso** del grafo non ancora aggiunto all'insieme.\n 2. Assicuriamoci che **non si creino cicli**: se non se ne verrebbero a creare, possiamo **aggiungere l'arco all'insieme**.\n - Gli archi devono quindi connettere nodi in **componenti connesse diverse**.\n - Possiamo rappresentare le componenti connesse con un **Disjoint Set**.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | `O(archi²)` |\n \n ### Scomposizione\n \n - DisjointSet.__init__(): `O(archi)`\n - Per ogni ciclo: `O(archi²)`\n - DisjointSet.find_set(): `O(1)`\n - DisjointSet.union(): `O(archi)`\n \n ## Pseudocodice\n \n ```python\n def minimum_spanning_tree_kruskal(graph):\n ds = DisjointSet()\n for node in graph.nodes:\n ds.create_set(node)\n arcs = []\n sorted_arcs = sorted(graph.arcs, key=lambda arc: arc.cost)\n for arc in sorted_arcs:\n if ds.find_set(node.start) != ds.find_set(node.end):\n arcs.append(arc)\n ds.union(node.start, node.end)\n return arcs\n ```\n ")),n(a.a,null,n(o.a,null,"\n # Algoritmo di Prim\n \n L'_Algoritmo di Prim_ è un altro algoritmo **greedy** che **trova il minimum spanning tree** di un grafo.\n \n ## Funzionamento\n \n Creo una **coda con priorità** in cui inserisco tutti gli archi visibili dal mio albero, in cui la chiave è il **costo dell'arco**.\n \n Per trovare l'arco con costo più piccolo posso **estrarre un arco** dalla coda: la priorità ci garantisce che esso è l'**arco meno costoso**.\n \n Aggiungo allora un nuovo nodo all'albero, e con esso, **aggiungo alla coda** tutti gli **archi che scoprono un nuovo nodo**.\n \n ## Costo computazionale\n \n | Categoria | Upper bound |\n |-----------|-------------|\n | Tempo | `O(archi + nodi log nodi)` |\n \n ## Pseudocodice\n \n ```python\n import math\n \n def minimum_spanning_tree_prim(graph, cost_array, start_node):\n # E' un Array di bool: se l'indice corrispondente al nodo è uguale a true, vuol dire che il (nodo è contenuto nell'albero.\n contains = [False for _ in range(len(graph))]\n # Contiene il precedente di ogni nodo \n prev = [None for _ in range(len(graph))]\n # Contiene il costo per arrivare a quel nodo\n cost = [math.inf for _ in range(len(graph))]\n # Creo la priority queue\n pq = PriorityQueue(graph.arcs, key=lambda arc: arc.cost)\n # Parto dal nodo `start_index`\n # Il costo dell'origine è 0.\n cost[start_node.index] = 0\n contains[start_node.index] = True\n \n while not pq.is_empty():\n new_node = pq.pop()\n contains[new_node.index] = True\n for arc in new_node.connections:\n other_node = arc.other(new_node)\n if not contains[other_node.index] and cost[other_node.index] > arc.cost:\n cost[other_node.index] = arc.cost\n prev[other_node.index] = new_node\n pq.decrease_priority_for(other_node, arc.cost)\n # L'array di prev rappresenta un albero.\n return prev\n ```_\n ")),n(a.a,null,n(o.a,null,"\n # Compressione\n\n _Comprimere_ un file significa **ridurne le dimensioni** senza modificarne il significato.\n \n ## Categorie\n \n ### Compressione lossless\n \n Nella _compressione lossless_, i dati possono essere decompressi riottenendo una copia identica dell'originale.\n \n > Immaginiamo un file che contiene solo le lettere `a, b, c, d, e, f`.\n >\n > Le lettere compaiono con questa frequenza:\n > |a|b|c|d|e|f|\n > |45%|13%|12%|16%|9%|5%|\n >\n > Possiamo codificare le lettere nel seguente modo:\n > |a|b|c|d|e|f|\n > |`0b0`|`0b100`|`0b101`|`0b111`|`0b1100`|`0b1101`|\n >\n > Scrivere `abacadae` richiederebbe 64 bits con la codifica ASCII estesa, ma in questo modo riusciamo a scriverlo con soli 17 bits!\n \n Le codifiche di un file compresso devono rispettare la proprietà del _Codice a prefisso_, che dice che **nessun codice deve essere il prefisso di un altro codice**; altrimenti, si avrebbero ambiguità nella decodifica.\n \n > a = `1`\n > b = `11`\n >\n > `111` è `ab`, `ba` oppure `aaa`?\n \n Creiamo allora un _albero di decodifica_: un **albero binario** che, leggendo uno ad uno i bit codificati, ci permette di arrivare al **valore del codice presente sulle foglie** dell'albero.\n \n Gli alberi di decodifica sono sempre **completi**.\n \n > Un albero di decodifica incompleto sarebbe non ottimizzato!\n \n #### Esempi\n \n - .png\n - .flac\n - .zip\n - ...\n \n ### Compressione lossy\n \n Nella _compressione lossy_, alcuni dati [solitamente](http://needsmorejpeg.com/) irrilevanti vengono perduti: non si può, dunque, ricostruire l'originale.\n \n #### Esempi\n \n - .jpeg\n - .mp3\n - ...\n ")),n(a.a,null,n(o.a,null,"\n # Algoritmo di Huffman\n\n L'_Algoritmo di Huffman_ è un **algoritmo greedy** per la **costruzione di un albero di decodifica**.\n \n ## Funzionamento\n \n 1. Costruisco **un albero** (con un solo nodo) **per ogni elemento dell'alfabeto**.\n 2. Associo ad **ogni albero la frequenza dell'elemento** da cui è stato creato, per poi inserire tutti gli elementi in una coda con priorità.\n 3. Finchè non ho **un albero solo**:\n 1. Estraggo dalla coda i **due alberi con frequenza minore**.\n 2. **Li rendo fratelli**, creando un nuovo nodo in cui sono uno figlio destro e uno figlio sinistro.\n 3. Associo al nuovo nodo la **somma delle frequenze dei due alberi**, e inserisco il nuovo albero nella coda.\n \n > È molto raro che venga un albero \"dritto\"; se succede, probabilmente c'è qualcosa che non va.\n ")),n(a.a,null,n(o.a,null,"\n # Dizionario\n \n Un _dizionario_ è una struttura dati che **associa dei valori a delle chiavi**.\n \n ## Proprietà\n \n - Ogni elemento del dizionario è un **valore** che è stato **associato a una chiave**.\n - Possiamo aggiungere nuovi elementi con il **metodo `add(chiave, valore)`**.\n - Posiamo estrarre elementi con il **metodo `get(chiave)`**, che restituirà il valore associato a `chiave`.\n - E' possibile rimuovere elementi con il **metodo `delete(chiave)`**.\n - Due elementi con **chiavi diverse** non devono **mai restituire lo stesso valore**.\n \n ## Metodi\n \n Beh... Non ha molto senso in questo caso...\n \n ```python\n dict()\n ```\n \n ## Implementazione con tabella hash\n \n Una _tabella hash_ è un'array di coppie **chiave-valore**, che formano l'insieme _universo_.\n \n Per determinare l'**indice dell'array** in cui inserire una coppia, usiamo una [funzione _hash_](https://it.wikipedia.org/wiki/Hash#Algoritmo_di_hash) sulla chiave, che restituirà **numeri da `0` a `len(hash_table)`**.\n \n ### Risoluzione collisioni\n \n Potrebbe capitare però che **due chiavi diverse abbiano lo stesso indice**. Dobbiamo allora usare un metodo di _risoluzione collisioni_, che mi permetta di distinguere tra chiavi diverse.\n \n #### Lista di trabocco\n \n Possiamo salvare nell'array **liste di coppie** chiave-valore; in caso di collisione, **aggiungo un nuovo elemento alla lista**.\n \n In media, ciascuna di queste liste conterrà `elementi_inseriti / dimensione_tabella` elementi.\n \n #### Indirizzamento aperto\n \n Possiamo decidere di mettere le coppie che non trovano posto nel loro indice in **un altro indirizzo vuoto** dell'array.\n \n Ci sono diversi modi in cui decidere il nuovo indirizzo, ognuno con vantaggi e svantaggi: si può scegliere quello successivo, oppure il primo vuoto dell'array, oppure un indirizzo casuale.\n \n > Python, nei `dict`, usa indirizzamento aperto pseudorandom.\n \n ### Costo computazionale\n \n - Aggiungere una chiave: `O(n)`\n - Trovare una chiave: `O(n)`\n - Eliminare una chiave: `O(n)`\n ")),n(a.a,null,n(o.a,null,"\n # Programmazione dinamica\n \n La _programmazione dinamica_ è una **tecnica** di programmazione che prevede l'**estensione di una soluzione ottima precedente**.\n \n Tutti i problemi in cui si può applicare si possono risolvere anche con la **ricorsione**, ma a differenza della ricorsione, questa tecnica riesce ad evitare di ricalcolare la soluzione per ogni chiamata ricorsiva, ottenendo quindi tempi molto migliori.\n \n Si può applicare solo se un problema ha una **sottostruttura ottimale**, ovvero se la soluzione ottima di un sottoproblema è inclusa nella soluzione ottima del problema. \n \n ## Esempi\n \n - _Problema dello zaino_\n - ...\n \n > Il cammino minimo per raggiungere un nodo in un DAG è dato da `arco.costo + arco.primo_nodo.costo_cammino_minimo()`.\n >\n > ```python\n > def SPD_PD(graph, start):\n > distance = [float(inf) for node in graph.nodes]:\n > distance[start] = 0\n > # I nodi devono essere in ordine di linearizzazione\n > for node in graph.nodes:\n > distance[node] = min([(arc.cost + distance[arc.other(node)] for arc in node.connections])\n > ```\n \n > Ho una sequenza di interi da `a_1` a `a_n`. Voglio trovare la sottosequenza crescente più lunga.\n >\n > 5 2 3 4 7 3 6 3 1 6\n >\n > Trovo tutte le sequenze lunghe 1, e le rendo nodi di un grafo diretto.\n >\n > Da ogni nodo, creo una connessione verso i suoi maggiori.\n >\n > Infine, cerco i cammini massimi del grafo. \n > \n > Essi saranno la soluzione del problema.\n \n > Trova la lunghezza della sottosequenza più lunga che termina con `j`.\n >\n > `L[j]` = lunghezza della sottosequenza più lunga che termina in `j`\n > \n > ```python\n > L[j] = max([1 + L[node] for arc in node.connections)]\n > ```\n >\n > Esempio:\n > ```python\n > L[9] = max([1+L[8], 1+L[3], 1+L[6]])\n > ```\n ")),n(a.a,null,n(o.a,null,"\n # Problema dello zaino\n \n Il problema dello zaino è un problema _pseudo-trattabile_: non abbiamo dimostrazioni di se sia trattabile o intrattabile.\n \n ## Descrizione\n \n > Sei un ladro, e devi mettere **più refurtiva possibile** nello zaino per scappare. \n > Lo zaino può portare **al massimo `dim` kili**.\n >\n > **Quali** (e quanti) oggetti scegli?\n \n | Input | Output |\n |-------|--------|\n | `dim`ensione_zaino, `n`umero_oggetti, `oggetto.peso`, `oggetto.valore` | `profitto_massimo` |\n \n ## Categorie\n \n ### Problema con ripetizione\n \n Puoi prendere **tutte le copie che vuoi** di un oggetto.\n \n #### Soluzione\n \n `K(dim)` è il valore massimo ottenibile con uno zaino di capacità `dim`.\n \n > Se `i` appartenesse alla soluzione ottima, allora `K(dim) = i.valore + K(dim - i.peso)`...\n \n Possiamo dire che `K(dim) = max(i.valore + K(dim - i.peso))`.\n \n Inoltre, `K(0) = 0`.\n \n Ci salviamo tutte le soluzioni da `K(0)` a `K(dim)`, e le usiamo per calcolare il massimo in seguito.\n \n Calcolare `K(dim)` avrà allora un costo di `O(n * dim)`:\n - `n`, perchè trovare il massimo è un'operazione lineare\n - `dim`, perchè `dim` sono tutti i casi tra i quali devo andare a provare\n \n Il costo computazionale, allora, è in `O(n * dim)`. \n \n Però, il **tempo richiesto** dal nostro algoritmo dipende non dalla lunghezza dell'input, bensì dal **valore numerico** di `dim`, che corrisponde alla dimensione dell'array delle soluzioni. \n Allora, si dice che l'algoritmo è in **tempo _pseudo-polinomiale_**.\n \n ### Problema senza ripetizione\n \n Si può prendere **ogni oggetto una volta sola**.\n \n #### Soluzione _bruteforce_\n \n Scelgo se prendere o no l'item 1.\n \n Si creano due percorsi:\n - Non prendo l'oggetto: `valore = 0, peso = 0`\n - Prendo l'oggetto: `valore = oggetto.valore, peso = oggetto.peso`\n \n Continuo a creare percorsi, creando una specie di albero binario.\n \n Se a un certo punto vedo che `valore = x, peso = K` e `valore < x, peso = K`, allora posso escludere automaticamente tutto il sottoalbero destro, perchè non può essere migliore del sinistro: allora, sarò riuscito a ridurre il numero dei casi rispetto alla ricorsione.\n \n ### Problema in due variabili\n \n `K(j, w)` = massimo valore ottenibile con uno zaino di capacità `w` scegliendo gli item da `1` a `j`.\n \n Non possiamo più applicare la soluzione bruteforce, perchè abbiamo due variabili, `j` e `w`.\n \n Allora, prendo l'elemento `j`. Esso può essere o non essere nella soluzione: mi calcolo entrambe le alternative, e mi tengo l'alternativa dal valore più alto.\n \n Se `j` non è nella soluzione, il risultato diventerà `K(j-1, w)`; se invece è nella soluzione, il risultato sarà `j.valore + K(j-1, w-j.peso)`.\n \n In pratica, prendiamo\n \n ```latex\n K(j, w) = max\n \\begin{cases}\n V_j + K(j-1, w-w_j)\n K(j-1, w)\n \\end{cases}\n ```\n \n Costruisco allora una matrice con `j` su un asse e `w` sull'altro. \n Riempio le caselle con il valore di `K(j, w)`. \n Nella casella con `K(j, w)` avremo la soluzione ottima.\n \n Il tempo necessario per riempire tutte le caselle è nuovamente `O(n * w)`, ancora **pseudopolinomiale**.\n \n Per sapere che oggetti ho messo o no devo tenere traccia in qualche modo della catena del calcolo, usando, ad esempio, una pila.\n ")),n(a.a,null,n(o.a,null,"\n # Problemi intrattabili\n \n ## Problema di Set-Cover\n \n ### Input\n \n `U`niverso di `e`lementi\n \n `S`ottoinsieme di `s`ottoinsiemi di elementi di `U`\n \n ### Output\n \n Il minimo `S'`ottoinsieme di `s`ottoinsiemi che copra completamente `U`.\n \n ### Soluzione in `O(n^d)`\n \n Non c'è.\n \n ### Non-soluzione alternativa\n \n Faccio una scelta greedy, ma non posso dimostrare in alcun modo che la soluzione ottenuta sia quella ottima. \n Infatti, l'algoritmo non dà sempre la soluzione ottima, ma dà una soluzione accettabile in tempo polinomiale.\n \n Seleziono sempre il sottoinsieme che copre più elementi mancanti possibili.\n \n #### Costo computazionale\n \n `Costo greedy <= log(numero_elementi) * Costo ottimo`\n ")))}}.call(this,i("hosL").h)}}]); -//# sourceMappingURL=route-AlgoritmiEStruttureDati.chunk.02d3a.esm.js.map \ No newline at end of file +//# sourceMappingURL=route-AlgoritmiEStruttureDati.chunk.92b93.esm.js.map \ No newline at end of file diff --git a/docs/route-AlgoritmiEStruttureDati.chunk.02d3a.esm.js.map b/docs/route-AlgoritmiEStruttureDati.chunk.92b93.esm.js.map similarity index 51% rename from docs/route-AlgoritmiEStruttureDati.chunk.02d3a.esm.js.map rename to docs/route-AlgoritmiEStruttureDati.chunk.92b93.esm.js.map index 7c2cc27..1404a03 100644 --- a/docs/route-AlgoritmiEStruttureDati.chunk.02d3a.esm.js.map +++ b/docs/route-AlgoritmiEStruttureDati.chunk.92b93.esm.js.map @@ -1 +1 @@ -{"version":3,"sources":[],"names":[],"mappings":"","file":"route-AlgoritmiEStruttureDati.chunk.02d3a.esm.js","sourceRoot":""} \ No newline at end of file +{"version":3,"sources":[],"names":[],"mappings":"","file":"route-AlgoritmiEStruttureDati.chunk.92b93.esm.js","sourceRoot":""} \ No newline at end of file diff --git a/docs/route-AlgoritmiEStruttureDati~route-VlDiGeometria.chunk.eee3f.esm.js b/docs/route-AlgoritmiEStruttureDati~route-VlDiGeometria.chunk.15a59.esm.js similarity index 99% rename from docs/route-AlgoritmiEStruttureDati~route-VlDiGeometria.chunk.eee3f.esm.js rename to docs/route-AlgoritmiEStruttureDati~route-VlDiGeometria.chunk.15a59.esm.js index 594e0f3..e43383c 100644 --- a/docs/route-AlgoritmiEStruttureDati~route-VlDiGeometria.chunk.eee3f.esm.js +++ b/docs/route-AlgoritmiEStruttureDati~route-VlDiGeometria.chunk.15a59.esm.js @@ -1,3 +1,3 @@ -/*! 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e}}),i.helper.regexes={asteriskDashAndColon:/([*_:~])/g},i.helper.emojis={"+1":"👍","-1":"👎",100:"💯",1234:"🔢","1st_place_medal":"🥇","2nd_place_medal":"🥈","3rd_place_medal":"🥉","8ball":"🎱",a:"🅰️",ab:"🆎",abc:"🔤",abcd:"🔡",accept:"🉑",aerial_tramway:"🚡",airplane:"✈️",alarm_clock:"⏰",alembic:"⚗️",alien:"👽",ambulance:"🚑",amphora:"🏺",anchor:"⚓️",angel:"👼",anger:"💢",angry:"😠",anguished:"😧",ant:"🐜",apple:"🍎",aquarius:"♒️",aries:"♈️",arrow_backward:"◀️",arrow_double_down:"⏬",arrow_double_up:"⏫",arrow_down:"⬇️",arrow_down_small:"🔽",arrow_forward:"▶️",arrow_heading_down:"⤵️",arrow_heading_up:"⤴️",arrow_left:"⬅️",arrow_lower_left:"↙️",arrow_lower_right:"↘️",arrow_right:"➡️",arrow_right_hook:"↪️",arrow_up:"⬆️",arrow_up_down:"↕️",arrow_up_small:"🔼",arrow_upper_left:"↖️",arrow_upper_right:"↗️",arrows_clockwise:"🔃",arrows_counterclockwise:"🔄",art:"🎨",articulated_lorry:"🚛",artificial_satellite:"🛰",astonished:"😲",athletic_shoe:"👟",atm:"🏧",atom_symbol:"⚛️",avocado:"🥑",b:"🅱️",baby:"👶",baby_bottle:"🍼",baby_chick:"🐤",baby_symbol:"🚼",back:"🔙",bacon:"🥓",badminton:"🏸",baggage_claim:"🛄",baguette_bread:"🥖",balance_scale:"⚖️",balloon:"🎈",ballot_box:"🗳",ballot_box_with_check:"☑️",bamboo:"🎍",banana:"🍌",bangbang:"‼️",bank:"🏦",bar_chart:"📊",barber:"💈",baseball:"⚾️",basketball:"🏀",basketball_man:"⛹️",basketball_woman:"⛹️‍♀️",bat:"🦇",bath:"🛀",bathtub:"🛁",battery:"🔋",beach_umbrella:"🏖",bear:"🐻",bed:"🛏",bee:"🐝",beer:"🍺",beers:"🍻",beetle:"🐞",beginner:"🔰",bell:"🔔",bellhop_bell:"🛎",bento:"🍱",biking_man:"🚴",bike:"🚲",biking_woman:"🚴‍♀️",bikini:"👙",biohazard:"☣️",bird:"🐦",birthday:"🎂",black_circle:"⚫️",black_flag:"🏴",black_heart:"🖤",black_joker:"🃏",black_large_square:"⬛️",black_medium_small_square:"◾️",black_medium_square:"◼️",black_nib:"✒️",black_small_square:"▪️",black_square_button:"🔲",blonde_man:"👱",blonde_woman:"👱‍♀️",blossom:"🌼",blowfish:"🐡",blue_book:"📘",blue_car:"🚙",blue_heart:"💙",blush:"😊",boar:"🐗",boat:"⛵️",bomb:"💣",book:"📖",bookmark:"🔖",bookmark_tabs:"📑",books:"📚",boom:"💥",boot:"👢",bouquet:"💐",bowing_man:"🙇",bow_and_arrow:"🏹",bowing_woman:"🙇‍♀️",bowling:"🎳",boxing_glove:"🥊",boy:"👦",bread:"🍞",bride_with_veil:"👰",bridge_at_night:"🌉",briefcase:"💼",broken_heart:"💔",bug:"🐛",building_construction:"🏗",bulb:"💡",bullettrain_front:"🚅",bullettrain_side:"🚄",burrito:"🌯",bus:"🚌",business_suit_levitating:"🕴",busstop:"🚏",bust_in_silhouette:"👤",busts_in_silhouette:"👥",butterfly:"🦋",cactus:"🌵",cake:"🍰",calendar:"📆",call_me_hand:"🤙",calling:"📲",camel:"🐫",camera:"📷",camera_flash:"📸",camping:"🏕",cancer:"♋️",candle:"🕯",candy:"🍬",canoe:"🛶",capital_abcd:"🔠",capricorn:"♑️",car:"🚗",card_file_box:"🗃",card_index:"📇",card_index_dividers:"🗂",carousel_horse:"🎠",carrot:"🥕",cat:"🐱",cat2:"🐈",cd:"💿",chains:"⛓",champagne:"🍾",chart:"💹",chart_with_downwards_trend:"📉",chart_with_upwards_trend:"📈",checkered_flag:"🏁",cheese:"🧀",cherries:"🍒",cherry_blossom:"🌸",chestnut:"🌰",chicken:"🐔",children_crossing:"🚸",chipmunk:"🐿",chocolate_bar:"🍫",christmas_tree:"🎄",church:"⛪️",cinema:"🎦",circus_tent:"🎪",city_sunrise:"🌇",city_sunset:"🌆",cityscape:"🏙",cl:"🆑",clamp:"🗜",clap:"👏",clapper:"🎬",classical_building:"🏛",clinking_glasses:"🥂",clipboard:"📋",clock1:"🕐",clock10:"🕙",clock1030:"🕥",clock11:"🕚",clock1130:"🕦",clock12:"🕛",clock1230:"🕧",clock130:"🕜",clock2:"🕑",clock230:"🕝",clock3:"🕒",clock330:"🕞",clock4:"🕓",clock430:"🕟",clock5:"🕔",clock530:"🕠",clock6:"🕕",clock630:"🕡",clock7:"🕖",clock730:"🕢",clock8:"🕗",clock830:"🕣",clock9:"🕘",clock930:"🕤",closed_book:"📕",closed_lock_with_key:"🔐",closed_umbrella:"🌂",cloud:"☁️",cloud_with_lightning:"🌩",cloud_with_lightning_and_rain:"⛈",cloud_with_rain:"🌧",cloud_with_snow:"🌨",clown_face:"🤡",clubs:"♣️",cocktail:"🍸",coffee:"☕️",coffin:"⚰️",cold_sweat:"😰",comet:"☄️",computer:"💻",computer_mouse:"🖱",confetti_ball:"🎊",confounded:"😖",confused:"😕",congratulations:"㊗️",construction:"🚧",construction_worker_man:"👷",construction_worker_woman:"👷‍♀️",control_knobs:"🎛",convenience_store:"🏪",cookie:"🍪",cool:"🆒",policeman:"👮",copyright:"©️",corn:"🌽",couch_and_lamp:"🛋",couple:"👫",couple_with_heart_woman_man:"💑",couple_with_heart_man_man:"👨‍❤️‍👨",couple_with_heart_woman_woman:"👩‍❤️‍👩",couplekiss_man_man:"👨‍❤️‍💋‍👨",couplekiss_man_woman:"💏",couplekiss_woman_woman:"👩‍❤️‍💋‍👩",cow:"🐮",cow2:"🐄",cowboy_hat_face:"🤠",crab:"🦀",crayon:"🖍",credit_card:"💳",crescent_moon:"🌙",cricket:"🏏",crocodile:"🐊",croissant:"🥐",crossed_fingers:"🤞",crossed_flags:"🎌",crossed_swords:"⚔️",crown:"👑",cry:"😢",crying_cat_face:"😿",crystal_ball:"🔮",cucumber:"🥒",cupid:"💘",curly_loop:"➰",currency_exchange:"💱",curry:"🍛",custard:"🍮",customs:"🛃",cyclone:"🌀",dagger:"🗡",dancer:"💃",dancing_women:"👯",dancing_men:"👯‍♂️",dango:"🍡",dark_sunglasses:"🕶",dart:"🎯",dash:"💨",date:"📅",deciduous_tree:"🌳",deer:"🦌",department_store:"🏬",derelict_house:"🏚",desert:"🏜",desert_island:"🏝",desktop_computer:"🖥",male_detective:"🕵️",diamond_shape_with_a_dot_inside:"💠",diamonds:"♦️",disappointed:"😞",disappointed_relieved:"😥",dizzy:"💫",dizzy_face:"😵",do_not_litter:"🚯",dog:"🐶",dog2:"🐕",dollar:"💵",dolls:"🎎",dolphin:"🐬",door:"🚪",doughnut:"🍩",dove:"🕊",dragon:"🐉",dragon_face:"🐲",dress:"👗",dromedary_camel:"🐪",drooling_face:"🤤",droplet:"💧",drum:"🥁",duck:"🦆",dvd:"📀","e-mail":"📧",eagle:"🦅",ear:"👂",ear_of_rice:"🌾",earth_africa:"🌍",earth_americas:"🌎",earth_asia:"🌏",egg:"🥚",eggplant:"🍆",eight_pointed_black_star:"✴️",eight_spoked_asterisk:"✳️",electric_plug:"🔌",elephant:"🐘",email:"✉️",end:"🔚",envelope_with_arrow:"📩",euro:"💶",european_castle:"🏰",european_post_office:"🏤",evergreen_tree:"🌲",exclamation:"❗️",expressionless:"😑",eye:"👁",eye_speech_bubble:"👁‍🗨",eyeglasses:"👓",eyes:"👀",face_with_head_bandage:"🤕",face_with_thermometer:"🤒",fist_oncoming:"👊",factory:"🏭",fallen_leaf:"🍂",family_man_woman_boy:"👪",family_man_boy:"👨‍👦",family_man_boy_boy:"👨‍👦‍👦",family_man_girl:"👨‍👧",family_man_girl_boy:"👨‍👧‍👦",family_man_girl_girl:"👨‍👧‍👧",family_man_man_boy:"👨‍👨‍👦",family_man_man_boy_boy:"👨‍👨‍👦‍👦",family_man_man_girl:"👨‍👨‍👧",family_man_man_girl_boy:"👨‍👨‍👧‍👦",family_man_man_girl_girl:"👨‍👨‍👧‍👧",family_man_woman_boy_boy:"👨‍👩‍👦‍👦",family_man_woman_girl:"👨‍👩‍👧",family_man_woman_girl_boy:"👨‍👩‍👧‍👦",family_man_woman_girl_girl:"👨‍👩‍👧‍👧",family_woman_boy:"👩‍👦",family_woman_boy_boy:"👩‍👦‍👦",family_woman_girl:"👩‍👧",family_woman_girl_boy:"👩‍👧‍👦",family_woman_girl_girl:"👩‍👧‍👧",family_woman_woman_boy:"👩‍👩‍👦",family_woman_woman_boy_boy:"👩‍👩‍👦‍👦",family_woman_woman_girl:"👩‍👩‍👧",family_woman_woman_girl_boy:"👩‍👩‍👧‍👦",family_woman_woman_girl_girl:"👩‍👩‍👧‍👧",fast_forward:"⏩",fax:"📠",fearful:"😨",feet:"🐾",female_detective:"🕵️‍♀️",ferris_wheel:"🎡",ferry:"⛴",field_hockey:"🏑",file_cabinet:"🗄",file_folder:"📁",film_projector:"📽",film_strip:"🎞",fire:"🔥",fire_engine:"🚒",fireworks:"🎆",first_quarter_moon:"🌓",first_quarter_moon_with_face:"🌛",fish:"🐟",fish_cake:"🍥",fishing_pole_and_fish:"🎣",fist_raised:"✊",fist_left:"🤛",fist_right:"🤜",flags:"🎏",flashlight:"🔦",fleur_de_lis:"⚜️",flight_arrival:"🛬",flight_departure:"🛫",floppy_disk:"💾",flower_playing_cards:"🎴",flushed:"😳",fog:"🌫",foggy:"🌁",football:"🏈",footprints:"👣",fork_and_knife:"🍴",fountain:"⛲️",fountain_pen:"🖋",four_leaf_clover:"🍀",fox_face:"🦊",framed_picture:"🖼",free:"🆓",fried_egg:"🍳",fried_shrimp:"🍤",fries:"🍟",frog:"🐸",frowning:"😦",frowning_face:"☹️",frowning_man:"🙍‍♂️",frowning_woman:"🙍",middle_finger:"🖕",fuelpump:"⛽️",full_moon:"🌕",full_moon_with_face:"🌝",funeral_urn:"⚱️",game_die:"🎲",gear:"⚙️",gem:"💎",gemini:"♊️",ghost:"👻",gift:"🎁",gift_heart:"💝",girl:"👧",globe_with_meridians:"🌐",goal_net:"🥅",goat:"🐐",golf:"⛳️",golfing_man:"🏌️",golfing_woman:"🏌️‍♀️",gorilla:"🦍",grapes:"🍇",green_apple:"🍏",green_book:"📗",green_heart:"💚",green_salad:"🥗",grey_exclamation:"❕",grey_question:"❔",grimacing:"😬",grin:"😁",grinning:"😀",guardsman:"💂",guardswoman:"💂‍♀️",guitar:"🎸",gun:"🔫",haircut_woman:"💇",haircut_man:"💇‍♂️",hamburger:"🍔",hammer:"🔨",hammer_and_pick:"⚒",hammer_and_wrench:"🛠",hamster:"🐹",hand:"✋",handbag:"👜",handshake:"🤝",hankey:"💩",hatched_chick:"🐥",hatching_chick:"🐣",headphones:"🎧",hear_no_evil:"🙉",heart:"❤️",heart_decoration:"💟",heart_eyes:"😍",heart_eyes_cat:"😻",heartbeat:"💓",heartpulse:"💗",hearts:"♥️",heavy_check_mark:"✔️",heavy_division_sign:"➗",heavy_dollar_sign:"💲",heavy_heart_exclamation:"❣️",heavy_minus_sign:"➖",heavy_multiplication_x:"✖️",heavy_plus_sign:"➕",helicopter:"🚁",herb:"🌿",hibiscus:"🌺",high_brightness:"🔆",high_heel:"👠",hocho:"🔪",hole:"🕳",honey_pot:"🍯",horse:"🐴",horse_racing:"🏇",hospital:"🏥",hot_pepper:"🌶",hotdog:"🌭",hotel:"🏨",hotsprings:"♨️",hourglass:"⌛️",hourglass_flowing_sand:"⏳",house:"🏠",house_with_garden:"🏡",houses:"🏘",hugs:"🤗",hushed:"😯",ice_cream:"🍨",ice_hockey:"🏒",ice_skate:"⛸",icecream:"🍦",id:"🆔",ideograph_advantage:"🉐",imp:"👿",inbox_tray:"📥",incoming_envelope:"📨",tipping_hand_woman:"💁",information_source:"ℹ️",innocent:"😇",interrobang:"⁉️",iphone:"📱",izakaya_lantern:"🏮",jack_o_lantern:"🎃",japan:"🗾",japanese_castle:"🏯",japanese_goblin:"👺",japanese_ogre:"👹",jeans:"👖",joy:"😂",joy_cat:"😹",joystick:"🕹",kaaba:"🕋",key:"🔑",keyboard:"⌨️",keycap_ten:"🔟",kick_scooter:"🛴",kimono:"👘",kiss:"💋",kissing:"😗",kissing_cat:"😽",kissing_closed_eyes:"😚",kissing_heart:"😘",kissing_smiling_eyes:"😙",kiwi_fruit:"🥝",koala:"🐨",koko:"🈁",label:"🏷",large_blue_circle:"🔵",large_blue_diamond:"🔷",large_orange_diamond:"🔶",last_quarter_moon:"🌗",last_quarter_moon_with_face:"🌜",latin_cross:"✝️",laughing:"😆",leaves:"🍃",ledger:"📒",left_luggage:"🛅",left_right_arrow:"↔️",leftwards_arrow_with_hook:"↩️",lemon:"🍋",leo:"♌️",leopard:"🐆",level_slider:"🎚",libra:"♎️",light_rail:"🚈",link:"🔗",lion:"🦁",lips:"👄",lipstick:"💄",lizard:"🦎",lock:"🔒",lock_with_ink_pen:"🔏",lollipop:"🍭",loop:"➿",loud_sound:"🔊",loudspeaker:"📢",love_hotel:"🏩",love_letter:"💌",low_brightness:"🔅",lying_face:"🤥",m:"Ⓜ️",mag:"🔍",mag_right:"🔎",mahjong:"🀄️",mailbox:"📫",mailbox_closed:"📪",mailbox_with_mail:"📬",mailbox_with_no_mail:"📭",man:"👨",man_artist:"👨‍🎨",man_astronaut:"👨‍🚀",man_cartwheeling:"🤸‍♂️",man_cook:"👨‍🍳",man_dancing:"🕺",man_facepalming:"🤦‍♂️",man_factory_worker:"👨‍🏭",man_farmer:"👨‍🌾",man_firefighter:"👨‍🚒",man_health_worker:"👨‍⚕️",man_in_tuxedo:"🤵",man_judge:"👨‍⚖️",man_juggling:"🤹‍♂️",man_mechanic:"👨‍🔧",man_office_worker:"👨‍💼",man_pilot:"👨‍✈️",man_playing_handball:"🤾‍♂️",man_playing_water_polo:"🤽‍♂️",man_scientist:"👨‍🔬",man_shrugging:"🤷‍♂️",man_singer:"👨‍🎤",man_student:"👨‍🎓",man_teacher:"👨‍🏫",man_technologist:"👨‍💻",man_with_gua_pi_mao:"👲",man_with_turban:"👳",tangerine:"🍊",mans_shoe:"👞",mantelpiece_clock:"🕰",maple_leaf:"🍁",martial_arts_uniform:"🥋",mask:"😷",massage_woman:"💆",massage_man:"💆‍♂️",meat_on_bone:"🍖",medal_military:"🎖",medal_sports:"🏅",mega:"📣",melon:"🍈",memo:"📝",men_wrestling:"🤼‍♂️",menorah:"🕎",mens:"🚹",metal:"🤘",metro:"🚇",microphone:"🎤",microscope:"🔬",milk_glass:"🥛",milky_way:"🌌",minibus:"🚐",minidisc:"💽",mobile_phone_off:"📴",money_mouth_face:"🤑",money_with_wings:"💸",moneybag:"💰",monkey:"🐒",monkey_face:"🐵",monorail:"🚝",moon:"🌔",mortar_board:"🎓",mosque:"🕌",motor_boat:"🛥",motor_scooter:"🛵",motorcycle:"🏍",motorway:"🛣",mount_fuji:"🗻",mountain:"⛰",mountain_biking_man:"🚵",mountain_biking_woman:"🚵‍♀️",mountain_cableway:"🚠",mountain_railway:"🚞",mountain_snow:"🏔",mouse:"🐭",mouse2:"🐁",movie_camera:"🎥",moyai:"🗿",mrs_claus:"🤶",muscle:"💪",mushroom:"🍄",musical_keyboard:"🎹",musical_note:"🎵",musical_score:"🎼",mute:"🔇",nail_care:"💅",name_badge:"📛",national_park:"🏞",nauseated_face:"🤢",necktie:"👔",negative_squared_cross_mark:"❎",nerd_face:"🤓",neutral_face:"😐",new:"🆕",new_moon:"🌑",new_moon_with_face:"🌚",newspaper:"📰",newspaper_roll:"🗞",next_track_button:"⏭",ng:"🆖",no_good_man:"🙅‍♂️",no_good_woman:"🙅",night_with_stars:"🌃",no_bell:"🔕",no_bicycles:"🚳",no_entry:"⛔️",no_entry_sign:"🚫",no_mobile_phones:"📵",no_mouth:"😶",no_pedestrians:"🚷",no_smoking:"🚭","non-potable_water":"🚱",nose:"👃",notebook:"📓",notebook_with_decorative_cover:"📔",notes:"🎶",nut_and_bolt:"🔩",o:"⭕️",o2:"🅾️",ocean:"🌊",octopus:"🐙",oden:"🍢",office:"🏢",oil_drum:"🛢",ok:"🆗",ok_hand:"👌",ok_man:"🙆‍♂️",ok_woman:"🙆",old_key:"🗝",older_man:"👴",older_woman:"👵",om:"🕉",on:"🔛",oncoming_automobile:"🚘",oncoming_bus:"🚍",oncoming_police_car:"🚔",oncoming_taxi:"🚖",open_file_folder:"📂",open_hands:"👐",open_mouth:"😮",open_umbrella:"☂️",ophiuchus:"⛎",orange_book:"📙",orthodox_cross:"☦️",outbox_tray:"📤",owl:"🦉",ox:"🐂",package:"📦",page_facing_up:"📄",page_with_curl:"📃",pager:"📟",paintbrush:"🖌",palm_tree:"🌴",pancakes:"🥞",panda_face:"🐼",paperclip:"📎",paperclips:"🖇",parasol_on_ground:"⛱",parking:"🅿️",part_alternation_mark:"〽️",partly_sunny:"⛅️",passenger_ship:"🛳",passport_control:"🛂",pause_button:"⏸",peace_symbol:"☮️",peach:"🍑",peanuts:"🥜",pear:"🍐",pen:"🖊",pencil2:"✏️",penguin:"🐧",pensive:"😔",performing_arts:"🎭",persevere:"😣",person_fencing:"🤺",pouting_woman:"🙎",phone:"☎️",pick:"⛏",pig:"🐷",pig2:"🐖",pig_nose:"🐽",pill:"💊",pineapple:"🍍",ping_pong:"🏓",pisces:"♓️",pizza:"🍕",place_of_worship:"🛐",plate_with_cutlery:"🍽",play_or_pause_button:"⏯",point_down:"👇",point_left:"👈",point_right:"👉",point_up:"☝️",point_up_2:"👆",police_car:"🚓",policewoman:"👮‍♀️",poodle:"🐩",popcorn:"🍿",post_office:"🏣",postal_horn:"📯",postbox:"📮",potable_water:"🚰",potato:"🥔",pouch:"👝",poultry_leg:"🍗",pound:"💷",rage:"😡",pouting_cat:"😾",pouting_man:"🙎‍♂️",pray:"🙏",prayer_beads:"📿",pregnant_woman:"🤰",previous_track_button:"⏮",prince:"🤴",princess:"👸",printer:"🖨",purple_heart:"💜",purse:"👛",pushpin:"📌",put_litter_in_its_place:"🚮",question:"❓",rabbit:"🐰",rabbit2:"🐇",racehorse:"🐎",racing_car:"🏎",radio:"📻",radio_button:"🔘",radioactive:"☢️",railway_car:"🚃",railway_track:"🛤",rainbow:"🌈",rainbow_flag:"🏳️‍🌈",raised_back_of_hand:"🤚",raised_hand_with_fingers_splayed:"🖐",raised_hands:"🙌",raising_hand_woman:"🙋",raising_hand_man:"🙋‍♂️",ram:"🐏",ramen:"🍜",rat:"🐀",record_button:"⏺",recycle:"♻️",red_circle:"🔴",registered:"®️",relaxed:"☺️",relieved:"😌",reminder_ribbon:"🎗",repeat:"🔁",repeat_one:"🔂",rescue_worker_helmet:"⛑",restroom:"🚻",revolving_hearts:"💞",rewind:"⏪",rhinoceros:"🦏",ribbon:"🎀",rice:"🍚",rice_ball:"🍙",rice_cracker:"🍘",rice_scene:"🎑",right_anger_bubble:"🗯",ring:"💍",robot:"🤖",rocket:"🚀",rofl:"🤣",roll_eyes:"🙄",roller_coaster:"🎢",rooster:"🐓",rose:"🌹",rosette:"🏵",rotating_light:"🚨",round_pushpin:"📍",rowing_man:"🚣",rowing_woman:"🚣‍♀️",rugby_football:"🏉",running_man:"🏃",running_shirt_with_sash:"🎽",running_woman:"🏃‍♀️",sa:"🈂️",sagittarius:"♐️",sake:"🍶",sandal:"👡",santa:"🎅",satellite:"📡",saxophone:"🎷",school:"🏫",school_satchel:"🎒",scissors:"✂️",scorpion:"🦂",scorpius:"♏️",scream:"😱",scream_cat:"🙀",scroll:"📜",seat:"💺",secret:"㊙️",see_no_evil:"🙈",seedling:"🌱",selfie:"🤳",shallow_pan_of_food:"🥘",shamrock:"☘️",shark:"🦈",shaved_ice:"🍧",sheep:"🐑",shell:"🐚",shield:"🛡",shinto_shrine:"⛩",ship:"🚢",shirt:"👕",shopping:"🛍",shopping_cart:"🛒",shower:"🚿",shrimp:"🦐",signal_strength:"📶",six_pointed_star:"🔯",ski:"🎿",skier:"⛷",skull:"💀",skull_and_crossbones:"☠️",sleeping:"😴",sleeping_bed:"🛌",sleepy:"😪",slightly_frowning_face:"🙁",slightly_smiling_face:"🙂",slot_machine:"🎰",small_airplane:"🛩",small_blue_diamond:"🔹",small_orange_diamond:"🔸",small_red_triangle:"🔺",small_red_triangle_down:"🔻",smile:"😄",smile_cat:"😸",smiley:"😃",smiley_cat:"😺",smiling_imp:"😈",smirk:"😏",smirk_cat:"😼",smoking:"🚬",snail:"🐌",snake:"🐍",sneezing_face:"🤧",snowboarder:"🏂",snowflake:"❄️",snowman:"⛄️",snowman_with_snow:"☃️",sob:"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e}}),i.helper.regexes={asteriskDashAndColon:/([*_:~])/g},i.helper.emojis={"+1":"👍","-1":"👎",100:"💯",1234:"🔢","1st_place_medal":"🥇","2nd_place_medal":"🥈","3rd_place_medal":"🥉","8ball":"🎱",a:"🅰️",ab:"🆎",abc:"🔤",abcd:"🔡",accept:"🉑",aerial_tramway:"🚡",airplane:"✈️",alarm_clock:"⏰",alembic:"⚗️",alien:"👽",ambulance:"🚑",amphora:"🏺",anchor:"⚓️",angel:"👼",anger:"💢",angry:"😠",anguished:"😧",ant:"🐜",apple:"🍎",aquarius:"♒️",aries:"♈️",arrow_backward:"◀️",arrow_double_down:"⏬",arrow_double_up:"⏫",arrow_down:"⬇️",arrow_down_small:"🔽",arrow_forward:"▶️",arrow_heading_down:"⤵️",arrow_heading_up:"⤴️",arrow_left:"⬅️",arrow_lower_left:"↙️",arrow_lower_right:"↘️",arrow_right:"➡️",arrow_right_hook:"↪️",arrow_up:"⬆️",arrow_up_down:"↕️",arrow_up_small:"🔼",arrow_upper_left:"↖️",arrow_upper_right:"↗️",arrows_clockwise:"🔃",arrows_counterclockwise:"🔄",art:"🎨",articulated_lorry:"🚛",artificial_satellite:"🛰",astonished:"😲",athletic_shoe:"👟",atm:"🏧",atom_symbol:"⚛️",avocado:"🥑",b:"🅱️",baby:"👶",baby_bottle:"🍼",baby_chick:"🐤",baby_symbol:"🚼",back:"🔙",bacon:"🥓",badminton:"🏸",baggage_claim:"🛄",baguette_bread:"🥖",balance_scale:"⚖️",balloon:"🎈",ballot_box:"🗳",ballot_box_with_check:"☑️",bamboo:"🎍",banana:"🍌",bangbang:"‼️",bank:"🏦",bar_chart:"📊",barber:"💈",baseball:"⚾️",basketball:"🏀",basketball_man:"⛹️",basketball_woman:"⛹️‍♀️",bat:"🦇",bath:"🛀",bathtub:"🛁",battery:"🔋",beach_umbrella:"🏖",bear:"🐻",bed:"🛏",bee:"🐝",beer:"🍺",beers:"🍻",beetle:"🐞",beginner:"🔰",bell:"🔔",bellhop_bell:"🛎",bento:"🍱",biking_man:"🚴",bike:"🚲",biking_woman:"🚴‍♀️",bikini:"👙",biohazard:"☣️",bird:"🐦",birthday:"🎂",black_circle:"⚫️",black_flag:"🏴",black_heart:"🖤",black_joker:"🃏",black_large_square:"⬛️",black_medium_small_square:"◾️",black_medium_square:"◼️",black_nib:"✒️",black_small_square:"▪️",black_square_button:"🔲",blonde_man:"👱",blonde_woman:"👱‍♀️",blossom:"🌼",blowfish:"🐡",blue_book:"📘",blue_car:"🚙",blue_heart:"💙",blush:"😊",boar:"🐗",boat:"⛵️",bomb:"💣",book:"📖",bookmark:"🔖",bookmark_tabs:"📑",books:"📚",boom:"💥",boot:"👢",bouquet:"💐",bowing_man:"🙇",bow_and_arrow:"🏹",bowing_woman:"🙇‍♀️",bowling:"🎳",boxing_glove:"🥊",boy:"👦",bread:"🍞",bride_with_veil:"👰",bridge_at_night:"🌉",briefcase:"💼",broken_heart:"💔",bug:"🐛",building_construction:"🏗",bulb:"💡",bullettrain_front:"🚅",bullettrain_side:"🚄",burrito:"🌯",bus:"🚌",business_suit_levitating:"🕴",busstop:"🚏",bust_in_silhouette:"👤",busts_in_silhouette:"👥",butterfly:"🦋",cactus:"🌵",cake:"🍰",calendar:"📆",call_me_hand:"🤙",calling:"📲",camel:"🐫",camera:"📷",camera_flash:"📸",camping:"🏕",cancer:"♋️",candle:"🕯",candy:"🍬",canoe:"🛶",capital_abcd:"🔠",capricorn:"♑️",car:"🚗",card_file_box:"🗃",card_index:"📇",card_index_dividers:"🗂",carousel_horse:"🎠",carrot:"🥕",cat:"🐱",cat2:"🐈",cd:"💿",chains:"⛓",champagne:"🍾",chart:"💹",chart_with_downwards_trend:"📉",chart_with_upwards_trend:"📈",checkered_flag:"🏁",cheese:"🧀",cherries:"🍒",cherry_blossom:"🌸",chestnut:"🌰",chicken:"🐔",children_crossing:"🚸",chipmunk:"🐿",chocolate_bar:"🍫",christmas_tree:"🎄",church:"⛪️",cinema:"🎦",circus_tent:"🎪",city_sunrise:"🌇",city_sunset:"🌆",cityscape:"🏙",cl:"🆑",clamp:"🗜",clap:"👏",clapper:"🎬",classical_building:"🏛",clinking_glasses:"🥂",clipboard:"📋",clock1:"🕐",clock10:"🕙",clock1030:"🕥",clock11:"🕚",clock1130:"🕦",clock12:"🕛",clock1230:"🕧",clock130:"🕜",clock2:"🕑",clock230:"🕝",clock3:"🕒",clock330:"🕞",clock4:"🕓",clock430:"🕟",clock5:"🕔",clock530:"🕠",clock6:"🕕",clock630:"🕡",clock7:"🕖",clock730:"🕢",clock8:"🕗",clock830:"🕣",clock9:"🕘",clock930:"🕤",closed_book:"📕",closed_lock_with_key:"🔐",closed_umbrella:"🌂",cloud:"☁️",cloud_with_lightning:"🌩",cloud_with_lightning_and_rain:"⛈",cloud_with_rain:"🌧",cloud_with_snow:"🌨",clown_face:"🤡",clubs:"♣️",cocktail:"🍸",coffee:"☕️",coffin:"⚰️",cold_sweat:"😰",comet:"☄️",computer:"💻",computer_mouse:"🖱",confetti_ball:"🎊",confounded:"😖",confused:"😕",congratulations:"㊗️",construction:"🚧",construction_worker_man:"👷",construction_worker_woman:"👷‍♀️",control_knobs:"🎛",convenience_store:"🏪",cookie:"🍪",cool:"🆒",policeman:"👮",copyright:"©️",corn:"🌽",couch_and_lamp:"🛋",couple:"👫",couple_with_heart_woman_man:"💑",couple_with_heart_man_man:"👨‍❤️‍👨",couple_with_heart_woman_woman:"👩‍❤️‍👩",couplekiss_man_man:"👨‍❤️‍💋‍👨",couplekiss_man_woman:"💏",couplekiss_woman_woman:"👩‍❤️‍💋‍👩",cow:"🐮",cow2:"🐄",cowboy_hat_face:"🤠",crab:"🦀",crayon:"🖍",credit_card:"💳",crescent_moon:"🌙",cricket:"🏏",crocodile:"🐊",croissant:"🥐",crossed_fingers:"🤞",crossed_flags:"🎌",crossed_swords:"⚔️",crown:"👑",cry:"😢",crying_cat_face:"😿",crystal_ball:"🔮",cucumber:"🥒",cupid:"💘",curly_loop:"➰",currency_exchange:"💱",curry:"🍛",custard:"🍮",customs:"🛃",cyclone:"🌀",dagger:"🗡",dancer:"💃",dancing_women:"👯",dancing_men:"👯‍♂️",dango:"🍡",dark_sunglasses:"🕶",dart:"🎯",dash:"💨",date:"📅",deciduous_tree:"🌳",deer:"🦌",department_store:"🏬",derelict_house:"🏚",desert:"🏜",desert_island:"🏝",desktop_computer:"🖥",male_detective:"🕵️",diamond_shape_with_a_dot_inside:"💠",diamonds:"♦️",disappointed:"😞",disappointed_relieved:"😥",dizzy:"💫",dizzy_face:"😵",do_not_litter:"🚯",dog:"🐶",dog2:"🐕",dollar:"💵",dolls:"🎎",dolphin:"🐬",door:"🚪",doughnut:"🍩",dove:"🕊",dragon:"🐉",dragon_face:"🐲",dress:"👗",dromedary_camel:"🐪",drooling_face:"🤤",droplet:"💧",drum:"🥁",duck:"🦆",dvd:"📀","e-mail":"📧",eagle:"🦅",ear:"👂",ear_of_rice:"🌾",earth_africa:"🌍",earth_americas:"🌎",earth_asia:"🌏",egg:"🥚",eggplant:"🍆",eight_pointed_black_star:"✴️",eight_spoked_asterisk:"✳️",electric_plug:"🔌",elephant:"🐘",email:"✉️",end:"🔚",envelope_with_arrow:"📩",euro:"💶",european_castle:"🏰",european_post_office:"🏤",evergreen_tree:"🌲",exclamation:"❗️",expressionless:"😑",eye:"👁",eye_speech_bubble:"👁‍🗨",eyeglasses:"👓",eyes:"👀",face_with_head_bandage:"🤕",face_with_thermometer:"🤒",fist_oncoming:"👊",factory:"🏭",fallen_leaf:"🍂",family_man_woman_boy:"👪",family_man_boy:"👨‍👦",family_man_boy_boy:"👨‍👦‍👦",family_man_girl:"👨‍👧",family_man_girl_boy:"👨‍👧‍👦",family_man_girl_girl:"👨‍👧‍👧",family_man_man_boy:"👨‍👨‍👦",family_man_man_boy_boy:"👨‍👨‍👦‍👦",family_man_man_girl:"👨‍👨‍👧",family_man_man_girl_boy:"👨‍👨‍👧‍👦",family_man_man_girl_girl:"👨‍👨‍👧‍👧",family_man_woman_boy_boy:"👨‍👩‍👦‍👦",family_man_woman_girl:"👨‍👩‍👧",family_man_woman_girl_boy:"👨‍👩‍👧‍👦",family_man_woman_girl_girl:"👨‍👩‍👧‍👧",family_woman_boy:"👩‍👦",family_woman_boy_boy:"👩‍👦‍👦",family_woman_girl:"👩‍👧",family_woman_girl_boy:"👩‍👧‍👦",family_woman_girl_girl:"👩‍👧‍👧",family_woman_woman_boy:"👩‍👩‍👦",family_woman_woman_boy_boy:"👩‍👩‍👦‍👦",family_woman_woman_girl:"👩‍👩‍👧",family_woman_woman_girl_boy:"👩‍👩‍👧‍👦",family_woman_woman_girl_girl:"👩‍👩‍👧‍👧",fast_forward:"⏩",fax:"📠",fearful:"😨",feet:"🐾",female_detective:"🕵️‍♀️",ferris_wheel:"🎡",ferry:"⛴",field_hockey:"🏑",file_cabinet:"🗄",file_folder:"📁",film_projector:"📽",film_strip:"🎞",fire:"🔥",fire_engine:"🚒",fireworks:"🎆",first_quarter_moon:"🌓",first_quarter_moon_with_face:"🌛",fish:"🐟",fish_cake:"🍥",fishing_pole_and_fish:"🎣",fist_raised:"✊",fist_left:"🤛",fist_right:"🤜",flags:"🎏",flashlight:"🔦",fleur_de_lis:"⚜️",flight_arrival:"🛬",flight_departure:"🛫",floppy_disk:"💾",flower_playing_cards:"🎴",flushed:"😳",fog:"🌫",foggy:"🌁",football:"🏈",footprints:"👣",fork_and_knife:"🍴",fountain:"⛲️",fountain_pen:"🖋",four_leaf_clover:"🍀",fox_face:"🦊",framed_picture:"🖼",free:"🆓",fried_egg:"🍳",fried_shrimp:"🍤",fries:"🍟",frog:"🐸",frowning:"😦",frowning_face:"☹️",frowning_man:"🙍‍♂️",frowning_woman:"🙍",middle_finger:"🖕",fuelpump:"⛽️",full_moon:"🌕",full_moon_with_face:"🌝",funeral_urn:"⚱️",game_die:"🎲",gear:"⚙️",gem:"💎",gemini:"♊️",ghost:"👻",gift:"🎁",gift_heart:"💝",girl:"👧",globe_with_meridians:"🌐",goal_net:"🥅",goat:"🐐",golf:"⛳️",golfing_man:"🏌️",golfing_woman:"🏌️‍♀️",gorilla:"🦍",grapes:"🍇",green_apple:"🍏",green_book:"📗",green_heart:"💚",green_salad:"🥗",grey_exclamation:"❕",grey_question:"❔",grimacing:"😬",grin:"😁",grinning:"😀",guardsman:"💂",guardswoman:"💂‍♀️",guitar:"🎸",gun:"🔫",haircut_woman:"💇",haircut_man:"💇‍♂️",hamburger:"🍔",hammer:"🔨",hammer_and_pick:"⚒",hammer_and_wrench:"🛠",hamster:"🐹",hand:"✋",handbag:"👜",handshake:"🤝",hankey:"💩",hatched_chick:"🐥",hatching_chick:"🐣",headphones:"🎧",hear_no_evil:"🙉",heart:"❤️",heart_decoration:"💟",heart_eyes:"😍",heart_eyes_cat:"😻",heartbeat:"💓",heartpulse:"💗",hearts:"♥️",heavy_check_mark:"✔️",heavy_division_sign:"➗",heavy_dollar_sign:"💲",heavy_heart_exclamation:"❣️",heavy_minus_sign:"➖",heavy_multiplication_x:"✖️",heavy_plus_sign:"➕",helicopter:"🚁",herb:"🌿",hibiscus:"🌺",high_brightness:"🔆",high_heel:"👠",hocho:"🔪",hole:"🕳",honey_pot:"🍯",horse:"🐴",horse_racing:"🏇",hospital:"🏥",hot_pepper:"🌶",hotdog:"🌭",hotel:"🏨",hotsprings:"♨️",hourglass:"⌛️",hourglass_flowing_sand:"⏳",house:"🏠",house_with_garden:"🏡",houses:"🏘",hugs:"🤗",hushed:"😯",ice_cream:"🍨",ice_hockey:"🏒",ice_skate:"⛸",icecream:"🍦",id:"🆔",ideograph_advantage:"🉐",imp:"👿",inbox_tray:"📥",incoming_envelope:"📨",tipping_hand_woman:"💁",information_source:"ℹ️",innocent:"😇",interrobang:"⁉️",iphone:"📱",izakaya_lantern:"🏮",jack_o_lantern:"🎃",japan:"🗾",japanese_castle:"🏯",japanese_goblin:"👺",japanese_ogre:"👹",jeans:"👖",joy:"😂",joy_cat:"😹",joystick:"🕹",kaaba:"🕋",key:"🔑",keyboard:"⌨️",keycap_ten:"🔟",kick_scooter:"🛴",kimono:"👘",kiss:"💋",kissing:"😗",kissing_cat:"😽",kissing_closed_eyes:"😚",kissing_heart:"😘",kissing_smiling_eyes:"😙",kiwi_fruit:"🥝",koala:"🐨",koko:"🈁",label:"🏷",large_blue_circle:"🔵",large_blue_diamond:"🔷",large_orange_diamond:"🔶",last_quarter_moon:"🌗",last_quarter_moon_with_face:"🌜",latin_cross:"✝️",laughing:"😆",leaves:"🍃",ledger:"📒",left_luggage:"🛅",left_right_arrow:"↔️",leftwards_arrow_with_hook:"↩️",lemon:"🍋",leo:"♌️",leopard:"🐆",level_slider:"🎚",libra:"♎️",light_rail:"🚈",link:"🔗",lion:"🦁",lips:"👄",lipstick:"💄",lizard:"🦎",lock:"🔒",lock_with_ink_pen:"🔏",lollipop:"🍭",loop:"➿",loud_sound:"🔊",loudspeaker:"📢",love_hotel:"🏩",love_letter:"💌",low_brightness:"🔅",lying_face:"🤥",m:"Ⓜ️",mag:"🔍",mag_right:"🔎",mahjong:"🀄️",mailbox:"📫",mailbox_closed:"📪",mailbox_with_mail:"📬",mailbox_with_no_mail:"📭",man:"👨",man_artist:"👨‍🎨",man_astronaut:"👨‍🚀",man_cartwheeling:"🤸‍♂️",man_cook:"👨‍🍳",man_dancing:"🕺",man_facepalming:"🤦‍♂️",man_factory_worker:"👨‍🏭",man_farmer:"👨‍🌾",man_firefighter:"👨‍🚒",man_health_worker:"👨‍⚕️",man_in_tuxedo:"🤵",man_judge:"👨‍⚖️",man_juggling:"🤹‍♂️",man_mechanic:"👨‍🔧",man_office_worker:"👨‍💼",man_pilot:"👨‍✈️",man_playing_handball:"🤾‍♂️",man_playing_water_polo:"🤽‍♂️",man_scientist:"👨‍🔬",man_shrugging:"🤷‍♂️",man_singer:"👨‍🎤",man_student:"👨‍🎓",man_teacher:"👨‍🏫",man_technologist:"👨‍💻",man_with_gua_pi_mao:"👲",man_with_turban:"👳",tangerine:"🍊",mans_shoe:"👞",mantelpiece_clock:"🕰",maple_leaf:"🍁",martial_arts_uniform:"🥋",mask:"😷",massage_woman:"💆",massage_man:"💆‍♂️",meat_on_bone:"🍖",medal_military:"🎖",medal_sports:"🏅",mega:"📣",melon:"🍈",memo:"📝",men_wrestling:"🤼‍♂️",menorah:"🕎",mens:"🚹",metal:"🤘",metro:"🚇",microphone:"🎤",microscope:"🔬",milk_glass:"🥛",milky_way:"🌌",minibus:"🚐",minidisc:"💽",mobile_phone_off:"📴",money_mouth_face:"🤑",money_with_wings:"💸",moneybag:"💰",monkey:"🐒",monkey_face:"🐵",monorail:"🚝",moon:"🌔",mortar_board:"🎓",mosque:"🕌",motor_boat:"🛥",motor_scooter:"🛵",motorcycle:"🏍",motorway:"🛣",mount_fuji:"🗻",mountain:"⛰",mountain_biking_man:"🚵",mountain_biking_woman:"🚵‍♀️",mountain_cableway:"🚠",mountain_railway:"🚞",mountain_snow:"🏔",mouse:"🐭",mouse2:"🐁",movie_camera:"🎥",moyai:"🗿",mrs_claus:"🤶",muscle:"💪",mushroom:"🍄",musical_keyboard:"🎹",musical_note:"🎵",musical_score:"🎼",mute:"🔇",nail_care:"💅",name_badge:"📛",national_park:"🏞",nauseated_face:"🤢",necktie:"👔",negative_squared_cross_mark:"❎",nerd_face:"🤓",neutral_face:"😐",new:"🆕",new_moon:"🌑",new_moon_with_face:"🌚",newspaper:"📰",newspaper_roll:"🗞",next_track_button:"⏭",ng:"🆖",no_good_man:"🙅‍♂️",no_good_woman:"🙅",night_with_stars:"🌃",no_bell:"🔕",no_bicycles:"🚳",no_entry:"⛔️",no_entry_sign:"🚫",no_mobile_phones:"📵",no_mouth:"😶",no_pedestrians:"🚷",no_smoking:"🚭","non-potable_water":"🚱",nose:"👃",notebook:"📓",notebook_with_decorative_cover:"📔",notes:"🎶",nut_and_bolt:"🔩",o:"⭕️",o2:"🅾️",ocean:"🌊",octopus:"🐙",oden:"🍢",office:"🏢",oil_drum:"🛢",ok:"🆗",ok_hand:"👌",ok_man:"🙆‍♂️",ok_woman:"🙆",old_key:"🗝",older_man:"👴",older_woman:"👵",om:"🕉",on:"🔛",oncoming_automobile:"🚘",oncoming_bus:"🚍",oncoming_police_car:"🚔",oncoming_taxi:"🚖",open_file_folder:"📂",open_hands:"👐",open_mouth:"😮",open_umbrella:"☂️",ophiuchus:"⛎",orange_book:"📙",orthodox_cross:"☦️",outbox_tray:"📤",owl:"🦉",ox:"🐂",package:"📦",page_facing_up:"📄",page_with_curl:"📃",pager:"📟",paintbrush:"🖌",palm_tree:"🌴",pancakes:"🥞",panda_face:"🐼",paperclip:"📎",paperclips:"🖇",parasol_on_ground:"⛱",parking:"🅿️",part_alternation_mark:"〽️",partly_sunny:"⛅️",passenger_ship:"🛳",passport_control:"🛂",pause_button:"⏸",peace_symbol:"☮️",peach:"🍑",peanuts:"🥜",pear:"🍐",pen:"🖊",pencil2:"✏️",penguin:"🐧",pensive:"😔",performing_arts:"🎭",persevere:"😣",person_fencing:"🤺",pouting_woman:"🙎",phone:"☎️",pick:"⛏",pig:"🐷",pig2:"🐖",pig_nose:"🐽",pill:"💊",pineapple:"🍍",ping_pong:"🏓",pisces:"♓️",pizza:"🍕",place_of_worship:"🛐",plate_with_cutlery:"🍽",play_or_pause_button:"⏯",point_down:"👇",point_left:"👈",point_right:"👉",point_up:"☝️",point_up_2:"👆",police_car:"🚓",policewoman:"👮‍♀️",poodle:"🐩",popcorn:"🍿",post_office:"🏣",postal_horn:"📯",postbox:"📮",potable_water:"🚰",potato:"🥔",pouch:"👝",poultry_leg:"🍗",pound:"💷",rage:"😡",pouting_cat:"😾",pouting_man:"🙎‍♂️",pray:"🙏",prayer_beads:"📿",pregnant_woman:"🤰",previous_track_button:"⏮",prince:"🤴",princess:"👸",printer:"🖨",purple_heart:"💜",purse:"👛",pushpin:"📌",put_litter_in_its_place:"🚮",question:"❓",rabbit:"🐰",rabbit2:"🐇",racehorse:"🐎",racing_car:"🏎",radio:"📻",radio_button:"🔘",radioactive:"☢️",railway_car:"🚃",railway_track:"🛤",rainbow:"🌈",rainbow_flag:"🏳️‍🌈",raised_back_of_hand:"🤚",raised_hand_with_fingers_splayed:"🖐",raised_hands:"🙌",raising_hand_woman:"🙋",raising_hand_man:"🙋‍♂️",ram:"🐏",ramen:"🍜",rat:"🐀",record_button:"⏺",recycle:"♻️",red_circle:"🔴",registered:"®️",relaxed:"☺️",relieved:"😌",reminder_ribbon:"🎗",repeat:"🔁",repeat_one:"🔂",rescue_worker_helmet:"⛑",restroom:"🚻",revolving_hearts:"💞",rewind:"⏪",rhinoceros:"🦏",ribbon:"🎀",rice:"🍚",rice_ball:"🍙",rice_cracker:"🍘",rice_scene:"🎑",right_anger_bubble:"🗯",ring:"💍",robot:"🤖",rocket:"🚀",rofl:"🤣",roll_eyes:"🙄",roller_coaster:"🎢",rooster:"🐓",rose:"🌹",rosette:"🏵",rotating_light:"🚨",round_pushpin:"📍",rowing_man:"🚣",rowing_woman:"🚣‍♀️",rugby_football:"🏉",running_man:"🏃",running_shirt_with_sash:"🎽",running_woman:"🏃‍♀️",sa:"🈂️",sagittarius:"♐️",sake:"🍶",sandal:"👡",santa:"🎅",satellite:"📡",saxophone:"🎷",school:"🏫",school_satchel:"🎒",scissors:"✂️",scorpion:"🦂",scorpius:"♏️",scream:"😱",scream_cat:"🙀",scroll:"📜",seat:"💺",secret:"㊙️",see_no_evil:"🙈",seedling:"🌱",selfie:"🤳",shallow_pan_of_food:"🥘",shamrock:"☘️",shark:"🦈",shaved_ice:"🍧",sheep:"🐑",shell:"🐚",shield:"🛡",shinto_shrine:"⛩",ship:"🚢",shirt:"👕",shopping:"🛍",shopping_cart:"🛒",shower:"🚿",shrimp:"🦐",signal_strength:"📶",six_pointed_star:"🔯",ski:"🎿",skier:"⛷",skull:"💀",skull_and_crossbones:"☠️",sleeping:"😴",sleeping_bed:"🛌",sleepy:"😪",slightly_frowning_face:"🙁",slightly_smiling_face:"🙂",slot_machine:"🎰",small_airplane:"🛩",small_blue_diamond:"🔹",small_orange_diamond:"🔸",small_red_triangle:"🔺",small_red_triangle_down:"🔻",smile:"😄",smile_cat:"😸",smiley:"😃",smiley_cat:"😺",smiling_imp:"😈",smirk:"😏",smirk_cat:"😼",smoking:"🚬",snail:"🐌",snake:"🐍",sneezing_face:"🤧",snowboarder:"🏂",snowflake:"❄️",snowman:"⛄️",snowman_with_snow:"☃️",sob:"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'Error in ' + name + ' extension->' : 'Error in unnamed extension',\n ret = {\n valid: true,\n error: ''\n };\n\n if (!showdown.helper.isArray(extension)) {\n extension = [extension];\n }\n\n for (var i = 0; i < extension.length; ++i) {\n var baseMsg = errMsg + ' sub-extension ' + i + ': ',\n ext = extension[i];\n if (typeof ext !== 'object') {\n ret.valid = false;\n ret.error = baseMsg + 'must be an object, but ' + typeof ext + ' given';\n return ret;\n }\n\n if (!showdown.helper.isString(ext.type)) {\n ret.valid = false;\n ret.error = baseMsg + 'property \"type\" must be a string, but ' + typeof ext.type + ' given';\n return ret;\n }\n\n var type = ext.type = ext.type.toLowerCase();\n\n // normalize extension type\n if (type === 'language') {\n type = ext.type = 'lang';\n }\n\n if (type === 'html') {\n type = ext.type = 'output';\n }\n\n if (type !== 'lang' && type !== 'output' && type !== 'listener') {\n ret.valid = false;\n ret.error = baseMsg + 'type ' + type + ' is not recognized. Valid values: \"lang/language\", \"output/html\" or \"listener\"';\n return ret;\n }\n\n if (type === 'listener') {\n if (showdown.helper.isUndefined(ext.listeners)) {\n ret.valid = false;\n ret.error = baseMsg + '. Extensions of type \"listener\" must have a property called \"listeners\"';\n return ret;\n }\n } else {\n if (showdown.helper.isUndefined(ext.filter) && showdown.helper.isUndefined(ext.regex)) {\n ret.valid = false;\n ret.error = baseMsg + type + ' extensions must define either a \"regex\" property or a \"filter\" method';\n return ret;\n }\n }\n\n if (ext.listeners) {\n if (typeof ext.listeners !== 'object') {\n ret.valid = false;\n ret.error = baseMsg + '\"listeners\" property must be an object but ' + typeof ext.listeners + ' given';\n return ret;\n }\n for (var ln in ext.listeners) {\n if (ext.listeners.hasOwnProperty(ln)) {\n if (typeof ext.listeners[ln] !== 'function') {\n ret.valid = false;\n ret.error = baseMsg + '\"listeners\" property must be an hash of [event name]: [callback]. listeners.' + ln +\n ' must be a function but ' + typeof ext.listeners[ln] + ' given';\n return ret;\n }\n }\n }\n }\n\n if (ext.filter) {\n if (typeof ext.filter !== 'function') {\n ret.valid = false;\n ret.error = baseMsg + '\"filter\" must be a function, but ' + typeof ext.filter + ' given';\n return ret;\n }\n } else if (ext.regex) {\n if (showdown.helper.isString(ext.regex)) {\n ext.regex = new RegExp(ext.regex, 'g');\n }\n if (!(ext.regex instanceof RegExp)) {\n ret.valid = false;\n ret.error = baseMsg + '\"regex\" property must either be a string or a RegExp object, but ' + typeof ext.regex + ' given';\n return ret;\n }\n if (showdown.helper.isUndefined(ext.replace)) {\n ret.valid = false;\n ret.error = baseMsg + '\"regex\" extensions must implement a replace string or function';\n return ret;\n }\n }\n }\n return ret;\n}\n\n/**\n * Validate extension\n * @param {object} ext\n * @returns {boolean}\n */\nshowdown.validateExtension = function (ext) {\n 'use strict';\n\n var validateExtension = validate(ext, null);\n if (!validateExtension.valid) {\n console.warn(validateExtension.error);\n return false;\n }\n return true;\n};\n","/**\n * showdownjs helper functions\n */\n\nif (!showdown.hasOwnProperty('helper')) {\n showdown.helper = {};\n}\n\n/**\n * Check if var is string\n * @static\n * @param {string} a\n * @returns {boolean}\n */\nshowdown.helper.isString = function (a) {\n 'use strict';\n return (typeof a === 'string' || a instanceof String);\n};\n\n/**\n * Check if var is a function\n * @static\n * @param {*} a\n * @returns {boolean}\n */\nshowdown.helper.isFunction = function (a) {\n 'use strict';\n var getType = {};\n return a && getType.toString.call(a) === '[object Function]';\n};\n\n/**\n * isArray helper function\n * @static\n * @param {*} a\n * @returns {boolean}\n */\nshowdown.helper.isArray = function (a) {\n 'use strict';\n return Array.isArray(a);\n};\n\n/**\n * Check if value is undefined\n * @static\n * @param {*} value The value to check.\n * @returns {boolean} Returns `true` if `value` is `undefined`, else `false`.\n */\nshowdown.helper.isUndefined = function (value) {\n 'use strict';\n return typeof value === 'undefined';\n};\n\n/**\n * ForEach helper function\n * Iterates over Arrays and Objects (own properties only)\n * @static\n * @param {*} obj\n * @param {function} callback Accepts 3 params: 1. value, 2. key, 3. the original array/object\n */\nshowdown.helper.forEach = function (obj, callback) {\n 'use strict';\n // check if obj is defined\n if (showdown.helper.isUndefined(obj)) {\n throw new Error('obj param is required');\n }\n\n if (showdown.helper.isUndefined(callback)) {\n throw new Error('callback param is required');\n }\n\n if (!showdown.helper.isFunction(callback)) {\n throw new Error('callback param must be a function/closure');\n }\n\n if (typeof obj.forEach === 'function') {\n obj.forEach(callback);\n } else if (showdown.helper.isArray(obj)) {\n for (var i = 0; i < obj.length; i++) {\n callback(obj[i], i, obj);\n }\n } else if (typeof (obj) === 'object') {\n for (var prop in obj) {\n if (obj.hasOwnProperty(prop)) {\n callback(obj[prop], prop, obj);\n }\n }\n } else {\n throw new Error('obj does not seem to be an array or an iterable object');\n }\n};\n\n/**\n * Standardidize extension name\n * @static\n * @param {string} s extension name\n * @returns {string}\n */\nshowdown.helper.stdExtName = function (s) {\n 'use strict';\n return s.replace(/[_?*+\\/\\\\.^-]/g, '').replace(/\\s/g, '').toLowerCase();\n};\n\nfunction escapeCharactersCallback (wholeMatch, m1) {\n 'use strict';\n var charCodeToEscape = m1.charCodeAt(0);\n return '¨E' + charCodeToEscape + 'E';\n}\n\n/**\n * Callback used to escape characters when passing through String.replace\n * @static\n * @param {string} wholeMatch\n * @param {string} m1\n * @returns {string}\n */\nshowdown.helper.escapeCharactersCallback = escapeCharactersCallback;\n\n/**\n * Escape characters in a string\n * @static\n * @param {string} text\n * @param {string} charsToEscape\n * @param {boolean} afterBackslash\n * @returns {XML|string|void|*}\n */\nshowdown.helper.escapeCharacters = function (text, charsToEscape, afterBackslash) {\n 'use strict';\n // First we have to escape the escape characters so that\n // we can build a character class out of them\n var regexString = '([' + charsToEscape.replace(/([\\[\\]\\\\])/g, '\\\\$1') + '])';\n\n if (afterBackslash) {\n regexString = '\\\\\\\\' + regexString;\n }\n\n var regex = new RegExp(regexString, 'g');\n text = text.replace(regex, escapeCharactersCallback);\n\n return text;\n};\n\n/**\n * Unescape HTML entities\n * @param txt\n * @returns {string}\n */\nshowdown.helper.unescapeHTMLEntities = function (txt) {\n 'use strict';\n\n return txt\n .replace(/"/g, '\"')\n .replace(/</g, '<')\n .replace(/>/g, '>')\n .replace(/&/g, '&');\n};\n\nvar rgxFindMatchPos = function (str, left, right, flags) {\n 'use strict';\n var f = flags || '',\n g = f.indexOf('g') > -1,\n x = new RegExp(left + '|' + right, 'g' + f.replace(/g/g, '')),\n l = new RegExp(left, f.replace(/g/g, '')),\n pos = [],\n t, s, m, start, end;\n\n do {\n t = 0;\n while ((m = x.exec(str))) {\n if (l.test(m[0])) {\n if (!(t++)) {\n s = x.lastIndex;\n start = s - m[0].length;\n }\n } else if (t) {\n if (!--t) {\n end = m.index + m[0].length;\n var obj = {\n left: {start: start, end: s},\n match: {start: s, end: m.index},\n right: {start: m.index, end: end},\n wholeMatch: {start: start, end: end}\n };\n pos.push(obj);\n if (!g) {\n return pos;\n }\n }\n }\n }\n } while (t && (x.lastIndex = s));\n\n return pos;\n};\n\n/**\n * matchRecursiveRegExp\n *\n * (c) 2007 Steven Levithan \n * MIT License\n *\n * Accepts a string to search, a left and right format delimiter\n * as regex patterns, and optional regex flags. Returns an array\n * of matches, allowing nested instances of left/right delimiters.\n * Use the \"g\" flag to return all matches, otherwise only the\n * first is returned. Be careful to ensure that the left and\n * right format delimiters produce mutually exclusive matches.\n * Backreferences are not supported within the right delimiter\n * due to how it is internally combined with the left delimiter.\n * When matching strings whose format delimiters are unbalanced\n * to the left or right, the output is intentionally as a\n * conventional regex library with recursion support would\n * produce, e.g. \"<\" and \">\" both produce [\"x\"] when using\n * \"<\" and \">\" as the delimiters (both strings contain a single,\n * balanced instance of \"\").\n *\n * examples:\n * matchRecursiveRegExp(\"test\", \"\\\\(\", \"\\\\)\")\n * returns: []\n * matchRecursiveRegExp(\">>t<>\", \"<\", \">\", \"g\")\n * returns: [\"t<>\", \"\"]\n * matchRecursiveRegExp(\"
test
\", \"]*>\", \"\", \"gi\")\n * returns: [\"test\"]\n */\nshowdown.helper.matchRecursiveRegExp = function (str, left, right, flags) {\n 'use strict';\n\n var matchPos = rgxFindMatchPos (str, left, right, flags),\n results = [];\n\n for (var i = 0; i < matchPos.length; ++i) {\n results.push([\n str.slice(matchPos[i].wholeMatch.start, matchPos[i].wholeMatch.end),\n str.slice(matchPos[i].match.start, matchPos[i].match.end),\n str.slice(matchPos[i].left.start, matchPos[i].left.end),\n str.slice(matchPos[i].right.start, matchPos[i].right.end)\n ]);\n }\n return results;\n};\n\n/**\n *\n * @param {string} str\n * @param {string|function} replacement\n * @param {string} left\n * @param {string} right\n * @param {string} flags\n * @returns {string}\n */\nshowdown.helper.replaceRecursiveRegExp = function (str, replacement, left, right, flags) {\n 'use strict';\n\n if (!showdown.helper.isFunction(replacement)) {\n var repStr = replacement;\n replacement = function () {\n return repStr;\n };\n }\n\n var matchPos = rgxFindMatchPos(str, left, right, flags),\n finalStr = str,\n lng = matchPos.length;\n\n if (lng > 0) {\n var bits = [];\n if (matchPos[0].wholeMatch.start !== 0) {\n bits.push(str.slice(0, matchPos[0].wholeMatch.start));\n }\n for (var i = 0; i < lng; ++i) {\n bits.push(\n replacement(\n str.slice(matchPos[i].wholeMatch.start, matchPos[i].wholeMatch.end),\n str.slice(matchPos[i].match.start, matchPos[i].match.end),\n str.slice(matchPos[i].left.start, matchPos[i].left.end),\n str.slice(matchPos[i].right.start, matchPos[i].right.end)\n )\n );\n if (i < lng - 1) {\n bits.push(str.slice(matchPos[i].wholeMatch.end, matchPos[i + 1].wholeMatch.start));\n }\n }\n if (matchPos[lng - 1].wholeMatch.end < str.length) {\n bits.push(str.slice(matchPos[lng - 1].wholeMatch.end));\n }\n finalStr = bits.join('');\n }\n return finalStr;\n};\n\n/**\n * Returns the index within the passed String object of the first occurrence of the specified regex,\n * starting the search at fromIndex. Returns -1 if the value is not found.\n *\n * @param {string} str string to search\n * @param {RegExp} regex Regular expression to search\n * @param {int} [fromIndex = 0] Index to start the search\n * @returns {Number}\n * @throws InvalidArgumentError\n */\nshowdown.helper.regexIndexOf = function (str, regex, fromIndex) {\n 'use strict';\n if (!showdown.helper.isString(str)) {\n throw 'InvalidArgumentError: first parameter of showdown.helper.regexIndexOf function must be a string';\n }\n if (regex instanceof RegExp === false) {\n throw 'InvalidArgumentError: second parameter of showdown.helper.regexIndexOf function must be an instance of RegExp';\n }\n var indexOf = str.substring(fromIndex || 0).search(regex);\n return (indexOf >= 0) ? (indexOf + (fromIndex || 0)) : indexOf;\n};\n\n/**\n * Splits the passed string object at the defined index, and returns an array composed of the two substrings\n * @param {string} str string to split\n * @param {int} index index to split string at\n * @returns {[string,string]}\n * @throws InvalidArgumentError\n */\nshowdown.helper.splitAtIndex = function (str, index) {\n 'use strict';\n if (!showdown.helper.isString(str)) {\n throw 'InvalidArgumentError: first parameter of showdown.helper.regexIndexOf function must be a string';\n }\n return [str.substring(0, index), str.substring(index)];\n};\n\n/**\n * Obfuscate an e-mail address through the use of Character Entities,\n * transforming ASCII characters into their equivalent decimal or hex entities.\n *\n * Since it has a random component, subsequent calls to this function produce different results\n *\n * @param {string} mail\n * @returns {string}\n */\nshowdown.helper.encodeEmailAddress = function (mail) {\n 'use strict';\n var encode = [\n function (ch) {\n return '&#' + ch.charCodeAt(0) + ';';\n },\n function (ch) {\n return '&#x' + ch.charCodeAt(0).toString(16) + ';';\n },\n function (ch) {\n return ch;\n }\n ];\n\n mail = mail.replace(/./g, function (ch) {\n if (ch === '@') {\n // this *must* be encoded. I insist.\n ch = encode[Math.floor(Math.random() * 2)](ch);\n } else {\n var r = Math.random();\n // roughly 10% raw, 45% hex, 45% dec\n ch = (\n r > 0.9 ? encode[2](ch) : r > 0.45 ? encode[1](ch) : encode[0](ch)\n );\n }\n return ch;\n });\n\n return mail;\n};\n\n/**\n *\n * @param str\n * @param targetLength\n * @param padString\n * @returns {string}\n */\nshowdown.helper.padEnd = function padEnd (str, targetLength, padString) {\n 'use strict';\n /*jshint bitwise: false*/\n // eslint-disable-next-line space-infix-ops\n targetLength = targetLength>>0; //floor if number or convert non-number to 0;\n /*jshint bitwise: true*/\n padString = String(padString || ' ');\n if (str.length > targetLength) {\n return String(str);\n } else {\n targetLength = targetLength - str.length;\n if (targetLength > padString.length) {\n padString += padString.repeat(targetLength / padString.length); //append to original to ensure we are longer than needed\n }\n return String(str) + padString.slice(0,targetLength);\n }\n};\n\n/**\n * POLYFILLS\n */\n// use this instead of builtin is undefined for IE8 compatibility\nif (typeof console === 'undefined') {\n console = {\n warn: function (msg) {\n 'use strict';\n alert(msg);\n },\n log: function (msg) {\n 'use strict';\n alert(msg);\n },\n error: function (msg) {\n 'use strict';\n throw msg;\n }\n };\n}\n\n/**\n * Common regexes.\n * We declare some common regexes to improve performance\n */\nshowdown.helper.regexes = {\n asteriskDashAndColon: /([*_:~])/g\n};\n\n/**\n * EMOJIS LIST\n */\nshowdown.helper.emojis = {\n '+1':'\\ud83d\\udc4d',\n '-1':'\\ud83d\\udc4e',\n '100':'\\ud83d\\udcaf',\n '1234':'\\ud83d\\udd22',\n '1st_place_medal':'\\ud83e\\udd47',\n '2nd_place_medal':'\\ud83e\\udd48',\n '3rd_place_medal':'\\ud83e\\udd49',\n '8ball':'\\ud83c\\udfb1',\n 'a':'\\ud83c\\udd70\\ufe0f',\n 'ab':'\\ud83c\\udd8e',\n 'abc':'\\ud83d\\udd24',\n 'abcd':'\\ud83d\\udd21',\n 'accept':'\\ud83c\\ude51',\n 'aerial_tramway':'\\ud83d\\udea1',\n 'airplane':'\\u2708\\ufe0f',\n 'alarm_clock':'\\u23f0',\n 'alembic':'\\u2697\\ufe0f',\n 'alien':'\\ud83d\\udc7d',\n 'ambulance':'\\ud83d\\ude91',\n 'amphora':'\\ud83c\\udffa',\n 'anchor':'\\u2693\\ufe0f',\n 'angel':'\\ud83d\\udc7c',\n 'anger':'\\ud83d\\udca2',\n 'angry':'\\ud83d\\ude20',\n 'anguished':'\\ud83d\\ude27',\n 'ant':'\\ud83d\\udc1c',\n 'apple':'\\ud83c\\udf4e',\n 'aquarius':'\\u2652\\ufe0f',\n 'aries':'\\u2648\\ufe0f',\n 'arrow_backward':'\\u25c0\\ufe0f',\n 'arrow_double_down':'\\u23ec',\n 'arrow_double_up':'\\u23eb',\n 'arrow_down':'\\u2b07\\ufe0f',\n 'arrow_down_small':'\\ud83d\\udd3d',\n 'arrow_forward':'\\u25b6\\ufe0f',\n 'arrow_heading_down':'\\u2935\\ufe0f',\n 'arrow_heading_up':'\\u2934\\ufe0f',\n 'arrow_left':'\\u2b05\\ufe0f',\n 'arrow_lower_left':'\\u2199\\ufe0f',\n 'arrow_lower_right':'\\u2198\\ufe0f',\n 'arrow_right':'\\u27a1\\ufe0f',\n 'arrow_right_hook':'\\u21aa\\ufe0f',\n 'arrow_up':'\\u2b06\\ufe0f',\n 'arrow_up_down':'\\u2195\\ufe0f',\n 'arrow_up_small':'\\ud83d\\udd3c',\n 'arrow_upper_left':'\\u2196\\ufe0f',\n 'arrow_upper_right':'\\u2197\\ufe0f',\n 'arrows_clockwise':'\\ud83d\\udd03',\n 'arrows_counterclockwise':'\\ud83d\\udd04',\n 'art':'\\ud83c\\udfa8',\n 'articulated_lorry':'\\ud83d\\ude9b',\n 'artificial_satellite':'\\ud83d\\udef0',\n 'astonished':'\\ud83d\\ude32',\n 'athletic_shoe':'\\ud83d\\udc5f',\n 'atm':'\\ud83c\\udfe7',\n 'atom_symbol':'\\u269b\\ufe0f',\n 'avocado':'\\ud83e\\udd51',\n 'b':'\\ud83c\\udd71\\ufe0f',\n 'baby':'\\ud83d\\udc76',\n 'baby_bottle':'\\ud83c\\udf7c',\n 'baby_chick':'\\ud83d\\udc24',\n 'baby_symbol':'\\ud83d\\udebc',\n 'back':'\\ud83d\\udd19',\n 'bacon':'\\ud83e\\udd53',\n 'badminton':'\\ud83c\\udff8',\n 'baggage_claim':'\\ud83d\\udec4',\n 'baguette_bread':'\\ud83e\\udd56',\n 'balance_scale':'\\u2696\\ufe0f',\n 'balloon':'\\ud83c\\udf88',\n 'ballot_box':'\\ud83d\\uddf3',\n 'ballot_box_with_check':'\\u2611\\ufe0f',\n 'bamboo':'\\ud83c\\udf8d',\n 'banana':'\\ud83c\\udf4c',\n 'bangbang':'\\u203c\\ufe0f',\n 'bank':'\\ud83c\\udfe6',\n 'bar_chart':'\\ud83d\\udcca',\n 'barber':'\\ud83d\\udc88',\n 'baseball':'\\u26be\\ufe0f',\n 'basketball':'\\ud83c\\udfc0',\n 'basketball_man':'\\u26f9\\ufe0f',\n 'basketball_woman':'\\u26f9\\ufe0f‍\\u2640\\ufe0f',\n 'bat':'\\ud83e\\udd87',\n 'bath':'\\ud83d\\udec0',\n 'bathtub':'\\ud83d\\udec1',\n 'battery':'\\ud83d\\udd0b',\n 'beach_umbrella':'\\ud83c\\udfd6',\n 'bear':'\\ud83d\\udc3b',\n 'bed':'\\ud83d\\udecf',\n 'bee':'\\ud83d\\udc1d',\n 'beer':'\\ud83c\\udf7a',\n 'beers':'\\ud83c\\udf7b',\n 'beetle':'\\ud83d\\udc1e',\n 'beginner':'\\ud83d\\udd30',\n 'bell':'\\ud83d\\udd14',\n 'bellhop_bell':'\\ud83d\\udece',\n 'bento':'\\ud83c\\udf71',\n 'biking_man':'\\ud83d\\udeb4',\n 'bike':'\\ud83d\\udeb2',\n 'biking_woman':'\\ud83d\\udeb4‍\\u2640\\ufe0f',\n 'bikini':'\\ud83d\\udc59',\n 'biohazard':'\\u2623\\ufe0f',\n 'bird':'\\ud83d\\udc26',\n 'birthday':'\\ud83c\\udf82',\n 'black_circle':'\\u26ab\\ufe0f',\n 'black_flag':'\\ud83c\\udff4',\n 'black_heart':'\\ud83d\\udda4',\n 'black_joker':'\\ud83c\\udccf',\n 'black_large_square':'\\u2b1b\\ufe0f',\n 'black_medium_small_square':'\\u25fe\\ufe0f',\n 'black_medium_square':'\\u25fc\\ufe0f',\n 'black_nib':'\\u2712\\ufe0f',\n 'black_small_square':'\\u25aa\\ufe0f',\n 'black_square_button':'\\ud83d\\udd32',\n 'blonde_man':'\\ud83d\\udc71',\n 'blonde_woman':'\\ud83d\\udc71‍\\u2640\\ufe0f',\n 'blossom':'\\ud83c\\udf3c',\n 'blowfish':'\\ud83d\\udc21',\n 'blue_book':'\\ud83d\\udcd8',\n 'blue_car':'\\ud83d\\ude99',\n 'blue_heart':'\\ud83d\\udc99',\n 'blush':'\\ud83d\\ude0a',\n 'boar':'\\ud83d\\udc17',\n 'boat':'\\u26f5\\ufe0f',\n 'bomb':'\\ud83d\\udca3',\n 'book':'\\ud83d\\udcd6',\n 'bookmark':'\\ud83d\\udd16',\n 'bookmark_tabs':'\\ud83d\\udcd1',\n 'books':'\\ud83d\\udcda',\n 'boom':'\\ud83d\\udca5',\n 'boot':'\\ud83d\\udc62',\n 'bouquet':'\\ud83d\\udc90',\n 'bowing_man':'\\ud83d\\ude47',\n 'bow_and_arrow':'\\ud83c\\udff9',\n 'bowing_woman':'\\ud83d\\ude47‍\\u2640\\ufe0f',\n 'bowling':'\\ud83c\\udfb3',\n 'boxing_glove':'\\ud83e\\udd4a',\n 'boy':'\\ud83d\\udc66',\n 'bread':'\\ud83c\\udf5e',\n 'bride_with_veil':'\\ud83d\\udc70',\n 'bridge_at_night':'\\ud83c\\udf09',\n 'briefcase':'\\ud83d\\udcbc',\n 'broken_heart':'\\ud83d\\udc94',\n 'bug':'\\ud83d\\udc1b',\n 'building_construction':'\\ud83c\\udfd7',\n 'bulb':'\\ud83d\\udca1',\n 'bullettrain_front':'\\ud83d\\ude85',\n 'bullettrain_side':'\\ud83d\\ude84',\n 'burrito':'\\ud83c\\udf2f',\n 'bus':'\\ud83d\\ude8c',\n 'business_suit_levitating':'\\ud83d\\udd74',\n 'busstop':'\\ud83d\\ude8f',\n 'bust_in_silhouette':'\\ud83d\\udc64',\n 'busts_in_silhouette':'\\ud83d\\udc65',\n 'butterfly':'\\ud83e\\udd8b',\n 'cactus':'\\ud83c\\udf35',\n 'cake':'\\ud83c\\udf70',\n 'calendar':'\\ud83d\\udcc6',\n 'call_me_hand':'\\ud83e\\udd19',\n 'calling':'\\ud83d\\udcf2',\n 'camel':'\\ud83d\\udc2b',\n 'camera':'\\ud83d\\udcf7',\n 'camera_flash':'\\ud83d\\udcf8',\n 'camping':'\\ud83c\\udfd5',\n 'cancer':'\\u264b\\ufe0f',\n 'candle':'\\ud83d\\udd6f',\n 'candy':'\\ud83c\\udf6c',\n 'canoe':'\\ud83d\\udef6',\n 'capital_abcd':'\\ud83d\\udd20',\n 'capricorn':'\\u2651\\ufe0f',\n 'car':'\\ud83d\\ude97',\n 'card_file_box':'\\ud83d\\uddc3',\n 'card_index':'\\ud83d\\udcc7',\n 'card_index_dividers':'\\ud83d\\uddc2',\n 'carousel_horse':'\\ud83c\\udfa0',\n 'carrot':'\\ud83e\\udd55',\n 'cat':'\\ud83d\\udc31',\n 'cat2':'\\ud83d\\udc08',\n 'cd':'\\ud83d\\udcbf',\n 'chains':'\\u26d3',\n 'champagne':'\\ud83c\\udf7e',\n 'chart':'\\ud83d\\udcb9',\n 'chart_with_downwards_trend':'\\ud83d\\udcc9',\n 'chart_with_upwards_trend':'\\ud83d\\udcc8',\n 'checkered_flag':'\\ud83c\\udfc1',\n 'cheese':'\\ud83e\\uddc0',\n 'cherries':'\\ud83c\\udf52',\n 'cherry_blossom':'\\ud83c\\udf38',\n 'chestnut':'\\ud83c\\udf30',\n 'chicken':'\\ud83d\\udc14',\n 'children_crossing':'\\ud83d\\udeb8',\n 'chipmunk':'\\ud83d\\udc3f',\n 'chocolate_bar':'\\ud83c\\udf6b',\n 'christmas_tree':'\\ud83c\\udf84',\n 'church':'\\u26ea\\ufe0f',\n 'cinema':'\\ud83c\\udfa6',\n 'circus_tent':'\\ud83c\\udfaa',\n 'city_sunrise':'\\ud83c\\udf07',\n 'city_sunset':'\\ud83c\\udf06',\n 'cityscape':'\\ud83c\\udfd9',\n 'cl':'\\ud83c\\udd91',\n 'clamp':'\\ud83d\\udddc',\n 'clap':'\\ud83d\\udc4f',\n 'clapper':'\\ud83c\\udfac',\n 'classical_building':'\\ud83c\\udfdb',\n 'clinking_glasses':'\\ud83e\\udd42',\n 'clipboard':'\\ud83d\\udccb',\n 'clock1':'\\ud83d\\udd50',\n 'clock10':'\\ud83d\\udd59',\n 'clock1030':'\\ud83d\\udd65',\n 'clock11':'\\ud83d\\udd5a',\n 'clock1130':'\\ud83d\\udd66',\n 'clock12':'\\ud83d\\udd5b',\n 'clock1230':'\\ud83d\\udd67',\n 'clock130':'\\ud83d\\udd5c',\n 'clock2':'\\ud83d\\udd51',\n 'clock230':'\\ud83d\\udd5d',\n 'clock3':'\\ud83d\\udd52',\n 'clock330':'\\ud83d\\udd5e',\n 'clock4':'\\ud83d\\udd53',\n 'clock430':'\\ud83d\\udd5f',\n 'clock5':'\\ud83d\\udd54',\n 'clock530':'\\ud83d\\udd60',\n 'clock6':'\\ud83d\\udd55',\n 'clock630':'\\ud83d\\udd61',\n 'clock7':'\\ud83d\\udd56',\n 'clock730':'\\ud83d\\udd62',\n 'clock8':'\\ud83d\\udd57',\n 'clock830':'\\ud83d\\udd63',\n 'clock9':'\\ud83d\\udd58',\n 'clock930':'\\ud83d\\udd64',\n 'closed_book':'\\ud83d\\udcd5',\n 'closed_lock_with_key':'\\ud83d\\udd10',\n 'closed_umbrella':'\\ud83c\\udf02',\n 'cloud':'\\u2601\\ufe0f',\n 'cloud_with_lightning':'\\ud83c\\udf29',\n 'cloud_with_lightning_and_rain':'\\u26c8',\n 'cloud_with_rain':'\\ud83c\\udf27',\n 'cloud_with_snow':'\\ud83c\\udf28',\n 'clown_face':'\\ud83e\\udd21',\n 'clubs':'\\u2663\\ufe0f',\n 'cocktail':'\\ud83c\\udf78',\n 'coffee':'\\u2615\\ufe0f',\n 'coffin':'\\u26b0\\ufe0f',\n 'cold_sweat':'\\ud83d\\ude30',\n 'comet':'\\u2604\\ufe0f',\n 'computer':'\\ud83d\\udcbb',\n 'computer_mouse':'\\ud83d\\uddb1',\n 'confetti_ball':'\\ud83c\\udf8a',\n 'confounded':'\\ud83d\\ude16',\n 'confused':'\\ud83d\\ude15',\n 'congratulations':'\\u3297\\ufe0f',\n 'construction':'\\ud83d\\udea7',\n 'construction_worker_man':'\\ud83d\\udc77',\n 'construction_worker_woman':'\\ud83d\\udc77‍\\u2640\\ufe0f',\n 'control_knobs':'\\ud83c\\udf9b',\n 'convenience_store':'\\ud83c\\udfea',\n 'cookie':'\\ud83c\\udf6a',\n 'cool':'\\ud83c\\udd92',\n 'policeman':'\\ud83d\\udc6e',\n 'copyright':'\\u00a9\\ufe0f',\n 'corn':'\\ud83c\\udf3d',\n 'couch_and_lamp':'\\ud83d\\udecb',\n 'couple':'\\ud83d\\udc6b',\n 'couple_with_heart_woman_man':'\\ud83d\\udc91',\n 'couple_with_heart_man_man':'\\ud83d\\udc68‍\\u2764\\ufe0f‍\\ud83d\\udc68',\n 'couple_with_heart_woman_woman':'\\ud83d\\udc69‍\\u2764\\ufe0f‍\\ud83d\\udc69',\n 'couplekiss_man_man':'\\ud83d\\udc68‍\\u2764\\ufe0f‍\\ud83d\\udc8b‍\\ud83d\\udc68',\n 'couplekiss_man_woman':'\\ud83d\\udc8f',\n 'couplekiss_woman_woman':'\\ud83d\\udc69‍\\u2764\\ufe0f‍\\ud83d\\udc8b‍\\ud83d\\udc69',\n 'cow':'\\ud83d\\udc2e',\n 'cow2':'\\ud83d\\udc04',\n 'cowboy_hat_face':'\\ud83e\\udd20',\n 'crab':'\\ud83e\\udd80',\n 'crayon':'\\ud83d\\udd8d',\n 'credit_card':'\\ud83d\\udcb3',\n 'crescent_moon':'\\ud83c\\udf19',\n 'cricket':'\\ud83c\\udfcf',\n 'crocodile':'\\ud83d\\udc0a',\n 'croissant':'\\ud83e\\udd50',\n 'crossed_fingers':'\\ud83e\\udd1e',\n 'crossed_flags':'\\ud83c\\udf8c',\n 'crossed_swords':'\\u2694\\ufe0f',\n 'crown':'\\ud83d\\udc51',\n 'cry':'\\ud83d\\ude22',\n 'crying_cat_face':'\\ud83d\\ude3f',\n 'crystal_ball':'\\ud83d\\udd2e',\n 'cucumber':'\\ud83e\\udd52',\n 'cupid':'\\ud83d\\udc98',\n 'curly_loop':'\\u27b0',\n 'currency_exchange':'\\ud83d\\udcb1',\n 'curry':'\\ud83c\\udf5b',\n 'custard':'\\ud83c\\udf6e',\n 'customs':'\\ud83d\\udec3',\n 'cyclone':'\\ud83c\\udf00',\n 'dagger':'\\ud83d\\udde1',\n 'dancer':'\\ud83d\\udc83',\n 'dancing_women':'\\ud83d\\udc6f',\n 'dancing_men':'\\ud83d\\udc6f‍\\u2642\\ufe0f',\n 'dango':'\\ud83c\\udf61',\n 'dark_sunglasses':'\\ud83d\\udd76',\n 'dart':'\\ud83c\\udfaf',\n 'dash':'\\ud83d\\udca8',\n 'date':'\\ud83d\\udcc5',\n 'deciduous_tree':'\\ud83c\\udf33',\n 'deer':'\\ud83e\\udd8c',\n 'department_store':'\\ud83c\\udfec',\n 'derelict_house':'\\ud83c\\udfda',\n 'desert':'\\ud83c\\udfdc',\n 'desert_island':'\\ud83c\\udfdd',\n 'desktop_computer':'\\ud83d\\udda5',\n 'male_detective':'\\ud83d\\udd75\\ufe0f',\n 'diamond_shape_with_a_dot_inside':'\\ud83d\\udca0',\n 'diamonds':'\\u2666\\ufe0f',\n 'disappointed':'\\ud83d\\ude1e',\n 'disappointed_relieved':'\\ud83d\\ude25',\n 'dizzy':'\\ud83d\\udcab',\n 'dizzy_face':'\\ud83d\\ude35',\n 'do_not_litter':'\\ud83d\\udeaf',\n 'dog':'\\ud83d\\udc36',\n 'dog2':'\\ud83d\\udc15',\n 'dollar':'\\ud83d\\udcb5',\n 'dolls':'\\ud83c\\udf8e',\n 'dolphin':'\\ud83d\\udc2c',\n 'door':'\\ud83d\\udeaa',\n 'doughnut':'\\ud83c\\udf69',\n 'dove':'\\ud83d\\udd4a',\n 'dragon':'\\ud83d\\udc09',\n 'dragon_face':'\\ud83d\\udc32',\n 'dress':'\\ud83d\\udc57',\n 'dromedary_camel':'\\ud83d\\udc2a',\n 'drooling_face':'\\ud83e\\udd24',\n 'droplet':'\\ud83d\\udca7',\n 'drum':'\\ud83e\\udd41',\n 'duck':'\\ud83e\\udd86',\n 'dvd':'\\ud83d\\udcc0',\n 'e-mail':'\\ud83d\\udce7',\n 'eagle':'\\ud83e\\udd85',\n 'ear':'\\ud83d\\udc42',\n 'ear_of_rice':'\\ud83c\\udf3e',\n 'earth_africa':'\\ud83c\\udf0d',\n 'earth_americas':'\\ud83c\\udf0e',\n 'earth_asia':'\\ud83c\\udf0f',\n 'egg':'\\ud83e\\udd5a',\n 'eggplant':'\\ud83c\\udf46',\n 'eight_pointed_black_star':'\\u2734\\ufe0f',\n 'eight_spoked_asterisk':'\\u2733\\ufe0f',\n 'electric_plug':'\\ud83d\\udd0c',\n 'elephant':'\\ud83d\\udc18',\n 'email':'\\u2709\\ufe0f',\n 'end':'\\ud83d\\udd1a',\n 'envelope_with_arrow':'\\ud83d\\udce9',\n 'euro':'\\ud83d\\udcb6',\n 'european_castle':'\\ud83c\\udff0',\n 'european_post_office':'\\ud83c\\udfe4',\n 'evergreen_tree':'\\ud83c\\udf32',\n 'exclamation':'\\u2757\\ufe0f',\n 'expressionless':'\\ud83d\\ude11',\n 'eye':'\\ud83d\\udc41',\n 'eye_speech_bubble':'\\ud83d\\udc41‍\\ud83d\\udde8',\n 'eyeglasses':'\\ud83d\\udc53',\n 'eyes':'\\ud83d\\udc40',\n 'face_with_head_bandage':'\\ud83e\\udd15',\n 'face_with_thermometer':'\\ud83e\\udd12',\n 'fist_oncoming':'\\ud83d\\udc4a',\n 'factory':'\\ud83c\\udfed',\n 'fallen_leaf':'\\ud83c\\udf42',\n 'family_man_woman_boy':'\\ud83d\\udc6a',\n 'family_man_boy':'\\ud83d\\udc68‍\\ud83d\\udc66',\n 'family_man_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc66‍\\ud83d\\udc66',\n 'family_man_girl':'\\ud83d\\udc68‍\\ud83d\\udc67',\n 'family_man_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc66',\n 'family_man_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc67',\n 'family_man_man_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc66',\n 'family_man_man_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc66‍\\ud83d\\udc66',\n 'family_man_man_girl':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67',\n 'family_man_man_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc66',\n 'family_man_man_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc67',\n 'family_man_woman_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n 'family_man_woman_girl':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67',\n 'family_man_woman_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n 'family_man_woman_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n 'family_woman_boy':'\\ud83d\\udc69‍\\ud83d\\udc66',\n 'family_woman_boy_boy':'\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n 'family_woman_girl':'\\ud83d\\udc69‍\\ud83d\\udc67',\n 'family_woman_girl_boy':'\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n 'family_woman_girl_girl':'\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n 'family_woman_woman_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc66',\n 'family_woman_woman_boy_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n 'family_woman_woman_girl':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67',\n 'family_woman_woman_girl_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n 'family_woman_woman_girl_girl':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n 'fast_forward':'\\u23e9',\n 'fax':'\\ud83d\\udce0',\n 'fearful':'\\ud83d\\ude28',\n 'feet':'\\ud83d\\udc3e',\n 'female_detective':'\\ud83d\\udd75\\ufe0f‍\\u2640\\ufe0f',\n 'ferris_wheel':'\\ud83c\\udfa1',\n 'ferry':'\\u26f4',\n 'field_hockey':'\\ud83c\\udfd1',\n 'file_cabinet':'\\ud83d\\uddc4',\n 'file_folder':'\\ud83d\\udcc1',\n 'film_projector':'\\ud83d\\udcfd',\n 'film_strip':'\\ud83c\\udf9e',\n 'fire':'\\ud83d\\udd25',\n 'fire_engine':'\\ud83d\\ude92',\n 'fireworks':'\\ud83c\\udf86',\n 'first_quarter_moon':'\\ud83c\\udf13',\n 'first_quarter_moon_with_face':'\\ud83c\\udf1b',\n 'fish':'\\ud83d\\udc1f',\n 'fish_cake':'\\ud83c\\udf65',\n 'fishing_pole_and_fish':'\\ud83c\\udfa3',\n 'fist_raised':'\\u270a',\n 'fist_left':'\\ud83e\\udd1b',\n 'fist_right':'\\ud83e\\udd1c',\n 'flags':'\\ud83c\\udf8f',\n 'flashlight':'\\ud83d\\udd26',\n 'fleur_de_lis':'\\u269c\\ufe0f',\n 'flight_arrival':'\\ud83d\\udeec',\n 'flight_departure':'\\ud83d\\udeeb',\n 'floppy_disk':'\\ud83d\\udcbe',\n 'flower_playing_cards':'\\ud83c\\udfb4',\n 'flushed':'\\ud83d\\ude33',\n 'fog':'\\ud83c\\udf2b',\n 'foggy':'\\ud83c\\udf01',\n 'football':'\\ud83c\\udfc8',\n 'footprints':'\\ud83d\\udc63',\n 'fork_and_knife':'\\ud83c\\udf74',\n 'fountain':'\\u26f2\\ufe0f',\n 'fountain_pen':'\\ud83d\\udd8b',\n 'four_leaf_clover':'\\ud83c\\udf40',\n 'fox_face':'\\ud83e\\udd8a',\n 'framed_picture':'\\ud83d\\uddbc',\n 'free':'\\ud83c\\udd93',\n 'fried_egg':'\\ud83c\\udf73',\n 'fried_shrimp':'\\ud83c\\udf64',\n 'fries':'\\ud83c\\udf5f',\n 'frog':'\\ud83d\\udc38',\n 'frowning':'\\ud83d\\ude26',\n 'frowning_face':'\\u2639\\ufe0f',\n 'frowning_man':'\\ud83d\\ude4d‍\\u2642\\ufe0f',\n 'frowning_woman':'\\ud83d\\ude4d',\n 'middle_finger':'\\ud83d\\udd95',\n 'fuelpump':'\\u26fd\\ufe0f',\n 'full_moon':'\\ud83c\\udf15',\n 'full_moon_with_face':'\\ud83c\\udf1d',\n 'funeral_urn':'\\u26b1\\ufe0f',\n 'game_die':'\\ud83c\\udfb2',\n 'gear':'\\u2699\\ufe0f',\n 'gem':'\\ud83d\\udc8e',\n 'gemini':'\\u264a\\ufe0f',\n 'ghost':'\\ud83d\\udc7b',\n 'gift':'\\ud83c\\udf81',\n 'gift_heart':'\\ud83d\\udc9d',\n 'girl':'\\ud83d\\udc67',\n 'globe_with_meridians':'\\ud83c\\udf10',\n 'goal_net':'\\ud83e\\udd45',\n 'goat':'\\ud83d\\udc10',\n 'golf':'\\u26f3\\ufe0f',\n 'golfing_man':'\\ud83c\\udfcc\\ufe0f',\n 'golfing_woman':'\\ud83c\\udfcc\\ufe0f‍\\u2640\\ufe0f',\n 'gorilla':'\\ud83e\\udd8d',\n 'grapes':'\\ud83c\\udf47',\n 'green_apple':'\\ud83c\\udf4f',\n 'green_book':'\\ud83d\\udcd7',\n 'green_heart':'\\ud83d\\udc9a',\n 'green_salad':'\\ud83e\\udd57',\n 'grey_exclamation':'\\u2755',\n 'grey_question':'\\u2754',\n 'grimacing':'\\ud83d\\ude2c',\n 'grin':'\\ud83d\\ude01',\n 'grinning':'\\ud83d\\ude00',\n 'guardsman':'\\ud83d\\udc82',\n 'guardswoman':'\\ud83d\\udc82‍\\u2640\\ufe0f',\n 'guitar':'\\ud83c\\udfb8',\n 'gun':'\\ud83d\\udd2b',\n 'haircut_woman':'\\ud83d\\udc87',\n 'haircut_man':'\\ud83d\\udc87‍\\u2642\\ufe0f',\n 'hamburger':'\\ud83c\\udf54',\n 'hammer':'\\ud83d\\udd28',\n 'hammer_and_pick':'\\u2692',\n 'hammer_and_wrench':'\\ud83d\\udee0',\n 'hamster':'\\ud83d\\udc39',\n 'hand':'\\u270b',\n 'handbag':'\\ud83d\\udc5c',\n 'handshake':'\\ud83e\\udd1d',\n 'hankey':'\\ud83d\\udca9',\n 'hatched_chick':'\\ud83d\\udc25',\n 'hatching_chick':'\\ud83d\\udc23',\n 'headphones':'\\ud83c\\udfa7',\n 'hear_no_evil':'\\ud83d\\ude49',\n 'heart':'\\u2764\\ufe0f',\n 'heart_decoration':'\\ud83d\\udc9f',\n 'heart_eyes':'\\ud83d\\ude0d',\n 'heart_eyes_cat':'\\ud83d\\ude3b',\n 'heartbeat':'\\ud83d\\udc93',\n 'heartpulse':'\\ud83d\\udc97',\n 'hearts':'\\u2665\\ufe0f',\n 'heavy_check_mark':'\\u2714\\ufe0f',\n 'heavy_division_sign':'\\u2797',\n 'heavy_dollar_sign':'\\ud83d\\udcb2',\n 'heavy_heart_exclamation':'\\u2763\\ufe0f',\n 'heavy_minus_sign':'\\u2796',\n 'heavy_multiplication_x':'\\u2716\\ufe0f',\n 'heavy_plus_sign':'\\u2795',\n 'helicopter':'\\ud83d\\ude81',\n 'herb':'\\ud83c\\udf3f',\n 'hibiscus':'\\ud83c\\udf3a',\n 'high_brightness':'\\ud83d\\udd06',\n 'high_heel':'\\ud83d\\udc60',\n 'hocho':'\\ud83d\\udd2a',\n 'hole':'\\ud83d\\udd73',\n 'honey_pot':'\\ud83c\\udf6f',\n 'horse':'\\ud83d\\udc34',\n 'horse_racing':'\\ud83c\\udfc7',\n 'hospital':'\\ud83c\\udfe5',\n 'hot_pepper':'\\ud83c\\udf36',\n 'hotdog':'\\ud83c\\udf2d',\n 'hotel':'\\ud83c\\udfe8',\n 'hotsprings':'\\u2668\\ufe0f',\n 'hourglass':'\\u231b\\ufe0f',\n 'hourglass_flowing_sand':'\\u23f3',\n 'house':'\\ud83c\\udfe0',\n 'house_with_garden':'\\ud83c\\udfe1',\n 'houses':'\\ud83c\\udfd8',\n 'hugs':'\\ud83e\\udd17',\n 'hushed':'\\ud83d\\ude2f',\n 'ice_cream':'\\ud83c\\udf68',\n 'ice_hockey':'\\ud83c\\udfd2',\n 'ice_skate':'\\u26f8',\n 'icecream':'\\ud83c\\udf66',\n 'id':'\\ud83c\\udd94',\n 'ideograph_advantage':'\\ud83c\\ude50',\n 'imp':'\\ud83d\\udc7f',\n 'inbox_tray':'\\ud83d\\udce5',\n 'incoming_envelope':'\\ud83d\\udce8',\n 'tipping_hand_woman':'\\ud83d\\udc81',\n 'information_source':'\\u2139\\ufe0f',\n 'innocent':'\\ud83d\\ude07',\n 'interrobang':'\\u2049\\ufe0f',\n 'iphone':'\\ud83d\\udcf1',\n 'izakaya_lantern':'\\ud83c\\udfee',\n 'jack_o_lantern':'\\ud83c\\udf83',\n 'japan':'\\ud83d\\uddfe',\n 'japanese_castle':'\\ud83c\\udfef',\n 'japanese_goblin':'\\ud83d\\udc7a',\n 'japanese_ogre':'\\ud83d\\udc79',\n 'jeans':'\\ud83d\\udc56',\n 'joy':'\\ud83d\\ude02',\n 'joy_cat':'\\ud83d\\ude39',\n 'joystick':'\\ud83d\\udd79',\n 'kaaba':'\\ud83d\\udd4b',\n 'key':'\\ud83d\\udd11',\n 'keyboard':'\\u2328\\ufe0f',\n 'keycap_ten':'\\ud83d\\udd1f',\n 'kick_scooter':'\\ud83d\\udef4',\n 'kimono':'\\ud83d\\udc58',\n 'kiss':'\\ud83d\\udc8b',\n 'kissing':'\\ud83d\\ude17',\n 'kissing_cat':'\\ud83d\\ude3d',\n 'kissing_closed_eyes':'\\ud83d\\ude1a',\n 'kissing_heart':'\\ud83d\\ude18',\n 'kissing_smiling_eyes':'\\ud83d\\ude19',\n 'kiwi_fruit':'\\ud83e\\udd5d',\n 'koala':'\\ud83d\\udc28',\n 'koko':'\\ud83c\\ude01',\n 'label':'\\ud83c\\udff7',\n 'large_blue_circle':'\\ud83d\\udd35',\n 'large_blue_diamond':'\\ud83d\\udd37',\n 'large_orange_diamond':'\\ud83d\\udd36',\n 'last_quarter_moon':'\\ud83c\\udf17',\n 'last_quarter_moon_with_face':'\\ud83c\\udf1c',\n 'latin_cross':'\\u271d\\ufe0f',\n 'laughing':'\\ud83d\\ude06',\n 'leaves':'\\ud83c\\udf43',\n 'ledger':'\\ud83d\\udcd2',\n 'left_luggage':'\\ud83d\\udec5',\n 'left_right_arrow':'\\u2194\\ufe0f',\n 'leftwards_arrow_with_hook':'\\u21a9\\ufe0f',\n 'lemon':'\\ud83c\\udf4b',\n 'leo':'\\u264c\\ufe0f',\n 'leopard':'\\ud83d\\udc06',\n 'level_slider':'\\ud83c\\udf9a',\n 'libra':'\\u264e\\ufe0f',\n 'light_rail':'\\ud83d\\ude88',\n 'link':'\\ud83d\\udd17',\n 'lion':'\\ud83e\\udd81',\n 'lips':'\\ud83d\\udc44',\n 'lipstick':'\\ud83d\\udc84',\n 'lizard':'\\ud83e\\udd8e',\n 'lock':'\\ud83d\\udd12',\n 'lock_with_ink_pen':'\\ud83d\\udd0f',\n 'lollipop':'\\ud83c\\udf6d',\n 'loop':'\\u27bf',\n 'loud_sound':'\\ud83d\\udd0a',\n 'loudspeaker':'\\ud83d\\udce2',\n 'love_hotel':'\\ud83c\\udfe9',\n 'love_letter':'\\ud83d\\udc8c',\n 'low_brightness':'\\ud83d\\udd05',\n 'lying_face':'\\ud83e\\udd25',\n 'm':'\\u24c2\\ufe0f',\n 'mag':'\\ud83d\\udd0d',\n 'mag_right':'\\ud83d\\udd0e',\n 'mahjong':'\\ud83c\\udc04\\ufe0f',\n 'mailbox':'\\ud83d\\udceb',\n 'mailbox_closed':'\\ud83d\\udcea',\n 'mailbox_with_mail':'\\ud83d\\udcec',\n 'mailbox_with_no_mail':'\\ud83d\\udced',\n 'man':'\\ud83d\\udc68',\n 'man_artist':'\\ud83d\\udc68‍\\ud83c\\udfa8',\n 'man_astronaut':'\\ud83d\\udc68‍\\ud83d\\ude80',\n 'man_cartwheeling':'\\ud83e\\udd38‍\\u2642\\ufe0f',\n 'man_cook':'\\ud83d\\udc68‍\\ud83c\\udf73',\n 'man_dancing':'\\ud83d\\udd7a',\n 'man_facepalming':'\\ud83e\\udd26‍\\u2642\\ufe0f',\n 'man_factory_worker':'\\ud83d\\udc68‍\\ud83c\\udfed',\n 'man_farmer':'\\ud83d\\udc68‍\\ud83c\\udf3e',\n 'man_firefighter':'\\ud83d\\udc68‍\\ud83d\\ude92',\n 'man_health_worker':'\\ud83d\\udc68‍\\u2695\\ufe0f',\n 'man_in_tuxedo':'\\ud83e\\udd35',\n 'man_judge':'\\ud83d\\udc68‍\\u2696\\ufe0f',\n 'man_juggling':'\\ud83e\\udd39‍\\u2642\\ufe0f',\n 'man_mechanic':'\\ud83d\\udc68‍\\ud83d\\udd27',\n 'man_office_worker':'\\ud83d\\udc68‍\\ud83d\\udcbc',\n 'man_pilot':'\\ud83d\\udc68‍\\u2708\\ufe0f',\n 'man_playing_handball':'\\ud83e\\udd3e‍\\u2642\\ufe0f',\n 'man_playing_water_polo':'\\ud83e\\udd3d‍\\u2642\\ufe0f',\n 'man_scientist':'\\ud83d\\udc68‍\\ud83d\\udd2c',\n 'man_shrugging':'\\ud83e\\udd37‍\\u2642\\ufe0f',\n 'man_singer':'\\ud83d\\udc68‍\\ud83c\\udfa4',\n 'man_student':'\\ud83d\\udc68‍\\ud83c\\udf93',\n 'man_teacher':'\\ud83d\\udc68‍\\ud83c\\udfeb',\n 'man_technologist':'\\ud83d\\udc68‍\\ud83d\\udcbb',\n 'man_with_gua_pi_mao':'\\ud83d\\udc72',\n 'man_with_turban':'\\ud83d\\udc73',\n 'tangerine':'\\ud83c\\udf4a',\n 'mans_shoe':'\\ud83d\\udc5e',\n 'mantelpiece_clock':'\\ud83d\\udd70',\n 'maple_leaf':'\\ud83c\\udf41',\n 'martial_arts_uniform':'\\ud83e\\udd4b',\n 'mask':'\\ud83d\\ude37',\n 'massage_woman':'\\ud83d\\udc86',\n 'massage_man':'\\ud83d\\udc86‍\\u2642\\ufe0f',\n 'meat_on_bone':'\\ud83c\\udf56',\n 'medal_military':'\\ud83c\\udf96',\n 'medal_sports':'\\ud83c\\udfc5',\n 'mega':'\\ud83d\\udce3',\n 'melon':'\\ud83c\\udf48',\n 'memo':'\\ud83d\\udcdd',\n 'men_wrestling':'\\ud83e\\udd3c‍\\u2642\\ufe0f',\n 'menorah':'\\ud83d\\udd4e',\n 'mens':'\\ud83d\\udeb9',\n 'metal':'\\ud83e\\udd18',\n 'metro':'\\ud83d\\ude87',\n 'microphone':'\\ud83c\\udfa4',\n 'microscope':'\\ud83d\\udd2c',\n 'milk_glass':'\\ud83e\\udd5b',\n 'milky_way':'\\ud83c\\udf0c',\n 'minibus':'\\ud83d\\ude90',\n 'minidisc':'\\ud83d\\udcbd',\n 'mobile_phone_off':'\\ud83d\\udcf4',\n 'money_mouth_face':'\\ud83e\\udd11',\n 'money_with_wings':'\\ud83d\\udcb8',\n 'moneybag':'\\ud83d\\udcb0',\n 'monkey':'\\ud83d\\udc12',\n 'monkey_face':'\\ud83d\\udc35',\n 'monorail':'\\ud83d\\ude9d',\n 'moon':'\\ud83c\\udf14',\n 'mortar_board':'\\ud83c\\udf93',\n 'mosque':'\\ud83d\\udd4c',\n 'motor_boat':'\\ud83d\\udee5',\n 'motor_scooter':'\\ud83d\\udef5',\n 'motorcycle':'\\ud83c\\udfcd',\n 'motorway':'\\ud83d\\udee3',\n 'mount_fuji':'\\ud83d\\uddfb',\n 'mountain':'\\u26f0',\n 'mountain_biking_man':'\\ud83d\\udeb5',\n 'mountain_biking_woman':'\\ud83d\\udeb5‍\\u2640\\ufe0f',\n 'mountain_cableway':'\\ud83d\\udea0',\n 'mountain_railway':'\\ud83d\\ude9e',\n 'mountain_snow':'\\ud83c\\udfd4',\n 'mouse':'\\ud83d\\udc2d',\n 'mouse2':'\\ud83d\\udc01',\n 'movie_camera':'\\ud83c\\udfa5',\n 'moyai':'\\ud83d\\uddff',\n 'mrs_claus':'\\ud83e\\udd36',\n 'muscle':'\\ud83d\\udcaa',\n 'mushroom':'\\ud83c\\udf44',\n 'musical_keyboard':'\\ud83c\\udfb9',\n 'musical_note':'\\ud83c\\udfb5',\n 'musical_score':'\\ud83c\\udfbc',\n 'mute':'\\ud83d\\udd07',\n 'nail_care':'\\ud83d\\udc85',\n 'name_badge':'\\ud83d\\udcdb',\n 'national_park':'\\ud83c\\udfde',\n 'nauseated_face':'\\ud83e\\udd22',\n 'necktie':'\\ud83d\\udc54',\n 'negative_squared_cross_mark':'\\u274e',\n 'nerd_face':'\\ud83e\\udd13',\n 'neutral_face':'\\ud83d\\ude10',\n 'new':'\\ud83c\\udd95',\n 'new_moon':'\\ud83c\\udf11',\n 'new_moon_with_face':'\\ud83c\\udf1a',\n 'newspaper':'\\ud83d\\udcf0',\n 'newspaper_roll':'\\ud83d\\uddde',\n 'next_track_button':'\\u23ed',\n 'ng':'\\ud83c\\udd96',\n 'no_good_man':'\\ud83d\\ude45‍\\u2642\\ufe0f',\n 'no_good_woman':'\\ud83d\\ude45',\n 'night_with_stars':'\\ud83c\\udf03',\n 'no_bell':'\\ud83d\\udd15',\n 'no_bicycles':'\\ud83d\\udeb3',\n 'no_entry':'\\u26d4\\ufe0f',\n 'no_entry_sign':'\\ud83d\\udeab',\n 'no_mobile_phones':'\\ud83d\\udcf5',\n 'no_mouth':'\\ud83d\\ude36',\n 'no_pedestrians':'\\ud83d\\udeb7',\n 'no_smoking':'\\ud83d\\udead',\n 'non-potable_water':'\\ud83d\\udeb1',\n 'nose':'\\ud83d\\udc43',\n 'notebook':'\\ud83d\\udcd3',\n 'notebook_with_decorative_cover':'\\ud83d\\udcd4',\n 'notes':'\\ud83c\\udfb6',\n 'nut_and_bolt':'\\ud83d\\udd29',\n 'o':'\\u2b55\\ufe0f',\n 'o2':'\\ud83c\\udd7e\\ufe0f',\n 'ocean':'\\ud83c\\udf0a',\n 'octopus':'\\ud83d\\udc19',\n 'oden':'\\ud83c\\udf62',\n 'office':'\\ud83c\\udfe2',\n 'oil_drum':'\\ud83d\\udee2',\n 'ok':'\\ud83c\\udd97',\n 'ok_hand':'\\ud83d\\udc4c',\n 'ok_man':'\\ud83d\\ude46‍\\u2642\\ufe0f',\n 'ok_woman':'\\ud83d\\ude46',\n 'old_key':'\\ud83d\\udddd',\n 'older_man':'\\ud83d\\udc74',\n 'older_woman':'\\ud83d\\udc75',\n 'om':'\\ud83d\\udd49',\n 'on':'\\ud83d\\udd1b',\n 'oncoming_automobile':'\\ud83d\\ude98',\n 'oncoming_bus':'\\ud83d\\ude8d',\n 'oncoming_police_car':'\\ud83d\\ude94',\n 'oncoming_taxi':'\\ud83d\\ude96',\n 'open_file_folder':'\\ud83d\\udcc2',\n 'open_hands':'\\ud83d\\udc50',\n 'open_mouth':'\\ud83d\\ude2e',\n 'open_umbrella':'\\u2602\\ufe0f',\n 'ophiuchus':'\\u26ce',\n 'orange_book':'\\ud83d\\udcd9',\n 'orthodox_cross':'\\u2626\\ufe0f',\n 'outbox_tray':'\\ud83d\\udce4',\n 'owl':'\\ud83e\\udd89',\n 'ox':'\\ud83d\\udc02',\n 'package':'\\ud83d\\udce6',\n 'page_facing_up':'\\ud83d\\udcc4',\n 'page_with_curl':'\\ud83d\\udcc3',\n 'pager':'\\ud83d\\udcdf',\n 'paintbrush':'\\ud83d\\udd8c',\n 'palm_tree':'\\ud83c\\udf34',\n 'pancakes':'\\ud83e\\udd5e',\n 'panda_face':'\\ud83d\\udc3c',\n 'paperclip':'\\ud83d\\udcce',\n 'paperclips':'\\ud83d\\udd87',\n 'parasol_on_ground':'\\u26f1',\n 'parking':'\\ud83c\\udd7f\\ufe0f',\n 'part_alternation_mark':'\\u303d\\ufe0f',\n 'partly_sunny':'\\u26c5\\ufe0f',\n 'passenger_ship':'\\ud83d\\udef3',\n 'passport_control':'\\ud83d\\udec2',\n 'pause_button':'\\u23f8',\n 'peace_symbol':'\\u262e\\ufe0f',\n 'peach':'\\ud83c\\udf51',\n 'peanuts':'\\ud83e\\udd5c',\n 'pear':'\\ud83c\\udf50',\n 'pen':'\\ud83d\\udd8a',\n 'pencil2':'\\u270f\\ufe0f',\n 'penguin':'\\ud83d\\udc27',\n 'pensive':'\\ud83d\\ude14',\n 'performing_arts':'\\ud83c\\udfad',\n 'persevere':'\\ud83d\\ude23',\n 'person_fencing':'\\ud83e\\udd3a',\n 'pouting_woman':'\\ud83d\\ude4e',\n 'phone':'\\u260e\\ufe0f',\n 'pick':'\\u26cf',\n 'pig':'\\ud83d\\udc37',\n 'pig2':'\\ud83d\\udc16',\n 'pig_nose':'\\ud83d\\udc3d',\n 'pill':'\\ud83d\\udc8a',\n 'pineapple':'\\ud83c\\udf4d',\n 'ping_pong':'\\ud83c\\udfd3',\n 'pisces':'\\u2653\\ufe0f',\n 'pizza':'\\ud83c\\udf55',\n 'place_of_worship':'\\ud83d\\uded0',\n 'plate_with_cutlery':'\\ud83c\\udf7d',\n 'play_or_pause_button':'\\u23ef',\n 'point_down':'\\ud83d\\udc47',\n 'point_left':'\\ud83d\\udc48',\n 'point_right':'\\ud83d\\udc49',\n 'point_up':'\\u261d\\ufe0f',\n 'point_up_2':'\\ud83d\\udc46',\n 'police_car':'\\ud83d\\ude93',\n 'policewoman':'\\ud83d\\udc6e‍\\u2640\\ufe0f',\n 'poodle':'\\ud83d\\udc29',\n 'popcorn':'\\ud83c\\udf7f',\n 'post_office':'\\ud83c\\udfe3',\n 'postal_horn':'\\ud83d\\udcef',\n 'postbox':'\\ud83d\\udcee',\n 'potable_water':'\\ud83d\\udeb0',\n 'potato':'\\ud83e\\udd54',\n 'pouch':'\\ud83d\\udc5d',\n 'poultry_leg':'\\ud83c\\udf57',\n 'pound':'\\ud83d\\udcb7',\n 'rage':'\\ud83d\\ude21',\n 'pouting_cat':'\\ud83d\\ude3e',\n 'pouting_man':'\\ud83d\\ude4e‍\\u2642\\ufe0f',\n 'pray':'\\ud83d\\ude4f',\n 'prayer_beads':'\\ud83d\\udcff',\n 'pregnant_woman':'\\ud83e\\udd30',\n 'previous_track_button':'\\u23ee',\n 'prince':'\\ud83e\\udd34',\n 'princess':'\\ud83d\\udc78',\n 'printer':'\\ud83d\\udda8',\n 'purple_heart':'\\ud83d\\udc9c',\n 'purse':'\\ud83d\\udc5b',\n 'pushpin':'\\ud83d\\udccc',\n 'put_litter_in_its_place':'\\ud83d\\udeae',\n 'question':'\\u2753',\n 'rabbit':'\\ud83d\\udc30',\n 'rabbit2':'\\ud83d\\udc07',\n 'racehorse':'\\ud83d\\udc0e',\n 'racing_car':'\\ud83c\\udfce',\n 'radio':'\\ud83d\\udcfb',\n 'radio_button':'\\ud83d\\udd18',\n 'radioactive':'\\u2622\\ufe0f',\n 'railway_car':'\\ud83d\\ude83',\n 'railway_track':'\\ud83d\\udee4',\n 'rainbow':'\\ud83c\\udf08',\n 'rainbow_flag':'\\ud83c\\udff3\\ufe0f‍\\ud83c\\udf08',\n 'raised_back_of_hand':'\\ud83e\\udd1a',\n 'raised_hand_with_fingers_splayed':'\\ud83d\\udd90',\n 'raised_hands':'\\ud83d\\ude4c',\n 'raising_hand_woman':'\\ud83d\\ude4b',\n 'raising_hand_man':'\\ud83d\\ude4b‍\\u2642\\ufe0f',\n 'ram':'\\ud83d\\udc0f',\n 'ramen':'\\ud83c\\udf5c',\n 'rat':'\\ud83d\\udc00',\n 'record_button':'\\u23fa',\n 'recycle':'\\u267b\\ufe0f',\n 'red_circle':'\\ud83d\\udd34',\n 'registered':'\\u00ae\\ufe0f',\n 'relaxed':'\\u263a\\ufe0f',\n 'relieved':'\\ud83d\\ude0c',\n 'reminder_ribbon':'\\ud83c\\udf97',\n 'repeat':'\\ud83d\\udd01',\n 'repeat_one':'\\ud83d\\udd02',\n 'rescue_worker_helmet':'\\u26d1',\n 'restroom':'\\ud83d\\udebb',\n 'revolving_hearts':'\\ud83d\\udc9e',\n 'rewind':'\\u23ea',\n 'rhinoceros':'\\ud83e\\udd8f',\n 'ribbon':'\\ud83c\\udf80',\n 'rice':'\\ud83c\\udf5a',\n 'rice_ball':'\\ud83c\\udf59',\n 'rice_cracker':'\\ud83c\\udf58',\n 'rice_scene':'\\ud83c\\udf91',\n 'right_anger_bubble':'\\ud83d\\uddef',\n 'ring':'\\ud83d\\udc8d',\n 'robot':'\\ud83e\\udd16',\n 'rocket':'\\ud83d\\ude80',\n 'rofl':'\\ud83e\\udd23',\n 'roll_eyes':'\\ud83d\\ude44',\n 'roller_coaster':'\\ud83c\\udfa2',\n 'rooster':'\\ud83d\\udc13',\n 'rose':'\\ud83c\\udf39',\n 'rosette':'\\ud83c\\udff5',\n 'rotating_light':'\\ud83d\\udea8',\n 'round_pushpin':'\\ud83d\\udccd',\n 'rowing_man':'\\ud83d\\udea3',\n 'rowing_woman':'\\ud83d\\udea3‍\\u2640\\ufe0f',\n 'rugby_football':'\\ud83c\\udfc9',\n 'running_man':'\\ud83c\\udfc3',\n 'running_shirt_with_sash':'\\ud83c\\udfbd',\n 'running_woman':'\\ud83c\\udfc3‍\\u2640\\ufe0f',\n 'sa':'\\ud83c\\ude02\\ufe0f',\n 'sagittarius':'\\u2650\\ufe0f',\n 'sake':'\\ud83c\\udf76',\n 'sandal':'\\ud83d\\udc61',\n 'santa':'\\ud83c\\udf85',\n 'satellite':'\\ud83d\\udce1',\n 'saxophone':'\\ud83c\\udfb7',\n 'school':'\\ud83c\\udfeb',\n 'school_satchel':'\\ud83c\\udf92',\n 'scissors':'\\u2702\\ufe0f',\n 'scorpion':'\\ud83e\\udd82',\n 'scorpius':'\\u264f\\ufe0f',\n 'scream':'\\ud83d\\ude31',\n 'scream_cat':'\\ud83d\\ude40',\n 'scroll':'\\ud83d\\udcdc',\n 'seat':'\\ud83d\\udcba',\n 'secret':'\\u3299\\ufe0f',\n 'see_no_evil':'\\ud83d\\ude48',\n 'seedling':'\\ud83c\\udf31',\n 'selfie':'\\ud83e\\udd33',\n 'shallow_pan_of_food':'\\ud83e\\udd58',\n 'shamrock':'\\u2618\\ufe0f',\n 'shark':'\\ud83e\\udd88',\n 'shaved_ice':'\\ud83c\\udf67',\n 'sheep':'\\ud83d\\udc11',\n 'shell':'\\ud83d\\udc1a',\n 'shield':'\\ud83d\\udee1',\n 'shinto_shrine':'\\u26e9',\n 'ship':'\\ud83d\\udea2',\n 'shirt':'\\ud83d\\udc55',\n 'shopping':'\\ud83d\\udecd',\n 'shopping_cart':'\\ud83d\\uded2',\n 'shower':'\\ud83d\\udebf',\n 'shrimp':'\\ud83e\\udd90',\n 'signal_strength':'\\ud83d\\udcf6',\n 'six_pointed_star':'\\ud83d\\udd2f',\n 'ski':'\\ud83c\\udfbf',\n 'skier':'\\u26f7',\n 'skull':'\\ud83d\\udc80',\n 'skull_and_crossbones':'\\u2620\\ufe0f',\n 'sleeping':'\\ud83d\\ude34',\n 'sleeping_bed':'\\ud83d\\udecc',\n 'sleepy':'\\ud83d\\ude2a',\n 'slightly_frowning_face':'\\ud83d\\ude41',\n 'slightly_smiling_face':'\\ud83d\\ude42',\n 'slot_machine':'\\ud83c\\udfb0',\n 'small_airplane':'\\ud83d\\udee9',\n 'small_blue_diamond':'\\ud83d\\udd39',\n 'small_orange_diamond':'\\ud83d\\udd38',\n 'small_red_triangle':'\\ud83d\\udd3a',\n 'small_red_triangle_down':'\\ud83d\\udd3b',\n 'smile':'\\ud83d\\ude04',\n 'smile_cat':'\\ud83d\\ude38',\n 'smiley':'\\ud83d\\ude03',\n 'smiley_cat':'\\ud83d\\ude3a',\n 'smiling_imp':'\\ud83d\\ude08',\n 'smirk':'\\ud83d\\ude0f',\n 'smirk_cat':'\\ud83d\\ude3c',\n 'smoking':'\\ud83d\\udeac',\n 'snail':'\\ud83d\\udc0c',\n 'snake':'\\ud83d\\udc0d',\n 'sneezing_face':'\\ud83e\\udd27',\n 'snowboarder':'\\ud83c\\udfc2',\n 'snowflake':'\\u2744\\ufe0f',\n 'snowman':'\\u26c4\\ufe0f',\n 'snowman_with_snow':'\\u2603\\ufe0f',\n 'sob':'\\ud83d\\ude2d',\n 'soccer':'\\u26bd\\ufe0f',\n 'soon':'\\ud83d\\udd1c',\n 'sos':'\\ud83c\\udd98',\n 'sound':'\\ud83d\\udd09',\n 'space_invader':'\\ud83d\\udc7e',\n 'spades':'\\u2660\\ufe0f',\n 'spaghetti':'\\ud83c\\udf5d',\n 'sparkle':'\\u2747\\ufe0f',\n 'sparkler':'\\ud83c\\udf87',\n 'sparkles':'\\u2728',\n 'sparkling_heart':'\\ud83d\\udc96',\n 'speak_no_evil':'\\ud83d\\ude4a',\n 'speaker':'\\ud83d\\udd08',\n 'speaking_head':'\\ud83d\\udde3',\n 'speech_balloon':'\\ud83d\\udcac',\n 'speedboat':'\\ud83d\\udea4',\n 'spider':'\\ud83d\\udd77',\n 'spider_web':'\\ud83d\\udd78',\n 'spiral_calendar':'\\ud83d\\uddd3',\n 'spiral_notepad':'\\ud83d\\uddd2',\n 'spoon':'\\ud83e\\udd44',\n 'squid':'\\ud83e\\udd91',\n 'stadium':'\\ud83c\\udfdf',\n 'star':'\\u2b50\\ufe0f',\n 'star2':'\\ud83c\\udf1f',\n 'star_and_crescent':'\\u262a\\ufe0f',\n 'star_of_david':'\\u2721\\ufe0f',\n 'stars':'\\ud83c\\udf20',\n 'station':'\\ud83d\\ude89',\n 'statue_of_liberty':'\\ud83d\\uddfd',\n 'steam_locomotive':'\\ud83d\\ude82',\n 'stew':'\\ud83c\\udf72',\n 'stop_button':'\\u23f9',\n 'stop_sign':'\\ud83d\\uded1',\n 'stopwatch':'\\u23f1',\n 'straight_ruler':'\\ud83d\\udccf',\n 'strawberry':'\\ud83c\\udf53',\n 'stuck_out_tongue':'\\ud83d\\ude1b',\n 'stuck_out_tongue_closed_eyes':'\\ud83d\\ude1d',\n 'stuck_out_tongue_winking_eye':'\\ud83d\\ude1c',\n 'studio_microphone':'\\ud83c\\udf99',\n 'stuffed_flatbread':'\\ud83e\\udd59',\n 'sun_behind_large_cloud':'\\ud83c\\udf25',\n 'sun_behind_rain_cloud':'\\ud83c\\udf26',\n 'sun_behind_small_cloud':'\\ud83c\\udf24',\n 'sun_with_face':'\\ud83c\\udf1e',\n 'sunflower':'\\ud83c\\udf3b',\n 'sunglasses':'\\ud83d\\ude0e',\n 'sunny':'\\u2600\\ufe0f',\n 'sunrise':'\\ud83c\\udf05',\n 'sunrise_over_mountains':'\\ud83c\\udf04',\n 'surfing_man':'\\ud83c\\udfc4',\n 'surfing_woman':'\\ud83c\\udfc4‍\\u2640\\ufe0f',\n 'sushi':'\\ud83c\\udf63',\n 'suspension_railway':'\\ud83d\\ude9f',\n 'sweat':'\\ud83d\\ude13',\n 'sweat_drops':'\\ud83d\\udca6',\n 'sweat_smile':'\\ud83d\\ude05',\n 'sweet_potato':'\\ud83c\\udf60',\n 'swimming_man':'\\ud83c\\udfca',\n 'swimming_woman':'\\ud83c\\udfca‍\\u2640\\ufe0f',\n 'symbols':'\\ud83d\\udd23',\n 'synagogue':'\\ud83d\\udd4d',\n 'syringe':'\\ud83d\\udc89',\n 'taco':'\\ud83c\\udf2e',\n 'tada':'\\ud83c\\udf89',\n 'tanabata_tree':'\\ud83c\\udf8b',\n 'taurus':'\\u2649\\ufe0f',\n 'taxi':'\\ud83d\\ude95',\n 'tea':'\\ud83c\\udf75',\n 'telephone_receiver':'\\ud83d\\udcde',\n 'telescope':'\\ud83d\\udd2d',\n 'tennis':'\\ud83c\\udfbe',\n 'tent':'\\u26fa\\ufe0f',\n 'thermometer':'\\ud83c\\udf21',\n 'thinking':'\\ud83e\\udd14',\n 'thought_balloon':'\\ud83d\\udcad',\n 'ticket':'\\ud83c\\udfab',\n 'tickets':'\\ud83c\\udf9f',\n 'tiger':'\\ud83d\\udc2f',\n 'tiger2':'\\ud83d\\udc05',\n 'timer_clock':'\\u23f2',\n 'tipping_hand_man':'\\ud83d\\udc81‍\\u2642\\ufe0f',\n 'tired_face':'\\ud83d\\ude2b',\n 'tm':'\\u2122\\ufe0f',\n 'toilet':'\\ud83d\\udebd',\n 'tokyo_tower':'\\ud83d\\uddfc',\n 'tomato':'\\ud83c\\udf45',\n 'tongue':'\\ud83d\\udc45',\n 'top':'\\ud83d\\udd1d',\n 'tophat':'\\ud83c\\udfa9',\n 'tornado':'\\ud83c\\udf2a',\n 'trackball':'\\ud83d\\uddb2',\n 'tractor':'\\ud83d\\ude9c',\n 'traffic_light':'\\ud83d\\udea5',\n 'train':'\\ud83d\\ude8b',\n 'train2':'\\ud83d\\ude86',\n 'tram':'\\ud83d\\ude8a',\n 'triangular_flag_on_post':'\\ud83d\\udea9',\n 'triangular_ruler':'\\ud83d\\udcd0',\n 'trident':'\\ud83d\\udd31',\n 'triumph':'\\ud83d\\ude24',\n 'trolleybus':'\\ud83d\\ude8e',\n 'trophy':'\\ud83c\\udfc6',\n 'tropical_drink':'\\ud83c\\udf79',\n 'tropical_fish':'\\ud83d\\udc20',\n 'truck':'\\ud83d\\ude9a',\n 'trumpet':'\\ud83c\\udfba',\n 'tulip':'\\ud83c\\udf37',\n 'tumbler_glass':'\\ud83e\\udd43',\n 'turkey':'\\ud83e\\udd83',\n 'turtle':'\\ud83d\\udc22',\n 'tv':'\\ud83d\\udcfa',\n 'twisted_rightwards_arrows':'\\ud83d\\udd00',\n 'two_hearts':'\\ud83d\\udc95',\n 'two_men_holding_hands':'\\ud83d\\udc6c',\n 'two_women_holding_hands':'\\ud83d\\udc6d',\n 'u5272':'\\ud83c\\ude39',\n 'u5408':'\\ud83c\\ude34',\n 'u55b6':'\\ud83c\\ude3a',\n 'u6307':'\\ud83c\\ude2f\\ufe0f',\n 'u6708':'\\ud83c\\ude37\\ufe0f',\n 'u6709':'\\ud83c\\ude36',\n 'u6e80':'\\ud83c\\ude35',\n 'u7121':'\\ud83c\\ude1a\\ufe0f',\n 'u7533':'\\ud83c\\ude38',\n 'u7981':'\\ud83c\\ude32',\n 'u7a7a':'\\ud83c\\ude33',\n 'umbrella':'\\u2614\\ufe0f',\n 'unamused':'\\ud83d\\ude12',\n 'underage':'\\ud83d\\udd1e',\n 'unicorn':'\\ud83e\\udd84',\n 'unlock':'\\ud83d\\udd13',\n 'up':'\\ud83c\\udd99',\n 'upside_down_face':'\\ud83d\\ude43',\n 'v':'\\u270c\\ufe0f',\n 'vertical_traffic_light':'\\ud83d\\udea6',\n 'vhs':'\\ud83d\\udcfc',\n 'vibration_mode':'\\ud83d\\udcf3',\n 'video_camera':'\\ud83d\\udcf9',\n 'video_game':'\\ud83c\\udfae',\n 'violin':'\\ud83c\\udfbb',\n 'virgo':'\\u264d\\ufe0f',\n 'volcano':'\\ud83c\\udf0b',\n 'volleyball':'\\ud83c\\udfd0',\n 'vs':'\\ud83c\\udd9a',\n 'vulcan_salute':'\\ud83d\\udd96',\n 'walking_man':'\\ud83d\\udeb6',\n 'walking_woman':'\\ud83d\\udeb6‍\\u2640\\ufe0f',\n 'waning_crescent_moon':'\\ud83c\\udf18',\n 'waning_gibbous_moon':'\\ud83c\\udf16',\n 'warning':'\\u26a0\\ufe0f',\n 'wastebasket':'\\ud83d\\uddd1',\n 'watch':'\\u231a\\ufe0f',\n 'water_buffalo':'\\ud83d\\udc03',\n 'watermelon':'\\ud83c\\udf49',\n 'wave':'\\ud83d\\udc4b',\n 'wavy_dash':'\\u3030\\ufe0f',\n 'waxing_crescent_moon':'\\ud83c\\udf12',\n 'wc':'\\ud83d\\udebe',\n 'weary':'\\ud83d\\ude29',\n 'wedding':'\\ud83d\\udc92',\n 'weight_lifting_man':'\\ud83c\\udfcb\\ufe0f',\n 'weight_lifting_woman':'\\ud83c\\udfcb\\ufe0f‍\\u2640\\ufe0f',\n 'whale':'\\ud83d\\udc33',\n 'whale2':'\\ud83d\\udc0b',\n 'wheel_of_dharma':'\\u2638\\ufe0f',\n 'wheelchair':'\\u267f\\ufe0f',\n 'white_check_mark':'\\u2705',\n 'white_circle':'\\u26aa\\ufe0f',\n 'white_flag':'\\ud83c\\udff3\\ufe0f',\n 'white_flower':'\\ud83d\\udcae',\n 'white_large_square':'\\u2b1c\\ufe0f',\n 'white_medium_small_square':'\\u25fd\\ufe0f',\n 'white_medium_square':'\\u25fb\\ufe0f',\n 'white_small_square':'\\u25ab\\ufe0f',\n 'white_square_button':'\\ud83d\\udd33',\n 'wilted_flower':'\\ud83e\\udd40',\n 'wind_chime':'\\ud83c\\udf90',\n 'wind_face':'\\ud83c\\udf2c',\n 'wine_glass':'\\ud83c\\udf77',\n 'wink':'\\ud83d\\ude09',\n 'wolf':'\\ud83d\\udc3a',\n 'woman':'\\ud83d\\udc69',\n 'woman_artist':'\\ud83d\\udc69‍\\ud83c\\udfa8',\n 'woman_astronaut':'\\ud83d\\udc69‍\\ud83d\\ude80',\n 'woman_cartwheeling':'\\ud83e\\udd38‍\\u2640\\ufe0f',\n 'woman_cook':'\\ud83d\\udc69‍\\ud83c\\udf73',\n 'woman_facepalming':'\\ud83e\\udd26‍\\u2640\\ufe0f',\n 'woman_factory_worker':'\\ud83d\\udc69‍\\ud83c\\udfed',\n 'woman_farmer':'\\ud83d\\udc69‍\\ud83c\\udf3e',\n 'woman_firefighter':'\\ud83d\\udc69‍\\ud83d\\ude92',\n 'woman_health_worker':'\\ud83d\\udc69‍\\u2695\\ufe0f',\n 'woman_judge':'\\ud83d\\udc69‍\\u2696\\ufe0f',\n 'woman_juggling':'\\ud83e\\udd39‍\\u2640\\ufe0f',\n 'woman_mechanic':'\\ud83d\\udc69‍\\ud83d\\udd27',\n 'woman_office_worker':'\\ud83d\\udc69‍\\ud83d\\udcbc',\n 'woman_pilot':'\\ud83d\\udc69‍\\u2708\\ufe0f',\n 'woman_playing_handball':'\\ud83e\\udd3e‍\\u2640\\ufe0f',\n 'woman_playing_water_polo':'\\ud83e\\udd3d‍\\u2640\\ufe0f',\n 'woman_scientist':'\\ud83d\\udc69‍\\ud83d\\udd2c',\n 'woman_shrugging':'\\ud83e\\udd37‍\\u2640\\ufe0f',\n 'woman_singer':'\\ud83d\\udc69‍\\ud83c\\udfa4',\n 'woman_student':'\\ud83d\\udc69‍\\ud83c\\udf93',\n 'woman_teacher':'\\ud83d\\udc69‍\\ud83c\\udfeb',\n 'woman_technologist':'\\ud83d\\udc69‍\\ud83d\\udcbb',\n 'woman_with_turban':'\\ud83d\\udc73‍\\u2640\\ufe0f',\n 'womans_clothes':'\\ud83d\\udc5a',\n 'womans_hat':'\\ud83d\\udc52',\n 'women_wrestling':'\\ud83e\\udd3c‍\\u2640\\ufe0f',\n 'womens':'\\ud83d\\udeba',\n 'world_map':'\\ud83d\\uddfa',\n 'worried':'\\ud83d\\ude1f',\n 'wrench':'\\ud83d\\udd27',\n 'writing_hand':'\\u270d\\ufe0f',\n 'x':'\\u274c',\n 'yellow_heart':'\\ud83d\\udc9b',\n 'yen':'\\ud83d\\udcb4',\n 'yin_yang':'\\u262f\\ufe0f',\n 'yum':'\\ud83d\\ude0b',\n 'zap':'\\u26a1\\ufe0f',\n 'zipper_mouth_face':'\\ud83e\\udd10',\n 'zzz':'\\ud83d\\udca4',\n\n /* special emojis :P */\n 'octocat': '\":octocat:\"',\n 'showdown': 'S'\n};\n","/**\n * Created by Estevao on 31-05-2015.\n */\n\n/**\n * Showdown Converter class\n * @class\n * @param {object} [converterOptions]\n * @returns {Converter}\n */\nshowdown.Converter = function (converterOptions) {\n 'use strict';\n\n var\n /**\n * Options used by this converter\n * @private\n * @type {{}}\n */\n options = {},\n\n /**\n * Language extensions used by this converter\n * @private\n * @type {Array}\n */\n langExtensions = [],\n\n /**\n * Output modifiers extensions used by this converter\n * @private\n * @type {Array}\n */\n outputModifiers = [],\n\n /**\n * Event listeners\n * @private\n * @type {{}}\n */\n listeners = {},\n\n /**\n * The flavor set in this converter\n */\n setConvFlavor = setFlavor,\n\n /**\n * Metadata of the document\n * @type {{parsed: {}, raw: string, format: string}}\n */\n metadata = {\n parsed: {},\n raw: '',\n format: ''\n };\n\n _constructor();\n\n /**\n * Converter constructor\n * @private\n */\n function _constructor () {\n converterOptions = converterOptions || {};\n\n for (var gOpt in globalOptions) {\n if (globalOptions.hasOwnProperty(gOpt)) {\n options[gOpt] = globalOptions[gOpt];\n }\n }\n\n // Merge options\n if (typeof converterOptions === 'object') {\n for (var opt in converterOptions) {\n if (converterOptions.hasOwnProperty(opt)) {\n options[opt] = converterOptions[opt];\n }\n }\n } else {\n throw Error('Converter expects the passed parameter to be an object, but ' + typeof converterOptions +\n ' was passed instead.');\n }\n\n if (options.extensions) {\n showdown.helper.forEach(options.extensions, _parseExtension);\n }\n }\n\n /**\n * Parse extension\n * @param {*} ext\n * @param {string} [name='']\n * @private\n */\n function _parseExtension (ext, name) {\n\n name = name || null;\n // If it's a string, the extension was previously loaded\n if (showdown.helper.isString(ext)) {\n ext = showdown.helper.stdExtName(ext);\n name = ext;\n\n // LEGACY_SUPPORT CODE\n if (showdown.extensions[ext]) {\n console.warn('DEPRECATION WARNING: ' + ext + ' is an old extension that uses a deprecated loading method.' +\n 'Please inform the developer that the extension should be updated!');\n legacyExtensionLoading(showdown.extensions[ext], ext);\n return;\n // END LEGACY SUPPORT CODE\n\n } else if (!showdown.helper.isUndefined(extensions[ext])) {\n ext = extensions[ext];\n\n } else {\n throw Error('Extension \"' + ext + '\" could not be loaded. It was either not found or is not a valid extension.');\n }\n }\n\n if (typeof ext === 'function') {\n ext = ext();\n }\n\n if (!showdown.helper.isArray(ext)) {\n ext = [ext];\n }\n\n var validExt = validate(ext, name);\n if (!validExt.valid) {\n throw Error(validExt.error);\n }\n\n for (var i = 0; i < ext.length; ++i) {\n switch (ext[i].type) {\n\n case 'lang':\n langExtensions.push(ext[i]);\n break;\n\n case 'output':\n outputModifiers.push(ext[i]);\n break;\n }\n if (ext[i].hasOwnProperty('listeners')) {\n for (var ln in ext[i].listeners) {\n if (ext[i].listeners.hasOwnProperty(ln)) {\n listen(ln, ext[i].listeners[ln]);\n }\n }\n }\n }\n\n }\n\n /**\n * LEGACY_SUPPORT\n * @param {*} ext\n * @param {string} name\n */\n function legacyExtensionLoading (ext, name) {\n if (typeof ext === 'function') {\n ext = ext(new showdown.Converter());\n }\n if (!showdown.helper.isArray(ext)) {\n ext = [ext];\n }\n var valid = validate(ext, name);\n\n if (!valid.valid) {\n throw Error(valid.error);\n }\n\n for (var i = 0; i < ext.length; ++i) {\n switch (ext[i].type) {\n case 'lang':\n langExtensions.push(ext[i]);\n break;\n case 'output':\n outputModifiers.push(ext[i]);\n break;\n default:// should never reach here\n throw Error('Extension loader error: Type unrecognized!!!');\n }\n }\n }\n\n /**\n * Listen to an event\n * @param {string} name\n * @param {function} callback\n */\n function listen (name, callback) {\n if (!showdown.helper.isString(name)) {\n throw Error('Invalid argument in converter.listen() method: name must be a string, but ' + typeof name + ' given');\n }\n\n if (typeof callback !== 'function') {\n throw Error('Invalid argument in converter.listen() method: callback must be a function, but ' + typeof callback + ' given');\n }\n\n if (!listeners.hasOwnProperty(name)) {\n listeners[name] = [];\n }\n listeners[name].push(callback);\n }\n\n function rTrimInputText (text) {\n var rsp = text.match(/^\\s*/)[0].length,\n rgx = new RegExp('^\\\\s{0,' + rsp + '}', 'gm');\n return text.replace(rgx, '');\n }\n\n /**\n * Dispatch an event\n * @private\n * @param {string} evtName Event name\n * @param {string} text Text\n * @param {{}} options Converter Options\n * @param {{}} globals\n * @returns {string}\n */\n this._dispatch = function dispatch (evtName, text, options, globals) {\n if (listeners.hasOwnProperty(evtName)) {\n for (var ei = 0; ei < listeners[evtName].length; ++ei) {\n var nText = listeners[evtName][ei](evtName, text, this, options, globals);\n if (nText && typeof nText !== 'undefined') {\n text = nText;\n }\n }\n }\n return text;\n };\n\n /**\n * Listen to an event\n * @param {string} name\n * @param {function} callback\n * @returns {showdown.Converter}\n */\n this.listen = function (name, callback) {\n listen(name, callback);\n return this;\n };\n\n /**\n * Converts a markdown string into HTML\n * @param {string} text\n * @returns {*}\n */\n this.makeHtml = function (text) {\n //check if text is not falsy\n if (!text) {\n return text;\n }\n\n var globals = {\n gHtmlBlocks: [],\n gHtmlMdBlocks: [],\n gHtmlSpans: [],\n gUrls: {},\n gTitles: {},\n gDimensions: {},\n gListLevel: 0,\n hashLinkCounts: {},\n langExtensions: langExtensions,\n outputModifiers: outputModifiers,\n converter: this,\n ghCodeBlocks: [],\n metadata: {\n parsed: {},\n raw: '',\n format: ''\n }\n };\n\n // This lets us use ¨ trema as an escape char to avoid md5 hashes\n // The choice of character is arbitrary; anything that isn't\n // magic in Markdown will work.\n text = text.replace(/¨/g, '¨T');\n\n // Replace $ with ¨D\n // RegExp interprets $ as a special character\n // when it's in a replacement string\n text = text.replace(/\\$/g, '¨D');\n\n // Standardize line endings\n text = text.replace(/\\r\\n/g, '\\n'); // DOS to Unix\n text = text.replace(/\\r/g, '\\n'); // Mac to Unix\n\n // Stardardize line spaces\n text = text.replace(/\\u00A0/g, ' ');\n\n if (options.smartIndentationFix) {\n text = rTrimInputText(text);\n }\n\n // Make sure text begins and ends with a couple of newlines:\n text = '\\n\\n' + text + '\\n\\n';\n\n // detab\n text = showdown.subParser('detab')(text, options, globals);\n\n /**\n * Strip any lines consisting only of spaces and tabs.\n * This makes subsequent regexs easier to write, because we can\n * match consecutive blank lines with /\\n+/ instead of something\n * contorted like /[ \\t]*\\n+/\n */\n text = text.replace(/^[ \\t]+$/mg, '');\n\n //run languageExtensions\n showdown.helper.forEach(langExtensions, function (ext) {\n text = showdown.subParser('runExtension')(ext, text, options, globals);\n });\n\n // run the sub parsers\n text = showdown.subParser('metadata')(text, options, globals);\n text = showdown.subParser('hashPreCodeTags')(text, options, globals);\n text = showdown.subParser('githubCodeBlocks')(text, options, globals);\n text = showdown.subParser('hashHTMLBlocks')(text, options, globals);\n text = showdown.subParser('hashCodeTags')(text, options, globals);\n text = showdown.subParser('stripLinkDefinitions')(text, options, globals);\n text = showdown.subParser('blockGamut')(text, options, globals);\n text = showdown.subParser('unhashHTMLSpans')(text, options, globals);\n text = showdown.subParser('unescapeSpecialChars')(text, options, globals);\n\n // attacklab: Restore dollar signs\n text = text.replace(/¨D/g, '$$');\n\n // attacklab: Restore tremas\n text = text.replace(/¨T/g, '¨');\n\n // render a complete html document instead of a partial if the option is enabled\n text = showdown.subParser('completeHTMLDocument')(text, options, globals);\n\n // Run output modifiers\n showdown.helper.forEach(outputModifiers, function (ext) {\n text = showdown.subParser('runExtension')(ext, text, options, globals);\n });\n\n // update metadata\n metadata = globals.metadata;\n return text;\n };\n\n /**\n * Converts an HTML string into a markdown string\n * @param src\n * @param [HTMLParser] A WHATWG DOM and HTML parser, such as JSDOM. If none is supplied, window.document will be used.\n * @returns {string}\n */\n this.makeMarkdown = this.makeMd = function (src, HTMLParser) {\n\n // replace \\r\\n with \\n\n src = src.replace(/\\r\\n/g, '\\n');\n src = src.replace(/\\r/g, '\\n'); // old macs\n\n // due to an edge case, we need to find this: > <\n // to prevent removing of non silent white spaces\n // ex: this is sparta\n src = src.replace(/>[ \\t]+¨NBSP;<');\n\n if (!HTMLParser) {\n if (window && window.document) {\n HTMLParser = window.document;\n } else {\n throw new Error('HTMLParser is undefined. If in a webworker or nodejs environment, you need to provide a WHATWG DOM and HTML such as JSDOM');\n }\n }\n\n var doc = HTMLParser.createElement('div');\n doc.innerHTML = src;\n\n var globals = {\n preList: substitutePreCodeTags(doc)\n };\n\n // remove all newlines and collapse spaces\n clean(doc);\n\n // some stuff, like accidental reference links must now be escaped\n // TODO\n // doc.innerHTML = doc.innerHTML.replace(/\\[[\\S\\t ]]/);\n\n var nodes = doc.childNodes,\n mdDoc = '';\n\n for (var i = 0; i < nodes.length; i++) {\n mdDoc += showdown.subParser('makeMarkdown.node')(nodes[i], globals);\n }\n\n function clean (node) {\n for (var n = 0; n < node.childNodes.length; ++n) {\n var child = node.childNodes[n];\n if (child.nodeType === 3) {\n if (!/\\S/.test(child.nodeValue)) {\n node.removeChild(child);\n --n;\n } else {\n child.nodeValue = child.nodeValue.split('\\n').join(' ');\n child.nodeValue = child.nodeValue.replace(/(\\s)+/g, '$1');\n }\n } else if (child.nodeType === 1) {\n clean(child);\n }\n }\n }\n\n // find all pre tags and replace contents with placeholder\n // we need this so that we can remove all indentation from html\n // to ease up parsing\n function substitutePreCodeTags (doc) {\n\n var pres = doc.querySelectorAll('pre'),\n presPH = [];\n\n for (var i = 0; i < pres.length; ++i) {\n\n if (pres[i].childElementCount === 1 && pres[i].firstChild.tagName.toLowerCase() === 'code') {\n var content = pres[i].firstChild.innerHTML.trim(),\n language = pres[i].firstChild.getAttribute('data-language') || '';\n\n // if data-language attribute is not defined, then we look for class language-*\n if (language === '') {\n var classes = pres[i].firstChild.className.split(' ');\n for (var c = 0; c < classes.length; ++c) {\n var matches = classes[c].match(/^language-(.+)$/);\n if (matches !== null) {\n language = matches[1];\n break;\n }\n }\n }\n\n // unescape html entities in content\n content = showdown.helper.unescapeHTMLEntities(content);\n\n presPH.push(content);\n pres[i].outerHTML = '';\n } else {\n presPH.push(pres[i].innerHTML);\n pres[i].innerHTML = '';\n pres[i].setAttribute('prenum', i.toString());\n }\n }\n return presPH;\n }\n\n return mdDoc;\n };\n\n /**\n * Set an option of this Converter instance\n * @param {string} key\n * @param {*} value\n */\n this.setOption = function (key, value) {\n options[key] = value;\n };\n\n /**\n * Get the option of this Converter instance\n * @param {string} key\n * @returns {*}\n */\n this.getOption = function (key) {\n return options[key];\n };\n\n /**\n * Get the options of this Converter instance\n * @returns {{}}\n */\n this.getOptions = function () {\n return options;\n };\n\n /**\n * Add extension to THIS converter\n * @param {{}} extension\n * @param {string} [name=null]\n */\n this.addExtension = function (extension, name) {\n name = name || null;\n _parseExtension(extension, name);\n };\n\n /**\n * Use a global registered extension with THIS converter\n * @param {string} extensionName Name of the previously registered extension\n */\n this.useExtension = function (extensionName) {\n _parseExtension(extensionName);\n };\n\n /**\n * Set the flavor THIS converter should use\n * @param {string} name\n */\n this.setFlavor = function (name) {\n if (!flavor.hasOwnProperty(name)) {\n throw Error(name + ' flavor was not found');\n }\n var preset = flavor[name];\n setConvFlavor = name;\n for (var option in preset) {\n if (preset.hasOwnProperty(option)) {\n options[option] = preset[option];\n }\n }\n };\n\n /**\n * Get the currently set flavor of this converter\n * @returns {string}\n */\n this.getFlavor = function () {\n return setConvFlavor;\n };\n\n /**\n * Remove an extension from THIS converter.\n * Note: This is a costly operation. It's better to initialize a new converter\n * and specify the extensions you wish to use\n * @param {Array} extension\n */\n this.removeExtension = function (extension) {\n if (!showdown.helper.isArray(extension)) {\n extension = [extension];\n }\n for (var a = 0; a < extension.length; ++a) {\n var ext = extension[a];\n for (var i = 0; i < langExtensions.length; ++i) {\n if (langExtensions[i] === ext) {\n langExtensions[i].splice(i, 1);\n }\n }\n for (var ii = 0; ii < outputModifiers.length; ++i) {\n if (outputModifiers[ii] === ext) {\n outputModifiers[ii].splice(i, 1);\n }\n }\n }\n };\n\n /**\n * Get all extension of THIS converter\n * @returns {{language: Array, output: Array}}\n */\n this.getAllExtensions = function () {\n return {\n language: langExtensions,\n output: outputModifiers\n };\n };\n\n /**\n * Get the metadata of the previously parsed document\n * @param raw\n * @returns {string|{}}\n */\n this.getMetadata = function (raw) {\n if (raw) {\n return metadata.raw;\n } else {\n return metadata.parsed;\n }\n };\n\n /**\n * Get the metadata format of the previously parsed document\n * @returns {string}\n */\n this.getMetadataFormat = function () {\n return metadata.format;\n };\n\n /**\n * Private: set a single key, value metadata pair\n * @param {string} key\n * @param {string} value\n */\n this._setMetadataPair = function (key, value) {\n metadata.parsed[key] = value;\n };\n\n /**\n * Private: set metadata format\n * @param {string} format\n */\n this._setMetadataFormat = function (format) {\n metadata.format = format;\n };\n\n /**\n * Private: set metadata raw text\n * @param {string} raw\n */\n this._setMetadataRaw = function (raw) {\n metadata.raw = raw;\n };\n};\n","/**\n * Turn Markdown link shortcuts into XHTML tags.\n */\nshowdown.subParser('anchors', function (text, options, globals) {\n 'use strict';\n\n text = globals.converter._dispatch('anchors.before', text, options, globals);\n\n var writeAnchorTag = function (wholeMatch, linkText, linkId, url, m5, m6, title) {\n if (showdown.helper.isUndefined(title)) {\n title = '';\n }\n linkId = linkId.toLowerCase();\n\n // Special case for explicit empty url\n if (wholeMatch.search(/\\(? ?(['\"].*['\"])?\\)$/m) > -1) {\n url = '';\n } else if (!url) {\n if (!linkId) {\n // lower-case and turn embedded newlines into spaces\n linkId = linkText.toLowerCase().replace(/ ?\\n/g, ' ');\n }\n url = '#' + linkId;\n\n if (!showdown.helper.isUndefined(globals.gUrls[linkId])) {\n url = globals.gUrls[linkId];\n if (!showdown.helper.isUndefined(globals.gTitles[linkId])) {\n title = globals.gTitles[linkId];\n }\n } else {\n return wholeMatch;\n }\n }\n\n //url = showdown.helper.escapeCharacters(url, '*_', false); // replaced line to improve performance\n url = url.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n\n var result = '';\n\n return result;\n };\n\n // First, handle reference-style links: [link text] [id]\n text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)] ?(?:\\n *)?\\[(.*?)]()()()()/g, writeAnchorTag);\n\n // Next, inline-style links: [link text](url \"optional title\")\n // cases with crazy urls like ./image/cat1).png\n text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)]()[ \\t]*\\([ \\t]?<([^>]*)>(?:[ \\t]*(([\"'])([^\"]*?)\\5))?[ \\t]?\\)/g,\n writeAnchorTag);\n\n // normal cases\n text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)]()[ \\t]*\\([ \\t]??(?:[ \\t]*(([\"'])([^\"]*?)\\5))?[ \\t]?\\)/g,\n writeAnchorTag);\n\n // handle reference-style shortcuts: [link text]\n // These must come last in case you've also got [link test][1]\n // or [link test](/foo)\n text = text.replace(/\\[([^\\[\\]]+)]()()()()()/g, writeAnchorTag);\n\n // Lastly handle GithubMentions if option is enabled\n if (options.ghMentions) {\n text = text.replace(/(^|\\s)(\\\\)?(@([a-z\\d]+(?:[a-z\\d.-]+?[a-z\\d]+)*))/gmi, function (wm, st, escape, mentions, username) {\n if (escape === '\\\\') {\n return st + mentions;\n }\n\n //check if options.ghMentionsLink is a string\n if (!showdown.helper.isString(options.ghMentionsLink)) {\n throw new Error('ghMentionsLink option must be a string');\n }\n var lnk = options.ghMentionsLink.replace(/\\{u}/g, username),\n target = '';\n if (options.openLinksInNewWindow) {\n target = ' rel=\"noopener noreferrer\" target=\"¨E95Eblank\"';\n }\n return st + '' + mentions + '';\n });\n }\n\n text = globals.converter._dispatch('anchors.after', text, options, globals);\n return text;\n});\n","// url allowed chars [a-z\\d_.~:/?#[]@!$&'()*+,;=-]\n\nvar simpleURLRegex = /([*~_]+|\\b)(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+?\\.[^'\">\\s]+?)()(\\1)?(?=\\s|$)(?![\"<>])/gi,\n simpleURLRegex2 = /([*~_]+|\\b)(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+\\.[^'\">\\s]+?)([.!?,()\\[\\]])?(\\1)?(?=\\s|$)(?![\"<>])/gi,\n delimUrlRegex = /()<(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+)()>()/gi,\n simpleMailRegex = /(^|\\s)(?:mailto:)?([A-Za-z0-9!#$%&'*+-/=?^_`{|}~.]+@[-a-z0-9]+(\\.[-a-z0-9]+)*\\.[a-z]+)(?=$|\\s)/gmi,\n delimMailRegex = /<()(?:mailto:)?([-.\\w]+@[-a-z0-9]+(\\.[-a-z0-9]+)*\\.[a-z]+)>/gi,\n\n replaceLink = function (options) {\n 'use strict';\n return function (wm, leadingMagicChars, link, m2, m3, trailingPunctuation, trailingMagicChars) {\n link = link.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n var lnkTxt = link,\n append = '',\n target = '',\n lmc = leadingMagicChars || '',\n tmc = trailingMagicChars || '';\n if (/^www\\./i.test(link)) {\n link = link.replace(/^www\\./i, 'http://www.');\n }\n if (options.excludeTrailingPunctuationFromURLs && trailingPunctuation) {\n append = trailingPunctuation;\n }\n if (options.openLinksInNewWindow) {\n target = ' rel=\"noopener noreferrer\" target=\"¨E95Eblank\"';\n }\n return lmc + '' + lnkTxt + '' + append + tmc;\n };\n },\n\n replaceMail = function (options, globals) {\n 'use strict';\n return function (wholeMatch, b, mail) {\n var href = 'mailto:';\n b = b || '';\n mail = showdown.subParser('unescapeSpecialChars')(mail, options, globals);\n if (options.encodeEmails) {\n href = showdown.helper.encodeEmailAddress(href + mail);\n mail = showdown.helper.encodeEmailAddress(mail);\n } else {\n href = href + mail;\n }\n return b + '' + mail + '';\n };\n };\n\nshowdown.subParser('autoLinks', function (text, options, globals) {\n 'use strict';\n\n text = globals.converter._dispatch('autoLinks.before', text, options, globals);\n\n text = text.replace(delimUrlRegex, replaceLink(options));\n text = text.replace(delimMailRegex, replaceMail(options, globals));\n\n text = globals.converter._dispatch('autoLinks.after', text, options, globals);\n\n return text;\n});\n\nshowdown.subParser('simplifiedAutoLinks', function (text, options, globals) {\n 'use strict';\n\n if (!options.simplifiedAutoLink) {\n return text;\n }\n\n text = globals.converter._dispatch('simplifiedAutoLinks.before', text, options, globals);\n\n if (options.excludeTrailingPunctuationFromURLs) {\n text = text.replace(simpleURLRegex2, replaceLink(options));\n } else {\n text = text.replace(simpleURLRegex, replaceLink(options));\n }\n text = text.replace(simpleMailRegex, replaceMail(options, globals));\n\n text = globals.converter._dispatch('simplifiedAutoLinks.after', text, options, globals);\n\n return text;\n});\n","/**\n * These are all the transformations that form block-level\n * tags like paragraphs, headers, and list items.\n */\nshowdown.subParser('blockGamut', function (text, options, globals) {\n 'use strict';\n\n text = globals.converter._dispatch('blockGamut.before', text, options, globals);\n\n // we parse blockquotes first so that we can have headings and hrs\n // inside blockquotes\n text = showdown.subParser('blockQuotes')(text, options, globals);\n text = showdown.subParser('headers')(text, options, globals);\n\n // Do Horizontal Rules:\n text = showdown.subParser('horizontalRule')(text, options, globals);\n\n text = showdown.subParser('lists')(text, options, globals);\n text = showdown.subParser('codeBlocks')(text, options, globals);\n text = showdown.subParser('tables')(text, options, globals);\n\n // We already ran _HashHTMLBlocks() before, in Markdown(), but that\n // was to escape raw HTML in the original Markdown source. This time,\n // we're escaping the markup we've just created, so that we don't wrap\n //

tags around block-level tags.\n text = showdown.subParser('hashHTMLBlocks')(text, options, globals);\n text = showdown.subParser('paragraphs')(text, options, globals);\n\n text = globals.converter._dispatch('blockGamut.after', text, options, globals);\n\n return text;\n});\n","showdown.subParser('blockQuotes', function (text, options, globals) {\n 'use strict';\n\n text = globals.converter._dispatch('blockQuotes.before', text, options, globals);\n\n // add a couple extra lines after the text and endtext mark\n text = text + '\\n\\n';\n\n var rgx = /(^ {0,3}>[ \\t]?.+\\n(.+\\n)*\\n*)+/gm;\n\n if (options.splitAdjacentBlockquotes) {\n rgx = /^ {0,3}>[\\s\\S]*?(?:\\n\\n)/gm;\n }\n\n text = text.replace(rgx, function (bq) {\n // attacklab: hack around Konqueror 3.5.4 bug:\n // \"----------bug\".replace(/^-/g,\"\") == \"bug\"\n bq = bq.replace(/^[ \\t]*>[ \\t]?/gm, ''); // trim one level of quoting\n\n // attacklab: clean up hack\n bq = bq.replace(/¨0/g, '');\n\n bq = bq.replace(/^[ \\t]+$/gm, ''); // trim whitespace-only lines\n bq = showdown.subParser('githubCodeBlocks')(bq, options, globals);\n bq = showdown.subParser('blockGamut')(bq, options, globals); // recurse\n\n bq = bq.replace(/(^|\\n)/g, '$1 ');\n // These leading spaces screw with 

 content, so we need to fix that:\n    bq = bq.replace(/(\\s*
[^\\r]+?<\\/pre>)/gm, function (wholeMatch, m1) {\n      var pre = m1;\n      // attacklab: hack around Konqueror 3.5.4 bug:\n      pre = pre.replace(/^  /mg, '¨0');\n      pre = pre.replace(/¨0/g, '');\n      return pre;\n    });\n\n    return showdown.subParser('hashBlock')('
\\n' + bq + '\\n
', options, globals);\n  });\n\n  text = globals.converter._dispatch('blockQuotes.after', text, options, globals);\n  return text;\n});\n","/**\n * Process Markdown `
` blocks.\n */\nshowdown.subParser('codeBlocks', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('codeBlocks.before', text, options, globals);\n\n  // sentinel workarounds for lack of \\A and \\Z, safari\\khtml bug\n  text += '¨0';\n\n  var pattern = /(?:\\n\\n|^)((?:(?:[ ]{4}|\\t).*\\n+)+)(\\n*[ ]{0,3}[^ \\t\\n]|(?=¨0))/g;\n  text = text.replace(pattern, function (wholeMatch, m1, m2) {\n    var codeblock = m1,\n        nextChar = m2,\n        end = '\\n';\n\n    codeblock = showdown.subParser('outdent')(codeblock, options, globals);\n    codeblock = showdown.subParser('encodeCode')(codeblock, options, globals);\n    codeblock = showdown.subParser('detab')(codeblock, options, globals);\n    codeblock = codeblock.replace(/^\\n+/g, ''); // trim leading newlines\n    codeblock = codeblock.replace(/\\n+$/g, ''); // trim trailing newlines\n\n    if (options.omitExtraWLInCodeBlocks) {\n      end = '';\n    }\n\n    codeblock = '
' + codeblock + end + '
';\n\n    return showdown.subParser('hashBlock')(codeblock, options, globals) + nextChar;\n  });\n\n  // strip sentinel\n  text = text.replace(/¨0/, '');\n\n  text = globals.converter._dispatch('codeBlocks.after', text, options, globals);\n  return text;\n});\n","/**\n *\n *   *  Backtick quotes are used for  spans.\n *\n *   *  You can use multiple backticks as the delimiters if you want to\n *     include literal backticks in the code span. So, this input:\n *\n *         Just type ``foo `bar` baz`` at the prompt.\n *\n *       Will translate to:\n *\n *         
Just type foo `bar` baz at the prompt.
\n *\n *    There's no arbitrary limit to the number of backticks you\n *    can use as delimters. If you need three consecutive backticks\n *    in your code, use four for delimiters, etc.\n *\n *  *  You can use spaces to get literal backticks at the edges:\n *\n *         ... type `` `bar` `` ...\n *\n *       Turns to:\n *\n *         ... type `bar` ...\n */\nshowdown.subParser('codeSpans', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('codeSpans.before', text, options, globals);\n\n  if (typeof text === 'undefined') {\n    text = '';\n  }\n  text = text.replace(/(^|[^\\\\])(`+)([^\\r]*?[^`])\\2(?!`)/gm,\n    function (wholeMatch, m1, m2, m3) {\n      var c = m3;\n      c = c.replace(/^([ \\t]*)/g, '');\t// leading whitespace\n      c = c.replace(/[ \\t]*$/g, '');\t// trailing whitespace\n      c = showdown.subParser('encodeCode')(c, options, globals);\n      c = m1 + '' + c + '';\n      c = showdown.subParser('hashHTMLSpans')(c, options, globals);\n      return c;\n    }\n  );\n\n  text = globals.converter._dispatch('codeSpans.after', text, options, globals);\n  return text;\n});\n","/**\n * Create a full HTML document from the processed markdown\n */\nshowdown.subParser('completeHTMLDocument', function (text, options, globals) {\n  'use strict';\n\n  if (!options.completeHTMLDocument) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('completeHTMLDocument.before', text, options, globals);\n\n  var doctype = 'html',\n      doctypeParsed = '\\n',\n      title = '',\n      charset = '\\n',\n      lang = '',\n      metadata = '';\n\n  if (typeof globals.metadata.parsed.doctype !== 'undefined') {\n    doctypeParsed = '\\n';\n    doctype = globals.metadata.parsed.doctype.toString().toLowerCase();\n    if (doctype === 'html' || doctype === 'html5') {\n      charset = '';\n    }\n  }\n\n  for (var meta in globals.metadata.parsed) {\n    if (globals.metadata.parsed.hasOwnProperty(meta)) {\n      switch (meta.toLowerCase()) {\n        case 'doctype':\n          break;\n\n        case 'title':\n          title = '' +  globals.metadata.parsed.title + '\\n';\n          break;\n\n        case 'charset':\n          if (doctype === 'html' || doctype === 'html5') {\n            charset = '\\n';\n          } else {\n            charset = '\\n';\n          }\n          break;\n\n        case 'language':\n        case 'lang':\n          lang = ' lang=\"' + globals.metadata.parsed[meta] + '\"';\n          metadata += '\\n';\n          break;\n\n        default:\n          metadata += '\\n';\n      }\n    }\n  }\n\n  text = doctypeParsed + '\\n\\n' + title + charset + metadata + '\\n\\n' + text.trim() + '\\n\\n';\n\n  text = globals.converter._dispatch('completeHTMLDocument.after', text, options, globals);\n  return text;\n});\n","/**\n * Convert all tabs to spaces\n */\nshowdown.subParser('detab', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('detab.before', text, options, globals);\n\n  // expand first n-1 tabs\n  text = text.replace(/\\t(?=\\t)/g, '    '); // g_tab_width\n\n  // replace the nth with two sentinels\n  text = text.replace(/\\t/g, '¨A¨B');\n\n  // use the sentinel to anchor our regex so it doesn't explode\n  text = text.replace(/¨B(.+?)¨A/g, function (wholeMatch, m1) {\n    var leadingText = m1,\n        numSpaces = 4 - leadingText.length % 4;  // g_tab_width\n\n    // there *must* be a better way to do this:\n    for (var i = 0; i < numSpaces; i++) {\n      leadingText += ' ';\n    }\n\n    return leadingText;\n  });\n\n  // clean up sentinels\n  text = text.replace(/¨A/g, '    ');  // g_tab_width\n  text = text.replace(/¨B/g, '');\n\n  text = globals.converter._dispatch('detab.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('ellipsis', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('ellipsis.before', text, options, globals);\n\n  text = text.replace(/\\.\\.\\./g, '…');\n\n  text = globals.converter._dispatch('ellipsis.after', text, options, globals);\n\n  return text;\n});\n","/**\n * Turn emoji codes into emojis\n *\n * List of supported emojis: https://github.com/showdownjs/showdown/wiki/Emojis\n */\nshowdown.subParser('emoji', function (text, options, globals) {\n  'use strict';\n\n  if (!options.emoji) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('emoji.before', text, options, globals);\n\n  var emojiRgx = /:([\\S]+?):/g;\n\n  text = text.replace(emojiRgx, function (wm, emojiCode) {\n    if (showdown.helper.emojis.hasOwnProperty(emojiCode)) {\n      return showdown.helper.emojis[emojiCode];\n    }\n    return wm;\n  });\n\n  text = globals.converter._dispatch('emoji.after', text, options, globals);\n\n  return text;\n});\n","/**\n * Smart processing for ampersands and angle brackets that need to be encoded.\n */\nshowdown.subParser('encodeAmpsAndAngles', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('encodeAmpsAndAngles.before', text, options, globals);\n\n  // Ampersand-encoding based entirely on Nat Irons's Amputator MT plugin:\n  // http://bumppo.net/projects/amputator/\n  text = text.replace(/&(?!#?[xX]?(?:[0-9a-fA-F]+|\\w+);)/g, '&');\n\n  // Encode naked <'s\n  text = text.replace(/<(?![a-z\\/?$!])/gi, '<');\n\n  // Encode <\n  text = text.replace(/\n  text = text.replace(/>/g, '>');\n\n  text = globals.converter._dispatch('encodeAmpsAndAngles.after', text, options, globals);\n  return text;\n});\n","/**\n * Returns the string, with after processing the following backslash escape sequences.\n *\n * attacklab: The polite way to do this is with the new escapeCharacters() function:\n *\n *    text = escapeCharacters(text,\"\\\\\",true);\n *    text = escapeCharacters(text,\"`*_{}[]()>#+-.!\",true);\n *\n * ...but we're sidestepping its use of the (slow) RegExp constructor\n * as an optimization for Firefox.  This function gets called a LOT.\n */\nshowdown.subParser('encodeBackslashEscapes', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('encodeBackslashEscapes.before', text, options, globals);\n\n  text = text.replace(/\\\\(\\\\)/g, showdown.helper.escapeCharactersCallback);\n  text = text.replace(/\\\\([`*_{}\\[\\]()>#+.!~=|-])/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('encodeBackslashEscapes.after', text, options, globals);\n  return text;\n});\n","/**\n * Encode/escape certain characters inside Markdown code runs.\n * The point is that in code, these characters are literals,\n * and lose their special Markdown meanings.\n */\nshowdown.subParser('encodeCode', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('encodeCode.before', text, options, globals);\n\n  // Encode all ampersands; HTML entities are not\n  // entities within a Markdown code span.\n  text = text\n    .replace(/&/g, '&')\n  // Do the angle bracket song and dance:\n    .replace(//g, '>')\n  // Now, escape characters that are magic in Markdown:\n    .replace(/([*_{}\\[\\]\\\\=~-])/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('encodeCode.after', text, options, globals);\n  return text;\n});\n","/**\n * Within tags -- meaning between < and > -- encode [\\ ` * _ ~ =] so they\n * don't conflict with their use in Markdown for code, italics and strong.\n */\nshowdown.subParser('escapeSpecialCharsWithinTagAttributes', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('escapeSpecialCharsWithinTagAttributes.before', text, options, globals);\n\n  // Build a regex to find HTML tags.\n  var tags     = /<\\/?[a-z\\d_:-]+(?:[\\s]+[\\s\\S]+?)?>/gi,\n      comments = /-]|-[^>])(?:[^-]|-[^-])*)--)>/gi;\n\n  text = text.replace(tags, function (wholeMatch) {\n    return wholeMatch\n      .replace(/(.)<\\/?code>(?=.)/g, '$1`')\n      .replace(/([\\\\`*_~=|])/g, showdown.helper.escapeCharactersCallback);\n  });\n\n  text = text.replace(comments, function (wholeMatch) {\n    return wholeMatch\n      .replace(/([\\\\`*_~=|])/g, showdown.helper.escapeCharactersCallback);\n  });\n\n  text = globals.converter._dispatch('escapeSpecialCharsWithinTagAttributes.after', text, options, globals);\n  return text;\n});\n","/**\n * Handle github codeblocks prior to running HashHTML so that\n * HTML contained within the codeblock gets escaped properly\n * Example:\n * ```ruby\n *     def hello_world(x)\n *       puts \"Hello, #{x}\"\n *     end\n * ```\n */\nshowdown.subParser('githubCodeBlocks', function (text, options, globals) {\n  'use strict';\n\n  // early exit if option is not enabled\n  if (!options.ghCodeBlocks) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('githubCodeBlocks.before', text, options, globals);\n\n  text += '¨0';\n\n  text = text.replace(/(?:^|\\n)(?: {0,3})(```+|~~~+)(?: *)([^\\s`~]*)\\n([\\s\\S]*?)\\n(?: {0,3})\\1/g, function (wholeMatch, delim, language, codeblock) {\n    var end = (options.omitExtraWLInCodeBlocks) ? '' : '\\n';\n\n    // First parse the github code block\n    codeblock = showdown.subParser('encodeCode')(codeblock, options, globals);\n    codeblock = showdown.subParser('detab')(codeblock, options, globals);\n    codeblock = codeblock.replace(/^\\n+/g, ''); // trim leading newlines\n    codeblock = codeblock.replace(/\\n+$/g, ''); // trim trailing whitespace\n\n    codeblock = '
' + codeblock + end + '
';\n\n    codeblock = showdown.subParser('hashBlock')(codeblock, options, globals);\n\n    // Since GHCodeblocks can be false positives, we need to\n    // store the primitive text and the parsed text in a global var,\n    // and then return a token\n    return '\\n\\n¨G' + (globals.ghCodeBlocks.push({text: wholeMatch, codeblock: codeblock}) - 1) + 'G\\n\\n';\n  });\n\n  // attacklab: strip sentinel\n  text = text.replace(/¨0/, '');\n\n  return globals.converter._dispatch('githubCodeBlocks.after', text, options, globals);\n});\n","showdown.subParser('hashBlock', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashBlock.before', text, options, globals);\n  text = text.replace(/(^\\n+|\\n+$)/g, '');\n  text = '\\n\\n¨K' + (globals.gHtmlBlocks.push(text) - 1) + 'K\\n\\n';\n  text = globals.converter._dispatch('hashBlock.after', text, options, globals);\n  return text;\n});\n","/**\n * Hash and escape  elements that should not be parsed as markdown\n */\nshowdown.subParser('hashCodeTags', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashCodeTags.before', text, options, globals);\n\n  var repFunc = function (wholeMatch, match, left, right) {\n    var codeblock = left + showdown.subParser('encodeCode')(match, options, globals) + right;\n    return '¨C' + (globals.gHtmlSpans.push(codeblock) - 1) + 'C';\n  };\n\n  // Hash naked \n  text = showdown.helper.replaceRecursiveRegExp(text, repFunc, ']*>', '', 'gim');\n\n  text = globals.converter._dispatch('hashCodeTags.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('hashElement', function (text, options, globals) {\n  'use strict';\n\n  return function (wholeMatch, m1) {\n    var blockText = m1;\n\n    // Undo double lines\n    blockText = blockText.replace(/\\n\\n/g, '\\n');\n    blockText = blockText.replace(/^\\n/, '');\n\n    // strip trailing blank lines\n    blockText = blockText.replace(/\\n+$/g, '');\n\n    // Replace the element text with a marker (\"¨KxK\" where x is its key)\n    blockText = '\\n\\n¨K' + (globals.gHtmlBlocks.push(blockText) - 1) + 'K\\n\\n';\n\n    return blockText;\n  };\n});\n","showdown.subParser('hashHTMLBlocks', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashHTMLBlocks.before', text, options, globals);\n\n  var blockTags = [\n        'pre',\n        'div',\n        'h1',\n        'h2',\n        'h3',\n        'h4',\n        'h5',\n        'h6',\n        'blockquote',\n        'table',\n        'dl',\n        'ol',\n        'ul',\n        'script',\n        'noscript',\n        'form',\n        'fieldset',\n        'iframe',\n        'math',\n        'style',\n        'section',\n        'header',\n        'footer',\n        'nav',\n        'article',\n        'aside',\n        'address',\n        'audio',\n        'canvas',\n        'figure',\n        'hgroup',\n        'output',\n        'video',\n        'p'\n      ],\n      repFunc = function (wholeMatch, match, left, right) {\n        var txt = wholeMatch;\n        // check if this html element is marked as markdown\n        // if so, it's contents should be parsed as markdown\n        if (left.search(/\\bmarkdown\\b/) !== -1) {\n          txt = left + globals.converter.makeHtml(match) + right;\n        }\n        return '\\n\\n¨K' + (globals.gHtmlBlocks.push(txt) - 1) + 'K\\n\\n';\n      };\n\n  if (options.backslashEscapesHTMLTags) {\n    // encode backslash escaped HTML tags\n    text = text.replace(/\\\\<(\\/?[^>]+?)>/g, function (wm, inside) {\n      return '<' + inside + '>';\n    });\n  }\n\n  // hash HTML Blocks\n  for (var i = 0; i < blockTags.length; ++i) {\n\n    var opTagPos,\n        rgx1     = new RegExp('^ {0,3}(<' + blockTags[i] + '\\\\b[^>]*>)', 'im'),\n        patLeft  = '<' + blockTags[i] + '\\\\b[^>]*>',\n        patRight = '';\n    // 1. Look for the first position of the first opening HTML tag in the text\n    while ((opTagPos = showdown.helper.regexIndexOf(text, rgx1)) !== -1) {\n\n      // if the HTML tag is \\ escaped, we need to escape it and break\n\n\n      //2. Split the text in that position\n      var subTexts = showdown.helper.splitAtIndex(text, opTagPos),\n          //3. Match recursively\n          newSubText1 = showdown.helper.replaceRecursiveRegExp(subTexts[1], repFunc, patLeft, patRight, 'im');\n\n      // prevent an infinite loop\n      if (newSubText1 === subTexts[1]) {\n        break;\n      }\n      text = subTexts[0].concat(newSubText1);\n    }\n  }\n  // HR SPECIAL CASE\n  text = text.replace(/(\\n {0,3}(<(hr)\\b([^<>])*?\\/?>)[ \\t]*(?=\\n{2,}))/g,\n    showdown.subParser('hashElement')(text, options, globals));\n\n  // Special case for standalone HTML comments\n  text = showdown.helper.replaceRecursiveRegExp(text, function (txt) {\n    return '\\n\\n¨K' + (globals.gHtmlBlocks.push(txt) - 1) + 'K\\n\\n';\n  }, '^ {0,3}', 'gm');\n\n  // PHP and ASP-style processor instructions ( and <%...%>)\n  text = text.replace(/(?:\\n\\n)( {0,3}(?:<([?%])[^\\r]*?\\2>)[ \\t]*(?=\\n{2,}))/g,\n    showdown.subParser('hashElement')(text, options, globals));\n\n  text = globals.converter._dispatch('hashHTMLBlocks.after', text, options, globals);\n  return text;\n});\n","/**\n * Hash span elements that should not be parsed as markdown\n */\nshowdown.subParser('hashHTMLSpans', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashHTMLSpans.before', text, options, globals);\n\n  function hashHTMLSpan (html) {\n    return '¨C' + (globals.gHtmlSpans.push(html) - 1) + 'C';\n  }\n\n  // Hash Self Closing tags\n  text = text.replace(/<[^>]+?\\/>/gi, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash tags without properties\n  text = text.replace(/<([^>]+?)>[\\s\\S]*?<\\/\\1>/g, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash tags with properties\n  text = text.replace(/<([^>]+?)\\s[^>]+?>[\\s\\S]*?<\\/\\1>/g, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash self closing tags without />\n  text = text.replace(/<[^>]+?>/gi, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  /*showdown.helper.matchRecursiveRegExp(text, ']*>', '', 'gi');*/\n\n  text = globals.converter._dispatch('hashHTMLSpans.after', text, options, globals);\n  return text;\n});\n\n/**\n * Unhash HTML spans\n */\nshowdown.subParser('unhashHTMLSpans', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('unhashHTMLSpans.before', text, options, globals);\n\n  for (var i = 0; i < globals.gHtmlSpans.length; ++i) {\n    var repText = globals.gHtmlSpans[i],\n        // limiter to prevent infinite loop (assume 10 as limit for recurse)\n        limit = 0;\n\n    while (/¨C(\\d+)C/.test(repText)) {\n      var num = RegExp.$1;\n      repText = repText.replace('¨C' + num + 'C', globals.gHtmlSpans[num]);\n      if (limit === 10) {\n        console.error('maximum nesting of 10 spans reached!!!');\n        break;\n      }\n      ++limit;\n    }\n    text = text.replace('¨C' + i + 'C', repText);\n  }\n\n  text = globals.converter._dispatch('unhashHTMLSpans.after', text, options, globals);\n  return text;\n});\n","/**\n * Hash and escape 
 elements that should not be parsed as markdown\n */\nshowdown.subParser('hashPreCodeTags', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashPreCodeTags.before', text, options, globals);\n\n  var repFunc = function (wholeMatch, match, left, right) {\n    // encode html entities\n    var codeblock = left + showdown.subParser('encodeCode')(match, options, globals) + right;\n    return '\\n\\n¨G' + (globals.ghCodeBlocks.push({text: wholeMatch, codeblock: codeblock}) - 1) + 'G\\n\\n';\n  };\n\n  // Hash 
\n  text = showdown.helper.replaceRecursiveRegExp(text, repFunc, '^ {0,3}]*>\\\\s*]*>', '^ {0,3}\\\\s*
', 'gim');\n\n  text = globals.converter._dispatch('hashPreCodeTags.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('headers', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('headers.before', text, options, globals);\n\n  var headerLevelStart = (isNaN(parseInt(options.headerLevelStart))) ? 1 : parseInt(options.headerLevelStart),\n\n      // Set text-style headers:\n      //\tHeader 1\n      //\t========\n      //\n      //\tHeader 2\n      //\t--------\n      //\n      setextRegexH1 = (options.smoothLivePreview) ? /^(.+)[ \\t]*\\n={2,}[ \\t]*\\n+/gm : /^(.+)[ \\t]*\\n=+[ \\t]*\\n+/gm,\n      setextRegexH2 = (options.smoothLivePreview) ? /^(.+)[ \\t]*\\n-{2,}[ \\t]*\\n+/gm : /^(.+)[ \\t]*\\n-+[ \\t]*\\n+/gm;\n\n  text = text.replace(setextRegexH1, function (wholeMatch, m1) {\n\n    var spanGamut = showdown.subParser('spanGamut')(m1, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m1) + '\"',\n        hLevel = headerLevelStart,\n        hashBlock = '' + spanGamut + '';\n    return showdown.subParser('hashBlock')(hashBlock, options, globals);\n  });\n\n  text = text.replace(setextRegexH2, function (matchFound, m1) {\n    var spanGamut = showdown.subParser('spanGamut')(m1, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m1) + '\"',\n        hLevel = headerLevelStart + 1,\n        hashBlock = '' + spanGamut + '';\n    return showdown.subParser('hashBlock')(hashBlock, options, globals);\n  });\n\n  // atx-style headers:\n  //  # Header 1\n  //  ## Header 2\n  //  ## Header 2 with closing hashes ##\n  //  ...\n  //  ###### Header 6\n  //\n  var atxStyle = (options.requireSpaceBeforeHeadingText) ? /^(#{1,6})[ \\t]+(.+?)[ \\t]*#*\\n+/gm : /^(#{1,6})[ \\t]*(.+?)[ \\t]*#*\\n+/gm;\n\n  text = text.replace(atxStyle, function (wholeMatch, m1, m2) {\n    var hText = m2;\n    if (options.customizedHeaderId) {\n      hText = m2.replace(/\\s?\\{([^{]+?)}\\s*$/, '');\n    }\n\n    var span = showdown.subParser('spanGamut')(hText, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m2) + '\"',\n        hLevel = headerLevelStart - 1 + m1.length,\n        header = '' + span + '';\n\n    return showdown.subParser('hashBlock')(header, options, globals);\n  });\n\n  function headerId (m) {\n    var title,\n        prefix;\n\n    // It is separate from other options to allow combining prefix and customized\n    if (options.customizedHeaderId) {\n      var match = m.match(/\\{([^{]+?)}\\s*$/);\n      if (match && match[1]) {\n        m = match[1];\n      }\n    }\n\n    title = m;\n\n    // Prefix id to prevent causing inadvertent pre-existing style matches.\n    if (showdown.helper.isString(options.prefixHeaderId)) {\n      prefix = options.prefixHeaderId;\n    } else if (options.prefixHeaderId === true) {\n      prefix = 'section-';\n    } else {\n      prefix = '';\n    }\n\n    if (!options.rawPrefixHeaderId) {\n      title = prefix + title;\n    }\n\n    if (options.ghCompatibleHeaderId) {\n      title = title\n        .replace(/ /g, '-')\n        // replace previously escaped chars (&, ¨ and $)\n        .replace(/&/g, '')\n        .replace(/¨T/g, '')\n        .replace(/¨D/g, '')\n        // replace rest of the chars (&~$ are repeated as they might have been escaped)\n        // borrowed from github's redcarpet (some they should produce similar results)\n        .replace(/[&+$,\\/:;=?@\"#{}|^¨~\\[\\]`\\\\*)(%.!'<>]/g, '')\n        .toLowerCase();\n    } else if (options.rawHeaderId) {\n      title = title\n        .replace(/ /g, '-')\n        // replace previously escaped chars (&, ¨ and $)\n        .replace(/&/g, '&')\n        .replace(/¨T/g, '¨')\n        .replace(/¨D/g, '$')\n        // replace \" and '\n        .replace(/[\"']/g, '-')\n        .toLowerCase();\n    } else {\n      title = title\n        .replace(/[^\\w]/g, '')\n        .toLowerCase();\n    }\n\n    if (options.rawPrefixHeaderId) {\n      title = prefix + title;\n    }\n\n    if (globals.hashLinkCounts[title]) {\n      title = title + '-' + (globals.hashLinkCounts[title]++);\n    } else {\n      globals.hashLinkCounts[title] = 1;\n    }\n    return title;\n  }\n\n  text = globals.converter._dispatch('headers.after', text, options, globals);\n  return text;\n});\n","/**\n * Turn Markdown link shortcuts into XHTML  tags.\n */\nshowdown.subParser('horizontalRule', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('horizontalRule.before', text, options, globals);\n\n  var key = showdown.subParser('hashBlock')('
', options, globals);\n  text = text.replace(/^ {0,2}( ?-){3,}[ \\t]*$/gm, key);\n  text = text.replace(/^ {0,2}( ?\\*){3,}[ \\t]*$/gm, key);\n  text = text.replace(/^ {0,2}( ?_){3,}[ \\t]*$/gm, key);\n\n  text = globals.converter._dispatch('horizontalRule.after', text, options, globals);\n  return text;\n});\n","/**\n * Turn Markdown image shortcuts into  tags.\n */\nshowdown.subParser('images', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('images.before', text, options, globals);\n\n  var inlineRegExp      = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]??(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:([\"'])([^\"]*?)\\6)?[ \\t]?\\)/g,\n      crazyRegExp       = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]?<([^>]*)>(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:(?:([\"'])([^\"]*?)\\6))?[ \\t]?\\)/g,\n      base64RegExp      = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]??(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:([\"'])([^\"]*?)\\6)?[ \\t]?\\)/g,\n      referenceRegExp   = /!\\[([^\\]]*?)] ?(?:\\n *)?\\[([\\s\\S]*?)]()()()()()/g,\n      refShortcutRegExp = /!\\[([^\\[\\]]+)]()()()()()/g;\n\n  function writeImageTagBase64 (wholeMatch, altText, linkId, url, width, height, m5, title) {\n    url = url.replace(/\\s/g, '');\n    return writeImageTag (wholeMatch, altText, linkId, url, width, height, m5, title);\n  }\n\n  function writeImageTag (wholeMatch, altText, linkId, url, width, height, m5, title) {\n\n    var gUrls   = globals.gUrls,\n        gTitles = globals.gTitles,\n        gDims   = globals.gDimensions;\n\n    linkId = linkId.toLowerCase();\n\n    if (!title) {\n      title = '';\n    }\n    // Special case for explicit empty url\n    if (wholeMatch.search(/\\(? ?(['\"].*['\"])?\\)$/m) > -1) {\n      url = '';\n\n    } else if (url === '' || url === null) {\n      if (linkId === '' || linkId === null) {\n        // lower-case and turn embedded newlines into spaces\n        linkId = altText.toLowerCase().replace(/ ?\\n/g, ' ');\n      }\n      url = '#' + linkId;\n\n      if (!showdown.helper.isUndefined(gUrls[linkId])) {\n        url = gUrls[linkId];\n        if (!showdown.helper.isUndefined(gTitles[linkId])) {\n          title = gTitles[linkId];\n        }\n        if (!showdown.helper.isUndefined(gDims[linkId])) {\n          width = gDims[linkId].width;\n          height = gDims[linkId].height;\n        }\n      } else {\n        return wholeMatch;\n      }\n    }\n\n    altText = altText\n      .replace(/\"/g, '"')\n    //altText = showdown.helper.escapeCharacters(altText, '*_', false);\n      .replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n    //url = showdown.helper.escapeCharacters(url, '*_', false);\n    url = url.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n    var result = '\"'x \"optional title\")\n\n  // base64 encoded images\n  text = text.replace(base64RegExp, writeImageTagBase64);\n\n  // cases with crazy urls like ./image/cat1).png\n  text = text.replace(crazyRegExp, writeImageTag);\n\n  // normal cases\n  text = text.replace(inlineRegExp, writeImageTag);\n\n  // handle reference-style shortcuts: ![img text]\n  text = text.replace(refShortcutRegExp, writeImageTag);\n\n  text = globals.converter._dispatch('images.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('italicsAndBold', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('italicsAndBold.before', text, options, globals);\n\n  // it's faster to have 3 separate regexes for each case than have just one\n  // because of backtracing, in some cases, it could lead to an exponential effect\n  // called \"catastrophic backtrace\". Ominous!\n\n  function parseInside (txt, left, right) {\n    /*\n    if (options.simplifiedAutoLink) {\n      txt = showdown.subParser('simplifiedAutoLinks')(txt, options, globals);\n    }\n    */\n    return left + txt + right;\n  }\n\n  // Parse underscores\n  if (options.literalMidWordUnderscores) {\n    text = text.replace(/\\b___(\\S[\\s\\S]*?)___\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n    text = text.replace(/\\b__(\\S[\\s\\S]*?)__\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n    text = text.replace(/\\b_(\\S[\\s\\S]*?)_\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n  } else {\n    text = text.replace(/___(\\S[\\s\\S]*?)___/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/__(\\S[\\s\\S]*?)__/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/_([^\\s_][\\s\\S]*?)_/g, function (wm, m) {\n      // !/^_[^_]/.test(m) - test if it doesn't start with __ (since it seems redundant, we removed it)\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n  }\n\n  // Now parse asterisks\n  if (options.literalMidWordAsterisks) {\n    text = text.replace(/([^*]|^)\\B\\*\\*\\*(\\S[\\s\\S]*?)\\*\\*\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n    text = text.replace(/([^*]|^)\\B\\*\\*(\\S[\\s\\S]*?)\\*\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n    text = text.replace(/([^*]|^)\\B\\*(\\S[\\s\\S]*?)\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n  } else {\n    text = text.replace(/\\*\\*\\*(\\S[\\s\\S]*?)\\*\\*\\*/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/\\*\\*(\\S[\\s\\S]*?)\\*\\*/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/\\*([^\\s*][\\s\\S]*?)\\*/g, function (wm, m) {\n      // !/^\\*[^*]/.test(m) - test if it doesn't start with ** (since it seems redundant, we removed it)\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n  }\n\n\n  text = globals.converter._dispatch('italicsAndBold.after', text, options, globals);\n  return text;\n});\n","/**\n * Form HTML ordered (numbered) and unordered (bulleted) lists.\n */\nshowdown.subParser('lists', function (text, options, globals) {\n  'use strict';\n\n  /**\n   * Process the contents of a single ordered or unordered list, splitting it\n   * into individual list items.\n   * @param {string} listStr\n   * @param {boolean} trimTrailing\n   * @returns {string}\n   */\n  function processListItems (listStr, trimTrailing) {\n    // The $g_list_level global keeps track of when we're inside a list.\n    // Each time we enter a list, we increment it; when we leave a list,\n    // we decrement. If it's zero, we're not in a list anymore.\n    //\n    // We do this because when we're not inside a list, we want to treat\n    // something like this:\n    //\n    //    I recommend upgrading to version\n    //    8. Oops, now this line is treated\n    //    as a sub-list.\n    //\n    // As a single paragraph, despite the fact that the second line starts\n    // with a digit-period-space sequence.\n    //\n    // Whereas when we're inside a list (or sub-list), that line will be\n    // treated as the start of a sub-list. What a kludge, huh? This is\n    // an aspect of Markdown's syntax that's hard to parse perfectly\n    // without resorting to mind-reading. Perhaps the solution is to\n    // change the syntax rules such that sub-lists must start with a\n    // starting cardinal number; e.g. \"1.\" or \"a.\".\n    globals.gListLevel++;\n\n    // trim trailing blank lines:\n    listStr = listStr.replace(/\\n{2,}$/, '\\n');\n\n    // attacklab: add sentinel to emulate \\z\n    listStr += '¨0';\n\n    var rgx = /(\\n)?(^ {0,3})([*+-]|\\d+[.])[ \\t]+((\\[(x|X| )?])?[ \\t]*[^\\r]+?(\\n{1,2}))(?=\\n*(¨0| {0,3}([*+-]|\\d+[.])[ \\t]+))/gm,\n        isParagraphed = (/\\n[ \\t]*\\n(?!¨0)/.test(listStr));\n\n    // Since version 1.5, nesting sublists requires 4 spaces (or 1 tab) indentation,\n    // which is a syntax breaking change\n    // activating this option reverts to old behavior\n    if (options.disableForced4SpacesIndentedSublists) {\n      rgx = /(\\n)?(^ {0,3})([*+-]|\\d+[.])[ \\t]+((\\[(x|X| )?])?[ \\t]*[^\\r]+?(\\n{1,2}))(?=\\n*(¨0|\\2([*+-]|\\d+[.])[ \\t]+))/gm;\n    }\n\n    listStr = listStr.replace(rgx, function (wholeMatch, m1, m2, m3, m4, taskbtn, checked) {\n      checked = (checked && checked.trim() !== '');\n\n      var item = showdown.subParser('outdent')(m4, options, globals),\n          bulletStyle = '';\n\n      // Support for github tasklists\n      if (taskbtn && options.tasklists) {\n        bulletStyle = ' class=\"task-list-item\" style=\"list-style-type: none;\"';\n        item = item.replace(/^[ \\t]*\\[(x|X| )?]/m, function () {\n          var otp = '
  • a
    • \n      // instead of:\n      // 
    • - - a
    \n      // So, to prevent it, we will put a marker (¨A)in the beginning of the line\n      // Kind of hackish/monkey patching, but seems more effective than overcomplicating the list parser\n      item = item.replace(/^([-*+]|\\d\\.)[ \\t]+[\\S\\n ]*/g, function (wm2) {\n        return '¨A' + wm2;\n      });\n\n      // m1 - Leading line or\n      // Has a double return (multi paragraph) or\n      // Has sublist\n      if (m1 || (item.search(/\\n{2,}/) > -1)) {\n        item = showdown.subParser('githubCodeBlocks')(item, options, globals);\n        item = showdown.subParser('blockGamut')(item, options, globals);\n      } else {\n        // Recursion for sub-lists:\n        item = showdown.subParser('lists')(item, options, globals);\n        item = item.replace(/\\n$/, ''); // chomp(item)\n        item = showdown.subParser('hashHTMLBlocks')(item, options, globals);\n\n        // Colapse double linebreaks\n        item = item.replace(/\\n\\n+/g, '\\n\\n');\n        if (isParagraphed) {\n          item = showdown.subParser('paragraphs')(item, options, globals);\n        } else {\n          item = showdown.subParser('spanGamut')(item, options, globals);\n        }\n      }\n\n      // now we need to remove the marker (¨A)\n      item = item.replace('¨A', '');\n      // we can finally wrap the line in list item tags\n      item =  '' + item + '\\n';\n\n      return item;\n    });\n\n    // attacklab: strip sentinel\n    listStr = listStr.replace(/¨0/g, '');\n\n    globals.gListLevel--;\n\n    if (trimTrailing) {\n      listStr = listStr.replace(/\\s+$/, '');\n    }\n\n    return listStr;\n  }\n\n  function styleStartNumber (list, listType) {\n    // check if ol and starts by a number different than 1\n    if (listType === 'ol') {\n      var res = list.match(/^ *(\\d+)\\./);\n      if (res && res[1] !== '1') {\n        return ' start=\"' + res[1] + '\"';\n      }\n    }\n    return '';\n  }\n\n  /**\n   * Check and parse consecutive lists (better fix for issue #142)\n   * @param {string} list\n   * @param {string} listType\n   * @param {boolean} trimTrailing\n   * @returns {string}\n   */\n  function parseConsecutiveLists (list, listType, trimTrailing) {\n    // check if we caught 2 or more consecutive lists by mistake\n    // we use the counterRgx, meaning if listType is UL we look for OL and vice versa\n    var olRgx = (options.disableForced4SpacesIndentedSublists) ? /^ ?\\d+\\.[ \\t]/gm : /^ {0,3}\\d+\\.[ \\t]/gm,\n        ulRgx = (options.disableForced4SpacesIndentedSublists) ? /^ ?[*+-][ \\t]/gm : /^ {0,3}[*+-][ \\t]/gm,\n        counterRxg = (listType === 'ul') ? olRgx : ulRgx,\n        result = '';\n\n    if (list.search(counterRxg) !== -1) {\n      (function parseCL (txt) {\n        var pos = txt.search(counterRxg),\n            style = styleStartNumber(list, listType);\n        if (pos !== -1) {\n          // slice\n          result += '\\n\\n<' + listType + style + '>\\n' + processListItems(txt.slice(0, pos), !!trimTrailing) + '\\n';\n\n          // invert counterType and listType\n          listType = (listType === 'ul') ? 'ol' : 'ul';\n          counterRxg = (listType === 'ul') ? olRgx : ulRgx;\n\n          //recurse\n          parseCL(txt.slice(pos));\n        } else {\n          result += '\\n\\n<' + listType + style + '>\\n' + processListItems(txt, !!trimTrailing) + '\\n';\n        }\n      })(list);\n    } else {\n      var style = styleStartNumber(list, listType);\n      result = '\\n\\n<' + listType + style + '>\\n' + processListItems(list, !!trimTrailing) + '\\n';\n    }\n\n    return result;\n  }\n\n  /** Start of list parsing **/\n  text = globals.converter._dispatch('lists.before', text, options, globals);\n  // add sentinel to hack around khtml/safari bug:\n  // http://bugs.webkit.org/show_bug.cgi?id=11231\n  text += '¨0';\n\n  if (globals.gListLevel) {\n    text = text.replace(/^(( {0,3}([*+-]|\\d+[.])[ \\t]+)[^\\r]+?(¨0|\\n{2,}(?=\\S)(?![ \\t]*(?:[*+-]|\\d+[.])[ \\t]+)))/gm,\n      function (wholeMatch, list, m2) {\n        var listType = (m2.search(/[*+-]/g) > -1) ? 'ul' : 'ol';\n        return parseConsecutiveLists(list, listType, true);\n      }\n    );\n  } else {\n    text = text.replace(/(\\n\\n|^\\n?)(( {0,3}([*+-]|\\d+[.])[ \\t]+)[^\\r]+?(¨0|\\n{2,}(?=\\S)(?![ \\t]*(?:[*+-]|\\d+[.])[ \\t]+)))/gm,\n      function (wholeMatch, m1, list, m3) {\n        var listType = (m3.search(/[*+-]/g) > -1) ? 'ul' : 'ol';\n        return parseConsecutiveLists(list, listType, false);\n      }\n    );\n  }\n\n  // strip sentinel\n  text = text.replace(/¨0/, '');\n  text = globals.converter._dispatch('lists.after', text, options, globals);\n  return text;\n});\n","/**\n * Parse metadata at the top of the document\n */\nshowdown.subParser('metadata', function (text, options, globals) {\n  'use strict';\n\n  if (!options.metadata) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('metadata.before', text, options, globals);\n\n  function parseMetadataContents (content) {\n    // raw is raw so it's not changed in any way\n    globals.metadata.raw = content;\n\n    // escape chars forbidden in html attributes\n    // double quotes\n    content = content\n      // ampersand first\n      .replace(/&/g, '&')\n      // double quotes\n      .replace(/\"/g, '"');\n\n    content = content.replace(/\\n {4}/g, ' ');\n    content.replace(/^([\\S ]+): +([\\s\\S]+?)$/gm, function (wm, key, value) {\n      globals.metadata.parsed[key] = value;\n      return '';\n    });\n  }\n\n  text = text.replace(/^\\s*«««+(\\S*?)\\n([\\s\\S]+?)\\n»»»+\\n/, function (wholematch, format, content) {\n    parseMetadataContents(content);\n    return '¨M';\n  });\n\n  text = text.replace(/^\\s*---+(\\S*?)\\n([\\s\\S]+?)\\n---+\\n/, function (wholematch, format, content) {\n    if (format) {\n      globals.metadata.format = format;\n    }\n    parseMetadataContents(content);\n    return '¨M';\n  });\n\n  text = text.replace(/¨M/g, '');\n\n  text = globals.converter._dispatch('metadata.after', text, options, globals);\n  return text;\n});\n","/**\n * Remove one level of line-leading tabs or spaces\n */\nshowdown.subParser('outdent', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('outdent.before', text, options, globals);\n\n  // attacklab: hack around Konqueror 3.5.4 bug:\n  // \"----------bug\".replace(/^-/g,\"\") == \"bug\"\n  text = text.replace(/^(\\t|[ ]{1,4})/gm, '¨0'); // attacklab: g_tab_width\n\n  // attacklab: clean up hack\n  text = text.replace(/¨0/g, '');\n\n  text = globals.converter._dispatch('outdent.after', text, options, globals);\n  return text;\n});\n","/**\n *\n */\nshowdown.subParser('paragraphs', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('paragraphs.before', text, options, globals);\n  // Strip leading and trailing lines:\n  text = text.replace(/^\\n+/g, '');\n  text = text.replace(/\\n+$/g, '');\n\n  var grafs = text.split(/\\n{2,}/g),\n      grafsOut = [],\n      end = grafs.length; // Wrap 
     tags\n\n  for (var i = 0; i < end; i++) {\n    var str = grafs[i];\n    // if this is an HTML marker, copy it\n    if (str.search(/¨(K|G)(\\d+)\\1/g) >= 0) {\n      grafsOut.push(str);\n\n    // test for presence of characters to prevent empty lines being parsed\n    // as paragraphs (resulting in undesired extra empty paragraphs)\n    } else if (str.search(/\\S/) >= 0) {\n      str = showdown.subParser('spanGamut')(str, options, globals);\n      str = str.replace(/^([ \\t]*)/g, '
    ');\n      str += '
    ';\n      grafsOut.push(str);\n    }\n  }\n\n  /** Unhashify HTML blocks */\n  end = grafsOut.length;\n  for (i = 0; i < end; i++) {\n    var blockText = '',\n        grafsOutIt = grafsOut[i],\n        codeFlag = false;\n    // if this is a marker for an html block...\n    // use RegExp.test instead of string.search because of QML bug\n    while (/¨(K|G)(\\d+)\\1/.test(grafsOutIt)) {\n      var delim = RegExp.$1,\n          num   = RegExp.$2;\n\n      if (delim === 'K') {\n        blockText = globals.gHtmlBlocks[num];\n      } else {\n        // we need to check if ghBlock is a false positive\n        if (codeFlag) {\n          // use encoded version of all text\n          blockText = showdown.subParser('encodeCode')(globals.ghCodeBlocks[num].text, options, globals);\n        } else {\n          blockText = globals.ghCodeBlocks[num].codeblock;\n        }\n      }\n      blockText = blockText.replace(/\\$/g, '$$$$'); // Escape any dollar signs\n\n      grafsOutIt = grafsOutIt.replace(/(\\n\\n)?¨(K|G)\\d+\\2(\\n\\n)?/, blockText);\n      // Check if grafsOutIt is a pre->code\n      if (/^]*>\\s*]*>/.test(grafsOutIt)) {\n        codeFlag = true;\n      }\n    }\n    grafsOut[i] = grafsOutIt;\n  }\n  text = grafsOut.join('\\n');\n  // Strip leading and trailing lines:\n  text = text.replace(/^\\n+/g, '');\n  text = text.replace(/\\n+$/g, '');\n  return globals.converter._dispatch('paragraphs.after', text, options, globals);\n});\n","/**\n * Run extension\n */\nshowdown.subParser('runExtension', function (ext, text, options, globals) {\n  'use strict';\n\n  if (ext.filter) {\n    text = ext.filter(text, globals.converter, options);\n\n  } else if (ext.regex) {\n    // TODO remove this when old extension loading mechanism is deprecated\n    var re = ext.regex;\n    if (!(re instanceof RegExp)) {\n      re = new RegExp(re, 'g');\n    }\n    text = text.replace(re, ext.replace);\n  }\n\n  return text;\n});\n","/**\n * These are all the transformations that occur *within* block-level\n * tags like paragraphs, headers, and list items.\n */\nshowdown.subParser('spanGamut', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('spanGamut.before', text, options, globals);\n  text = showdown.subParser('codeSpans')(text, options, globals);\n  text = showdown.subParser('escapeSpecialCharsWithinTagAttributes')(text, options, globals);\n  text = showdown.subParser('encodeBackslashEscapes')(text, options, globals);\n\n  // Process anchor and image tags. Images must come first,\n  // because ![foo][f] looks like an anchor.\n  text = showdown.subParser('images')(text, options, globals);\n  text = showdown.subParser('anchors')(text, options, globals);\n\n  // Make links out of things like ``\n  // Must come after anchors, because you can use < and >\n  // delimiters in inline links like [this]().\n  text = showdown.subParser('autoLinks')(text, options, globals);\n  text = showdown.subParser('simplifiedAutoLinks')(text, options, globals);\n  text = showdown.subParser('emoji')(text, options, globals);\n  text = showdown.subParser('underline')(text, options, globals);\n  text = showdown.subParser('italicsAndBold')(text, options, globals);\n  text = showdown.subParser('strikethrough')(text, options, globals);\n  text = showdown.subParser('ellipsis')(text, options, globals);\n\n  // we need to hash HTML tags inside spans\n  text = showdown.subParser('hashHTMLSpans')(text, options, globals);\n\n  // now we encode amps and angles\n  text = showdown.subParser('encodeAmpsAndAngles')(text, options, globals);\n\n  // Do hard breaks\n  if (options.simpleLineBreaks) {\n    // GFM style hard breaks\n    // only add line breaks if the text does not contain a block (special case for lists)\n    if (!/\\n\\n¨K/.test(text)) {\n      text = text.replace(/\\n+/g, '
    \\n');\n    }\n  } else {\n    // Vanilla hard breaks\n    text = text.replace(/  +\\n/g, '
    \\n');\n  }\n\n  text = globals.converter._dispatch('spanGamut.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('strikethrough', function (text, options, globals) {\n  'use strict';\n\n  function parseInside (txt) {\n    if (options.simplifiedAutoLink) {\n      txt = showdown.subParser('simplifiedAutoLinks')(txt, options, globals);\n    }\n    return '' + txt + '';\n  }\n\n  if (options.strikethrough) {\n    text = globals.converter._dispatch('strikethrough.before', text, options, globals);\n    text = text.replace(/(?:~){2}([\\s\\S]+?)(?:~){2}/g, function (wm, txt) { return parseInside(txt); });\n    text = globals.converter._dispatch('strikethrough.after', text, options, globals);\n  }\n\n  return text;\n});\n","/**\n * Strips link definitions from text, stores the URLs and titles in\n * hash references.\n * Link defs are in the form: ^[id]: url \"optional title\"\n */\nshowdown.subParser('stripLinkDefinitions', function (text, options, globals) {\n  'use strict';\n\n  var regex       = /^ {0,3}\\[(.+)]:[ \\t]*\\n?[ \\t]*\\s]+)>?(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*\\n?[ \\t]*(?:(\\n*)[\"|'(](.+?)[\"|')][ \\t]*)?(?:\\n+|(?=¨0))/gm,\n      base64Regex = /^ {0,3}\\[(.+)]:[ \\t]*\\n?[ \\t]*?(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*\\n?[ \\t]*(?:(\\n*)[\"|'(](.+?)[\"|')][ \\t]*)?(?:\\n\\n|(?=¨0)|(?=\\n\\[))/gm;\n\n  // attacklab: sentinel workarounds for lack of \\A and \\Z, safari\\khtml bug\n  text += '¨0';\n\n  var replaceFunc = function (wholeMatch, linkId, url, width, height, blankLines, title) {\n    linkId = linkId.toLowerCase();\n    if (url.match(/^data:.+?\\/.+?;base64,/)) {\n      // remove newlines\n      globals.gUrls[linkId] = url.replace(/\\s/g, '');\n    } else {\n      globals.gUrls[linkId] = showdown.subParser('encodeAmpsAndAngles')(url, options, globals);  // Link IDs are case-insensitive\n    }\n\n    if (blankLines) {\n      // Oops, found blank lines, so it's not a title.\n      // Put back the parenthetical statement we stole.\n      return blankLines + title;\n\n    } else {\n      if (title) {\n        globals.gTitles[linkId] = title.replace(/\"|'/g, '"');\n      }\n      if (options.parseImgDimensions && width && height) {\n        globals.gDimensions[linkId] = {\n          width:  width,\n          height: height\n        };\n      }\n    }\n    // Completely remove the definition from the text\n    return '';\n  };\n\n  // first we try to find base64 link references\n  text = text.replace(base64Regex, replaceFunc);\n\n  text = text.replace(regex, replaceFunc);\n\n  // attacklab: strip sentinel\n  text = text.replace(/¨0/, '');\n\n  return text;\n});\n","showdown.subParser('tables', function (text, options, globals) {\n  'use strict';\n\n  if (!options.tables) {\n    return text;\n  }\n\n  var tableRgx       = /^ {0,3}\\|?.+\\|.+\\n {0,3}\\|?[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[\\s\\S]+?(?:\\n\\n|¨0)/gm,\n      //singeColTblRgx = /^ {0,3}\\|.+\\|\\n {0,3}\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*\\n(?: {0,3}\\|.+\\|\\n)+(?:\\n\\n|¨0)/gm;\n      singeColTblRgx = /^ {0,3}\\|.+\\|[ \\t]*\\n {0,3}\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*\\n( {0,3}\\|.+\\|[ \\t]*\\n)*(?:\\n|¨0)/gm;\n\n  function parseStyles (sLine) {\n    if (/^:[ \\t]*--*$/.test(sLine)) {\n      return ' style=\"text-align:left;\"';\n    } else if (/^--*[ \\t]*:[ \\t]*$/.test(sLine)) {\n      return ' style=\"text-align:right;\"';\n    } else if (/^:[ \\t]*--*[ \\t]*:$/.test(sLine)) {\n      return ' style=\"text-align:center;\"';\n    } else {\n      return '';\n    }\n  }\n\n  function parseHeaders (header, style) {\n    var id = '';\n    header = header.trim();\n    // support both tablesHeaderId and tableHeaderId due to error in documentation so we don't break backwards compatibility\n    if (options.tablesHeaderId || options.tableHeaderId) {\n      id = ' id=\"' + header.replace(/ /g, '_').toLowerCase() + '\"';\n    }\n    header = showdown.subParser('spanGamut')(header, options, globals);\n\n    return '' + header + '\\n';\n  }\n\n  function parseCells (cell, style) {\n    var subText = showdown.subParser('spanGamut')(cell, options, globals);\n    return '' + subText + '\\n';\n  }\n\n  function buildTable (headers, cells) {\n    var tb = '\\n\\n\\n',\n        tblLgn = headers.length;\n\n    for (var i = 0; i < tblLgn; ++i) {\n      tb += headers[i];\n    }\n    tb += '\\n\\n\\n';\n\n    for (i = 0; i < cells.length; ++i) {\n      tb += '\\n';\n      for (var ii = 0; ii < tblLgn; ++ii) {\n        tb += cells[i][ii];\n      }\n      tb += '\\n';\n    }\n    tb += '\\n
    \\n';\n    return tb;\n  }\n\n  function parseTable (rawTable) {\n    var i, tableLines = rawTable.split('\\n');\n\n    for (i = 0; i < tableLines.length; ++i) {\n      // strip wrong first and last column if wrapped tables are used\n      if (/^ {0,3}\\|/.test(tableLines[i])) {\n        tableLines[i] = tableLines[i].replace(/^ {0,3}\\|/, '');\n      }\n      if (/\\|[ \\t]*$/.test(tableLines[i])) {\n        tableLines[i] = tableLines[i].replace(/\\|[ \\t]*$/, '');\n      }\n      // parse code spans first, but we only support one line code spans\n      tableLines[i] = showdown.subParser('codeSpans')(tableLines[i], options, globals);\n    }\n\n    var rawHeaders = tableLines[0].split('|').map(function (s) { return s.trim();}),\n        rawStyles = tableLines[1].split('|').map(function (s) { return s.trim();}),\n        rawCells = [],\n        headers = [],\n        styles = [],\n        cells = [];\n\n    tableLines.shift();\n    tableLines.shift();\n\n    for (i = 0; i < tableLines.length; ++i) {\n      if (tableLines[i].trim() === '') {\n        continue;\n      }\n      rawCells.push(\n        tableLines[i]\n          .split('|')\n          .map(function (s) {\n            return s.trim();\n          })\n      );\n    }\n\n    if (rawHeaders.length < rawStyles.length) {\n      return rawTable;\n    }\n\n    for (i = 0; i < rawStyles.length; ++i) {\n      styles.push(parseStyles(rawStyles[i]));\n    }\n\n    for (i = 0; i < rawHeaders.length; ++i) {\n      if (showdown.helper.isUndefined(styles[i])) {\n        styles[i] = '';\n      }\n      headers.push(parseHeaders(rawHeaders[i], styles[i]));\n    }\n\n    for (i = 0; i < rawCells.length; ++i) {\n      var row = [];\n      for (var ii = 0; ii < headers.length; ++ii) {\n        if (showdown.helper.isUndefined(rawCells[i][ii])) {\n\n        }\n        row.push(parseCells(rawCells[i][ii], styles[ii]));\n      }\n      cells.push(row);\n    }\n\n    return buildTable(headers, cells);\n  }\n\n  text = globals.converter._dispatch('tables.before', text, options, globals);\n\n  // find escaped pipe characters\n  text = text.replace(/\\\\(\\|)/g, showdown.helper.escapeCharactersCallback);\n\n  // parse multi column tables\n  text = text.replace(tableRgx, parseTable);\n\n  // parse one column tables\n  text = text.replace(singeColTblRgx, parseTable);\n\n  text = globals.converter._dispatch('tables.after', text, options, globals);\n\n  return text;\n});\n","showdown.subParser('underline', function (text, options, globals) {\n  'use strict';\n\n  if (!options.underline) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('underline.before', text, options, globals);\n\n  if (options.literalMidWordUnderscores) {\n    text = text.replace(/\\b___(\\S[\\s\\S]*?)___\\b/g, function (wm, txt) {\n      return '' + txt + '';\n    });\n    text = text.replace(/\\b__(\\S[\\s\\S]*?)__\\b/g, function (wm, txt) {\n      return '' + txt + '';\n    });\n  } else {\n    text = text.replace(/___(\\S[\\s\\S]*?)___/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? '' + m + '' : wm;\n    });\n    text = text.replace(/__(\\S[\\s\\S]*?)__/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? '' + m + '' : wm;\n    });\n  }\n\n  // escape remaining underscores to prevent them being parsed by italic and bold\n  text = text.replace(/(_)/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('underline.after', text, options, globals);\n\n  return text;\n});\n","/**\n * Swap back in all the special characters we've hidden.\n */\nshowdown.subParser('unescapeSpecialChars', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('unescapeSpecialChars.before', text, options, globals);\n\n  text = text.replace(/¨E(\\d+)E/g, function (wholeMatch, m1) {\n    var charCodeToReplace = parseInt(m1);\n    return String.fromCharCode(charCodeToReplace);\n  });\n\n  text = globals.converter._dispatch('unescapeSpecialChars.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('makeMarkdown.blockquote', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    var children = node.childNodes,\n        childrenLength = children.length;\n\n    for (var i = 0; i < childrenLength; ++i) {\n      var innerTxt = showdown.subParser('makeMarkdown.node')(children[i], globals);\n\n      if (innerTxt === '') {\n        continue;\n      }\n      txt += innerTxt;\n    }\n  }\n  // cleanup\n  txt = txt.trim();\n  txt = '> ' + txt.split('\\n').join('\\n> ');\n  return txt;\n});\n","showdown.subParser('makeMarkdown.codeBlock', function (node, globals) {\n  'use strict';\n\n  var lang = node.getAttribute('language'),\n      num  = node.getAttribute('precodenum');\n  return '```' + lang + '\\n' + globals.preList[num] + '\\n```';\n});\n","showdown.subParser('makeMarkdown.codeSpan', function (node) {\n  'use strict';\n\n  return '`' + node.innerHTML + '`';\n});\n","showdown.subParser('makeMarkdown.emphasis', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    txt += '*';\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '*';\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.header', function (node, globals, headerLevel) {\n  'use strict';\n\n  var headerMark = new Array(headerLevel + 1).join('#'),\n      txt = '';\n\n  if (node.hasChildNodes()) {\n    txt = headerMark + ' ';\n    var children = node.childNodes,\n        childrenLength = children.length;\n\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.hr', function () {\n  'use strict';\n\n  return '---';\n});\n","showdown.subParser('makeMarkdown.image', function (node) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasAttribute('src')) {\n    txt += '![' + node.getAttribute('alt') + '](';\n    txt += '<' + node.getAttribute('src') + '>';\n    if (node.hasAttribute('width') && node.hasAttribute('height')) {\n      txt += ' =' + node.getAttribute('width') + 'x' + node.getAttribute('height');\n    }\n\n    if (node.hasAttribute('title')) {\n      txt += ' \"' + node.getAttribute('title') + '\"';\n    }\n    txt += ')';\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.links', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes() && node.hasAttribute('href')) {\n    var children = node.childNodes,\n        childrenLength = children.length;\n    txt = '[';\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '](';\n    txt += '<' + node.getAttribute('href') + '>';\n    if (node.hasAttribute('title')) {\n      txt += ' \"' + node.getAttribute('title') + '\"';\n    }\n    txt += ')';\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.list', function (node, globals, type) {\n  'use strict';\n\n  var txt = '';\n  if (!node.hasChildNodes()) {\n    return '';\n  }\n  var listItems       = node.childNodes,\n      listItemsLenght = listItems.length,\n      listNum = node.getAttribute('start') || 1;\n\n  for (var i = 0; i < listItemsLenght; ++i) {\n    if (typeof listItems[i].tagName === 'undefined' || listItems[i].tagName.toLowerCase() !== 'li') {\n      continue;\n    }\n\n    // define the bullet to use in list\n    var bullet = '';\n    if (type === 'ol') {\n      bullet = listNum.toString() + '. ';\n    } else {\n      bullet = '- ';\n    }\n\n    // parse list item\n    txt += bullet + showdown.subParser('makeMarkdown.listItem')(listItems[i], globals);\n    ++listNum;\n  }\n\n  // add comment at the end to prevent consecutive lists to be parsed as one\n  txt += '\\n\\n';\n  return txt.trim();\n});\n","showdown.subParser('makeMarkdown.listItem', function (node, globals) {\n  'use strict';\n\n  var listItemTxt = '';\n\n  var children = node.childNodes,\n      childrenLenght = children.length;\n\n  for (var i = 0; i < childrenLenght; ++i) {\n    listItemTxt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n  }\n  // if it's only one liner, we need to add a newline at the end\n  if (!/\\n$/.test(listItemTxt)) {\n    listItemTxt += '\\n';\n  } else {\n    // it's multiparagraph, so we need to indent\n    listItemTxt = listItemTxt\n      .split('\\n')\n      .join('\\n    ')\n      .replace(/^ {4}$/gm, '')\n      .replace(/\\n\\n+/g, '\\n\\n');\n  }\n\n  return listItemTxt;\n});\n","\n\nshowdown.subParser('makeMarkdown.node', function (node, globals, spansOnly) {\n  'use strict';\n\n  spansOnly = spansOnly || false;\n\n  var txt = '';\n\n  // edge case of text without wrapper paragraph\n  if (node.nodeType === 3) {\n    return showdown.subParser('makeMarkdown.txt')(node, globals);\n  }\n\n  // HTML comment\n  if (node.nodeType === 8) {\n    return '\\n\\n';\n  }\n\n  // process only node elements\n  if (node.nodeType !== 1) {\n    return '';\n  }\n\n  var tagName = node.tagName.toLowerCase();\n\n  switch (tagName) {\n\n    //\n    // BLOCKS\n    //\n    case 'h1':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 1) + '\\n\\n'; }\n      break;\n    case 'h2':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 2) + '\\n\\n'; }\n      break;\n    case 'h3':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 3) + '\\n\\n'; }\n      break;\n    case 'h4':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 4) + '\\n\\n'; }\n      break;\n    case 'h5':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 5) + '\\n\\n'; }\n      break;\n    case 'h6':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 6) + '\\n\\n'; }\n      break;\n\n    case 'p':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.paragraph')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'blockquote':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.blockquote')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'hr':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.hr')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'ol':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.list')(node, globals, 'ol') + '\\n\\n'; }\n      break;\n\n    case 'ul':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.list')(node, globals, 'ul') + '\\n\\n'; }\n      break;\n\n    case 'precode':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.codeBlock')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'pre':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.pre')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'table':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.table')(node, globals) + '\\n\\n'; }\n      break;\n\n    //\n    // SPANS\n    //\n    case 'code':\n      txt = showdown.subParser('makeMarkdown.codeSpan')(node, globals);\n      break;\n\n    case 'em':\n    case 'i':\n      txt = showdown.subParser('makeMarkdown.emphasis')(node, globals);\n      break;\n\n    case 'strong':\n    case 'b':\n      txt = showdown.subParser('makeMarkdown.strong')(node, globals);\n      break;\n\n    case 'del':\n      txt = showdown.subParser('makeMarkdown.strikethrough')(node, globals);\n      break;\n\n    case 'a':\n      txt = showdown.subParser('makeMarkdown.links')(node, globals);\n      break;\n\n    case 'img':\n      txt = showdown.subParser('makeMarkdown.image')(node, globals);\n      break;\n\n    default:\n      txt = node.outerHTML + '\\n\\n';\n  }\n\n  // common normalization\n  // TODO eventually\n\n  return txt;\n});\n","showdown.subParser('makeMarkdown.paragraph', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n  }\n\n  // some text normalization\n  txt = txt.trim();\n\n  return txt;\n});\n","showdown.subParser('makeMarkdown.pre', function (node, globals) {\n  'use strict';\n\n  var num  = node.getAttribute('prenum');\n  return '
    ' + globals.preList[num] + '
    ';\n});\n","showdown.subParser('makeMarkdown.strikethrough', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    txt += '~~';\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '~~';\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.strong', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    txt += '**';\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '**';\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.table', function (node, globals) {\n  'use strict';\n\n  var txt = '',\n      tableArray = [[], []],\n      headings   = node.querySelectorAll('thead>tr>th'),\n      rows       = node.querySelectorAll('tbody>tr'),\n      i, ii;\n  for (i = 0; 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extracted by mini-css-extract-plugin\nmodule.exports = {\"box\":\"box__3cKyY\",\"default\":\"default__v-emJ\",\"red\":\"red__339Cz\",\"orange\":\"orange__24_8v\",\"yellow\":\"yellow__1Jo9W\",\"lime\":\"lime__34yV5\",\"cyan\":\"cyan__3RqLr\",\"blue\":\"blue__13Wnj\",\"magenta\":\"magenta__2tkzq\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"title\":\"title__3ZVpg\",\"contents\":\"contents__20_NI\"};","/**\n * Created by Tivie on 13-07-2015.\n */\n\nfunction getDefaultOpts (simple) {\n  'use strict';\n\n  var defaultOptions = {\n    omitExtraWLInCodeBlocks: {\n      defaultValue: false,\n      describe: 'Omit the default extra whiteline added to code blocks',\n      type: 'boolean'\n    },\n    noHeaderId: {\n      defaultValue: false,\n      describe: 'Turn on/off generated header id',\n      type: 'boolean'\n    },\n    prefixHeaderId: {\n      defaultValue: false,\n      describe: 'Add a prefix to the generated header ids. 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    foo\\
    ',\n      type: 'boolean'\n    },\n    emoji: {\n      defaultValue: false,\n      description: 'Enable emoji support. Ex: `this is a :smile: emoji`',\n      type: 'boolean'\n    },\n    underline: {\n      defaultValue: false,\n      description: 'Enable support for underline. Syntax is double or triple underscores: `__underline word__`. With this option enabled, underscores no longer parses into `` and ``',\n      type: 'boolean'\n    },\n    completeHTMLDocument: {\n      defaultValue: false,\n      description: 'Outputs a complete html document, including ``, `` and `` tags',\n      type: 'boolean'\n    },\n    metadata: {\n      defaultValue: false,\n      description: 'Enable support for document metadata (defined at the top of the document between `«««` and `»»»` or between `---` and `---`).',\n      type: 'boolean'\n    },\n    splitAdjacentBlockquotes: {\n      defaultValue: false,\n      description: 'Split adjacent blockquote blocks',\n      type: 'boolean'\n    }\n  };\n  if (simple === false) {\n    return JSON.parse(JSON.stringify(defaultOptions));\n  }\n  var ret = {};\n  for (var opt in defaultOptions) {\n    if (defaultOptions.hasOwnProperty(opt)) {\n      ret[opt] = defaultOptions[opt].defaultValue;\n    }\n  }\n  return ret;\n}\n\nfunction allOptionsOn () {\n  'use strict';\n  var options = getDefaultOpts(true),\n      ret = {};\n  for (var opt in options) {\n    if (options.hasOwnProperty(opt)) {\n      ret[opt] = true;\n    }\n  }\n  return ret;\n}\n","/**\n * Created by Tivie on 06-01-2015.\n */\n\n// Private properties\nvar showdown = {},\n    parsers = {},\n    extensions = {},\n    globalOptions = getDefaultOpts(true),\n    setFlavor = 'vanilla',\n    flavor = {\n      github: {\n        omitExtraWLInCodeBlocks:              true,\n        simplifiedAutoLink:                   true,\n        excludeTrailingPunctuationFromURLs:   true,\n        literalMidWordUnderscores:            true,\n        strikethrough:                        true,\n        tables:                               true,\n        tablesHeaderId:                       true,\n        ghCodeBlocks:                         true,\n        tasklists:                            true,\n        disableForced4SpacesIndentedSublists: true,\n        simpleLineBreaks:                     true,\n        requireSpaceBeforeHeadingText:        true,\n        ghCompatibleHeaderId:                 true,\n        ghMentions:                           true,\n        backslashEscapesHTMLTags:             true,\n        emoji:                                true,\n        splitAdjacentBlockquotes:             true\n      },\n      original: {\n        noHeaderId:                           true,\n        ghCodeBlocks:                         false\n      },\n      ghost: {\n        omitExtraWLInCodeBlocks:              true,\n        parseImgDimensions:                   true,\n        simplifiedAutoLink:                   true,\n        excludeTrailingPunctuationFromURLs:   true,\n        literalMidWordUnderscores:            true,\n        strikethrough:                        true,\n        tables:                               true,\n        tablesHeaderId:                       true,\n        ghCodeBlocks:                         true,\n        tasklists:                            true,\n        smoothLivePreview:                    true,\n        simpleLineBreaks:                     true,\n        requireSpaceBeforeHeadingText:        true,\n        ghMentions:                           false,\n        encodeEmails:                         true\n      },\n      vanilla: getDefaultOpts(true),\n      allOn: allOptionsOn()\n    };\n\n/**\n * helper namespace\n * @type {{}}\n */\nshowdown.helper = {};\n\n/**\n * TODO LEGACY SUPPORT CODE\n * @type {{}}\n */\nshowdown.extensions = {};\n\n/**\n * Set a global option\n * @static\n * @param {string} key\n * @param {*} value\n * @returns {showdown}\n */\nshowdown.setOption = function (key, value) {\n  'use strict';\n  globalOptions[key] = value;\n  return this;\n};\n\n/**\n * Get a global option\n * @static\n * @param {string} key\n * @returns {*}\n */\nshowdown.getOption = function (key) {\n  'use strict';\n  return globalOptions[key];\n};\n\n/**\n * Get the global options\n * @static\n * @returns {{}}\n */\nshowdown.getOptions = function () {\n  'use strict';\n  return globalOptions;\n};\n\n/**\n * Reset global options to the default values\n * @static\n */\nshowdown.resetOptions = function () {\n  'use strict';\n  globalOptions = getDefaultOpts(true);\n};\n\n/**\n * Set the flavor showdown should use as default\n * @param {string} name\n */\nshowdown.setFlavor = function (name) {\n  'use strict';\n  if (!flavor.hasOwnProperty(name)) {\n    throw Error(name + ' flavor was not found');\n  }\n  showdown.resetOptions();\n  var preset = flavor[name];\n  setFlavor = name;\n  for (var option in preset) {\n    if (preset.hasOwnProperty(option)) {\n      globalOptions[option] = preset[option];\n    }\n  }\n};\n\n/**\n * Get the currently set flavor\n * @returns {string}\n */\nshowdown.getFlavor = function () {\n  'use strict';\n  return setFlavor;\n};\n\n/**\n * Get the options of a specified flavor. Returns undefined if the flavor was not found\n * @param {string} name Name of the flavor\n * @returns {{}|undefined}\n */\nshowdown.getFlavorOptions = function (name) {\n  'use strict';\n  if (flavor.hasOwnProperty(name)) {\n    return flavor[name];\n  }\n};\n\n/**\n * Get the default options\n * @static\n * @param {boolean} [simple=true]\n * @returns {{}}\n */\nshowdown.getDefaultOptions = function (simple) {\n  'use strict';\n  return getDefaultOpts(simple);\n};\n\n/**\n * Get or set a subParser\n *\n * subParser(name)       - Get a registered subParser\n * subParser(name, func) - Register a subParser\n * @static\n * @param {string} name\n * @param {function} [func]\n * @returns {*}\n */\nshowdown.subParser = function (name, func) {\n  'use strict';\n  if (showdown.helper.isString(name)) {\n    if (typeof func !== 'undefined') {\n      parsers[name] = func;\n    } else {\n      if (parsers.hasOwnProperty(name)) {\n        return parsers[name];\n      } else {\n        throw Error('SubParser named ' + name + ' not registered!');\n      }\n    }\n  }\n};\n\n/**\n * Gets or registers an extension\n * @static\n * @param {string} name\n * @param {object|function=} ext\n * @returns {*}\n */\nshowdown.extension = function (name, ext) {\n  'use strict';\n\n  if (!showdown.helper.isString(name)) {\n    throw Error('Extension \\'name\\' must be a string');\n  }\n\n  name = showdown.helper.stdExtName(name);\n\n  // Getter\n  if (showdown.helper.isUndefined(ext)) {\n    if (!extensions.hasOwnProperty(name)) {\n      throw Error('Extension named ' + name + ' is not registered!');\n    }\n    return extensions[name];\n\n    // Setter\n  } else {\n    // Expand extension if it's wrapped in a function\n    if (typeof ext === 'function') {\n      ext = ext();\n    }\n\n    // Ensure extension is an array\n    if (!showdown.helper.isArray(ext)) {\n      ext = [ext];\n    }\n\n    var validExtension = validate(ext, name);\n\n    if (validExtension.valid) {\n      extensions[name] = ext;\n    } else {\n      throw Error(validExtension.error);\n    }\n  }\n};\n\n/**\n * Gets all extensions registered\n * @returns {{}}\n */\nshowdown.getAllExtensions = function () {\n  'use strict';\n  return extensions;\n};\n\n/**\n * Remove an extension\n * @param {string} name\n */\nshowdown.removeExtension = function (name) {\n  'use strict';\n  delete extensions[name];\n};\n\n/**\n * Removes all extensions\n */\nshowdown.resetExtensions = function () {\n  'use strict';\n  extensions = {};\n};\n\n/**\n * Validate extension\n * @param {array} extension\n * @param {string} name\n * @returns {{valid: boolean, error: string}}\n */\nfunction validate (extension, name) {\n  'use strict';\n\n  var errMsg = (name) ? 'Error in ' + name + ' extension->' : 'Error in unnamed extension',\n      ret = {\n        valid: true,\n        error: ''\n      };\n\n  if (!showdown.helper.isArray(extension)) {\n    extension = [extension];\n  }\n\n  for (var i = 0; i < extension.length; ++i) {\n    var baseMsg = errMsg + ' sub-extension ' + i + ': ',\n        ext = extension[i];\n    if (typeof ext !== 'object') {\n      ret.valid = false;\n      ret.error = baseMsg + 'must be an object, but ' + typeof ext + ' given';\n      return ret;\n    }\n\n    if (!showdown.helper.isString(ext.type)) {\n      ret.valid = false;\n      ret.error = baseMsg + 'property \"type\" must be a string, but ' + typeof ext.type + ' given';\n      return ret;\n    }\n\n    var type = ext.type = ext.type.toLowerCase();\n\n    // normalize extension type\n    if (type === 'language') {\n      type = ext.type = 'lang';\n    }\n\n    if (type === 'html') {\n      type = ext.type = 'output';\n    }\n\n    if (type !== 'lang' && type !== 'output' && type !== 'listener') {\n      ret.valid = false;\n      ret.error = baseMsg + 'type ' + type + ' is not recognized. Valid values: \"lang/language\", \"output/html\" or \"listener\"';\n      return ret;\n    }\n\n    if (type === 'listener') {\n      if (showdown.helper.isUndefined(ext.listeners)) {\n        ret.valid = false;\n        ret.error = baseMsg + '. Extensions of type \"listener\" must have a property called \"listeners\"';\n        return ret;\n      }\n    } else {\n      if (showdown.helper.isUndefined(ext.filter) && showdown.helper.isUndefined(ext.regex)) {\n        ret.valid = false;\n        ret.error = baseMsg + type + ' extensions must define either a \"regex\" property or a \"filter\" method';\n        return ret;\n      }\n    }\n\n    if (ext.listeners) {\n      if (typeof ext.listeners !== 'object') {\n        ret.valid = false;\n        ret.error = baseMsg + '\"listeners\" property must be an object but ' + typeof ext.listeners + ' given';\n        return ret;\n      }\n      for (var ln in ext.listeners) {\n        if (ext.listeners.hasOwnProperty(ln)) {\n          if (typeof ext.listeners[ln] !== 'function') {\n            ret.valid = false;\n            ret.error = baseMsg + '\"listeners\" property must be an hash of [event name]: [callback]. listeners.' + ln +\n              ' must be a function but ' + typeof ext.listeners[ln] + ' given';\n            return ret;\n          }\n        }\n      }\n    }\n\n    if (ext.filter) {\n      if (typeof ext.filter !== 'function') {\n        ret.valid = false;\n        ret.error = baseMsg + '\"filter\" must be a function, but ' + typeof ext.filter + ' given';\n        return ret;\n      }\n    } else if (ext.regex) {\n      if (showdown.helper.isString(ext.regex)) {\n        ext.regex = new RegExp(ext.regex, 'g');\n      }\n      if (!(ext.regex instanceof RegExp)) {\n        ret.valid = false;\n        ret.error = baseMsg + '\"regex\" property must either be a string or a RegExp object, but ' + typeof ext.regex + ' given';\n        return ret;\n      }\n      if (showdown.helper.isUndefined(ext.replace)) {\n        ret.valid = false;\n        ret.error = baseMsg + '\"regex\" extensions must implement a replace string or function';\n        return ret;\n      }\n    }\n  }\n  return ret;\n}\n\n/**\n * Validate extension\n * @param {object} ext\n * @returns {boolean}\n */\nshowdown.validateExtension = function (ext) {\n  'use strict';\n\n  var validateExtension = validate(ext, null);\n  if (!validateExtension.valid) {\n    console.warn(validateExtension.error);\n    return false;\n  }\n  return true;\n};\n","/**\n * showdownjs helper functions\n */\n\nif (!showdown.hasOwnProperty('helper')) {\n  showdown.helper = {};\n}\n\n/**\n * Check if var is string\n * @static\n * @param {string} a\n * @returns {boolean}\n */\nshowdown.helper.isString = function (a) {\n  'use strict';\n  return (typeof a === 'string' || a instanceof String);\n};\n\n/**\n * Check if var is a function\n * @static\n * @param {*} a\n * @returns {boolean}\n */\nshowdown.helper.isFunction = function (a) {\n  'use strict';\n  var getType = {};\n  return a && getType.toString.call(a) === '[object Function]';\n};\n\n/**\n * isArray helper function\n * @static\n * @param {*} a\n * @returns {boolean}\n */\nshowdown.helper.isArray = function (a) {\n  'use strict';\n  return Array.isArray(a);\n};\n\n/**\n * Check if value is undefined\n * @static\n * @param {*} value The value to check.\n * @returns {boolean} Returns `true` if `value` is `undefined`, else `false`.\n */\nshowdown.helper.isUndefined = function (value) {\n  'use strict';\n  return typeof value === 'undefined';\n};\n\n/**\n * ForEach helper function\n * Iterates over Arrays and Objects (own properties only)\n * @static\n * @param {*} obj\n * @param {function} callback Accepts 3 params: 1. value, 2. key, 3. the original array/object\n */\nshowdown.helper.forEach = function (obj, callback) {\n  'use strict';\n  // check if obj is defined\n  if (showdown.helper.isUndefined(obj)) {\n    throw new Error('obj param is required');\n  }\n\n  if (showdown.helper.isUndefined(callback)) {\n    throw new Error('callback param is required');\n  }\n\n  if (!showdown.helper.isFunction(callback)) {\n    throw new Error('callback param must be a function/closure');\n  }\n\n  if (typeof obj.forEach === 'function') {\n    obj.forEach(callback);\n  } else if (showdown.helper.isArray(obj)) {\n    for (var i = 0; i < obj.length; i++) {\n      callback(obj[i], i, obj);\n    }\n  } else if (typeof (obj) === 'object') {\n    for (var prop in obj) {\n      if (obj.hasOwnProperty(prop)) {\n        callback(obj[prop], prop, obj);\n      }\n    }\n  } else {\n    throw new Error('obj does not seem to be an array or an iterable object');\n  }\n};\n\n/**\n * Standardidize extension name\n * @static\n * @param {string} s extension name\n * @returns {string}\n */\nshowdown.helper.stdExtName = function (s) {\n  'use strict';\n  return s.replace(/[_?*+\\/\\\\.^-]/g, '').replace(/\\s/g, '').toLowerCase();\n};\n\nfunction escapeCharactersCallback (wholeMatch, m1) {\n  'use strict';\n  var charCodeToEscape = m1.charCodeAt(0);\n  return '¨E' + charCodeToEscape + 'E';\n}\n\n/**\n * Callback used to escape characters when passing through String.replace\n * @static\n * @param {string} wholeMatch\n * @param {string} m1\n * @returns {string}\n */\nshowdown.helper.escapeCharactersCallback = escapeCharactersCallback;\n\n/**\n * Escape characters in a string\n * @static\n * @param {string} text\n * @param {string} charsToEscape\n * @param {boolean} afterBackslash\n * @returns {XML|string|void|*}\n */\nshowdown.helper.escapeCharacters = function (text, charsToEscape, afterBackslash) {\n  'use strict';\n  // First we have to escape the escape characters so that\n  // we can build a character class out of them\n  var regexString = '([' + charsToEscape.replace(/([\\[\\]\\\\])/g, '\\\\$1') + '])';\n\n  if (afterBackslash) {\n    regexString = '\\\\\\\\' + regexString;\n  }\n\n  var regex = new RegExp(regexString, 'g');\n  text = text.replace(regex, escapeCharactersCallback);\n\n  return text;\n};\n\n/**\n * Unescape HTML entities\n * @param txt\n * @returns {string}\n */\nshowdown.helper.unescapeHTMLEntities = function (txt) {\n  'use strict';\n\n  return txt\n    .replace(/"/g, '\"')\n    .replace(/</g, '<')\n    .replace(/>/g, '>')\n    .replace(/&/g, '&');\n};\n\nvar rgxFindMatchPos = function (str, left, right, flags) {\n  'use strict';\n  var f = flags || '',\n      g = f.indexOf('g') > -1,\n      x = new RegExp(left + '|' + right, 'g' + f.replace(/g/g, '')),\n      l = new RegExp(left, f.replace(/g/g, '')),\n      pos = [],\n      t, s, m, start, end;\n\n  do {\n    t = 0;\n    while ((m = x.exec(str))) {\n      if (l.test(m[0])) {\n        if (!(t++)) {\n          s = x.lastIndex;\n          start = s - m[0].length;\n        }\n      } else if (t) {\n        if (!--t) {\n          end = m.index + m[0].length;\n          var obj = {\n            left: {start: start, end: s},\n            match: {start: s, end: m.index},\n            right: {start: m.index, end: end},\n            wholeMatch: {start: start, end: end}\n          };\n          pos.push(obj);\n          if (!g) {\n            return pos;\n          }\n        }\n      }\n    }\n  } while (t && (x.lastIndex = s));\n\n  return pos;\n};\n\n/**\n * matchRecursiveRegExp\n *\n * (c) 2007 Steven Levithan \n * MIT License\n *\n * Accepts a string to search, a left and right format delimiter\n * as regex patterns, and optional regex flags. Returns an array\n * of matches, allowing nested instances of left/right delimiters.\n * Use the \"g\" flag to return all matches, otherwise only the\n * first is returned. Be careful to ensure that the left and\n * right format delimiters produce mutually exclusive matches.\n * Backreferences are not supported within the right delimiter\n * due to how it is internally combined with the left delimiter.\n * When matching strings whose format delimiters are unbalanced\n * to the left or right, the output is intentionally as a\n * conventional regex library with recursion support would\n * produce, e.g. \"<\" and \">\" both produce [\"x\"] when using\n * \"<\" and \">\" as the delimiters (both strings contain a single,\n * balanced instance of \"\").\n *\n * examples:\n * matchRecursiveRegExp(\"test\", \"\\\\(\", \"\\\\)\")\n * returns: []\n * matchRecursiveRegExp(\">>t<>\", \"<\", \">\", \"g\")\n * returns: [\"t<>\", \"\"]\n * matchRecursiveRegExp(\"
    test
    \", \"]*>\", \"
    \", \"gi\")\n * returns: [\"test\"]\n */\nshowdown.helper.matchRecursiveRegExp = function (str, left, right, flags) {\n  'use strict';\n\n  var matchPos = rgxFindMatchPos (str, left, right, flags),\n      results = [];\n\n  for (var i = 0; i < matchPos.length; ++i) {\n    results.push([\n      str.slice(matchPos[i].wholeMatch.start, matchPos[i].wholeMatch.end),\n      str.slice(matchPos[i].match.start, matchPos[i].match.end),\n      str.slice(matchPos[i].left.start, matchPos[i].left.end),\n      str.slice(matchPos[i].right.start, matchPos[i].right.end)\n    ]);\n  }\n  return results;\n};\n\n/**\n *\n * @param {string} str\n * @param {string|function} replacement\n * @param {string} left\n * @param {string} right\n * @param {string} flags\n * @returns {string}\n */\nshowdown.helper.replaceRecursiveRegExp = function (str, replacement, left, right, flags) {\n  'use strict';\n\n  if (!showdown.helper.isFunction(replacement)) {\n    var repStr = replacement;\n    replacement = function () {\n      return repStr;\n    };\n  }\n\n  var matchPos = rgxFindMatchPos(str, left, right, flags),\n      finalStr = str,\n      lng = matchPos.length;\n\n  if (lng > 0) {\n    var bits = [];\n    if (matchPos[0].wholeMatch.start !== 0) {\n      bits.push(str.slice(0, matchPos[0].wholeMatch.start));\n    }\n    for (var i = 0; i < lng; ++i) {\n      bits.push(\n        replacement(\n          str.slice(matchPos[i].wholeMatch.start, matchPos[i].wholeMatch.end),\n          str.slice(matchPos[i].match.start, matchPos[i].match.end),\n          str.slice(matchPos[i].left.start, matchPos[i].left.end),\n          str.slice(matchPos[i].right.start, matchPos[i].right.end)\n        )\n      );\n      if (i < lng - 1) {\n        bits.push(str.slice(matchPos[i].wholeMatch.end, matchPos[i + 1].wholeMatch.start));\n      }\n    }\n    if (matchPos[lng - 1].wholeMatch.end < str.length) {\n      bits.push(str.slice(matchPos[lng - 1].wholeMatch.end));\n    }\n    finalStr = bits.join('');\n  }\n  return finalStr;\n};\n\n/**\n * Returns the index within the passed String object of the first occurrence of the specified regex,\n * starting the search at fromIndex. Returns -1 if the value is not found.\n *\n * @param {string} str string to search\n * @param {RegExp} regex Regular expression to search\n * @param {int} [fromIndex = 0] Index to start the search\n * @returns {Number}\n * @throws InvalidArgumentError\n */\nshowdown.helper.regexIndexOf = function (str, regex, fromIndex) {\n  'use strict';\n  if (!showdown.helper.isString(str)) {\n    throw 'InvalidArgumentError: first parameter of showdown.helper.regexIndexOf function must be a string';\n  }\n  if (regex instanceof RegExp === false) {\n    throw 'InvalidArgumentError: second parameter of showdown.helper.regexIndexOf function must be an instance of RegExp';\n  }\n  var indexOf = str.substring(fromIndex || 0).search(regex);\n  return (indexOf >= 0) ? (indexOf + (fromIndex || 0)) : indexOf;\n};\n\n/**\n * Splits the passed string object at the defined index, and returns an array composed of the two substrings\n * @param {string} str string to split\n * @param {int} index index to split string at\n * @returns {[string,string]}\n * @throws InvalidArgumentError\n */\nshowdown.helper.splitAtIndex = function (str, index) {\n  'use strict';\n  if (!showdown.helper.isString(str)) {\n    throw 'InvalidArgumentError: first parameter of showdown.helper.regexIndexOf function must be a string';\n  }\n  return [str.substring(0, index), str.substring(index)];\n};\n\n/**\n * Obfuscate an e-mail address through the use of Character Entities,\n * transforming ASCII characters into their equivalent decimal or hex entities.\n *\n * Since it has a random component, subsequent calls to this function produce different results\n *\n * @param {string} mail\n * @returns {string}\n */\nshowdown.helper.encodeEmailAddress = function (mail) {\n  'use strict';\n  var encode = [\n    function (ch) {\n      return '&#' + ch.charCodeAt(0) + ';';\n    },\n    function (ch) {\n      return '&#x' + ch.charCodeAt(0).toString(16) + ';';\n    },\n    function (ch) {\n      return ch;\n    }\n  ];\n\n  mail = mail.replace(/./g, function (ch) {\n    if (ch === '@') {\n      // this *must* be encoded. I insist.\n      ch = encode[Math.floor(Math.random() * 2)](ch);\n    } else {\n      var r = Math.random();\n      // roughly 10% raw, 45% hex, 45% dec\n      ch = (\n        r > 0.9 ? encode[2](ch) : r > 0.45 ? encode[1](ch) : encode[0](ch)\n      );\n    }\n    return ch;\n  });\n\n  return mail;\n};\n\n/**\n *\n * @param str\n * @param targetLength\n * @param padString\n * @returns {string}\n */\nshowdown.helper.padEnd = function padEnd (str, targetLength, padString) {\n  'use strict';\n  /*jshint bitwise: false*/\n  // eslint-disable-next-line space-infix-ops\n  targetLength = targetLength>>0; //floor if number or convert non-number to 0;\n  /*jshint bitwise: true*/\n  padString = String(padString || ' ');\n  if (str.length > targetLength) {\n    return String(str);\n  } else {\n    targetLength = targetLength - str.length;\n    if (targetLength > padString.length) {\n      padString += padString.repeat(targetLength / padString.length); //append to original to ensure we are longer than needed\n    }\n    return String(str) + padString.slice(0,targetLength);\n  }\n};\n\n/**\n * POLYFILLS\n */\n// use this instead of builtin is undefined for IE8 compatibility\nif (typeof console === 'undefined') {\n  console = {\n    warn: function (msg) {\n      'use strict';\n      alert(msg);\n    },\n    log: function (msg) {\n      'use strict';\n      alert(msg);\n    },\n    error: function (msg) {\n      'use strict';\n      throw msg;\n    }\n  };\n}\n\n/**\n * Common regexes.\n * We declare some common regexes to improve performance\n */\nshowdown.helper.regexes = {\n  asteriskDashAndColon: /([*_:~])/g\n};\n\n/**\n * EMOJIS LIST\n */\nshowdown.helper.emojis = {\n  '+1':'\\ud83d\\udc4d',\n  '-1':'\\ud83d\\udc4e',\n  '100':'\\ud83d\\udcaf',\n  '1234':'\\ud83d\\udd22',\n  '1st_place_medal':'\\ud83e\\udd47',\n  '2nd_place_medal':'\\ud83e\\udd48',\n  '3rd_place_medal':'\\ud83e\\udd49',\n  '8ball':'\\ud83c\\udfb1',\n  'a':'\\ud83c\\udd70\\ufe0f',\n  'ab':'\\ud83c\\udd8e',\n  'abc':'\\ud83d\\udd24',\n  'abcd':'\\ud83d\\udd21',\n  'accept':'\\ud83c\\ude51',\n  'aerial_tramway':'\\ud83d\\udea1',\n  'airplane':'\\u2708\\ufe0f',\n  'alarm_clock':'\\u23f0',\n  'alembic':'\\u2697\\ufe0f',\n  'alien':'\\ud83d\\udc7d',\n  'ambulance':'\\ud83d\\ude91',\n  'amphora':'\\ud83c\\udffa',\n  'anchor':'\\u2693\\ufe0f',\n  'angel':'\\ud83d\\udc7c',\n  'anger':'\\ud83d\\udca2',\n  'angry':'\\ud83d\\ude20',\n  'anguished':'\\ud83d\\ude27',\n  'ant':'\\ud83d\\udc1c',\n  'apple':'\\ud83c\\udf4e',\n  'aquarius':'\\u2652\\ufe0f',\n  'aries':'\\u2648\\ufe0f',\n  'arrow_backward':'\\u25c0\\ufe0f',\n  'arrow_double_down':'\\u23ec',\n  'arrow_double_up':'\\u23eb',\n  'arrow_down':'\\u2b07\\ufe0f',\n  'arrow_down_small':'\\ud83d\\udd3d',\n  'arrow_forward':'\\u25b6\\ufe0f',\n  'arrow_heading_down':'\\u2935\\ufe0f',\n  'arrow_heading_up':'\\u2934\\ufe0f',\n  'arrow_left':'\\u2b05\\ufe0f',\n  'arrow_lower_left':'\\u2199\\ufe0f',\n  'arrow_lower_right':'\\u2198\\ufe0f',\n  'arrow_right':'\\u27a1\\ufe0f',\n  'arrow_right_hook':'\\u21aa\\ufe0f',\n  'arrow_up':'\\u2b06\\ufe0f',\n  'arrow_up_down':'\\u2195\\ufe0f',\n  'arrow_up_small':'\\ud83d\\udd3c',\n  'arrow_upper_left':'\\u2196\\ufe0f',\n  'arrow_upper_right':'\\u2197\\ufe0f',\n  'arrows_clockwise':'\\ud83d\\udd03',\n  'arrows_counterclockwise':'\\ud83d\\udd04',\n  'art':'\\ud83c\\udfa8',\n  'articulated_lorry':'\\ud83d\\ude9b',\n  'artificial_satellite':'\\ud83d\\udef0',\n  'astonished':'\\ud83d\\ude32',\n  'athletic_shoe':'\\ud83d\\udc5f',\n  'atm':'\\ud83c\\udfe7',\n  'atom_symbol':'\\u269b\\ufe0f',\n  'avocado':'\\ud83e\\udd51',\n  'b':'\\ud83c\\udd71\\ufe0f',\n  'baby':'\\ud83d\\udc76',\n  'baby_bottle':'\\ud83c\\udf7c',\n  'baby_chick':'\\ud83d\\udc24',\n  'baby_symbol':'\\ud83d\\udebc',\n  'back':'\\ud83d\\udd19',\n  'bacon':'\\ud83e\\udd53',\n  'badminton':'\\ud83c\\udff8',\n  'baggage_claim':'\\ud83d\\udec4',\n  'baguette_bread':'\\ud83e\\udd56',\n  'balance_scale':'\\u2696\\ufe0f',\n  'balloon':'\\ud83c\\udf88',\n  'ballot_box':'\\ud83d\\uddf3',\n  'ballot_box_with_check':'\\u2611\\ufe0f',\n  'bamboo':'\\ud83c\\udf8d',\n  'banana':'\\ud83c\\udf4c',\n  'bangbang':'\\u203c\\ufe0f',\n  'bank':'\\ud83c\\udfe6',\n  'bar_chart':'\\ud83d\\udcca',\n  'barber':'\\ud83d\\udc88',\n  'baseball':'\\u26be\\ufe0f',\n  'basketball':'\\ud83c\\udfc0',\n  'basketball_man':'\\u26f9\\ufe0f',\n  'basketball_woman':'\\u26f9\\ufe0f‍\\u2640\\ufe0f',\n  'bat':'\\ud83e\\udd87',\n  'bath':'\\ud83d\\udec0',\n  'bathtub':'\\ud83d\\udec1',\n  'battery':'\\ud83d\\udd0b',\n  'beach_umbrella':'\\ud83c\\udfd6',\n  'bear':'\\ud83d\\udc3b',\n  'bed':'\\ud83d\\udecf',\n  'bee':'\\ud83d\\udc1d',\n  'beer':'\\ud83c\\udf7a',\n  'beers':'\\ud83c\\udf7b',\n  'beetle':'\\ud83d\\udc1e',\n  'beginner':'\\ud83d\\udd30',\n  'bell':'\\ud83d\\udd14',\n  'bellhop_bell':'\\ud83d\\udece',\n  'bento':'\\ud83c\\udf71',\n  'biking_man':'\\ud83d\\udeb4',\n  'bike':'\\ud83d\\udeb2',\n  'biking_woman':'\\ud83d\\udeb4‍\\u2640\\ufe0f',\n  'bikini':'\\ud83d\\udc59',\n  'biohazard':'\\u2623\\ufe0f',\n  'bird':'\\ud83d\\udc26',\n  'birthday':'\\ud83c\\udf82',\n  'black_circle':'\\u26ab\\ufe0f',\n  'black_flag':'\\ud83c\\udff4',\n  'black_heart':'\\ud83d\\udda4',\n  'black_joker':'\\ud83c\\udccf',\n  'black_large_square':'\\u2b1b\\ufe0f',\n  'black_medium_small_square':'\\u25fe\\ufe0f',\n  'black_medium_square':'\\u25fc\\ufe0f',\n  'black_nib':'\\u2712\\ufe0f',\n  'black_small_square':'\\u25aa\\ufe0f',\n  'black_square_button':'\\ud83d\\udd32',\n  'blonde_man':'\\ud83d\\udc71',\n  'blonde_woman':'\\ud83d\\udc71‍\\u2640\\ufe0f',\n  'blossom':'\\ud83c\\udf3c',\n  'blowfish':'\\ud83d\\udc21',\n  'blue_book':'\\ud83d\\udcd8',\n  'blue_car':'\\ud83d\\ude99',\n  'blue_heart':'\\ud83d\\udc99',\n  'blush':'\\ud83d\\ude0a',\n  'boar':'\\ud83d\\udc17',\n  'boat':'\\u26f5\\ufe0f',\n  'bomb':'\\ud83d\\udca3',\n  'book':'\\ud83d\\udcd6',\n  'bookmark':'\\ud83d\\udd16',\n  'bookmark_tabs':'\\ud83d\\udcd1',\n  'books':'\\ud83d\\udcda',\n  'boom':'\\ud83d\\udca5',\n  'boot':'\\ud83d\\udc62',\n  'bouquet':'\\ud83d\\udc90',\n  'bowing_man':'\\ud83d\\ude47',\n  'bow_and_arrow':'\\ud83c\\udff9',\n  'bowing_woman':'\\ud83d\\ude47‍\\u2640\\ufe0f',\n  'bowling':'\\ud83c\\udfb3',\n  'boxing_glove':'\\ud83e\\udd4a',\n  'boy':'\\ud83d\\udc66',\n  'bread':'\\ud83c\\udf5e',\n  'bride_with_veil':'\\ud83d\\udc70',\n  'bridge_at_night':'\\ud83c\\udf09',\n  'briefcase':'\\ud83d\\udcbc',\n  'broken_heart':'\\ud83d\\udc94',\n  'bug':'\\ud83d\\udc1b',\n  'building_construction':'\\ud83c\\udfd7',\n  'bulb':'\\ud83d\\udca1',\n  'bullettrain_front':'\\ud83d\\ude85',\n  'bullettrain_side':'\\ud83d\\ude84',\n  'burrito':'\\ud83c\\udf2f',\n  'bus':'\\ud83d\\ude8c',\n  'business_suit_levitating':'\\ud83d\\udd74',\n  'busstop':'\\ud83d\\ude8f',\n  'bust_in_silhouette':'\\ud83d\\udc64',\n  'busts_in_silhouette':'\\ud83d\\udc65',\n  'butterfly':'\\ud83e\\udd8b',\n  'cactus':'\\ud83c\\udf35',\n  'cake':'\\ud83c\\udf70',\n  'calendar':'\\ud83d\\udcc6',\n  'call_me_hand':'\\ud83e\\udd19',\n  'calling':'\\ud83d\\udcf2',\n  'camel':'\\ud83d\\udc2b',\n  'camera':'\\ud83d\\udcf7',\n  'camera_flash':'\\ud83d\\udcf8',\n  'camping':'\\ud83c\\udfd5',\n  'cancer':'\\u264b\\ufe0f',\n  'candle':'\\ud83d\\udd6f',\n  'candy':'\\ud83c\\udf6c',\n  'canoe':'\\ud83d\\udef6',\n  'capital_abcd':'\\ud83d\\udd20',\n  'capricorn':'\\u2651\\ufe0f',\n  'car':'\\ud83d\\ude97',\n  'card_file_box':'\\ud83d\\uddc3',\n  'card_index':'\\ud83d\\udcc7',\n  'card_index_dividers':'\\ud83d\\uddc2',\n  'carousel_horse':'\\ud83c\\udfa0',\n  'carrot':'\\ud83e\\udd55',\n  'cat':'\\ud83d\\udc31',\n  'cat2':'\\ud83d\\udc08',\n  'cd':'\\ud83d\\udcbf',\n  'chains':'\\u26d3',\n  'champagne':'\\ud83c\\udf7e',\n  'chart':'\\ud83d\\udcb9',\n  'chart_with_downwards_trend':'\\ud83d\\udcc9',\n  'chart_with_upwards_trend':'\\ud83d\\udcc8',\n  'checkered_flag':'\\ud83c\\udfc1',\n  'cheese':'\\ud83e\\uddc0',\n  'cherries':'\\ud83c\\udf52',\n  'cherry_blossom':'\\ud83c\\udf38',\n  'chestnut':'\\ud83c\\udf30',\n  'chicken':'\\ud83d\\udc14',\n  'children_crossing':'\\ud83d\\udeb8',\n  'chipmunk':'\\ud83d\\udc3f',\n  'chocolate_bar':'\\ud83c\\udf6b',\n  'christmas_tree':'\\ud83c\\udf84',\n  'church':'\\u26ea\\ufe0f',\n  'cinema':'\\ud83c\\udfa6',\n  'circus_tent':'\\ud83c\\udfaa',\n  'city_sunrise':'\\ud83c\\udf07',\n  'city_sunset':'\\ud83c\\udf06',\n  'cityscape':'\\ud83c\\udfd9',\n  'cl':'\\ud83c\\udd91',\n  'clamp':'\\ud83d\\udddc',\n  'clap':'\\ud83d\\udc4f',\n  'clapper':'\\ud83c\\udfac',\n  'classical_building':'\\ud83c\\udfdb',\n  'clinking_glasses':'\\ud83e\\udd42',\n  'clipboard':'\\ud83d\\udccb',\n  'clock1':'\\ud83d\\udd50',\n  'clock10':'\\ud83d\\udd59',\n  'clock1030':'\\ud83d\\udd65',\n  'clock11':'\\ud83d\\udd5a',\n  'clock1130':'\\ud83d\\udd66',\n  'clock12':'\\ud83d\\udd5b',\n  'clock1230':'\\ud83d\\udd67',\n  'clock130':'\\ud83d\\udd5c',\n  'clock2':'\\ud83d\\udd51',\n  'clock230':'\\ud83d\\udd5d',\n  'clock3':'\\ud83d\\udd52',\n  'clock330':'\\ud83d\\udd5e',\n  'clock4':'\\ud83d\\udd53',\n  'clock430':'\\ud83d\\udd5f',\n  'clock5':'\\ud83d\\udd54',\n  'clock530':'\\ud83d\\udd60',\n  'clock6':'\\ud83d\\udd55',\n  'clock630':'\\ud83d\\udd61',\n  'clock7':'\\ud83d\\udd56',\n  'clock730':'\\ud83d\\udd62',\n  'clock8':'\\ud83d\\udd57',\n  'clock830':'\\ud83d\\udd63',\n  'clock9':'\\ud83d\\udd58',\n  'clock930':'\\ud83d\\udd64',\n  'closed_book':'\\ud83d\\udcd5',\n  'closed_lock_with_key':'\\ud83d\\udd10',\n  'closed_umbrella':'\\ud83c\\udf02',\n  'cloud':'\\u2601\\ufe0f',\n  'cloud_with_lightning':'\\ud83c\\udf29',\n  'cloud_with_lightning_and_rain':'\\u26c8',\n  'cloud_with_rain':'\\ud83c\\udf27',\n  'cloud_with_snow':'\\ud83c\\udf28',\n  'clown_face':'\\ud83e\\udd21',\n  'clubs':'\\u2663\\ufe0f',\n  'cocktail':'\\ud83c\\udf78',\n  'coffee':'\\u2615\\ufe0f',\n  'coffin':'\\u26b0\\ufe0f',\n  'cold_sweat':'\\ud83d\\ude30',\n  'comet':'\\u2604\\ufe0f',\n  'computer':'\\ud83d\\udcbb',\n  'computer_mouse':'\\ud83d\\uddb1',\n  'confetti_ball':'\\ud83c\\udf8a',\n  'confounded':'\\ud83d\\ude16',\n  'confused':'\\ud83d\\ude15',\n  'congratulations':'\\u3297\\ufe0f',\n  'construction':'\\ud83d\\udea7',\n  'construction_worker_man':'\\ud83d\\udc77',\n  'construction_worker_woman':'\\ud83d\\udc77‍\\u2640\\ufe0f',\n  'control_knobs':'\\ud83c\\udf9b',\n  'convenience_store':'\\ud83c\\udfea',\n  'cookie':'\\ud83c\\udf6a',\n  'cool':'\\ud83c\\udd92',\n  'policeman':'\\ud83d\\udc6e',\n  'copyright':'\\u00a9\\ufe0f',\n  'corn':'\\ud83c\\udf3d',\n  'couch_and_lamp':'\\ud83d\\udecb',\n  'couple':'\\ud83d\\udc6b',\n  'couple_with_heart_woman_man':'\\ud83d\\udc91',\n  'couple_with_heart_man_man':'\\ud83d\\udc68‍\\u2764\\ufe0f‍\\ud83d\\udc68',\n  'couple_with_heart_woman_woman':'\\ud83d\\udc69‍\\u2764\\ufe0f‍\\ud83d\\udc69',\n  'couplekiss_man_man':'\\ud83d\\udc68‍\\u2764\\ufe0f‍\\ud83d\\udc8b‍\\ud83d\\udc68',\n  'couplekiss_man_woman':'\\ud83d\\udc8f',\n  'couplekiss_woman_woman':'\\ud83d\\udc69‍\\u2764\\ufe0f‍\\ud83d\\udc8b‍\\ud83d\\udc69',\n  'cow':'\\ud83d\\udc2e',\n  'cow2':'\\ud83d\\udc04',\n  'cowboy_hat_face':'\\ud83e\\udd20',\n  'crab':'\\ud83e\\udd80',\n  'crayon':'\\ud83d\\udd8d',\n  'credit_card':'\\ud83d\\udcb3',\n  'crescent_moon':'\\ud83c\\udf19',\n  'cricket':'\\ud83c\\udfcf',\n  'crocodile':'\\ud83d\\udc0a',\n  'croissant':'\\ud83e\\udd50',\n  'crossed_fingers':'\\ud83e\\udd1e',\n  'crossed_flags':'\\ud83c\\udf8c',\n  'crossed_swords':'\\u2694\\ufe0f',\n  'crown':'\\ud83d\\udc51',\n  'cry':'\\ud83d\\ude22',\n  'crying_cat_face':'\\ud83d\\ude3f',\n  'crystal_ball':'\\ud83d\\udd2e',\n  'cucumber':'\\ud83e\\udd52',\n  'cupid':'\\ud83d\\udc98',\n  'curly_loop':'\\u27b0',\n  'currency_exchange':'\\ud83d\\udcb1',\n  'curry':'\\ud83c\\udf5b',\n  'custard':'\\ud83c\\udf6e',\n  'customs':'\\ud83d\\udec3',\n  'cyclone':'\\ud83c\\udf00',\n  'dagger':'\\ud83d\\udde1',\n  'dancer':'\\ud83d\\udc83',\n  'dancing_women':'\\ud83d\\udc6f',\n  'dancing_men':'\\ud83d\\udc6f‍\\u2642\\ufe0f',\n  'dango':'\\ud83c\\udf61',\n  'dark_sunglasses':'\\ud83d\\udd76',\n  'dart':'\\ud83c\\udfaf',\n  'dash':'\\ud83d\\udca8',\n  'date':'\\ud83d\\udcc5',\n  'deciduous_tree':'\\ud83c\\udf33',\n  'deer':'\\ud83e\\udd8c',\n  'department_store':'\\ud83c\\udfec',\n  'derelict_house':'\\ud83c\\udfda',\n  'desert':'\\ud83c\\udfdc',\n  'desert_island':'\\ud83c\\udfdd',\n  'desktop_computer':'\\ud83d\\udda5',\n  'male_detective':'\\ud83d\\udd75\\ufe0f',\n  'diamond_shape_with_a_dot_inside':'\\ud83d\\udca0',\n  'diamonds':'\\u2666\\ufe0f',\n  'disappointed':'\\ud83d\\ude1e',\n  'disappointed_relieved':'\\ud83d\\ude25',\n  'dizzy':'\\ud83d\\udcab',\n  'dizzy_face':'\\ud83d\\ude35',\n  'do_not_litter':'\\ud83d\\udeaf',\n  'dog':'\\ud83d\\udc36',\n  'dog2':'\\ud83d\\udc15',\n  'dollar':'\\ud83d\\udcb5',\n  'dolls':'\\ud83c\\udf8e',\n  'dolphin':'\\ud83d\\udc2c',\n  'door':'\\ud83d\\udeaa',\n  'doughnut':'\\ud83c\\udf69',\n  'dove':'\\ud83d\\udd4a',\n  'dragon':'\\ud83d\\udc09',\n  'dragon_face':'\\ud83d\\udc32',\n  'dress':'\\ud83d\\udc57',\n  'dromedary_camel':'\\ud83d\\udc2a',\n  'drooling_face':'\\ud83e\\udd24',\n  'droplet':'\\ud83d\\udca7',\n  'drum':'\\ud83e\\udd41',\n  'duck':'\\ud83e\\udd86',\n  'dvd':'\\ud83d\\udcc0',\n  'e-mail':'\\ud83d\\udce7',\n  'eagle':'\\ud83e\\udd85',\n  'ear':'\\ud83d\\udc42',\n  'ear_of_rice':'\\ud83c\\udf3e',\n  'earth_africa':'\\ud83c\\udf0d',\n  'earth_americas':'\\ud83c\\udf0e',\n  'earth_asia':'\\ud83c\\udf0f',\n  'egg':'\\ud83e\\udd5a',\n  'eggplant':'\\ud83c\\udf46',\n  'eight_pointed_black_star':'\\u2734\\ufe0f',\n  'eight_spoked_asterisk':'\\u2733\\ufe0f',\n  'electric_plug':'\\ud83d\\udd0c',\n  'elephant':'\\ud83d\\udc18',\n  'email':'\\u2709\\ufe0f',\n  'end':'\\ud83d\\udd1a',\n  'envelope_with_arrow':'\\ud83d\\udce9',\n  'euro':'\\ud83d\\udcb6',\n  'european_castle':'\\ud83c\\udff0',\n  'european_post_office':'\\ud83c\\udfe4',\n  'evergreen_tree':'\\ud83c\\udf32',\n  'exclamation':'\\u2757\\ufe0f',\n  'expressionless':'\\ud83d\\ude11',\n  'eye':'\\ud83d\\udc41',\n  'eye_speech_bubble':'\\ud83d\\udc41‍\\ud83d\\udde8',\n  'eyeglasses':'\\ud83d\\udc53',\n  'eyes':'\\ud83d\\udc40',\n  'face_with_head_bandage':'\\ud83e\\udd15',\n  'face_with_thermometer':'\\ud83e\\udd12',\n  'fist_oncoming':'\\ud83d\\udc4a',\n  'factory':'\\ud83c\\udfed',\n  'fallen_leaf':'\\ud83c\\udf42',\n  'family_man_woman_boy':'\\ud83d\\udc6a',\n  'family_man_boy':'\\ud83d\\udc68‍\\ud83d\\udc66',\n  'family_man_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_man_girl':'\\ud83d\\udc68‍\\ud83d\\udc67',\n  'family_man_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_man_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_man_man_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc66',\n  'family_man_man_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_man_man_girl':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67',\n  'family_man_man_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_man_man_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_man_woman_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_man_woman_girl':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67',\n  'family_man_woman_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_man_woman_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_woman_boy':'\\ud83d\\udc69‍\\ud83d\\udc66',\n  'family_woman_boy_boy':'\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_woman_girl':'\\ud83d\\udc69‍\\ud83d\\udc67',\n  'family_woman_girl_boy':'\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_woman_girl_girl':'\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_woman_woman_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc66',\n  'family_woman_woman_boy_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_woman_woman_girl':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67',\n  'family_woman_woman_girl_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_woman_woman_girl_girl':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'fast_forward':'\\u23e9',\n  'fax':'\\ud83d\\udce0',\n  'fearful':'\\ud83d\\ude28',\n  'feet':'\\ud83d\\udc3e',\n  'female_detective':'\\ud83d\\udd75\\ufe0f‍\\u2640\\ufe0f',\n  'ferris_wheel':'\\ud83c\\udfa1',\n  'ferry':'\\u26f4',\n  'field_hockey':'\\ud83c\\udfd1',\n  'file_cabinet':'\\ud83d\\uddc4',\n  'file_folder':'\\ud83d\\udcc1',\n  'film_projector':'\\ud83d\\udcfd',\n  'film_strip':'\\ud83c\\udf9e',\n  'fire':'\\ud83d\\udd25',\n  'fire_engine':'\\ud83d\\ude92',\n  'fireworks':'\\ud83c\\udf86',\n  'first_quarter_moon':'\\ud83c\\udf13',\n  'first_quarter_moon_with_face':'\\ud83c\\udf1b',\n  'fish':'\\ud83d\\udc1f',\n  'fish_cake':'\\ud83c\\udf65',\n  'fishing_pole_and_fish':'\\ud83c\\udfa3',\n  'fist_raised':'\\u270a',\n  'fist_left':'\\ud83e\\udd1b',\n  'fist_right':'\\ud83e\\udd1c',\n  'flags':'\\ud83c\\udf8f',\n  'flashlight':'\\ud83d\\udd26',\n  'fleur_de_lis':'\\u269c\\ufe0f',\n  'flight_arrival':'\\ud83d\\udeec',\n  'flight_departure':'\\ud83d\\udeeb',\n  'floppy_disk':'\\ud83d\\udcbe',\n  'flower_playing_cards':'\\ud83c\\udfb4',\n  'flushed':'\\ud83d\\ude33',\n  'fog':'\\ud83c\\udf2b',\n  'foggy':'\\ud83c\\udf01',\n  'football':'\\ud83c\\udfc8',\n  'footprints':'\\ud83d\\udc63',\n  'fork_and_knife':'\\ud83c\\udf74',\n  'fountain':'\\u26f2\\ufe0f',\n  'fountain_pen':'\\ud83d\\udd8b',\n  'four_leaf_clover':'\\ud83c\\udf40',\n  'fox_face':'\\ud83e\\udd8a',\n  'framed_picture':'\\ud83d\\uddbc',\n  'free':'\\ud83c\\udd93',\n  'fried_egg':'\\ud83c\\udf73',\n  'fried_shrimp':'\\ud83c\\udf64',\n  'fries':'\\ud83c\\udf5f',\n  'frog':'\\ud83d\\udc38',\n  'frowning':'\\ud83d\\ude26',\n  'frowning_face':'\\u2639\\ufe0f',\n  'frowning_man':'\\ud83d\\ude4d‍\\u2642\\ufe0f',\n  'frowning_woman':'\\ud83d\\ude4d',\n  'middle_finger':'\\ud83d\\udd95',\n  'fuelpump':'\\u26fd\\ufe0f',\n  'full_moon':'\\ud83c\\udf15',\n  'full_moon_with_face':'\\ud83c\\udf1d',\n  'funeral_urn':'\\u26b1\\ufe0f',\n  'game_die':'\\ud83c\\udfb2',\n  'gear':'\\u2699\\ufe0f',\n  'gem':'\\ud83d\\udc8e',\n  'gemini':'\\u264a\\ufe0f',\n  'ghost':'\\ud83d\\udc7b',\n  'gift':'\\ud83c\\udf81',\n  'gift_heart':'\\ud83d\\udc9d',\n  'girl':'\\ud83d\\udc67',\n  'globe_with_meridians':'\\ud83c\\udf10',\n  'goal_net':'\\ud83e\\udd45',\n  'goat':'\\ud83d\\udc10',\n  'golf':'\\u26f3\\ufe0f',\n  'golfing_man':'\\ud83c\\udfcc\\ufe0f',\n  'golfing_woman':'\\ud83c\\udfcc\\ufe0f‍\\u2640\\ufe0f',\n  'gorilla':'\\ud83e\\udd8d',\n  'grapes':'\\ud83c\\udf47',\n  'green_apple':'\\ud83c\\udf4f',\n  'green_book':'\\ud83d\\udcd7',\n  'green_heart':'\\ud83d\\udc9a',\n  'green_salad':'\\ud83e\\udd57',\n  'grey_exclamation':'\\u2755',\n  'grey_question':'\\u2754',\n  'grimacing':'\\ud83d\\ude2c',\n  'grin':'\\ud83d\\ude01',\n  'grinning':'\\ud83d\\ude00',\n  'guardsman':'\\ud83d\\udc82',\n  'guardswoman':'\\ud83d\\udc82‍\\u2640\\ufe0f',\n  'guitar':'\\ud83c\\udfb8',\n  'gun':'\\ud83d\\udd2b',\n  'haircut_woman':'\\ud83d\\udc87',\n  'haircut_man':'\\ud83d\\udc87‍\\u2642\\ufe0f',\n  'hamburger':'\\ud83c\\udf54',\n  'hammer':'\\ud83d\\udd28',\n  'hammer_and_pick':'\\u2692',\n  'hammer_and_wrench':'\\ud83d\\udee0',\n  'hamster':'\\ud83d\\udc39',\n  'hand':'\\u270b',\n  'handbag':'\\ud83d\\udc5c',\n  'handshake':'\\ud83e\\udd1d',\n  'hankey':'\\ud83d\\udca9',\n  'hatched_chick':'\\ud83d\\udc25',\n  'hatching_chick':'\\ud83d\\udc23',\n  'headphones':'\\ud83c\\udfa7',\n  'hear_no_evil':'\\ud83d\\ude49',\n  'heart':'\\u2764\\ufe0f',\n  'heart_decoration':'\\ud83d\\udc9f',\n  'heart_eyes':'\\ud83d\\ude0d',\n  'heart_eyes_cat':'\\ud83d\\ude3b',\n  'heartbeat':'\\ud83d\\udc93',\n  'heartpulse':'\\ud83d\\udc97',\n  'hearts':'\\u2665\\ufe0f',\n  'heavy_check_mark':'\\u2714\\ufe0f',\n  'heavy_division_sign':'\\u2797',\n  'heavy_dollar_sign':'\\ud83d\\udcb2',\n  'heavy_heart_exclamation':'\\u2763\\ufe0f',\n  'heavy_minus_sign':'\\u2796',\n  'heavy_multiplication_x':'\\u2716\\ufe0f',\n  'heavy_plus_sign':'\\u2795',\n  'helicopter':'\\ud83d\\ude81',\n  'herb':'\\ud83c\\udf3f',\n  'hibiscus':'\\ud83c\\udf3a',\n  'high_brightness':'\\ud83d\\udd06',\n  'high_heel':'\\ud83d\\udc60',\n  'hocho':'\\ud83d\\udd2a',\n  'hole':'\\ud83d\\udd73',\n  'honey_pot':'\\ud83c\\udf6f',\n  'horse':'\\ud83d\\udc34',\n  'horse_racing':'\\ud83c\\udfc7',\n  'hospital':'\\ud83c\\udfe5',\n  'hot_pepper':'\\ud83c\\udf36',\n  'hotdog':'\\ud83c\\udf2d',\n  'hotel':'\\ud83c\\udfe8',\n  'hotsprings':'\\u2668\\ufe0f',\n  'hourglass':'\\u231b\\ufe0f',\n  'hourglass_flowing_sand':'\\u23f3',\n  'house':'\\ud83c\\udfe0',\n  'house_with_garden':'\\ud83c\\udfe1',\n  'houses':'\\ud83c\\udfd8',\n  'hugs':'\\ud83e\\udd17',\n  'hushed':'\\ud83d\\ude2f',\n  'ice_cream':'\\ud83c\\udf68',\n  'ice_hockey':'\\ud83c\\udfd2',\n  'ice_skate':'\\u26f8',\n  'icecream':'\\ud83c\\udf66',\n  'id':'\\ud83c\\udd94',\n  'ideograph_advantage':'\\ud83c\\ude50',\n  'imp':'\\ud83d\\udc7f',\n  'inbox_tray':'\\ud83d\\udce5',\n  'incoming_envelope':'\\ud83d\\udce8',\n  'tipping_hand_woman':'\\ud83d\\udc81',\n  'information_source':'\\u2139\\ufe0f',\n  'innocent':'\\ud83d\\ude07',\n  'interrobang':'\\u2049\\ufe0f',\n  'iphone':'\\ud83d\\udcf1',\n  'izakaya_lantern':'\\ud83c\\udfee',\n  'jack_o_lantern':'\\ud83c\\udf83',\n  'japan':'\\ud83d\\uddfe',\n  'japanese_castle':'\\ud83c\\udfef',\n  'japanese_goblin':'\\ud83d\\udc7a',\n  'japanese_ogre':'\\ud83d\\udc79',\n  'jeans':'\\ud83d\\udc56',\n  'joy':'\\ud83d\\ude02',\n  'joy_cat':'\\ud83d\\ude39',\n  'joystick':'\\ud83d\\udd79',\n  'kaaba':'\\ud83d\\udd4b',\n  'key':'\\ud83d\\udd11',\n  'keyboard':'\\u2328\\ufe0f',\n  'keycap_ten':'\\ud83d\\udd1f',\n  'kick_scooter':'\\ud83d\\udef4',\n  'kimono':'\\ud83d\\udc58',\n  'kiss':'\\ud83d\\udc8b',\n  'kissing':'\\ud83d\\ude17',\n  'kissing_cat':'\\ud83d\\ude3d',\n  'kissing_closed_eyes':'\\ud83d\\ude1a',\n  'kissing_heart':'\\ud83d\\ude18',\n  'kissing_smiling_eyes':'\\ud83d\\ude19',\n  'kiwi_fruit':'\\ud83e\\udd5d',\n  'koala':'\\ud83d\\udc28',\n  'koko':'\\ud83c\\ude01',\n  'label':'\\ud83c\\udff7',\n  'large_blue_circle':'\\ud83d\\udd35',\n  'large_blue_diamond':'\\ud83d\\udd37',\n  'large_orange_diamond':'\\ud83d\\udd36',\n  'last_quarter_moon':'\\ud83c\\udf17',\n  'last_quarter_moon_with_face':'\\ud83c\\udf1c',\n  'latin_cross':'\\u271d\\ufe0f',\n  'laughing':'\\ud83d\\ude06',\n  'leaves':'\\ud83c\\udf43',\n  'ledger':'\\ud83d\\udcd2',\n  'left_luggage':'\\ud83d\\udec5',\n  'left_right_arrow':'\\u2194\\ufe0f',\n  'leftwards_arrow_with_hook':'\\u21a9\\ufe0f',\n  'lemon':'\\ud83c\\udf4b',\n  'leo':'\\u264c\\ufe0f',\n  'leopard':'\\ud83d\\udc06',\n  'level_slider':'\\ud83c\\udf9a',\n  'libra':'\\u264e\\ufe0f',\n  'light_rail':'\\ud83d\\ude88',\n  'link':'\\ud83d\\udd17',\n  'lion':'\\ud83e\\udd81',\n  'lips':'\\ud83d\\udc44',\n  'lipstick':'\\ud83d\\udc84',\n  'lizard':'\\ud83e\\udd8e',\n  'lock':'\\ud83d\\udd12',\n  'lock_with_ink_pen':'\\ud83d\\udd0f',\n  'lollipop':'\\ud83c\\udf6d',\n  'loop':'\\u27bf',\n  'loud_sound':'\\ud83d\\udd0a',\n  'loudspeaker':'\\ud83d\\udce2',\n  'love_hotel':'\\ud83c\\udfe9',\n  'love_letter':'\\ud83d\\udc8c',\n  'low_brightness':'\\ud83d\\udd05',\n  'lying_face':'\\ud83e\\udd25',\n  'm':'\\u24c2\\ufe0f',\n  'mag':'\\ud83d\\udd0d',\n  'mag_right':'\\ud83d\\udd0e',\n  'mahjong':'\\ud83c\\udc04\\ufe0f',\n  'mailbox':'\\ud83d\\udceb',\n  'mailbox_closed':'\\ud83d\\udcea',\n  'mailbox_with_mail':'\\ud83d\\udcec',\n  'mailbox_with_no_mail':'\\ud83d\\udced',\n  'man':'\\ud83d\\udc68',\n  'man_artist':'\\ud83d\\udc68‍\\ud83c\\udfa8',\n  'man_astronaut':'\\ud83d\\udc68‍\\ud83d\\ude80',\n  'man_cartwheeling':'\\ud83e\\udd38‍\\u2642\\ufe0f',\n  'man_cook':'\\ud83d\\udc68‍\\ud83c\\udf73',\n  'man_dancing':'\\ud83d\\udd7a',\n  'man_facepalming':'\\ud83e\\udd26‍\\u2642\\ufe0f',\n  'man_factory_worker':'\\ud83d\\udc68‍\\ud83c\\udfed',\n  'man_farmer':'\\ud83d\\udc68‍\\ud83c\\udf3e',\n  'man_firefighter':'\\ud83d\\udc68‍\\ud83d\\ude92',\n  'man_health_worker':'\\ud83d\\udc68‍\\u2695\\ufe0f',\n  'man_in_tuxedo':'\\ud83e\\udd35',\n  'man_judge':'\\ud83d\\udc68‍\\u2696\\ufe0f',\n  'man_juggling':'\\ud83e\\udd39‍\\u2642\\ufe0f',\n  'man_mechanic':'\\ud83d\\udc68‍\\ud83d\\udd27',\n  'man_office_worker':'\\ud83d\\udc68‍\\ud83d\\udcbc',\n  'man_pilot':'\\ud83d\\udc68‍\\u2708\\ufe0f',\n  'man_playing_handball':'\\ud83e\\udd3e‍\\u2642\\ufe0f',\n  'man_playing_water_polo':'\\ud83e\\udd3d‍\\u2642\\ufe0f',\n  'man_scientist':'\\ud83d\\udc68‍\\ud83d\\udd2c',\n  'man_shrugging':'\\ud83e\\udd37‍\\u2642\\ufe0f',\n  'man_singer':'\\ud83d\\udc68‍\\ud83c\\udfa4',\n  'man_student':'\\ud83d\\udc68‍\\ud83c\\udf93',\n  'man_teacher':'\\ud83d\\udc68‍\\ud83c\\udfeb',\n  'man_technologist':'\\ud83d\\udc68‍\\ud83d\\udcbb',\n  'man_with_gua_pi_mao':'\\ud83d\\udc72',\n  'man_with_turban':'\\ud83d\\udc73',\n  'tangerine':'\\ud83c\\udf4a',\n  'mans_shoe':'\\ud83d\\udc5e',\n  'mantelpiece_clock':'\\ud83d\\udd70',\n  'maple_leaf':'\\ud83c\\udf41',\n  'martial_arts_uniform':'\\ud83e\\udd4b',\n  'mask':'\\ud83d\\ude37',\n  'massage_woman':'\\ud83d\\udc86',\n  'massage_man':'\\ud83d\\udc86‍\\u2642\\ufe0f',\n  'meat_on_bone':'\\ud83c\\udf56',\n  'medal_military':'\\ud83c\\udf96',\n  'medal_sports':'\\ud83c\\udfc5',\n  'mega':'\\ud83d\\udce3',\n  'melon':'\\ud83c\\udf48',\n  'memo':'\\ud83d\\udcdd',\n  'men_wrestling':'\\ud83e\\udd3c‍\\u2642\\ufe0f',\n  'menorah':'\\ud83d\\udd4e',\n  'mens':'\\ud83d\\udeb9',\n  'metal':'\\ud83e\\udd18',\n  'metro':'\\ud83d\\ude87',\n  'microphone':'\\ud83c\\udfa4',\n  'microscope':'\\ud83d\\udd2c',\n  'milk_glass':'\\ud83e\\udd5b',\n  'milky_way':'\\ud83c\\udf0c',\n  'minibus':'\\ud83d\\ude90',\n  'minidisc':'\\ud83d\\udcbd',\n  'mobile_phone_off':'\\ud83d\\udcf4',\n  'money_mouth_face':'\\ud83e\\udd11',\n  'money_with_wings':'\\ud83d\\udcb8',\n  'moneybag':'\\ud83d\\udcb0',\n  'monkey':'\\ud83d\\udc12',\n  'monkey_face':'\\ud83d\\udc35',\n  'monorail':'\\ud83d\\ude9d',\n  'moon':'\\ud83c\\udf14',\n  'mortar_board':'\\ud83c\\udf93',\n  'mosque':'\\ud83d\\udd4c',\n  'motor_boat':'\\ud83d\\udee5',\n  'motor_scooter':'\\ud83d\\udef5',\n  'motorcycle':'\\ud83c\\udfcd',\n  'motorway':'\\ud83d\\udee3',\n  'mount_fuji':'\\ud83d\\uddfb',\n  'mountain':'\\u26f0',\n  'mountain_biking_man':'\\ud83d\\udeb5',\n  'mountain_biking_woman':'\\ud83d\\udeb5‍\\u2640\\ufe0f',\n  'mountain_cableway':'\\ud83d\\udea0',\n  'mountain_railway':'\\ud83d\\ude9e',\n  'mountain_snow':'\\ud83c\\udfd4',\n  'mouse':'\\ud83d\\udc2d',\n  'mouse2':'\\ud83d\\udc01',\n  'movie_camera':'\\ud83c\\udfa5',\n  'moyai':'\\ud83d\\uddff',\n  'mrs_claus':'\\ud83e\\udd36',\n  'muscle':'\\ud83d\\udcaa',\n  'mushroom':'\\ud83c\\udf44',\n  'musical_keyboard':'\\ud83c\\udfb9',\n  'musical_note':'\\ud83c\\udfb5',\n  'musical_score':'\\ud83c\\udfbc',\n  'mute':'\\ud83d\\udd07',\n  'nail_care':'\\ud83d\\udc85',\n  'name_badge':'\\ud83d\\udcdb',\n  'national_park':'\\ud83c\\udfde',\n  'nauseated_face':'\\ud83e\\udd22',\n  'necktie':'\\ud83d\\udc54',\n  'negative_squared_cross_mark':'\\u274e',\n  'nerd_face':'\\ud83e\\udd13',\n  'neutral_face':'\\ud83d\\ude10',\n  'new':'\\ud83c\\udd95',\n  'new_moon':'\\ud83c\\udf11',\n  'new_moon_with_face':'\\ud83c\\udf1a',\n  'newspaper':'\\ud83d\\udcf0',\n  'newspaper_roll':'\\ud83d\\uddde',\n  'next_track_button':'\\u23ed',\n  'ng':'\\ud83c\\udd96',\n  'no_good_man':'\\ud83d\\ude45‍\\u2642\\ufe0f',\n  'no_good_woman':'\\ud83d\\ude45',\n  'night_with_stars':'\\ud83c\\udf03',\n  'no_bell':'\\ud83d\\udd15',\n  'no_bicycles':'\\ud83d\\udeb3',\n  'no_entry':'\\u26d4\\ufe0f',\n  'no_entry_sign':'\\ud83d\\udeab',\n  'no_mobile_phones':'\\ud83d\\udcf5',\n  'no_mouth':'\\ud83d\\ude36',\n  'no_pedestrians':'\\ud83d\\udeb7',\n  'no_smoking':'\\ud83d\\udead',\n  'non-potable_water':'\\ud83d\\udeb1',\n  'nose':'\\ud83d\\udc43',\n  'notebook':'\\ud83d\\udcd3',\n  'notebook_with_decorative_cover':'\\ud83d\\udcd4',\n  'notes':'\\ud83c\\udfb6',\n  'nut_and_bolt':'\\ud83d\\udd29',\n  'o':'\\u2b55\\ufe0f',\n  'o2':'\\ud83c\\udd7e\\ufe0f',\n  'ocean':'\\ud83c\\udf0a',\n  'octopus':'\\ud83d\\udc19',\n  'oden':'\\ud83c\\udf62',\n  'office':'\\ud83c\\udfe2',\n  'oil_drum':'\\ud83d\\udee2',\n  'ok':'\\ud83c\\udd97',\n  'ok_hand':'\\ud83d\\udc4c',\n  'ok_man':'\\ud83d\\ude46‍\\u2642\\ufe0f',\n  'ok_woman':'\\ud83d\\ude46',\n  'old_key':'\\ud83d\\udddd',\n  'older_man':'\\ud83d\\udc74',\n  'older_woman':'\\ud83d\\udc75',\n  'om':'\\ud83d\\udd49',\n  'on':'\\ud83d\\udd1b',\n  'oncoming_automobile':'\\ud83d\\ude98',\n  'oncoming_bus':'\\ud83d\\ude8d',\n  'oncoming_police_car':'\\ud83d\\ude94',\n  'oncoming_taxi':'\\ud83d\\ude96',\n  'open_file_folder':'\\ud83d\\udcc2',\n  'open_hands':'\\ud83d\\udc50',\n  'open_mouth':'\\ud83d\\ude2e',\n  'open_umbrella':'\\u2602\\ufe0f',\n  'ophiuchus':'\\u26ce',\n  'orange_book':'\\ud83d\\udcd9',\n  'orthodox_cross':'\\u2626\\ufe0f',\n  'outbox_tray':'\\ud83d\\udce4',\n  'owl':'\\ud83e\\udd89',\n  'ox':'\\ud83d\\udc02',\n  'package':'\\ud83d\\udce6',\n  'page_facing_up':'\\ud83d\\udcc4',\n  'page_with_curl':'\\ud83d\\udcc3',\n  'pager':'\\ud83d\\udcdf',\n  'paintbrush':'\\ud83d\\udd8c',\n  'palm_tree':'\\ud83c\\udf34',\n  'pancakes':'\\ud83e\\udd5e',\n  'panda_face':'\\ud83d\\udc3c',\n  'paperclip':'\\ud83d\\udcce',\n  'paperclips':'\\ud83d\\udd87',\n  'parasol_on_ground':'\\u26f1',\n  'parking':'\\ud83c\\udd7f\\ufe0f',\n  'part_alternation_mark':'\\u303d\\ufe0f',\n  'partly_sunny':'\\u26c5\\ufe0f',\n  'passenger_ship':'\\ud83d\\udef3',\n  'passport_control':'\\ud83d\\udec2',\n  'pause_button':'\\u23f8',\n  'peace_symbol':'\\u262e\\ufe0f',\n  'peach':'\\ud83c\\udf51',\n  'peanuts':'\\ud83e\\udd5c',\n  'pear':'\\ud83c\\udf50',\n  'pen':'\\ud83d\\udd8a',\n  'pencil2':'\\u270f\\ufe0f',\n  'penguin':'\\ud83d\\udc27',\n  'pensive':'\\ud83d\\ude14',\n  'performing_arts':'\\ud83c\\udfad',\n  'persevere':'\\ud83d\\ude23',\n  'person_fencing':'\\ud83e\\udd3a',\n  'pouting_woman':'\\ud83d\\ude4e',\n  'phone':'\\u260e\\ufe0f',\n  'pick':'\\u26cf',\n  'pig':'\\ud83d\\udc37',\n  'pig2':'\\ud83d\\udc16',\n  'pig_nose':'\\ud83d\\udc3d',\n  'pill':'\\ud83d\\udc8a',\n  'pineapple':'\\ud83c\\udf4d',\n  'ping_pong':'\\ud83c\\udfd3',\n  'pisces':'\\u2653\\ufe0f',\n  'pizza':'\\ud83c\\udf55',\n  'place_of_worship':'\\ud83d\\uded0',\n  'plate_with_cutlery':'\\ud83c\\udf7d',\n  'play_or_pause_button':'\\u23ef',\n  'point_down':'\\ud83d\\udc47',\n  'point_left':'\\ud83d\\udc48',\n  'point_right':'\\ud83d\\udc49',\n  'point_up':'\\u261d\\ufe0f',\n  'point_up_2':'\\ud83d\\udc46',\n  'police_car':'\\ud83d\\ude93',\n  'policewoman':'\\ud83d\\udc6e‍\\u2640\\ufe0f',\n  'poodle':'\\ud83d\\udc29',\n  'popcorn':'\\ud83c\\udf7f',\n  'post_office':'\\ud83c\\udfe3',\n  'postal_horn':'\\ud83d\\udcef',\n  'postbox':'\\ud83d\\udcee',\n  'potable_water':'\\ud83d\\udeb0',\n  'potato':'\\ud83e\\udd54',\n  'pouch':'\\ud83d\\udc5d',\n  'poultry_leg':'\\ud83c\\udf57',\n  'pound':'\\ud83d\\udcb7',\n  'rage':'\\ud83d\\ude21',\n  'pouting_cat':'\\ud83d\\ude3e',\n  'pouting_man':'\\ud83d\\ude4e‍\\u2642\\ufe0f',\n  'pray':'\\ud83d\\ude4f',\n  'prayer_beads':'\\ud83d\\udcff',\n  'pregnant_woman':'\\ud83e\\udd30',\n  'previous_track_button':'\\u23ee',\n  'prince':'\\ud83e\\udd34',\n  'princess':'\\ud83d\\udc78',\n  'printer':'\\ud83d\\udda8',\n  'purple_heart':'\\ud83d\\udc9c',\n  'purse':'\\ud83d\\udc5b',\n  'pushpin':'\\ud83d\\udccc',\n  'put_litter_in_its_place':'\\ud83d\\udeae',\n  'question':'\\u2753',\n  'rabbit':'\\ud83d\\udc30',\n  'rabbit2':'\\ud83d\\udc07',\n  'racehorse':'\\ud83d\\udc0e',\n  'racing_car':'\\ud83c\\udfce',\n  'radio':'\\ud83d\\udcfb',\n  'radio_button':'\\ud83d\\udd18',\n  'radioactive':'\\u2622\\ufe0f',\n  'railway_car':'\\ud83d\\ude83',\n  'railway_track':'\\ud83d\\udee4',\n  'rainbow':'\\ud83c\\udf08',\n  'rainbow_flag':'\\ud83c\\udff3\\ufe0f‍\\ud83c\\udf08',\n  'raised_back_of_hand':'\\ud83e\\udd1a',\n  'raised_hand_with_fingers_splayed':'\\ud83d\\udd90',\n  'raised_hands':'\\ud83d\\ude4c',\n  'raising_hand_woman':'\\ud83d\\ude4b',\n  'raising_hand_man':'\\ud83d\\ude4b‍\\u2642\\ufe0f',\n  'ram':'\\ud83d\\udc0f',\n  'ramen':'\\ud83c\\udf5c',\n  'rat':'\\ud83d\\udc00',\n  'record_button':'\\u23fa',\n  'recycle':'\\u267b\\ufe0f',\n  'red_circle':'\\ud83d\\udd34',\n  'registered':'\\u00ae\\ufe0f',\n  'relaxed':'\\u263a\\ufe0f',\n  'relieved':'\\ud83d\\ude0c',\n  'reminder_ribbon':'\\ud83c\\udf97',\n  'repeat':'\\ud83d\\udd01',\n  'repeat_one':'\\ud83d\\udd02',\n  'rescue_worker_helmet':'\\u26d1',\n  'restroom':'\\ud83d\\udebb',\n  'revolving_hearts':'\\ud83d\\udc9e',\n  'rewind':'\\u23ea',\n  'rhinoceros':'\\ud83e\\udd8f',\n  'ribbon':'\\ud83c\\udf80',\n  'rice':'\\ud83c\\udf5a',\n  'rice_ball':'\\ud83c\\udf59',\n  'rice_cracker':'\\ud83c\\udf58',\n  'rice_scene':'\\ud83c\\udf91',\n  'right_anger_bubble':'\\ud83d\\uddef',\n  'ring':'\\ud83d\\udc8d',\n  'robot':'\\ud83e\\udd16',\n  'rocket':'\\ud83d\\ude80',\n  'rofl':'\\ud83e\\udd23',\n  'roll_eyes':'\\ud83d\\ude44',\n  'roller_coaster':'\\ud83c\\udfa2',\n  'rooster':'\\ud83d\\udc13',\n  'rose':'\\ud83c\\udf39',\n  'rosette':'\\ud83c\\udff5',\n  'rotating_light':'\\ud83d\\udea8',\n  'round_pushpin':'\\ud83d\\udccd',\n  'rowing_man':'\\ud83d\\udea3',\n  'rowing_woman':'\\ud83d\\udea3‍\\u2640\\ufe0f',\n  'rugby_football':'\\ud83c\\udfc9',\n  'running_man':'\\ud83c\\udfc3',\n  'running_shirt_with_sash':'\\ud83c\\udfbd',\n  'running_woman':'\\ud83c\\udfc3‍\\u2640\\ufe0f',\n  'sa':'\\ud83c\\ude02\\ufe0f',\n  'sagittarius':'\\u2650\\ufe0f',\n  'sake':'\\ud83c\\udf76',\n  'sandal':'\\ud83d\\udc61',\n  'santa':'\\ud83c\\udf85',\n  'satellite':'\\ud83d\\udce1',\n  'saxophone':'\\ud83c\\udfb7',\n  'school':'\\ud83c\\udfeb',\n  'school_satchel':'\\ud83c\\udf92',\n  'scissors':'\\u2702\\ufe0f',\n  'scorpion':'\\ud83e\\udd82',\n  'scorpius':'\\u264f\\ufe0f',\n  'scream':'\\ud83d\\ude31',\n  'scream_cat':'\\ud83d\\ude40',\n  'scroll':'\\ud83d\\udcdc',\n  'seat':'\\ud83d\\udcba',\n  'secret':'\\u3299\\ufe0f',\n  'see_no_evil':'\\ud83d\\ude48',\n  'seedling':'\\ud83c\\udf31',\n  'selfie':'\\ud83e\\udd33',\n  'shallow_pan_of_food':'\\ud83e\\udd58',\n  'shamrock':'\\u2618\\ufe0f',\n  'shark':'\\ud83e\\udd88',\n  'shaved_ice':'\\ud83c\\udf67',\n  'sheep':'\\ud83d\\udc11',\n  'shell':'\\ud83d\\udc1a',\n  'shield':'\\ud83d\\udee1',\n  'shinto_shrine':'\\u26e9',\n  'ship':'\\ud83d\\udea2',\n  'shirt':'\\ud83d\\udc55',\n  'shopping':'\\ud83d\\udecd',\n  'shopping_cart':'\\ud83d\\uded2',\n  'shower':'\\ud83d\\udebf',\n  'shrimp':'\\ud83e\\udd90',\n  'signal_strength':'\\ud83d\\udcf6',\n  'six_pointed_star':'\\ud83d\\udd2f',\n  'ski':'\\ud83c\\udfbf',\n  'skier':'\\u26f7',\n  'skull':'\\ud83d\\udc80',\n  'skull_and_crossbones':'\\u2620\\ufe0f',\n  'sleeping':'\\ud83d\\ude34',\n  'sleeping_bed':'\\ud83d\\udecc',\n  'sleepy':'\\ud83d\\ude2a',\n  'slightly_frowning_face':'\\ud83d\\ude41',\n  'slightly_smiling_face':'\\ud83d\\ude42',\n  'slot_machine':'\\ud83c\\udfb0',\n  'small_airplane':'\\ud83d\\udee9',\n  'small_blue_diamond':'\\ud83d\\udd39',\n  'small_orange_diamond':'\\ud83d\\udd38',\n  'small_red_triangle':'\\ud83d\\udd3a',\n  'small_red_triangle_down':'\\ud83d\\udd3b',\n  'smile':'\\ud83d\\ude04',\n  'smile_cat':'\\ud83d\\ude38',\n  'smiley':'\\ud83d\\ude03',\n  'smiley_cat':'\\ud83d\\ude3a',\n  'smiling_imp':'\\ud83d\\ude08',\n  'smirk':'\\ud83d\\ude0f',\n  'smirk_cat':'\\ud83d\\ude3c',\n  'smoking':'\\ud83d\\udeac',\n  'snail':'\\ud83d\\udc0c',\n  'snake':'\\ud83d\\udc0d',\n  'sneezing_face':'\\ud83e\\udd27',\n  'snowboarder':'\\ud83c\\udfc2',\n  'snowflake':'\\u2744\\ufe0f',\n  'snowman':'\\u26c4\\ufe0f',\n  'snowman_with_snow':'\\u2603\\ufe0f',\n  'sob':'\\ud83d\\ude2d',\n  'soccer':'\\u26bd\\ufe0f',\n  'soon':'\\ud83d\\udd1c',\n  'sos':'\\ud83c\\udd98',\n  'sound':'\\ud83d\\udd09',\n  'space_invader':'\\ud83d\\udc7e',\n  'spades':'\\u2660\\ufe0f',\n  'spaghetti':'\\ud83c\\udf5d',\n  'sparkle':'\\u2747\\ufe0f',\n  'sparkler':'\\ud83c\\udf87',\n  'sparkles':'\\u2728',\n  'sparkling_heart':'\\ud83d\\udc96',\n  'speak_no_evil':'\\ud83d\\ude4a',\n  'speaker':'\\ud83d\\udd08',\n  'speaking_head':'\\ud83d\\udde3',\n  'speech_balloon':'\\ud83d\\udcac',\n  'speedboat':'\\ud83d\\udea4',\n  'spider':'\\ud83d\\udd77',\n  'spider_web':'\\ud83d\\udd78',\n  'spiral_calendar':'\\ud83d\\uddd3',\n  'spiral_notepad':'\\ud83d\\uddd2',\n  'spoon':'\\ud83e\\udd44',\n  'squid':'\\ud83e\\udd91',\n  'stadium':'\\ud83c\\udfdf',\n  'star':'\\u2b50\\ufe0f',\n  'star2':'\\ud83c\\udf1f',\n  'star_and_crescent':'\\u262a\\ufe0f',\n  'star_of_david':'\\u2721\\ufe0f',\n  'stars':'\\ud83c\\udf20',\n  'station':'\\ud83d\\ude89',\n  'statue_of_liberty':'\\ud83d\\uddfd',\n  'steam_locomotive':'\\ud83d\\ude82',\n  'stew':'\\ud83c\\udf72',\n  'stop_button':'\\u23f9',\n  'stop_sign':'\\ud83d\\uded1',\n  'stopwatch':'\\u23f1',\n  'straight_ruler':'\\ud83d\\udccf',\n  'strawberry':'\\ud83c\\udf53',\n  'stuck_out_tongue':'\\ud83d\\ude1b',\n  'stuck_out_tongue_closed_eyes':'\\ud83d\\ude1d',\n  'stuck_out_tongue_winking_eye':'\\ud83d\\ude1c',\n  'studio_microphone':'\\ud83c\\udf99',\n  'stuffed_flatbread':'\\ud83e\\udd59',\n  'sun_behind_large_cloud':'\\ud83c\\udf25',\n  'sun_behind_rain_cloud':'\\ud83c\\udf26',\n  'sun_behind_small_cloud':'\\ud83c\\udf24',\n  'sun_with_face':'\\ud83c\\udf1e',\n  'sunflower':'\\ud83c\\udf3b',\n  'sunglasses':'\\ud83d\\ude0e',\n  'sunny':'\\u2600\\ufe0f',\n  'sunrise':'\\ud83c\\udf05',\n  'sunrise_over_mountains':'\\ud83c\\udf04',\n  'surfing_man':'\\ud83c\\udfc4',\n  'surfing_woman':'\\ud83c\\udfc4‍\\u2640\\ufe0f',\n  'sushi':'\\ud83c\\udf63',\n  'suspension_railway':'\\ud83d\\ude9f',\n  'sweat':'\\ud83d\\ude13',\n  'sweat_drops':'\\ud83d\\udca6',\n  'sweat_smile':'\\ud83d\\ude05',\n  'sweet_potato':'\\ud83c\\udf60',\n  'swimming_man':'\\ud83c\\udfca',\n  'swimming_woman':'\\ud83c\\udfca‍\\u2640\\ufe0f',\n  'symbols':'\\ud83d\\udd23',\n  'synagogue':'\\ud83d\\udd4d',\n  'syringe':'\\ud83d\\udc89',\n  'taco':'\\ud83c\\udf2e',\n  'tada':'\\ud83c\\udf89',\n  'tanabata_tree':'\\ud83c\\udf8b',\n  'taurus':'\\u2649\\ufe0f',\n  'taxi':'\\ud83d\\ude95',\n  'tea':'\\ud83c\\udf75',\n  'telephone_receiver':'\\ud83d\\udcde',\n  'telescope':'\\ud83d\\udd2d',\n  'tennis':'\\ud83c\\udfbe',\n  'tent':'\\u26fa\\ufe0f',\n  'thermometer':'\\ud83c\\udf21',\n  'thinking':'\\ud83e\\udd14',\n  'thought_balloon':'\\ud83d\\udcad',\n  'ticket':'\\ud83c\\udfab',\n  'tickets':'\\ud83c\\udf9f',\n  'tiger':'\\ud83d\\udc2f',\n  'tiger2':'\\ud83d\\udc05',\n  'timer_clock':'\\u23f2',\n  'tipping_hand_man':'\\ud83d\\udc81‍\\u2642\\ufe0f',\n  'tired_face':'\\ud83d\\ude2b',\n  'tm':'\\u2122\\ufe0f',\n  'toilet':'\\ud83d\\udebd',\n  'tokyo_tower':'\\ud83d\\uddfc',\n  'tomato':'\\ud83c\\udf45',\n  'tongue':'\\ud83d\\udc45',\n  'top':'\\ud83d\\udd1d',\n  'tophat':'\\ud83c\\udfa9',\n  'tornado':'\\ud83c\\udf2a',\n  'trackball':'\\ud83d\\uddb2',\n  'tractor':'\\ud83d\\ude9c',\n  'traffic_light':'\\ud83d\\udea5',\n  'train':'\\ud83d\\ude8b',\n  'train2':'\\ud83d\\ude86',\n  'tram':'\\ud83d\\ude8a',\n  'triangular_flag_on_post':'\\ud83d\\udea9',\n  'triangular_ruler':'\\ud83d\\udcd0',\n  'trident':'\\ud83d\\udd31',\n  'triumph':'\\ud83d\\ude24',\n  'trolleybus':'\\ud83d\\ude8e',\n  'trophy':'\\ud83c\\udfc6',\n  'tropical_drink':'\\ud83c\\udf79',\n  'tropical_fish':'\\ud83d\\udc20',\n  'truck':'\\ud83d\\ude9a',\n  'trumpet':'\\ud83c\\udfba',\n  'tulip':'\\ud83c\\udf37',\n  'tumbler_glass':'\\ud83e\\udd43',\n  'turkey':'\\ud83e\\udd83',\n  'turtle':'\\ud83d\\udc22',\n  'tv':'\\ud83d\\udcfa',\n  'twisted_rightwards_arrows':'\\ud83d\\udd00',\n  'two_hearts':'\\ud83d\\udc95',\n  'two_men_holding_hands':'\\ud83d\\udc6c',\n  'two_women_holding_hands':'\\ud83d\\udc6d',\n  'u5272':'\\ud83c\\ude39',\n  'u5408':'\\ud83c\\ude34',\n  'u55b6':'\\ud83c\\ude3a',\n  'u6307':'\\ud83c\\ude2f\\ufe0f',\n  'u6708':'\\ud83c\\ude37\\ufe0f',\n  'u6709':'\\ud83c\\ude36',\n  'u6e80':'\\ud83c\\ude35',\n  'u7121':'\\ud83c\\ude1a\\ufe0f',\n  'u7533':'\\ud83c\\ude38',\n  'u7981':'\\ud83c\\ude32',\n  'u7a7a':'\\ud83c\\ude33',\n  'umbrella':'\\u2614\\ufe0f',\n  'unamused':'\\ud83d\\ude12',\n  'underage':'\\ud83d\\udd1e',\n  'unicorn':'\\ud83e\\udd84',\n  'unlock':'\\ud83d\\udd13',\n  'up':'\\ud83c\\udd99',\n  'upside_down_face':'\\ud83d\\ude43',\n  'v':'\\u270c\\ufe0f',\n  'vertical_traffic_light':'\\ud83d\\udea6',\n  'vhs':'\\ud83d\\udcfc',\n  'vibration_mode':'\\ud83d\\udcf3',\n  'video_camera':'\\ud83d\\udcf9',\n  'video_game':'\\ud83c\\udfae',\n  'violin':'\\ud83c\\udfbb',\n  'virgo':'\\u264d\\ufe0f',\n  'volcano':'\\ud83c\\udf0b',\n  'volleyball':'\\ud83c\\udfd0',\n  'vs':'\\ud83c\\udd9a',\n  'vulcan_salute':'\\ud83d\\udd96',\n  'walking_man':'\\ud83d\\udeb6',\n  'walking_woman':'\\ud83d\\udeb6‍\\u2640\\ufe0f',\n  'waning_crescent_moon':'\\ud83c\\udf18',\n  'waning_gibbous_moon':'\\ud83c\\udf16',\n  'warning':'\\u26a0\\ufe0f',\n  'wastebasket':'\\ud83d\\uddd1',\n  'watch':'\\u231a\\ufe0f',\n  'water_buffalo':'\\ud83d\\udc03',\n  'watermelon':'\\ud83c\\udf49',\n  'wave':'\\ud83d\\udc4b',\n  'wavy_dash':'\\u3030\\ufe0f',\n  'waxing_crescent_moon':'\\ud83c\\udf12',\n  'wc':'\\ud83d\\udebe',\n  'weary':'\\ud83d\\ude29',\n  'wedding':'\\ud83d\\udc92',\n  'weight_lifting_man':'\\ud83c\\udfcb\\ufe0f',\n  'weight_lifting_woman':'\\ud83c\\udfcb\\ufe0f‍\\u2640\\ufe0f',\n  'whale':'\\ud83d\\udc33',\n  'whale2':'\\ud83d\\udc0b',\n  'wheel_of_dharma':'\\u2638\\ufe0f',\n  'wheelchair':'\\u267f\\ufe0f',\n  'white_check_mark':'\\u2705',\n  'white_circle':'\\u26aa\\ufe0f',\n  'white_flag':'\\ud83c\\udff3\\ufe0f',\n  'white_flower':'\\ud83d\\udcae',\n  'white_large_square':'\\u2b1c\\ufe0f',\n  'white_medium_small_square':'\\u25fd\\ufe0f',\n  'white_medium_square':'\\u25fb\\ufe0f',\n  'white_small_square':'\\u25ab\\ufe0f',\n  'white_square_button':'\\ud83d\\udd33',\n  'wilted_flower':'\\ud83e\\udd40',\n  'wind_chime':'\\ud83c\\udf90',\n  'wind_face':'\\ud83c\\udf2c',\n  'wine_glass':'\\ud83c\\udf77',\n  'wink':'\\ud83d\\ude09',\n  'wolf':'\\ud83d\\udc3a',\n  'woman':'\\ud83d\\udc69',\n  'woman_artist':'\\ud83d\\udc69‍\\ud83c\\udfa8',\n  'woman_astronaut':'\\ud83d\\udc69‍\\ud83d\\ude80',\n  'woman_cartwheeling':'\\ud83e\\udd38‍\\u2640\\ufe0f',\n  'woman_cook':'\\ud83d\\udc69‍\\ud83c\\udf73',\n  'woman_facepalming':'\\ud83e\\udd26‍\\u2640\\ufe0f',\n  'woman_factory_worker':'\\ud83d\\udc69‍\\ud83c\\udfed',\n  'woman_farmer':'\\ud83d\\udc69‍\\ud83c\\udf3e',\n  'woman_firefighter':'\\ud83d\\udc69‍\\ud83d\\ude92',\n  'woman_health_worker':'\\ud83d\\udc69‍\\u2695\\ufe0f',\n  'woman_judge':'\\ud83d\\udc69‍\\u2696\\ufe0f',\n  'woman_juggling':'\\ud83e\\udd39‍\\u2640\\ufe0f',\n  'woman_mechanic':'\\ud83d\\udc69‍\\ud83d\\udd27',\n  'woman_office_worker':'\\ud83d\\udc69‍\\ud83d\\udcbc',\n  'woman_pilot':'\\ud83d\\udc69‍\\u2708\\ufe0f',\n  'woman_playing_handball':'\\ud83e\\udd3e‍\\u2640\\ufe0f',\n  'woman_playing_water_polo':'\\ud83e\\udd3d‍\\u2640\\ufe0f',\n  'woman_scientist':'\\ud83d\\udc69‍\\ud83d\\udd2c',\n  'woman_shrugging':'\\ud83e\\udd37‍\\u2640\\ufe0f',\n  'woman_singer':'\\ud83d\\udc69‍\\ud83c\\udfa4',\n  'woman_student':'\\ud83d\\udc69‍\\ud83c\\udf93',\n  'woman_teacher':'\\ud83d\\udc69‍\\ud83c\\udfeb',\n  'woman_technologist':'\\ud83d\\udc69‍\\ud83d\\udcbb',\n  'woman_with_turban':'\\ud83d\\udc73‍\\u2640\\ufe0f',\n  'womans_clothes':'\\ud83d\\udc5a',\n  'womans_hat':'\\ud83d\\udc52',\n  'women_wrestling':'\\ud83e\\udd3c‍\\u2640\\ufe0f',\n  'womens':'\\ud83d\\udeba',\n  'world_map':'\\ud83d\\uddfa',\n  'worried':'\\ud83d\\ude1f',\n  'wrench':'\\ud83d\\udd27',\n  'writing_hand':'\\u270d\\ufe0f',\n  'x':'\\u274c',\n  'yellow_heart':'\\ud83d\\udc9b',\n  'yen':'\\ud83d\\udcb4',\n  'yin_yang':'\\u262f\\ufe0f',\n  'yum':'\\ud83d\\ude0b',\n  'zap':'\\u26a1\\ufe0f',\n  'zipper_mouth_face':'\\ud83e\\udd10',\n  'zzz':'\\ud83d\\udca4',\n\n  /* special emojis :P */\n  'octocat':  '\":octocat:\"',\n  'showdown': 'S'\n};\n","/**\n * Created by Estevao on 31-05-2015.\n */\n\n/**\n * Showdown Converter class\n * @class\n * @param {object} [converterOptions]\n * @returns {Converter}\n */\nshowdown.Converter = function (converterOptions) {\n  'use strict';\n\n  var\n      /**\n       * Options used by this converter\n       * @private\n       * @type {{}}\n       */\n      options = {},\n\n      /**\n       * Language extensions used by this converter\n       * @private\n       * @type {Array}\n       */\n      langExtensions = [],\n\n      /**\n       * Output modifiers extensions used by this converter\n       * @private\n       * @type {Array}\n       */\n      outputModifiers = [],\n\n      /**\n       * Event listeners\n       * @private\n       * @type {{}}\n       */\n      listeners = {},\n\n      /**\n       * The flavor set in this converter\n       */\n      setConvFlavor = setFlavor,\n\n      /**\n       * Metadata of the document\n       * @type {{parsed: {}, raw: string, format: string}}\n       */\n      metadata = {\n        parsed: {},\n        raw: '',\n        format: ''\n      };\n\n  _constructor();\n\n  /**\n   * Converter constructor\n   * @private\n   */\n  function _constructor () {\n    converterOptions = converterOptions || {};\n\n    for (var gOpt in globalOptions) {\n      if (globalOptions.hasOwnProperty(gOpt)) {\n        options[gOpt] = globalOptions[gOpt];\n      }\n    }\n\n    // Merge options\n    if (typeof converterOptions === 'object') {\n      for (var opt in converterOptions) {\n        if (converterOptions.hasOwnProperty(opt)) {\n          options[opt] = converterOptions[opt];\n        }\n      }\n    } else {\n      throw Error('Converter expects the passed parameter to be an object, but ' + typeof converterOptions +\n      ' was passed instead.');\n    }\n\n    if (options.extensions) {\n      showdown.helper.forEach(options.extensions, _parseExtension);\n    }\n  }\n\n  /**\n   * Parse extension\n   * @param {*} ext\n   * @param {string} [name='']\n   * @private\n   */\n  function _parseExtension (ext, name) {\n\n    name = name || null;\n    // If it's a string, the extension was previously loaded\n    if (showdown.helper.isString(ext)) {\n      ext = showdown.helper.stdExtName(ext);\n      name = ext;\n\n      // LEGACY_SUPPORT CODE\n      if (showdown.extensions[ext]) {\n        console.warn('DEPRECATION WARNING: ' + ext + ' is an old extension that uses a deprecated loading method.' +\n          'Please inform the developer that the extension should be updated!');\n        legacyExtensionLoading(showdown.extensions[ext], ext);\n        return;\n        // END LEGACY SUPPORT CODE\n\n      } else if (!showdown.helper.isUndefined(extensions[ext])) {\n        ext = extensions[ext];\n\n      } else {\n        throw Error('Extension \"' + ext + '\" could not be loaded. It was either not found or is not a valid extension.');\n      }\n    }\n\n    if (typeof ext === 'function') {\n      ext = ext();\n    }\n\n    if (!showdown.helper.isArray(ext)) {\n      ext = [ext];\n    }\n\n    var validExt = validate(ext, name);\n    if (!validExt.valid) {\n      throw Error(validExt.error);\n    }\n\n    for (var i = 0; i < ext.length; ++i) {\n      switch (ext[i].type) {\n\n        case 'lang':\n          langExtensions.push(ext[i]);\n          break;\n\n        case 'output':\n          outputModifiers.push(ext[i]);\n          break;\n      }\n      if (ext[i].hasOwnProperty('listeners')) {\n        for (var ln in ext[i].listeners) {\n          if (ext[i].listeners.hasOwnProperty(ln)) {\n            listen(ln, ext[i].listeners[ln]);\n          }\n        }\n      }\n    }\n\n  }\n\n  /**\n   * LEGACY_SUPPORT\n   * @param {*} ext\n   * @param {string} name\n   */\n  function legacyExtensionLoading (ext, name) {\n    if (typeof ext === 'function') {\n      ext = ext(new showdown.Converter());\n    }\n    if (!showdown.helper.isArray(ext)) {\n      ext = [ext];\n    }\n    var valid = validate(ext, name);\n\n    if (!valid.valid) {\n      throw Error(valid.error);\n    }\n\n    for (var i = 0; i < ext.length; ++i) {\n      switch (ext[i].type) {\n        case 'lang':\n          langExtensions.push(ext[i]);\n          break;\n        case 'output':\n          outputModifiers.push(ext[i]);\n          break;\n        default:// should never reach here\n          throw Error('Extension loader error: Type unrecognized!!!');\n      }\n    }\n  }\n\n  /**\n   * Listen to an event\n   * @param {string} name\n   * @param {function} callback\n   */\n  function listen (name, callback) {\n    if (!showdown.helper.isString(name)) {\n      throw Error('Invalid argument in converter.listen() method: name must be a string, but ' + typeof name + ' given');\n    }\n\n    if (typeof callback !== 'function') {\n      throw Error('Invalid argument in converter.listen() method: callback must be a function, but ' + typeof callback + ' given');\n    }\n\n    if (!listeners.hasOwnProperty(name)) {\n      listeners[name] = [];\n    }\n    listeners[name].push(callback);\n  }\n\n  function rTrimInputText (text) {\n    var rsp = text.match(/^\\s*/)[0].length,\n        rgx = new RegExp('^\\\\s{0,' + rsp + '}', 'gm');\n    return text.replace(rgx, '');\n  }\n\n  /**\n   * Dispatch an event\n   * @private\n   * @param {string} evtName Event name\n   * @param {string} text Text\n   * @param {{}} options Converter Options\n   * @param {{}} globals\n   * @returns {string}\n   */\n  this._dispatch = function dispatch (evtName, text, options, globals) {\n    if (listeners.hasOwnProperty(evtName)) {\n      for (var ei = 0; ei < listeners[evtName].length; ++ei) {\n        var nText = listeners[evtName][ei](evtName, text, this, options, globals);\n        if (nText && typeof nText !== 'undefined') {\n          text = nText;\n        }\n      }\n    }\n    return text;\n  };\n\n  /**\n   * Listen to an event\n   * @param {string} name\n   * @param {function} callback\n   * @returns {showdown.Converter}\n   */\n  this.listen = function (name, callback) {\n    listen(name, callback);\n    return this;\n  };\n\n  /**\n   * Converts a markdown string into HTML\n   * @param {string} text\n   * @returns {*}\n   */\n  this.makeHtml = function (text) {\n    //check if text is not falsy\n    if (!text) {\n      return text;\n    }\n\n    var globals = {\n      gHtmlBlocks:     [],\n      gHtmlMdBlocks:   [],\n      gHtmlSpans:      [],\n      gUrls:           {},\n      gTitles:         {},\n      gDimensions:     {},\n      gListLevel:      0,\n      hashLinkCounts:  {},\n      langExtensions:  langExtensions,\n      outputModifiers: outputModifiers,\n      converter:       this,\n      ghCodeBlocks:    [],\n      metadata: {\n        parsed: {},\n        raw: '',\n        format: ''\n      }\n    };\n\n    // This lets us use ¨ trema as an escape char to avoid md5 hashes\n    // The choice of character is arbitrary; anything that isn't\n    // magic in Markdown will work.\n    text = text.replace(/¨/g, '¨T');\n\n    // Replace $ with ¨D\n    // RegExp interprets $ as a special character\n    // when it's in a replacement string\n    text = text.replace(/\\$/g, '¨D');\n\n    // Standardize line endings\n    text = text.replace(/\\r\\n/g, '\\n'); // DOS to Unix\n    text = text.replace(/\\r/g, '\\n'); // Mac to Unix\n\n    // Stardardize line spaces\n    text = text.replace(/\\u00A0/g, ' ');\n\n    if (options.smartIndentationFix) {\n      text = rTrimInputText(text);\n    }\n\n    // Make sure text begins and ends with a couple of newlines:\n    text = '\\n\\n' + text + '\\n\\n';\n\n    // detab\n    text = showdown.subParser('detab')(text, options, globals);\n\n    /**\n     * Strip any lines consisting only of spaces and tabs.\n     * This makes subsequent regexs easier to write, because we can\n     * match consecutive blank lines with /\\n+/ instead of something\n     * contorted like /[ \\t]*\\n+/\n     */\n    text = text.replace(/^[ \\t]+$/mg, '');\n\n    //run languageExtensions\n    showdown.helper.forEach(langExtensions, function (ext) {\n      text = showdown.subParser('runExtension')(ext, text, options, globals);\n    });\n\n    // run the sub parsers\n    text = showdown.subParser('metadata')(text, options, globals);\n    text = showdown.subParser('hashPreCodeTags')(text, options, globals);\n    text = showdown.subParser('githubCodeBlocks')(text, options, globals);\n    text = showdown.subParser('hashHTMLBlocks')(text, options, globals);\n    text = showdown.subParser('hashCodeTags')(text, options, globals);\n    text = showdown.subParser('stripLinkDefinitions')(text, options, globals);\n    text = showdown.subParser('blockGamut')(text, options, globals);\n    text = showdown.subParser('unhashHTMLSpans')(text, options, globals);\n    text = showdown.subParser('unescapeSpecialChars')(text, options, globals);\n\n    // attacklab: Restore dollar signs\n    text = text.replace(/¨D/g, '$$');\n\n    // attacklab: Restore tremas\n    text = text.replace(/¨T/g, '¨');\n\n    // render a complete html document instead of a partial if the option is enabled\n    text = showdown.subParser('completeHTMLDocument')(text, options, globals);\n\n    // Run output modifiers\n    showdown.helper.forEach(outputModifiers, function (ext) {\n      text = showdown.subParser('runExtension')(ext, text, options, globals);\n    });\n\n    // update metadata\n    metadata = globals.metadata;\n    return text;\n  };\n\n  /**\n   * Converts an HTML string into a markdown string\n   * @param src\n   * @param [HTMLParser] A WHATWG DOM and HTML parser, such as JSDOM. If none is supplied, window.document will be used.\n   * @returns {string}\n   */\n  this.makeMarkdown = this.makeMd = function (src, HTMLParser) {\n\n    // replace \\r\\n with \\n\n    src = src.replace(/\\r\\n/g, '\\n');\n    src = src.replace(/\\r/g, '\\n'); // old macs\n\n    // due to an edge case, we need to find this: > <\n    // to prevent removing of non silent white spaces\n    // ex: this is sparta\n    src = src.replace(/>[ \\t]+¨NBSP;<');\n\n    if (!HTMLParser) {\n      if (window && window.document) {\n        HTMLParser = window.document;\n      } else {\n        throw new Error('HTMLParser is undefined. If in a webworker or nodejs environment, you need to provide a WHATWG DOM and HTML such as JSDOM');\n      }\n    }\n\n    var doc = HTMLParser.createElement('div');\n    doc.innerHTML = src;\n\n    var globals = {\n      preList: substitutePreCodeTags(doc)\n    };\n\n    // remove all newlines and collapse spaces\n    clean(doc);\n\n    // some stuff, like accidental reference links must now be escaped\n    // TODO\n    // doc.innerHTML = doc.innerHTML.replace(/\\[[\\S\\t ]]/);\n\n    var nodes = doc.childNodes,\n        mdDoc = '';\n\n    for (var i = 0; i < nodes.length; i++) {\n      mdDoc += showdown.subParser('makeMarkdown.node')(nodes[i], globals);\n    }\n\n    function clean (node) {\n      for (var n = 0; n < node.childNodes.length; ++n) {\n        var child = node.childNodes[n];\n        if (child.nodeType === 3) {\n          if (!/\\S/.test(child.nodeValue)) {\n            node.removeChild(child);\n            --n;\n          } else {\n            child.nodeValue = child.nodeValue.split('\\n').join(' ');\n            child.nodeValue = child.nodeValue.replace(/(\\s)+/g, '$1');\n          }\n        } else if (child.nodeType === 1) {\n          clean(child);\n        }\n      }\n    }\n\n    // find all pre tags and replace contents with placeholder\n    // we need this so that we can remove all indentation from html\n    // to ease up parsing\n    function substitutePreCodeTags (doc) {\n\n      var pres = doc.querySelectorAll('pre'),\n          presPH = [];\n\n      for (var i = 0; i < pres.length; ++i) {\n\n        if (pres[i].childElementCount === 1 && pres[i].firstChild.tagName.toLowerCase() === 'code') {\n          var content = pres[i].firstChild.innerHTML.trim(),\n              language = pres[i].firstChild.getAttribute('data-language') || '';\n\n          // if data-language attribute is not defined, then we look for class language-*\n          if (language === '') {\n            var classes = pres[i].firstChild.className.split(' ');\n            for (var c = 0; c < classes.length; ++c) {\n              var matches = classes[c].match(/^language-(.+)$/);\n              if (matches !== null) {\n                language = matches[1];\n                break;\n              }\n            }\n          }\n\n          // unescape html entities in content\n          content = showdown.helper.unescapeHTMLEntities(content);\n\n          presPH.push(content);\n          pres[i].outerHTML = '';\n        } else {\n          presPH.push(pres[i].innerHTML);\n          pres[i].innerHTML = '';\n          pres[i].setAttribute('prenum', i.toString());\n        }\n      }\n      return presPH;\n    }\n\n    return mdDoc;\n  };\n\n  /**\n   * Set an option of this Converter instance\n   * @param {string} key\n   * @param {*} value\n   */\n  this.setOption = function (key, value) {\n    options[key] = value;\n  };\n\n  /**\n   * Get the option of this Converter instance\n   * @param {string} key\n   * @returns {*}\n   */\n  this.getOption = function (key) {\n    return options[key];\n  };\n\n  /**\n   * Get the options of this Converter instance\n   * @returns {{}}\n   */\n  this.getOptions = function () {\n    return options;\n  };\n\n  /**\n   * Add extension to THIS converter\n   * @param {{}} extension\n   * @param {string} [name=null]\n   */\n  this.addExtension = function (extension, name) {\n    name = name || null;\n    _parseExtension(extension, name);\n  };\n\n  /**\n   * Use a global registered extension with THIS converter\n   * @param {string} extensionName Name of the previously registered extension\n   */\n  this.useExtension = function (extensionName) {\n    _parseExtension(extensionName);\n  };\n\n  /**\n   * Set the flavor THIS converter should use\n   * @param {string} name\n   */\n  this.setFlavor = function (name) {\n    if (!flavor.hasOwnProperty(name)) {\n      throw Error(name + ' flavor was not found');\n    }\n    var preset = flavor[name];\n    setConvFlavor = name;\n    for (var option in preset) {\n      if (preset.hasOwnProperty(option)) {\n        options[option] = preset[option];\n      }\n    }\n  };\n\n  /**\n   * Get the currently set flavor of this converter\n   * @returns {string}\n   */\n  this.getFlavor = function () {\n    return setConvFlavor;\n  };\n\n  /**\n   * Remove an extension from THIS converter.\n   * Note: This is a costly operation. It's better to initialize a new converter\n   * and specify the extensions you wish to use\n   * @param {Array} extension\n   */\n  this.removeExtension = function (extension) {\n    if (!showdown.helper.isArray(extension)) {\n      extension = [extension];\n    }\n    for (var a = 0; a < extension.length; ++a) {\n      var ext = extension[a];\n      for (var i = 0; i < langExtensions.length; ++i) {\n        if (langExtensions[i] === ext) {\n          langExtensions[i].splice(i, 1);\n        }\n      }\n      for (var ii = 0; ii < outputModifiers.length; ++i) {\n        if (outputModifiers[ii] === ext) {\n          outputModifiers[ii].splice(i, 1);\n        }\n      }\n    }\n  };\n\n  /**\n   * Get all extension of THIS converter\n   * @returns {{language: Array, output: Array}}\n   */\n  this.getAllExtensions = function () {\n    return {\n      language: langExtensions,\n      output: outputModifiers\n    };\n  };\n\n  /**\n   * Get the metadata of the previously parsed document\n   * @param raw\n   * @returns {string|{}}\n   */\n  this.getMetadata = function (raw) {\n    if (raw) {\n      return metadata.raw;\n    } else {\n      return metadata.parsed;\n    }\n  };\n\n  /**\n   * Get the metadata format of the previously parsed document\n   * @returns {string}\n   */\n  this.getMetadataFormat = function () {\n    return metadata.format;\n  };\n\n  /**\n   * Private: set a single key, value metadata pair\n   * @param {string} key\n   * @param {string} value\n   */\n  this._setMetadataPair = function (key, value) {\n    metadata.parsed[key] = value;\n  };\n\n  /**\n   * Private: set metadata format\n   * @param {string} format\n   */\n  this._setMetadataFormat = function (format) {\n    metadata.format = format;\n  };\n\n  /**\n   * Private: set metadata raw text\n   * @param {string} raw\n   */\n  this._setMetadataRaw = function (raw) {\n    metadata.raw = raw;\n  };\n};\n","/**\n * Turn Markdown link shortcuts into XHTML      tags.\n */\nshowdown.subParser('anchors', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('anchors.before', text, options, globals);\n\n  var writeAnchorTag = function (wholeMatch, linkText, linkId, url, m5, m6, title) {\n    if (showdown.helper.isUndefined(title)) {\n      title = '';\n    }\n    linkId = linkId.toLowerCase();\n\n    // Special case for explicit empty url\n    if (wholeMatch.search(/\\(? ?(['\"].*['\"])?\\)$/m) > -1) {\n      url = '';\n    } else if (!url) {\n      if (!linkId) {\n        // lower-case and turn embedded newlines into spaces\n        linkId = linkText.toLowerCase().replace(/ ?\\n/g, ' ');\n      }\n      url = '#' + linkId;\n\n      if (!showdown.helper.isUndefined(globals.gUrls[linkId])) {\n        url = globals.gUrls[linkId];\n        if (!showdown.helper.isUndefined(globals.gTitles[linkId])) {\n          title = globals.gTitles[linkId];\n        }\n      } else {\n        return wholeMatch;\n      }\n    }\n\n    //url = showdown.helper.escapeCharacters(url, '*_', false); // replaced line to improve performance\n    url = url.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n\n    var result = '';\n\n    return result;\n  };\n\n  // First, handle reference-style links: [link text] [id]\n  text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)] ?(?:\\n *)?\\[(.*?)]()()()()/g, writeAnchorTag);\n\n  // Next, inline-style links: [link text](url \"optional title\")\n  // cases with crazy urls like ./image/cat1).png\n  text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)]()[ \\t]*\\([ \\t]?<([^>]*)>(?:[ \\t]*(([\"'])([^\"]*?)\\5))?[ \\t]?\\)/g,\n    writeAnchorTag);\n\n  // normal cases\n  text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)]()[ \\t]*\\([ \\t]??(?:[ \\t]*(([\"'])([^\"]*?)\\5))?[ \\t]?\\)/g,\n    writeAnchorTag);\n\n  // handle reference-style shortcuts: [link text]\n  // These must come last in case you've also got [link test][1]\n  // or [link test](/foo)\n  text = text.replace(/\\[([^\\[\\]]+)]()()()()()/g, writeAnchorTag);\n\n  // Lastly handle GithubMentions if option is enabled\n  if (options.ghMentions) {\n    text = text.replace(/(^|\\s)(\\\\)?(@([a-z\\d]+(?:[a-z\\d.-]+?[a-z\\d]+)*))/gmi, function (wm, st, escape, mentions, username) {\n      if (escape === '\\\\') {\n        return st + mentions;\n      }\n\n      //check if options.ghMentionsLink is a string\n      if (!showdown.helper.isString(options.ghMentionsLink)) {\n        throw new Error('ghMentionsLink option must be a string');\n      }\n      var lnk = options.ghMentionsLink.replace(/\\{u}/g, username),\n          target = '';\n      if (options.openLinksInNewWindow) {\n        target = ' rel=\"noopener noreferrer\" target=\"¨E95Eblank\"';\n      }\n      return st + '' + mentions + '';\n    });\n  }\n\n  text = globals.converter._dispatch('anchors.after', text, options, globals);\n  return text;\n});\n","// url allowed chars [a-z\\d_.~:/?#[]@!$&'()*+,;=-]\n\nvar simpleURLRegex  = /([*~_]+|\\b)(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+?\\.[^'\">\\s]+?)()(\\1)?(?=\\s|$)(?![\"<>])/gi,\n    simpleURLRegex2 = /([*~_]+|\\b)(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+\\.[^'\">\\s]+?)([.!?,()\\[\\]])?(\\1)?(?=\\s|$)(?![\"<>])/gi,\n    delimUrlRegex   = /()<(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+)()>()/gi,\n    simpleMailRegex = /(^|\\s)(?:mailto:)?([A-Za-z0-9!#$%&'*+-/=?^_`{|}~.]+@[-a-z0-9]+(\\.[-a-z0-9]+)*\\.[a-z]+)(?=$|\\s)/gmi,\n    delimMailRegex  = /<()(?:mailto:)?([-.\\w]+@[-a-z0-9]+(\\.[-a-z0-9]+)*\\.[a-z]+)>/gi,\n\n    replaceLink = function (options) {\n      'use strict';\n      return function (wm, leadingMagicChars, link, m2, m3, trailingPunctuation, trailingMagicChars) {\n        link = link.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n        var lnkTxt = link,\n            append = '',\n            target = '',\n            lmc    = leadingMagicChars || '',\n            tmc    = trailingMagicChars || '';\n        if (/^www\\./i.test(link)) {\n          link = link.replace(/^www\\./i, 'http://www.');\n        }\n        if (options.excludeTrailingPunctuationFromURLs && trailingPunctuation) {\n          append = trailingPunctuation;\n        }\n        if (options.openLinksInNewWindow) {\n          target = ' rel=\"noopener noreferrer\" target=\"¨E95Eblank\"';\n        }\n        return lmc + '' + lnkTxt + '' + append + tmc;\n      };\n    },\n\n    replaceMail = function (options, globals) {\n      'use strict';\n      return function (wholeMatch, b, mail) {\n        var href = 'mailto:';\n        b = b || '';\n        mail = showdown.subParser('unescapeSpecialChars')(mail, options, globals);\n        if (options.encodeEmails) {\n          href = showdown.helper.encodeEmailAddress(href + mail);\n          mail = showdown.helper.encodeEmailAddress(mail);\n        } else {\n          href = href + mail;\n        }\n        return b + '' + mail + '';\n      };\n    };\n\nshowdown.subParser('autoLinks', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('autoLinks.before', text, options, globals);\n\n  text = text.replace(delimUrlRegex, replaceLink(options));\n  text = text.replace(delimMailRegex, replaceMail(options, globals));\n\n  text = globals.converter._dispatch('autoLinks.after', text, options, globals);\n\n  return text;\n});\n\nshowdown.subParser('simplifiedAutoLinks', function (text, options, globals) {\n  'use strict';\n\n  if (!options.simplifiedAutoLink) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('simplifiedAutoLinks.before', text, options, globals);\n\n  if (options.excludeTrailingPunctuationFromURLs) {\n    text = text.replace(simpleURLRegex2, replaceLink(options));\n  } else {\n    text = text.replace(simpleURLRegex, replaceLink(options));\n  }\n  text = text.replace(simpleMailRegex, replaceMail(options, globals));\n\n  text = globals.converter._dispatch('simplifiedAutoLinks.after', text, options, globals);\n\n  return text;\n});\n","/**\n * These are all the transformations that form block-level\n * tags like paragraphs, headers, and list items.\n */\nshowdown.subParser('blockGamut', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('blockGamut.before', text, options, globals);\n\n  // we parse blockquotes first so that we can have headings and hrs\n  // inside blockquotes\n  text = showdown.subParser('blockQuotes')(text, options, globals);\n  text = showdown.subParser('headers')(text, options, globals);\n\n  // Do Horizontal Rules:\n  text = showdown.subParser('horizontalRule')(text, options, globals);\n\n  text = showdown.subParser('lists')(text, options, globals);\n  text = showdown.subParser('codeBlocks')(text, options, globals);\n  text = showdown.subParser('tables')(text, options, globals);\n\n  // We already ran _HashHTMLBlocks() before, in Markdown(), but that\n  // was to escape raw HTML in the original Markdown source. This time,\n  // we're escaping the markup we've just created, so that we don't wrap\n  // 
     tags around block-level tags.\n  text = showdown.subParser('hashHTMLBlocks')(text, options, globals);\n  text = showdown.subParser('paragraphs')(text, options, globals);\n\n  text = globals.converter._dispatch('blockGamut.after', text, options, globals);\n\n  return text;\n});\n","showdown.subParser('blockQuotes', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('blockQuotes.before', text, options, globals);\n\n  // add a couple extra lines after the text and endtext mark\n  text = text + '\\n\\n';\n\n  var rgx = /(^ {0,3}>[ \\t]?.+\\n(.+\\n)*\\n*)+/gm;\n\n  if (options.splitAdjacentBlockquotes) {\n    rgx = /^ {0,3}>[\\s\\S]*?(?:\\n\\n)/gm;\n  }\n\n  text = text.replace(rgx, function (bq) {\n    // attacklab: hack around Konqueror 3.5.4 bug:\n    // \"----------bug\".replace(/^-/g,\"\") == \"bug\"\n    bq = bq.replace(/^[ \\t]*>[ \\t]?/gm, ''); // trim one level of quoting\n\n    // attacklab: clean up hack\n    bq = bq.replace(/¨0/g, '');\n\n    bq = bq.replace(/^[ \\t]+$/gm, ''); // trim whitespace-only lines\n    bq = showdown.subParser('githubCodeBlocks')(bq, options, globals);\n    bq = showdown.subParser('blockGamut')(bq, options, globals); // recurse\n\n    bq = bq.replace(/(^|\\n)/g, '$1  ');\n    // These leading spaces screw with 
     content, so we need to fix that:\n    bq = bq.replace(/(\\s*
    [^\\r]+?<\\/pre>)/gm, function (wholeMatch, m1) {\n      var pre = m1;\n      // attacklab: hack around Konqueror 3.5.4 bug:\n      pre = pre.replace(/^  /mg, '¨0');\n      pre = pre.replace(/¨0/g, '');\n      return pre;\n    });\n\n    return showdown.subParser('hashBlock')('
    \\n' + bq + '\\n
    ', options, globals);\n  });\n\n  text = globals.converter._dispatch('blockQuotes.after', text, options, globals);\n  return text;\n});\n","/**\n * Process Markdown `
    ` blocks.\n */\nshowdown.subParser('codeBlocks', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('codeBlocks.before', text, options, globals);\n\n  // sentinel workarounds for lack of \\A and \\Z, safari\\khtml bug\n  text += '¨0';\n\n  var pattern = /(?:\\n\\n|^)((?:(?:[ ]{4}|\\t).*\\n+)+)(\\n*[ ]{0,3}[^ \\t\\n]|(?=¨0))/g;\n  text = text.replace(pattern, function (wholeMatch, m1, m2) {\n    var codeblock = m1,\n        nextChar = m2,\n        end = '\\n';\n\n    codeblock = showdown.subParser('outdent')(codeblock, options, globals);\n    codeblock = showdown.subParser('encodeCode')(codeblock, options, globals);\n    codeblock = showdown.subParser('detab')(codeblock, options, globals);\n    codeblock = codeblock.replace(/^\\n+/g, ''); // trim leading newlines\n    codeblock = codeblock.replace(/\\n+$/g, ''); // trim trailing newlines\n\n    if (options.omitExtraWLInCodeBlocks) {\n      end = '';\n    }\n\n    codeblock = '
    ' + codeblock + end + '
    ';\n\n    return showdown.subParser('hashBlock')(codeblock, options, globals) + nextChar;\n  });\n\n  // strip sentinel\n  text = text.replace(/¨0/, '');\n\n  text = globals.converter._dispatch('codeBlocks.after', text, options, globals);\n  return text;\n});\n","/**\n *\n *   *  Backtick quotes are used for  spans.\n *\n *   *  You can use multiple backticks as the delimiters if you want to\n *     include literal backticks in the code span. So, this input:\n *\n *         Just type ``foo `bar` baz`` at the prompt.\n *\n *       Will translate to:\n *\n *         
    Just type foo `bar` baz at the prompt.
    \n *\n *    There's no arbitrary limit to the number of backticks you\n *    can use as delimters. If you need three consecutive backticks\n *    in your code, use four for delimiters, etc.\n *\n *  *  You can use spaces to get literal backticks at the edges:\n *\n *         ... type `` `bar` `` ...\n *\n *       Turns to:\n *\n *         ... type `bar` ...\n */\nshowdown.subParser('codeSpans', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('codeSpans.before', text, options, globals);\n\n  if (typeof text === 'undefined') {\n    text = '';\n  }\n  text = text.replace(/(^|[^\\\\])(`+)([^\\r]*?[^`])\\2(?!`)/gm,\n    function (wholeMatch, m1, m2, m3) {\n      var c = m3;\n      c = c.replace(/^([ \\t]*)/g, '');\t// leading whitespace\n      c = c.replace(/[ \\t]*$/g, '');\t// trailing whitespace\n      c = showdown.subParser('encodeCode')(c, options, globals);\n      c = m1 + '' + c + '';\n      c = showdown.subParser('hashHTMLSpans')(c, options, globals);\n      return c;\n    }\n  );\n\n  text = globals.converter._dispatch('codeSpans.after', text, options, globals);\n  return text;\n});\n","/**\n * Create a full HTML document from the processed markdown\n */\nshowdown.subParser('completeHTMLDocument', function (text, options, globals) {\n  'use strict';\n\n  if (!options.completeHTMLDocument) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('completeHTMLDocument.before', text, options, globals);\n\n  var doctype = 'html',\n      doctypeParsed = '\\n',\n      title = '',\n      charset = '\\n',\n      lang = '',\n      metadata = '';\n\n  if (typeof globals.metadata.parsed.doctype !== 'undefined') {\n    doctypeParsed = '\\n';\n    doctype = globals.metadata.parsed.doctype.toString().toLowerCase();\n    if (doctype === 'html' || doctype === 'html5') {\n      charset = '';\n    }\n  }\n\n  for (var meta in globals.metadata.parsed) {\n    if (globals.metadata.parsed.hasOwnProperty(meta)) {\n      switch (meta.toLowerCase()) {\n        case 'doctype':\n          break;\n\n        case 'title':\n          title = '' +  globals.metadata.parsed.title + '\\n';\n          break;\n\n        case 'charset':\n          if (doctype === 'html' || doctype === 'html5') {\n            charset = '\\n';\n          } else {\n            charset = '\\n';\n          }\n          break;\n\n        case 'language':\n        case 'lang':\n          lang = ' lang=\"' + globals.metadata.parsed[meta] + '\"';\n          metadata += '\\n';\n          break;\n\n        default:\n          metadata += '\\n';\n      }\n    }\n  }\n\n  text = doctypeParsed + '\\n\\n' + title + charset + metadata + '\\n\\n' + text.trim() + '\\n\\n';\n\n  text = globals.converter._dispatch('completeHTMLDocument.after', text, options, globals);\n  return text;\n});\n","/**\n * Convert all tabs to spaces\n */\nshowdown.subParser('detab', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('detab.before', text, options, globals);\n\n  // expand first n-1 tabs\n  text = text.replace(/\\t(?=\\t)/g, '    '); // g_tab_width\n\n  // replace the nth with two sentinels\n  text = text.replace(/\\t/g, '¨A¨B');\n\n  // use the sentinel to anchor our regex so it doesn't explode\n  text = text.replace(/¨B(.+?)¨A/g, function (wholeMatch, m1) {\n    var leadingText = m1,\n        numSpaces = 4 - leadingText.length % 4;  // g_tab_width\n\n    // there *must* be a better way to do this:\n    for (var i = 0; i < numSpaces; i++) {\n      leadingText += ' ';\n    }\n\n    return leadingText;\n  });\n\n  // clean up sentinels\n  text = text.replace(/¨A/g, '    ');  // g_tab_width\n  text = text.replace(/¨B/g, '');\n\n  text = globals.converter._dispatch('detab.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('ellipsis', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('ellipsis.before', text, options, globals);\n\n  text = text.replace(/\\.\\.\\./g, '…');\n\n  text = globals.converter._dispatch('ellipsis.after', text, options, globals);\n\n  return text;\n});\n","/**\n * Turn emoji codes into emojis\n *\n * List of supported emojis: https://github.com/showdownjs/showdown/wiki/Emojis\n */\nshowdown.subParser('emoji', function (text, options, globals) {\n  'use strict';\n\n  if (!options.emoji) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('emoji.before', text, options, globals);\n\n  var emojiRgx = /:([\\S]+?):/g;\n\n  text = text.replace(emojiRgx, function (wm, emojiCode) {\n    if (showdown.helper.emojis.hasOwnProperty(emojiCode)) {\n      return showdown.helper.emojis[emojiCode];\n    }\n    return wm;\n  });\n\n  text = globals.converter._dispatch('emoji.after', text, options, globals);\n\n  return text;\n});\n","/**\n * Smart processing for ampersands and angle brackets that need to be encoded.\n */\nshowdown.subParser('encodeAmpsAndAngles', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('encodeAmpsAndAngles.before', text, options, globals);\n\n  // Ampersand-encoding based entirely on Nat Irons's Amputator MT plugin:\n  // http://bumppo.net/projects/amputator/\n  text = text.replace(/&(?!#?[xX]?(?:[0-9a-fA-F]+|\\w+);)/g, '&');\n\n  // Encode naked <'s\n  text = text.replace(/<(?![a-z\\/?$!])/gi, '<');\n\n  // Encode <\n  text = text.replace(/\n  text = text.replace(/>/g, '>');\n\n  text = globals.converter._dispatch('encodeAmpsAndAngles.after', text, options, globals);\n  return text;\n});\n","/**\n * Returns the string, with after processing the following backslash escape sequences.\n *\n * attacklab: The polite way to do this is with the new escapeCharacters() function:\n *\n *    text = escapeCharacters(text,\"\\\\\",true);\n *    text = escapeCharacters(text,\"`*_{}[]()>#+-.!\",true);\n *\n * ...but we're sidestepping its use of the (slow) RegExp constructor\n * as an optimization for Firefox.  This function gets called a LOT.\n */\nshowdown.subParser('encodeBackslashEscapes', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('encodeBackslashEscapes.before', text, options, globals);\n\n  text = text.replace(/\\\\(\\\\)/g, showdown.helper.escapeCharactersCallback);\n  text = text.replace(/\\\\([`*_{}\\[\\]()>#+.!~=|-])/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('encodeBackslashEscapes.after', text, options, globals);\n  return text;\n});\n","/**\n * Encode/escape certain characters inside Markdown code runs.\n * The point is that in code, these characters are literals,\n * and lose their special Markdown meanings.\n */\nshowdown.subParser('encodeCode', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('encodeCode.before', text, options, globals);\n\n  // Encode all ampersands; HTML entities are not\n  // entities within a Markdown code span.\n  text = text\n    .replace(/&/g, '&')\n  // Do the angle bracket song and dance:\n    .replace(//g, '>')\n  // Now, escape characters that are magic in Markdown:\n    .replace(/([*_{}\\[\\]\\\\=~-])/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('encodeCode.after', text, options, globals);\n  return text;\n});\n","/**\n * Within tags -- meaning between < and > -- encode [\\ ` * _ ~ =] so they\n * don't conflict with their use in Markdown for code, italics and strong.\n */\nshowdown.subParser('escapeSpecialCharsWithinTagAttributes', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('escapeSpecialCharsWithinTagAttributes.before', text, options, globals);\n\n  // Build a regex to find HTML tags.\n  var tags     = /<\\/?[a-z\\d_:-]+(?:[\\s]+[\\s\\S]+?)?>/gi,\n      comments = /-]|-[^>])(?:[^-]|-[^-])*)--)>/gi;\n\n  text = text.replace(tags, function (wholeMatch) {\n    return wholeMatch\n      .replace(/(.)<\\/?code>(?=.)/g, '$1`')\n      .replace(/([\\\\`*_~=|])/g, showdown.helper.escapeCharactersCallback);\n  });\n\n  text = text.replace(comments, function (wholeMatch) {\n    return wholeMatch\n      .replace(/([\\\\`*_~=|])/g, showdown.helper.escapeCharactersCallback);\n  });\n\n  text = globals.converter._dispatch('escapeSpecialCharsWithinTagAttributes.after', text, options, globals);\n  return text;\n});\n","/**\n * Handle github codeblocks prior to running HashHTML so that\n * HTML contained within the codeblock gets escaped properly\n * Example:\n * ```ruby\n *     def hello_world(x)\n *       puts \"Hello, #{x}\"\n *     end\n * ```\n */\nshowdown.subParser('githubCodeBlocks', function (text, options, globals) {\n  'use strict';\n\n  // early exit if option is not enabled\n  if (!options.ghCodeBlocks) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('githubCodeBlocks.before', text, options, globals);\n\n  text += '¨0';\n\n  text = text.replace(/(?:^|\\n)(?: {0,3})(```+|~~~+)(?: *)([^\\s`~]*)\\n([\\s\\S]*?)\\n(?: {0,3})\\1/g, function (wholeMatch, delim, language, codeblock) {\n    var end = (options.omitExtraWLInCodeBlocks) ? '' : '\\n';\n\n    // First parse the github code block\n    codeblock = showdown.subParser('encodeCode')(codeblock, options, globals);\n    codeblock = showdown.subParser('detab')(codeblock, options, globals);\n    codeblock = codeblock.replace(/^\\n+/g, ''); // trim leading newlines\n    codeblock = codeblock.replace(/\\n+$/g, ''); // trim trailing whitespace\n\n    codeblock = '
    ' + codeblock + end + '
    ';\n\n    codeblock = showdown.subParser('hashBlock')(codeblock, options, globals);\n\n    // Since GHCodeblocks can be false positives, we need to\n    // store the primitive text and the parsed text in a global var,\n    // and then return a token\n    return '\\n\\n¨G' + (globals.ghCodeBlocks.push({text: wholeMatch, codeblock: codeblock}) - 1) + 'G\\n\\n';\n  });\n\n  // attacklab: strip sentinel\n  text = text.replace(/¨0/, '');\n\n  return globals.converter._dispatch('githubCodeBlocks.after', text, options, globals);\n});\n","showdown.subParser('hashBlock', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashBlock.before', text, options, globals);\n  text = text.replace(/(^\\n+|\\n+$)/g, '');\n  text = '\\n\\n¨K' + (globals.gHtmlBlocks.push(text) - 1) + 'K\\n\\n';\n  text = globals.converter._dispatch('hashBlock.after', text, options, globals);\n  return text;\n});\n","/**\n * Hash and escape  elements that should not be parsed as markdown\n */\nshowdown.subParser('hashCodeTags', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashCodeTags.before', text, options, globals);\n\n  var repFunc = function (wholeMatch, match, left, right) {\n    var codeblock = left + showdown.subParser('encodeCode')(match, options, globals) + right;\n    return '¨C' + (globals.gHtmlSpans.push(codeblock) - 1) + 'C';\n  };\n\n  // Hash naked \n  text = showdown.helper.replaceRecursiveRegExp(text, repFunc, ']*>', '', 'gim');\n\n  text = globals.converter._dispatch('hashCodeTags.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('hashElement', function (text, options, globals) {\n  'use strict';\n\n  return function (wholeMatch, m1) {\n    var blockText = m1;\n\n    // Undo double lines\n    blockText = blockText.replace(/\\n\\n/g, '\\n');\n    blockText = blockText.replace(/^\\n/, '');\n\n    // strip trailing blank lines\n    blockText = blockText.replace(/\\n+$/g, '');\n\n    // Replace the element text with a marker (\"¨KxK\" where x is its key)\n    blockText = '\\n\\n¨K' + (globals.gHtmlBlocks.push(blockText) - 1) + 'K\\n\\n';\n\n    return blockText;\n  };\n});\n","showdown.subParser('hashHTMLBlocks', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashHTMLBlocks.before', text, options, globals);\n\n  var blockTags = [\n        'pre',\n        'div',\n        'h1',\n        'h2',\n        'h3',\n        'h4',\n        'h5',\n        'h6',\n        'blockquote',\n        'table',\n        'dl',\n        'ol',\n        'ul',\n        'script',\n        'noscript',\n        'form',\n        'fieldset',\n        'iframe',\n        'math',\n        'style',\n        'section',\n        'header',\n        'footer',\n        'nav',\n        'article',\n        'aside',\n        'address',\n        'audio',\n        'canvas',\n        'figure',\n        'hgroup',\n        'output',\n        'video',\n        'p'\n      ],\n      repFunc = function (wholeMatch, match, left, right) {\n        var txt = wholeMatch;\n        // check if this html element is marked as markdown\n        // if so, it's contents should be parsed as markdown\n        if (left.search(/\\bmarkdown\\b/) !== -1) {\n          txt = left + globals.converter.makeHtml(match) + right;\n        }\n        return '\\n\\n¨K' + (globals.gHtmlBlocks.push(txt) - 1) + 'K\\n\\n';\n      };\n\n  if (options.backslashEscapesHTMLTags) {\n    // encode backslash escaped HTML tags\n    text = text.replace(/\\\\<(\\/?[^>]+?)>/g, function (wm, inside) {\n      return '<' + inside + '>';\n    });\n  }\n\n  // hash HTML Blocks\n  for (var i = 0; i < blockTags.length; ++i) {\n\n    var opTagPos,\n        rgx1     = new RegExp('^ {0,3}(<' + blockTags[i] + '\\\\b[^>]*>)', 'im'),\n        patLeft  = '<' + blockTags[i] + '\\\\b[^>]*>',\n        patRight = '';\n    // 1. Look for the first position of the first opening HTML tag in the text\n    while ((opTagPos = showdown.helper.regexIndexOf(text, rgx1)) !== -1) {\n\n      // if the HTML tag is \\ escaped, we need to escape it and break\n\n\n      //2. Split the text in that position\n      var subTexts = showdown.helper.splitAtIndex(text, opTagPos),\n          //3. Match recursively\n          newSubText1 = showdown.helper.replaceRecursiveRegExp(subTexts[1], repFunc, patLeft, patRight, 'im');\n\n      // prevent an infinite loop\n      if (newSubText1 === subTexts[1]) {\n        break;\n      }\n      text = subTexts[0].concat(newSubText1);\n    }\n  }\n  // HR SPECIAL CASE\n  text = text.replace(/(\\n {0,3}(<(hr)\\b([^<>])*?\\/?>)[ \\t]*(?=\\n{2,}))/g,\n    showdown.subParser('hashElement')(text, options, globals));\n\n  // Special case for standalone HTML comments\n  text = showdown.helper.replaceRecursiveRegExp(text, function (txt) {\n    return '\\n\\n¨K' + (globals.gHtmlBlocks.push(txt) - 1) + 'K\\n\\n';\n  }, '^ {0,3}', 'gm');\n\n  // PHP and ASP-style processor instructions ( and <%...%>)\n  text = text.replace(/(?:\\n\\n)( {0,3}(?:<([?%])[^\\r]*?\\2>)[ \\t]*(?=\\n{2,}))/g,\n    showdown.subParser('hashElement')(text, options, globals));\n\n  text = globals.converter._dispatch('hashHTMLBlocks.after', text, options, globals);\n  return text;\n});\n","/**\n * Hash span elements that should not be parsed as markdown\n */\nshowdown.subParser('hashHTMLSpans', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashHTMLSpans.before', text, options, globals);\n\n  function hashHTMLSpan (html) {\n    return '¨C' + (globals.gHtmlSpans.push(html) - 1) + 'C';\n  }\n\n  // Hash Self Closing tags\n  text = text.replace(/<[^>]+?\\/>/gi, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash tags without properties\n  text = text.replace(/<([^>]+?)>[\\s\\S]*?<\\/\\1>/g, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash tags with properties\n  text = text.replace(/<([^>]+?)\\s[^>]+?>[\\s\\S]*?<\\/\\1>/g, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash self closing tags without />\n  text = text.replace(/<[^>]+?>/gi, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  /*showdown.helper.matchRecursiveRegExp(text, ']*>', '', 'gi');*/\n\n  text = globals.converter._dispatch('hashHTMLSpans.after', text, options, globals);\n  return text;\n});\n\n/**\n * Unhash HTML spans\n */\nshowdown.subParser('unhashHTMLSpans', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('unhashHTMLSpans.before', text, options, globals);\n\n  for (var i = 0; i < globals.gHtmlSpans.length; ++i) {\n    var repText = globals.gHtmlSpans[i],\n        // limiter to prevent infinite loop (assume 10 as limit for recurse)\n        limit = 0;\n\n    while (/¨C(\\d+)C/.test(repText)) {\n      var num = RegExp.$1;\n      repText = repText.replace('¨C' + num + 'C', globals.gHtmlSpans[num]);\n      if (limit === 10) {\n        console.error('maximum nesting of 10 spans reached!!!');\n        break;\n      }\n      ++limit;\n    }\n    text = text.replace('¨C' + i + 'C', repText);\n  }\n\n  text = globals.converter._dispatch('unhashHTMLSpans.after', text, options, globals);\n  return text;\n});\n","/**\n * Hash and escape 
     elements that should not be parsed as markdown\n */\nshowdown.subParser('hashPreCodeTags', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashPreCodeTags.before', text, options, globals);\n\n  var repFunc = function (wholeMatch, match, left, right) {\n    // encode html entities\n    var codeblock = left + showdown.subParser('encodeCode')(match, options, globals) + right;\n    return '\\n\\n¨G' + (globals.ghCodeBlocks.push({text: wholeMatch, codeblock: codeblock}) - 1) + 'G\\n\\n';\n  };\n\n  // Hash 
    \n  text = showdown.helper.replaceRecursiveRegExp(text, repFunc, '^ {0,3}]*>\\\\s*]*>', '^ {0,3}\\\\s*
    ', 'gim');\n\n  text = globals.converter._dispatch('hashPreCodeTags.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('headers', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('headers.before', text, options, globals);\n\n  var headerLevelStart = (isNaN(parseInt(options.headerLevelStart))) ? 1 : parseInt(options.headerLevelStart),\n\n      // Set text-style headers:\n      //\tHeader 1\n      //\t========\n      //\n      //\tHeader 2\n      //\t--------\n      //\n      setextRegexH1 = (options.smoothLivePreview) ? /^(.+)[ \\t]*\\n={2,}[ \\t]*\\n+/gm : /^(.+)[ \\t]*\\n=+[ \\t]*\\n+/gm,\n      setextRegexH2 = (options.smoothLivePreview) ? /^(.+)[ \\t]*\\n-{2,}[ \\t]*\\n+/gm : /^(.+)[ \\t]*\\n-+[ \\t]*\\n+/gm;\n\n  text = text.replace(setextRegexH1, function (wholeMatch, m1) {\n\n    var spanGamut = showdown.subParser('spanGamut')(m1, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m1) + '\"',\n        hLevel = headerLevelStart,\n        hashBlock = '' + spanGamut + '';\n    return showdown.subParser('hashBlock')(hashBlock, options, globals);\n  });\n\n  text = text.replace(setextRegexH2, function (matchFound, m1) {\n    var spanGamut = showdown.subParser('spanGamut')(m1, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m1) + '\"',\n        hLevel = headerLevelStart + 1,\n        hashBlock = '' + spanGamut + '';\n    return showdown.subParser('hashBlock')(hashBlock, options, globals);\n  });\n\n  // atx-style headers:\n  //  # Header 1\n  //  ## Header 2\n  //  ## Header 2 with closing hashes ##\n  //  ...\n  //  ###### Header 6\n  //\n  var atxStyle = (options.requireSpaceBeforeHeadingText) ? /^(#{1,6})[ \\t]+(.+?)[ \\t]*#*\\n+/gm : /^(#{1,6})[ \\t]*(.+?)[ \\t]*#*\\n+/gm;\n\n  text = text.replace(atxStyle, function (wholeMatch, m1, m2) {\n    var hText = m2;\n    if (options.customizedHeaderId) {\n      hText = m2.replace(/\\s?\\{([^{]+?)}\\s*$/, '');\n    }\n\n    var span = showdown.subParser('spanGamut')(hText, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m2) + '\"',\n        hLevel = headerLevelStart - 1 + m1.length,\n        header = '' + span + '';\n\n    return showdown.subParser('hashBlock')(header, options, globals);\n  });\n\n  function headerId (m) {\n    var title,\n        prefix;\n\n    // It is separate from other options to allow combining prefix and customized\n    if (options.customizedHeaderId) {\n      var match = m.match(/\\{([^{]+?)}\\s*$/);\n      if (match && match[1]) {\n        m = match[1];\n      }\n    }\n\n    title = m;\n\n    // Prefix id to prevent causing inadvertent pre-existing style matches.\n    if (showdown.helper.isString(options.prefixHeaderId)) {\n      prefix = options.prefixHeaderId;\n    } else if (options.prefixHeaderId === true) {\n      prefix = 'section-';\n    } else {\n      prefix = '';\n    }\n\n    if (!options.rawPrefixHeaderId) {\n      title = prefix + title;\n    }\n\n    if (options.ghCompatibleHeaderId) {\n      title = title\n        .replace(/ /g, '-')\n        // replace previously escaped chars (&, ¨ and $)\n        .replace(/&/g, '')\n        .replace(/¨T/g, '')\n        .replace(/¨D/g, '')\n        // replace rest of the chars (&~$ are repeated as they might have been escaped)\n        // borrowed from github's redcarpet (some they should produce similar results)\n        .replace(/[&+$,\\/:;=?@\"#{}|^¨~\\[\\]`\\\\*)(%.!'<>]/g, '')\n        .toLowerCase();\n    } else if (options.rawHeaderId) {\n      title = title\n        .replace(/ /g, '-')\n        // replace previously escaped chars (&, ¨ and $)\n        .replace(/&/g, '&')\n        .replace(/¨T/g, '¨')\n        .replace(/¨D/g, '$')\n        // replace \" and '\n        .replace(/[\"']/g, '-')\n        .toLowerCase();\n    } else {\n      title = title\n        .replace(/[^\\w]/g, '')\n        .toLowerCase();\n    }\n\n    if (options.rawPrefixHeaderId) {\n      title = prefix + title;\n    }\n\n    if (globals.hashLinkCounts[title]) {\n      title = title + '-' + (globals.hashLinkCounts[title]++);\n    } else {\n      globals.hashLinkCounts[title] = 1;\n    }\n    return title;\n  }\n\n  text = globals.converter._dispatch('headers.after', text, options, globals);\n  return text;\n});\n","/**\n * Turn Markdown link shortcuts into XHTML  tags.\n */\nshowdown.subParser('horizontalRule', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('horizontalRule.before', text, options, globals);\n\n  var key = showdown.subParser('hashBlock')('
    ', options, globals);\n  text = text.replace(/^ {0,2}( ?-){3,}[ \\t]*$/gm, key);\n  text = text.replace(/^ {0,2}( ?\\*){3,}[ \\t]*$/gm, key);\n  text = text.replace(/^ {0,2}( ?_){3,}[ \\t]*$/gm, key);\n\n  text = globals.converter._dispatch('horizontalRule.after', text, options, globals);\n  return text;\n});\n","/**\n * Turn Markdown image shortcuts into  tags.\n */\nshowdown.subParser('images', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('images.before', text, options, globals);\n\n  var inlineRegExp      = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]??(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:([\"'])([^\"]*?)\\6)?[ \\t]?\\)/g,\n      crazyRegExp       = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]?<([^>]*)>(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:(?:([\"'])([^\"]*?)\\6))?[ \\t]?\\)/g,\n      base64RegExp      = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]??(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:([\"'])([^\"]*?)\\6)?[ \\t]?\\)/g,\n      referenceRegExp   = /!\\[([^\\]]*?)] ?(?:\\n *)?\\[([\\s\\S]*?)]()()()()()/g,\n      refShortcutRegExp = /!\\[([^\\[\\]]+)]()()()()()/g;\n\n  function writeImageTagBase64 (wholeMatch, altText, linkId, url, width, height, m5, title) {\n    url = url.replace(/\\s/g, '');\n    return writeImageTag (wholeMatch, altText, linkId, url, width, height, m5, title);\n  }\n\n  function writeImageTag (wholeMatch, altText, linkId, url, width, height, m5, title) {\n\n    var gUrls   = globals.gUrls,\n        gTitles = globals.gTitles,\n        gDims   = globals.gDimensions;\n\n    linkId = linkId.toLowerCase();\n\n    if (!title) {\n      title = '';\n    }\n    // Special case for explicit empty url\n    if (wholeMatch.search(/\\(? ?(['\"].*['\"])?\\)$/m) > -1) {\n      url = '';\n\n    } else if (url === '' || url === null) {\n      if (linkId === '' || linkId === null) {\n        // lower-case and turn embedded newlines into spaces\n        linkId = altText.toLowerCase().replace(/ ?\\n/g, ' ');\n      }\n      url = '#' + linkId;\n\n      if (!showdown.helper.isUndefined(gUrls[linkId])) {\n        url = gUrls[linkId];\n        if (!showdown.helper.isUndefined(gTitles[linkId])) {\n          title = gTitles[linkId];\n        }\n        if (!showdown.helper.isUndefined(gDims[linkId])) {\n          width = gDims[linkId].width;\n          height = gDims[linkId].height;\n        }\n      } else {\n        return wholeMatch;\n      }\n    }\n\n    altText = altText\n      .replace(/\"/g, '"')\n    //altText = showdown.helper.escapeCharacters(altText, '*_', false);\n      .replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n    //url = showdown.helper.escapeCharacters(url, '*_', false);\n    url = url.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n    var result = '\"'x \"optional title\")\n\n  // base64 encoded images\n  text = text.replace(base64RegExp, writeImageTagBase64);\n\n  // cases with crazy urls like ./image/cat1).png\n  text = text.replace(crazyRegExp, writeImageTag);\n\n  // normal cases\n  text = text.replace(inlineRegExp, writeImageTag);\n\n  // handle reference-style shortcuts: ![img text]\n  text = text.replace(refShortcutRegExp, writeImageTag);\n\n  text = globals.converter._dispatch('images.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('italicsAndBold', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('italicsAndBold.before', text, options, globals);\n\n  // it's faster to have 3 separate regexes for each case than have just one\n  // because of backtracing, in some cases, it could lead to an exponential effect\n  // called \"catastrophic backtrace\". Ominous!\n\n  function parseInside (txt, left, right) {\n    /*\n    if (options.simplifiedAutoLink) {\n      txt = showdown.subParser('simplifiedAutoLinks')(txt, options, globals);\n    }\n    */\n    return left + txt + right;\n  }\n\n  // Parse underscores\n  if (options.literalMidWordUnderscores) {\n    text = text.replace(/\\b___(\\S[\\s\\S]*?)___\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n    text = text.replace(/\\b__(\\S[\\s\\S]*?)__\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n    text = text.replace(/\\b_(\\S[\\s\\S]*?)_\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n  } else {\n    text = text.replace(/___(\\S[\\s\\S]*?)___/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/__(\\S[\\s\\S]*?)__/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/_([^\\s_][\\s\\S]*?)_/g, function (wm, m) {\n      // !/^_[^_]/.test(m) - test if it doesn't start with __ (since it seems redundant, we removed it)\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n  }\n\n  // Now parse asterisks\n  if (options.literalMidWordAsterisks) {\n    text = text.replace(/([^*]|^)\\B\\*\\*\\*(\\S[\\s\\S]*?)\\*\\*\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n    text = text.replace(/([^*]|^)\\B\\*\\*(\\S[\\s\\S]*?)\\*\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n    text = text.replace(/([^*]|^)\\B\\*(\\S[\\s\\S]*?)\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n  } else {\n    text = text.replace(/\\*\\*\\*(\\S[\\s\\S]*?)\\*\\*\\*/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/\\*\\*(\\S[\\s\\S]*?)\\*\\*/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/\\*([^\\s*][\\s\\S]*?)\\*/g, function (wm, m) {\n      // !/^\\*[^*]/.test(m) - test if it doesn't start with ** (since it seems redundant, we removed it)\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n  }\n\n\n  text = globals.converter._dispatch('italicsAndBold.after', text, options, globals);\n  return text;\n});\n","/**\n * Form HTML ordered (numbered) and unordered (bulleted) lists.\n */\nshowdown.subParser('lists', function (text, options, globals) {\n  'use strict';\n\n  /**\n   * Process the contents of a single ordered or unordered list, splitting it\n   * into individual list items.\n   * @param {string} listStr\n   * @param {boolean} trimTrailing\n   * @returns {string}\n   */\n  function processListItems (listStr, trimTrailing) {\n    // The $g_list_level global keeps track of when we're inside a list.\n    // Each time we enter a list, we increment it; when we leave a list,\n    // we decrement. If it's zero, we're not in a list anymore.\n    //\n    // We do this because when we're not inside a list, we want to treat\n    // something like this:\n    //\n    //    I recommend upgrading to version\n    //    8. Oops, now this line is treated\n    //    as a sub-list.\n    //\n    // As a single paragraph, despite the fact that the second line starts\n    // with a digit-period-space sequence.\n    //\n    // Whereas when we're inside a list (or sub-list), that line will be\n    // treated as the start of a sub-list. What a kludge, huh? This is\n    // an aspect of Markdown's syntax that's hard to parse perfectly\n    // without resorting to mind-reading. Perhaps the solution is to\n    // change the syntax rules such that sub-lists must start with a\n    // starting cardinal number; e.g. \"1.\" or \"a.\".\n    globals.gListLevel++;\n\n    // trim trailing blank lines:\n    listStr = listStr.replace(/\\n{2,}$/, '\\n');\n\n    // attacklab: add sentinel to emulate \\z\n    listStr += '¨0';\n\n    var rgx = /(\\n)?(^ {0,3})([*+-]|\\d+[.])[ \\t]+((\\[(x|X| )?])?[ \\t]*[^\\r]+?(\\n{1,2}))(?=\\n*(¨0| {0,3}([*+-]|\\d+[.])[ \\t]+))/gm,\n        isParagraphed = (/\\n[ \\t]*\\n(?!¨0)/.test(listStr));\n\n    // Since version 1.5, nesting sublists requires 4 spaces (or 1 tab) indentation,\n    // which is a syntax breaking change\n    // activating this option reverts to old behavior\n    if (options.disableForced4SpacesIndentedSublists) {\n      rgx = /(\\n)?(^ {0,3})([*+-]|\\d+[.])[ \\t]+((\\[(x|X| )?])?[ \\t]*[^\\r]+?(\\n{1,2}))(?=\\n*(¨0|\\2([*+-]|\\d+[.])[ \\t]+))/gm;\n    }\n\n    listStr = listStr.replace(rgx, function (wholeMatch, m1, m2, m3, m4, taskbtn, checked) {\n      checked = (checked && checked.trim() !== '');\n\n      var item = showdown.subParser('outdent')(m4, options, globals),\n          bulletStyle = '';\n\n      // Support for github tasklists\n      if (taskbtn && options.tasklists) {\n        bulletStyle = ' class=\"task-list-item\" style=\"list-style-type: none;\"';\n        item = item.replace(/^[ \\t]*\\[(x|X| )?]/m, function () {\n          var otp = '
  • a
    • \n      // instead of:\n      // 
    • - - a
    \n      // So, to prevent it, we will put a marker (¨A)in the beginning of the line\n      // Kind of hackish/monkey patching, but seems more effective than overcomplicating the list parser\n      item = item.replace(/^([-*+]|\\d\\.)[ \\t]+[\\S\\n ]*/g, function (wm2) {\n        return '¨A' + wm2;\n      });\n\n      // m1 - Leading line or\n      // Has a double return (multi paragraph) or\n      // Has sublist\n      if (m1 || (item.search(/\\n{2,}/) > -1)) {\n        item = showdown.subParser('githubCodeBlocks')(item, options, globals);\n        item = showdown.subParser('blockGamut')(item, options, globals);\n      } else {\n        // Recursion for sub-lists:\n        item = showdown.subParser('lists')(item, options, globals);\n        item = item.replace(/\\n$/, ''); // chomp(item)\n        item = showdown.subParser('hashHTMLBlocks')(item, options, globals);\n\n        // Colapse double linebreaks\n        item = item.replace(/\\n\\n+/g, '\\n\\n');\n        if (isParagraphed) {\n          item = showdown.subParser('paragraphs')(item, options, globals);\n        } else {\n          item = showdown.subParser('spanGamut')(item, options, globals);\n        }\n      }\n\n      // now we need to remove the marker (¨A)\n      item = item.replace('¨A', '');\n      // we can finally wrap the line in list item tags\n      item =  '' + item + '\\n';\n\n      return item;\n    });\n\n    // attacklab: strip sentinel\n    listStr = listStr.replace(/¨0/g, '');\n\n    globals.gListLevel--;\n\n    if (trimTrailing) {\n      listStr = listStr.replace(/\\s+$/, '');\n    }\n\n    return listStr;\n  }\n\n  function styleStartNumber (list, listType) {\n    // check if ol and starts by a number different than 1\n    if (listType === 'ol') {\n      var res = list.match(/^ *(\\d+)\\./);\n      if (res && res[1] !== '1') {\n        return ' start=\"' + res[1] + '\"';\n      }\n    }\n    return '';\n  }\n\n  /**\n   * Check and parse consecutive lists (better fix for issue #142)\n   * @param {string} list\n   * @param {string} listType\n   * @param {boolean} trimTrailing\n   * @returns {string}\n   */\n  function parseConsecutiveLists (list, listType, trimTrailing) {\n    // check if we caught 2 or more consecutive lists by mistake\n    // we use the counterRgx, meaning if listType is UL we look for OL and vice versa\n    var olRgx = (options.disableForced4SpacesIndentedSublists) ? /^ ?\\d+\\.[ \\t]/gm : /^ {0,3}\\d+\\.[ \\t]/gm,\n        ulRgx = (options.disableForced4SpacesIndentedSublists) ? /^ ?[*+-][ \\t]/gm : /^ {0,3}[*+-][ \\t]/gm,\n        counterRxg = (listType === 'ul') ? olRgx : ulRgx,\n        result = '';\n\n    if (list.search(counterRxg) !== -1) {\n      (function parseCL (txt) {\n        var pos = txt.search(counterRxg),\n            style = styleStartNumber(list, listType);\n        if (pos !== -1) {\n          // slice\n          result += '\\n\\n<' + listType + style + '>\\n' + processListItems(txt.slice(0, pos), !!trimTrailing) + '\\n';\n\n          // invert counterType and listType\n          listType = (listType === 'ul') ? 'ol' : 'ul';\n          counterRxg = (listType === 'ul') ? olRgx : ulRgx;\n\n          //recurse\n          parseCL(txt.slice(pos));\n        } else {\n          result += '\\n\\n<' + listType + style + '>\\n' + processListItems(txt, !!trimTrailing) + '\\n';\n        }\n      })(list);\n    } else {\n      var style = styleStartNumber(list, listType);\n      result = '\\n\\n<' + listType + style + '>\\n' + processListItems(list, !!trimTrailing) + '\\n';\n    }\n\n    return result;\n  }\n\n  /** Start of list parsing **/\n  text = globals.converter._dispatch('lists.before', text, options, globals);\n  // add sentinel to hack around khtml/safari bug:\n  // http://bugs.webkit.org/show_bug.cgi?id=11231\n  text += '¨0';\n\n  if (globals.gListLevel) {\n    text = text.replace(/^(( {0,3}([*+-]|\\d+[.])[ \\t]+)[^\\r]+?(¨0|\\n{2,}(?=\\S)(?![ \\t]*(?:[*+-]|\\d+[.])[ \\t]+)))/gm,\n      function (wholeMatch, list, m2) {\n        var listType = (m2.search(/[*+-]/g) > -1) ? 'ul' : 'ol';\n        return parseConsecutiveLists(list, listType, true);\n      }\n    );\n  } else {\n    text = text.replace(/(\\n\\n|^\\n?)(( {0,3}([*+-]|\\d+[.])[ \\t]+)[^\\r]+?(¨0|\\n{2,}(?=\\S)(?![ \\t]*(?:[*+-]|\\d+[.])[ \\t]+)))/gm,\n      function (wholeMatch, m1, list, m3) {\n        var listType = (m3.search(/[*+-]/g) > -1) ? 'ul' : 'ol';\n        return parseConsecutiveLists(list, listType, false);\n      }\n    );\n  }\n\n  // strip sentinel\n  text = text.replace(/¨0/, '');\n  text = globals.converter._dispatch('lists.after', text, options, globals);\n  return text;\n});\n","/**\n * Parse metadata at the top of the document\n */\nshowdown.subParser('metadata', function (text, options, globals) {\n  'use strict';\n\n  if (!options.metadata) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('metadata.before', text, options, globals);\n\n  function parseMetadataContents (content) {\n    // raw is raw so it's not changed in any way\n    globals.metadata.raw = content;\n\n    // escape chars forbidden in html attributes\n    // double quotes\n    content = content\n      // ampersand first\n      .replace(/&/g, '&')\n      // double quotes\n      .replace(/\"/g, '"');\n\n    content = content.replace(/\\n {4}/g, ' ');\n    content.replace(/^([\\S ]+): +([\\s\\S]+?)$/gm, function (wm, key, value) {\n      globals.metadata.parsed[key] = value;\n      return '';\n    });\n  }\n\n  text = text.replace(/^\\s*«««+(\\S*?)\\n([\\s\\S]+?)\\n»»»+\\n/, function (wholematch, format, content) {\n    parseMetadataContents(content);\n    return '¨M';\n  });\n\n  text = text.replace(/^\\s*---+(\\S*?)\\n([\\s\\S]+?)\\n---+\\n/, function (wholematch, format, content) {\n    if (format) {\n      globals.metadata.format = format;\n    }\n    parseMetadataContents(content);\n    return '¨M';\n  });\n\n  text = text.replace(/¨M/g, '');\n\n  text = globals.converter._dispatch('metadata.after', text, options, globals);\n  return text;\n});\n","/**\n * Remove one level of line-leading tabs or spaces\n */\nshowdown.subParser('outdent', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('outdent.before', text, options, globals);\n\n  // attacklab: hack around Konqueror 3.5.4 bug:\n  // \"----------bug\".replace(/^-/g,\"\") == \"bug\"\n  text = text.replace(/^(\\t|[ ]{1,4})/gm, '¨0'); // attacklab: g_tab_width\n\n  // attacklab: clean up hack\n  text = text.replace(/¨0/g, '');\n\n  text = globals.converter._dispatch('outdent.after', text, options, globals);\n  return text;\n});\n","/**\n *\n */\nshowdown.subParser('paragraphs', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('paragraphs.before', text, options, globals);\n  // Strip leading and trailing lines:\n  text = text.replace(/^\\n+/g, '');\n  text = text.replace(/\\n+$/g, '');\n\n  var grafs = text.split(/\\n{2,}/g),\n      grafsOut = [],\n      end = grafs.length; // Wrap 
     tags\n\n  for (var i = 0; i < end; i++) {\n    var str = grafs[i];\n    // if this is an HTML marker, copy it\n    if (str.search(/¨(K|G)(\\d+)\\1/g) >= 0) {\n      grafsOut.push(str);\n\n    // test for presence of characters to prevent empty lines being parsed\n    // as paragraphs (resulting in undesired extra empty paragraphs)\n    } else if (str.search(/\\S/) >= 0) {\n      str = showdown.subParser('spanGamut')(str, options, globals);\n      str = str.replace(/^([ \\t]*)/g, '
    ');\n      str += '
    ';\n      grafsOut.push(str);\n    }\n  }\n\n  /** Unhashify HTML blocks */\n  end = grafsOut.length;\n  for (i = 0; i < end; i++) {\n    var blockText = '',\n        grafsOutIt = grafsOut[i],\n        codeFlag = false;\n    // if this is a marker for an html block...\n    // use RegExp.test instead of string.search because of QML bug\n    while (/¨(K|G)(\\d+)\\1/.test(grafsOutIt)) {\n      var delim = RegExp.$1,\n          num   = RegExp.$2;\n\n      if (delim === 'K') {\n        blockText = globals.gHtmlBlocks[num];\n      } else {\n        // we need to check if ghBlock is a false positive\n        if (codeFlag) {\n          // use encoded version of all text\n          blockText = showdown.subParser('encodeCode')(globals.ghCodeBlocks[num].text, options, globals);\n        } else {\n          blockText = globals.ghCodeBlocks[num].codeblock;\n        }\n      }\n      blockText = blockText.replace(/\\$/g, '$$$$'); // Escape any dollar signs\n\n      grafsOutIt = grafsOutIt.replace(/(\\n\\n)?¨(K|G)\\d+\\2(\\n\\n)?/, blockText);\n      // Check if grafsOutIt is a pre->code\n      if (/^]*>\\s*]*>/.test(grafsOutIt)) {\n        codeFlag = true;\n      }\n    }\n    grafsOut[i] = grafsOutIt;\n  }\n  text = grafsOut.join('\\n');\n  // Strip leading and trailing lines:\n  text = text.replace(/^\\n+/g, '');\n  text = text.replace(/\\n+$/g, '');\n  return globals.converter._dispatch('paragraphs.after', text, options, globals);\n});\n","/**\n * Run extension\n */\nshowdown.subParser('runExtension', function (ext, text, options, globals) {\n  'use strict';\n\n  if (ext.filter) {\n    text = ext.filter(text, globals.converter, options);\n\n  } else if (ext.regex) {\n    // TODO remove this when old extension loading mechanism is deprecated\n    var re = ext.regex;\n    if (!(re instanceof RegExp)) {\n      re = new RegExp(re, 'g');\n    }\n    text = text.replace(re, ext.replace);\n  }\n\n  return text;\n});\n","/**\n * These are all the transformations that occur *within* block-level\n * tags like paragraphs, headers, and list items.\n */\nshowdown.subParser('spanGamut', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('spanGamut.before', text, options, globals);\n  text = showdown.subParser('codeSpans')(text, options, globals);\n  text = showdown.subParser('escapeSpecialCharsWithinTagAttributes')(text, options, globals);\n  text = showdown.subParser('encodeBackslashEscapes')(text, options, globals);\n\n  // Process anchor and image tags. Images must come first,\n  // because ![foo][f] looks like an anchor.\n  text = showdown.subParser('images')(text, options, globals);\n  text = showdown.subParser('anchors')(text, options, globals);\n\n  // Make links out of things like ``\n  // Must come after anchors, because you can use < and >\n  // delimiters in inline links like [this]().\n  text = showdown.subParser('autoLinks')(text, options, globals);\n  text = showdown.subParser('simplifiedAutoLinks')(text, options, globals);\n  text = showdown.subParser('emoji')(text, options, globals);\n  text = showdown.subParser('underline')(text, options, globals);\n  text = showdown.subParser('italicsAndBold')(text, options, globals);\n  text = showdown.subParser('strikethrough')(text, options, globals);\n  text = showdown.subParser('ellipsis')(text, options, globals);\n\n  // we need to hash HTML tags inside spans\n  text = showdown.subParser('hashHTMLSpans')(text, options, globals);\n\n  // now we encode amps and angles\n  text = showdown.subParser('encodeAmpsAndAngles')(text, options, globals);\n\n  // Do hard breaks\n  if (options.simpleLineBreaks) {\n    // GFM style hard breaks\n    // only add line breaks if the text does not contain a block (special case for lists)\n    if (!/\\n\\n¨K/.test(text)) {\n      text = text.replace(/\\n+/g, '
    \\n');\n    }\n  } else {\n    // Vanilla hard breaks\n    text = text.replace(/  +\\n/g, '
    \\n');\n  }\n\n  text = globals.converter._dispatch('spanGamut.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('strikethrough', function (text, options, globals) {\n  'use strict';\n\n  function parseInside (txt) {\n    if (options.simplifiedAutoLink) {\n      txt = showdown.subParser('simplifiedAutoLinks')(txt, options, globals);\n    }\n    return '' + txt + '';\n  }\n\n  if (options.strikethrough) {\n    text = globals.converter._dispatch('strikethrough.before', text, options, globals);\n    text = text.replace(/(?:~){2}([\\s\\S]+?)(?:~){2}/g, function (wm, txt) { return parseInside(txt); });\n    text = globals.converter._dispatch('strikethrough.after', text, options, globals);\n  }\n\n  return text;\n});\n","/**\n * Strips link definitions from text, stores the URLs and titles in\n * hash references.\n * Link defs are in the form: ^[id]: url \"optional title\"\n */\nshowdown.subParser('stripLinkDefinitions', function (text, options, globals) {\n  'use strict';\n\n  var regex       = /^ {0,3}\\[(.+)]:[ \\t]*\\n?[ \\t]*\\s]+)>?(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*\\n?[ \\t]*(?:(\\n*)[\"|'(](.+?)[\"|')][ \\t]*)?(?:\\n+|(?=¨0))/gm,\n      base64Regex = /^ {0,3}\\[(.+)]:[ \\t]*\\n?[ \\t]*?(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*\\n?[ \\t]*(?:(\\n*)[\"|'(](.+?)[\"|')][ \\t]*)?(?:\\n\\n|(?=¨0)|(?=\\n\\[))/gm;\n\n  // attacklab: sentinel workarounds for lack of \\A and \\Z, safari\\khtml bug\n  text += '¨0';\n\n  var replaceFunc = function (wholeMatch, linkId, url, width, height, blankLines, title) {\n    linkId = linkId.toLowerCase();\n    if (url.match(/^data:.+?\\/.+?;base64,/)) {\n      // remove newlines\n      globals.gUrls[linkId] = url.replace(/\\s/g, '');\n    } else {\n      globals.gUrls[linkId] = showdown.subParser('encodeAmpsAndAngles')(url, options, globals);  // Link IDs are case-insensitive\n    }\n\n    if (blankLines) {\n      // Oops, found blank lines, so it's not a title.\n      // Put back the parenthetical statement we stole.\n      return blankLines + title;\n\n    } else {\n      if (title) {\n        globals.gTitles[linkId] = title.replace(/\"|'/g, '"');\n      }\n      if (options.parseImgDimensions && width && height) {\n        globals.gDimensions[linkId] = {\n          width:  width,\n          height: height\n        };\n      }\n    }\n    // Completely remove the definition from the text\n    return '';\n  };\n\n  // first we try to find base64 link references\n  text = text.replace(base64Regex, replaceFunc);\n\n  text = text.replace(regex, replaceFunc);\n\n  // attacklab: strip sentinel\n  text = text.replace(/¨0/, '');\n\n  return text;\n});\n","showdown.subParser('tables', function (text, options, globals) {\n  'use strict';\n\n  if (!options.tables) {\n    return text;\n  }\n\n  var tableRgx       = /^ {0,3}\\|?.+\\|.+\\n {0,3}\\|?[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[\\s\\S]+?(?:\\n\\n|¨0)/gm,\n      //singeColTblRgx = /^ {0,3}\\|.+\\|\\n {0,3}\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*\\n(?: {0,3}\\|.+\\|\\n)+(?:\\n\\n|¨0)/gm;\n      singeColTblRgx = /^ {0,3}\\|.+\\|[ \\t]*\\n {0,3}\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*\\n( {0,3}\\|.+\\|[ \\t]*\\n)*(?:\\n|¨0)/gm;\n\n  function parseStyles (sLine) {\n    if (/^:[ \\t]*--*$/.test(sLine)) {\n      return ' style=\"text-align:left;\"';\n    } else if (/^--*[ \\t]*:[ \\t]*$/.test(sLine)) {\n      return ' style=\"text-align:right;\"';\n    } else if (/^:[ \\t]*--*[ \\t]*:$/.test(sLine)) {\n      return ' style=\"text-align:center;\"';\n    } else {\n      return '';\n    }\n  }\n\n  function parseHeaders (header, style) {\n    var id = '';\n    header = header.trim();\n    // support both tablesHeaderId and tableHeaderId due to error in documentation so we don't break backwards compatibility\n    if (options.tablesHeaderId || options.tableHeaderId) {\n      id = ' id=\"' + header.replace(/ /g, '_').toLowerCase() + '\"';\n    }\n    header = showdown.subParser('spanGamut')(header, options, globals);\n\n    return '' + header + '\\n';\n  }\n\n  function parseCells (cell, style) {\n    var subText = showdown.subParser('spanGamut')(cell, options, globals);\n    return '' + subText + '\\n';\n  }\n\n  function buildTable (headers, cells) {\n    var tb = '\\n\\n\\n',\n        tblLgn = headers.length;\n\n    for (var i = 0; i < tblLgn; ++i) {\n      tb += headers[i];\n    }\n    tb += '\\n\\n\\n';\n\n    for (i = 0; i < cells.length; ++i) {\n      tb += '\\n';\n      for (var ii = 0; ii < tblLgn; ++ii) {\n        tb += cells[i][ii];\n      }\n      tb += '\\n';\n    }\n    tb += '\\n
    \\n';\n    return tb;\n  }\n\n  function parseTable (rawTable) {\n    var i, tableLines = rawTable.split('\\n');\n\n    for (i = 0; i < tableLines.length; ++i) {\n      // strip wrong first and last column if wrapped tables are used\n      if (/^ {0,3}\\|/.test(tableLines[i])) {\n        tableLines[i] = tableLines[i].replace(/^ {0,3}\\|/, '');\n      }\n      if (/\\|[ \\t]*$/.test(tableLines[i])) {\n        tableLines[i] = tableLines[i].replace(/\\|[ \\t]*$/, '');\n      }\n      // parse code spans first, but we only support one line code spans\n      tableLines[i] = showdown.subParser('codeSpans')(tableLines[i], options, globals);\n    }\n\n    var rawHeaders = tableLines[0].split('|').map(function (s) { return s.trim();}),\n        rawStyles = tableLines[1].split('|').map(function (s) { return s.trim();}),\n        rawCells = [],\n        headers = [],\n        styles = [],\n        cells = [];\n\n    tableLines.shift();\n    tableLines.shift();\n\n    for (i = 0; i < tableLines.length; ++i) {\n      if (tableLines[i].trim() === '') {\n        continue;\n      }\n      rawCells.push(\n        tableLines[i]\n          .split('|')\n          .map(function (s) {\n            return s.trim();\n          })\n      );\n    }\n\n    if (rawHeaders.length < rawStyles.length) {\n      return rawTable;\n    }\n\n    for (i = 0; i < rawStyles.length; ++i) {\n      styles.push(parseStyles(rawStyles[i]));\n    }\n\n    for (i = 0; i < rawHeaders.length; ++i) {\n      if (showdown.helper.isUndefined(styles[i])) {\n        styles[i] = '';\n      }\n      headers.push(parseHeaders(rawHeaders[i], styles[i]));\n    }\n\n    for (i = 0; i < rawCells.length; ++i) {\n      var row = [];\n      for (var ii = 0; ii < headers.length; ++ii) {\n        if (showdown.helper.isUndefined(rawCells[i][ii])) {\n\n        }\n        row.push(parseCells(rawCells[i][ii], styles[ii]));\n      }\n      cells.push(row);\n    }\n\n    return buildTable(headers, cells);\n  }\n\n  text = globals.converter._dispatch('tables.before', text, options, globals);\n\n  // find escaped pipe characters\n  text = text.replace(/\\\\(\\|)/g, showdown.helper.escapeCharactersCallback);\n\n  // parse multi column tables\n  text = text.replace(tableRgx, parseTable);\n\n  // parse one column tables\n  text = text.replace(singeColTblRgx, parseTable);\n\n  text = globals.converter._dispatch('tables.after', text, options, globals);\n\n  return text;\n});\n","showdown.subParser('underline', function (text, options, globals) {\n  'use strict';\n\n  if (!options.underline) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('underline.before', text, options, globals);\n\n  if (options.literalMidWordUnderscores) {\n    text = text.replace(/\\b___(\\S[\\s\\S]*?)___\\b/g, function (wm, txt) {\n      return '' + txt + '';\n    });\n    text = text.replace(/\\b__(\\S[\\s\\S]*?)__\\b/g, function (wm, txt) {\n      return '' + txt + '';\n    });\n  } else {\n    text = text.replace(/___(\\S[\\s\\S]*?)___/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? '' + m + '' : wm;\n    });\n    text = text.replace(/__(\\S[\\s\\S]*?)__/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? '' + m + '' : wm;\n    });\n  }\n\n  // escape remaining underscores to prevent them being parsed by italic and bold\n  text = text.replace(/(_)/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('underline.after', text, options, globals);\n\n  return text;\n});\n","/**\n * Swap back in all the special characters we've hidden.\n */\nshowdown.subParser('unescapeSpecialChars', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('unescapeSpecialChars.before', text, options, globals);\n\n  text = text.replace(/¨E(\\d+)E/g, function (wholeMatch, m1) {\n    var charCodeToReplace = parseInt(m1);\n    return String.fromCharCode(charCodeToReplace);\n  });\n\n  text = globals.converter._dispatch('unescapeSpecialChars.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('makeMarkdown.blockquote', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    var children = node.childNodes,\n        childrenLength = children.length;\n\n    for (var i = 0; i < childrenLength; ++i) {\n      var innerTxt = showdown.subParser('makeMarkdown.node')(children[i], globals);\n\n      if (innerTxt === '') {\n        continue;\n      }\n      txt += innerTxt;\n    }\n  }\n  // cleanup\n  txt = txt.trim();\n  txt = '> ' + txt.split('\\n').join('\\n> ');\n  return txt;\n});\n","showdown.subParser('makeMarkdown.codeBlock', function (node, globals) {\n  'use strict';\n\n  var lang = node.getAttribute('language'),\n      num  = node.getAttribute('precodenum');\n  return '```' + lang + '\\n' + globals.preList[num] + '\\n```';\n});\n","showdown.subParser('makeMarkdown.codeSpan', function (node) {\n  'use strict';\n\n  return '`' + node.innerHTML + '`';\n});\n","showdown.subParser('makeMarkdown.emphasis', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    txt += '*';\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '*';\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.header', function (node, globals, headerLevel) {\n  'use strict';\n\n  var headerMark = new Array(headerLevel + 1).join('#'),\n      txt = '';\n\n  if (node.hasChildNodes()) {\n    txt = headerMark + ' ';\n    var children = node.childNodes,\n        childrenLength = children.length;\n\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.hr', function () {\n  'use strict';\n\n  return '---';\n});\n","showdown.subParser('makeMarkdown.image', function (node) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasAttribute('src')) {\n    txt += '![' + node.getAttribute('alt') + '](';\n    txt += '<' + node.getAttribute('src') + '>';\n    if (node.hasAttribute('width') && node.hasAttribute('height')) {\n      txt += ' =' + node.getAttribute('width') + 'x' + node.getAttribute('height');\n    }\n\n    if (node.hasAttribute('title')) {\n      txt += ' \"' + node.getAttribute('title') + '\"';\n    }\n    txt += ')';\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.links', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes() && node.hasAttribute('href')) {\n    var children = node.childNodes,\n        childrenLength = children.length;\n    txt = '[';\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '](';\n    txt += '<' + node.getAttribute('href') + '>';\n    if (node.hasAttribute('title')) {\n      txt += ' \"' + node.getAttribute('title') + '\"';\n    }\n    txt += ')';\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.list', function (node, globals, type) {\n  'use strict';\n\n  var txt = '';\n  if (!node.hasChildNodes()) {\n    return '';\n  }\n  var listItems       = node.childNodes,\n      listItemsLenght = listItems.length,\n      listNum = node.getAttribute('start') || 1;\n\n  for (var i = 0; i < listItemsLenght; ++i) {\n    if (typeof listItems[i].tagName === 'undefined' || listItems[i].tagName.toLowerCase() !== 'li') {\n      continue;\n    }\n\n    // define the bullet to use in list\n    var bullet = '';\n    if (type === 'ol') {\n      bullet = listNum.toString() + '. ';\n    } else {\n      bullet = '- ';\n    }\n\n    // parse list item\n    txt += bullet + showdown.subParser('makeMarkdown.listItem')(listItems[i], globals);\n    ++listNum;\n  }\n\n  // add comment at the end to prevent consecutive lists to be parsed as one\n  txt += '\\n\\n';\n  return txt.trim();\n});\n","showdown.subParser('makeMarkdown.listItem', function (node, globals) {\n  'use strict';\n\n  var listItemTxt = '';\n\n  var children = node.childNodes,\n      childrenLenght = children.length;\n\n  for (var i = 0; i < childrenLenght; ++i) {\n    listItemTxt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n  }\n  // if it's only one liner, we need to add a newline at the end\n  if (!/\\n$/.test(listItemTxt)) {\n    listItemTxt += '\\n';\n  } else {\n    // it's multiparagraph, so we need to indent\n    listItemTxt = listItemTxt\n      .split('\\n')\n      .join('\\n    ')\n      .replace(/^ {4}$/gm, '')\n      .replace(/\\n\\n+/g, '\\n\\n');\n  }\n\n  return listItemTxt;\n});\n","\n\nshowdown.subParser('makeMarkdown.node', function (node, globals, spansOnly) {\n  'use strict';\n\n  spansOnly = spansOnly || false;\n\n  var txt = '';\n\n  // edge case of text without wrapper paragraph\n  if (node.nodeType === 3) {\n    return showdown.subParser('makeMarkdown.txt')(node, globals);\n  }\n\n  // HTML comment\n  if (node.nodeType === 8) {\n    return '\\n\\n';\n  }\n\n  // process only node elements\n  if (node.nodeType !== 1) {\n    return '';\n  }\n\n  var tagName = node.tagName.toLowerCase();\n\n  switch (tagName) {\n\n    //\n    // BLOCKS\n    //\n    case 'h1':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 1) + '\\n\\n'; }\n      break;\n    case 'h2':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 2) + '\\n\\n'; }\n      break;\n    case 'h3':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 3) + '\\n\\n'; }\n      break;\n    case 'h4':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 4) + '\\n\\n'; }\n      break;\n    case 'h5':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 5) + '\\n\\n'; }\n      break;\n    case 'h6':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 6) + '\\n\\n'; }\n      break;\n\n    case 'p':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.paragraph')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'blockquote':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.blockquote')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'hr':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.hr')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'ol':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.list')(node, globals, 'ol') + '\\n\\n'; }\n      break;\n\n    case 'ul':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.list')(node, globals, 'ul') + '\\n\\n'; }\n      break;\n\n    case 'precode':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.codeBlock')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'pre':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.pre')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'table':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.table')(node, globals) + '\\n\\n'; }\n      break;\n\n    //\n    // SPANS\n    //\n    case 'code':\n      txt = showdown.subParser('makeMarkdown.codeSpan')(node, globals);\n      break;\n\n    case 'em':\n    case 'i':\n      txt = showdown.subParser('makeMarkdown.emphasis')(node, globals);\n      break;\n\n    case 'strong':\n    case 'b':\n      txt = showdown.subParser('makeMarkdown.strong')(node, globals);\n      break;\n\n    case 'del':\n      txt = showdown.subParser('makeMarkdown.strikethrough')(node, globals);\n      break;\n\n    case 'a':\n      txt = showdown.subParser('makeMarkdown.links')(node, globals);\n      break;\n\n    case 'img':\n      txt = showdown.subParser('makeMarkdown.image')(node, globals);\n      break;\n\n    default:\n      txt = node.outerHTML + '\\n\\n';\n  }\n\n  // common normalization\n  // TODO eventually\n\n  return txt;\n});\n","showdown.subParser('makeMarkdown.paragraph', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n  }\n\n  // some text normalization\n  txt = txt.trim();\n\n  return txt;\n});\n","showdown.subParser('makeMarkdown.pre', function (node, globals) {\n  'use strict';\n\n  var num  = node.getAttribute('prenum');\n  return '
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t=e.getLanguage("cpp").exports;return{aliases:["sqf"],case_insensitive:!0,keywords:{keyword:"case catch default do else exit exitWith for forEach from if private switch then throw to try waitUntil while with",built_in:"abs accTime acos action actionIDs actionKeys actionKeysImages actionKeysNames actionKeysNamesArray actionName actionParams activateAddons activatedAddons activateKey add3DENConnection add3DENEventHandler add3DENLayer addAction addBackpack addBackpackCargo addBackpackCargoGlobal addBackpackGlobal addCamShake addCuratorAddons addCuratorCameraArea addCuratorEditableObjects addCuratorEditingArea addCuratorPoints addEditorObject addEventHandler addForce addGoggles addGroupIcon addHandgunItem addHeadgear addItem addItemCargo addItemCargoGlobal addItemPool addItemToBackpack addItemToUniform addItemToVest addLiveStats addMagazine addMagazineAmmoCargo addMagazineCargo addMagazineCargoGlobal addMagazineGlobal addMagazinePool addMagazines addMagazineTurret addMenu addMenuItem addMissionEventHandler addMPEventHandler addMusicEventHandler addOwnedMine addPlayerScores addPrimaryWeaponItem addPublicVariableEventHandler addRating addResources addScore addScoreSide addSecondaryWeaponItem addSwitchableUnit addTeamMember addToRemainsCollector addTorque addUniform addVehicle addVest addWaypoint addWeapon addWeaponCargo addWeaponCargoGlobal addWeaponGlobal addWeaponItem addWeaponPool addWeaponTurret admin agent agents AGLToASL aimedAtTarget aimPos airDensityRTD airplaneThrottle airportSide AISFinishHeal alive all3DENEntities allAirports allControls allCurators allCutLayers allDead allDeadMen allDisplays allGroups allMapMarkers allMines allMissionObjects allow3DMode allowCrewInImmobile allowCuratorLogicIgnoreAreas allowDamage allowDammage allowFileOperations allowFleeing allowGetIn allowSprint allPlayers allSimpleObjects allSites allTurrets allUnits allUnitsUAV allVariables ammo ammoOnPylon and animate animateBay animateDoor animatePylon animateSource animationNames animationPhase animationSourcePhase animationState append apply armoryPoints arrayIntersect asin ASLToAGL ASLToATL assert assignAsCargo assignAsCargoIndex assignAsCommander assignAsDriver assignAsGunner assignAsTurret assignCurator assignedCargo assignedCommander assignedDriver assignedGunner assignedItems assignedTarget assignedTeam assignedVehicle assignedVehicleRole assignItem assignTeam assignToAirport atan atan2 atg ATLToASL attachedObject attachedObjects attachedTo attachObject attachTo attackEnabled backpack backpackCargo backpackContainer backpackItems backpackMagazines backpackSpaceFor behaviour benchmark binocular boundingBox boundingBoxReal boundingCenter breakOut breakTo briefingName buildingExit buildingPos buttonAction buttonSetAction cadetMode call callExtension camCommand camCommit camCommitPrepared camCommitted camConstuctionSetParams camCreate camDestroy cameraEffect cameraEffectEnableHUD cameraInterest cameraOn cameraView campaignConfigFile camPreload camPreloaded camPrepareBank camPrepareDir camPrepareDive camPrepareFocus camPrepareFov camPrepareFovRange camPreparePos camPrepareRelPos camPrepareTarget camSetBank camSetDir camSetDive camSetFocus camSetFov camSetFovRange camSetPos camSetRelPos camSetTarget camTarget camUseNVG canAdd canAddItemToBackpack canAddItemToUniform canAddItemToVest cancelSimpleTaskDestination canFire canMove canSlingLoad canStand canSuspend canTriggerDynamicSimulation canUnloadInCombat canVehicleCargo captive captiveNum cbChecked cbSetChecked ceil channelEnabled cheatsEnabled checkAIFeature checkVisibility className clearAllItemsFromBackpack clearBackpackCargo clearBackpackCargoGlobal clearGroupIcons clearItemCargo clearItemCargoGlobal clearItemPool clearMagazineCargo clearMagazineCargoGlobal clearMagazinePool clearOverlay clearRadio clearWeaponCargo clearWeaponCargoGlobal clearWeaponPool clientOwner closeDialog closeDisplay closeOverlay collapseObjectTree collect3DENHistory collectiveRTD combatMode commandArtilleryFire commandChat commander commandFire commandFollow commandFSM commandGetOut commandingMenu commandMove commandRadio commandStop commandSuppressiveFire commandTarget commandWatch comment commitOverlay compile compileFinal completedFSM composeText configClasses configFile configHierarchy configName configProperties configSourceAddonList configSourceMod configSourceModList confirmSensorTarget connectTerminalToUAV controlsGroupCtrl copyFromClipboard copyToClipboard copyWaypoints cos count countEnemy countFriendly countSide countType countUnknown create3DENComposition create3DENEntity createAgent createCenter createDialog createDiaryLink createDiaryRecord createDiarySubject createDisplay createGearDialog createGroup createGuardedPoint createLocation createMarker createMarkerLocal createMenu createMine createMissionDisplay createMPCampaignDisplay createSimpleObject createSimpleTask createSite createSoundSource createTask createTeam createTrigger createUnit createVehicle createVehicleCrew createVehicleLocal crew ctAddHeader ctAddRow ctClear ctCurSel ctData ctFindHeaderRows ctFindRowHeader ctHeaderControls ctHeaderCount ctRemoveHeaders ctRemoveRows ctrlActivate ctrlAddEventHandler ctrlAngle ctrlAutoScrollDelay ctrlAutoScrollRewind ctrlAutoScrollSpeed ctrlChecked ctrlClassName ctrlCommit ctrlCommitted ctrlCreate ctrlDelete ctrlEnable ctrlEnabled ctrlFade ctrlHTMLLoaded ctrlIDC ctrlIDD ctrlMapAnimAdd ctrlMapAnimClear ctrlMapAnimCommit ctrlMapAnimDone ctrlMapCursor ctrlMapMouseOver ctrlMapScale ctrlMapScreenToWorld ctrlMapWorldToScreen ctrlModel ctrlModelDirAndUp ctrlModelScale ctrlParent ctrlParentControlsGroup ctrlPosition ctrlRemoveAllEventHandlers ctrlRemoveEventHandler ctrlScale ctrlSetActiveColor ctrlSetAngle ctrlSetAutoScrollDelay ctrlSetAutoScrollRewind ctrlSetAutoScrollSpeed ctrlSetBackgroundColor ctrlSetChecked ctrlSetEventHandler ctrlSetFade ctrlSetFocus ctrlSetFont ctrlSetFontH1 ctrlSetFontH1B ctrlSetFontH2 ctrlSetFontH2B ctrlSetFontH3 ctrlSetFontH3B ctrlSetFontH4 ctrlSetFontH4B ctrlSetFontH5 ctrlSetFontH5B ctrlSetFontH6 ctrlSetFontH6B ctrlSetFontHeight ctrlSetFontHeightH1 ctrlSetFontHeightH2 ctrlSetFontHeightH3 ctrlSetFontHeightH4 ctrlSetFontHeightH5 ctrlSetFontHeightH6 ctrlSetFontHeightSecondary ctrlSetFontP ctrlSetFontPB ctrlSetFontSecondary ctrlSetForegroundColor ctrlSetModel ctrlSetModelDirAndUp ctrlSetModelScale ctrlSetPixelPrecision ctrlSetPosition ctrlSetScale ctrlSetStructuredText ctrlSetText ctrlSetTextColor ctrlSetTooltip ctrlSetTooltipColorBox ctrlSetTooltipColorShade ctrlSetTooltipColorText ctrlShow ctrlShown ctrlText ctrlTextHeight ctrlTextWidth ctrlType ctrlVisible ctRowControls ctRowCount ctSetCurSel ctSetData ctSetHeaderTemplate ctSetRowTemplate ctSetValue ctValue curatorAddons curatorCamera curatorCameraArea curatorCameraAreaCeiling curatorCoef curatorEditableObjects curatorEditingArea curatorEditingAreaType curatorMouseOver curatorPoints curatorRegisteredObjects curatorSelected curatorWaypointCost current3DENOperation currentChannel currentCommand currentMagazine currentMagazineDetail currentMagazineDetailTurret currentMagazineTurret currentMuzzle currentNamespace currentTask currentTasks currentThrowable currentVisionMode currentWaypoint currentWeapon currentWeaponMode currentWeaponTurret currentZeroing cursorObject cursorTarget customChat customRadio cutFadeOut cutObj cutRsc cutText damage date dateToNumber daytime deActivateKey debriefingText debugFSM debugLog deg delete3DENEntities deleteAt deleteCenter deleteCollection deleteEditorObject deleteGroup deleteGroupWhenEmpty deleteIdentity deleteLocation deleteMarker deleteMarkerLocal deleteRange deleteResources deleteSite deleteStatus deleteTeam deleteVehicle deleteVehicleCrew deleteWaypoint detach detectedMines diag_activeMissionFSMs diag_activeScripts diag_activeSQFScripts diag_activeSQSScripts diag_captureFrame diag_captureFrameToFile diag_captureSlowFrame diag_codePerformance diag_drawMode diag_enable diag_enabled diag_fps diag_fpsMin diag_frameNo diag_lightNewLoad diag_list diag_log diag_logSlowFrame diag_mergeConfigFile diag_recordTurretLimits diag_setLightNew diag_tickTime diag_toggle dialog diarySubjectExists didJIP didJIPOwner difficulty difficultyEnabled difficultyEnabledRTD difficultyOption direction directSay disableAI disableCollisionWith disableConversation disableDebriefingStats disableMapIndicators disableNVGEquipment disableRemoteSensors disableSerialization disableTIEquipment disableUAVConnectability disableUserInput displayAddEventHandler displayCtrl displayParent displayRemoveAllEventHandlers displayRemoveEventHandler displaySetEventHandler dissolveTeam distance distance2D distanceSqr distributionRegion do3DENAction doArtilleryFire doFire doFollow doFSM doGetOut doMove doorPhase doStop doSuppressiveFire doTarget doWatch drawArrow drawEllipse drawIcon drawIcon3D drawLine drawLine3D drawLink drawLocation drawPolygon drawRectangle drawTriangle driver drop dynamicSimulationDistance dynamicSimulationDistanceCoef dynamicSimulationEnabled dynamicSimulationSystemEnabled echo edit3DENMissionAttributes editObject editorSetEventHandler effectiveCommander emptyPositions enableAI enableAIFeature enableAimPrecision enableAttack enableAudioFeature enableAutoStartUpRTD enableAutoTrimRTD enableCamShake enableCaustics enableChannel enableCollisionWith enableCopilot enableDebriefingStats enableDiagLegend enableDynamicSimulation enableDynamicSimulationSystem enableEndDialog enableEngineArtillery enableEnvironment enableFatigue enableGunLights enableInfoPanelComponent enableIRLasers enableMimics enablePersonTurret enableRadio enableReload enableRopeAttach enableSatNormalOnDetail enableSaving enableSentences enableSimulation enableSimulationGlobal enableStamina enableTeamSwitch enableTraffic enableUAVConnectability enableUAVWaypoints enableVehicleCargo enableVehicleSensor enableWeaponDisassembly endLoadingScreen endMission engineOn enginesIsOnRTD enginesRpmRTD enginesTorqueRTD entities environmentEnabled estimatedEndServerTime estimatedTimeLeft evalObjectArgument everyBackpack everyContainer exec execEditorScript execFSM execVM exp expectedDestination exportJIPMessages eyeDirection eyePos face faction fadeMusic fadeRadio fadeSound fadeSpeech failMission fillWeaponsFromPool find findCover findDisplay findEditorObject findEmptyPosition findEmptyPositionReady findIf findNearestEnemy finishMissionInit finite fire fireAtTarget firstBackpack flag flagAnimationPhase flagOwner flagSide flagTexture fleeing floor flyInHeight flyInHeightASL fog fogForecast fogParams forceAddUniform forcedMap forceEnd forceFlagTexture forceFollowRoad forceMap forceRespawn forceSpeed forceWalk forceWeaponFire forceWeatherChange forEachMember forEachMemberAgent forEachMemberTeam forgetTarget format formation formationDirection formationLeader formationMembers formationPosition formationTask formatText formLeader freeLook fromEditor fuel fullCrew gearIDCAmmoCount gearSlotAmmoCount gearSlotData get3DENActionState get3DENAttribute get3DENCamera get3DENConnections get3DENEntity get3DENEntityID get3DENGrid get3DENIconsVisible get3DENLayerEntities get3DENLinesVisible get3DENMissionAttribute get3DENMouseOver get3DENSelected getAimingCoef getAllEnvSoundControllers getAllHitPointsDamage getAllOwnedMines getAllSoundControllers getAmmoCargo getAnimAimPrecision getAnimSpeedCoef getArray getArtilleryAmmo getArtilleryComputerSettings getArtilleryETA getAssignedCuratorLogic getAssignedCuratorUnit getBackpackCargo getBleedingRemaining getBurningValue getCameraViewDirection getCargoIndex getCenterOfMass getClientState getClientStateNumber getCompatiblePylonMagazines getConnectedUAV getContainerMaxLoad getCursorObjectParams getCustomAimCoef getDammage getDescription getDir getDirVisual getDLCAssetsUsage getDLCAssetsUsageByName getDLCs getEditorCamera getEditorMode getEditorObjectScope getElevationOffset getEnvSoundController getFatigue getForcedFlagTexture getFriend getFSMVariable getFuelCargo getGroupIcon getGroupIconParams getGroupIcons getHideFrom getHit getHitIndex getHitPointDamage getItemCargo getMagazineCargo getMarkerColor getMarkerPos getMarkerSize getMarkerType getMass getMissionConfig getMissionConfigValue getMissionDLCs getMissionLayerEntities getModelInfo getMousePosition getMusicPlayedTime getNumber getObjectArgument getObjectChildren getObjectDLC getObjectMaterials getObjectProxy getObjectTextures getObjectType getObjectViewDistance getOxygenRemaining getPersonUsedDLCs getPilotCameraDirection getPilotCameraPosition getPilotCameraRotation getPilotCameraTarget getPlateNumber getPlayerChannel getPlayerScores getPlayerUID getPos getPosASL getPosASLVisual getPosASLW getPosATL getPosATLVisual getPosVisual getPosWorld getPylonMagazines getRelDir getRelPos getRemoteSensorsDisabled getRepairCargo getResolution getShadowDistance getShotParents getSlingLoad getSoundController getSoundControllerResult getSpeed getStamina getStatValue getSuppression getTerrainGrid getTerrainHeightASL getText getTotalDLCUsageTime getUnitLoadout getUnitTrait getUserMFDText getUserMFDvalue getVariable getVehicleCargo getWeaponCargo getWeaponSway getWingsOrientationRTD getWingsPositionRTD getWPPos glanceAt globalChat globalRadio goggles goto group groupChat groupFromNetId groupIconSelectable groupIconsVisible groupId groupOwner groupRadio groupSelectedUnits groupSelectUnit gunner gusts halt handgunItems handgunMagazine handgunWeapon handsHit hasInterface hasPilotCamera hasWeapon hcAllGroups hcGroupParams hcLeader hcRemoveAllGroups hcRemoveGroup hcSelected hcSelectGroup hcSetGroup hcShowBar hcShownBar headgear hideBody hideObject hideObjectGlobal hideSelection hint hintC hintCadet hintSilent hmd hostMission htmlLoad HUDMovementLevels humidity image importAllGroups importance in inArea inAreaArray incapacitatedState inflame inflamed infoPanel infoPanelComponentEnabled infoPanelComponents infoPanels inGameUISetEventHandler inheritsFrom initAmbientLife inPolygon inputAction inRangeOfArtillery insertEditorObject intersect is3DEN is3DENMultiplayer isAbleToBreathe isAgent isArray isAutoHoverOn isAutonomous isAutotest isBleeding isBurning isClass isCollisionLightOn isCopilotEnabled isDamageAllowed isDedicated isDLCAvailable isEngineOn isEqualTo isEqualType isEqualTypeAll isEqualTypeAny isEqualTypeArray isEqualTypeParams isFilePatchingEnabled isFlashlightOn isFlatEmpty isForcedWalk isFormationLeader isGroupDeletedWhenEmpty isHidden isInRemainsCollector isInstructorFigureEnabled isIRLaserOn isKeyActive isKindOf isLaserOn isLightOn isLocalized isManualFire isMarkedForCollection isMultiplayer isMultiplayerSolo isNil isNull isNumber isObjectHidden isObjectRTD isOnRoad isPipEnabled isPlayer isRealTime isRemoteExecuted isRemoteExecutedJIP isServer isShowing3DIcons isSimpleObject isSprintAllowed isStaminaEnabled isSteamMission isStreamFriendlyUIEnabled isText isTouchingGround isTurnedOut isTutHintsEnabled isUAVConnectable isUAVConnected isUIContext isUniformAllowed isVehicleCargo isVehicleRadarOn isVehicleSensorEnabled isWalking isWeaponDeployed isWeaponRested itemCargo items itemsWithMagazines join joinAs joinAsSilent joinSilent joinString kbAddDatabase kbAddDatabaseTargets kbAddTopic kbHasTopic kbReact kbRemoveTopic kbTell kbWasSaid keyImage keyName knowsAbout land landAt landResult language laserTarget lbAdd lbClear lbColor lbColorRight lbCurSel lbData lbDelete lbIsSelected lbPicture lbPictureRight lbSelection lbSetColor lbSetColorRight lbSetCurSel lbSetData lbSetPicture lbSetPictureColor lbSetPictureColorDisabled lbSetPictureColorSelected lbSetPictureRight lbSetPictureRightColor lbSetPictureRightColorDisabled lbSetPictureRightColorSelected lbSetSelectColor lbSetSelectColorRight lbSetSelected lbSetText lbSetTextRight lbSetTooltip lbSetValue lbSize lbSort lbSortByValue lbText lbTextRight lbValue leader leaderboardDeInit leaderboardGetRows leaderboardInit leaderboardRequestRowsFriends leaderboardsRequestUploadScore leaderboardsRequestUploadScoreKeepBest leaderboardState leaveVehicle libraryCredits libraryDisclaimers lifeState lightAttachObject lightDetachObject lightIsOn lightnings limitSpeed linearConversion lineIntersects lineIntersectsObjs lineIntersectsSurfaces lineIntersectsWith linkItem list listObjects listRemoteTargets listVehicleSensors ln lnbAddArray lnbAddColumn lnbAddRow lnbClear lnbColor lnbCurSelRow lnbData lnbDeleteColumn lnbDeleteRow lnbGetColumnsPosition lnbPicture lnbSetColor lnbSetColumnsPos lnbSetCurSelRow lnbSetData lnbSetPicture lnbSetText lnbSetValue lnbSize lnbSort lnbSortByValue lnbText lnbValue load loadAbs loadBackpack loadFile loadGame loadIdentity loadMagazine loadOverlay loadStatus loadUniform loadVest local localize locationPosition lock lockCameraTo lockCargo lockDriver locked lockedCargo lockedDriver lockedTurret lockIdentity lockTurret lockWP log logEntities logNetwork logNetworkTerminate lookAt lookAtPos magazineCargo magazines magazinesAllTurrets magazinesAmmo magazinesAmmoCargo magazinesAmmoFull magazinesDetail magazinesDetailBackpack magazinesDetailUniform magazinesDetailVest magazinesTurret magazineTurretAmmo mapAnimAdd mapAnimClear mapAnimCommit mapAnimDone mapCenterOnCamera mapGridPosition markAsFinishedOnSteam markerAlpha markerBrush markerColor markerDir markerPos markerShape markerSize markerText markerType max members menuAction menuAdd menuChecked menuClear menuCollapse menuData menuDelete menuEnable menuEnabled menuExpand menuHover menuPicture menuSetAction menuSetCheck menuSetData menuSetPicture menuSetValue menuShortcut menuShortcutText menuSize menuSort menuText menuURL menuValue min mineActive mineDetectedBy missionConfigFile missionDifficulty missionName missionNamespace missionStart missionVersion mod modelToWorld modelToWorldVisual modelToWorldVisualWorld modelToWorldWorld modParams moonIntensity moonPhase morale move move3DENCamera moveInAny moveInCargo moveInCommander moveInDriver moveInGunner moveInTurret moveObjectToEnd moveOut moveTime moveTo moveToCompleted moveToFailed musicVolume name nameSound nearEntities nearestBuilding nearestLocation nearestLocations nearestLocationWithDubbing nearestObject nearestObjects nearestTerrainObjects nearObjects nearObjectsReady nearRoads nearSupplies nearTargets needReload netId netObjNull newOverlay nextMenuItemIndex nextWeatherChange nMenuItems not numberOfEnginesRTD numberToDate objectCurators objectFromNetId objectParent objStatus onBriefingGroup onBriefingNotes onBriefingPlan onBriefingTeamSwitch onCommandModeChanged onDoubleClick onEachFrame onGroupIconClick onGroupIconOverEnter onGroupIconOverLeave onHCGroupSelectionChanged onMapSingleClick onPlayerConnected onPlayerDisconnected onPreloadFinished onPreloadStarted onShowNewObject onTeamSwitch openCuratorInterface openDLCPage openMap openSteamApp openYoutubeVideo or orderGetIn overcast overcastForecast owner param params parseNumber parseSimpleArray parseText parsingNamespace particlesQuality pickWeaponPool pitch pixelGrid pixelGridBase pixelGridNoUIScale pixelH pixelW playableSlotsNumber playableUnits playAction playActionNow player playerRespawnTime playerSide playersNumber playGesture playMission playMove playMoveNow playMusic playScriptedMission playSound playSound3D position positionCameraToWorld posScreenToWorld posWorldToScreen ppEffectAdjust ppEffectCommit ppEffectCommitted ppEffectCreate ppEffectDestroy ppEffectEnable ppEffectEnabled ppEffectForceInNVG precision preloadCamera preloadObject preloadSound preloadTitleObj preloadTitleRsc preprocessFile preprocessFileLineNumbers primaryWeapon primaryWeaponItems primaryWeaponMagazine priority processDiaryLink productVersion profileName profileNamespace profileNameSteam progressLoadingScreen progressPosition progressSetPosition publicVariable publicVariableClient publicVariableServer pushBack pushBackUnique putWeaponPool queryItemsPool queryMagazinePool queryWeaponPool rad radioChannelAdd radioChannelCreate radioChannelRemove radioChannelSetCallSign radioChannelSetLabel radioVolume rain rainbow random rank rankId rating rectangular registeredTasks registerTask reload reloadEnabled remoteControl remoteExec remoteExecCall remoteExecutedOwner remove3DENConnection remove3DENEventHandler remove3DENLayer removeAction removeAll3DENEventHandlers removeAllActions removeAllAssignedItems removeAllContainers removeAllCuratorAddons removeAllCuratorCameraAreas removeAllCuratorEditingAreas removeAllEventHandlers removeAllHandgunItems removeAllItems removeAllItemsWithMagazines removeAllMissionEventHandlers removeAllMPEventHandlers removeAllMusicEventHandlers removeAllOwnedMines removeAllPrimaryWeaponItems removeAllWeapons removeBackpack removeBackpackGlobal removeCuratorAddons removeCuratorCameraArea removeCuratorEditableObjects removeCuratorEditingArea removeDrawIcon removeDrawLinks removeEventHandler removeFromRemainsCollector removeGoggles removeGroupIcon removeHandgunItem removeHeadgear removeItem removeItemFromBackpack removeItemFromUniform removeItemFromVest removeItems removeMagazine removeMagazineGlobal removeMagazines removeMagazinesTurret removeMagazineTurret removeMenuItem removeMissionEventHandler removeMPEventHandler removeMusicEventHandler removeOwnedMine removePrimaryWeaponItem removeSecondaryWeaponItem removeSimpleTask removeSwitchableUnit removeTeamMember removeUniform removeVest removeWeapon removeWeaponAttachmentCargo removeWeaponCargo removeWeaponGlobal removeWeaponTurret reportRemoteTarget requiredVersion resetCamShake resetSubgroupDirection resize resources respawnVehicle restartEditorCamera reveal revealMine reverse reversedMouseY roadAt roadsConnectedTo roleDescription ropeAttachedObjects ropeAttachedTo ropeAttachEnabled ropeAttachTo ropeCreate ropeCut ropeDestroy ropeDetach ropeEndPosition ropeLength ropes ropeUnwind ropeUnwound rotorsForcesRTD rotorsRpmRTD round runInitScript safeZoneH safeZoneW safeZoneWAbs safeZoneX safeZoneXAbs safeZoneY save3DENInventory saveGame saveIdentity saveJoysticks saveOverlay saveProfileNamespace saveStatus saveVar savingEnabled say say2D say3D scopeName score scoreSide screenshot screenToWorld scriptDone scriptName scudState secondaryWeapon secondaryWeaponItems secondaryWeaponMagazine select selectBestPlaces selectDiarySubject selectedEditorObjects selectEditorObject selectionNames selectionPosition selectLeader selectMax selectMin selectNoPlayer selectPlayer selectRandom selectRandomWeighted selectWeapon selectWeaponTurret sendAUMessage sendSimpleCommand sendTask sendTaskResult sendUDPMessage serverCommand serverCommandAvailable serverCommandExecutable serverName serverTime set set3DENAttribute set3DENAttributes set3DENGrid set3DENIconsVisible set3DENLayer set3DENLinesVisible set3DENLogicType set3DENMissionAttribute set3DENMissionAttributes set3DENModelsVisible set3DENObjectType set3DENSelected setAccTime setActualCollectiveRTD setAirplaneThrottle setAirportSide setAmmo setAmmoCargo setAmmoOnPylon setAnimSpeedCoef setAperture setApertureNew setArmoryPoints setAttributes setAutonomous setBehaviour setBleedingRemaining setBrakesRTD setCameraInterest setCamShakeDefParams setCamShakeParams setCamUseTI setCaptive setCenterOfMass setCollisionLight setCombatMode setCompassOscillation setConvoySeparation setCuratorCameraAreaCeiling setCuratorCoef setCuratorEditingAreaType setCuratorWaypointCost setCurrentChannel setCurrentTask setCurrentWaypoint setCustomAimCoef setCustomWeightRTD setDamage setDammage setDate setDebriefingText setDefaultCamera setDestination setDetailMapBlendPars setDir setDirection setDrawIcon setDriveOnPath setDropInterval setDynamicSimulationDistance setDynamicSimulationDistanceCoef setEditorMode setEditorObjectScope setEffectCondition setEngineRPMRTD setFace setFaceAnimation setFatigue setFeatureType setFlagAnimationPhase setFlagOwner setFlagSide setFlagTexture setFog setFormation setFormationTask setFormDir setFriend setFromEditor setFSMVariable setFuel setFuelCargo setGroupIcon setGroupIconParams setGroupIconsSelectable setGroupIconsVisible setGroupId setGroupIdGlobal setGroupOwner setGusts setHideBehind setHit setHitIndex setHitPointDamage setHorizonParallaxCoef setHUDMovementLevels setIdentity setImportance setInfoPanel setLeader setLightAmbient setLightAttenuation setLightBrightness setLightColor setLightDayLight setLightFlareMaxDistance setLightFlareSize setLightIntensity setLightnings setLightUseFlare setLocalWindParams setMagazineTurretAmmo setMarkerAlpha setMarkerAlphaLocal setMarkerBrush setMarkerBrushLocal setMarkerColor setMarkerColorLocal setMarkerDir setMarkerDirLocal setMarkerPos setMarkerPosLocal setMarkerShape setMarkerShapeLocal setMarkerSize setMarkerSizeLocal setMarkerText setMarkerTextLocal setMarkerType setMarkerTypeLocal setMass setMimic setMousePosition setMusicEffect setMusicEventHandler setName setNameSound setObjectArguments setObjectMaterial setObjectMaterialGlobal setObjectProxy setObjectTexture setObjectTextureGlobal setObjectViewDistance setOvercast setOwner setOxygenRemaining setParticleCircle setParticleClass setParticleFire setParticleParams setParticleRandom setPilotCameraDirection setPilotCameraRotation setPilotCameraTarget setPilotLight setPiPEffect setPitch setPlateNumber setPlayable setPlayerRespawnTime setPos setPosASL setPosASL2 setPosASLW setPosATL setPosition setPosWorld setPylonLoadOut setPylonsPriority setRadioMsg setRain setRainbow setRandomLip setRank setRectangular setRepairCargo setRotorBrakeRTD setShadowDistance setShotParents setSide setSimpleTaskAlwaysVisible setSimpleTaskCustomData setSimpleTaskDescription setSimpleTaskDestination setSimpleTaskTarget setSimpleTaskType setSimulWeatherLayers setSize setSkill setSlingLoad setSoundEffect setSpeaker setSpeech setSpeedMode setStamina setStaminaScheme setStatValue setSuppression setSystemOfUnits setTargetAge setTaskMarkerOffset setTaskResult setTaskState setTerrainGrid setText setTimeMultiplier setTitleEffect setTrafficDensity setTrafficDistance setTrafficGap setTrafficSpeed setTriggerActivation setTriggerArea setTriggerStatements setTriggerText setTriggerTimeout setTriggerType setType setUnconscious setUnitAbility setUnitLoadout setUnitPos setUnitPosWeak setUnitRank setUnitRecoilCoefficient setUnitTrait setUnloadInCombat setUserActionText setUserMFDText setUserMFDvalue setVariable setVectorDir setVectorDirAndUp setVectorUp setVehicleAmmo setVehicleAmmoDef setVehicleArmor setVehicleCargo setVehicleId setVehicleLock setVehiclePosition setVehicleRadar setVehicleReceiveRemoteTargets setVehicleReportOwnPosition setVehicleReportRemoteTargets setVehicleTIPars setVehicleVarName setVelocity setVelocityModelSpace setVelocityTransformation setViewDistance setVisibleIfTreeCollapsed setWantedRPMRTD setWaves setWaypointBehaviour setWaypointCombatMode setWaypointCompletionRadius setWaypointDescription setWaypointForceBehaviour setWaypointFormation setWaypointHousePosition setWaypointLoiterRadius setWaypointLoiterType setWaypointName setWaypointPosition setWaypointScript setWaypointSpeed setWaypointStatements setWaypointTimeout setWaypointType setWaypointVisible setWeaponReloadingTime setWind setWindDir setWindForce setWindStr setWingForceScaleRTD setWPPos show3DIcons showChat showCinemaBorder showCommandingMenu showCompass showCuratorCompass showGPS showHUD showLegend showMap shownArtilleryComputer shownChat shownCompass shownCuratorCompass showNewEditorObject shownGPS shownHUD shownMap shownPad shownRadio shownScoretable shownUAVFeed shownWarrant shownWatch showPad showRadio showScoretable showSubtitles showUAVFeed showWarrant showWatch showWaypoint showWaypoints side sideChat sideEnemy sideFriendly sideRadio simpleTasks simulationEnabled simulCloudDensity simulCloudOcclusion simulInClouds simulWeatherSync sin size sizeOf skill skillFinal skipTime sleep sliderPosition sliderRange sliderSetPosition sliderSetRange sliderSetSpeed sliderSpeed slingLoadAssistantShown soldierMagazines someAmmo sort soundVolume spawn speaker speed speedMode splitString sqrt squadParams stance startLoadingScreen step stop stopEngineRTD stopped str sunOrMoon supportInfo suppressFor surfaceIsWater surfaceNormal surfaceType swimInDepth switchableUnits switchAction switchCamera switchGesture switchLight switchMove synchronizedObjects synchronizedTriggers synchronizedWaypoints synchronizeObjectsAdd synchronizeObjectsRemove synchronizeTrigger synchronizeWaypoint systemChat systemOfUnits tan targetKnowledge targets targetsAggregate targetsQuery taskAlwaysVisible taskChildren taskCompleted taskCustomData taskDescription taskDestination taskHint taskMarkerOffset taskParent taskResult taskState taskType teamMember teamName teams teamSwitch teamSwitchEnabled teamType terminate terrainIntersect terrainIntersectASL terrainIntersectAtASL text textLog textLogFormat tg time timeMultiplier titleCut titleFadeOut titleObj titleRsc titleText toArray toFixed toLower toString toUpper triggerActivated triggerActivation triggerArea triggerAttachedVehicle triggerAttachObject triggerAttachVehicle triggerDynamicSimulation triggerStatements triggerText triggerTimeout triggerTimeoutCurrent triggerType turretLocal turretOwner turretUnit tvAdd tvClear tvCollapse tvCollapseAll tvCount tvCurSel tvData tvDelete tvExpand tvExpandAll tvPicture tvSetColor tvSetCurSel tvSetData tvSetPicture tvSetPictureColor tvSetPictureColorDisabled tvSetPictureColorSelected tvSetPictureRight tvSetPictureRightColor tvSetPictureRightColorDisabled tvSetPictureRightColorSelected tvSetText tvSetTooltip tvSetValue tvSort tvSortByValue tvText tvTooltip tvValue type typeName typeOf UAVControl uiNamespace uiSleep unassignCurator unassignItem unassignTeam unassignVehicle underwater uniform uniformContainer uniformItems uniformMagazines unitAddons unitAimPosition unitAimPositionVisual unitBackpack unitIsUAV unitPos unitReady unitRecoilCoefficient units unitsBelowHeight unlinkItem unlockAchievement unregisterTask updateDrawIcon updateMenuItem updateObjectTree useAISteeringComponent useAudioTimeForMoves userInputDisabled vectorAdd vectorCos vectorCrossProduct vectorDiff vectorDir vectorDirVisual vectorDistance vectorDistanceSqr vectorDotProduct vectorFromTo vectorMagnitude vectorMagnitudeSqr vectorModelToWorld vectorModelToWorldVisual vectorMultiply vectorNormalized vectorUp vectorUpVisual vectorWorldToModel vectorWorldToModelVisual vehicle vehicleCargoEnabled vehicleChat vehicleRadio vehicleReceiveRemoteTargets vehicleReportOwnPosition vehicleReportRemoteTargets vehicles vehicleVarName velocity velocityModelSpace verifySignature vest vestContainer vestItems vestMagazines viewDistance visibleCompass visibleGPS visibleMap visiblePosition visiblePositionASL visibleScoretable visibleWatch waves waypointAttachedObject waypointAttachedVehicle waypointAttachObject waypointAttachVehicle waypointBehaviour waypointCombatMode waypointCompletionRadius waypointDescription 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part_type_colour_rgb part_type_colour_hsv part_type_color1 part_type_color2 part_type_color3 part_type_color_mix part_type_color_rgb part_type_color_hsv part_type_alpha1 part_type_alpha2 part_type_alpha3 part_type_blend part_system_create part_system_create_layer part_system_destroy part_system_exists part_system_clear part_system_draw_order part_system_depth part_system_position part_system_automatic_update part_system_automatic_draw part_system_update part_system_drawit part_system_get_layer part_system_layer part_particles_create part_particles_create_colour part_particles_create_color part_particles_clear part_particles_count part_emitter_create part_emitter_destroy part_emitter_destroy_all part_emitter_exists part_emitter_clear part_emitter_region part_emitter_burst part_emitter_stream external_call external_define external_free window_handle window_device matrix_get matrix_set matrix_build_identity matrix_build matrix_build_lookat matrix_build_projection_ortho matrix_build_projection_perspective matrix_build_projection_perspective_fov matrix_multiply matrix_transform_vertex matrix_stack_push matrix_stack_pop matrix_stack_multiply matrix_stack_set matrix_stack_clear matrix_stack_top matrix_stack_is_empty browser_input_capture os_get_config os_get_info os_get_language os_get_region os_lock_orientation display_get_dpi_x display_get_dpi_y display_set_gui_size display_set_gui_maximise display_set_gui_maximize device_mouse_dbclick_enable display_set_timing_method display_get_timing_method display_set_sleep_margin display_get_sleep_margin virtual_key_add virtual_key_hide virtual_key_delete virtual_key_show draw_enable_drawevent draw_enable_swf_aa draw_set_swf_aa_level draw_get_swf_aa_level draw_texture_flush draw_flush gpu_set_blendenable gpu_set_ztestenable gpu_set_zfunc gpu_set_zwriteenable gpu_set_lightingenable gpu_set_fog gpu_set_cullmode gpu_set_blendmode gpu_set_blendmode_ext gpu_set_blendmode_ext_sepalpha gpu_set_colorwriteenable gpu_set_colourwriteenable gpu_set_alphatestenable gpu_set_alphatestref gpu_set_alphatestfunc gpu_set_texfilter gpu_set_texfilter_ext gpu_set_texrepeat gpu_set_texrepeat_ext gpu_set_tex_filter gpu_set_tex_filter_ext gpu_set_tex_repeat gpu_set_tex_repeat_ext gpu_set_tex_mip_filter gpu_set_tex_mip_filter_ext gpu_set_tex_mip_bias gpu_set_tex_mip_bias_ext gpu_set_tex_min_mip gpu_set_tex_min_mip_ext gpu_set_tex_max_mip gpu_set_tex_max_mip_ext gpu_set_tex_max_aniso gpu_set_tex_max_aniso_ext gpu_set_tex_mip_enable gpu_set_tex_mip_enable_ext gpu_get_blendenable gpu_get_ztestenable gpu_get_zfunc gpu_get_zwriteenable gpu_get_lightingenable gpu_get_fog gpu_get_cullmode gpu_get_blendmode gpu_get_blendmode_ext gpu_get_blendmode_ext_sepalpha gpu_get_blendmode_src gpu_get_blendmode_dest gpu_get_blendmode_srcalpha gpu_get_blendmode_destalpha gpu_get_colorwriteenable gpu_get_colourwriteenable gpu_get_alphatestenable gpu_get_alphatestref gpu_get_alphatestfunc gpu_get_texfilter gpu_get_texfilter_ext gpu_get_texrepeat gpu_get_texrepeat_ext gpu_get_tex_filter gpu_get_tex_filter_ext gpu_get_tex_repeat gpu_get_tex_repeat_ext gpu_get_tex_mip_filter gpu_get_tex_mip_filter_ext gpu_get_tex_mip_bias gpu_get_tex_mip_bias_ext gpu_get_tex_min_mip gpu_get_tex_min_mip_ext gpu_get_tex_max_mip gpu_get_tex_max_mip_ext gpu_get_tex_max_aniso gpu_get_tex_max_aniso_ext gpu_get_tex_mip_enable gpu_get_tex_mip_enable_ext gpu_push_state gpu_pop_state gpu_get_state gpu_set_state draw_light_define_ambient draw_light_define_direction draw_light_define_point draw_light_enable draw_set_lighting draw_light_get_ambient draw_light_get draw_get_lighting shop_leave_rating url_get_domain url_open url_open_ext url_open_full get_timer achievement_login achievement_logout achievement_post achievement_increment achievement_post_score achievement_available achievement_show_achievements achievement_show_leaderboards achievement_load_friends achievement_load_leaderboard achievement_send_challenge achievement_load_progress achievement_reset achievement_login_status achievement_get_pic achievement_show_challenge_notifications achievement_get_challenges achievement_event achievement_show achievement_get_info cloud_file_save cloud_string_save cloud_synchronise ads_enable ads_disable ads_setup ads_engagement_launch ads_engagement_available ads_engagement_active ads_event ads_event_preload ads_set_reward_callback ads_get_display_height ads_get_display_width ads_move ads_interstitial_available ads_interstitial_display device_get_tilt_x device_get_tilt_y device_get_tilt_z device_is_keypad_open device_mouse_check_button device_mouse_check_button_pressed device_mouse_check_button_released device_mouse_x device_mouse_y device_mouse_raw_x device_mouse_raw_y device_mouse_x_to_gui device_mouse_y_to_gui iap_activate iap_status iap_enumerate_products iap_restore_all iap_acquire iap_consume iap_product_details iap_purchase_details facebook_init facebook_login facebook_status facebook_graph_request facebook_dialog facebook_logout facebook_launch_offerwall facebook_post_message facebook_send_invite facebook_user_id facebook_accesstoken facebook_check_permission facebook_request_read_permissions facebook_request_publish_permissions gamepad_is_supported gamepad_get_device_count gamepad_is_connected gamepad_get_description gamepad_get_button_threshold gamepad_set_button_threshold gamepad_get_axis_deadzone gamepad_set_axis_deadzone gamepad_button_count gamepad_button_check gamepad_button_check_pressed gamepad_button_check_released gamepad_button_value gamepad_axis_count gamepad_axis_value gamepad_set_vibration gamepad_set_colour gamepad_set_color os_is_paused window_has_focus code_is_compiled http_get http_get_file http_post_string http_request json_encode json_decode zip_unzip load_csv base64_encode base64_decode md5_string_unicode md5_string_utf8 md5_file os_is_network_connected sha1_string_unicode sha1_string_utf8 sha1_file os_powersave_enable analytics_event analytics_event_ext win8_livetile_tile_notification win8_livetile_tile_clear win8_livetile_badge_notification win8_livetile_badge_clear win8_livetile_queue_enable win8_secondarytile_pin win8_secondarytile_badge_notification win8_secondarytile_delete win8_livetile_notification_begin win8_livetile_notification_secondary_begin win8_livetile_notification_expiry win8_livetile_notification_tag win8_livetile_notification_text_add win8_livetile_notification_image_add win8_livetile_notification_end win8_appbar_enable win8_appbar_add_element win8_appbar_remove_element win8_settingscharm_add_entry win8_settingscharm_add_html_entry win8_settingscharm_add_xaml_entry win8_settingscharm_set_xaml_property win8_settingscharm_get_xaml_property win8_settingscharm_remove_entry win8_share_image win8_share_screenshot win8_share_file win8_share_url win8_share_text win8_search_enable win8_search_disable win8_search_add_suggestions win8_device_touchscreen_available win8_license_initialize_sandbox win8_license_trial_version winphone_license_trial_version winphone_tile_title winphone_tile_count winphone_tile_back_title winphone_tile_back_content winphone_tile_back_content_wide winphone_tile_front_image winphone_tile_front_image_small winphone_tile_front_image_wide winphone_tile_back_image winphone_tile_back_image_wide winphone_tile_background_colour winphone_tile_background_color winphone_tile_icon_image winphone_tile_small_icon_image winphone_tile_wide_content winphone_tile_cycle_images winphone_tile_small_background_image physics_world_create physics_world_gravity physics_world_update_speed physics_world_update_iterations physics_world_draw_debug physics_pause_enable physics_fixture_create physics_fixture_set_kinematic physics_fixture_set_density physics_fixture_set_awake physics_fixture_set_restitution physics_fixture_set_friction physics_fixture_set_collision_group physics_fixture_set_sensor physics_fixture_set_linear_damping physics_fixture_set_angular_damping physics_fixture_set_circle_shape physics_fixture_set_box_shape physics_fixture_set_edge_shape physics_fixture_set_polygon_shape physics_fixture_set_chain_shape physics_fixture_add_point physics_fixture_bind physics_fixture_bind_ext physics_fixture_delete physics_apply_force physics_apply_impulse physics_apply_angular_impulse physics_apply_local_force physics_apply_local_impulse physics_apply_torque physics_mass_properties physics_draw_debug physics_test_overlap physics_remove_fixture physics_set_friction physics_set_density physics_set_restitution physics_get_friction physics_get_density physics_get_restitution physics_joint_distance_create physics_joint_rope_create physics_joint_revolute_create physics_joint_prismatic_create physics_joint_pulley_create physics_joint_wheel_create physics_joint_weld_create physics_joint_friction_create physics_joint_gear_create physics_joint_enable_motor physics_joint_get_value physics_joint_set_value physics_joint_delete physics_particle_create physics_particle_delete physics_particle_delete_region_circle physics_particle_delete_region_box physics_particle_delete_region_poly physics_particle_set_flags physics_particle_set_category_flags physics_particle_draw physics_particle_draw_ext physics_particle_count physics_particle_get_data physics_particle_get_data_particle physics_particle_group_begin physics_particle_group_circle physics_particle_group_box physics_particle_group_polygon physics_particle_group_add_point physics_particle_group_end physics_particle_group_join physics_particle_group_delete physics_particle_group_count physics_particle_group_get_data physics_particle_group_get_mass physics_particle_group_get_inertia physics_particle_group_get_centre_x physics_particle_group_get_centre_y physics_particle_group_get_vel_x physics_particle_group_get_vel_y physics_particle_group_get_ang_vel physics_particle_group_get_x physics_particle_group_get_y physics_particle_group_get_angle physics_particle_set_group_flags physics_particle_get_group_flags physics_particle_get_max_count physics_particle_get_radius physics_particle_get_density physics_particle_get_damping physics_particle_get_gravity_scale physics_particle_set_max_count physics_particle_set_radius physics_particle_set_density physics_particle_set_damping physics_particle_set_gravity_scale network_create_socket network_create_socket_ext network_create_server network_create_server_raw network_connect network_connect_raw network_send_packet network_send_raw network_send_broadcast network_send_udp network_send_udp_raw network_set_timeout network_set_config network_resolve network_destroy buffer_create buffer_write buffer_read buffer_seek buffer_get_surface buffer_set_surface buffer_delete buffer_exists buffer_get_type buffer_get_alignment buffer_poke buffer_peek buffer_save buffer_save_ext buffer_load buffer_load_ext buffer_load_partial buffer_copy buffer_fill buffer_get_size buffer_tell buffer_resize buffer_md5 buffer_sha1 buffer_base64_encode buffer_base64_decode buffer_base64_decode_ext buffer_sizeof buffer_get_address buffer_create_from_vertex_buffer buffer_create_from_vertex_buffer_ext buffer_copy_from_vertex_buffer buffer_async_group_begin buffer_async_group_option buffer_async_group_end buffer_load_async buffer_save_async gml_release_mode gml_pragma steam_activate_overlay steam_is_overlay_enabled steam_is_overlay_activated steam_get_persona_name steam_initialised steam_is_cloud_enabled_for_app steam_is_cloud_enabled_for_account steam_file_persisted steam_get_quota_total steam_get_quota_free steam_file_write steam_file_write_file steam_file_read steam_file_delete steam_file_exists steam_file_size steam_file_share steam_is_screenshot_requested steam_send_screenshot steam_is_user_logged_on steam_get_user_steam_id steam_user_owns_dlc steam_user_installed_dlc steam_set_achievement steam_get_achievement steam_clear_achievement steam_set_stat_int steam_set_stat_float steam_set_stat_avg_rate steam_get_stat_int steam_get_stat_float steam_get_stat_avg_rate steam_reset_all_stats steam_reset_all_stats_achievements steam_stats_ready steam_create_leaderboard steam_upload_score steam_upload_score_ext steam_download_scores_around_user steam_download_scores steam_download_friends_scores steam_upload_score_buffer steam_upload_score_buffer_ext steam_current_game_language steam_available_languages steam_activate_overlay_browser steam_activate_overlay_user steam_activate_overlay_store steam_get_user_persona_name steam_get_app_id steam_get_user_account_id steam_ugc_download steam_ugc_create_item steam_ugc_start_item_update steam_ugc_set_item_title steam_ugc_set_item_description steam_ugc_set_item_visibility steam_ugc_set_item_tags steam_ugc_set_item_content steam_ugc_set_item_preview steam_ugc_submit_item_update steam_ugc_get_item_update_progress steam_ugc_subscribe_item steam_ugc_unsubscribe_item steam_ugc_num_subscribed_items steam_ugc_get_subscribed_items steam_ugc_get_item_install_info steam_ugc_get_item_update_info steam_ugc_request_item_details steam_ugc_create_query_user steam_ugc_create_query_user_ex steam_ugc_create_query_all steam_ugc_create_query_all_ex steam_ugc_query_set_cloud_filename_filter steam_ugc_query_set_match_any_tag steam_ugc_query_set_search_text steam_ugc_query_set_ranked_by_trend_days steam_ugc_query_add_required_tag steam_ugc_query_add_excluded_tag steam_ugc_query_set_return_long_description steam_ugc_query_set_return_total_only steam_ugc_query_set_allow_cached_response steam_ugc_send_query shader_set shader_get_name shader_reset shader_current shader_is_compiled shader_get_sampler_index shader_get_uniform shader_set_uniform_i shader_set_uniform_i_array shader_set_uniform_f shader_set_uniform_f_array shader_set_uniform_matrix shader_set_uniform_matrix_array shader_enable_corner_id texture_set_stage texture_get_texel_width texture_get_texel_height shaders_are_supported vertex_format_begin vertex_format_end vertex_format_delete vertex_format_add_position vertex_format_add_position_3d vertex_format_add_colour vertex_format_add_color vertex_format_add_normal vertex_format_add_texcoord vertex_format_add_textcoord vertex_format_add_custom vertex_create_buffer vertex_create_buffer_ext vertex_delete_buffer vertex_begin vertex_end vertex_position vertex_position_3d vertex_colour vertex_color vertex_argb vertex_texcoord vertex_normal vertex_float1 vertex_float2 vertex_float3 vertex_float4 vertex_ubyte4 vertex_submit vertex_freeze vertex_get_number vertex_get_buffer_size vertex_create_buffer_from_buffer vertex_create_buffer_from_buffer_ext push_local_notification push_get_first_local_notification push_get_next_local_notification push_cancel_local_notification skeleton_animation_set skeleton_animation_get skeleton_animation_mix skeleton_animation_set_ext skeleton_animation_get_ext skeleton_animation_get_duration skeleton_animation_get_frames skeleton_animation_clear skeleton_skin_set skeleton_skin_get skeleton_attachment_set skeleton_attachment_get skeleton_attachment_create skeleton_collision_draw_set skeleton_bone_data_get skeleton_bone_data_set skeleton_bone_state_get skeleton_bone_state_set skeleton_get_minmax skeleton_get_num_bounds skeleton_get_bounds skeleton_animation_get_frame skeleton_animation_set_frame draw_skeleton draw_skeleton_time draw_skeleton_instance draw_skeleton_collision skeleton_animation_list skeleton_skin_list skeleton_slot_data layer_get_id layer_get_id_at_depth layer_get_depth layer_create layer_destroy layer_destroy_instances layer_add_instance layer_has_instance layer_set_visible layer_get_visible layer_exists layer_x layer_y layer_get_x layer_get_y layer_hspeed layer_vspeed layer_get_hspeed layer_get_vspeed layer_script_begin layer_script_end layer_shader layer_get_script_begin layer_get_script_end layer_get_shader layer_set_target_room layer_get_target_room layer_reset_target_room layer_get_all layer_get_all_elements layer_get_name layer_depth layer_get_element_layer layer_get_element_type layer_element_move layer_force_draw_depth layer_is_draw_depth_forced layer_get_forced_depth layer_background_get_id layer_background_exists layer_background_create layer_background_destroy layer_background_visible layer_background_change layer_background_sprite layer_background_htiled layer_background_vtiled layer_background_stretch layer_background_yscale layer_background_xscale layer_background_blend layer_background_alpha layer_background_index layer_background_speed layer_background_get_visible layer_background_get_sprite layer_background_get_htiled layer_background_get_vtiled layer_background_get_stretch layer_background_get_yscale layer_background_get_xscale layer_background_get_blend layer_background_get_alpha layer_background_get_index layer_background_get_speed layer_sprite_get_id layer_sprite_exists layer_sprite_create layer_sprite_destroy layer_sprite_change layer_sprite_index layer_sprite_speed layer_sprite_xscale layer_sprite_yscale layer_sprite_angle layer_sprite_blend layer_sprite_alpha layer_sprite_x layer_sprite_y layer_sprite_get_sprite layer_sprite_get_index layer_sprite_get_speed layer_sprite_get_xscale layer_sprite_get_yscale layer_sprite_get_angle layer_sprite_get_blend layer_sprite_get_alpha layer_sprite_get_x layer_sprite_get_y layer_tilemap_get_id layer_tilemap_exists layer_tilemap_create layer_tilemap_destroy tilemap_tileset tilemap_x tilemap_y tilemap_set tilemap_set_at_pixel tilemap_get_tileset tilemap_get_tile_width tilemap_get_tile_height tilemap_get_width tilemap_get_height tilemap_get_x tilemap_get_y tilemap_get tilemap_get_at_pixel tilemap_get_cell_x_at_pixel tilemap_get_cell_y_at_pixel tilemap_clear draw_tilemap draw_tile tilemap_set_global_mask tilemap_get_global_mask tilemap_set_mask tilemap_get_mask tilemap_get_frame tile_set_empty tile_set_index tile_set_flip tile_set_mirror tile_set_rotate tile_get_empty tile_get_index tile_get_flip tile_get_mirror tile_get_rotate layer_tile_exists layer_tile_create layer_tile_destroy layer_tile_change layer_tile_xscale layer_tile_yscale layer_tile_blend layer_tile_alpha layer_tile_x layer_tile_y layer_tile_region layer_tile_visible layer_tile_get_sprite layer_tile_get_xscale layer_tile_get_yscale layer_tile_get_blend layer_tile_get_alpha layer_tile_get_x layer_tile_get_y layer_tile_get_region layer_tile_get_visible layer_instance_get_instance instance_activate_layer instance_deactivate_layer camera_create camera_create_view camera_destroy camera_apply camera_get_active camera_get_default camera_set_default camera_set_view_mat camera_set_proj_mat camera_set_update_script camera_set_begin_script camera_set_end_script camera_set_view_pos camera_set_view_size camera_set_view_speed camera_set_view_border camera_set_view_angle camera_set_view_target camera_get_view_mat camera_get_proj_mat camera_get_update_script camera_get_begin_script camera_get_end_script camera_get_view_x camera_get_view_y camera_get_view_width camera_get_view_height camera_get_view_speed_x camera_get_view_speed_y camera_get_view_border_x camera_get_view_border_y camera_get_view_angle camera_get_view_target view_get_camera view_get_visible view_get_xport view_get_yport view_get_wport view_get_hport view_get_surface_id view_set_camera view_set_visible view_set_xport view_set_yport view_set_wport view_set_hport view_set_surface_id gesture_drag_time gesture_drag_distance gesture_flick_speed gesture_double_tap_time gesture_double_tap_distance gesture_pinch_distance gesture_pinch_angle_towards gesture_pinch_angle_away gesture_rotate_time gesture_rotate_angle gesture_tap_count gesture_get_drag_time gesture_get_drag_distance gesture_get_flick_speed gesture_get_double_tap_time gesture_get_double_tap_distance gesture_get_pinch_distance gesture_get_pinch_angle_towards gesture_get_pinch_angle_away gesture_get_rotate_time gesture_get_rotate_angle gesture_get_tap_count keyboard_virtual_show keyboard_virtual_hide keyboard_virtual_status keyboard_virtual_height",literal:"self other all noone global local undefined pointer_invalid pointer_null path_action_stop path_action_restart path_action_continue path_action_reverse true false pi GM_build_date GM_version GM_runtime_version  timezone_local timezone_utc gamespeed_fps gamespeed_microseconds  ev_create ev_destroy ev_step ev_alarm ev_keyboard ev_mouse ev_collision ev_other ev_draw ev_draw_begin ev_draw_end ev_draw_pre ev_draw_post ev_keypress ev_keyrelease ev_trigger ev_left_button ev_right_button ev_middle_button ev_no_button ev_left_press ev_right_press ev_middle_press ev_left_release ev_right_release ev_middle_release ev_mouse_enter ev_mouse_leave ev_mouse_wheel_up ev_mouse_wheel_down ev_global_left_button ev_global_right_button ev_global_middle_button ev_global_left_press ev_global_right_press ev_global_middle_press ev_global_left_release ev_global_right_release ev_global_middle_release ev_joystick1_left ev_joystick1_right ev_joystick1_up ev_joystick1_down 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iso_c_binding c_loc c_funloc c_associated  c_f_pointer ' +\n      'c_ptr c_funptr iso_fortran_env character_storage_size error_unit file_storage_size input_unit iostat_end iostat_eor ' +\n      'numeric_storage_size output_unit c_f_procpointer ieee_arithmetic ieee_support_underflow_control ' +\n      'ieee_get_underflow_mode ieee_set_underflow_mode newunit contiguous recursive ' +\n      'pad position action delim readwrite eor advance nml interface procedure namelist include sequence elemental pure ' +\n      'integer real character complex logical dimension allocatable|10 parameter ' +\n      'external implicit|10 none double precision assign intent optional pointer ' +\n      'target in out common equivalence data ' +\n      // IRPF90 special keywords\n      'begin_provider &begin_provider end_provider begin_shell end_shell begin_template end_template subst assert touch ' +\n      'soft_touch provide no_dep free irp_if irp_else irp_endif irp_write irp_read',\n    built_in: 'alog alog10 amax0 amax1 amin0 amin1 amod cabs ccos cexp clog csin csqrt dabs dacos dasin datan datan2 dcos dcosh ddim dexp dint ' +\n      'dlog dlog10 dmax1 dmin1 dmod dnint dsign dsin dsinh dsqrt dtan dtanh float iabs idim idint idnint ifix isign max0 max1 min0 min1 sngl ' +\n      'algama cdabs cdcos cdexp cdlog cdsin cdsqrt cqabs cqcos cqexp cqlog cqsin cqsqrt dcmplx dconjg derf derfc dfloat dgamma dimag dlgama ' +\n      'iqint qabs qacos qasin qatan qatan2 qcmplx qconjg qcos qcosh qdim qerf qerfc qexp qgamma qimag qlgama qlog qlog10 qmax1 qmin1 qmod ' +\n      'qnint qsign qsin qsinh qsqrt qtan qtanh abs acos aimag aint anint asin atan atan2 char cmplx conjg cos cosh exp ichar index int log ' +\n      'log10 max min nint sign sin sinh sqrt tan tanh print write dim lge lgt lle llt mod nullify allocate deallocate ' +\n      'adjustl adjustr all allocated any associated bit_size btest ceiling count cshift date_and_time digits dot_product ' +\n      'eoshift epsilon exponent floor fraction huge iand ibclr ibits ibset ieor ior ishft ishftc lbound len_trim matmul ' +\n      'maxexponent maxloc maxval merge minexponent minloc minval modulo mvbits nearest pack present product ' +\n      'radix random_number random_seed range repeat reshape rrspacing scale scan selected_int_kind selected_real_kind ' +\n      'set_exponent shape size spacing spread sum system_clock tiny transpose trim ubound unpack verify achar iachar transfer ' +\n      'dble entry dprod cpu_time command_argument_count get_command get_command_argument get_environment_variable is_iostat_end ' +\n      'ieee_arithmetic ieee_support_underflow_control ieee_get_underflow_mode ieee_set_underflow_mode ' +\n      'is_iostat_eor move_alloc new_line selected_char_kind same_type_as extends_type_of'  +\n      'acosh asinh atanh bessel_j0 bessel_j1 bessel_jn bessel_y0 bessel_y1 bessel_yn erf erfc erfc_scaled gamma log_gamma hypot norm2 ' +\n      'atomic_define atomic_ref execute_command_line leadz trailz 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t=e.getLanguage("cpp").exports;return{aliases:["sqf"],case_insensitive:!0,keywords:{keyword:"case catch default do else exit exitWith for forEach from if private switch then throw to try waitUntil while with",built_in:"abs accTime acos action actionIDs actionKeys actionKeysImages actionKeysNames actionKeysNamesArray actionName actionParams activateAddons activatedAddons activateKey add3DENConnection add3DENEventHandler add3DENLayer addAction addBackpack addBackpackCargo addBackpackCargoGlobal addBackpackGlobal addCamShake addCuratorAddons addCuratorCameraArea addCuratorEditableObjects addCuratorEditingArea addCuratorPoints addEditorObject addEventHandler addForce addGoggles addGroupIcon addHandgunItem addHeadgear addItem addItemCargo addItemCargoGlobal addItemPool addItemToBackpack addItemToUniform addItemToVest addLiveStats addMagazine addMagazineAmmoCargo addMagazineCargo addMagazineCargoGlobal addMagazineGlobal addMagazinePool addMagazines addMagazineTurret addMenu addMenuItem addMissionEventHandler addMPEventHandler addMusicEventHandler addOwnedMine addPlayerScores addPrimaryWeaponItem addPublicVariableEventHandler addRating addResources addScore addScoreSide addSecondaryWeaponItem addSwitchableUnit addTeamMember addToRemainsCollector addTorque addUniform addVehicle addVest addWaypoint addWeapon addWeaponCargo addWeaponCargoGlobal addWeaponGlobal addWeaponItem addWeaponPool addWeaponTurret admin agent agents AGLToASL aimedAtTarget aimPos airDensityRTD airplaneThrottle airportSide AISFinishHeal alive all3DENEntities allAirports allControls allCurators allCutLayers allDead allDeadMen allDisplays allGroups allMapMarkers allMines allMissionObjects allow3DMode allowCrewInImmobile allowCuratorLogicIgnoreAreas allowDamage allowDammage allowFileOperations allowFleeing allowGetIn allowSprint allPlayers allSimpleObjects allSites allTurrets allUnits allUnitsUAV allVariables ammo ammoOnPylon and animate animateBay animateDoor animatePylon animateSource animationNames animationPhase animationSourcePhase animationState append apply armoryPoints arrayIntersect asin ASLToAGL ASLToATL assert assignAsCargo assignAsCargoIndex assignAsCommander assignAsDriver assignAsGunner assignAsTurret assignCurator assignedCargo assignedCommander assignedDriver assignedGunner assignedItems assignedTarget assignedTeam assignedVehicle assignedVehicleRole assignItem assignTeam assignToAirport atan atan2 atg ATLToASL attachedObject attachedObjects attachedTo attachObject attachTo attackEnabled backpack backpackCargo backpackContainer backpackItems backpackMagazines backpackSpaceFor behaviour benchmark binocular boundingBox boundingBoxReal boundingCenter breakOut breakTo briefingName buildingExit buildingPos buttonAction buttonSetAction cadetMode call callExtension camCommand camCommit camCommitPrepared camCommitted camConstuctionSetParams camCreate camDestroy cameraEffect cameraEffectEnableHUD cameraInterest cameraOn cameraView campaignConfigFile camPreload camPreloaded camPrepareBank camPrepareDir camPrepareDive camPrepareFocus camPrepareFov camPrepareFovRange camPreparePos camPrepareRelPos camPrepareTarget camSetBank camSetDir camSetDive camSetFocus camSetFov camSetFovRange camSetPos camSetRelPos camSetTarget camTarget camUseNVG canAdd canAddItemToBackpack canAddItemToUniform canAddItemToVest cancelSimpleTaskDestination canFire canMove canSlingLoad canStand canSuspend canTriggerDynamicSimulation canUnloadInCombat canVehicleCargo captive captiveNum cbChecked cbSetChecked ceil channelEnabled cheatsEnabled checkAIFeature checkVisibility className clearAllItemsFromBackpack clearBackpackCargo clearBackpackCargoGlobal clearGroupIcons clearItemCargo clearItemCargoGlobal clearItemPool clearMagazineCargo clearMagazineCargoGlobal clearMagazinePool clearOverlay clearRadio clearWeaponCargo clearWeaponCargoGlobal clearWeaponPool clientOwner closeDialog closeDisplay closeOverlay collapseObjectTree collect3DENHistory collectiveRTD combatMode commandArtilleryFire commandChat commander commandFire commandFollow commandFSM commandGetOut commandingMenu commandMove commandRadio commandStop commandSuppressiveFire commandTarget commandWatch comment commitOverlay compile compileFinal completedFSM composeText configClasses configFile configHierarchy configName configProperties configSourceAddonList configSourceMod configSourceModList confirmSensorTarget connectTerminalToUAV controlsGroupCtrl copyFromClipboard copyToClipboard copyWaypoints cos count countEnemy countFriendly countSide countType countUnknown create3DENComposition create3DENEntity createAgent createCenter createDialog createDiaryLink createDiaryRecord createDiarySubject createDisplay createGearDialog createGroup createGuardedPoint createLocation createMarker createMarkerLocal createMenu createMine createMissionDisplay createMPCampaignDisplay createSimpleObject createSimpleTask createSite createSoundSource createTask createTeam createTrigger createUnit createVehicle createVehicleCrew createVehicleLocal crew ctAddHeader ctAddRow ctClear ctCurSel ctData ctFindHeaderRows ctFindRowHeader ctHeaderControls ctHeaderCount ctRemoveHeaders ctRemoveRows ctrlActivate ctrlAddEventHandler ctrlAngle ctrlAutoScrollDelay ctrlAutoScrollRewind ctrlAutoScrollSpeed ctrlChecked ctrlClassName ctrlCommit ctrlCommitted ctrlCreate ctrlDelete ctrlEnable ctrlEnabled ctrlFade ctrlHTMLLoaded ctrlIDC ctrlIDD ctrlMapAnimAdd ctrlMapAnimClear ctrlMapAnimCommit ctrlMapAnimDone ctrlMapCursor ctrlMapMouseOver ctrlMapScale ctrlMapScreenToWorld ctrlMapWorldToScreen ctrlModel ctrlModelDirAndUp ctrlModelScale ctrlParent ctrlParentControlsGroup ctrlPosition ctrlRemoveAllEventHandlers ctrlRemoveEventHandler ctrlScale ctrlSetActiveColor ctrlSetAngle ctrlSetAutoScrollDelay ctrlSetAutoScrollRewind ctrlSetAutoScrollSpeed ctrlSetBackgroundColor ctrlSetChecked ctrlSetEventHandler ctrlSetFade ctrlSetFocus ctrlSetFont ctrlSetFontH1 ctrlSetFontH1B ctrlSetFontH2 ctrlSetFontH2B ctrlSetFontH3 ctrlSetFontH3B ctrlSetFontH4 ctrlSetFontH4B ctrlSetFontH5 ctrlSetFontH5B ctrlSetFontH6 ctrlSetFontH6B ctrlSetFontHeight ctrlSetFontHeightH1 ctrlSetFontHeightH2 ctrlSetFontHeightH3 ctrlSetFontHeightH4 ctrlSetFontHeightH5 ctrlSetFontHeightH6 ctrlSetFontHeightSecondary ctrlSetFontP ctrlSetFontPB ctrlSetFontSecondary ctrlSetForegroundColor ctrlSetModel ctrlSetModelDirAndUp ctrlSetModelScale ctrlSetPixelPrecision ctrlSetPosition ctrlSetScale ctrlSetStructuredText ctrlSetText ctrlSetTextColor ctrlSetTooltip ctrlSetTooltipColorBox ctrlSetTooltipColorShade ctrlSetTooltipColorText ctrlShow ctrlShown ctrlText ctrlTextHeight ctrlTextWidth ctrlType ctrlVisible ctRowControls ctRowCount ctSetCurSel ctSetData ctSetHeaderTemplate ctSetRowTemplate ctSetValue ctValue curatorAddons curatorCamera curatorCameraArea curatorCameraAreaCeiling curatorCoef curatorEditableObjects curatorEditingArea curatorEditingAreaType curatorMouseOver curatorPoints curatorRegisteredObjects curatorSelected curatorWaypointCost current3DENOperation currentChannel currentCommand currentMagazine currentMagazineDetail currentMagazineDetailTurret currentMagazineTurret currentMuzzle currentNamespace currentTask currentTasks currentThrowable currentVisionMode currentWaypoint currentWeapon currentWeaponMode currentWeaponTurret currentZeroing cursorObject cursorTarget customChat customRadio cutFadeOut cutObj cutRsc cutText damage date dateToNumber daytime deActivateKey debriefingText debugFSM debugLog deg delete3DENEntities deleteAt deleteCenter deleteCollection deleteEditorObject deleteGroup deleteGroupWhenEmpty deleteIdentity deleteLocation deleteMarker deleteMarkerLocal deleteRange deleteResources deleteSite deleteStatus deleteTeam deleteVehicle deleteVehicleCrew deleteWaypoint detach detectedMines diag_activeMissionFSMs diag_activeScripts diag_activeSQFScripts diag_activeSQSScripts diag_captureFrame diag_captureFrameToFile diag_captureSlowFrame diag_codePerformance diag_drawMode diag_enable diag_enabled diag_fps diag_fpsMin diag_frameNo diag_lightNewLoad diag_list diag_log diag_logSlowFrame diag_mergeConfigFile diag_recordTurretLimits diag_setLightNew diag_tickTime diag_toggle dialog diarySubjectExists didJIP didJIPOwner difficulty difficultyEnabled difficultyEnabledRTD difficultyOption direction directSay disableAI disableCollisionWith disableConversation disableDebriefingStats disableMapIndicators disableNVGEquipment disableRemoteSensors disableSerialization disableTIEquipment disableUAVConnectability disableUserInput displayAddEventHandler displayCtrl displayParent displayRemoveAllEventHandlers displayRemoveEventHandler displaySetEventHandler dissolveTeam distance distance2D distanceSqr distributionRegion do3DENAction doArtilleryFire doFire doFollow doFSM doGetOut doMove doorPhase doStop doSuppressiveFire doTarget doWatch drawArrow drawEllipse drawIcon drawIcon3D drawLine drawLine3D drawLink drawLocation drawPolygon drawRectangle drawTriangle driver drop dynamicSimulationDistance dynamicSimulationDistanceCoef dynamicSimulationEnabled dynamicSimulationSystemEnabled echo edit3DENMissionAttributes editObject editorSetEventHandler effectiveCommander emptyPositions enableAI enableAIFeature enableAimPrecision enableAttack enableAudioFeature enableAutoStartUpRTD enableAutoTrimRTD enableCamShake enableCaustics enableChannel enableCollisionWith enableCopilot enableDebriefingStats enableDiagLegend enableDynamicSimulation enableDynamicSimulationSystem enableEndDialog enableEngineArtillery enableEnvironment enableFatigue enableGunLights enableInfoPanelComponent enableIRLasers enableMimics enablePersonTurret enableRadio enableReload enableRopeAttach enableSatNormalOnDetail enableSaving enableSentences enableSimulation enableSimulationGlobal enableStamina enableTeamSwitch enableTraffic enableUAVConnectability enableUAVWaypoints enableVehicleCargo enableVehicleSensor enableWeaponDisassembly endLoadingScreen endMission engineOn enginesIsOnRTD enginesRpmRTD enginesTorqueRTD entities environmentEnabled estimatedEndServerTime estimatedTimeLeft evalObjectArgument everyBackpack everyContainer exec execEditorScript execFSM execVM exp expectedDestination exportJIPMessages eyeDirection eyePos face faction fadeMusic fadeRadio fadeSound fadeSpeech failMission fillWeaponsFromPool find findCover findDisplay findEditorObject findEmptyPosition findEmptyPositionReady findIf findNearestEnemy finishMissionInit finite fire fireAtTarget firstBackpack flag flagAnimationPhase flagOwner flagSide flagTexture fleeing floor flyInHeight flyInHeightASL fog fogForecast fogParams forceAddUniform forcedMap forceEnd forceFlagTexture forceFollowRoad forceMap forceRespawn forceSpeed forceWalk forceWeaponFire forceWeatherChange forEachMember forEachMemberAgent forEachMemberTeam forgetTarget format formation formationDirection formationLeader formationMembers formationPosition formationTask formatText formLeader freeLook fromEditor fuel fullCrew gearIDCAmmoCount gearSlotAmmoCount gearSlotData get3DENActionState get3DENAttribute get3DENCamera get3DENConnections get3DENEntity get3DENEntityID get3DENGrid get3DENIconsVisible get3DENLayerEntities get3DENLinesVisible get3DENMissionAttribute get3DENMouseOver get3DENSelected getAimingCoef getAllEnvSoundControllers getAllHitPointsDamage getAllOwnedMines getAllSoundControllers getAmmoCargo getAnimAimPrecision getAnimSpeedCoef getArray getArtilleryAmmo getArtilleryComputerSettings getArtilleryETA getAssignedCuratorLogic getAssignedCuratorUnit getBackpackCargo getBleedingRemaining getBurningValue getCameraViewDirection getCargoIndex getCenterOfMass getClientState getClientStateNumber getCompatiblePylonMagazines getConnectedUAV getContainerMaxLoad getCursorObjectParams getCustomAimCoef getDammage getDescription getDir getDirVisual getDLCAssetsUsage getDLCAssetsUsageByName getDLCs getEditorCamera getEditorMode getEditorObjectScope getElevationOffset getEnvSoundController getFatigue getForcedFlagTexture getFriend getFSMVariable getFuelCargo getGroupIcon getGroupIconParams getGroupIcons getHideFrom getHit getHitIndex getHitPointDamage getItemCargo getMagazineCargo getMarkerColor getMarkerPos getMarkerSize getMarkerType getMass getMissionConfig getMissionConfigValue getMissionDLCs getMissionLayerEntities getModelInfo getMousePosition getMusicPlayedTime getNumber getObjectArgument getObjectChildren getObjectDLC getObjectMaterials getObjectProxy getObjectTextures getObjectType getObjectViewDistance getOxygenRemaining getPersonUsedDLCs getPilotCameraDirection getPilotCameraPosition getPilotCameraRotation getPilotCameraTarget getPlateNumber getPlayerChannel getPlayerScores getPlayerUID getPos getPosASL getPosASLVisual getPosASLW getPosATL getPosATLVisual getPosVisual getPosWorld getPylonMagazines getRelDir getRelPos getRemoteSensorsDisabled getRepairCargo getResolution getShadowDistance getShotParents getSlingLoad getSoundController getSoundControllerResult getSpeed getStamina getStatValue getSuppression getTerrainGrid getTerrainHeightASL getText getTotalDLCUsageTime getUnitLoadout getUnitTrait getUserMFDText getUserMFDvalue getVariable getVehicleCargo getWeaponCargo getWeaponSway getWingsOrientationRTD getWingsPositionRTD getWPPos glanceAt globalChat globalRadio goggles goto group groupChat groupFromNetId groupIconSelectable groupIconsVisible groupId groupOwner groupRadio groupSelectedUnits groupSelectUnit gunner gusts halt handgunItems handgunMagazine handgunWeapon handsHit hasInterface hasPilotCamera hasWeapon hcAllGroups hcGroupParams hcLeader hcRemoveAllGroups hcRemoveGroup hcSelected hcSelectGroup hcSetGroup hcShowBar hcShownBar headgear hideBody hideObject hideObjectGlobal hideSelection hint hintC hintCadet hintSilent hmd hostMission htmlLoad HUDMovementLevels humidity image importAllGroups importance in inArea inAreaArray incapacitatedState inflame inflamed infoPanel infoPanelComponentEnabled infoPanelComponents infoPanels inGameUISetEventHandler inheritsFrom initAmbientLife inPolygon inputAction inRangeOfArtillery insertEditorObject intersect is3DEN is3DENMultiplayer isAbleToBreathe isAgent isArray isAutoHoverOn isAutonomous isAutotest isBleeding isBurning isClass isCollisionLightOn isCopilotEnabled isDamageAllowed isDedicated isDLCAvailable isEngineOn isEqualTo isEqualType isEqualTypeAll isEqualTypeAny isEqualTypeArray isEqualTypeParams isFilePatchingEnabled isFlashlightOn isFlatEmpty isForcedWalk isFormationLeader isGroupDeletedWhenEmpty isHidden isInRemainsCollector isInstructorFigureEnabled isIRLaserOn isKeyActive isKindOf isLaserOn isLightOn isLocalized isManualFire isMarkedForCollection isMultiplayer isMultiplayerSolo isNil isNull isNumber isObjectHidden isObjectRTD isOnRoad isPipEnabled isPlayer isRealTime isRemoteExecuted isRemoteExecutedJIP isServer isShowing3DIcons isSimpleObject isSprintAllowed isStaminaEnabled isSteamMission isStreamFriendlyUIEnabled isText isTouchingGround isTurnedOut isTutHintsEnabled isUAVConnectable isUAVConnected isUIContext isUniformAllowed isVehicleCargo isVehicleRadarOn isVehicleSensorEnabled isWalking isWeaponDeployed isWeaponRested itemCargo items itemsWithMagazines join joinAs joinAsSilent joinSilent joinString kbAddDatabase kbAddDatabaseTargets kbAddTopic kbHasTopic kbReact kbRemoveTopic kbTell kbWasSaid keyImage keyName knowsAbout land landAt landResult language laserTarget lbAdd lbClear lbColor lbColorRight lbCurSel lbData lbDelete lbIsSelected lbPicture lbPictureRight lbSelection lbSetColor lbSetColorRight lbSetCurSel lbSetData lbSetPicture lbSetPictureColor lbSetPictureColorDisabled lbSetPictureColorSelected lbSetPictureRight lbSetPictureRightColor lbSetPictureRightColorDisabled lbSetPictureRightColorSelected lbSetSelectColor lbSetSelectColorRight lbSetSelected lbSetText lbSetTextRight lbSetTooltip lbSetValue lbSize lbSort lbSortByValue lbText lbTextRight lbValue leader leaderboardDeInit leaderboardGetRows leaderboardInit leaderboardRequestRowsFriends leaderboardsRequestUploadScore leaderboardsRequestUploadScoreKeepBest leaderboardState leaveVehicle libraryCredits libraryDisclaimers lifeState lightAttachObject lightDetachObject lightIsOn lightnings limitSpeed linearConversion lineIntersects lineIntersectsObjs lineIntersectsSurfaces lineIntersectsWith linkItem list listObjects listRemoteTargets listVehicleSensors ln lnbAddArray lnbAddColumn lnbAddRow lnbClear lnbColor lnbCurSelRow lnbData lnbDeleteColumn lnbDeleteRow lnbGetColumnsPosition lnbPicture lnbSetColor lnbSetColumnsPos lnbSetCurSelRow lnbSetData lnbSetPicture lnbSetText lnbSetValue lnbSize lnbSort lnbSortByValue lnbText lnbValue load loadAbs loadBackpack loadFile loadGame loadIdentity loadMagazine loadOverlay loadStatus loadUniform loadVest local localize locationPosition lock lockCameraTo lockCargo lockDriver locked lockedCargo lockedDriver lockedTurret lockIdentity lockTurret lockWP log logEntities logNetwork logNetworkTerminate lookAt lookAtPos magazineCargo magazines magazinesAllTurrets magazinesAmmo magazinesAmmoCargo magazinesAmmoFull magazinesDetail magazinesDetailBackpack magazinesDetailUniform magazinesDetailVest magazinesTurret magazineTurretAmmo mapAnimAdd mapAnimClear mapAnimCommit mapAnimDone mapCenterOnCamera mapGridPosition markAsFinishedOnSteam markerAlpha markerBrush markerColor markerDir markerPos markerShape markerSize markerText markerType max members menuAction menuAdd menuChecked menuClear menuCollapse menuData menuDelete menuEnable menuEnabled menuExpand menuHover menuPicture menuSetAction menuSetCheck menuSetData menuSetPicture menuSetValue menuShortcut menuShortcutText menuSize menuSort menuText menuURL menuValue min mineActive mineDetectedBy missionConfigFile missionDifficulty missionName missionNamespace missionStart missionVersion mod modelToWorld modelToWorldVisual modelToWorldVisualWorld modelToWorldWorld modParams moonIntensity moonPhase morale move move3DENCamera moveInAny moveInCargo moveInCommander moveInDriver moveInGunner moveInTurret moveObjectToEnd moveOut moveTime moveTo moveToCompleted moveToFailed musicVolume name nameSound nearEntities nearestBuilding nearestLocation nearestLocations nearestLocationWithDubbing nearestObject nearestObjects nearestTerrainObjects nearObjects nearObjectsReady nearRoads nearSupplies nearTargets needReload netId netObjNull newOverlay nextMenuItemIndex nextWeatherChange nMenuItems not numberOfEnginesRTD numberToDate objectCurators objectFromNetId objectParent objStatus onBriefingGroup onBriefingNotes onBriefingPlan onBriefingTeamSwitch onCommandModeChanged onDoubleClick onEachFrame onGroupIconClick onGroupIconOverEnter onGroupIconOverLeave onHCGroupSelectionChanged onMapSingleClick onPlayerConnected onPlayerDisconnected onPreloadFinished onPreloadStarted onShowNewObject onTeamSwitch openCuratorInterface openDLCPage openMap openSteamApp openYoutubeVideo or orderGetIn overcast overcastForecast owner param params parseNumber parseSimpleArray parseText parsingNamespace particlesQuality pickWeaponPool pitch pixelGrid pixelGridBase pixelGridNoUIScale pixelH pixelW playableSlotsNumber playableUnits playAction playActionNow player playerRespawnTime playerSide playersNumber playGesture playMission playMove playMoveNow playMusic playScriptedMission playSound playSound3D position positionCameraToWorld posScreenToWorld posWorldToScreen ppEffectAdjust ppEffectCommit ppEffectCommitted ppEffectCreate ppEffectDestroy ppEffectEnable ppEffectEnabled ppEffectForceInNVG precision preloadCamera preloadObject preloadSound preloadTitleObj preloadTitleRsc preprocessFile preprocessFileLineNumbers primaryWeapon primaryWeaponItems primaryWeaponMagazine priority processDiaryLink productVersion profileName profileNamespace profileNameSteam progressLoadingScreen progressPosition progressSetPosition publicVariable publicVariableClient publicVariableServer pushBack pushBackUnique putWeaponPool queryItemsPool queryMagazinePool queryWeaponPool rad radioChannelAdd radioChannelCreate radioChannelRemove radioChannelSetCallSign radioChannelSetLabel radioVolume rain rainbow random rank rankId rating rectangular registeredTasks registerTask reload reloadEnabled remoteControl remoteExec remoteExecCall remoteExecutedOwner remove3DENConnection remove3DENEventHandler remove3DENLayer removeAction removeAll3DENEventHandlers removeAllActions removeAllAssignedItems removeAllContainers removeAllCuratorAddons removeAllCuratorCameraAreas removeAllCuratorEditingAreas removeAllEventHandlers removeAllHandgunItems removeAllItems removeAllItemsWithMagazines removeAllMissionEventHandlers removeAllMPEventHandlers removeAllMusicEventHandlers removeAllOwnedMines removeAllPrimaryWeaponItems removeAllWeapons removeBackpack removeBackpackGlobal removeCuratorAddons removeCuratorCameraArea removeCuratorEditableObjects removeCuratorEditingArea removeDrawIcon removeDrawLinks removeEventHandler removeFromRemainsCollector removeGoggles removeGroupIcon removeHandgunItem removeHeadgear removeItem removeItemFromBackpack removeItemFromUniform removeItemFromVest removeItems removeMagazine removeMagazineGlobal removeMagazines removeMagazinesTurret removeMagazineTurret removeMenuItem removeMissionEventHandler removeMPEventHandler removeMusicEventHandler removeOwnedMine removePrimaryWeaponItem removeSecondaryWeaponItem removeSimpleTask removeSwitchableUnit removeTeamMember removeUniform removeVest removeWeapon removeWeaponAttachmentCargo removeWeaponCargo removeWeaponGlobal removeWeaponTurret reportRemoteTarget requiredVersion resetCamShake resetSubgroupDirection resize resources respawnVehicle restartEditorCamera reveal revealMine reverse reversedMouseY roadAt roadsConnectedTo roleDescription ropeAttachedObjects ropeAttachedTo ropeAttachEnabled ropeAttachTo ropeCreate ropeCut ropeDestroy ropeDetach ropeEndPosition ropeLength ropes ropeUnwind ropeUnwound rotorsForcesRTD rotorsRpmRTD round runInitScript safeZoneH safeZoneW safeZoneWAbs safeZoneX safeZoneXAbs safeZoneY save3DENInventory saveGame saveIdentity saveJoysticks saveOverlay saveProfileNamespace saveStatus saveVar savingEnabled say say2D say3D scopeName score scoreSide screenshot screenToWorld scriptDone scriptName scudState secondaryWeapon secondaryWeaponItems secondaryWeaponMagazine select selectBestPlaces selectDiarySubject selectedEditorObjects selectEditorObject selectionNames selectionPosition selectLeader selectMax selectMin selectNoPlayer selectPlayer selectRandom selectRandomWeighted selectWeapon selectWeaponTurret sendAUMessage sendSimpleCommand sendTask sendTaskResult sendUDPMessage serverCommand serverCommandAvailable serverCommandExecutable serverName serverTime set set3DENAttribute set3DENAttributes set3DENGrid set3DENIconsVisible set3DENLayer set3DENLinesVisible set3DENLogicType set3DENMissionAttribute set3DENMissionAttributes set3DENModelsVisible set3DENObjectType set3DENSelected setAccTime setActualCollectiveRTD setAirplaneThrottle setAirportSide setAmmo setAmmoCargo setAmmoOnPylon setAnimSpeedCoef setAperture setApertureNew setArmoryPoints setAttributes setAutonomous setBehaviour setBleedingRemaining setBrakesRTD setCameraInterest setCamShakeDefParams setCamShakeParams setCamUseTI setCaptive setCenterOfMass setCollisionLight setCombatMode setCompassOscillation setConvoySeparation setCuratorCameraAreaCeiling setCuratorCoef setCuratorEditingAreaType setCuratorWaypointCost setCurrentChannel setCurrentTask setCurrentWaypoint setCustomAimCoef setCustomWeightRTD setDamage setDammage setDate setDebriefingText setDefaultCamera setDestination setDetailMapBlendPars setDir setDirection setDrawIcon setDriveOnPath setDropInterval setDynamicSimulationDistance setDynamicSimulationDistanceCoef setEditorMode setEditorObjectScope setEffectCondition setEngineRPMRTD setFace setFaceAnimation setFatigue setFeatureType setFlagAnimationPhase setFlagOwner setFlagSide setFlagTexture setFog setFormation setFormationTask setFormDir setFriend setFromEditor setFSMVariable setFuel setFuelCargo setGroupIcon setGroupIconParams setGroupIconsSelectable setGroupIconsVisible setGroupId setGroupIdGlobal setGroupOwner setGusts setHideBehind setHit setHitIndex setHitPointDamage setHorizonParallaxCoef setHUDMovementLevels setIdentity setImportance setInfoPanel setLeader setLightAmbient setLightAttenuation setLightBrightness setLightColor setLightDayLight setLightFlareMaxDistance setLightFlareSize setLightIntensity setLightnings setLightUseFlare setLocalWindParams setMagazineTurretAmmo setMarkerAlpha setMarkerAlphaLocal setMarkerBrush setMarkerBrushLocal setMarkerColor setMarkerColorLocal setMarkerDir setMarkerDirLocal setMarkerPos setMarkerPosLocal setMarkerShape setMarkerShapeLocal setMarkerSize setMarkerSizeLocal setMarkerText setMarkerTextLocal setMarkerType setMarkerTypeLocal setMass setMimic setMousePosition setMusicEffect setMusicEventHandler setName setNameSound setObjectArguments setObjectMaterial setObjectMaterialGlobal setObjectProxy setObjectTexture setObjectTextureGlobal setObjectViewDistance setOvercast setOwner setOxygenRemaining setParticleCircle setParticleClass setParticleFire setParticleParams setParticleRandom setPilotCameraDirection setPilotCameraRotation setPilotCameraTarget setPilotLight setPiPEffect setPitch setPlateNumber setPlayable setPlayerRespawnTime setPos setPosASL setPosASL2 setPosASLW setPosATL setPosition setPosWorld setPylonLoadOut setPylonsPriority setRadioMsg setRain setRainbow setRandomLip setRank setRectangular setRepairCargo setRotorBrakeRTD setShadowDistance setShotParents setSide setSimpleTaskAlwaysVisible setSimpleTaskCustomData setSimpleTaskDescription setSimpleTaskDestination setSimpleTaskTarget setSimpleTaskType setSimulWeatherLayers setSize setSkill setSlingLoad setSoundEffect setSpeaker setSpeech setSpeedMode setStamina setStaminaScheme setStatValue setSuppression setSystemOfUnits setTargetAge setTaskMarkerOffset setTaskResult setTaskState setTerrainGrid setText setTimeMultiplier setTitleEffect setTrafficDensity setTrafficDistance setTrafficGap setTrafficSpeed setTriggerActivation setTriggerArea setTriggerStatements setTriggerText setTriggerTimeout setTriggerType setType setUnconscious setUnitAbility setUnitLoadout setUnitPos setUnitPosWeak setUnitRank setUnitRecoilCoefficient setUnitTrait setUnloadInCombat setUserActionText setUserMFDText setUserMFDvalue setVariable setVectorDir setVectorDirAndUp setVectorUp setVehicleAmmo setVehicleAmmoDef setVehicleArmor setVehicleCargo setVehicleId setVehicleLock setVehiclePosition setVehicleRadar setVehicleReceiveRemoteTargets setVehicleReportOwnPosition setVehicleReportRemoteTargets setVehicleTIPars setVehicleVarName setVelocity setVelocityModelSpace setVelocityTransformation setViewDistance setVisibleIfTreeCollapsed setWantedRPMRTD setWaves setWaypointBehaviour setWaypointCombatMode setWaypointCompletionRadius setWaypointDescription setWaypointForceBehaviour setWaypointFormation setWaypointHousePosition setWaypointLoiterRadius setWaypointLoiterType setWaypointName setWaypointPosition setWaypointScript setWaypointSpeed setWaypointStatements setWaypointTimeout setWaypointType setWaypointVisible setWeaponReloadingTime setWind setWindDir setWindForce setWindStr setWingForceScaleRTD setWPPos show3DIcons showChat showCinemaBorder showCommandingMenu showCompass showCuratorCompass showGPS showHUD showLegend showMap shownArtilleryComputer shownChat shownCompass shownCuratorCompass showNewEditorObject shownGPS shownHUD shownMap shownPad shownRadio shownScoretable shownUAVFeed shownWarrant shownWatch showPad showRadio showScoretable showSubtitles showUAVFeed showWarrant showWatch showWaypoint showWaypoints side sideChat sideEnemy sideFriendly sideRadio simpleTasks simulationEnabled simulCloudDensity simulCloudOcclusion simulInClouds simulWeatherSync sin size sizeOf skill skillFinal skipTime sleep sliderPosition sliderRange sliderSetPosition sliderSetRange sliderSetSpeed sliderSpeed slingLoadAssistantShown soldierMagazines someAmmo sort soundVolume spawn speaker speed speedMode splitString sqrt squadParams stance startLoadingScreen step stop stopEngineRTD stopped str sunOrMoon supportInfo suppressFor surfaceIsWater surfaceNormal surfaceType swimInDepth switchableUnits switchAction switchCamera switchGesture switchLight switchMove synchronizedObjects synchronizedTriggers synchronizedWaypoints synchronizeObjectsAdd synchronizeObjectsRemove synchronizeTrigger synchronizeWaypoint systemChat systemOfUnits tan targetKnowledge targets targetsAggregate targetsQuery taskAlwaysVisible taskChildren taskCompleted taskCustomData taskDescription taskDestination taskHint taskMarkerOffset taskParent taskResult taskState taskType teamMember teamName teams teamSwitch teamSwitchEnabled teamType terminate terrainIntersect terrainIntersectASL terrainIntersectAtASL text textLog textLogFormat tg time timeMultiplier titleCut titleFadeOut titleObj titleRsc titleText toArray toFixed toLower toString toUpper triggerActivated triggerActivation triggerArea triggerAttachedVehicle triggerAttachObject triggerAttachVehicle triggerDynamicSimulation triggerStatements triggerText triggerTimeout triggerTimeoutCurrent triggerType turretLocal turretOwner turretUnit tvAdd tvClear tvCollapse tvCollapseAll tvCount tvCurSel tvData tvDelete tvExpand tvExpandAll tvPicture tvSetColor tvSetCurSel tvSetData tvSetPicture tvSetPictureColor tvSetPictureColorDisabled tvSetPictureColorSelected tvSetPictureRight tvSetPictureRightColor tvSetPictureRightColorDisabled tvSetPictureRightColorSelected tvSetText tvSetTooltip tvSetValue tvSort tvSortByValue tvText tvTooltip tvValue type typeName typeOf UAVControl uiNamespace uiSleep unassignCurator unassignItem unassignTeam unassignVehicle underwater uniform uniformContainer uniformItems uniformMagazines unitAddons unitAimPosition unitAimPositionVisual unitBackpack unitIsUAV unitPos unitReady unitRecoilCoefficient units unitsBelowHeight unlinkItem unlockAchievement unregisterTask updateDrawIcon updateMenuItem updateObjectTree useAISteeringComponent useAudioTimeForMoves userInputDisabled vectorAdd vectorCos vectorCrossProduct vectorDiff vectorDir vectorDirVisual vectorDistance vectorDistanceSqr vectorDotProduct vectorFromTo vectorMagnitude vectorMagnitudeSqr vectorModelToWorld vectorModelToWorldVisual vectorMultiply vectorNormalized vectorUp vectorUpVisual vectorWorldToModel vectorWorldToModelVisual vehicle vehicleCargoEnabled vehicleChat vehicleRadio vehicleReceiveRemoteTargets vehicleReportOwnPosition vehicleReportRemoteTargets vehicles vehicleVarName velocity velocityModelSpace verifySignature vest vestContainer vestItems vestMagazines viewDistance visibleCompass visibleGPS visibleMap visiblePosition visiblePositionASL visibleScoretable visibleWatch waves waypointAttachedObject waypointAttachedVehicle waypointAttachObject waypointAttachVehicle waypointBehaviour waypointCombatMode waypointCompletionRadius waypointDescription 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part_type_colour_rgb part_type_colour_hsv part_type_color1 part_type_color2 part_type_color3 part_type_color_mix part_type_color_rgb part_type_color_hsv part_type_alpha1 part_type_alpha2 part_type_alpha3 part_type_blend part_system_create part_system_create_layer part_system_destroy part_system_exists part_system_clear part_system_draw_order part_system_depth part_system_position part_system_automatic_update part_system_automatic_draw part_system_update part_system_drawit part_system_get_layer part_system_layer part_particles_create part_particles_create_colour part_particles_create_color part_particles_clear part_particles_count part_emitter_create part_emitter_destroy part_emitter_destroy_all part_emitter_exists part_emitter_clear part_emitter_region part_emitter_burst part_emitter_stream external_call external_define external_free window_handle window_device matrix_get matrix_set matrix_build_identity matrix_build matrix_build_lookat matrix_build_projection_ortho matrix_build_projection_perspective matrix_build_projection_perspective_fov matrix_multiply matrix_transform_vertex matrix_stack_push matrix_stack_pop matrix_stack_multiply matrix_stack_set matrix_stack_clear matrix_stack_top matrix_stack_is_empty browser_input_capture os_get_config os_get_info os_get_language os_get_region os_lock_orientation display_get_dpi_x display_get_dpi_y display_set_gui_size display_set_gui_maximise display_set_gui_maximize device_mouse_dbclick_enable display_set_timing_method display_get_timing_method display_set_sleep_margin display_get_sleep_margin virtual_key_add virtual_key_hide virtual_key_delete virtual_key_show draw_enable_drawevent draw_enable_swf_aa draw_set_swf_aa_level draw_get_swf_aa_level draw_texture_flush draw_flush gpu_set_blendenable gpu_set_ztestenable gpu_set_zfunc gpu_set_zwriteenable gpu_set_lightingenable gpu_set_fog gpu_set_cullmode gpu_set_blendmode gpu_set_blendmode_ext gpu_set_blendmode_ext_sepalpha gpu_set_colorwriteenable gpu_set_colourwriteenable gpu_set_alphatestenable gpu_set_alphatestref gpu_set_alphatestfunc gpu_set_texfilter gpu_set_texfilter_ext gpu_set_texrepeat gpu_set_texrepeat_ext gpu_set_tex_filter gpu_set_tex_filter_ext gpu_set_tex_repeat gpu_set_tex_repeat_ext gpu_set_tex_mip_filter gpu_set_tex_mip_filter_ext gpu_set_tex_mip_bias gpu_set_tex_mip_bias_ext gpu_set_tex_min_mip gpu_set_tex_min_mip_ext gpu_set_tex_max_mip gpu_set_tex_max_mip_ext gpu_set_tex_max_aniso gpu_set_tex_max_aniso_ext gpu_set_tex_mip_enable gpu_set_tex_mip_enable_ext gpu_get_blendenable gpu_get_ztestenable gpu_get_zfunc gpu_get_zwriteenable gpu_get_lightingenable gpu_get_fog gpu_get_cullmode gpu_get_blendmode gpu_get_blendmode_ext gpu_get_blendmode_ext_sepalpha gpu_get_blendmode_src gpu_get_blendmode_dest gpu_get_blendmode_srcalpha gpu_get_blendmode_destalpha gpu_get_colorwriteenable gpu_get_colourwriteenable gpu_get_alphatestenable gpu_get_alphatestref gpu_get_alphatestfunc gpu_get_texfilter gpu_get_texfilter_ext gpu_get_texrepeat gpu_get_texrepeat_ext gpu_get_tex_filter gpu_get_tex_filter_ext gpu_get_tex_repeat gpu_get_tex_repeat_ext gpu_get_tex_mip_filter gpu_get_tex_mip_filter_ext gpu_get_tex_mip_bias gpu_get_tex_mip_bias_ext gpu_get_tex_min_mip gpu_get_tex_min_mip_ext gpu_get_tex_max_mip gpu_get_tex_max_mip_ext gpu_get_tex_max_aniso gpu_get_tex_max_aniso_ext gpu_get_tex_mip_enable gpu_get_tex_mip_enable_ext gpu_push_state gpu_pop_state gpu_get_state gpu_set_state draw_light_define_ambient draw_light_define_direction draw_light_define_point draw_light_enable draw_set_lighting draw_light_get_ambient draw_light_get draw_get_lighting shop_leave_rating url_get_domain url_open url_open_ext url_open_full get_timer achievement_login achievement_logout achievement_post achievement_increment achievement_post_score achievement_available achievement_show_achievements achievement_show_leaderboards achievement_load_friends achievement_load_leaderboard achievement_send_challenge achievement_load_progress achievement_reset achievement_login_status achievement_get_pic achievement_show_challenge_notifications achievement_get_challenges achievement_event achievement_show achievement_get_info cloud_file_save cloud_string_save cloud_synchronise ads_enable ads_disable ads_setup ads_engagement_launch ads_engagement_available ads_engagement_active ads_event ads_event_preload ads_set_reward_callback ads_get_display_height ads_get_display_width ads_move ads_interstitial_available ads_interstitial_display device_get_tilt_x device_get_tilt_y device_get_tilt_z device_is_keypad_open device_mouse_check_button device_mouse_check_button_pressed device_mouse_check_button_released device_mouse_x device_mouse_y device_mouse_raw_x device_mouse_raw_y device_mouse_x_to_gui device_mouse_y_to_gui iap_activate iap_status iap_enumerate_products iap_restore_all iap_acquire iap_consume iap_product_details iap_purchase_details facebook_init facebook_login facebook_status facebook_graph_request facebook_dialog facebook_logout facebook_launch_offerwall facebook_post_message facebook_send_invite facebook_user_id facebook_accesstoken facebook_check_permission facebook_request_read_permissions facebook_request_publish_permissions gamepad_is_supported gamepad_get_device_count gamepad_is_connected gamepad_get_description gamepad_get_button_threshold gamepad_set_button_threshold gamepad_get_axis_deadzone gamepad_set_axis_deadzone gamepad_button_count gamepad_button_check gamepad_button_check_pressed gamepad_button_check_released gamepad_button_value gamepad_axis_count gamepad_axis_value gamepad_set_vibration gamepad_set_colour gamepad_set_color os_is_paused window_has_focus code_is_compiled http_get http_get_file http_post_string http_request json_encode json_decode zip_unzip load_csv base64_encode base64_decode md5_string_unicode md5_string_utf8 md5_file os_is_network_connected sha1_string_unicode sha1_string_utf8 sha1_file os_powersave_enable analytics_event analytics_event_ext win8_livetile_tile_notification win8_livetile_tile_clear win8_livetile_badge_notification win8_livetile_badge_clear win8_livetile_queue_enable win8_secondarytile_pin win8_secondarytile_badge_notification win8_secondarytile_delete win8_livetile_notification_begin win8_livetile_notification_secondary_begin win8_livetile_notification_expiry win8_livetile_notification_tag win8_livetile_notification_text_add win8_livetile_notification_image_add win8_livetile_notification_end win8_appbar_enable win8_appbar_add_element win8_appbar_remove_element win8_settingscharm_add_entry win8_settingscharm_add_html_entry win8_settingscharm_add_xaml_entry win8_settingscharm_set_xaml_property win8_settingscharm_get_xaml_property win8_settingscharm_remove_entry win8_share_image win8_share_screenshot win8_share_file win8_share_url win8_share_text win8_search_enable win8_search_disable win8_search_add_suggestions win8_device_touchscreen_available win8_license_initialize_sandbox win8_license_trial_version winphone_license_trial_version winphone_tile_title winphone_tile_count winphone_tile_back_title winphone_tile_back_content winphone_tile_back_content_wide winphone_tile_front_image winphone_tile_front_image_small winphone_tile_front_image_wide winphone_tile_back_image winphone_tile_back_image_wide winphone_tile_background_colour winphone_tile_background_color winphone_tile_icon_image winphone_tile_small_icon_image winphone_tile_wide_content winphone_tile_cycle_images winphone_tile_small_background_image physics_world_create physics_world_gravity physics_world_update_speed physics_world_update_iterations physics_world_draw_debug physics_pause_enable physics_fixture_create physics_fixture_set_kinematic physics_fixture_set_density physics_fixture_set_awake physics_fixture_set_restitution physics_fixture_set_friction physics_fixture_set_collision_group physics_fixture_set_sensor physics_fixture_set_linear_damping physics_fixture_set_angular_damping physics_fixture_set_circle_shape physics_fixture_set_box_shape physics_fixture_set_edge_shape physics_fixture_set_polygon_shape physics_fixture_set_chain_shape physics_fixture_add_point physics_fixture_bind physics_fixture_bind_ext physics_fixture_delete physics_apply_force physics_apply_impulse physics_apply_angular_impulse physics_apply_local_force physics_apply_local_impulse physics_apply_torque physics_mass_properties physics_draw_debug physics_test_overlap physics_remove_fixture physics_set_friction physics_set_density physics_set_restitution physics_get_friction physics_get_density physics_get_restitution physics_joint_distance_create physics_joint_rope_create physics_joint_revolute_create physics_joint_prismatic_create physics_joint_pulley_create physics_joint_wheel_create physics_joint_weld_create physics_joint_friction_create physics_joint_gear_create physics_joint_enable_motor physics_joint_get_value physics_joint_set_value physics_joint_delete physics_particle_create physics_particle_delete physics_particle_delete_region_circle physics_particle_delete_region_box physics_particle_delete_region_poly physics_particle_set_flags physics_particle_set_category_flags physics_particle_draw physics_particle_draw_ext physics_particle_count physics_particle_get_data physics_particle_get_data_particle physics_particle_group_begin physics_particle_group_circle physics_particle_group_box physics_particle_group_polygon physics_particle_group_add_point physics_particle_group_end physics_particle_group_join physics_particle_group_delete physics_particle_group_count physics_particle_group_get_data physics_particle_group_get_mass physics_particle_group_get_inertia physics_particle_group_get_centre_x physics_particle_group_get_centre_y physics_particle_group_get_vel_x physics_particle_group_get_vel_y physics_particle_group_get_ang_vel physics_particle_group_get_x physics_particle_group_get_y physics_particle_group_get_angle physics_particle_set_group_flags physics_particle_get_group_flags physics_particle_get_max_count physics_particle_get_radius physics_particle_get_density physics_particle_get_damping physics_particle_get_gravity_scale physics_particle_set_max_count physics_particle_set_radius physics_particle_set_density physics_particle_set_damping physics_particle_set_gravity_scale network_create_socket network_create_socket_ext network_create_server network_create_server_raw network_connect network_connect_raw network_send_packet network_send_raw network_send_broadcast network_send_udp network_send_udp_raw network_set_timeout network_set_config network_resolve network_destroy buffer_create buffer_write buffer_read buffer_seek buffer_get_surface buffer_set_surface buffer_delete buffer_exists buffer_get_type buffer_get_alignment buffer_poke buffer_peek buffer_save buffer_save_ext buffer_load buffer_load_ext buffer_load_partial buffer_copy buffer_fill buffer_get_size buffer_tell buffer_resize buffer_md5 buffer_sha1 buffer_base64_encode buffer_base64_decode buffer_base64_decode_ext buffer_sizeof buffer_get_address buffer_create_from_vertex_buffer buffer_create_from_vertex_buffer_ext buffer_copy_from_vertex_buffer buffer_async_group_begin buffer_async_group_option buffer_async_group_end buffer_load_async buffer_save_async gml_release_mode gml_pragma steam_activate_overlay steam_is_overlay_enabled steam_is_overlay_activated steam_get_persona_name steam_initialised steam_is_cloud_enabled_for_app steam_is_cloud_enabled_for_account steam_file_persisted steam_get_quota_total steam_get_quota_free steam_file_write steam_file_write_file steam_file_read steam_file_delete steam_file_exists steam_file_size steam_file_share steam_is_screenshot_requested steam_send_screenshot steam_is_user_logged_on steam_get_user_steam_id steam_user_owns_dlc steam_user_installed_dlc steam_set_achievement steam_get_achievement steam_clear_achievement steam_set_stat_int steam_set_stat_float steam_set_stat_avg_rate steam_get_stat_int steam_get_stat_float steam_get_stat_avg_rate steam_reset_all_stats steam_reset_all_stats_achievements steam_stats_ready steam_create_leaderboard steam_upload_score steam_upload_score_ext steam_download_scores_around_user steam_download_scores steam_download_friends_scores steam_upload_score_buffer steam_upload_score_buffer_ext steam_current_game_language steam_available_languages steam_activate_overlay_browser steam_activate_overlay_user steam_activate_overlay_store steam_get_user_persona_name steam_get_app_id steam_get_user_account_id steam_ugc_download steam_ugc_create_item steam_ugc_start_item_update steam_ugc_set_item_title steam_ugc_set_item_description steam_ugc_set_item_visibility steam_ugc_set_item_tags steam_ugc_set_item_content steam_ugc_set_item_preview steam_ugc_submit_item_update steam_ugc_get_item_update_progress steam_ugc_subscribe_item steam_ugc_unsubscribe_item steam_ugc_num_subscribed_items steam_ugc_get_subscribed_items steam_ugc_get_item_install_info steam_ugc_get_item_update_info steam_ugc_request_item_details steam_ugc_create_query_user steam_ugc_create_query_user_ex steam_ugc_create_query_all steam_ugc_create_query_all_ex steam_ugc_query_set_cloud_filename_filter steam_ugc_query_set_match_any_tag steam_ugc_query_set_search_text steam_ugc_query_set_ranked_by_trend_days steam_ugc_query_add_required_tag steam_ugc_query_add_excluded_tag steam_ugc_query_set_return_long_description steam_ugc_query_set_return_total_only steam_ugc_query_set_allow_cached_response steam_ugc_send_query shader_set shader_get_name shader_reset shader_current shader_is_compiled shader_get_sampler_index shader_get_uniform shader_set_uniform_i shader_set_uniform_i_array shader_set_uniform_f shader_set_uniform_f_array shader_set_uniform_matrix shader_set_uniform_matrix_array shader_enable_corner_id texture_set_stage texture_get_texel_width texture_get_texel_height shaders_are_supported vertex_format_begin vertex_format_end vertex_format_delete vertex_format_add_position vertex_format_add_position_3d vertex_format_add_colour vertex_format_add_color vertex_format_add_normal vertex_format_add_texcoord vertex_format_add_textcoord vertex_format_add_custom vertex_create_buffer vertex_create_buffer_ext vertex_delete_buffer vertex_begin vertex_end vertex_position vertex_position_3d vertex_colour vertex_color vertex_argb vertex_texcoord vertex_normal vertex_float1 vertex_float2 vertex_float3 vertex_float4 vertex_ubyte4 vertex_submit vertex_freeze vertex_get_number vertex_get_buffer_size vertex_create_buffer_from_buffer vertex_create_buffer_from_buffer_ext push_local_notification push_get_first_local_notification push_get_next_local_notification push_cancel_local_notification skeleton_animation_set skeleton_animation_get skeleton_animation_mix skeleton_animation_set_ext skeleton_animation_get_ext skeleton_animation_get_duration skeleton_animation_get_frames skeleton_animation_clear skeleton_skin_set skeleton_skin_get skeleton_attachment_set skeleton_attachment_get skeleton_attachment_create skeleton_collision_draw_set skeleton_bone_data_get skeleton_bone_data_set skeleton_bone_state_get skeleton_bone_state_set skeleton_get_minmax skeleton_get_num_bounds skeleton_get_bounds skeleton_animation_get_frame skeleton_animation_set_frame draw_skeleton draw_skeleton_time draw_skeleton_instance draw_skeleton_collision skeleton_animation_list skeleton_skin_list skeleton_slot_data layer_get_id layer_get_id_at_depth layer_get_depth layer_create layer_destroy layer_destroy_instances layer_add_instance layer_has_instance layer_set_visible layer_get_visible layer_exists layer_x layer_y layer_get_x layer_get_y layer_hspeed layer_vspeed layer_get_hspeed layer_get_vspeed layer_script_begin layer_script_end layer_shader layer_get_script_begin layer_get_script_end layer_get_shader layer_set_target_room layer_get_target_room layer_reset_target_room layer_get_all layer_get_all_elements layer_get_name layer_depth layer_get_element_layer layer_get_element_type layer_element_move layer_force_draw_depth layer_is_draw_depth_forced layer_get_forced_depth layer_background_get_id layer_background_exists layer_background_create layer_background_destroy layer_background_visible layer_background_change layer_background_sprite layer_background_htiled layer_background_vtiled layer_background_stretch layer_background_yscale layer_background_xscale layer_background_blend layer_background_alpha layer_background_index layer_background_speed layer_background_get_visible layer_background_get_sprite layer_background_get_htiled layer_background_get_vtiled layer_background_get_stretch layer_background_get_yscale layer_background_get_xscale layer_background_get_blend layer_background_get_alpha layer_background_get_index layer_background_get_speed layer_sprite_get_id layer_sprite_exists layer_sprite_create layer_sprite_destroy layer_sprite_change layer_sprite_index layer_sprite_speed layer_sprite_xscale layer_sprite_yscale layer_sprite_angle layer_sprite_blend layer_sprite_alpha layer_sprite_x layer_sprite_y layer_sprite_get_sprite layer_sprite_get_index layer_sprite_get_speed layer_sprite_get_xscale layer_sprite_get_yscale layer_sprite_get_angle layer_sprite_get_blend layer_sprite_get_alpha layer_sprite_get_x layer_sprite_get_y layer_tilemap_get_id layer_tilemap_exists layer_tilemap_create layer_tilemap_destroy tilemap_tileset tilemap_x tilemap_y tilemap_set tilemap_set_at_pixel tilemap_get_tileset tilemap_get_tile_width tilemap_get_tile_height tilemap_get_width tilemap_get_height tilemap_get_x tilemap_get_y tilemap_get tilemap_get_at_pixel tilemap_get_cell_x_at_pixel tilemap_get_cell_y_at_pixel tilemap_clear draw_tilemap draw_tile tilemap_set_global_mask tilemap_get_global_mask tilemap_set_mask tilemap_get_mask tilemap_get_frame tile_set_empty tile_set_index tile_set_flip tile_set_mirror tile_set_rotate tile_get_empty tile_get_index tile_get_flip tile_get_mirror tile_get_rotate layer_tile_exists layer_tile_create layer_tile_destroy layer_tile_change layer_tile_xscale layer_tile_yscale layer_tile_blend layer_tile_alpha layer_tile_x layer_tile_y layer_tile_region layer_tile_visible layer_tile_get_sprite layer_tile_get_xscale layer_tile_get_yscale layer_tile_get_blend layer_tile_get_alpha layer_tile_get_x layer_tile_get_y layer_tile_get_region layer_tile_get_visible layer_instance_get_instance instance_activate_layer instance_deactivate_layer camera_create camera_create_view camera_destroy camera_apply camera_get_active camera_get_default camera_set_default camera_set_view_mat camera_set_proj_mat camera_set_update_script camera_set_begin_script camera_set_end_script camera_set_view_pos camera_set_view_size camera_set_view_speed camera_set_view_border camera_set_view_angle camera_set_view_target camera_get_view_mat camera_get_proj_mat camera_get_update_script camera_get_begin_script camera_get_end_script camera_get_view_x camera_get_view_y camera_get_view_width camera_get_view_height camera_get_view_speed_x camera_get_view_speed_y camera_get_view_border_x camera_get_view_border_y camera_get_view_angle camera_get_view_target view_get_camera view_get_visible view_get_xport view_get_yport view_get_wport view_get_hport view_get_surface_id view_set_camera view_set_visible view_set_xport view_set_yport view_set_wport view_set_hport view_set_surface_id gesture_drag_time gesture_drag_distance gesture_flick_speed gesture_double_tap_time gesture_double_tap_distance gesture_pinch_distance gesture_pinch_angle_towards gesture_pinch_angle_away gesture_rotate_time gesture_rotate_angle gesture_tap_count gesture_get_drag_time gesture_get_drag_distance gesture_get_flick_speed gesture_get_double_tap_time gesture_get_double_tap_distance gesture_get_pinch_distance gesture_get_pinch_angle_towards gesture_get_pinch_angle_away gesture_get_rotate_time gesture_get_rotate_angle gesture_get_tap_count keyboard_virtual_show keyboard_virtual_hide keyboard_virtual_status keyboard_virtual_height",literal:"self other all noone global local undefined pointer_invalid pointer_null path_action_stop path_action_restart path_action_continue path_action_reverse true false pi GM_build_date GM_version GM_runtime_version  timezone_local timezone_utc gamespeed_fps gamespeed_microseconds  ev_create ev_destroy ev_step ev_alarm ev_keyboard ev_mouse ev_collision ev_other ev_draw ev_draw_begin ev_draw_end ev_draw_pre ev_draw_post ev_keypress ev_keyrelease ev_trigger ev_left_button ev_right_button ev_middle_button ev_no_button ev_left_press ev_right_press ev_middle_press ev_left_release ev_right_release ev_middle_release ev_mouse_enter ev_mouse_leave ev_mouse_wheel_up ev_mouse_wheel_down ev_global_left_button ev_global_right_button ev_global_middle_button ev_global_left_press ev_global_right_press ev_global_middle_press ev_global_left_release ev_global_right_release ev_global_middle_release ev_joystick1_left ev_joystick1_right ev_joystick1_up ev_joystick1_down 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    \n            
    Apprendimento ed evoluzione in sistemi artificiali
    \n            
    \n                \n                    \n                \n                \n                    
    \n                        Se sei uno studente dell'Unimore, puoi accedere all'archivio del corso su Google Drive..\n                    
    \n                    \n            
    \n            
    \n                \n                    
      \n                        
    • Scegli 2 tra 6 domande possibili
      • \n                        
    • 90 minuti
      • \n                    
    \n                    \n                \n                    
      \n                        
      2. \n                        
      3. \n                        
      4. \n                    
    \n                    \n            
    \n            
    \n                \n                    
    \n                        NetLogo è un software di modellazione sistemi multiagente, da noi usato per le lezioni di laboratorio.\n                    
    \n                    
    \n                        Si può scaricare o usare da browser.\n                    
    \n                    
    \n                        Il suo codice sorgente è disponibile su GitHub, e ha una pagina di documentazione.\n                    
    \n                    
    \n                        Consulta i miei appunti su NetLogo qui!\n                    
    \n                    \n            
    \n            
    \n                \n                    
    \n                        Sono sistemi con le seguenti caratteristiche:\n                    
    \n                    
      \n                        
    • Autonomia: agiscono gli uni indipendentemente dagli altri
      • \n                        
    • Reattività: percepiscono ciò che sta nel loro ambiente e reagiscono ai cambiamenti di quest'ultimo
      • \n                        
    • Proattività: agiscono in maniera tale da portare a termine i loro obiettivi
      • \n                        
    • Socialità: comunicano con gli altri agenti, scambiando informazioni
      • \n                    
    \n                    \n                \n                    
    \n                        Hanno anche caratteristiche di livello più alto derivate dalle quattro precedenti:\n                    
    \n                    
      \n                        
    • Conoscenza
      • \n                        
    • Intenzioni
      • \n                        
    • Emozioni
      • \n                        
    • Obblighi
      • \n                        
    • Obiettivi
      • \n                        
    • etc...
      • \n                    
    \n                    \n                \n                    
    \n                        Gli agenti solitamente hanno anche:\n                    
    \n                    
      \n                        
    • Mobilità: possono muoversi nell'ambiente
      • \n                        
    • Veridicità: producono informazioni corrette
      • \n                        
    • Benevolenza: agiscono nel modo corretto
      • \n                        
    • Razionalità: compiono le azioni necessarie per raggiungere i loro obiettivi, e non altre che glielo impedirebbero
      • \n                    
    \n                    \n            
    \n            
    \n                \n                    
    \n                        Classificazione in base a come prende le decisioni un agente:\n                    
    \n                    
      \n                        
    • Logic-based: prende le decisioni attraverso deduzioni logiche
      • \n                        
    • Reactive: mappa una reazione a ogni situazione dell'ambiente
      • \n                        
    • Belief-desire-intention: per decidere, considera le proprie assunzioni sul mondo (belief), i propri desideri (desire) e le sue intenzioni correnti (intention)
      • \n                        
    • Layered: utilizza diversi strati di capacità cognitive per giungere a una decisione
      • \n                    
    \n                    \n                \n                    
    \n                        Classificazione in base a come sono definiti gli obiettivi di un agente:\n                    
    \n                    
      \n                        
    • Teleonomico: gli obiettivi sono predefiniti ed espliciti
      • \n                        
    • Riflessivo: l'agente è libero di scegliere il suo obiettivo in base alle proprie percezioni interne
      • \n                    
    \n                    \n                \n                    
    \n                        Classificazione in base a quanto conosce dell'ambiente un agente:\n                    
    \n                    
      \n                        
    • Cognitivo: l'agente è immediatamente a conoscenza di tutto l'ambiente
      • \n                        
    • Reattivo: l'agente deve scoprire l'ambiente con le sue capacità sensoriali
      • \n                    
    \n                    \n            
    \n            
    \n                \n                    
      \n                        
    • Distribuzione: più agenti possono coprire aree di ambiente più vaste, o elaborare più in fretta zone più dense di informazione
      • \n                        
    • Rappresentazione: i sistemi multi-agente modellano più accuratamente il mondo reale
      • \n                    
    \n                    \n            
    \n        
    \n    )\n}\n","import {Component} from 'preact'\nimport style from \"./Timer.less\"\n\n\nexport default class Timer extends Component {\n    constructor() {\n        super();\n        this.state = {\n            \"now\": Date.now()\n        };\n        this.timer = null;\n    }\n\n    componentDidMount() {\n        this.timer = setInterval(() => {\n            this.setState({\"now\": Date.now()})\n        }, 1000)\n    }\n\n    componentWillUnmount() {\n        if(this.timer !== null) {\n            clearInterval(this.timer)\n        }\n    }\n\n    render() {\n        let dateTo = \"Unknown date\";\n        let className = style.timer;\n\n        let parts = {\n            milliseconds: \"?\",\n            seconds: \"?\",\n            minutes: \"?\",\n            hours: \"?\",\n            days: \"?\",\n        };\n\n        if(this.props.to) {\n            dateTo = new Date(this.props.to);\n            let timeLeft = dateTo - this.state.now;\n\n            if(timeLeft > 0) {\n                parts = {\n                    milliseconds: timeLeft % 1000,\n                    seconds: Math.floor(timeLeft / 1000) % 60,\n                    minutes: Math.floor(timeLeft / 60000) % 60,\n                    hours: Math.floor(timeLeft / 3600000) % 24,\n                    days: Math.floor(timeLeft / 86400000),\n                };\n            }\n\n            else {\n                parts = {\n                    milliseconds: 0,\n                    seconds: 0,\n                    minutes: 0,\n                    hours: 0,\n                    days: 0,\n                };\n\n                className += \" \" + style.expired;\n            }\n        }\n        else {\n            className += \" \" + style.unknown;\n        }\n\n        return (\n            
    \n                
    \n                    {parts.days}\n                
    \n                
    \n                    giorni\n                
    \n                
    \n                    {parts.hours}\n                
    \n                
    \n                    ore\n                
    \n                
    \n                    {parts.minutes}\n                
    \n                
    \n                    minuti\n                
    \n                
    \n                    {parts.seconds}\n                
    \n                
    \n                    secondi\n                
    \n            
    \n        )\n    }\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"timer\":\"timer__3Z2pL\",\"days\":\"days__myhe2\",\"hours\":\"hours__3JUDn\",\"minutes\":\"minutes__24lD7\",\"seconds\":\"seconds__2vZ4f\",\"count\":\"count__chi9X\",\"text\":\"text__34ldC\",\"unknown\":\"unknown__3sT2P\",\"expired\":\"expired__zNiuP\"};"],"sourceRoot":""}
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new file mode 100644
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Add-NodeKeys Add-NsxDynamicCriteria Add-NsxDynamicMemberSet Add-NsxEdgeInterfaceAddress Add-NsxFirewallExclusionListMember Add-NsxFirewallRuleMember Add-NsxIpSetMember Add-NsxLicense Add-NsxLoadBalancerPoolMember Add-NsxLoadBalancerVip Add-NsxSecondaryManager Add-NsxSecurityGroupMember Add-NsxSecurityPolicyRule Add-NsxSecurityPolicyRuleGroup Add-NsxSecurityPolicyRuleService Add-NsxServiceGroupMember Add-NsxTransportZoneMember Add-PassthroughDevice Add-VDSwitchPhysicalNetworkAdapter Add-VDSwitchVMHost Add-VMHost Add-VMHostNtpServer Add-VirtualSwitchPhysicalNetworkAdapter Add-XmlElement Add-vRACustomForm Add-vRAPrincipalToTenantRole Add-vRAReservationNetwork Add-vRAReservationStorage Clear-NsxEdgeInterface Clear-NsxManagerTimeSettings Compress-Archive Connect-CIServer Connect-CisServer Connect-HCXServer Connect-NIServer Connect-NsxLogicalSwitch Connect-NsxServer Connect-NsxtServer Connect-SrmServer Connect-VIServer Connect-Vmc Connect-vRAServer Connect-vRNIServer ConvertFrom-Markdown ConvertTo-MOFInstance Copy-DatastoreItem Copy-HardDisk Copy-NsxEdge Copy-VDisk Copy-VMGuestFile Debug-Runspace Disable-NsxEdgeSsh Disable-RunspaceDebug Disable-vRNIDataSource Disconnect-CIServer Disconnect-CisServer Disconnect-HCXServer Disconnect-NsxLogicalSwitch Disconnect-NsxServer Disconnect-NsxtServer Disconnect-SrmServer Disconnect-VIServer Disconnect-Vmc Disconnect-vRAServer Disconnect-vRNIServer Dismount-Tools Enable-NsxEdgeSsh Enable-RunspaceDebug Enable-vRNIDataSource Expand-Archive Export-NsxObject Export-SpbmStoragePolicy Export-VApp Export-VDPortGroup Export-VDSwitch Export-VMHostProfile Export-vRAIcon Export-vRAPackage Find-Command Find-DscResource Find-Module Find-NsxWhereVMUsed Find-Package Find-PackageProvider Find-RoleCapability Find-Script Format-Hex Format-VMHostDiskPartition Format-XML Generate-VersionInfo Get-AdvancedSetting Get-AlarmAction Get-AlarmActionTrigger Get-AlarmDefinition Get-Annotation Get-CDDrive Get-CIAccessControlRule Get-CIDatastore Get-CINetworkAdapter Get-CIRole Get-CIUser Get-CIVApp Get-CIVAppNetwork Get-CIVAppStartRule Get-CIVAppTemplate Get-CIVM Get-CIVMTemplate Get-CIView Get-Catalog Get-CisCommand Get-CisService Get-CloudCommand Get-Cluster Get-CompatibleVersionAddtionaPropertiesStr Get-ComplexResourceQualifier Get-ConfigurationErrorCount Get-ContentLibraryItem Get-CustomAttribute Get-DSCResourceModules Get-Datacenter Get-Datastore Get-DatastoreCluster Get-DrsClusterGroup Get-DrsRecommendation Get-DrsRule Get-DrsVMHostRule Get-DscResource Get-EdgeGateway Get-EncryptedPassword Get-ErrorReport Get-EsxCli Get-EsxTop Get-ExternalNetwork Get-FileHash Get-FloppyDrive Get-Folder Get-HAPrimaryVMHost Get-HCXAppliance Get-HCXApplianceCompute Get-HCXApplianceDVS Get-HCXApplianceDatastore Get-HCXApplianceNetwork Get-HCXContainer Get-HCXDatastore Get-HCXGateway Get-HCXInterconnectStatus Get-HCXJob Get-HCXMigration Get-HCXNetwork Get-HCXNetworkExtension Get-HCXReplication Get-HCXReplicationSnapshot Get-HCXService Get-HCXSite Get-HCXSitePairing Get-HCXVM Get-HardDisk Get-IScsiHbaTarget Get-InnerMostErrorRecord Get-InstallPath Get-InstalledModule Get-InstalledScript Get-Inventory Get-ItemPropertyValue Get-KeyManagementServer Get-KmipClientCertificate Get-KmsCluster Get-Log Get-LogType Get-MarkdownOption Get-Media Get-MofInstanceName Get-MofInstanceText Get-NetworkAdapter Get-NetworkPool Get-NfsUser Get-NicTeamingPolicy Get-NsxApplicableMember Get-NsxApplicableSecurityAction Get-NsxBackingDVSwitch Get-NsxBackingPortGroup Get-NsxCliDfwAddrSet Get-NsxCliDfwFilter Get-NsxCliDfwRule Get-NsxClusterStatus Get-NsxController Get-NsxDynamicCriteria Get-NsxDynamicMemberSet Get-NsxEdge Get-NsxEdgeBgp Get-NsxEdgeBgpNeighbour Get-NsxEdgeCertificate Get-NsxEdgeCsr Get-NsxEdgeFirewall Get-NsxEdgeFirewallRule Get-NsxEdgeInterface Get-NsxEdgeInterfaceAddress Get-NsxEdgeNat Get-NsxEdgeNatRule Get-NsxEdgeOspf Get-NsxEdgeOspfArea Get-NsxEdgeOspfInterface Get-NsxEdgePrefix Get-NsxEdgeRedistributionRule Get-NsxEdgeRouting Get-NsxEdgeStaticRoute Get-NsxEdgeSubInterface Get-NsxFirewallExclusionListMember Get-NsxFirewallGlobalConfiguration Get-NsxFirewallPublishStatus Get-NsxFirewallRule Get-NsxFirewallRuleMember Get-NsxFirewallSavedConfiguration Get-NsxFirewallSection Get-NsxFirewallThreshold Get-NsxIpPool Get-NsxIpSet Get-NsxLicense Get-NsxLoadBalancer Get-NsxLoadBalancerApplicationProfile Get-NsxLoadBalancerApplicationRule Get-NsxLoadBalancerMonitor Get-NsxLoadBalancerPool Get-NsxLoadBalancerPoolMember Get-NsxLoadBalancerStats Get-NsxLoadBalancerVip Get-NsxLogicalRouter Get-NsxLogicalRouterBgp Get-NsxLogicalRouterBgpNeighbour Get-NsxLogicalRouterBridge Get-NsxLogicalRouterBridging Get-NsxLogicalRouterInterface Get-NsxLogicalRouterOspf Get-NsxLogicalRouterOspfArea Get-NsxLogicalRouterOspfInterface Get-NsxLogicalRouterPrefix Get-NsxLogicalRouterRedistributionRule Get-NsxLogicalRouterRouting Get-NsxLogicalRouterStaticRoute Get-NsxLogicalSwitch Get-NsxMacSet Get-NsxManagerBackup Get-NsxManagerCertificate Get-NsxManagerComponentSummary Get-NsxManagerNetwork Get-NsxManagerRole Get-NsxManagerSsoConfig Get-NsxManagerSyncStatus Get-NsxManagerSyslogServer Get-NsxManagerSystemSummary Get-NsxManagerTimeSettings Get-NsxManagerVcenterConfig Get-NsxSecondaryManager Get-NsxSecurityGroup Get-NsxSecurityGroupEffectiveIpAddress Get-NsxSecurityGroupEffectiveMacAddress Get-NsxSecurityGroupEffectiveMember Get-NsxSecurityGroupEffectiveVirtualMachine Get-NsxSecurityGroupEffectiveVnic Get-NsxSecurityGroupMemberTypes Get-NsxSecurityPolicy Get-NsxSecurityPolicyHighestUsedPrecedence Get-NsxSecurityPolicyRule Get-NsxSecurityTag Get-NsxSecurityTagAssignment Get-NsxSegmentIdRange Get-NsxService Get-NsxServiceDefinition Get-NsxServiceGroup Get-NsxServiceGroupMember Get-NsxServiceProfile Get-NsxSpoofguardNic Get-NsxSpoofguardPolicy Get-NsxSslVpn Get-NsxSslVpnAuthServer Get-NsxSslVpnClientInstallationPackage Get-NsxSslVpnIpPool Get-NsxSslVpnPrivateNetwork Get-NsxSslVpnUser Get-NsxTransportZone Get-NsxUserRole Get-NsxVdsContext Get-NsxtPolicyService Get-NsxtService Get-OSCustomizationNicMapping Get-OSCustomizationSpec Get-Org Get-OrgNetwork Get-OrgVdc Get-OrgVdcNetwork Get-OvfConfiguration Get-PSCurrentConfigurationNode Get-PSDefaultConfigurationDocument Get-PSMetaConfigDocumentInstVersionInfo Get-PSMetaConfigurationProcessed Get-PSReadLineKeyHandler Get-PSReadLineOption Get-PSRepository Get-PSTopConfigurationName Get-PSVersion Get-Package Get-PackageProvider Get-PackageSource Get-PassthroughDevice Get-PositionInfo Get-PowerCLICommunity Get-PowerCLIConfiguration Get-PowerCLIHelp Get-PowerCLIVersion Get-PowerNsxVersion Get-ProviderVdc Get-PublicKeyFromFile Get-PublicKeyFromStore Get-ResourcePool Get-Runspace Get-RunspaceDebug Get-ScsiController Get-ScsiLun Get-ScsiLunPath Get-SecurityInfo Get-SecurityPolicy Get-Snapshot Get-SpbmCapability Get-SpbmCompatibleStorage Get-SpbmEntityConfiguration Get-SpbmFaultDomain Get-SpbmPointInTimeReplica Get-SpbmReplicationGroup Get-SpbmReplicationPair Get-SpbmStoragePolicy Get-Stat Get-StatInterval Get-StatType Get-Tag Get-TagAssignment Get-TagCategory Get-Task Get-Template Get-TimeZone Get-Uptime Get-UsbDevice Get-VAIOFilter Get-VApp Get-VDBlockedPolicy Get-VDPort Get-VDPortgroup Get-VDPortgroupOverridePolicy Get-VDSecurityPolicy Get-VDSwitch Get-VDSwitchPrivateVlan Get-VDTrafficShapingPolicy Get-VDUplinkLacpPolicy Get-VDUplinkTeamingPolicy Get-VDisk Get-VIAccount Get-VICommand Get-VICredentialStoreItem Get-VIEvent Get-VIObjectByVIView Get-VIPermission Get-VIPrivilege Get-VIProperty Get-VIRole Get-VM Get-VMGuest Get-VMHost Get-VMHostAccount Get-VMHostAdvancedConfiguration Get-VMHostAuthentication Get-VMHostAvailableTimeZone Get-VMHostDiagnosticPartition Get-VMHostDisk Get-VMHostDiskPartition Get-VMHostFirewallDefaultPolicy Get-VMHostFirewallException Get-VMHostFirmware Get-VMHostHardware Get-VMHostHba Get-VMHostModule Get-VMHostNetwork Get-VMHostNetworkAdapter Get-VMHostNtpServer Get-VMHostPatch Get-VMHostPciDevice Get-VMHostProfile Get-VMHostProfileImageCacheConfiguration Get-VMHostProfileRequiredInput Get-VMHostProfileStorageDeviceConfiguration Get-VMHostProfileUserConfiguration Get-VMHostProfileVmPortGroupConfiguration Get-VMHostRoute Get-VMHostService Get-VMHostSnmp Get-VMHostStartPolicy Get-VMHostStorage Get-VMHostSysLogServer Get-VMQuestion Get-VMResourceConfiguration Get-VMStartPolicy Get-VTpm Get-VTpmCSR Get-VTpmCertificate Get-VasaProvider Get-VasaStorageArray Get-View Get-VirtualPortGroup Get-VirtualSwitch Get-VmcSddcNetworkService Get-VmcService Get-VsanClusterConfiguration Get-VsanComponent Get-VsanDisk Get-VsanDiskGroup Get-VsanEvacuationPlan Get-VsanFaultDomain Get-VsanIscsiInitiatorGroup Get-VsanIscsiInitiatorGroupTargetAssociation Get-VsanIscsiLun Get-VsanIscsiTarget Get-VsanObject Get-VsanResyncingComponent Get-VsanRuntimeInfo Get-VsanSpaceUsage Get-VsanStat Get-VsanView Get-vRAApplianceServiceStatus Get-vRAAuthorizationRole Get-vRABlueprint Get-vRABusinessGroup Get-vRACatalogItem Get-vRACatalogItemRequestTemplate Get-vRACatalogPrincipal Get-vRAComponentRegistryService Get-vRAComponentRegistryServiceEndpoint Get-vRAComponentRegistryServiceStatus Get-vRAContent Get-vRAContentData Get-vRAContentType Get-vRACustomForm Get-vRAEntitledCatalogItem Get-vRAEntitledService Get-vRAEntitlement Get-vRAExternalNetworkProfile Get-vRAGroupPrincipal Get-vRAIcon Get-vRANATNetworkProfile Get-vRANetworkProfileIPAddressList Get-vRANetworkProfileIPRangeSummary Get-vRAPackage Get-vRAPackageContent Get-vRAPropertyDefinition Get-vRAPropertyGroup Get-vRARequest Get-vRARequestDetail Get-vRAReservation Get-vRAReservationComputeResource Get-vRAReservationComputeResourceMemory Get-vRAReservationComputeResourceNetwork Get-vRAReservationComputeResourceResourcePool Get-vRAReservationComputeResourceStorage Get-vRAReservationPolicy Get-vRAReservationTemplate Get-vRAReservationType Get-vRAResource Get-vRAResourceAction Get-vRAResourceActionRequestTemplate Get-vRAResourceMetric Get-vRAResourceOperation Get-vRAResourceType Get-vRARoutedNetworkProfile Get-vRAService Get-vRAServiceBlueprint Get-vRASourceMachine Get-vRAStorageReservationPolicy Get-vRATenant Get-vRATenantDirectory Get-vRATenantDirectoryStatus Get-vRATenantRole Get-vRAUserPrincipal Get-vRAUserPrincipalGroupMembership Get-vRAVersion Get-vRNIAPIVersion Get-vRNIApplication Get-vRNIApplicationTier Get-vRNIDataSource Get-vRNIDataSourceSNMPConfig Get-vRNIDatastore Get-vRNIDistributedSwitch Get-vRNIDistributedSwitchPortGroup Get-vRNIEntity Get-vRNIEntityName Get-vRNIFirewallRule Get-vRNIFlow Get-vRNIHost Get-vRNIHostVMKNic Get-vRNIIPSet Get-vRNIL2Network Get-vRNINSXManager Get-vRNINodes Get-vRNIProblem Get-vRNIRecommendedRules Get-vRNIRecommendedRulesNsxBundle Get-vRNISecurityGroup Get-vRNISecurityTag Get-vRNIService Get-vRNIServiceGroup Get-vRNIVM Get-vRNIVMvNIC Get-vRNIvCenter Get-vRNIvCenterCluster Get-vRNIvCenterDatacenter Get-vRNIvCenterFolder Grant-NsxSpoofguardNicApproval Import-CIVApp Import-CIVAppTemplate Import-NsxObject Import-PackageProvider Import-PowerShellDataFile Import-SpbmStoragePolicy Import-VApp Import-VMHostProfile Import-vRAContentData Import-vRAIcon Import-vRAPackage Initialize-ConfigurationRuntimeState Install-Module Install-NsxCluster Install-Package Install-PackageProvider Install-Script Install-VMHostPatch Invoke-DrsRecommendation Invoke-NsxCli Invoke-NsxClusterResolveAll Invoke-NsxManagerSync Invoke-NsxRestMethod Invoke-NsxWebRequest Invoke-VMHostProfile Invoke-VMScript Invoke-XpathQuery Invoke-vRADataCollection Invoke-vRARestMethod Invoke-vRATenantDirectorySync Invoke-vRNIRestMethod Join-String Mount-Tools Move-Cluster Move-Datacenter Move-Datastore Move-Folder Move-HardDisk Move-Inventory Move-NsxSecurityPolicyRule Move-ResourcePool Move-Template Move-VApp Move-VDisk Move-VM Move-VMHost New-AdvancedSetting New-AlarmAction New-AlarmActionTrigger New-CDDrive New-CIAccessControlRule New-CIVApp New-CIVAppNetwork New-CIVAppTemplate New-CIVM New-Cluster New-CustomAttribute New-Datacenter New-Datastore New-DatastoreCluster New-DatastoreDrive New-DrsClusterGroup New-DrsRule New-DrsVMHostRule New-DscChecksum New-FloppyDrive New-Folder New-Guid New-HCXAppliance New-HCXMigration New-HCXNetworkExtension New-HCXNetworkMapping New-HCXReplication New-HCXSitePairing New-HCXStaticRoute New-HardDisk New-IScsiHbaTarget New-KmipClientCertificate New-NetworkAdapter New-NfsUser New-NsxAddressSpec New-NsxClusterVxlanConfig New-NsxController New-NsxDynamicCriteriaSpec New-NsxEdge New-NsxEdgeBgpNeighbour New-NsxEdgeCsr New-NsxEdgeFirewallRule New-NsxEdgeInterfaceSpec New-NsxEdgeNatRule New-NsxEdgeOspfArea New-NsxEdgeOspfInterface New-NsxEdgePrefix New-NsxEdgeRedistributionRule New-NsxEdgeSelfSignedCertificate New-NsxEdgeStaticRoute New-NsxEdgeSubInterface New-NsxEdgeSubInterfaceSpec New-NsxFirewallRule New-NsxFirewallSavedConfiguration New-NsxFirewallSection New-NsxIpPool New-NsxIpSet New-NsxLoadBalancerApplicationProfile New-NsxLoadBalancerApplicationRule New-NsxLoadBalancerMemberSpec New-NsxLoadBalancerMonitor New-NsxLoadBalancerPool New-NsxLogicalRouter New-NsxLogicalRouterBgpNeighbour New-NsxLogicalRouterBridge New-NsxLogicalRouterInterface New-NsxLogicalRouterInterfaceSpec New-NsxLogicalRouterOspfArea New-NsxLogicalRouterOspfInterface New-NsxLogicalRouterPrefix New-NsxLogicalRouterRedistributionRule New-NsxLogicalRouterStaticRoute New-NsxLogicalSwitch New-NsxMacSet New-NsxManager New-NsxSecurityGroup New-NsxSecurityPolicy New-NsxSecurityPolicyAssignment New-NsxSecurityPolicyFirewallRuleSpec New-NsxSecurityPolicyGuestIntrospectionSpec New-NsxSecurityPolicyNetworkIntrospectionSpec New-NsxSecurityTag New-NsxSecurityTagAssignment New-NsxSegmentIdRange New-NsxService New-NsxServiceGroup New-NsxSpoofguardPolicy New-NsxSslVpnAuthServer New-NsxSslVpnClientInstallationPackage New-NsxSslVpnIpPool New-NsxSslVpnPrivateNetwork New-NsxSslVpnUser New-NsxTransportZone New-NsxVdsContext New-OSCustomizationNicMapping New-OSCustomizationSpec New-Org New-OrgNetwork New-OrgVdc New-OrgVdcNetwork New-ResourcePool New-ScriptFileInfo New-ScsiController New-Snapshot New-SpbmRule New-SpbmRuleSet New-SpbmStoragePolicy New-StatInterval New-Tag New-TagAssignment New-TagCategory New-Template New-TemporaryFile New-VAIOFilter New-VApp New-VDPortgroup New-VDSwitch New-VDSwitchPrivateVlan New-VDisk New-VICredentialStoreItem New-VIInventoryDrive New-VIPermission New-VIProperty New-VIRole New-VISamlSecurityContext New-VM New-VMHostAccount New-VMHostNetworkAdapter New-VMHostProfile New-VMHostProfileVmPortGroupConfiguration New-VMHostRoute New-VTpm New-VasaProvider New-VcsOAuthSecurityContext New-VirtualPortGroup New-VirtualSwitch New-VsanDisk New-VsanDiskGroup New-VsanFaultDomain New-VsanIscsiInitiatorGroup New-VsanIscsiInitiatorGroupTargetAssociation New-VsanIscsiLun New-VsanIscsiTarget New-vRABusinessGroup New-vRAEntitlement New-vRAExternalNetworkProfile New-vRAGroupPrincipal New-vRANATNetworkProfile New-vRANetworkProfileIPRangeDefinition New-vRAPackage New-vRAPropertyDefinition New-vRAPropertyGroup New-vRAReservation New-vRAReservationNetworkDefinition New-vRAReservationPolicy New-vRAReservationStorageDefinition New-vRARoutedNetworkProfile New-vRAService New-vRAStorageReservationPolicy New-vRATenant New-vRATenantDirectory New-vRAUserPrincipal New-vRNIApplication New-vRNIApplicationTier New-vRNIDataSource Open-VMConsoleWindow Publish-Module Publish-NsxSpoofguardPolicy Publish-Script Register-PSRepository Register-PackageSource Remove-AdvancedSetting Remove-AlarmAction Remove-AlarmActionTrigger Remove-Alias Remove-CDDrive Remove-CIAccessControlRule Remove-CIVApp Remove-CIVAppNetwork Remove-CIVAppTemplate Remove-Cluster Remove-CustomAttribute Remove-Datacenter Remove-Datastore Remove-DatastoreCluster Remove-DrsClusterGroup Remove-DrsRule Remove-DrsVMHostRule Remove-FloppyDrive Remove-Folder Remove-HCXAppliance Remove-HCXNetworkExtension Remove-HCXReplication Remove-HCXSitePairing Remove-HardDisk Remove-IScsiHbaTarget Remove-Inventory Remove-KeyManagementServer Remove-NetworkAdapter Remove-NfsUser Remove-NsxCluster Remove-NsxClusterVxlanConfig Remove-NsxController Remove-NsxDynamicCriteria Remove-NsxDynamicMemberSet Remove-NsxEdge Remove-NsxEdgeBgpNeighbour Remove-NsxEdgeCertificate Remove-NsxEdgeCsr Remove-NsxEdgeFirewallRule Remove-NsxEdgeInterfaceAddress Remove-NsxEdgeNatRule Remove-NsxEdgeOspfArea Remove-NsxEdgeOspfInterface Remove-NsxEdgePrefix Remove-NsxEdgeRedistributionRule Remove-NsxEdgeStaticRoute Remove-NsxEdgeSubInterface Remove-NsxFirewallExclusionListMember Remove-NsxFirewallRule Remove-NsxFirewallRuleMember Remove-NsxFirewallSavedConfiguration Remove-NsxFirewallSection Remove-NsxIpPool Remove-NsxIpSet Remove-NsxIpSetMember Remove-NsxLoadBalancerApplicationProfile Remove-NsxLoadBalancerMonitor Remove-NsxLoadBalancerPool Remove-NsxLoadBalancerPoolMember Remove-NsxLoadBalancerVip Remove-NsxLogicalRouter Remove-NsxLogicalRouterBgpNeighbour Remove-NsxLogicalRouterBridge Remove-NsxLogicalRouterInterface Remove-NsxLogicalRouterOspfArea Remove-NsxLogicalRouterOspfInterface Remove-NsxLogicalRouterPrefix Remove-NsxLogicalRouterRedistributionRule Remove-NsxLogicalRouterStaticRoute Remove-NsxLogicalSwitch Remove-NsxMacSet Remove-NsxSecondaryManager Remove-NsxSecurityGroup Remove-NsxSecurityGroupMember Remove-NsxSecurityPolicy Remove-NsxSecurityPolicyAssignment Remove-NsxSecurityPolicyRule Remove-NsxSecurityPolicyRuleGroup Remove-NsxSecurityPolicyRuleService Remove-NsxSecurityTag Remove-NsxSecurityTagAssignment Remove-NsxSegmentIdRange Remove-NsxService Remove-NsxServiceGroup Remove-NsxSpoofguardPolicy Remove-NsxSslVpnClientInstallationPackage Remove-NsxSslVpnIpPool Remove-NsxSslVpnPrivateNetwork Remove-NsxSslVpnUser Remove-NsxTransportZone Remove-NsxTransportZoneMember Remove-NsxVdsContext Remove-OSCustomizationNicMapping Remove-OSCustomizationSpec Remove-Org Remove-OrgNetwork Remove-OrgVdc Remove-OrgVdcNetwork Remove-PSReadLineKeyHandler Remove-PassthroughDevice Remove-ResourcePool Remove-Snapshot Remove-SpbmStoragePolicy Remove-StatInterval Remove-Tag Remove-TagAssignment Remove-TagCategory Remove-Template Remove-UsbDevice Remove-VAIOFilter Remove-VApp Remove-VDPortGroup Remove-VDSwitch Remove-VDSwitchPhysicalNetworkAdapter Remove-VDSwitchPrivateVlan Remove-VDSwitchVMHost Remove-VDisk Remove-VICredentialStoreItem Remove-VIPermission Remove-VIProperty Remove-VIRole Remove-VM Remove-VMHost Remove-VMHostAccount Remove-VMHostNetworkAdapter Remove-VMHostNtpServer Remove-VMHostProfile Remove-VMHostProfileVmPortGroupConfiguration Remove-VMHostRoute Remove-VTpm Remove-VasaProvider Remove-VirtualPortGroup Remove-VirtualSwitch Remove-VirtualSwitchPhysicalNetworkAdapter Remove-VsanDisk Remove-VsanDiskGroup Remove-VsanFaultDomain Remove-VsanIscsiInitiatorGroup Remove-VsanIscsiInitiatorGroupTargetAssociation Remove-VsanIscsiLun Remove-VsanIscsiTarget Remove-vRABusinessGroup Remove-vRACustomForm Remove-vRAExternalNetworkProfile Remove-vRAGroupPrincipal Remove-vRAIcon Remove-vRANATNetworkProfile Remove-vRAPackage Remove-vRAPrincipalFromTenantRole Remove-vRAPropertyDefinition Remove-vRAPropertyGroup Remove-vRAReservation Remove-vRAReservationNetwork Remove-vRAReservationPolicy Remove-vRAReservationStorage Remove-vRARoutedNetworkProfile Remove-vRAService Remove-vRAStorageReservationPolicy Remove-vRATenant Remove-vRATenantDirectory Remove-vRAUserPrincipal Remove-vRNIApplication Remove-vRNIApplicationTier Remove-vRNIDataSource Repair-NsxEdge Repair-VsanObject Request-vRACatalogItem Request-vRAResourceAction Restart-CIVApp Restart-CIVAppGuest Restart-CIVM Restart-CIVMGuest Restart-VM Restart-VMGuest Restart-VMHost Restart-VMHostService Resume-HCXReplication Revoke-NsxSpoofguardNicApproval Save-Module Save-Package Save-Script Search-Cloud Set-AdvancedSetting Set-AlarmDefinition Set-Annotation Set-CDDrive Set-CIAccessControlRule Set-CINetworkAdapter Set-CIVApp Set-CIVAppNetwork Set-CIVAppStartRule Set-CIVAppTemplate Set-Cluster Set-CustomAttribute Set-Datacenter Set-Datastore Set-DatastoreCluster Set-DrsClusterGroup Set-DrsRule Set-DrsVMHostRule Set-FloppyDrive Set-Folder Set-HCXAppliance Set-HCXMigration Set-HCXReplication Set-HardDisk Set-IScsiHbaTarget Set-KeyManagementServer Set-KmsCluster Set-MarkdownOption Set-NetworkAdapter Set-NfsUser Set-NicTeamingPolicy Set-NodeExclusiveResources Set-NodeManager Set-NodeResourceSource Set-NodeResources Set-NsxEdge Set-NsxEdgeBgp Set-NsxEdgeFirewall Set-NsxEdgeInterface Set-NsxEdgeNat Set-NsxEdgeOspf Set-NsxEdgeRouting Set-NsxFirewallGlobalConfiguration Set-NsxFirewallRule Set-NsxFirewallSavedConfiguration Set-NsxFirewallThreshold Set-NsxLoadBalancer Set-NsxLoadBalancerPoolMember Set-NsxLogicalRouter Set-NsxLogicalRouterBgp Set-NsxLogicalRouterBridging Set-NsxLogicalRouterInterface Set-NsxLogicalRouterOspf Set-NsxLogicalRouterRouting Set-NsxManager Set-NsxManagerRole Set-NsxManagerTimeSettings Set-NsxSecurityPolicy Set-NsxSecurityPolicyFirewallRule Set-NsxSslVpn Set-OSCustomizationNicMapping Set-OSCustomizationSpec Set-Org Set-OrgNetwork Set-OrgVdc Set-OrgVdcNetwork Set-PSCurrentConfigurationNode Set-PSDefaultConfigurationDocument Set-PSMetaConfigDocInsProcessedBeforeMeta Set-PSMetaConfigVersionInfoV2 Set-PSReadLineKeyHandler Set-PSReadLineOption Set-PSRepository Set-PSTopConfigurationName Set-PackageSource Set-PowerCLIConfiguration Set-ResourcePool Set-ScsiController Set-ScsiLun Set-ScsiLunPath Set-SecurityPolicy Set-Snapshot Set-SpbmEntityConfiguration Set-SpbmStoragePolicy Set-StatInterval Set-Tag Set-TagCategory Set-Template Set-VAIOFilter Set-VApp Set-VDBlockedPolicy Set-VDPort Set-VDPortgroup Set-VDPortgroupOverridePolicy Set-VDSecurityPolicy Set-VDSwitch Set-VDTrafficShapingPolicy Set-VDUplinkLacpPolicy Set-VDUplinkTeamingPolicy Set-VDVlanConfiguration Set-VDisk Set-VIPermission Set-VIRole Set-VM Set-VMHost Set-VMHostAccount Set-VMHostAdvancedConfiguration Set-VMHostAuthentication Set-VMHostDiagnosticPartition Set-VMHostFirewallDefaultPolicy Set-VMHostFirewallException Set-VMHostFirmware Set-VMHostHba Set-VMHostModule Set-VMHostNetwork Set-VMHostNetworkAdapter Set-VMHostProfile Set-VMHostProfileImageCacheConfiguration Set-VMHostProfileStorageDeviceConfiguration Set-VMHostProfileUserConfiguration Set-VMHostProfileVmPortGroupConfiguration Set-VMHostRoute Set-VMHostService Set-VMHostSnmp Set-VMHostStartPolicy Set-VMHostStorage Set-VMHostSysLogServer Set-VMQuestion Set-VMResourceConfiguration Set-VMStartPolicy Set-VTpm Set-VirtualPortGroup Set-VirtualSwitch Set-VsanClusterConfiguration Set-VsanFaultDomain Set-VsanIscsiInitiatorGroup Set-VsanIscsiLun Set-VsanIscsiTarget Set-vRABusinessGroup Set-vRACatalogItem Set-vRACustomForm Set-vRAEntitlement Set-vRAExternalNetworkProfile Set-vRANATNetworkProfile Set-vRAReservation Set-vRAReservationNetwork Set-vRAReservationPolicy Set-vRAReservationStorage Set-vRARoutedNetworkProfile Set-vRAService 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diag_fpsMin diag_frameNo diag_lightNewLoad diag_list diag_log diag_logSlowFrame diag_mergeConfigFile diag_recordTurretLimits diag_setLightNew diag_tickTime diag_toggle dialog diarySubjectExists didJIP didJIPOwner difficulty difficultyEnabled difficultyEnabledRTD difficultyOption direction directSay disableAI disableCollisionWith disableConversation disableDebriefingStats disableMapIndicators disableNVGEquipment disableRemoteSensors disableSerialization disableTIEquipment disableUAVConnectability disableUserInput displayAddEventHandler displayCtrl displayParent displayRemoveAllEventHandlers displayRemoveEventHandler displaySetEventHandler dissolveTeam distance distance2D distanceSqr distributionRegion do3DENAction doArtilleryFire doFire doFollow doFSM doGetOut doMove doorPhase doStop doSuppressiveFire doTarget doWatch drawArrow drawEllipse drawIcon drawIcon3D drawLine drawLine3D drawLink drawLocation drawPolygon drawRectangle drawTriangle driver drop dynamicSimulationDistance dynamicSimulationDistanceCoef dynamicSimulationEnabled dynamicSimulationSystemEnabled echo edit3DENMissionAttributes editObject editorSetEventHandler effectiveCommander emptyPositions enableAI enableAIFeature enableAimPrecision enableAttack enableAudioFeature enableAutoStartUpRTD enableAutoTrimRTD enableCamShake enableCaustics enableChannel enableCollisionWith enableCopilot enableDebriefingStats enableDiagLegend enableDynamicSimulation enableDynamicSimulationSystem enableEndDialog enableEngineArtillery enableEnvironment enableFatigue enableGunLights enableInfoPanelComponent enableIRLasers enableMimics enablePersonTurret enableRadio enableReload enableRopeAttach enableSatNormalOnDetail enableSaving enableSentences enableSimulation enableSimulationGlobal enableStamina enableTeamSwitch enableTraffic enableUAVConnectability enableUAVWaypoints enableVehicleCargo enableVehicleSensor enableWeaponDisassembly endLoadingScreen endMission engineOn enginesIsOnRTD enginesRpmRTD enginesTorqueRTD entities environmentEnabled estimatedEndServerTime estimatedTimeLeft evalObjectArgument everyBackpack everyContainer exec execEditorScript execFSM execVM exp expectedDestination exportJIPMessages eyeDirection eyePos face faction fadeMusic fadeRadio fadeSound fadeSpeech failMission fillWeaponsFromPool find findCover findDisplay findEditorObject findEmptyPosition findEmptyPositionReady findIf findNearestEnemy finishMissionInit finite fire fireAtTarget firstBackpack flag flagAnimationPhase flagOwner flagSide flagTexture fleeing floor flyInHeight flyInHeightASL fog fogForecast fogParams forceAddUniform forcedMap forceEnd forceFlagTexture forceFollowRoad forceMap forceRespawn forceSpeed forceWalk forceWeaponFire forceWeatherChange forEachMember forEachMemberAgent forEachMemberTeam forgetTarget format formation formationDirection formationLeader formationMembers formationPosition formationTask formatText formLeader freeLook fromEditor fuel fullCrew gearIDCAmmoCount gearSlotAmmoCount 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magazinesAllTurrets magazinesAmmo magazinesAmmoCargo magazinesAmmoFull magazinesDetail magazinesDetailBackpack magazinesDetailUniform magazinesDetailVest magazinesTurret magazineTurretAmmo mapAnimAdd mapAnimClear mapAnimCommit mapAnimDone mapCenterOnCamera mapGridPosition markAsFinishedOnSteam markerAlpha markerBrush markerColor markerDir markerPos markerShape markerSize markerText markerType max members menuAction menuAdd menuChecked menuClear menuCollapse menuData menuDelete menuEnable menuEnabled menuExpand menuHover menuPicture menuSetAction menuSetCheck menuSetData menuSetPicture menuSetValue menuShortcut menuShortcutText menuSize menuSort menuText menuURL menuValue min mineActive mineDetectedBy missionConfigFile missionDifficulty missionName missionNamespace missionStart missionVersion mod modelToWorld modelToWorldVisual modelToWorldVisualWorld modelToWorldWorld modParams moonIntensity moonPhase morale move move3DENCamera moveInAny moveInCargo moveInCommander moveInDriver moveInGunner moveInTurret moveObjectToEnd moveOut moveTime moveTo moveToCompleted moveToFailed musicVolume name nameSound nearEntities nearestBuilding nearestLocation nearestLocations nearestLocationWithDubbing nearestObject nearestObjects nearestTerrainObjects nearObjects nearObjectsReady nearRoads nearSupplies nearTargets needReload netId netObjNull newOverlay nextMenuItemIndex nextWeatherChange nMenuItems not numberOfEnginesRTD numberToDate objectCurators objectFromNetId objectParent objStatus onBriefingGroup onBriefingNotes onBriefingPlan onBriefingTeamSwitch onCommandModeChanged onDoubleClick onEachFrame onGroupIconClick onGroupIconOverEnter onGroupIconOverLeave onHCGroupSelectionChanged onMapSingleClick onPlayerConnected onPlayerDisconnected onPreloadFinished onPreloadStarted onShowNewObject onTeamSwitch openCuratorInterface openDLCPage openMap openSteamApp openYoutubeVideo or orderGetIn overcast overcastForecast owner param params parseNumber parseSimpleArray parseText parsingNamespace particlesQuality pickWeaponPool pitch pixelGrid pixelGridBase pixelGridNoUIScale pixelH pixelW playableSlotsNumber playableUnits playAction playActionNow player playerRespawnTime playerSide playersNumber playGesture playMission playMove playMoveNow playMusic playScriptedMission playSound playSound3D position positionCameraToWorld posScreenToWorld posWorldToScreen ppEffectAdjust ppEffectCommit ppEffectCommitted ppEffectCreate ppEffectDestroy ppEffectEnable ppEffectEnabled ppEffectForceInNVG precision preloadCamera preloadObject preloadSound preloadTitleObj preloadTitleRsc preprocessFile preprocessFileLineNumbers primaryWeapon primaryWeaponItems primaryWeaponMagazine priority processDiaryLink productVersion profileName profileNamespace profileNameSteam progressLoadingScreen progressPosition progressSetPosition publicVariable publicVariableClient publicVariableServer pushBack pushBackUnique putWeaponPool queryItemsPool queryMagazinePool queryWeaponPool rad radioChannelAdd radioChannelCreate radioChannelRemove radioChannelSetCallSign radioChannelSetLabel radioVolume rain rainbow random rank rankId rating rectangular registeredTasks registerTask reload reloadEnabled remoteControl remoteExec remoteExecCall remoteExecutedOwner remove3DENConnection remove3DENEventHandler remove3DENLayer removeAction removeAll3DENEventHandlers removeAllActions removeAllAssignedItems removeAllContainers removeAllCuratorAddons removeAllCuratorCameraAreas removeAllCuratorEditingAreas removeAllEventHandlers removeAllHandgunItems removeAllItems removeAllItemsWithMagazines removeAllMissionEventHandlers removeAllMPEventHandlers removeAllMusicEventHandlers removeAllOwnedMines removeAllPrimaryWeaponItems removeAllWeapons removeBackpack removeBackpackGlobal removeCuratorAddons removeCuratorCameraArea removeCuratorEditableObjects removeCuratorEditingArea removeDrawIcon removeDrawLinks removeEventHandler removeFromRemainsCollector removeGoggles removeGroupIcon removeHandgunItem removeHeadgear removeItem removeItemFromBackpack removeItemFromUniform removeItemFromVest removeItems removeMagazine removeMagazineGlobal removeMagazines removeMagazinesTurret removeMagazineTurret removeMenuItem removeMissionEventHandler removeMPEventHandler removeMusicEventHandler removeOwnedMine removePrimaryWeaponItem removeSecondaryWeaponItem removeSimpleTask removeSwitchableUnit removeTeamMember removeUniform removeVest removeWeapon removeWeaponAttachmentCargo removeWeaponCargo removeWeaponGlobal removeWeaponTurret reportRemoteTarget requiredVersion resetCamShake resetSubgroupDirection resize resources respawnVehicle restartEditorCamera reveal revealMine reverse reversedMouseY roadAt roadsConnectedTo roleDescription ropeAttachedObjects ropeAttachedTo ropeAttachEnabled ropeAttachTo ropeCreate ropeCut ropeDestroy ropeDetach ropeEndPosition ropeLength ropes ropeUnwind ropeUnwound rotorsForcesRTD rotorsRpmRTD round runInitScript safeZoneH safeZoneW safeZoneWAbs safeZoneX safeZoneXAbs 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setObjectTexture setObjectTextureGlobal setObjectViewDistance setOvercast setOwner setOxygenRemaining setParticleCircle setParticleClass setParticleFire setParticleParams setParticleRandom setPilotCameraDirection setPilotCameraRotation setPilotCameraTarget setPilotLight setPiPEffect setPitch setPlateNumber setPlayable setPlayerRespawnTime setPos setPosASL setPosASL2 setPosASLW setPosATL setPosition setPosWorld setPylonLoadOut setPylonsPriority setRadioMsg setRain setRainbow setRandomLip setRank setRectangular setRepairCargo setRotorBrakeRTD setShadowDistance setShotParents setSide setSimpleTaskAlwaysVisible setSimpleTaskCustomData setSimpleTaskDescription setSimpleTaskDestination setSimpleTaskTarget setSimpleTaskType setSimulWeatherLayers setSize setSkill setSlingLoad setSoundEffect setSpeaker setSpeech setSpeedMode setStamina setStaminaScheme setStatValue setSuppression setSystemOfUnits setTargetAge setTaskMarkerOffset setTaskResult setTaskState setTerrainGrid setText setTimeMultiplier setTitleEffect setTrafficDensity setTrafficDistance setTrafficGap setTrafficSpeed setTriggerActivation setTriggerArea setTriggerStatements setTriggerText setTriggerTimeout setTriggerType setType setUnconscious setUnitAbility setUnitLoadout setUnitPos setUnitPosWeak setUnitRank setUnitRecoilCoefficient setUnitTrait setUnloadInCombat setUserActionText setUserMFDText setUserMFDvalue setVariable setVectorDir setVectorDirAndUp setVectorUp setVehicleAmmo setVehicleAmmoDef setVehicleArmor setVehicleCargo setVehicleId setVehicleLock setVehiclePosition setVehicleRadar setVehicleReceiveRemoteTargets setVehicleReportOwnPosition setVehicleReportRemoteTargets setVehicleTIPars setVehicleVarName setVelocity setVelocityModelSpace setVelocityTransformation setViewDistance setVisibleIfTreeCollapsed setWantedRPMRTD setWaves setWaypointBehaviour setWaypointCombatMode setWaypointCompletionRadius setWaypointDescription setWaypointForceBehaviour setWaypointFormation setWaypointHousePosition setWaypointLoiterRadius setWaypointLoiterType setWaypointName setWaypointPosition setWaypointScript setWaypointSpeed setWaypointStatements setWaypointTimeout setWaypointType setWaypointVisible setWeaponReloadingTime setWind setWindDir setWindForce setWindStr setWingForceScaleRTD setWPPos show3DIcons showChat showCinemaBorder showCommandingMenu showCompass showCuratorCompass showGPS showHUD showLegend showMap shownArtilleryComputer shownChat shownCompass shownCuratorCompass showNewEditorObject shownGPS shownHUD shownMap shownPad shownRadio shownScoretable shownUAVFeed shownWarrant shownWatch showPad showRadio showScoretable showSubtitles showUAVFeed showWarrant showWatch showWaypoint showWaypoints side sideChat sideEnemy sideFriendly sideRadio simpleTasks simulationEnabled simulCloudDensity simulCloudOcclusion simulInClouds simulWeatherSync sin size sizeOf skill skillFinal skipTime sleep sliderPosition sliderRange sliderSetPosition sliderSetRange sliderSetSpeed sliderSpeed slingLoadAssistantShown soldierMagazines someAmmo sort soundVolume spawn speaker speed speedMode splitString sqrt squadParams stance startLoadingScreen step stop stopEngineRTD stopped str sunOrMoon supportInfo suppressFor surfaceIsWater surfaceNormal surfaceType swimInDepth switchableUnits switchAction switchCamera switchGesture switchLight switchMove synchronizedObjects synchronizedTriggers synchronizedWaypoints synchronizeObjectsAdd synchronizeObjectsRemove synchronizeTrigger synchronizeWaypoint systemChat systemOfUnits tan targetKnowledge targets targetsAggregate targetsQuery taskAlwaysVisible taskChildren taskCompleted taskCustomData taskDescription taskDestination taskHint taskMarkerOffset taskParent taskResult taskState taskType teamMember teamName teams teamSwitch teamSwitchEnabled teamType terminate terrainIntersect terrainIntersectASL terrainIntersectAtASL text textLog textLogFormat tg time timeMultiplier titleCut titleFadeOut titleObj titleRsc titleText toArray toFixed 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physics_particle_delete_region_circle physics_particle_delete_region_box physics_particle_delete_region_poly physics_particle_set_flags physics_particle_set_category_flags physics_particle_draw physics_particle_draw_ext physics_particle_count physics_particle_get_data physics_particle_get_data_particle physics_particle_group_begin physics_particle_group_circle physics_particle_group_box physics_particle_group_polygon physics_particle_group_add_point physics_particle_group_end physics_particle_group_join physics_particle_group_delete physics_particle_group_count physics_particle_group_get_data physics_particle_group_get_mass physics_particle_group_get_inertia physics_particle_group_get_centre_x physics_particle_group_get_centre_y physics_particle_group_get_vel_x physics_particle_group_get_vel_y physics_particle_group_get_ang_vel physics_particle_group_get_x physics_particle_group_get_y physics_particle_group_get_angle physics_particle_set_group_flags physics_particle_get_group_flags physics_particle_get_max_count physics_particle_get_radius physics_particle_get_density physics_particle_get_damping physics_particle_get_gravity_scale physics_particle_set_max_count physics_particle_set_radius physics_particle_set_density physics_particle_set_damping physics_particle_set_gravity_scale network_create_socket network_create_socket_ext network_create_server network_create_server_raw network_connect network_connect_raw network_send_packet network_send_raw network_send_broadcast network_send_udp network_send_udp_raw network_set_timeout network_set_config network_resolve network_destroy buffer_create buffer_write buffer_read buffer_seek buffer_get_surface buffer_set_surface buffer_delete buffer_exists buffer_get_type buffer_get_alignment buffer_poke buffer_peek buffer_save buffer_save_ext buffer_load buffer_load_ext buffer_load_partial buffer_copy buffer_fill buffer_get_size buffer_tell buffer_resize buffer_md5 buffer_sha1 buffer_base64_encode buffer_base64_decode buffer_base64_decode_ext buffer_sizeof buffer_get_address buffer_create_from_vertex_buffer buffer_create_from_vertex_buffer_ext buffer_copy_from_vertex_buffer buffer_async_group_begin buffer_async_group_option buffer_async_group_end buffer_load_async buffer_save_async gml_release_mode gml_pragma steam_activate_overlay steam_is_overlay_enabled steam_is_overlay_activated steam_get_persona_name steam_initialised steam_is_cloud_enabled_for_app steam_is_cloud_enabled_for_account steam_file_persisted steam_get_quota_total steam_get_quota_free steam_file_write steam_file_write_file steam_file_read steam_file_delete steam_file_exists steam_file_size steam_file_share steam_is_screenshot_requested steam_send_screenshot steam_is_user_logged_on steam_get_user_steam_id steam_user_owns_dlc steam_user_installed_dlc steam_set_achievement steam_get_achievement steam_clear_achievement steam_set_stat_int steam_set_stat_float steam_set_stat_avg_rate steam_get_stat_int steam_get_stat_float steam_get_stat_avg_rate steam_reset_all_stats steam_reset_all_stats_achievements steam_stats_ready steam_create_leaderboard steam_upload_score steam_upload_score_ext steam_download_scores_around_user steam_download_scores steam_download_friends_scores steam_upload_score_buffer steam_upload_score_buffer_ext steam_current_game_language steam_available_languages steam_activate_overlay_browser steam_activate_overlay_user steam_activate_overlay_store steam_get_user_persona_name steam_get_app_id steam_get_user_account_id steam_ugc_download steam_ugc_create_item steam_ugc_start_item_update steam_ugc_set_item_title steam_ugc_set_item_description steam_ugc_set_item_visibility steam_ugc_set_item_tags steam_ugc_set_item_content steam_ugc_set_item_preview steam_ugc_submit_item_update steam_ugc_get_item_update_progress steam_ugc_subscribe_item steam_ugc_unsubscribe_item steam_ugc_num_subscribed_items steam_ugc_get_subscribed_items steam_ugc_get_item_install_info steam_ugc_get_item_update_info steam_ugc_request_item_details steam_ugc_create_query_user steam_ugc_create_query_user_ex steam_ugc_create_query_all steam_ugc_create_query_all_ex steam_ugc_query_set_cloud_filename_filter steam_ugc_query_set_match_any_tag steam_ugc_query_set_search_text steam_ugc_query_set_ranked_by_trend_days steam_ugc_query_add_required_tag steam_ugc_query_add_excluded_tag steam_ugc_query_set_return_long_description steam_ugc_query_set_return_total_only steam_ugc_query_set_allow_cached_response steam_ugc_send_query shader_set shader_get_name shader_reset shader_current shader_is_compiled shader_get_sampler_index shader_get_uniform shader_set_uniform_i shader_set_uniform_i_array shader_set_uniform_f shader_set_uniform_f_array shader_set_uniform_matrix shader_set_uniform_matrix_array shader_enable_corner_id texture_set_stage texture_get_texel_width texture_get_texel_height shaders_are_supported vertex_format_begin vertex_format_end vertex_format_delete vertex_format_add_position vertex_format_add_position_3d vertex_format_add_colour vertex_format_add_color vertex_format_add_normal vertex_format_add_texcoord vertex_format_add_textcoord vertex_format_add_custom vertex_create_buffer vertex_create_buffer_ext vertex_delete_buffer vertex_begin vertex_end vertex_position vertex_position_3d vertex_colour vertex_color vertex_argb vertex_texcoord vertex_normal vertex_float1 vertex_float2 vertex_float3 vertex_float4 vertex_ubyte4 vertex_submit vertex_freeze vertex_get_number vertex_get_buffer_size vertex_create_buffer_from_buffer vertex_create_buffer_from_buffer_ext push_local_notification push_get_first_local_notification push_get_next_local_notification push_cancel_local_notification skeleton_animation_set skeleton_animation_get skeleton_animation_mix skeleton_animation_set_ext skeleton_animation_get_ext skeleton_animation_get_duration skeleton_animation_get_frames skeleton_animation_clear skeleton_skin_set skeleton_skin_get skeleton_attachment_set skeleton_attachment_get skeleton_attachment_create skeleton_collision_draw_set skeleton_bone_data_get skeleton_bone_data_set skeleton_bone_state_get skeleton_bone_state_set skeleton_get_minmax skeleton_get_num_bounds skeleton_get_bounds skeleton_animation_get_frame skeleton_animation_set_frame draw_skeleton draw_skeleton_time draw_skeleton_instance draw_skeleton_collision skeleton_animation_list skeleton_skin_list skeleton_slot_data layer_get_id layer_get_id_at_depth layer_get_depth layer_create layer_destroy layer_destroy_instances layer_add_instance layer_has_instance layer_set_visible layer_get_visible layer_exists layer_x layer_y layer_get_x layer_get_y layer_hspeed layer_vspeed layer_get_hspeed layer_get_vspeed layer_script_begin layer_script_end layer_shader layer_get_script_begin layer_get_script_end layer_get_shader layer_set_target_room layer_get_target_room layer_reset_target_room layer_get_all layer_get_all_elements layer_get_name layer_depth layer_get_element_layer layer_get_element_type layer_element_move layer_force_draw_depth layer_is_draw_depth_forced layer_get_forced_depth layer_background_get_id layer_background_exists layer_background_create layer_background_destroy layer_background_visible layer_background_change layer_background_sprite layer_background_htiled layer_background_vtiled layer_background_stretch layer_background_yscale layer_background_xscale layer_background_blend layer_background_alpha layer_background_index layer_background_speed layer_background_get_visible layer_background_get_sprite layer_background_get_htiled layer_background_get_vtiled layer_background_get_stretch layer_background_get_yscale layer_background_get_xscale layer_background_get_blend layer_background_get_alpha layer_background_get_index layer_background_get_speed layer_sprite_get_id layer_sprite_exists layer_sprite_create layer_sprite_destroy layer_sprite_change layer_sprite_index layer_sprite_speed layer_sprite_xscale layer_sprite_yscale layer_sprite_angle layer_sprite_blend layer_sprite_alpha layer_sprite_x layer_sprite_y layer_sprite_get_sprite layer_sprite_get_index layer_sprite_get_speed layer_sprite_get_xscale layer_sprite_get_yscale layer_sprite_get_angle layer_sprite_get_blend layer_sprite_get_alpha layer_sprite_get_x layer_sprite_get_y layer_tilemap_get_id layer_tilemap_exists layer_tilemap_create layer_tilemap_destroy tilemap_tileset tilemap_x tilemap_y tilemap_set tilemap_set_at_pixel tilemap_get_tileset tilemap_get_tile_width tilemap_get_tile_height tilemap_get_width tilemap_get_height tilemap_get_x tilemap_get_y tilemap_get tilemap_get_at_pixel tilemap_get_cell_x_at_pixel tilemap_get_cell_y_at_pixel tilemap_clear draw_tilemap draw_tile tilemap_set_global_mask tilemap_get_global_mask tilemap_set_mask tilemap_get_mask tilemap_get_frame tile_set_empty tile_set_index tile_set_flip tile_set_mirror tile_set_rotate tile_get_empty tile_get_index tile_get_flip tile_get_mirror tile_get_rotate layer_tile_exists layer_tile_create layer_tile_destroy layer_tile_change layer_tile_xscale layer_tile_yscale layer_tile_blend layer_tile_alpha layer_tile_x layer_tile_y layer_tile_region layer_tile_visible layer_tile_get_sprite layer_tile_get_xscale layer_tile_get_yscale layer_tile_get_blend layer_tile_get_alpha layer_tile_get_x layer_tile_get_y layer_tile_get_region layer_tile_get_visible layer_instance_get_instance instance_activate_layer instance_deactivate_layer camera_create camera_create_view camera_destroy camera_apply camera_get_active camera_get_default camera_set_default camera_set_view_mat camera_set_proj_mat camera_set_update_script camera_set_begin_script camera_set_end_script camera_set_view_pos camera_set_view_size camera_set_view_speed camera_set_view_border camera_set_view_angle camera_set_view_target camera_get_view_mat camera_get_proj_mat camera_get_update_script camera_get_begin_script camera_get_end_script camera_get_view_x camera_get_view_y camera_get_view_width camera_get_view_height camera_get_view_speed_x camera_get_view_speed_y camera_get_view_border_x camera_get_view_border_y camera_get_view_angle camera_get_view_target view_get_camera view_get_visible view_get_xport view_get_yport view_get_wport view_get_hport view_get_surface_id view_set_camera view_set_visible view_set_xport view_set_yport view_set_wport view_set_hport view_set_surface_id gesture_drag_time gesture_drag_distance gesture_flick_speed gesture_double_tap_time gesture_double_tap_distance gesture_pinch_distance gesture_pinch_angle_towards gesture_pinch_angle_away gesture_rotate_time gesture_rotate_angle gesture_tap_count gesture_get_drag_time gesture_get_drag_distance gesture_get_flick_speed gesture_get_double_tap_time gesture_get_double_tap_distance gesture_get_pinch_distance gesture_get_pinch_angle_towards gesture_get_pinch_angle_away gesture_get_rotate_time gesture_get_rotate_angle gesture_get_tap_count keyboard_virtual_show keyboard_virtual_hide keyboard_virtual_status keyboard_virtual_height",literal:"self other all noone global local undefined pointer_invalid pointer_null path_action_stop path_action_restart path_action_continue path_action_reverse true false pi GM_build_date GM_version GM_runtime_version  timezone_local timezone_utc gamespeed_fps gamespeed_microseconds  ev_create ev_destroy ev_step ev_alarm ev_keyboard ev_mouse ev_collision ev_other ev_draw ev_draw_begin ev_draw_end ev_draw_pre ev_draw_post ev_keypress ev_keyrelease ev_trigger ev_left_button ev_right_button ev_middle_button ev_no_button ev_left_press ev_right_press ev_middle_press ev_left_release ev_right_release ev_middle_release ev_mouse_enter ev_mouse_leave ev_mouse_wheel_up ev_mouse_wheel_down ev_global_left_button ev_global_right_button ev_global_middle_button ev_global_left_press ev_global_right_press ev_global_middle_press ev_global_left_release ev_global_right_release ev_global_middle_release ev_joystick1_left ev_joystick1_right ev_joystick1_up ev_joystick1_down ev_joystick1_button1 ev_joystick1_button2 ev_joystick1_button3 ev_joystick1_button4 ev_joystick1_button5 ev_joystick1_button6 ev_joystick1_button7 ev_joystick1_button8 ev_joystick2_left ev_joystick2_right ev_joystick2_up ev_joystick2_down ev_joystick2_button1 ev_joystick2_button2 ev_joystick2_button3 ev_joystick2_button4 ev_joystick2_button5 ev_joystick2_button6 ev_joystick2_button7 ev_joystick2_button8 ev_outside ev_boundary ev_game_start ev_game_end ev_room_start ev_room_end ev_no_more_lives ev_animation_end ev_end_of_path ev_no_more_health ev_close_button ev_user0 ev_user1 ev_user2 ev_user3 ev_user4 ev_user5 ev_user6 ev_user7 ev_user8 ev_user9 ev_user10 ev_user11 ev_user12 ev_user13 ev_user14 ev_user15 ev_step_normal ev_step_begin ev_step_end ev_gui ev_gui_begin ev_gui_end ev_cleanup ev_gesture ev_gesture_tap ev_gesture_double_tap ev_gesture_drag_start ev_gesture_dragging ev_gesture_drag_end ev_gesture_flick ev_gesture_pinch_start ev_gesture_pinch_in ev_gesture_pinch_out ev_gesture_pinch_end ev_gesture_rotate_start ev_gesture_rotating ev_gesture_rotate_end ev_global_gesture_tap ev_global_gesture_double_tap ev_global_gesture_drag_start ev_global_gesture_dragging ev_global_gesture_drag_end ev_global_gesture_flick ev_global_gesture_pinch_start ev_global_gesture_pinch_in ev_global_gesture_pinch_out ev_global_gesture_pinch_end ev_global_gesture_rotate_start ev_global_gesture_rotating ev_global_gesture_rotate_end vk_nokey vk_anykey vk_enter vk_return vk_shift vk_control vk_alt vk_escape vk_space vk_backspace vk_tab vk_pause vk_printscreen vk_left vk_right vk_up vk_down vk_home vk_end vk_delete vk_insert vk_pageup vk_pagedown vk_f1 vk_f2 vk_f3 vk_f4 vk_f5 vk_f6 vk_f7 vk_f8 vk_f9 vk_f10 vk_f11 vk_f12 vk_numpad0 vk_numpad1 vk_numpad2 vk_numpad3 vk_numpad4 vk_numpad5 vk_numpad6 vk_numpad7 vk_numpad8 vk_numpad9 vk_divide vk_multiply vk_subtract vk_add vk_decimal vk_lshift vk_lcontrol vk_lalt vk_rshift vk_rcontrol vk_ralt  mb_any mb_none mb_left mb_right mb_middle c_aqua c_black c_blue c_dkgray c_fuchsia c_gray c_green c_lime c_ltgray c_maroon c_navy c_olive c_purple c_red c_silver c_teal c_white c_yellow c_orange fa_left fa_center fa_right fa_top fa_middle fa_bottom pr_pointlist pr_linelist pr_linestrip pr_trianglelist pr_trianglestrip pr_trianglefan bm_complex bm_normal bm_add bm_max bm_subtract bm_zero bm_one bm_src_colour bm_inv_src_colour bm_src_color bm_inv_src_color bm_src_alpha bm_inv_src_alpha bm_dest_alpha bm_inv_dest_alpha bm_dest_colour bm_inv_dest_colour bm_dest_color bm_inv_dest_color bm_src_alpha_sat tf_point tf_linear tf_anisotropic mip_off mip_on mip_markedonly audio_falloff_none audio_falloff_inverse_distance audio_falloff_inverse_distance_clamped audio_falloff_linear_distance audio_falloff_linear_distance_clamped audio_falloff_exponent_distance audio_falloff_exponent_distance_clamped audio_old_system audio_new_system audio_mono audio_stereo audio_3d cr_default cr_none cr_arrow cr_cross cr_beam cr_size_nesw cr_size_ns cr_size_nwse cr_size_we cr_uparrow cr_hourglass cr_drag cr_appstart cr_handpoint cr_size_all spritespeed_framespersecond spritespeed_framespergameframe asset_object asset_unknown asset_sprite asset_sound asset_room asset_path asset_script asset_font asset_timeline asset_tiles asset_shader fa_readonly fa_hidden fa_sysfile fa_volumeid fa_directory fa_archive  ds_type_map ds_type_list ds_type_stack ds_type_queue ds_type_grid ds_type_priority ef_explosion ef_ring ef_ellipse ef_firework ef_smoke ef_smokeup ef_star ef_spark ef_flare ef_cloud ef_rain ef_snow pt_shape_pixel pt_shape_disk pt_shape_square pt_shape_line pt_shape_star pt_shape_circle pt_shape_ring pt_shape_sphere pt_shape_flare pt_shape_spark pt_shape_explosion pt_shape_cloud pt_shape_smoke pt_shape_snow ps_distr_linear ps_distr_gaussian ps_distr_invgaussian ps_shape_rectangle ps_shape_ellipse ps_shape_diamond ps_shape_line ty_real ty_string dll_cdecl dll_stdcall matrix_view matrix_projection matrix_world os_win32 os_windows os_macosx os_ios os_android os_symbian os_linux os_unknown os_winphone os_tizen os_win8native os_wiiu os_3ds  os_psvita os_bb10 os_ps4 os_xboxone os_ps3 os_xbox360 os_uwp os_tvos os_switch browser_not_a_browser browser_unknown browser_ie browser_firefox browser_chrome browser_safari browser_safari_mobile browser_opera browser_tizen browser_edge browser_windows_store browser_ie_mobile  device_ios_unknown device_ios_iphone device_ios_iphone_retina device_ios_ipad device_ios_ipad_retina device_ios_iphone5 device_ios_iphone6 device_ios_iphone6plus device_emulator device_tablet display_landscape display_landscape_flipped display_portrait display_portrait_flipped tm_sleep tm_countvsyncs of_challenge_win of_challen ge_lose of_challenge_tie leaderboard_type_number leaderboard_type_time_mins_secs cmpfunc_never cmpfunc_less cmpfunc_equal cmpfunc_lessequal cmpfunc_greater cmpfunc_notequal cmpfunc_greaterequal cmpfunc_always cull_noculling cull_clockwise cull_counterclockwise lighttype_dir lighttype_point iap_ev_storeload iap_ev_product iap_ev_purchase iap_ev_consume iap_ev_restore iap_storeload_ok iap_storeload_failed iap_status_uninitialised iap_status_unavailable iap_status_loading iap_status_available iap_status_processing iap_status_restoring iap_failed iap_unavailable iap_available iap_purchased iap_canceled iap_refunded fb_login_default fb_login_fallback_to_webview fb_login_no_fallback_to_webview fb_login_forcing_webview fb_login_use_system_account fb_login_forcing_safari  phy_joint_anchor_1_x phy_joint_anchor_1_y phy_joint_anchor_2_x phy_joint_anchor_2_y phy_joint_reaction_force_x phy_joint_reaction_force_y phy_joint_reaction_torque phy_joint_motor_speed phy_joint_angle phy_joint_motor_torque phy_joint_max_motor_torque phy_joint_translation phy_joint_speed phy_joint_motor_force phy_joint_max_motor_force phy_joint_length_1 phy_joint_length_2 phy_joint_damping_ratio phy_joint_frequency phy_joint_lower_angle_limit phy_joint_upper_angle_limit phy_joint_angle_limits phy_joint_max_length phy_joint_max_torque phy_joint_max_force phy_debug_render_aabb phy_debug_render_collision_pairs phy_debug_render_coms phy_debug_render_core_shapes phy_debug_render_joints phy_debug_render_obb phy_debug_render_shapes  phy_particle_flag_water phy_particle_flag_zombie phy_particle_flag_wall phy_particle_flag_spring phy_particle_flag_elastic phy_particle_flag_viscous phy_particle_flag_powder phy_particle_flag_tensile phy_particle_flag_colourmixing phy_particle_flag_colormixing phy_particle_group_flag_solid phy_particle_group_flag_rigid phy_particle_data_flag_typeflags phy_particle_data_flag_position phy_particle_data_flag_velocity phy_particle_data_flag_colour phy_particle_data_flag_color phy_particle_data_flag_category  achievement_our_info achievement_friends_info achievement_leaderboard_info achievement_achievement_info achievement_filter_all_players achievement_filter_friends_only achievement_filter_favorites_only achievement_type_achievement_challenge achievement_type_score_challenge achievement_pic_loaded  achievement_show_ui achievement_show_profile achievement_show_leaderboard achievement_show_achievement achievement_show_bank achievement_show_friend_picker achievement_show_purchase_prompt network_socket_tcp network_socket_udp network_socket_bluetooth network_type_connect network_type_disconnect network_type_data network_type_non_blocking_connect network_config_connect_timeout network_config_use_non_blocking_socket network_config_enable_reliable_udp network_config_disable_reliable_udp buffer_fixed buffer_grow buffer_wrap buffer_fast buffer_vbuffer buffer_network buffer_u8 buffer_s8 buffer_u16 buffer_s16 buffer_u32 buffer_s32 buffer_u64 buffer_f16 buffer_f32 buffer_f64 buffer_bool buffer_text buffer_string buffer_surface_copy buffer_seek_start buffer_seek_relative buffer_seek_end buffer_generalerror buffer_outofspace buffer_outofbounds buffer_invalidtype  text_type button_type input_type ANSI_CHARSET DEFAULT_CHARSET EASTEUROPE_CHARSET RUSSIAN_CHARSET SYMBOL_CHARSET SHIFTJIS_CHARSET HANGEUL_CHARSET GB2312_CHARSET CHINESEBIG5_CHARSET JOHAB_CHARSET HEBREW_CHARSET ARABIC_CHARSET GREEK_CHARSET TURKISH_CHARSET VIETNAMESE_CHARSET THAI_CHARSET MAC_CHARSET BALTIC_CHARSET OEM_CHARSET  gp_face1 gp_face2 gp_face3 gp_face4 gp_shoulderl gp_shoulderr gp_shoulderlb gp_shoulderrb gp_select gp_start gp_stickl gp_stickr gp_padu gp_padd gp_padl gp_padr gp_axislh gp_axislv gp_axisrh gp_axisrv ov_friends ov_community ov_players ov_settings ov_gamegroup ov_achievements lb_sort_none lb_sort_ascending lb_sort_descending lb_disp_none lb_disp_numeric lb_disp_time_sec lb_disp_time_ms ugc_result_success ugc_filetype_community ugc_filetype_microtrans ugc_visibility_public ugc_visibility_friends_only ugc_visibility_private ugc_query_RankedByVote ugc_query_RankedByPublicationDate ugc_query_AcceptedForGameRankedByAcceptanceDate ugc_query_RankedByTrend ugc_query_FavoritedByFriendsRankedByPublicationDate 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Add-NodeKeys Add-NsxDynamicCriteria Add-NsxDynamicMemberSet Add-NsxEdgeInterfaceAddress Add-NsxFirewallExclusionListMember Add-NsxFirewallRuleMember Add-NsxIpSetMember Add-NsxLicense Add-NsxLoadBalancerPoolMember Add-NsxLoadBalancerVip Add-NsxSecondaryManager Add-NsxSecurityGroupMember Add-NsxSecurityPolicyRule Add-NsxSecurityPolicyRuleGroup Add-NsxSecurityPolicyRuleService Add-NsxServiceGroupMember Add-NsxTransportZoneMember Add-PassthroughDevice Add-VDSwitchPhysicalNetworkAdapter Add-VDSwitchVMHost Add-VMHost Add-VMHostNtpServer Add-VirtualSwitchPhysicalNetworkAdapter Add-XmlElement Add-vRACustomForm Add-vRAPrincipalToTenantRole Add-vRAReservationNetwork Add-vRAReservationStorage Clear-NsxEdgeInterface Clear-NsxManagerTimeSettings Compress-Archive Connect-CIServer Connect-CisServer Connect-HCXServer Connect-NIServer Connect-NsxLogicalSwitch Connect-NsxServer Connect-NsxtServer Connect-SrmServer Connect-VIServer Connect-Vmc Connect-vRAServer Connect-vRNIServer ConvertFrom-Markdown ConvertTo-MOFInstance Copy-DatastoreItem Copy-HardDisk Copy-NsxEdge Copy-VDisk Copy-VMGuestFile Debug-Runspace Disable-NsxEdgeSsh Disable-RunspaceDebug Disable-vRNIDataSource Disconnect-CIServer Disconnect-CisServer Disconnect-HCXServer Disconnect-NsxLogicalSwitch Disconnect-NsxServer Disconnect-NsxtServer Disconnect-SrmServer Disconnect-VIServer Disconnect-Vmc Disconnect-vRAServer Disconnect-vRNIServer Dismount-Tools Enable-NsxEdgeSsh Enable-RunspaceDebug Enable-vRNIDataSource Expand-Archive Export-NsxObject Export-SpbmStoragePolicy Export-VApp Export-VDPortGroup Export-VDSwitch Export-VMHostProfile Export-vRAIcon Export-vRAPackage Find-Command Find-DscResource Find-Module Find-NsxWhereVMUsed Find-Package Find-PackageProvider Find-RoleCapability Find-Script Format-Hex Format-VMHostDiskPartition Format-XML Generate-VersionInfo Get-AdvancedSetting Get-AlarmAction Get-AlarmActionTrigger Get-AlarmDefinition Get-Annotation Get-CDDrive Get-CIAccessControlRule Get-CIDatastore Get-CINetworkAdapter Get-CIRole Get-CIUser Get-CIVApp Get-CIVAppNetwork Get-CIVAppStartRule Get-CIVAppTemplate Get-CIVM Get-CIVMTemplate Get-CIView Get-Catalog Get-CisCommand Get-CisService Get-CloudCommand Get-Cluster Get-CompatibleVersionAddtionaPropertiesStr Get-ComplexResourceQualifier Get-ConfigurationErrorCount Get-ContentLibraryItem Get-CustomAttribute Get-DSCResourceModules Get-Datacenter Get-Datastore Get-DatastoreCluster Get-DrsClusterGroup Get-DrsRecommendation Get-DrsRule Get-DrsVMHostRule Get-DscResource Get-EdgeGateway Get-EncryptedPassword Get-ErrorReport Get-EsxCli Get-EsxTop Get-ExternalNetwork Get-FileHash Get-FloppyDrive Get-Folder Get-HAPrimaryVMHost Get-HCXAppliance Get-HCXApplianceCompute Get-HCXApplianceDVS Get-HCXApplianceDatastore Get-HCXApplianceNetwork Get-HCXContainer Get-HCXDatastore Get-HCXGateway Get-HCXInterconnectStatus Get-HCXJob Get-HCXMigration Get-HCXNetwork Get-HCXNetworkExtension Get-HCXReplication Get-HCXReplicationSnapshot Get-HCXService Get-HCXSite Get-HCXSitePairing Get-HCXVM Get-HardDisk Get-IScsiHbaTarget Get-InnerMostErrorRecord Get-InstallPath Get-InstalledModule Get-InstalledScript Get-Inventory Get-ItemPropertyValue Get-KeyManagementServer Get-KmipClientCertificate Get-KmsCluster Get-Log Get-LogType Get-MarkdownOption Get-Media Get-MofInstanceName Get-MofInstanceText Get-NetworkAdapter Get-NetworkPool Get-NfsUser Get-NicTeamingPolicy Get-NsxApplicableMember Get-NsxApplicableSecurityAction Get-NsxBackingDVSwitch Get-NsxBackingPortGroup Get-NsxCliDfwAddrSet Get-NsxCliDfwFilter Get-NsxCliDfwRule Get-NsxClusterStatus Get-NsxController Get-NsxDynamicCriteria Get-NsxDynamicMemberSet Get-NsxEdge Get-NsxEdgeBgp Get-NsxEdgeBgpNeighbour Get-NsxEdgeCertificate Get-NsxEdgeCsr Get-NsxEdgeFirewall Get-NsxEdgeFirewallRule Get-NsxEdgeInterface Get-NsxEdgeInterfaceAddress Get-NsxEdgeNat Get-NsxEdgeNatRule Get-NsxEdgeOspf Get-NsxEdgeOspfArea Get-NsxEdgeOspfInterface Get-NsxEdgePrefix Get-NsxEdgeRedistributionRule Get-NsxEdgeRouting Get-NsxEdgeStaticRoute Get-NsxEdgeSubInterface Get-NsxFirewallExclusionListMember Get-NsxFirewallGlobalConfiguration Get-NsxFirewallPublishStatus Get-NsxFirewallRule Get-NsxFirewallRuleMember Get-NsxFirewallSavedConfiguration Get-NsxFirewallSection Get-NsxFirewallThreshold Get-NsxIpPool Get-NsxIpSet Get-NsxLicense Get-NsxLoadBalancer Get-NsxLoadBalancerApplicationProfile Get-NsxLoadBalancerApplicationRule Get-NsxLoadBalancerMonitor Get-NsxLoadBalancerPool Get-NsxLoadBalancerPoolMember Get-NsxLoadBalancerStats Get-NsxLoadBalancerVip Get-NsxLogicalRouter Get-NsxLogicalRouterBgp Get-NsxLogicalRouterBgpNeighbour Get-NsxLogicalRouterBridge Get-NsxLogicalRouterBridging Get-NsxLogicalRouterInterface Get-NsxLogicalRouterOspf Get-NsxLogicalRouterOspfArea Get-NsxLogicalRouterOspfInterface Get-NsxLogicalRouterPrefix Get-NsxLogicalRouterRedistributionRule Get-NsxLogicalRouterRouting Get-NsxLogicalRouterStaticRoute Get-NsxLogicalSwitch Get-NsxMacSet Get-NsxManagerBackup Get-NsxManagerCertificate Get-NsxManagerComponentSummary Get-NsxManagerNetwork Get-NsxManagerRole Get-NsxManagerSsoConfig Get-NsxManagerSyncStatus Get-NsxManagerSyslogServer Get-NsxManagerSystemSummary Get-NsxManagerTimeSettings Get-NsxManagerVcenterConfig Get-NsxSecondaryManager Get-NsxSecurityGroup Get-NsxSecurityGroupEffectiveIpAddress Get-NsxSecurityGroupEffectiveMacAddress Get-NsxSecurityGroupEffectiveMember Get-NsxSecurityGroupEffectiveVirtualMachine Get-NsxSecurityGroupEffectiveVnic Get-NsxSecurityGroupMemberTypes Get-NsxSecurityPolicy Get-NsxSecurityPolicyHighestUsedPrecedence Get-NsxSecurityPolicyRule Get-NsxSecurityTag Get-NsxSecurityTagAssignment Get-NsxSegmentIdRange Get-NsxService Get-NsxServiceDefinition Get-NsxServiceGroup Get-NsxServiceGroupMember Get-NsxServiceProfile Get-NsxSpoofguardNic Get-NsxSpoofguardPolicy Get-NsxSslVpn Get-NsxSslVpnAuthServer Get-NsxSslVpnClientInstallationPackage Get-NsxSslVpnIpPool Get-NsxSslVpnPrivateNetwork Get-NsxSslVpnUser Get-NsxTransportZone Get-NsxUserRole Get-NsxVdsContext Get-NsxtPolicyService Get-NsxtService Get-OSCustomizationNicMapping Get-OSCustomizationSpec Get-Org Get-OrgNetwork Get-OrgVdc Get-OrgVdcNetwork Get-OvfConfiguration Get-PSCurrentConfigurationNode Get-PSDefaultConfigurationDocument Get-PSMetaConfigDocumentInstVersionInfo Get-PSMetaConfigurationProcessed Get-PSReadLineKeyHandler Get-PSReadLineOption Get-PSRepository Get-PSTopConfigurationName Get-PSVersion Get-Package Get-PackageProvider Get-PackageSource Get-PassthroughDevice Get-PositionInfo Get-PowerCLICommunity Get-PowerCLIConfiguration Get-PowerCLIHelp Get-PowerCLIVersion Get-PowerNsxVersion Get-ProviderVdc Get-PublicKeyFromFile Get-PublicKeyFromStore Get-ResourcePool Get-Runspace Get-RunspaceDebug Get-ScsiController Get-ScsiLun Get-ScsiLunPath Get-SecurityInfo Get-SecurityPolicy Get-Snapshot Get-SpbmCapability Get-SpbmCompatibleStorage Get-SpbmEntityConfiguration Get-SpbmFaultDomain Get-SpbmPointInTimeReplica Get-SpbmReplicationGroup Get-SpbmReplicationPair Get-SpbmStoragePolicy Get-Stat Get-StatInterval Get-StatType Get-Tag Get-TagAssignment Get-TagCategory Get-Task Get-Template Get-TimeZone Get-Uptime Get-UsbDevice Get-VAIOFilter Get-VApp Get-VDBlockedPolicy Get-VDPort Get-VDPortgroup Get-VDPortgroupOverridePolicy Get-VDSecurityPolicy Get-VDSwitch Get-VDSwitchPrivateVlan Get-VDTrafficShapingPolicy Get-VDUplinkLacpPolicy Get-VDUplinkTeamingPolicy Get-VDisk Get-VIAccount Get-VICommand Get-VICredentialStoreItem Get-VIEvent Get-VIObjectByVIView Get-VIPermission Get-VIPrivilege Get-VIProperty Get-VIRole Get-VM Get-VMGuest Get-VMHost Get-VMHostAccount Get-VMHostAdvancedConfiguration Get-VMHostAuthentication Get-VMHostAvailableTimeZone Get-VMHostDiagnosticPartition Get-VMHostDisk Get-VMHostDiskPartition Get-VMHostFirewallDefaultPolicy Get-VMHostFirewallException Get-VMHostFirmware Get-VMHostHardware Get-VMHostHba Get-VMHostModule Get-VMHostNetwork Get-VMHostNetworkAdapter Get-VMHostNtpServer Get-VMHostPatch Get-VMHostPciDevice Get-VMHostProfile Get-VMHostProfileImageCacheConfiguration Get-VMHostProfileRequiredInput Get-VMHostProfileStorageDeviceConfiguration Get-VMHostProfileUserConfiguration Get-VMHostProfileVmPortGroupConfiguration Get-VMHostRoute Get-VMHostService Get-VMHostSnmp Get-VMHostStartPolicy Get-VMHostStorage Get-VMHostSysLogServer Get-VMQuestion Get-VMResourceConfiguration Get-VMStartPolicy Get-VTpm Get-VTpmCSR Get-VTpmCertificate Get-VasaProvider Get-VasaStorageArray Get-View Get-VirtualPortGroup Get-VirtualSwitch Get-VmcSddcNetworkService Get-VmcService Get-VsanClusterConfiguration Get-VsanComponent Get-VsanDisk Get-VsanDiskGroup Get-VsanEvacuationPlan Get-VsanFaultDomain Get-VsanIscsiInitiatorGroup Get-VsanIscsiInitiatorGroupTargetAssociation Get-VsanIscsiLun Get-VsanIscsiTarget Get-VsanObject Get-VsanResyncingComponent Get-VsanRuntimeInfo Get-VsanSpaceUsage Get-VsanStat Get-VsanView Get-vRAApplianceServiceStatus Get-vRAAuthorizationRole Get-vRABlueprint Get-vRABusinessGroup Get-vRACatalogItem Get-vRACatalogItemRequestTemplate Get-vRACatalogPrincipal Get-vRAComponentRegistryService Get-vRAComponentRegistryServiceEndpoint Get-vRAComponentRegistryServiceStatus Get-vRAContent Get-vRAContentData Get-vRAContentType Get-vRACustomForm Get-vRAEntitledCatalogItem Get-vRAEntitledService Get-vRAEntitlement Get-vRAExternalNetworkProfile Get-vRAGroupPrincipal Get-vRAIcon Get-vRANATNetworkProfile Get-vRANetworkProfileIPAddressList Get-vRANetworkProfileIPRangeSummary Get-vRAPackage Get-vRAPackageContent Get-vRAPropertyDefinition Get-vRAPropertyGroup Get-vRARequest Get-vRARequestDetail Get-vRAReservation Get-vRAReservationComputeResource Get-vRAReservationComputeResourceMemory Get-vRAReservationComputeResourceNetwork Get-vRAReservationComputeResourceResourcePool Get-vRAReservationComputeResourceStorage Get-vRAReservationPolicy Get-vRAReservationTemplate Get-vRAReservationType Get-vRAResource Get-vRAResourceAction Get-vRAResourceActionRequestTemplate Get-vRAResourceMetric Get-vRAResourceOperation Get-vRAResourceType Get-vRARoutedNetworkProfile Get-vRAService Get-vRAServiceBlueprint Get-vRASourceMachine Get-vRAStorageReservationPolicy Get-vRATenant Get-vRATenantDirectory Get-vRATenantDirectoryStatus Get-vRATenantRole Get-vRAUserPrincipal Get-vRAUserPrincipalGroupMembership Get-vRAVersion Get-vRNIAPIVersion Get-vRNIApplication Get-vRNIApplicationTier Get-vRNIDataSource Get-vRNIDataSourceSNMPConfig Get-vRNIDatastore Get-vRNIDistributedSwitch Get-vRNIDistributedSwitchPortGroup Get-vRNIEntity Get-vRNIEntityName Get-vRNIFirewallRule Get-vRNIFlow Get-vRNIHost Get-vRNIHostVMKNic Get-vRNIIPSet Get-vRNIL2Network Get-vRNINSXManager Get-vRNINodes Get-vRNIProblem Get-vRNIRecommendedRules Get-vRNIRecommendedRulesNsxBundle Get-vRNISecurityGroup Get-vRNISecurityTag Get-vRNIService Get-vRNIServiceGroup Get-vRNIVM Get-vRNIVMvNIC Get-vRNIvCenter Get-vRNIvCenterCluster Get-vRNIvCenterDatacenter Get-vRNIvCenterFolder Grant-NsxSpoofguardNicApproval Import-CIVApp Import-CIVAppTemplate Import-NsxObject Import-PackageProvider Import-PowerShellDataFile Import-SpbmStoragePolicy Import-VApp Import-VMHostProfile Import-vRAContentData Import-vRAIcon Import-vRAPackage Initialize-ConfigurationRuntimeState Install-Module Install-NsxCluster Install-Package Install-PackageProvider Install-Script Install-VMHostPatch Invoke-DrsRecommendation Invoke-NsxCli Invoke-NsxClusterResolveAll Invoke-NsxManagerSync Invoke-NsxRestMethod Invoke-NsxWebRequest Invoke-VMHostProfile Invoke-VMScript Invoke-XpathQuery Invoke-vRADataCollection Invoke-vRARestMethod Invoke-vRATenantDirectorySync Invoke-vRNIRestMethod Join-String Mount-Tools Move-Cluster Move-Datacenter Move-Datastore Move-Folder Move-HardDisk Move-Inventory Move-NsxSecurityPolicyRule Move-ResourcePool Move-Template Move-VApp Move-VDisk Move-VM Move-VMHost New-AdvancedSetting New-AlarmAction New-AlarmActionTrigger New-CDDrive New-CIAccessControlRule New-CIVApp New-CIVAppNetwork New-CIVAppTemplate New-CIVM New-Cluster New-CustomAttribute New-Datacenter New-Datastore New-DatastoreCluster New-DatastoreDrive New-DrsClusterGroup New-DrsRule New-DrsVMHostRule New-DscChecksum New-FloppyDrive New-Folder New-Guid New-HCXAppliance New-HCXMigration New-HCXNetworkExtension New-HCXNetworkMapping New-HCXReplication New-HCXSitePairing New-HCXStaticRoute New-HardDisk New-IScsiHbaTarget New-KmipClientCertificate New-NetworkAdapter New-NfsUser New-NsxAddressSpec New-NsxClusterVxlanConfig New-NsxController New-NsxDynamicCriteriaSpec New-NsxEdge New-NsxEdgeBgpNeighbour New-NsxEdgeCsr New-NsxEdgeFirewallRule New-NsxEdgeInterfaceSpec New-NsxEdgeNatRule New-NsxEdgeOspfArea New-NsxEdgeOspfInterface New-NsxEdgePrefix New-NsxEdgeRedistributionRule New-NsxEdgeSelfSignedCertificate New-NsxEdgeStaticRoute New-NsxEdgeSubInterface New-NsxEdgeSubInterfaceSpec New-NsxFirewallRule New-NsxFirewallSavedConfiguration New-NsxFirewallSection New-NsxIpPool New-NsxIpSet New-NsxLoadBalancerApplicationProfile New-NsxLoadBalancerApplicationRule New-NsxLoadBalancerMemberSpec New-NsxLoadBalancerMonitor New-NsxLoadBalancerPool New-NsxLogicalRouter New-NsxLogicalRouterBgpNeighbour New-NsxLogicalRouterBridge New-NsxLogicalRouterInterface New-NsxLogicalRouterInterfaceSpec New-NsxLogicalRouterOspfArea New-NsxLogicalRouterOspfInterface New-NsxLogicalRouterPrefix New-NsxLogicalRouterRedistributionRule New-NsxLogicalRouterStaticRoute New-NsxLogicalSwitch New-NsxMacSet New-NsxManager New-NsxSecurityGroup New-NsxSecurityPolicy New-NsxSecurityPolicyAssignment New-NsxSecurityPolicyFirewallRuleSpec New-NsxSecurityPolicyGuestIntrospectionSpec New-NsxSecurityPolicyNetworkIntrospectionSpec New-NsxSecurityTag New-NsxSecurityTagAssignment New-NsxSegmentIdRange New-NsxService New-NsxServiceGroup New-NsxSpoofguardPolicy New-NsxSslVpnAuthServer New-NsxSslVpnClientInstallationPackage New-NsxSslVpnIpPool New-NsxSslVpnPrivateNetwork New-NsxSslVpnUser New-NsxTransportZone New-NsxVdsContext New-OSCustomizationNicMapping New-OSCustomizationSpec New-Org New-OrgNetwork New-OrgVdc New-OrgVdcNetwork New-ResourcePool New-ScriptFileInfo New-ScsiController New-Snapshot New-SpbmRule New-SpbmRuleSet New-SpbmStoragePolicy New-StatInterval New-Tag New-TagAssignment New-TagCategory New-Template New-TemporaryFile New-VAIOFilter New-VApp New-VDPortgroup New-VDSwitch New-VDSwitchPrivateVlan New-VDisk New-VICredentialStoreItem New-VIInventoryDrive New-VIPermission New-VIProperty New-VIRole New-VISamlSecurityContext New-VM New-VMHostAccount New-VMHostNetworkAdapter New-VMHostProfile New-VMHostProfileVmPortGroupConfiguration New-VMHostRoute New-VTpm New-VasaProvider New-VcsOAuthSecurityContext New-VirtualPortGroup New-VirtualSwitch New-VsanDisk New-VsanDiskGroup New-VsanFaultDomain New-VsanIscsiInitiatorGroup New-VsanIscsiInitiatorGroupTargetAssociation New-VsanIscsiLun New-VsanIscsiTarget New-vRABusinessGroup New-vRAEntitlement New-vRAExternalNetworkProfile New-vRAGroupPrincipal New-vRANATNetworkProfile New-vRANetworkProfileIPRangeDefinition New-vRAPackage New-vRAPropertyDefinition New-vRAPropertyGroup New-vRAReservation New-vRAReservationNetworkDefinition New-vRAReservationPolicy New-vRAReservationStorageDefinition New-vRARoutedNetworkProfile New-vRAService New-vRAStorageReservationPolicy New-vRATenant New-vRATenantDirectory New-vRAUserPrincipal New-vRNIApplication New-vRNIApplicationTier New-vRNIDataSource Open-VMConsoleWindow Publish-Module Publish-NsxSpoofguardPolicy Publish-Script Register-PSRepository Register-PackageSource Remove-AdvancedSetting Remove-AlarmAction Remove-AlarmActionTrigger Remove-Alias Remove-CDDrive Remove-CIAccessControlRule Remove-CIVApp Remove-CIVAppNetwork Remove-CIVAppTemplate Remove-Cluster Remove-CustomAttribute Remove-Datacenter Remove-Datastore Remove-DatastoreCluster Remove-DrsClusterGroup Remove-DrsRule Remove-DrsVMHostRule Remove-FloppyDrive Remove-Folder Remove-HCXAppliance Remove-HCXNetworkExtension Remove-HCXReplication Remove-HCXSitePairing Remove-HardDisk Remove-IScsiHbaTarget Remove-Inventory Remove-KeyManagementServer Remove-NetworkAdapter Remove-NfsUser Remove-NsxCluster Remove-NsxClusterVxlanConfig Remove-NsxController Remove-NsxDynamicCriteria Remove-NsxDynamicMemberSet Remove-NsxEdge Remove-NsxEdgeBgpNeighbour Remove-NsxEdgeCertificate Remove-NsxEdgeCsr Remove-NsxEdgeFirewallRule Remove-NsxEdgeInterfaceAddress Remove-NsxEdgeNatRule Remove-NsxEdgeOspfArea Remove-NsxEdgeOspfInterface Remove-NsxEdgePrefix Remove-NsxEdgeRedistributionRule Remove-NsxEdgeStaticRoute Remove-NsxEdgeSubInterface Remove-NsxFirewallExclusionListMember Remove-NsxFirewallRule Remove-NsxFirewallRuleMember Remove-NsxFirewallSavedConfiguration Remove-NsxFirewallSection Remove-NsxIpPool Remove-NsxIpSet Remove-NsxIpSetMember Remove-NsxLoadBalancerApplicationProfile Remove-NsxLoadBalancerMonitor Remove-NsxLoadBalancerPool Remove-NsxLoadBalancerPoolMember Remove-NsxLoadBalancerVip Remove-NsxLogicalRouter Remove-NsxLogicalRouterBgpNeighbour Remove-NsxLogicalRouterBridge Remove-NsxLogicalRouterInterface Remove-NsxLogicalRouterOspfArea Remove-NsxLogicalRouterOspfInterface Remove-NsxLogicalRouterPrefix Remove-NsxLogicalRouterRedistributionRule Remove-NsxLogicalRouterStaticRoute Remove-NsxLogicalSwitch Remove-NsxMacSet Remove-NsxSecondaryManager Remove-NsxSecurityGroup Remove-NsxSecurityGroupMember Remove-NsxSecurityPolicy Remove-NsxSecurityPolicyAssignment Remove-NsxSecurityPolicyRule Remove-NsxSecurityPolicyRuleGroup Remove-NsxSecurityPolicyRuleService Remove-NsxSecurityTag Remove-NsxSecurityTagAssignment Remove-NsxSegmentIdRange Remove-NsxService Remove-NsxServiceGroup Remove-NsxSpoofguardPolicy Remove-NsxSslVpnClientInstallationPackage Remove-NsxSslVpnIpPool Remove-NsxSslVpnPrivateNetwork Remove-NsxSslVpnUser Remove-NsxTransportZone Remove-NsxTransportZoneMember Remove-NsxVdsContext Remove-OSCustomizationNicMapping Remove-OSCustomizationSpec Remove-Org Remove-OrgNetwork Remove-OrgVdc Remove-OrgVdcNetwork Remove-PSReadLineKeyHandler Remove-PassthroughDevice Remove-ResourcePool Remove-Snapshot Remove-SpbmStoragePolicy Remove-StatInterval Remove-Tag Remove-TagAssignment Remove-TagCategory Remove-Template Remove-UsbDevice Remove-VAIOFilter Remove-VApp Remove-VDPortGroup Remove-VDSwitch Remove-VDSwitchPhysicalNetworkAdapter Remove-VDSwitchPrivateVlan Remove-VDSwitchVMHost Remove-VDisk Remove-VICredentialStoreItem Remove-VIPermission Remove-VIProperty Remove-VIRole Remove-VM Remove-VMHost Remove-VMHostAccount Remove-VMHostNetworkAdapter Remove-VMHostNtpServer Remove-VMHostProfile Remove-VMHostProfileVmPortGroupConfiguration Remove-VMHostRoute Remove-VTpm Remove-VasaProvider Remove-VirtualPortGroup Remove-VirtualSwitch Remove-VirtualSwitchPhysicalNetworkAdapter Remove-VsanDisk Remove-VsanDiskGroup Remove-VsanFaultDomain Remove-VsanIscsiInitiatorGroup Remove-VsanIscsiInitiatorGroupTargetAssociation Remove-VsanIscsiLun Remove-VsanIscsiTarget Remove-vRABusinessGroup Remove-vRACustomForm Remove-vRAExternalNetworkProfile Remove-vRAGroupPrincipal Remove-vRAIcon Remove-vRANATNetworkProfile Remove-vRAPackage Remove-vRAPrincipalFromTenantRole Remove-vRAPropertyDefinition Remove-vRAPropertyGroup Remove-vRAReservation Remove-vRAReservationNetwork Remove-vRAReservationPolicy Remove-vRAReservationStorage Remove-vRARoutedNetworkProfile Remove-vRAService Remove-vRAStorageReservationPolicy Remove-vRATenant Remove-vRATenantDirectory Remove-vRAUserPrincipal Remove-vRNIApplication Remove-vRNIApplicationTier Remove-vRNIDataSource Repair-NsxEdge Repair-VsanObject Request-vRACatalogItem Request-vRAResourceAction Restart-CIVApp Restart-CIVAppGuest Restart-CIVM Restart-CIVMGuest Restart-VM Restart-VMGuest Restart-VMHost Restart-VMHostService Resume-HCXReplication Revoke-NsxSpoofguardNicApproval Save-Module Save-Package Save-Script Search-Cloud Set-AdvancedSetting Set-AlarmDefinition Set-Annotation Set-CDDrive Set-CIAccessControlRule Set-CINetworkAdapter Set-CIVApp Set-CIVAppNetwork Set-CIVAppStartRule Set-CIVAppTemplate Set-Cluster Set-CustomAttribute Set-Datacenter Set-Datastore Set-DatastoreCluster Set-DrsClusterGroup Set-DrsRule Set-DrsVMHostRule Set-FloppyDrive Set-Folder Set-HCXAppliance Set-HCXMigration Set-HCXReplication Set-HardDisk Set-IScsiHbaTarget Set-KeyManagementServer Set-KmsCluster Set-MarkdownOption Set-NetworkAdapter Set-NfsUser Set-NicTeamingPolicy Set-NodeExclusiveResources Set-NodeManager Set-NodeResourceSource Set-NodeResources Set-NsxEdge Set-NsxEdgeBgp Set-NsxEdgeFirewall Set-NsxEdgeInterface Set-NsxEdgeNat Set-NsxEdgeOspf Set-NsxEdgeRouting Set-NsxFirewallGlobalConfiguration Set-NsxFirewallRule Set-NsxFirewallSavedConfiguration Set-NsxFirewallThreshold Set-NsxLoadBalancer Set-NsxLoadBalancerPoolMember Set-NsxLogicalRouter Set-NsxLogicalRouterBgp Set-NsxLogicalRouterBridging Set-NsxLogicalRouterInterface Set-NsxLogicalRouterOspf Set-NsxLogicalRouterRouting Set-NsxManager Set-NsxManagerRole Set-NsxManagerTimeSettings Set-NsxSecurityPolicy Set-NsxSecurityPolicyFirewallRule Set-NsxSslVpn Set-OSCustomizationNicMapping Set-OSCustomizationSpec Set-Org Set-OrgNetwork Set-OrgVdc Set-OrgVdcNetwork Set-PSCurrentConfigurationNode Set-PSDefaultConfigurationDocument Set-PSMetaConfigDocInsProcessedBeforeMeta Set-PSMetaConfigVersionInfoV2 Set-PSReadLineKeyHandler Set-PSReadLineOption Set-PSRepository Set-PSTopConfigurationName Set-PackageSource Set-PowerCLIConfiguration Set-ResourcePool Set-ScsiController Set-ScsiLun Set-ScsiLunPath Set-SecurityPolicy Set-Snapshot Set-SpbmEntityConfiguration Set-SpbmStoragePolicy Set-StatInterval Set-Tag Set-TagCategory Set-Template Set-VAIOFilter Set-VApp Set-VDBlockedPolicy Set-VDPort Set-VDPortgroup Set-VDPortgroupOverridePolicy Set-VDSecurityPolicy Set-VDSwitch Set-VDTrafficShapingPolicy Set-VDUplinkLacpPolicy Set-VDUplinkTeamingPolicy Set-VDVlanConfiguration Set-VDisk Set-VIPermission Set-VIRole Set-VM Set-VMHost Set-VMHostAccount Set-VMHostAdvancedConfiguration Set-VMHostAuthentication Set-VMHostDiagnosticPartition Set-VMHostFirewallDefaultPolicy Set-VMHostFirewallException Set-VMHostFirmware Set-VMHostHba Set-VMHostModule Set-VMHostNetwork Set-VMHostNetworkAdapter Set-VMHostProfile Set-VMHostProfileImageCacheConfiguration Set-VMHostProfileStorageDeviceConfiguration Set-VMHostProfileUserConfiguration Set-VMHostProfileVmPortGroupConfiguration Set-VMHostRoute Set-VMHostService Set-VMHostSnmp Set-VMHostStartPolicy Set-VMHostStorage Set-VMHostSysLogServer Set-VMQuestion Set-VMResourceConfiguration Set-VMStartPolicy Set-VTpm Set-VirtualPortGroup Set-VirtualSwitch Set-VsanClusterConfiguration Set-VsanFaultDomain Set-VsanIscsiInitiatorGroup Set-VsanIscsiLun Set-VsanIscsiTarget Set-vRABusinessGroup Set-vRACatalogItem Set-vRACustomForm Set-vRAEntitlement Set-vRAExternalNetworkProfile Set-vRANATNetworkProfile Set-vRAReservation Set-vRAReservationNetwork Set-vRAReservationPolicy Set-vRAReservationStorage Set-vRARoutedNetworkProfile Set-vRAService 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diag_fpsMin diag_frameNo diag_lightNewLoad diag_list diag_log diag_logSlowFrame diag_mergeConfigFile diag_recordTurretLimits diag_setLightNew diag_tickTime diag_toggle dialog diarySubjectExists didJIP didJIPOwner difficulty difficultyEnabled difficultyEnabledRTD difficultyOption direction directSay disableAI disableCollisionWith disableConversation disableDebriefingStats disableMapIndicators disableNVGEquipment disableRemoteSensors disableSerialization disableTIEquipment disableUAVConnectability disableUserInput displayAddEventHandler displayCtrl displayParent displayRemoveAllEventHandlers displayRemoveEventHandler displaySetEventHandler dissolveTeam distance distance2D distanceSqr distributionRegion do3DENAction doArtilleryFire doFire doFollow doFSM doGetOut doMove doorPhase doStop doSuppressiveFire doTarget doWatch drawArrow drawEllipse drawIcon drawIcon3D drawLine drawLine3D drawLink drawLocation drawPolygon drawRectangle drawTriangle driver drop dynamicSimulationDistance dynamicSimulationDistanceCoef dynamicSimulationEnabled dynamicSimulationSystemEnabled echo edit3DENMissionAttributes editObject editorSetEventHandler effectiveCommander emptyPositions enableAI enableAIFeature enableAimPrecision enableAttack enableAudioFeature enableAutoStartUpRTD enableAutoTrimRTD enableCamShake enableCaustics enableChannel enableCollisionWith enableCopilot enableDebriefingStats enableDiagLegend enableDynamicSimulation enableDynamicSimulationSystem enableEndDialog enableEngineArtillery enableEnvironment enableFatigue enableGunLights enableInfoPanelComponent enableIRLasers enableMimics enablePersonTurret enableRadio enableReload enableRopeAttach enableSatNormalOnDetail enableSaving enableSentences enableSimulation enableSimulationGlobal enableStamina enableTeamSwitch enableTraffic enableUAVConnectability enableUAVWaypoints enableVehicleCargo enableVehicleSensor enableWeaponDisassembly endLoadingScreen endMission engineOn enginesIsOnRTD enginesRpmRTD enginesTorqueRTD entities environmentEnabled estimatedEndServerTime estimatedTimeLeft evalObjectArgument everyBackpack everyContainer exec execEditorScript execFSM execVM exp expectedDestination exportJIPMessages eyeDirection eyePos face faction fadeMusic fadeRadio fadeSound fadeSpeech failMission fillWeaponsFromPool find findCover findDisplay findEditorObject findEmptyPosition findEmptyPositionReady findIf findNearestEnemy finishMissionInit finite fire fireAtTarget firstBackpack flag flagAnimationPhase flagOwner flagSide flagTexture fleeing floor flyInHeight flyInHeightASL fog fogForecast fogParams forceAddUniform forcedMap forceEnd forceFlagTexture forceFollowRoad forceMap forceRespawn forceSpeed forceWalk forceWeaponFire forceWeatherChange forEachMember forEachMemberAgent forEachMemberTeam forgetTarget format formation formationDirection formationLeader formationMembers formationPosition formationTask formatText formLeader freeLook fromEditor fuel fullCrew gearIDCAmmoCount gearSlotAmmoCount 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isUAVConnected isUIContext isUniformAllowed isVehicleCargo isVehicleRadarOn isVehicleSensorEnabled isWalking isWeaponDeployed isWeaponRested itemCargo items itemsWithMagazines join joinAs joinAsSilent joinSilent joinString kbAddDatabase kbAddDatabaseTargets kbAddTopic kbHasTopic kbReact kbRemoveTopic kbTell kbWasSaid keyImage keyName knowsAbout land landAt landResult language laserTarget lbAdd lbClear lbColor lbColorRight lbCurSel lbData lbDelete lbIsSelected lbPicture lbPictureRight lbSelection lbSetColor lbSetColorRight lbSetCurSel lbSetData lbSetPicture lbSetPictureColor lbSetPictureColorDisabled lbSetPictureColorSelected lbSetPictureRight lbSetPictureRightColor lbSetPictureRightColorDisabled lbSetPictureRightColorSelected lbSetSelectColor lbSetSelectColorRight lbSetSelected lbSetText lbSetTextRight lbSetTooltip lbSetValue lbSize lbSort lbSortByValue lbText lbTextRight lbValue leader leaderboardDeInit leaderboardGetRows leaderboardInit leaderboardRequestRowsFriends leaderboardsRequestUploadScore leaderboardsRequestUploadScoreKeepBest leaderboardState leaveVehicle libraryCredits libraryDisclaimers lifeState lightAttachObject lightDetachObject lightIsOn lightnings limitSpeed linearConversion lineIntersects lineIntersectsObjs lineIntersectsSurfaces lineIntersectsWith linkItem list listObjects listRemoteTargets listVehicleSensors ln lnbAddArray lnbAddColumn lnbAddRow lnbClear lnbColor lnbCurSelRow lnbData lnbDeleteColumn lnbDeleteRow lnbGetColumnsPosition lnbPicture lnbSetColor lnbSetColumnsPos lnbSetCurSelRow lnbSetData lnbSetPicture lnbSetText lnbSetValue lnbSize lnbSort lnbSortByValue lnbText lnbValue load loadAbs loadBackpack loadFile loadGame loadIdentity loadMagazine loadOverlay loadStatus loadUniform loadVest local localize locationPosition lock lockCameraTo lockCargo lockDriver locked lockedCargo lockedDriver lockedTurret lockIdentity lockTurret lockWP log logEntities logNetwork logNetworkTerminate lookAt lookAtPos magazineCargo magazines magazinesAllTurrets magazinesAmmo magazinesAmmoCargo magazinesAmmoFull magazinesDetail magazinesDetailBackpack magazinesDetailUniform magazinesDetailVest magazinesTurret magazineTurretAmmo mapAnimAdd mapAnimClear mapAnimCommit mapAnimDone mapCenterOnCamera mapGridPosition markAsFinishedOnSteam markerAlpha markerBrush markerColor markerDir markerPos markerShape markerSize markerText markerType max members menuAction menuAdd menuChecked menuClear menuCollapse menuData menuDelete menuEnable menuEnabled menuExpand menuHover menuPicture menuSetAction menuSetCheck menuSetData menuSetPicture menuSetValue menuShortcut menuShortcutText menuSize menuSort menuText menuURL menuValue min mineActive mineDetectedBy missionConfigFile missionDifficulty missionName missionNamespace missionStart missionVersion mod modelToWorld modelToWorldVisual modelToWorldVisualWorld modelToWorldWorld modParams moonIntensity moonPhase morale move move3DENCamera moveInAny moveInCargo moveInCommander moveInDriver moveInGunner moveInTurret moveObjectToEnd moveOut moveTime moveTo moveToCompleted moveToFailed musicVolume name nameSound nearEntities nearestBuilding nearestLocation nearestLocations nearestLocationWithDubbing nearestObject nearestObjects nearestTerrainObjects nearObjects nearObjectsReady nearRoads nearSupplies nearTargets needReload netId netObjNull newOverlay nextMenuItemIndex nextWeatherChange nMenuItems not numberOfEnginesRTD numberToDate objectCurators objectFromNetId objectParent objStatus onBriefingGroup onBriefingNotes onBriefingPlan onBriefingTeamSwitch onCommandModeChanged onDoubleClick onEachFrame onGroupIconClick onGroupIconOverEnter onGroupIconOverLeave onHCGroupSelectionChanged onMapSingleClick onPlayerConnected onPlayerDisconnected onPreloadFinished onPreloadStarted onShowNewObject onTeamSwitch openCuratorInterface openDLCPage openMap openSteamApp openYoutubeVideo or orderGetIn overcast overcastForecast owner param params parseNumber parseSimpleArray parseText parsingNamespace particlesQuality pickWeaponPool pitch pixelGrid pixelGridBase pixelGridNoUIScale pixelH pixelW playableSlotsNumber playableUnits playAction playActionNow player playerRespawnTime playerSide playersNumber playGesture playMission playMove playMoveNow playMusic playScriptedMission playSound playSound3D position positionCameraToWorld posScreenToWorld posWorldToScreen ppEffectAdjust ppEffectCommit ppEffectCommitted ppEffectCreate ppEffectDestroy ppEffectEnable ppEffectEnabled ppEffectForceInNVG precision preloadCamera preloadObject preloadSound preloadTitleObj preloadTitleRsc preprocessFile preprocessFileLineNumbers primaryWeapon primaryWeaponItems primaryWeaponMagazine priority processDiaryLink productVersion profileName profileNamespace profileNameSteam progressLoadingScreen progressPosition progressSetPosition publicVariable publicVariableClient publicVariableServer pushBack pushBackUnique putWeaponPool queryItemsPool queryMagazinePool queryWeaponPool rad radioChannelAdd radioChannelCreate radioChannelRemove radioChannelSetCallSign radioChannelSetLabel radioVolume rain rainbow random rank rankId rating rectangular registeredTasks registerTask reload reloadEnabled remoteControl remoteExec remoteExecCall remoteExecutedOwner remove3DENConnection remove3DENEventHandler remove3DENLayer removeAction removeAll3DENEventHandlers removeAllActions removeAllAssignedItems removeAllContainers removeAllCuratorAddons removeAllCuratorCameraAreas removeAllCuratorEditingAreas removeAllEventHandlers removeAllHandgunItems removeAllItems removeAllItemsWithMagazines removeAllMissionEventHandlers removeAllMPEventHandlers removeAllMusicEventHandlers removeAllOwnedMines removeAllPrimaryWeaponItems removeAllWeapons removeBackpack removeBackpackGlobal removeCuratorAddons removeCuratorCameraArea removeCuratorEditableObjects removeCuratorEditingArea removeDrawIcon removeDrawLinks removeEventHandler removeFromRemainsCollector removeGoggles removeGroupIcon removeHandgunItem removeHeadgear removeItem removeItemFromBackpack removeItemFromUniform removeItemFromVest removeItems removeMagazine removeMagazineGlobal removeMagazines removeMagazinesTurret removeMagazineTurret removeMenuItem removeMissionEventHandler removeMPEventHandler removeMusicEventHandler removeOwnedMine removePrimaryWeaponItem removeSecondaryWeaponItem removeSimpleTask removeSwitchableUnit removeTeamMember removeUniform removeVest removeWeapon removeWeaponAttachmentCargo removeWeaponCargo removeWeaponGlobal removeWeaponTurret reportRemoteTarget requiredVersion resetCamShake resetSubgroupDirection resize resources respawnVehicle restartEditorCamera reveal revealMine reverse reversedMouseY roadAt roadsConnectedTo roleDescription ropeAttachedObjects ropeAttachedTo ropeAttachEnabled ropeAttachTo ropeCreate ropeCut ropeDestroy ropeDetach ropeEndPosition ropeLength ropes ropeUnwind ropeUnwound rotorsForcesRTD rotorsRpmRTD round runInitScript safeZoneH safeZoneW safeZoneWAbs safeZoneX safeZoneXAbs safeZoneY save3DENInventory saveGame saveIdentity saveJoysticks saveOverlay saveProfileNamespace saveStatus saveVar savingEnabled say say2D say3D scopeName score scoreSide screenshot screenToWorld scriptDone scriptName scudState secondaryWeapon secondaryWeaponItems secondaryWeaponMagazine select selectBestPlaces selectDiarySubject selectedEditorObjects selectEditorObject selectionNames selectionPosition selectLeader selectMax selectMin selectNoPlayer selectPlayer selectRandom selectRandomWeighted selectWeapon selectWeaponTurret sendAUMessage sendSimpleCommand sendTask sendTaskResult sendUDPMessage serverCommand serverCommandAvailable serverCommandExecutable serverName serverTime set set3DENAttribute set3DENAttributes set3DENGrid set3DENIconsVisible set3DENLayer set3DENLinesVisible set3DENLogicType set3DENMissionAttribute set3DENMissionAttributes set3DENModelsVisible set3DENObjectType set3DENSelected setAccTime setActualCollectiveRTD setAirplaneThrottle setAirportSide setAmmo 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setFSMVariable setFuel setFuelCargo setGroupIcon setGroupIconParams setGroupIconsSelectable setGroupIconsVisible setGroupId setGroupIdGlobal setGroupOwner setGusts setHideBehind setHit setHitIndex setHitPointDamage setHorizonParallaxCoef setHUDMovementLevels setIdentity setImportance setInfoPanel setLeader setLightAmbient setLightAttenuation setLightBrightness setLightColor setLightDayLight setLightFlareMaxDistance setLightFlareSize setLightIntensity setLightnings setLightUseFlare setLocalWindParams setMagazineTurretAmmo setMarkerAlpha setMarkerAlphaLocal setMarkerBrush setMarkerBrushLocal setMarkerColor setMarkerColorLocal setMarkerDir setMarkerDirLocal setMarkerPos setMarkerPosLocal setMarkerShape setMarkerShapeLocal setMarkerSize setMarkerSizeLocal setMarkerText setMarkerTextLocal setMarkerType setMarkerTypeLocal setMass setMimic setMousePosition setMusicEffect setMusicEventHandler setName setNameSound setObjectArguments setObjectMaterial setObjectMaterialGlobal setObjectProxy setObjectTexture setObjectTextureGlobal setObjectViewDistance setOvercast setOwner setOxygenRemaining setParticleCircle setParticleClass setParticleFire setParticleParams setParticleRandom setPilotCameraDirection setPilotCameraRotation setPilotCameraTarget setPilotLight setPiPEffect setPitch setPlateNumber setPlayable setPlayerRespawnTime setPos setPosASL setPosASL2 setPosASLW setPosATL setPosition setPosWorld setPylonLoadOut setPylonsPriority setRadioMsg setRain setRainbow setRandomLip setRank setRectangular setRepairCargo setRotorBrakeRTD setShadowDistance setShotParents setSide setSimpleTaskAlwaysVisible setSimpleTaskCustomData setSimpleTaskDescription setSimpleTaskDestination setSimpleTaskTarget setSimpleTaskType setSimulWeatherLayers setSize setSkill setSlingLoad setSoundEffect setSpeaker setSpeech setSpeedMode setStamina setStaminaScheme setStatValue setSuppression setSystemOfUnits setTargetAge setTaskMarkerOffset setTaskResult setTaskState setTerrainGrid setText setTimeMultiplier setTitleEffect setTrafficDensity setTrafficDistance setTrafficGap setTrafficSpeed setTriggerActivation setTriggerArea setTriggerStatements setTriggerText setTriggerTimeout setTriggerType setType setUnconscious setUnitAbility setUnitLoadout setUnitPos setUnitPosWeak setUnitRank setUnitRecoilCoefficient setUnitTrait setUnloadInCombat setUserActionText setUserMFDText setUserMFDvalue setVariable setVectorDir setVectorDirAndUp setVectorUp setVehicleAmmo setVehicleAmmoDef setVehicleArmor setVehicleCargo setVehicleId setVehicleLock setVehiclePosition setVehicleRadar setVehicleReceiveRemoteTargets setVehicleReportOwnPosition setVehicleReportRemoteTargets setVehicleTIPars setVehicleVarName setVelocity setVelocityModelSpace setVelocityTransformation setViewDistance setVisibleIfTreeCollapsed setWantedRPMRTD setWaves setWaypointBehaviour setWaypointCombatMode setWaypointCompletionRadius setWaypointDescription setWaypointForceBehaviour setWaypointFormation setWaypointHousePosition setWaypointLoiterRadius setWaypointLoiterType setWaypointName setWaypointPosition setWaypointScript setWaypointSpeed setWaypointStatements setWaypointTimeout setWaypointType setWaypointVisible setWeaponReloadingTime setWind setWindDir setWindForce setWindStr setWingForceScaleRTD setWPPos show3DIcons showChat showCinemaBorder showCommandingMenu showCompass showCuratorCompass showGPS showHUD showLegend showMap shownArtilleryComputer shownChat shownCompass shownCuratorCompass showNewEditorObject shownGPS shownHUD shownMap shownPad shownRadio shownScoretable shownUAVFeed shownWarrant shownWatch showPad showRadio showScoretable showSubtitles showUAVFeed showWarrant showWatch showWaypoint showWaypoints side sideChat sideEnemy sideFriendly sideRadio simpleTasks simulationEnabled simulCloudDensity simulCloudOcclusion simulInClouds simulWeatherSync sin size sizeOf skill skillFinal skipTime sleep sliderPosition sliderRange sliderSetPosition sliderSetRange sliderSetSpeed sliderSpeed slingLoadAssistantShown soldierMagazines someAmmo sort soundVolume spawn speaker speed speedMode splitString sqrt squadParams stance startLoadingScreen step stop stopEngineRTD stopped str sunOrMoon supportInfo suppressFor surfaceIsWater surfaceNormal surfaceType swimInDepth switchableUnits switchAction switchCamera switchGesture switchLight switchMove synchronizedObjects synchronizedTriggers synchronizedWaypoints synchronizeObjectsAdd synchronizeObjectsRemove synchronizeTrigger synchronizeWaypoint systemChat systemOfUnits tan targetKnowledge targets targetsAggregate targetsQuery taskAlwaysVisible taskChildren taskCompleted taskCustomData taskDescription taskDestination taskHint taskMarkerOffset taskParent taskResult taskState taskType teamMember teamName teams teamSwitch teamSwitchEnabled teamType terminate terrainIntersect terrainIntersectASL terrainIntersectAtASL text textLog textLogFormat tg time timeMultiplier titleCut titleFadeOut titleObj titleRsc titleText toArray toFixed toLower toString toUpper triggerActivated triggerActivation triggerArea triggerAttachedVehicle triggerAttachObject triggerAttachVehicle triggerDynamicSimulation triggerStatements triggerText triggerTimeout triggerTimeoutCurrent triggerType turretLocal turretOwner turretUnit tvAdd tvClear tvCollapse tvCollapseAll tvCount tvCurSel tvData tvDelete tvExpand tvExpandAll tvPicture tvSetColor tvSetCurSel tvSetData tvSetPicture tvSetPictureColor tvSetPictureColorDisabled tvSetPictureColorSelected tvSetPictureRight tvSetPictureRightColor tvSetPictureRightColorDisabled tvSetPictureRightColorSelected tvSetText tvSetTooltip tvSetValue tvSort tvSortByValue tvText tvTooltip tvValue type typeName typeOf UAVControl uiNamespace uiSleep unassignCurator unassignItem unassignTeam unassignVehicle underwater uniform uniformContainer uniformItems uniformMagazines unitAddons unitAimPosition unitAimPositionVisual unitBackpack unitIsUAV unitPos unitReady unitRecoilCoefficient units unitsBelowHeight unlinkItem 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physics_particle_delete_region_circle physics_particle_delete_region_box physics_particle_delete_region_poly physics_particle_set_flags physics_particle_set_category_flags physics_particle_draw physics_particle_draw_ext physics_particle_count physics_particle_get_data physics_particle_get_data_particle physics_particle_group_begin physics_particle_group_circle physics_particle_group_box physics_particle_group_polygon physics_particle_group_add_point physics_particle_group_end physics_particle_group_join physics_particle_group_delete physics_particle_group_count physics_particle_group_get_data physics_particle_group_get_mass physics_particle_group_get_inertia physics_particle_group_get_centre_x physics_particle_group_get_centre_y physics_particle_group_get_vel_x physics_particle_group_get_vel_y physics_particle_group_get_ang_vel physics_particle_group_get_x physics_particle_group_get_y physics_particle_group_get_angle physics_particle_set_group_flags physics_particle_get_group_flags physics_particle_get_max_count physics_particle_get_radius physics_particle_get_density physics_particle_get_damping physics_particle_get_gravity_scale physics_particle_set_max_count physics_particle_set_radius physics_particle_set_density physics_particle_set_damping physics_particle_set_gravity_scale network_create_socket network_create_socket_ext network_create_server network_create_server_raw network_connect network_connect_raw network_send_packet network_send_raw network_send_broadcast network_send_udp network_send_udp_raw network_set_timeout network_set_config network_resolve network_destroy buffer_create buffer_write buffer_read buffer_seek buffer_get_surface buffer_set_surface buffer_delete buffer_exists buffer_get_type buffer_get_alignment buffer_poke buffer_peek buffer_save buffer_save_ext buffer_load buffer_load_ext buffer_load_partial buffer_copy buffer_fill buffer_get_size buffer_tell buffer_resize buffer_md5 buffer_sha1 buffer_base64_encode buffer_base64_decode buffer_base64_decode_ext buffer_sizeof buffer_get_address buffer_create_from_vertex_buffer buffer_create_from_vertex_buffer_ext buffer_copy_from_vertex_buffer buffer_async_group_begin buffer_async_group_option buffer_async_group_end buffer_load_async buffer_save_async gml_release_mode gml_pragma steam_activate_overlay steam_is_overlay_enabled steam_is_overlay_activated steam_get_persona_name steam_initialised steam_is_cloud_enabled_for_app steam_is_cloud_enabled_for_account steam_file_persisted steam_get_quota_total steam_get_quota_free steam_file_write steam_file_write_file steam_file_read steam_file_delete steam_file_exists steam_file_size steam_file_share steam_is_screenshot_requested steam_send_screenshot steam_is_user_logged_on steam_get_user_steam_id steam_user_owns_dlc steam_user_installed_dlc steam_set_achievement steam_get_achievement steam_clear_achievement steam_set_stat_int steam_set_stat_float steam_set_stat_avg_rate steam_get_stat_int steam_get_stat_float steam_get_stat_avg_rate steam_reset_all_stats steam_reset_all_stats_achievements steam_stats_ready steam_create_leaderboard steam_upload_score steam_upload_score_ext steam_download_scores_around_user steam_download_scores steam_download_friends_scores steam_upload_score_buffer steam_upload_score_buffer_ext steam_current_game_language steam_available_languages steam_activate_overlay_browser steam_activate_overlay_user steam_activate_overlay_store steam_get_user_persona_name steam_get_app_id steam_get_user_account_id steam_ugc_download steam_ugc_create_item steam_ugc_start_item_update steam_ugc_set_item_title steam_ugc_set_item_description steam_ugc_set_item_visibility steam_ugc_set_item_tags steam_ugc_set_item_content steam_ugc_set_item_preview steam_ugc_submit_item_update steam_ugc_get_item_update_progress steam_ugc_subscribe_item steam_ugc_unsubscribe_item steam_ugc_num_subscribed_items steam_ugc_get_subscribed_items steam_ugc_get_item_install_info steam_ugc_get_item_update_info steam_ugc_request_item_details steam_ugc_create_query_user steam_ugc_create_query_user_ex steam_ugc_create_query_all steam_ugc_create_query_all_ex steam_ugc_query_set_cloud_filename_filter steam_ugc_query_set_match_any_tag steam_ugc_query_set_search_text steam_ugc_query_set_ranked_by_trend_days steam_ugc_query_add_required_tag steam_ugc_query_add_excluded_tag steam_ugc_query_set_return_long_description steam_ugc_query_set_return_total_only steam_ugc_query_set_allow_cached_response steam_ugc_send_query shader_set shader_get_name shader_reset shader_current shader_is_compiled shader_get_sampler_index shader_get_uniform shader_set_uniform_i shader_set_uniform_i_array shader_set_uniform_f shader_set_uniform_f_array shader_set_uniform_matrix shader_set_uniform_matrix_array shader_enable_corner_id texture_set_stage texture_get_texel_width texture_get_texel_height shaders_are_supported vertex_format_begin vertex_format_end vertex_format_delete vertex_format_add_position vertex_format_add_position_3d vertex_format_add_colour vertex_format_add_color vertex_format_add_normal vertex_format_add_texcoord vertex_format_add_textcoord vertex_format_add_custom vertex_create_buffer vertex_create_buffer_ext vertex_delete_buffer vertex_begin vertex_end vertex_position vertex_position_3d vertex_colour vertex_color vertex_argb vertex_texcoord vertex_normal vertex_float1 vertex_float2 vertex_float3 vertex_float4 vertex_ubyte4 vertex_submit vertex_freeze vertex_get_number vertex_get_buffer_size vertex_create_buffer_from_buffer vertex_create_buffer_from_buffer_ext push_local_notification push_get_first_local_notification push_get_next_local_notification push_cancel_local_notification skeleton_animation_set skeleton_animation_get skeleton_animation_mix skeleton_animation_set_ext skeleton_animation_get_ext skeleton_animation_get_duration skeleton_animation_get_frames skeleton_animation_clear skeleton_skin_set skeleton_skin_get skeleton_attachment_set skeleton_attachment_get skeleton_attachment_create skeleton_collision_draw_set skeleton_bone_data_get skeleton_bone_data_set skeleton_bone_state_get skeleton_bone_state_set skeleton_get_minmax skeleton_get_num_bounds skeleton_get_bounds skeleton_animation_get_frame skeleton_animation_set_frame draw_skeleton draw_skeleton_time draw_skeleton_instance draw_skeleton_collision skeleton_animation_list skeleton_skin_list skeleton_slot_data layer_get_id layer_get_id_at_depth layer_get_depth layer_create layer_destroy layer_destroy_instances layer_add_instance layer_has_instance layer_set_visible layer_get_visible layer_exists layer_x layer_y layer_get_x layer_get_y layer_hspeed layer_vspeed layer_get_hspeed layer_get_vspeed layer_script_begin layer_script_end layer_shader layer_get_script_begin layer_get_script_end layer_get_shader layer_set_target_room layer_get_target_room layer_reset_target_room layer_get_all layer_get_all_elements layer_get_name layer_depth layer_get_element_layer layer_get_element_type layer_element_move layer_force_draw_depth layer_is_draw_depth_forced layer_get_forced_depth layer_background_get_id layer_background_exists layer_background_create layer_background_destroy layer_background_visible layer_background_change layer_background_sprite layer_background_htiled layer_background_vtiled layer_background_stretch layer_background_yscale layer_background_xscale layer_background_blend layer_background_alpha layer_background_index layer_background_speed layer_background_get_visible layer_background_get_sprite layer_background_get_htiled layer_background_get_vtiled layer_background_get_stretch layer_background_get_yscale layer_background_get_xscale layer_background_get_blend layer_background_get_alpha layer_background_get_index layer_background_get_speed layer_sprite_get_id layer_sprite_exists layer_sprite_create layer_sprite_destroy layer_sprite_change layer_sprite_index layer_sprite_speed layer_sprite_xscale layer_sprite_yscale layer_sprite_angle layer_sprite_blend layer_sprite_alpha layer_sprite_x layer_sprite_y layer_sprite_get_sprite layer_sprite_get_index layer_sprite_get_speed layer_sprite_get_xscale layer_sprite_get_yscale layer_sprite_get_angle layer_sprite_get_blend layer_sprite_get_alpha layer_sprite_get_x layer_sprite_get_y layer_tilemap_get_id layer_tilemap_exists layer_tilemap_create layer_tilemap_destroy tilemap_tileset tilemap_x tilemap_y tilemap_set tilemap_set_at_pixel tilemap_get_tileset tilemap_get_tile_width tilemap_get_tile_height tilemap_get_width tilemap_get_height tilemap_get_x tilemap_get_y tilemap_get tilemap_get_at_pixel tilemap_get_cell_x_at_pixel tilemap_get_cell_y_at_pixel tilemap_clear draw_tilemap draw_tile tilemap_set_global_mask tilemap_get_global_mask tilemap_set_mask tilemap_get_mask tilemap_get_frame tile_set_empty tile_set_index tile_set_flip tile_set_mirror tile_set_rotate tile_get_empty tile_get_index tile_get_flip tile_get_mirror tile_get_rotate layer_tile_exists layer_tile_create layer_tile_destroy layer_tile_change layer_tile_xscale layer_tile_yscale layer_tile_blend layer_tile_alpha layer_tile_x layer_tile_y layer_tile_region layer_tile_visible layer_tile_get_sprite layer_tile_get_xscale layer_tile_get_yscale layer_tile_get_blend layer_tile_get_alpha layer_tile_get_x layer_tile_get_y layer_tile_get_region layer_tile_get_visible layer_instance_get_instance instance_activate_layer instance_deactivate_layer camera_create camera_create_view camera_destroy camera_apply camera_get_active camera_get_default camera_set_default camera_set_view_mat camera_set_proj_mat camera_set_update_script camera_set_begin_script camera_set_end_script camera_set_view_pos camera_set_view_size camera_set_view_speed camera_set_view_border camera_set_view_angle camera_set_view_target camera_get_view_mat camera_get_proj_mat camera_get_update_script camera_get_begin_script camera_get_end_script camera_get_view_x camera_get_view_y camera_get_view_width camera_get_view_height camera_get_view_speed_x camera_get_view_speed_y camera_get_view_border_x camera_get_view_border_y camera_get_view_angle camera_get_view_target view_get_camera view_get_visible view_get_xport view_get_yport view_get_wport view_get_hport view_get_surface_id view_set_camera view_set_visible view_set_xport view_set_yport view_set_wport view_set_hport view_set_surface_id gesture_drag_time gesture_drag_distance gesture_flick_speed gesture_double_tap_time gesture_double_tap_distance gesture_pinch_distance gesture_pinch_angle_towards gesture_pinch_angle_away gesture_rotate_time gesture_rotate_angle gesture_tap_count gesture_get_drag_time gesture_get_drag_distance gesture_get_flick_speed gesture_get_double_tap_time gesture_get_double_tap_distance gesture_get_pinch_distance gesture_get_pinch_angle_towards gesture_get_pinch_angle_away gesture_get_rotate_time gesture_get_rotate_angle gesture_get_tap_count keyboard_virtual_show keyboard_virtual_hide keyboard_virtual_status keyboard_virtual_height",literal:"self other all noone global local undefined pointer_invalid pointer_null path_action_stop path_action_restart path_action_continue path_action_reverse true false pi GM_build_date GM_version GM_runtime_version  timezone_local timezone_utc gamespeed_fps gamespeed_microseconds  ev_create ev_destroy ev_step ev_alarm ev_keyboard ev_mouse ev_collision ev_other ev_draw ev_draw_begin ev_draw_end ev_draw_pre ev_draw_post ev_keypress ev_keyrelease ev_trigger ev_left_button ev_right_button ev_middle_button ev_no_button ev_left_press ev_right_press ev_middle_press ev_left_release ev_right_release ev_middle_release ev_mouse_enter ev_mouse_leave ev_mouse_wheel_up ev_mouse_wheel_down ev_global_left_button ev_global_right_button ev_global_middle_button ev_global_left_press ev_global_right_press ev_global_middle_press ev_global_left_release ev_global_right_release ev_global_middle_release ev_joystick1_left ev_joystick1_right ev_joystick1_up ev_joystick1_down ev_joystick1_button1 ev_joystick1_button2 ev_joystick1_button3 ev_joystick1_button4 ev_joystick1_button5 ev_joystick1_button6 ev_joystick1_button7 ev_joystick1_button8 ev_joystick2_left ev_joystick2_right ev_joystick2_up ev_joystick2_down ev_joystick2_button1 ev_joystick2_button2 ev_joystick2_button3 ev_joystick2_button4 ev_joystick2_button5 ev_joystick2_button6 ev_joystick2_button7 ev_joystick2_button8 ev_outside ev_boundary ev_game_start ev_game_end ev_room_start ev_room_end ev_no_more_lives ev_animation_end ev_end_of_path ev_no_more_health ev_close_button ev_user0 ev_user1 ev_user2 ev_user3 ev_user4 ev_user5 ev_user6 ev_user7 ev_user8 ev_user9 ev_user10 ev_user11 ev_user12 ev_user13 ev_user14 ev_user15 ev_step_normal ev_step_begin ev_step_end ev_gui ev_gui_begin ev_gui_end ev_cleanup ev_gesture ev_gesture_tap ev_gesture_double_tap ev_gesture_drag_start ev_gesture_dragging ev_gesture_drag_end ev_gesture_flick ev_gesture_pinch_start ev_gesture_pinch_in ev_gesture_pinch_out ev_gesture_pinch_end ev_gesture_rotate_start ev_gesture_rotating ev_gesture_rotate_end ev_global_gesture_tap ev_global_gesture_double_tap ev_global_gesture_drag_start ev_global_gesture_dragging ev_global_gesture_drag_end ev_global_gesture_flick ev_global_gesture_pinch_start ev_global_gesture_pinch_in ev_global_gesture_pinch_out ev_global_gesture_pinch_end ev_global_gesture_rotate_start ev_global_gesture_rotating ev_global_gesture_rotate_end vk_nokey vk_anykey vk_enter vk_return vk_shift vk_control vk_alt vk_escape vk_space vk_backspace vk_tab vk_pause vk_printscreen vk_left vk_right vk_up vk_down vk_home vk_end vk_delete vk_insert vk_pageup vk_pagedown vk_f1 vk_f2 vk_f3 vk_f4 vk_f5 vk_f6 vk_f7 vk_f8 vk_f9 vk_f10 vk_f11 vk_f12 vk_numpad0 vk_numpad1 vk_numpad2 vk_numpad3 vk_numpad4 vk_numpad5 vk_numpad6 vk_numpad7 vk_numpad8 vk_numpad9 vk_divide vk_multiply vk_subtract vk_add vk_decimal vk_lshift vk_lcontrol vk_lalt vk_rshift vk_rcontrol vk_ralt  mb_any mb_none mb_left mb_right mb_middle c_aqua c_black c_blue c_dkgray c_fuchsia c_gray c_green c_lime c_ltgray c_maroon c_navy c_olive c_purple c_red c_silver c_teal c_white c_yellow c_orange fa_left fa_center fa_right fa_top fa_middle fa_bottom pr_pointlist pr_linelist pr_linestrip pr_trianglelist pr_trianglestrip pr_trianglefan bm_complex bm_normal bm_add bm_max bm_subtract bm_zero bm_one bm_src_colour bm_inv_src_colour bm_src_color bm_inv_src_color bm_src_alpha bm_inv_src_alpha bm_dest_alpha bm_inv_dest_alpha bm_dest_colour bm_inv_dest_colour bm_dest_color bm_inv_dest_color bm_src_alpha_sat tf_point tf_linear tf_anisotropic mip_off mip_on mip_markedonly audio_falloff_none audio_falloff_inverse_distance audio_falloff_inverse_distance_clamped audio_falloff_linear_distance audio_falloff_linear_distance_clamped audio_falloff_exponent_distance audio_falloff_exponent_distance_clamped audio_old_system audio_new_system audio_mono audio_stereo audio_3d cr_default cr_none cr_arrow cr_cross cr_beam cr_size_nesw cr_size_ns cr_size_nwse cr_size_we cr_uparrow cr_hourglass cr_drag cr_appstart cr_handpoint cr_size_all spritespeed_framespersecond spritespeed_framespergameframe asset_object asset_unknown asset_sprite asset_sound asset_room asset_path asset_script asset_font asset_timeline asset_tiles asset_shader fa_readonly fa_hidden fa_sysfile fa_volumeid fa_directory fa_archive  ds_type_map ds_type_list ds_type_stack ds_type_queue ds_type_grid ds_type_priority ef_explosion ef_ring ef_ellipse ef_firework ef_smoke ef_smokeup ef_star ef_spark ef_flare ef_cloud ef_rain ef_snow pt_shape_pixel pt_shape_disk pt_shape_square pt_shape_line pt_shape_star pt_shape_circle pt_shape_ring pt_shape_sphere pt_shape_flare pt_shape_spark pt_shape_explosion pt_shape_cloud pt_shape_smoke pt_shape_snow ps_distr_linear ps_distr_gaussian ps_distr_invgaussian ps_shape_rectangle ps_shape_ellipse ps_shape_diamond ps_shape_line ty_real ty_string dll_cdecl dll_stdcall matrix_view matrix_projection matrix_world os_win32 os_windows os_macosx os_ios os_android os_symbian os_linux os_unknown os_winphone os_tizen os_win8native os_wiiu os_3ds  os_psvita os_bb10 os_ps4 os_xboxone os_ps3 os_xbox360 os_uwp os_tvos os_switch browser_not_a_browser browser_unknown browser_ie browser_firefox browser_chrome browser_safari browser_safari_mobile browser_opera browser_tizen browser_edge browser_windows_store browser_ie_mobile  device_ios_unknown device_ios_iphone device_ios_iphone_retina device_ios_ipad device_ios_ipad_retina device_ios_iphone5 device_ios_iphone6 device_ios_iphone6plus device_emulator device_tablet display_landscape display_landscape_flipped display_portrait display_portrait_flipped tm_sleep tm_countvsyncs of_challenge_win of_challen ge_lose of_challenge_tie leaderboard_type_number leaderboard_type_time_mins_secs cmpfunc_never cmpfunc_less cmpfunc_equal cmpfunc_lessequal cmpfunc_greater cmpfunc_notequal cmpfunc_greaterequal cmpfunc_always cull_noculling cull_clockwise cull_counterclockwise lighttype_dir lighttype_point iap_ev_storeload iap_ev_product iap_ev_purchase iap_ev_consume iap_ev_restore iap_storeload_ok iap_storeload_failed iap_status_uninitialised iap_status_unavailable iap_status_loading iap_status_available iap_status_processing iap_status_restoring iap_failed iap_unavailable iap_available iap_purchased iap_canceled iap_refunded fb_login_default fb_login_fallback_to_webview fb_login_no_fallback_to_webview fb_login_forcing_webview fb_login_use_system_account fb_login_forcing_safari  phy_joint_anchor_1_x phy_joint_anchor_1_y phy_joint_anchor_2_x phy_joint_anchor_2_y phy_joint_reaction_force_x phy_joint_reaction_force_y phy_joint_reaction_torque phy_joint_motor_speed phy_joint_angle phy_joint_motor_torque phy_joint_max_motor_torque phy_joint_translation phy_joint_speed phy_joint_motor_force phy_joint_max_motor_force phy_joint_length_1 phy_joint_length_2 phy_joint_damping_ratio phy_joint_frequency phy_joint_lower_angle_limit phy_joint_upper_angle_limit phy_joint_angle_limits phy_joint_max_length phy_joint_max_torque phy_joint_max_force phy_debug_render_aabb phy_debug_render_collision_pairs phy_debug_render_coms phy_debug_render_core_shapes phy_debug_render_joints phy_debug_render_obb phy_debug_render_shapes  phy_particle_flag_water phy_particle_flag_zombie phy_particle_flag_wall phy_particle_flag_spring phy_particle_flag_elastic phy_particle_flag_viscous phy_particle_flag_powder phy_particle_flag_tensile phy_particle_flag_colourmixing phy_particle_flag_colormixing phy_particle_group_flag_solid phy_particle_group_flag_rigid phy_particle_data_flag_typeflags phy_particle_data_flag_position phy_particle_data_flag_velocity phy_particle_data_flag_colour phy_particle_data_flag_color phy_particle_data_flag_category  achievement_our_info achievement_friends_info achievement_leaderboard_info achievement_achievement_info achievement_filter_all_players achievement_filter_friends_only achievement_filter_favorites_only achievement_type_achievement_challenge achievement_type_score_challenge achievement_pic_loaded  achievement_show_ui achievement_show_profile achievement_show_leaderboard achievement_show_achievement achievement_show_bank achievement_show_friend_picker achievement_show_purchase_prompt network_socket_tcp network_socket_udp network_socket_bluetooth network_type_connect network_type_disconnect network_type_data network_type_non_blocking_connect network_config_connect_timeout network_config_use_non_blocking_socket network_config_enable_reliable_udp network_config_disable_reliable_udp buffer_fixed buffer_grow buffer_wrap buffer_fast buffer_vbuffer buffer_network buffer_u8 buffer_s8 buffer_u16 buffer_s16 buffer_u32 buffer_s32 buffer_u64 buffer_f16 buffer_f32 buffer_f64 buffer_bool buffer_text buffer_string buffer_surface_copy buffer_seek_start buffer_seek_relative buffer_seek_end buffer_generalerror buffer_outofspace buffer_outofbounds buffer_invalidtype  text_type button_type input_type ANSI_CHARSET DEFAULT_CHARSET EASTEUROPE_CHARSET RUSSIAN_CHARSET SYMBOL_CHARSET SHIFTJIS_CHARSET HANGEUL_CHARSET GB2312_CHARSET CHINESEBIG5_CHARSET JOHAB_CHARSET HEBREW_CHARSET ARABIC_CHARSET GREEK_CHARSET TURKISH_CHARSET VIETNAMESE_CHARSET THAI_CHARSET MAC_CHARSET BALTIC_CHARSET OEM_CHARSET  gp_face1 gp_face2 gp_face3 gp_face4 gp_shoulderl gp_shoulderr gp_shoulderlb gp_shoulderrb gp_select gp_start gp_stickl gp_stickr gp_padu gp_padd gp_padl gp_padr gp_axislh gp_axislv gp_axisrh gp_axisrv ov_friends ov_community ov_players ov_settings ov_gamegroup ov_achievements lb_sort_none lb_sort_ascending lb_sort_descending lb_disp_none lb_disp_numeric lb_disp_time_sec lb_disp_time_ms ugc_result_success ugc_filetype_community ugc_filetype_microtrans ugc_visibility_public ugc_visibility_friends_only ugc_visibility_private ugc_query_RankedByVote ugc_query_RankedByPublicationDate ugc_query_AcceptedForGameRankedByAcceptanceDate ugc_query_RankedByTrend ugc_query_FavoritedByFriendsRankedByPublicationDate 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    \n                    \n                        
    \n                            Uno scritto con tre domande:\n                        
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      • \n                            
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      • \n                            
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      4. \n                        
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    \n                            Va consegnato almeno 10 giorni prima dell'esame.\n                        
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extracted by mini-css-extract-plugin\nmodule.exports = {\"example\":\"example__9acWs\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"box\":\"box__3cKyY\",\"default\":\"default__v-emJ\",\"red\":\"red__339Cz\",\"orange\":\"orange__24_8v\",\"yellow\":\"yellow__1Jo9W\",\"lime\":\"lime__34yV5\",\"cyan\":\"cyan__3RqLr\",\"blue\":\"blue__13Wnj\",\"magenta\":\"magenta__2tkzq\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"inline\":\"inline__1yl8V\",\"block\":\"block__fPiiB\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"todo\":\"todo__2IWIS\"};","import Split from \"../Layout/Split\";\nimport {Fragment} from \"preact\";\n\nexport default function (props) {\n    return (\n        \n            
    \n                {props.title}\n            
    \n            \n                {props.children}\n            \n            \n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"title\":\"title__3ZVpg\",\"contents\":\"contents__20_NI\"};","import {createContext} from \"preact\";\n\nexport default createContext(null);\n","import style from './Latex.less';\nimport {useContext} from \"preact/hooks\";\nimport LatexRenderColor from \"../../contexts/LatexRenderColor\";\nimport LatexDefaultInline from \"../../contexts/LatexDefaultInline\";\nimport LatexDefaultDisplay from \"../../contexts/LatexDefaultDisplay\";\n\nexport const LatexDisplay = Object.freeze({\n    INLINE: style.inline,\n    BLOCK: style.block,\n})\n\nexport default function(props) {\n    // black, blue, brown, cyan, darkgray, gray, green, lightgray, lime, magenta, olive, orange, pink, purple, red, teal, violet, white, yellow\n    let renderColor = useContext(LatexRenderColor);\n    let defaultInline = useContext(LatexDefaultInline);\n    let defaultDisplay = useContext(LatexDefaultDisplay);\n\n    let inline;\n    if(props.inline === undefined) {\n        inline = defaultInline;\n    }\n    else {\n        inline = props.inline;\n    }\n\n    let display;\n    if(props.display === undefined) {\n        if(defaultDisplay === null) {\n            display = LatexDisplay.INLINE;\n        }\n        else {\n            display = defaultDisplay;\n        }\n    }\n    else {\n        display = props.display;\n    }\n\n    if(inline) {\n        let equation = `\\\\inline {\\\\color{${renderColor}} ${props.children} }`;\n        return (\n            {props.children}\n\n        );\n    }\n    else {\n        let equation = `{\\\\color{${renderColor}} ${props.children} }`;\n        return (\n            {props.children}\n\n        );\n    }\n}\n","import {Component} from 'preact'\nimport style from \"./Timer.less\"\n\n\nexport default class Timer extends Component {\n    constructor() {\n        super();\n        this.state = {\n            \"now\": Date.now()\n        };\n        this.timer = null;\n    }\n\n    componentDidMount() {\n        this.timer = setInterval(() => {\n            this.setState({\"now\": Date.now()})\n        }, 1000)\n    }\n\n    componentWillUnmount() {\n        if(this.timer !== null) {\n            clearInterval(this.timer)\n        }\n    }\n\n    render() {\n        let dateTo = \"Unknown date\";\n        let className = style.timer;\n\n        let parts = {\n            milliseconds: \"?\",\n            seconds: \"?\",\n            minutes: \"?\",\n            hours: \"?\",\n            days: \"?\",\n        };\n\n        if(this.props.to) {\n            dateTo = new Date(this.props.to);\n            let timeLeft = dateTo - this.state.now;\n\n            if(timeLeft > 0) {\n                parts = {\n                    milliseconds: timeLeft % 1000,\n                    seconds: Math.floor(timeLeft / 1000) % 60,\n                    minutes: Math.floor(timeLeft / 60000) % 60,\n                    hours: Math.floor(timeLeft / 3600000) % 24,\n                    days: Math.floor(timeLeft / 86400000),\n                };\n            }\n\n            else {\n                parts = {\n                    milliseconds: 0,\n                    seconds: 0,\n                    minutes: 0,\n                    hours: 0,\n                    days: 0,\n                };\n\n                className += \" \" + style.expired;\n            }\n        }\n        else {\n            className += \" \" + style.unknown;\n        }\n\n        return (\n            
    \n                
    \n                    {parts.days}\n                
    \n                
    \n                    giorni\n                
    \n                
    \n                    {parts.hours}\n                
    \n                
    \n                    ore\n                
    \n                
    \n                    {parts.minutes}\n                
    \n                
    \n                    minuti\n                
    \n                
    \n                    {parts.seconds}\n                
    \n                
    \n                    secondi\n                
    \n            
    \n        )\n    }\n}\n","import { options } from 'preact';\n\n/** @type {number} */\nlet currentIndex;\n\n/** @type {import('./internal').Component} */\nlet currentComponent;\n\n/** @type {number} */\nlet currentHook = 0;\n\n/** @type {Array} */\nlet afterPaintEffects = [];\n\nlet oldBeforeRender = options._render;\nlet oldAfterDiff = options.diffed;\nlet oldCommit = options._commit;\nlet oldBeforeUnmount = options.unmount;\n\nconst RAF_TIMEOUT = 100;\nlet prevRaf;\n\noptions._render = vnode => {\n\tif (oldBeforeRender) oldBeforeRender(vnode);\n\n\tcurrentComponent = vnode._component;\n\tcurrentIndex = 0;\n\n\tconst hooks = currentComponent.__hooks;\n\tif (hooks) {\n\t\thooks._pendingEffects.forEach(invokeCleanup);\n\t\thooks._pendingEffects.forEach(invokeEffect);\n\t\thooks._pendingEffects = [];\n\t}\n};\n\noptions.diffed = vnode => {\n\tif (oldAfterDiff) oldAfterDiff(vnode);\n\n\tconst c = vnode._component;\n\tif (c && c.__hooks && c.__hooks._pendingEffects.length) {\n\t\tafterPaint(afterPaintEffects.push(c));\n\t}\n};\n\noptions._commit = (vnode, commitQueue) => {\n\tcommitQueue.some(component => {\n\t\ttry {\n\t\t\tcomponent._renderCallbacks.forEach(invokeCleanup);\n\t\t\tcomponent._renderCallbacks = component._renderCallbacks.filter(cb =>\n\t\t\t\tcb._value ? invokeEffect(cb) : true\n\t\t\t);\n\t\t} catch (e) {\n\t\t\tcommitQueue.some(c => {\n\t\t\t\tif (c._renderCallbacks) c._renderCallbacks = [];\n\t\t\t});\n\t\t\tcommitQueue = [];\n\t\t\toptions._catchError(e, component._vnode);\n\t\t}\n\t});\n\n\tif (oldCommit) oldCommit(vnode, commitQueue);\n};\n\noptions.unmount = vnode => {\n\tif (oldBeforeUnmount) oldBeforeUnmount(vnode);\n\n\tconst c = vnode._component;\n\tif (c && c.__hooks) {\n\t\ttry {\n\t\t\tc.__hooks._list.forEach(invokeCleanup);\n\t\t} catch (e) {\n\t\t\toptions._catchError(e, c._vnode);\n\t\t}\n\t}\n};\n\n/**\n * Get a hook's state from the currentComponent\n * @param {number} index The index of the hook to get\n * @param {number} type The index of the hook to get\n * @returns {import('./internal').HookState}\n */\nfunction getHookState(index, type) {\n\tif (options._hook) {\n\t\toptions._hook(currentComponent, index, currentHook || type);\n\t}\n\tcurrentHook = 0;\n\n\t// Largely inspired by:\n\t// * https://github.com/michael-klein/funcy.js/blob/f6be73468e6ec46b0ff5aa3cc4c9baf72a29025a/src/hooks/core_hooks.mjs\n\t// * https://github.com/michael-klein/funcy.js/blob/650beaa58c43c33a74820a3c98b3c7079cf2e333/src/renderer.mjs\n\t// Other implementations to look at:\n\t// * https://codesandbox.io/s/mnox05qp8\n\tconst hooks =\n\t\tcurrentComponent.__hooks ||\n\t\t(currentComponent.__hooks = {\n\t\t\t_list: [],\n\t\t\t_pendingEffects: []\n\t\t});\n\n\tif (index >= hooks._list.length) {\n\t\thooks._list.push({});\n\t}\n\treturn hooks._list[index];\n}\n\n/**\n * @param {import('./index').StateUpdater} initialState\n */\nexport function useState(initialState) {\n\tcurrentHook = 1;\n\treturn useReducer(invokeOrReturn, initialState);\n}\n\n/**\n * @param {import('./index').Reducer} reducer\n * @param {import('./index').StateUpdater} initialState\n * @param {(initialState: any) => void} [init]\n * @returns {[ any, (state: any) => void ]}\n */\nexport function useReducer(reducer, initialState, init) {\n\t/** @type {import('./internal').ReducerHookState} */\n\tconst hookState = getHookState(currentIndex++, 2);\n\thookState._reducer = reducer;\n\tif (!hookState._component) {\n\t\thookState._component = currentComponent;\n\n\t\thookState._value = [\n\t\t\t!init ? invokeOrReturn(undefined, initialState) : init(initialState),\n\n\t\t\taction => {\n\t\t\t\tconst nextValue = hookState._reducer(hookState._value[0], action);\n\t\t\t\tif (hookState._value[0] !== nextValue) {\n\t\t\t\t\thookState._value[0] = nextValue;\n\t\t\t\t\thookState._component.setState({});\n\t\t\t\t}\n\t\t\t}\n\t\t];\n\t}\n\n\treturn hookState._value;\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++, 3);\n\tif (!options._skipEffects && argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent.__hooks._pendingEffects.push(state);\n\t}\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useLayoutEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++, 4);\n\tif (!options._skipEffects && argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent._renderCallbacks.push(state);\n\t}\n}\n\nexport function useRef(initialValue) {\n\tcurrentHook = 5;\n\treturn useMemo(() => ({ current: initialValue }), []);\n}\n\n/**\n * @param {object} ref\n * @param {() => object} createHandle\n * @param {any[]} args\n */\nexport function useImperativeHandle(ref, createHandle, args) {\n\tcurrentHook = 6;\n\tuseLayoutEffect(\n\t\t() => {\n\t\t\tif (typeof ref == 'function') ref(createHandle());\n\t\t\telse if (ref) ref.current = createHandle();\n\t\t},\n\t\targs == null ? args : args.concat(ref)\n\t);\n}\n\n/**\n * @param {() => any} factory\n * @param {any[]} args\n */\nexport function useMemo(factory, args) {\n\t/** @type {import('./internal').MemoHookState} */\n\tconst state = getHookState(currentIndex++, 7);\n\tif (argsChanged(state._args, args)) {\n\t\tstate._args = args;\n\t\tstate._factory = factory;\n\t\treturn (state._value = factory());\n\t}\n\n\treturn state._value;\n}\n\n/**\n * @param {() => void} callback\n * @param {any[]} args\n */\nexport function useCallback(callback, args) {\n\tcurrentHook = 8;\n\treturn useMemo(() => callback, args);\n}\n\n/**\n * @param {import('./internal').PreactContext} context\n */\nexport function useContext(context) {\n\tconst provider = currentComponent.context[context._id];\n\t// We could skip this call here, but than we'd not call\n\t// `options._hook`. We need to do that in order to make\n\t// the devtools aware of this hook.\n\tconst state = getHookState(currentIndex++, 9);\n\t// The devtools needs access to the context object to\n\t// be able to pull of the default value when no provider\n\t// is present in the tree.\n\tstate._context = context;\n\tif (!provider) return context._defaultValue;\n\t// This is probably not safe to convert to \"!\"\n\tif (state._value == null) {\n\t\tstate._value = true;\n\t\tprovider.sub(currentComponent);\n\t}\n\treturn provider.props.value;\n}\n\n/**\n * Display a custom label for a custom hook for the devtools panel\n * @type {(value: T, cb?: (value: T) => string | number) => void}\n */\nexport function useDebugValue(value, formatter) {\n\tif (options.useDebugValue) {\n\t\toptions.useDebugValue(formatter ? formatter(value) : value);\n\t}\n}\n\nexport function useErrorBoundary(cb) {\n\tconst state = getHookState(currentIndex++, 10);\n\tconst errState = useState();\n\tstate._value = cb;\n\tif (!currentComponent.componentDidCatch) {\n\t\tcurrentComponent.componentDidCatch = err => {\n\t\t\tif (state._value) state._value(err);\n\t\t\terrState[1](err);\n\t\t};\n\t}\n\treturn [\n\t\terrState[0],\n\t\t() => {\n\t\t\terrState[1](undefined);\n\t\t}\n\t];\n}\n\n/**\n * After paint effects consumer.\n */\nfunction flushAfterPaintEffects() {\n\tafterPaintEffects.some(component => {\n\t\tif (component._parentDom) {\n\t\t\ttry {\n\t\t\t\tcomponent.__hooks._pendingEffects.forEach(invokeCleanup);\n\t\t\t\tcomponent.__hooks._pendingEffects.forEach(invokeEffect);\n\t\t\t\tcomponent.__hooks._pendingEffects = [];\n\t\t\t} catch (e) {\n\t\t\t\tcomponent.__hooks._pendingEffects = [];\n\t\t\t\toptions._catchError(e, component._vnode);\n\t\t\t\treturn true;\n\t\t\t}\n\t\t}\n\t});\n\tafterPaintEffects = [];\n}\n\n/**\n * Schedule a callback to be invoked after the browser has a chance to paint a new frame.\n * Do this by combining requestAnimationFrame (rAF) + setTimeout to invoke a callback after\n * the next browser frame.\n *\n * Also, schedule a timeout in parallel to the the rAF to ensure the callback is invoked\n * even if RAF doesn't fire (for example if the browser tab is not visible)\n *\n * @param {() => void} callback\n */\nfunction afterNextFrame(callback) {\n\tconst done = () => {\n\t\tclearTimeout(timeout);\n\t\tcancelAnimationFrame(raf);\n\t\tsetTimeout(callback);\n\t};\n\tconst timeout = setTimeout(done, RAF_TIMEOUT);\n\n\tlet raf;\n\tif (typeof window != 'undefined') {\n\t\traf = requestAnimationFrame(done);\n\t}\n}\n\n// Note: if someone used options.debounceRendering = requestAnimationFrame,\n// then effects will ALWAYS run on the NEXT frame instead of the current one, incurring a ~16ms delay.\n// Perhaps this is not such a big deal.\n/**\n * Schedule afterPaintEffects flush after the browser paints\n * @param {number} newQueueLength\n */\nfunction afterPaint(newQueueLength) {\n\tif (newQueueLength === 1 || prevRaf !== options.requestAnimationFrame) {\n\t\tprevRaf = options.requestAnimationFrame;\n\t\t(prevRaf || afterNextFrame)(flushAfterPaintEffects);\n\t}\n}\n\n/**\n * @param {import('./internal').EffectHookState} hook\n */\nfunction invokeCleanup(hook) {\n\tif (typeof hook._cleanup == 'function') hook._cleanup();\n}\n\n/**\n * Invoke a Hook's effect\n * @param {import('./internal').EffectHookState} hook\n */\nfunction invokeEffect(hook) {\n\thook._cleanup = hook._value();\n}\n\n/**\n * @param {any[]} oldArgs\n * @param {any[]} newArgs\n */\nfunction argsChanged(oldArgs, newArgs) {\n\treturn !oldArgs || newArgs.some((arg, index) => arg !== oldArgs[index]);\n}\n\nfunction invokeOrReturn(arg, f) {\n\treturn typeof f == 'function' ? f(arg) : f;\n}\n","import style from \"./Todo.less\";\n\nexport default function (props) {\n\tif(process.env.NODE_ENV === \"development\") {\n\t\treturn {props.children};\n\t}\n\telse {\n\t\treturn null;\n\t}\n}\n","import style from \"./Split.less\";\n\nexport default function (props) {\n    let children;\n\n    if(Array.isArray(props.children)) {\n        children = props.children.map(element => {\n            return (\n                
    \n                    {element}\n                
    \n            );\n        });\n    }\n\n    else {\n        children = (\n            
    \n                {props.children}\n            
    \n        );\n    }\n    return (\n        
    \n            
    {children}
    \n        
    \n    );\n}\n","import style from \"./Example.less\";\nimport {Component} from \"preact\";\n\nexport default function(props) {\n    return (\n        
    \n            {props.children}\n        
    \n    );\n}\n","import style from \"./Box.less\";\n\nexport const BoxColors = Object.freeze({\n    RED: style.red,\n    ORANGE: style.orange,\n    YELLOW: style.yellow,\n    LIME: style.lime,\n    CYAN: style.cyan,\n    BLUE: style.blue,\n    MAGENTA: style.magenta,\n    DEFAULT: style.default\n})\n\nexport default function (props) {\n    let color = BoxColors.DEFAULT;\n    if(props.color) {\n        color = props.color;\n    }\n\n    return (\n        
    \n            {props.children}\n        
    \n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"timer\":\"timer__3Z2pL\",\"days\":\"days__myhe2\",\"hours\":\"hours__3JUDn\",\"minutes\":\"minutes__24lD7\",\"seconds\":\"seconds__2vZ4f\",\"count\":\"count__chi9X\",\"text\":\"text__34ldC\",\"unknown\":\"unknown__3sT2P\",\"expired\":\"expired__zNiuP\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"splitparent\":\"splitparent__3-wBs\",\"splitchild\":\"splitchild__begkX\"};","import style from \"./Panel.less\";\nimport Box from \"./Box\";\n\nexport default function(props) {\n\treturn (\n\t\t\n\t\t\t
    \n\t\t\t\t{props.title}\n\t\t\t
    \n\t\t\t
    \n\t\t\t\t{props.children}\n\t\t\t
    \n\t\t    \n\t);\n}\n","import {createContext} from \"preact\";\n\nexport default createContext(true);\n","import {Component} from 'preact'\nimport Section from \"../components/Elements/Section\";\nimport Latex from \"../components/Rendering/Latex\";\nimport Panel from \"../components/Elements/Panel\";\nimport Example from \"../components/Elements/Example\";\nimport Todo from \"../components/Elements/Todo\";\nimport Timer from \"../components/Elements/Timer\";\nimport LatexDefaultInline from \"../contexts/LatexDefaultInline\";\n\nconst r = String.raw;\n\nexport default function (props) {\n    return (\n        \n            
    \n                
    Calcolo Numerico
    \n                
    \n                    \n                        
    \n                            silvia.bonettini@unimore.it\n                        
    \n                        \n                    \n                        
    \n                            E' composto da:\n                        
    \n                        
      \n                            
    • 2 domande sugli argomenti teorici
      • \n                            
    • 1 domanda di implementazione algoritmo in MATLAB (facoltativa per i punteggi migliori del TBL)
      • \n                        
    \n                        \n                    \n                        
      \n                            
      2. \n                            
      3. \n                            
      4. \n                            
      5. \n                            
      6. \n                            
      7. \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Algoritmi che hanno:\n                        
    \n                        
      \n                            
    • numeri reali in input e output
      • \n                            
    • successioni delle quattro operazioni aritmetiche fondamentali come passi
      • \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Con i numeri floating point può capitare che un certo numero {r`\\alpha`} non sia rappresentato correttamente.\n                        
    \n                        
    \n                            In tal caso, il numero si indica con {r`\\alpha^*`}.\n                        
    \n                        \n                    \n                        
    \n                            È la differenza tra il numero desiderato e il numero rappresentato:\n                        
    \n                        
    \n                            {r`E_a = \\left | \\alpha - \\alpha^* \\right |`}\n                        
    \n                        \n                            Vale sempre 0, tranne in caso di underflow o overflow.\n                        \n                        \n                    \n                        
    \n                            Indica quanto il numero rappresentato differisce dal numero desiderato:\n                        
    \n                        
    \n                            {r`\\forall \\alpha \\neq 0, E_r = \\frac{E_a}{\\left | \\alpha \\right |}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            L'errore relativo di un numero reale rappresentato in virgola mobile è minore o uguale alla precisione di macchina:\n                        
    \n                        
    \n                            {r`E_r \\leq k \\cdot \\beta^{1-t}`}\n                        
    \n                        
      \n                            
    • \n                                \\beta è uguale alla base utilizzata (solitamente 2).\n                            
      • \n                            
    • \n                                t è uguale al numero di cifre della mantissa.\n                            
      • \n                            
    • \n                                k è uguale a 1 se il numero viene rappresentato per troncamento oppure a {r`\\frac{1}{2}`} se viene rappresentato per arrotondamento.\n                            
      • \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            L'insieme F è il sottoinsieme dei numeri reali rappresentabili in floating point dalla macchina che stiamo usando.\n                        
    \n                        
    \n                            Operazioni tra elementi di F producono risultati in {r`\\mathbb{R}`}, che però decaderanno nuovamente a elementi di F, perdendo informazioni.\n                        
    \n                        
    \n                            Il teorema della precisione di macchina si applica quindi anche ai risultati delle operazioni.\n                        
    \n                        \n                    \n                        
      \n                            
    • Hanno più di un elemento neutro.
      • \n                            
    • Un numero ha più opposti.
      • \n                            
    • Non sono associative.
      • \n                            
    • Non sono distributive.
      • \n                            
    • Non vale la legge di annullamento del prodotto.
      • \n                        
    \n                        \n                    \n                        
    \n                            Indica che un valore è soggetto alla precisione di macchina:\n                        
    \n                        
    \n                            {r`fl(x) = (x)(1 + \\epsilon_x)`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Errore dipendente solo dai dati.\n                        
    \n                        
    \n                            TODO: qual è la formula?\n                        
    \n                        
    \n                            È l'errore che si presenterebbe se {r`\\epsilon_1 = \\epsilon_2 = \\dots = 0`}.\n                        
    \n                        \n                    \n                        
    \n                            Errore dipendente solo dalle operazioni effettuate.\n                        
    \n                        
    \n                            TODO: qual è la formula?\n                        
    \n                        
    \n                            È l'errore che si presenterebbe se {r`\\epsilon_x = \\epsilon_y = \\dots = 0`}.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Un problema poco sensibile all'errore inerente.\n                        
    \n                        \n                            {r`y = \\frac{1}{x}`} è mal condizionato intorno allo 0 e ben condizionato lontano dallo 0.\n                        \n                        \n                    \n                        
    \n                            Un algoritmo poco sensibile all'errore algoritmico.\n                        
    \n                        \n                            
    \n                                Cerchiamo un algoritmo che risolva {r`2x = 4`}.\n                            
    \n                            
    \n                                Calcolare prima {r`t = fl \\left( \\frac{1}{4} \\right)`} e poi {r`x^* = fl ( 2 \\cdot t )`} porta a una perdita di precisione.\n                            
    \n                            
    \n                                Calcolare direttamente {r`x^* = fl \\left( \\frac{2}{4} \\right)`} non ha alcuna perdita di precisione e rende l'algoritmo più stabile del precedente.\n                            
    \n                            \n                        \n                
    \n                
    \n                    \n                        
    \n                            È il coefficiente di proporzionalità tra i dati e l'errore inerente.\n                        
    \n                        
    \n                            Essendo sempre maggiore di uno, si può dire che sia un coefficiente di amplificazione.\n                        
    \n                        
    \n                            Minore è l'indice di condizionamento, meglio condizionato è un problema.\n                        
    \n                        \n                    \n                        
    \n                            È il coefficiente di proporzionalità tra i dati e l'errore algoritmico.\n                        
    \n                        
    \n                            Essendo sempre maggiore di uno, si può dire che sia un coefficiente di amplificazione.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Matrice con determinante 0.\n                        
    \n                        
    \n                            Le matrici singolari non sono invertibili.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Funzione che associa un valore positivo a ogni vettore diverso da 0, e 0 al vettore zero.\n                        
    \n                        \n                            Esempi su Wikipedia\n                        \n                        \n                    \n                        
    \n                            Massimo dei valori assoluti di tutti gli elementi del vettore.\n                        
    \n                        
    \n                            {r`\\Vert x \\Vert_\\infty = max_{i = 1..n} | x_i |`}\n                        
    \n                        \n                    \n                        
    \n                            Somma dei valori assoluti di tutti gli elementi del vettore.\n                        
    \n                        
    \n                            {r`\\Vert x \\Vert_1 = \\sum_{i = 1}^n | x_i |`}\n                        
    \n                        \n                    \n                        
    \n                            Radice quadrata della somma dei quadrati di tutti gli elementi del vettore.\n                        
    \n                        
    \n                            {r`\\Vert x \\Vert_2 = \\sqrt{\\sum_{i = 1}^n x_i^2}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Funzione che associa un valore positivo a ogni matrice diversa da 0, e 0 alla matrice zero.\n                        
    \n                        
    \n                            Si ricavano dalle norme vettoriali:\n                        
    \n                        
    \n                            {r`\\Vert A \\Vert = sup_{x \\in \\mathbb{R}, x \\neq 0} \\frac{\\Vert A \\cdot x \\Vert}{\\Vert x \\Vert}`}\n                        
    \n                        \n                            sup è l'estremo superiore di un insieme. E' molto simile al massimo: ricordi le prime lezioni di Analisi?\n                        \n                        \n                    \n                        
    \n                            Massimo delle somme dei valori assoluti di tutti gli elementi di ogni riga di una matrice.\n                        
    \n                        
    \n                            {r`\\Vert A \\Vert_\\infty = max_{i = 1..n} \\sum_{j = 1}^n | a_{ij} |`}\n                        
    \n                        \n                    \n                        
    \n                            Massimo delle somme dei valori assoluti di tutti gli elementi di ogni colonna di una matrice.\n                        
    \n                        
    \n                            {r`\\Vert A \\Vert_1 = max_{j = 1..n} \\sum_{i = 1}^n | a_{ij} |`}\n                        
    \n                        \n                    \n                        
    \n                            Radice quadrata del rango del prodotto tra una matrice e la sua trasposta.\n                        
    \n                        
    \n                            {r`\\Vert A \\Vert_2 = \\sqrt{\\rho ( A^T \\times A ) }`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Le norme sono usate per calcolare l'errore relativo tra due vettori o matrici:\n                        
    \n                        
    \n                            {r`\\frac{\\Vert x - y \\Vert}{\\Vert x \\Vert}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            La fattorizzazione è il processo che permette di risolvere sistemi di equazioni lineari rappresentati in forma di matrice.\n                        
    \n                        
    \n                            Esistono molteplici algoritmi in grado di realizzarla: mentre tutti portano alla stessa soluzione, possono avere velocità e indici algoritmici diversi.\n                        
    \n                        
    \n                            Il sistema lineare da risolvere viene diviso in due parti: la matrice dei coefficienti e il vettore termine noto.\n                        
    \n                        \n                    \n                        
    \n\n                        
    \n                        \n                
    \n            
    \n            \n    )\n}\n"],"sourceRoot":""}
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precedente.")))),n(w.a,null,n(q.a,{title:"Indice di condizionamento"},n("p",null,"È il coefficiente di proporzionalità tra i dati e l'",n("b",null,"errore inerente"),"."),n("p",null,"Essendo sempre maggiore di uno, si può dire che sia un coefficiente di amplificazione."),n("p",null,"Minore è l'indice di condizionamento, meglio condizionato è un problema.")),n(q.a,{title:"Indice algoritmico"},n("p",null,"È il coefficiente di proporzionalità tra i dati e l'",n("b",null,"errore algoritmico"),"."),n("p",null,"Essendo sempre maggiore di uno, si può dire che sia un coefficiente di amplificazione."))),n(w.a,{title:"Le cose più difficili di Algebra Lineare"},n(q.a,{title:"Matrice singolare"},n("p",null,"Matrice con determinante 0."),n("p",null,"Le matrici singolari ",n("b",null,"non sono invertibili"),"."))),n(w.a,{title:"Norme"},n(q.a,{title:"Norma vettoriale"},n("p",null,"Funzione che associa un valore positivo a ogni vettore diverso da 0, e 0 al vettore zero."),n(O.a,null,n("a",{href:"https://it.wikipedia.org/wiki/Norma_(matematica)#/media/File:Vector_norms.svg"},"Esempi su Wikipedia"))),n(q.a,{title:"Norma a infinito"},n("p",null,"Massimo dei valori assoluti di tutti gli elementi del vettore."),n("p",null,n(N.b,null,C(s())))),n(q.a,{title:"Norma a 1"},n("p",null,"Somma dei valori assoluti di tutti gli elementi del vettore."),n("p",null,n(N.b,null,C(c())))),n(q.a,{title:"Norma a 2"},n("p",null,"Radice quadrata della somma dei quadrati di tutti gli elementi del vettore."),n("p",null,n(N.b,null,C(u()))))),n(w.a,null,n(q.a,{title:"Norma matriciale indotta"},n("p",null,"Funzione che associa un valore positivo a ogni matrice diversa da 0, e 0 alla matrice zero."),n("p",null,"Si ricavano dalle norme vettoriali:"),n("p",null,n(N.b,null,C(a()))),n(O.a,null,n(N.b,null,"sup")," è l'estremo superiore di un insieme. E' molto simile al massimo: ricordi le prime lezioni di Analisi?")),n(q.a,{title:"Norma a infinito"},n("p",null,"Massimo delle somme dei valori assoluti di tutti gli elementi di ogni riga di una matrice."),n("p",null,n(N.b,null,C(o())))),n(q.a,{title:"Norma a 1"},n("p",null,"Massimo delle somme dei valori assoluti di tutti gli elementi di ogni colonna di una matrice."),n("p",null,n(N.b,null,C(r())))),n(q.a,{title:"Norma a 2"},n("p",null,"Radice quadrata del rango del prodotto tra una matrice e la sua trasposta."),n("p",null,n(N.b,null,C(l()))))),n(w.a,null,n(q.a,{title:"Errore relativo tra vettori e matrici"},n("p",null,"Le norme sono usate per calcolare l'errore relativo tra due vettori o matrici:"),n("p",null,n(N.b,null,C(i()))))),n(w.a,{title:"Fattorizzazione"},n(q.a,{title:"Cos'è?"},n("p",null,"La fattorizzazione è il processo che permette di risolvere sistemi di equazioni lineari rappresentati in forma di matrice."),n("p",null,"Esistono molteplici algoritmi in grado di realizzarla: mentre tutti portano alla stessa soluzione, possono avere ",n("b",null,"velocità")," e ",n("b",null,"indici algoritmici")," diversi."),n("p",null,"Il sistema lineare da risolvere viene diviso in due parti: la ",n("i",null,"matrice dei coefficienti")," e il ",n("i",null,"vettore termine noto"),".")),n(q.a,{title:"Teorema di Rouché-Capélli"},n("p",null)))))}}.call(this,t("hosL").h)}}]);
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extracted by mini-css-extract-plugin\nmodule.exports = {\"example\":\"example__9acWs\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"box\":\"box__3cKyY\",\"default\":\"default__v-emJ\",\"red\":\"red__339Cz\",\"orange\":\"orange__24_8v\",\"yellow\":\"yellow__1Jo9W\",\"lime\":\"lime__34yV5\",\"cyan\":\"cyan__3RqLr\",\"blue\":\"blue__13Wnj\",\"magenta\":\"magenta__2tkzq\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"inline\":\"inline__1yl8V\",\"block\":\"block__fPiiB\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"todo\":\"todo__2IWIS\"};","import Split from \"../Layout/Split\";\nimport {Fragment} from \"preact\";\n\nexport default function (props) {\n    return (\n        \n            
    \n                {props.title}\n            
    \n            \n                {props.children}\n            \n            \n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"title\":\"title__3ZVpg\",\"contents\":\"contents__20_NI\"};","import {createContext} from \"preact\";\n\nexport default createContext(null);\n","import style from './Latex.less';\nimport {useContext} from \"preact/hooks\";\nimport LatexRenderColor from \"../../contexts/LatexRenderColor\";\nimport LatexDefaultInline from \"../../contexts/LatexDefaultInline\";\nimport LatexDefaultDisplay from \"../../contexts/LatexDefaultDisplay\";\n\nexport const LatexDisplay = Object.freeze({\n    INLINE: style.inline,\n    BLOCK: style.block,\n})\n\nexport default function(props) {\n    // black, blue, brown, cyan, darkgray, gray, green, lightgray, lime, magenta, olive, orange, pink, purple, red, teal, violet, white, yellow\n    let renderColor = useContext(LatexRenderColor);\n    let defaultInline = useContext(LatexDefaultInline);\n    let defaultDisplay = useContext(LatexDefaultDisplay);\n\n    let inline;\n    if(props.inline === undefined) {\n        inline = defaultInline;\n    }\n    else {\n        inline = props.inline;\n    }\n\n    let display;\n    if(props.display === undefined) {\n        if(defaultDisplay === null) {\n            display = LatexDisplay.INLINE;\n        }\n        else {\n            display = defaultDisplay;\n        }\n    }\n    else {\n        display = props.display;\n    }\n\n    if(inline) {\n        let equation = `\\\\inline {\\\\color{${renderColor}} ${props.children} }`;\n        return (\n            {props.children}\n\n        );\n    }\n    else {\n        let equation = `{\\\\color{${renderColor}} ${props.children} }`;\n        return (\n            {props.children}\n\n        );\n    }\n}\n","import {Component} from 'preact'\nimport style from \"./Timer.less\"\n\n\nexport default class Timer extends Component {\n    constructor() {\n        super();\n        this.state = {\n            \"now\": Date.now()\n        };\n        this.timer = null;\n    }\n\n    componentDidMount() {\n        this.timer = setInterval(() => {\n            this.setState({\"now\": Date.now()})\n        }, 1000)\n    }\n\n    componentWillUnmount() {\n        if(this.timer !== null) {\n            clearInterval(this.timer)\n        }\n    }\n\n    render() {\n        let dateTo = \"Unknown date\";\n        let className = style.timer;\n\n        let parts = {\n            milliseconds: \"?\",\n            seconds: \"?\",\n            minutes: \"?\",\n            hours: \"?\",\n            days: \"?\",\n        };\n\n        if(this.props.to) {\n            dateTo = new Date(this.props.to);\n            let timeLeft = dateTo - this.state.now;\n\n            if(timeLeft > 0) {\n                parts = {\n                    milliseconds: timeLeft % 1000,\n                    seconds: Math.floor(timeLeft / 1000) % 60,\n                    minutes: Math.floor(timeLeft / 60000) % 60,\n                    hours: Math.floor(timeLeft / 3600000) % 24,\n                    days: Math.floor(timeLeft / 86400000),\n                };\n            }\n\n            else {\n                parts = {\n                    milliseconds: 0,\n                    seconds: 0,\n                    minutes: 0,\n                    hours: 0,\n                    days: 0,\n                };\n\n                className += \" \" + style.expired;\n            }\n        }\n        else {\n            className += \" \" + style.unknown;\n        }\n\n        return (\n            
    \n                
    \n                    {parts.days}\n                
    \n                
    \n                    giorni\n                
    \n                
    \n                    {parts.hours}\n                
    \n                
    \n                    ore\n                
    \n                
    \n                    {parts.minutes}\n                
    \n                
    \n                    minuti\n                
    \n                
    \n                    {parts.seconds}\n                
    \n                
    \n                    secondi\n                
    \n            
    \n        )\n    }\n}\n","import { options } from 'preact';\n\n/** @type {number} */\nlet currentIndex;\n\n/** @type {import('./internal').Component} */\nlet currentComponent;\n\n/** @type {number} */\nlet currentHook = 0;\n\n/** @type {Array} */\nlet afterPaintEffects = [];\n\nlet oldBeforeRender = options._render;\nlet oldAfterDiff = options.diffed;\nlet oldCommit = options._commit;\nlet oldBeforeUnmount = options.unmount;\n\nconst RAF_TIMEOUT = 100;\nlet prevRaf;\n\noptions._render = vnode => {\n\tif (oldBeforeRender) oldBeforeRender(vnode);\n\n\tcurrentComponent = vnode._component;\n\tcurrentIndex = 0;\n\n\tconst hooks = currentComponent.__hooks;\n\tif (hooks) {\n\t\thooks._pendingEffects.forEach(invokeCleanup);\n\t\thooks._pendingEffects.forEach(invokeEffect);\n\t\thooks._pendingEffects = [];\n\t}\n};\n\noptions.diffed = vnode => {\n\tif (oldAfterDiff) oldAfterDiff(vnode);\n\n\tconst c = vnode._component;\n\tif (c && c.__hooks && c.__hooks._pendingEffects.length) {\n\t\tafterPaint(afterPaintEffects.push(c));\n\t}\n};\n\noptions._commit = (vnode, commitQueue) => {\n\tcommitQueue.some(component => {\n\t\ttry {\n\t\t\tcomponent._renderCallbacks.forEach(invokeCleanup);\n\t\t\tcomponent._renderCallbacks = component._renderCallbacks.filter(cb =>\n\t\t\t\tcb._value ? invokeEffect(cb) : true\n\t\t\t);\n\t\t} catch (e) {\n\t\t\tcommitQueue.some(c => {\n\t\t\t\tif (c._renderCallbacks) c._renderCallbacks = [];\n\t\t\t});\n\t\t\tcommitQueue = [];\n\t\t\toptions._catchError(e, component._vnode);\n\t\t}\n\t});\n\n\tif (oldCommit) oldCommit(vnode, commitQueue);\n};\n\noptions.unmount = vnode => {\n\tif (oldBeforeUnmount) oldBeforeUnmount(vnode);\n\n\tconst c = vnode._component;\n\tif (c && c.__hooks) {\n\t\ttry {\n\t\t\tc.__hooks._list.forEach(invokeCleanup);\n\t\t} catch (e) {\n\t\t\toptions._catchError(e, c._vnode);\n\t\t}\n\t}\n};\n\n/**\n * Get a hook's state from the currentComponent\n * @param {number} index The index of the hook to get\n * @param {number} type The index of the hook to get\n * @returns {import('./internal').HookState}\n */\nfunction getHookState(index, type) {\n\tif (options._hook) {\n\t\toptions._hook(currentComponent, index, currentHook || type);\n\t}\n\tcurrentHook = 0;\n\n\t// Largely inspired by:\n\t// * https://github.com/michael-klein/funcy.js/blob/f6be73468e6ec46b0ff5aa3cc4c9baf72a29025a/src/hooks/core_hooks.mjs\n\t// * https://github.com/michael-klein/funcy.js/blob/650beaa58c43c33a74820a3c98b3c7079cf2e333/src/renderer.mjs\n\t// Other implementations to look at:\n\t// * https://codesandbox.io/s/mnox05qp8\n\tconst hooks =\n\t\tcurrentComponent.__hooks ||\n\t\t(currentComponent.__hooks = {\n\t\t\t_list: [],\n\t\t\t_pendingEffects: []\n\t\t});\n\n\tif (index >= hooks._list.length) {\n\t\thooks._list.push({});\n\t}\n\treturn hooks._list[index];\n}\n\n/**\n * @param {import('./index').StateUpdater} initialState\n */\nexport function useState(initialState) {\n\tcurrentHook = 1;\n\treturn useReducer(invokeOrReturn, initialState);\n}\n\n/**\n * @param {import('./index').Reducer} reducer\n * @param {import('./index').StateUpdater} initialState\n * @param {(initialState: any) => void} [init]\n * @returns {[ any, (state: any) => void ]}\n */\nexport function useReducer(reducer, initialState, init) {\n\t/** @type {import('./internal').ReducerHookState} */\n\tconst hookState = getHookState(currentIndex++, 2);\n\thookState._reducer = reducer;\n\tif (!hookState._component) {\n\t\thookState._component = currentComponent;\n\n\t\thookState._value = [\n\t\t\t!init ? invokeOrReturn(undefined, initialState) : init(initialState),\n\n\t\t\taction => {\n\t\t\t\tconst nextValue = hookState._reducer(hookState._value[0], action);\n\t\t\t\tif (hookState._value[0] !== nextValue) {\n\t\t\t\t\thookState._value[0] = nextValue;\n\t\t\t\t\thookState._component.setState({});\n\t\t\t\t}\n\t\t\t}\n\t\t];\n\t}\n\n\treturn hookState._value;\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++, 3);\n\tif (!options._skipEffects && argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent.__hooks._pendingEffects.push(state);\n\t}\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useLayoutEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++, 4);\n\tif (!options._skipEffects && argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent._renderCallbacks.push(state);\n\t}\n}\n\nexport function useRef(initialValue) {\n\tcurrentHook = 5;\n\treturn useMemo(() => ({ current: initialValue }), []);\n}\n\n/**\n * @param {object} ref\n * @param {() => object} createHandle\n * @param {any[]} args\n */\nexport function useImperativeHandle(ref, createHandle, args) {\n\tcurrentHook = 6;\n\tuseLayoutEffect(\n\t\t() => {\n\t\t\tif (typeof ref == 'function') ref(createHandle());\n\t\t\telse if (ref) ref.current = createHandle();\n\t\t},\n\t\targs == null ? args : args.concat(ref)\n\t);\n}\n\n/**\n * @param {() => any} factory\n * @param {any[]} args\n */\nexport function useMemo(factory, args) {\n\t/** @type {import('./internal').MemoHookState} */\n\tconst state = getHookState(currentIndex++, 7);\n\tif (argsChanged(state._args, args)) {\n\t\tstate._args = args;\n\t\tstate._factory = factory;\n\t\treturn (state._value = factory());\n\t}\n\n\treturn state._value;\n}\n\n/**\n * @param {() => void} callback\n * @param {any[]} args\n */\nexport function useCallback(callback, args) {\n\tcurrentHook = 8;\n\treturn useMemo(() => callback, args);\n}\n\n/**\n * @param {import('./internal').PreactContext} context\n */\nexport function useContext(context) {\n\tconst provider = currentComponent.context[context._id];\n\t// We could skip this call here, but than we'd not call\n\t// `options._hook`. We need to do that in order to make\n\t// the devtools aware of this hook.\n\tconst state = getHookState(currentIndex++, 9);\n\t// The devtools needs access to the context object to\n\t// be able to pull of the default value when no provider\n\t// is present in the tree.\n\tstate._context = context;\n\tif (!provider) return context._defaultValue;\n\t// This is probably not safe to convert to \"!\"\n\tif (state._value == null) {\n\t\tstate._value = true;\n\t\tprovider.sub(currentComponent);\n\t}\n\treturn provider.props.value;\n}\n\n/**\n * Display a custom label for a custom hook for the devtools panel\n * @type {(value: T, cb?: (value: T) => string | number) => void}\n */\nexport function useDebugValue(value, formatter) {\n\tif (options.useDebugValue) {\n\t\toptions.useDebugValue(formatter ? formatter(value) : value);\n\t}\n}\n\nexport function useErrorBoundary(cb) {\n\tconst state = getHookState(currentIndex++, 10);\n\tconst errState = useState();\n\tstate._value = cb;\n\tif (!currentComponent.componentDidCatch) {\n\t\tcurrentComponent.componentDidCatch = err => {\n\t\t\tif (state._value) state._value(err);\n\t\t\terrState[1](err);\n\t\t};\n\t}\n\treturn [\n\t\terrState[0],\n\t\t() => {\n\t\t\terrState[1](undefined);\n\t\t}\n\t];\n}\n\n/**\n * After paint effects consumer.\n */\nfunction flushAfterPaintEffects() {\n\tafterPaintEffects.some(component => {\n\t\tif (component._parentDom) {\n\t\t\ttry {\n\t\t\t\tcomponent.__hooks._pendingEffects.forEach(invokeCleanup);\n\t\t\t\tcomponent.__hooks._pendingEffects.forEach(invokeEffect);\n\t\t\t\tcomponent.__hooks._pendingEffects = [];\n\t\t\t} catch (e) {\n\t\t\t\tcomponent.__hooks._pendingEffects = [];\n\t\t\t\toptions._catchError(e, component._vnode);\n\t\t\t\treturn true;\n\t\t\t}\n\t\t}\n\t});\n\tafterPaintEffects = [];\n}\n\n/**\n * Schedule a callback to be invoked after the browser has a chance to paint a new frame.\n * Do this by combining requestAnimationFrame (rAF) + setTimeout to invoke a callback after\n * the next browser frame.\n *\n * Also, schedule a timeout in parallel to the the rAF to ensure the callback is invoked\n * even if RAF doesn't fire (for example if the browser tab is not visible)\n *\n * @param {() => void} callback\n */\nfunction afterNextFrame(callback) {\n\tconst done = () => {\n\t\tclearTimeout(timeout);\n\t\tcancelAnimationFrame(raf);\n\t\tsetTimeout(callback);\n\t};\n\tconst timeout = setTimeout(done, RAF_TIMEOUT);\n\n\tlet raf;\n\tif (typeof window != 'undefined') {\n\t\traf = requestAnimationFrame(done);\n\t}\n}\n\n// Note: if someone used options.debounceRendering = requestAnimationFrame,\n// then effects will ALWAYS run on the NEXT frame instead of the current one, incurring a ~16ms delay.\n// Perhaps this is not such a big deal.\n/**\n * Schedule afterPaintEffects flush after the browser paints\n * @param {number} newQueueLength\n */\nfunction afterPaint(newQueueLength) {\n\tif (newQueueLength === 1 || prevRaf !== options.requestAnimationFrame) {\n\t\tprevRaf = options.requestAnimationFrame;\n\t\t(prevRaf || afterNextFrame)(flushAfterPaintEffects);\n\t}\n}\n\n/**\n * @param {import('./internal').EffectHookState} hook\n */\nfunction invokeCleanup(hook) {\n\tif (typeof hook._cleanup == 'function') hook._cleanup();\n}\n\n/**\n * Invoke a Hook's effect\n * @param {import('./internal').EffectHookState} hook\n */\nfunction invokeEffect(hook) {\n\thook._cleanup = hook._value();\n}\n\n/**\n * @param {any[]} oldArgs\n * @param {any[]} newArgs\n */\nfunction argsChanged(oldArgs, newArgs) {\n\treturn !oldArgs || newArgs.some((arg, index) => arg !== oldArgs[index]);\n}\n\nfunction invokeOrReturn(arg, f) {\n\treturn typeof f == 'function' ? f(arg) : f;\n}\n","import style from \"./Todo.less\";\n\nexport default function (props) {\n\tif(process.env.NODE_ENV === \"development\") {\n\t\treturn {props.children};\n\t}\n\telse {\n\t\treturn null;\n\t}\n}\n","import style from \"./Split.less\";\n\nexport default function (props) {\n    let children;\n\n    if(Array.isArray(props.children)) {\n        children = props.children.map(element => {\n            return (\n                
    \n                    {element}\n                
    \n            );\n        });\n    }\n\n    else {\n        children = (\n            
    \n                {props.children}\n            
    \n        );\n    }\n    return (\n        
    \n            
    {children}
    \n        
    \n    );\n}\n","import style from \"./Example.less\";\nimport {Component} from \"preact\";\n\nexport default function(props) {\n    return (\n        
    \n            {props.children}\n        
    \n    );\n}\n","import style from \"./Box.less\";\n\nexport const BoxColors = Object.freeze({\n    RED: style.red,\n    ORANGE: style.orange,\n    YELLOW: style.yellow,\n    LIME: style.lime,\n    CYAN: style.cyan,\n    BLUE: style.blue,\n    MAGENTA: style.magenta,\n    DEFAULT: style.default\n})\n\nexport default function (props) {\n    let color = BoxColors.DEFAULT;\n    if(props.color) {\n        color = props.color;\n    }\n\n    return (\n        
    \n            {props.children}\n        
    \n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"timer\":\"timer__3Z2pL\",\"days\":\"days__myhe2\",\"hours\":\"hours__3JUDn\",\"minutes\":\"minutes__24lD7\",\"seconds\":\"seconds__2vZ4f\",\"count\":\"count__chi9X\",\"text\":\"text__34ldC\",\"unknown\":\"unknown__3sT2P\",\"expired\":\"expired__zNiuP\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"splitparent\":\"splitparent__3-wBs\",\"splitchild\":\"splitchild__begkX\"};","import style from \"./Panel.less\";\nimport Box from \"./Box\";\n\nexport default function(props) {\n\treturn (\n\t\t\n\t\t\t
    \n\t\t\t\t{props.title}\n\t\t\t
    \n\t\t\t
    \n\t\t\t\t{props.children}\n\t\t\t
    \n\t\t    \n\t);\n}\n","import {createContext} from \"preact\";\n\nexport default createContext(true);\n","import {Component} from 'preact'\nimport Section from \"../components/Elements/Section\";\nimport Latex from \"../components/Rendering/Latex\";\nimport Panel from \"../components/Elements/Panel\";\nimport Example from \"../components/Elements/Example\";\nimport Todo from \"../components/Elements/Todo\";\nimport Timer from \"../components/Elements/Timer\";\nimport LatexDefaultInline from \"../contexts/LatexDefaultInline\";\n\nconst r = String.raw;\n\nexport default function (props) {\n    return (\n        \n            
    \n                
    Calcolo Numerico
    \n                
    \n                    \n                        \n                    \n                    \n                        
    \n                            Se sei uno studente dell'Unimore, puoi accedere all'archivio del corso su Google Drive..\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            E' composto da:\n                        
    \n                        
      \n                            
    • 2 domande sugli argomenti teorici
      • \n                            
    • 1 domanda di implementazione algoritmo in MATLAB
      • \n                        
    \n                        \n                    \n                        
      \n                            
      2. \n                            
      3. \n                            
      4. \n                            
      5. \n                            
      6. \n                            
      7. \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Algoritmi che hanno:\n                        
    \n                        
      \n                            
    • numeri reali in input e output
      • \n                            
    • successioni delle quattro operazioni aritmetiche fondamentali come passi
      • \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Con i numeri floating point può capitare che un certo numero {r`\\alpha`} non sia rappresentato correttamente.\n                        
    \n                        
    \n                            In tal caso, il numero si indica con {r`\\alpha^*`}.\n                        
    \n                        \n                    \n                        
    \n                            È la differenza tra il numero desiderato e il numero rappresentato:\n                        
    \n                        
    \n                            {r`E_a = \\left | \\alpha - \\alpha^* \\right |`}\n                        
    \n                        \n                            Vale sempre 0, tranne in caso di underflow o overflow.\n                        \n                        \n                    \n                        
    \n                            Indica quanto il numero rappresentato differisce dal numero desiderato:\n                        
    \n                        
    \n                            {r`\\forall \\alpha \\neq 0, E_r = \\frac{E_a}{\\left | \\alpha \\right |}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            L'errore relativo di un numero reale rappresentato in virgola mobile è minore o uguale alla precisione di macchina:\n                        
    \n                        
    \n                            {r`E_r \\leq k \\cdot \\beta^{1-t}`}\n                        
    \n                        
      \n                            
    • \n                                \\beta è uguale alla base utilizzata (solitamente 2).\n                            
      • \n                            
    • \n                                t è uguale al numero di cifre della mantissa.\n                            
      • \n                            
    • \n                                k è uguale a 1 se il numero viene rappresentato per troncamento oppure a {r`\\frac{1}{2}`} se viene rappresentato per arrotondamento.\n                            
      • \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            L'insieme F è il sottoinsieme dei numeri reali rappresentabili in floating point dalla macchina che stiamo usando.\n                        
    \n                        
    \n                            Operazioni tra elementi di F producono risultati in {r`\\mathbb{R}`}, che però decaderanno nuovamente a elementi di F, perdendo informazioni.\n                        
    \n                        
    \n                            Il teorema della precisione di macchina si applica quindi anche ai risultati delle operazioni.\n                        
    \n                        \n                    \n                        
      \n                            
    • Hanno più di un elemento neutro.
      • \n                            
    • Un numero ha più opposti.
      • \n                            
    • Non sono associative.
      • \n                            
    • Non sono distributive.
      • \n                            
    • Non vale la legge di annullamento del prodotto.
      • \n                        
    \n                        \n                    \n                        
    \n                            Indica che un valore è soggetto alla precisione di macchina:\n                        
    \n                        
    \n                            {r`fl(x) = (x)(1 + \\epsilon_x)`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Errore dipendente solo dai dati.\n                        
    \n                        
    \n                            TODO: qual è la formula?\n                        
    \n                        
    \n                            È l'errore che si presenterebbe se {r`\\epsilon_1 = \\epsilon_2 = \\dots = 0`}.\n                        
    \n                        \n                    \n                        
    \n                            Errore dipendente solo dalle operazioni effettuate.\n                        
    \n                        
    \n                            TODO: qual è la formula?\n                        
    \n                        
    \n                            È l'errore che si presenterebbe se {r`\\epsilon_x = \\epsilon_y = \\dots = 0`}.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Un problema poco sensibile all'errore inerente.\n                        
    \n                        \n                            {r`y = \\frac{1}{x}`} è mal condizionato intorno allo 0 e ben condizionato lontano dallo 0.\n                        \n                        \n                    \n                        
    \n                            Un algoritmo poco sensibile all'errore algoritmico.\n                        
    \n                        \n                            
    \n                                Cerchiamo un algoritmo che risolva {r`2x = 4`}.\n                            
    \n                            
    \n                                Calcolare prima {r`t = fl \\left( \\frac{1}{4} \\right)`} e poi {r`x^* = fl ( 2 \\cdot t )`} porta a una perdita di precisione.\n                            
    \n                            
    \n                                Calcolare direttamente {r`x^* = fl \\left( \\frac{2}{4} \\right)`} non ha alcuna perdita di precisione e rende l'algoritmo più stabile del precedente.\n                            
    \n                            \n                        \n                
    \n                
    \n                    \n                        
    \n                            È il coefficiente di proporzionalità tra i dati e l'errore inerente.\n                        
    \n                        
    \n                            Essendo sempre maggiore di uno, si può dire che sia un coefficiente di amplificazione.\n                        
    \n                        
    \n                            Minore è l'indice di condizionamento, meglio condizionato è un problema.\n                        
    \n                        \n                    \n                        
    \n                            È il coefficiente di proporzionalità tra i dati e l'errore algoritmico.\n                        
    \n                        
    \n                            Essendo sempre maggiore di uno, si può dire che sia un coefficiente di amplificazione.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Matrice con determinante 0.\n                        
    \n                        
    \n                            Le matrici singolari non sono invertibili.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Funzione che associa un valore positivo a ogni vettore diverso da 0, e 0 al vettore zero.\n                        
    \n                        \n                            Esempi su Wikipedia\n                        \n                        \n                    \n                        
    \n                            Massimo dei valori assoluti di tutti gli elementi del vettore.\n                        
    \n                        
    \n                            {r`\\Vert x \\Vert_\\infty = max_{i = 1..n} | x_i |`}\n                        
    \n                        \n                    \n                        
    \n                            Somma dei valori assoluti di tutti gli elementi del vettore.\n                        
    \n                        
    \n                            {r`\\Vert x \\Vert_1 = \\sum_{i = 1}^n | x_i |`}\n                        
    \n                        \n                    \n                        
    \n                            Radice quadrata della somma dei quadrati di tutti gli elementi del vettore.\n                        
    \n                        
    \n                            {r`\\Vert x \\Vert_2 = \\sqrt{\\sum_{i = 1}^n x_i^2}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Funzione che associa un valore positivo a ogni matrice diversa da 0, e 0 alla matrice zero.\n                        
    \n                        
    \n                            Si ricavano dalle norme vettoriali:\n                        
    \n                        
    \n                            {r`\\Vert A \\Vert = sup_{x \\in \\mathbb{R}, x \\neq 0} \\frac{\\Vert A \\cdot x \\Vert}{\\Vert x \\Vert}`}\n                        
    \n                        \n                            sup è l'estremo superiore di un insieme. E' molto simile al massimo: ricordi le prime lezioni di Analisi?\n                        \n                        \n                    \n                        
    \n                            Massimo delle somme dei valori assoluti di tutti gli elementi di ogni riga di una matrice.\n                        
    \n                        
    \n                            {r`\\Vert A \\Vert_\\infty = max_{i = 1..n} \\sum_{j = 1}^n | a_{ij} |`}\n                        
    \n                        \n                    \n                        
    \n                            Massimo delle somme dei valori assoluti di tutti gli elementi di ogni colonna di una matrice.\n                        
    \n                        
    \n                            {r`\\Vert A \\Vert_1 = max_{j = 1..n} \\sum_{i = 1}^n | a_{ij} |`}\n                        
    \n                        \n                    \n                        
    \n                            Radice quadrata del rango del prodotto tra una matrice e la sua trasposta.\n                        
    \n                        
    \n                            {r`\\Vert A \\Vert_2 = \\sqrt{\\rho ( A^T \\times A ) }`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Le norme sono usate per calcolare l'errore relativo tra due vettori o matrici:\n                        
    \n                        
    \n                            {r`\\frac{\\Vert x - y \\Vert}{\\Vert x \\Vert}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            La fattorizzazione è il processo che permette di risolvere sistemi di equazioni lineari rappresentati in forma di matrice.\n                        
    \n                        
    \n                            Esistono molteplici algoritmi in grado di realizzarla: mentre tutti portano alla stessa soluzione, possono avere velocità e indici algoritmici diversi.\n                        
    \n                        
    \n                            Il sistema lineare da risolvere viene diviso in due parti: la matrice dei coefficienti e il vettore termine noto.\n                        
    \n                        \n                    \n                        
    \n\n                        
    \n                        \n                
    \n            
    \n            \n    )\n}\n"],"sourceRoot":""}
\ No newline at end of file
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index 0000000..8a9ebe8
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E' molto simile al massimo: ricordi le prime lezioni di Analisi?")),e(o.a,{title:"Norma a infinito"},e("p",null,"Massimo delle somme dei valori assoluti di tutti gli elementi di ogni riga di una matrice."),e("p",null,e(t.b,null,M(q||(q=C`\Vert A \Vert_\infty = max_{i = 1..n} \sum_{j = 1}^n | a_{ij} |`))))),e(o.a,{title:"Norma a 1"},e("p",null,"Massimo delle somme dei valori assoluti di tutti gli elementi di ogni colonna di una matrice."),e("p",null,e(t.b,null,M(O||(O=C`\Vert A \Vert_1 = max_{j = 1..n} \sum_{i = 1}^n | a_{ij} |`))))),e(o.a,{title:"Norma a 2"},e("p",null,"Radice quadrata del rango del prodotto tra una matrice e la sua trasposta."),e("p",null,e(t.b,null,M(H||(H=C`\Vert A \Vert_2 = \sqrt{\rho ( A^T \times A ) }`)))))),e(l.a,null,e(o.a,{title:"Errore relativo tra vettori e matrici"},e("p",null,"Le norme sono usate per calcolare l'errore relativo tra due vettori o matrici:"),e("p",null,e(t.b,null,M(k||(k=C`\frac{\Vert x - y \Vert}{\Vert x \Vert}`)))))),e(l.a,{title:"Fattorizzazione"},e(o.a,{title:"Cos'è?"},e("p",null,"La fattorizzazione è il processo che permette di risolvere sistemi di equazioni lineari rappresentati in forma di matrice."),e("p",null,"Esistono molteplici algoritmi in grado di realizzarla: mentre tutti portano alla stessa soluzione, possono avere ",e("b",null,"velocità")," e ",e("b",null,"indici algoritmici")," diversi."),e("p",null,"Il sistema lineare da risolvere viene diviso in due parti: la ",e("i",null,"matrice dei coefficienti")," e il ",e("i",null,"vettore termine noto"),".")),e(o.a,{title:"Teorema di Rouché-Capélli"},e("p",null)))))}}.call(this,n("hosL").h)}}]);
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rename to docs/route-Fisica.chunk.09542.js
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ue=function(){return n},n}function ce(){var n=ke(["left | \vec{F} \right | leq mu_{d} left | \vec{F}_{normale} \right |"],["\\left | \\vec{F} \\right | \\leq \\mu_{d} \\left | \\vec{F}_{normale} \\right |"]);return ce=function(){return n},n}function se(){var n=ke(["left | \vec{F} \right | leq mu_{s} left | \vec{F}_{normale} \right |"],["\\left | \\vec{F} \\right | \\leq \\mu_{s} \\left | \\vec{F}_{normale} \\right |"]);return se=function(){return n},n}function pe(){var n=ke(["g_{marte} = 3.71 \frac{m}{s^2}"],["g_{marte} = 3.71 \\frac{m}{s^2}"]);return pe=function(){return n},n}function de(){var n=ke(["g_{luna} = 1.62 \frac{m}{s^2}"],["g_{luna} = 1.62 \\frac{m}{s^2}"]);return de=function(){return n},n}function fe(){var n=ke(["left | \vec{F} \right | = g m"],["\\left | \\vec{F} \\right | = g m"]);return fe=function(){return n},n}function ve(){var n=ke(["g = 9.81 \frac{m}{s^2}"],["g = 9.81 \\frac{m}{s^2}"]);return ve=function(){return n},n}function me(){var n=ke(["left | \vec{F} \right | = g m"],["\\left | \\vec{F} \\right | = g m"]);return me=function(){return n},n}function _e(){var n=ke(["G = 6.67 cdot 10^{-11} \frac{N m^2}{{kg}^2}"],["G = 6.67 \\cdot 10^{-11} \\frac{N m^2}{{kg}^2}"]);return _e=function(){return n},n}function ge(){var n=ke(["left | \vec{F} \right | = G \frac{m_1 m_2}{s^2}"],["\\left | \\vec{F} \\right | = G \\frac{m_1 m_2}{s^2}"]);return ge=function(){return n},n}function he(){var n=ke(["\vec{F}_{21} = -\vec{F}_{12}"],["\\vec{F}_{21} = -\\vec{F}_{12}"]);return he=function(){return n},n}function be(){var n=ke(["Sigma \vec{F} = m \vec{a}"],["\\Sigma \\vec{F} = m \\vec{a}"]);return be=function(){return n},n}function ze(){var n=ke(["Sigma \vec{F} = 0 Longleftrightarrow Delta v = 0"],["\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta v = 0"]);return ze=function(){return n},n}function De(){var n=ke(["left | \vec{c} \right | = left | \vec{a} \right | cdot left | \vec{b} \right | cdot sin(alpha)"],["\\left | \\vec{c} \\right | = \\left | \\vec{a} \\right | \\cdot \\left | \\vec{b} \\right | \\cdot \\sin(\\alpha)"]);return De=function(){return n},n}function Le(){var n=ke(["\vec{c} = \vec{a} \times \vec{b}"],["\\vec{c} = \\vec{a} \\times \\vec{b}"]);return Le=function(){return n},n}function Ee(){var n=ke(["\vec{b}"],["\\vec{b}"]);return Ee=function(){return n},n}function qe(){var n=ke(["\vec{a}"],["\\vec{a}"]);return qe=function(){return n},n}function Fe(){var n=ke(["\vec{v} cdot \vec{w} = left | \vec{v} \right | left | \vec{w} \right | cos alpha"],["\\vec{v} \\cdot \\vec{w} = \\left | \\vec{v} \\right | \\left | \\vec{w} \\right | \\cos \\alpha"]);return Fe=function(){return n},n}function Ae(){var n=ke(["\vec{v} - \vec{w} = (\vec{v}_x - \vec{w}_x) + (\vec{v}_y - \vec{w}_y)"],["\\vec{v} - \\vec{w} = (\\vec{v}_x - \\vec{w}_x) + (\\vec{v}_y - \\vec{w}_y)"]);return Ae=function(){return n},n}function Pe(){var n=ke(["\vec{v} + \vec{w} = (\vec{v}_x + \vec{w}_x) + (\vec{v}_y + \vec{w}_y)"],["\\vec{v} + \\vec{w} = (\\vec{v}_x + \\vec{w}_x) + (\\vec{v}_y + \\vec{w}_y)"]);return Pe=function(){return n},n}function Ce(){var n=ke(["left | \vec{v}_y \right | = left | \vec{v} \right | cos alpha"],["\\left | \\vec{v}_y \\right | = \\left | \\vec{v} \\right | \\cos \\alpha"]);return Ce=function(){return n},n}function Ie(){var n=ke(["left | \vec{v}_x \right | = left | \vec{v} \right | sin alpha"],["\\left | \\vec{v}_x \\right | = \\left | \\vec{v} \\right | \\sin \\alpha"]);return Ie=function(){return n},n}function we(){var n=ke(["\vec{v} = \vec{v}_x + \vec{v}_y"],["\\vec{v} = \\vec{v}_x + \\vec{v}_y"]);return we=function(){return n},n}function ke(n,e){return e||(e=n.slice(0)),n.raw=e,n}t("hosL");var Be=t("Q7TX"),Se=t("imVn"),Ne=t("OPqz"),xe=t("CfuJ"),Ve=t("4v1N"),Te=t("RMzO"),ye=t("wQ73"),Re=t("PGF6"),Oe=String.raw;e.default=function(){return n(ye.a.Provider,{value:!1},n(Re.a.Provider,{value:Be.a.INLINE},n("div",null,n("h1",null,"Fisica"),n(Ne.a,{title:"Vettori"},n(Se.a,{title:"Componenti cartesiane"},n("p",null,"Usa le regole base della trigonometria:"),n("p",null,n(Be.b,null,Oe(we()))),n("p",null,n(Be.b,null,Oe(Ie()))),n("p",null,n(Be.b,null,Oe(Ce())))),n(Se.a,{title:"Somma"},n("p",null,"Scomponi in componenti, poi sommali:"),n("p",null,n(Be.b,null,Oe(Pe()))),n("p",null,"Produce il vettore risultante dall'applicazione della regola del parallelogramma.")),n(Se.a,{title:"Differenza"},n("p",null,"Alla fine è sempre una somma:"),n("p",null,n(Be.b,null,Oe(Ae()))),n("p",null,"Produce il vettore che parte da ",n(Be.b,null,"w")," e arriva a ",n(Be.b,null,"v"),".")),n(Se.a,{title:"Prodotto scalare"},n("p",null,"Si chiama scalare perchè il risultato è uno scalare, non un vettore."),n("p",null,n(Be.b,null,Oe(Fe()))),n("p",null,"Produce il modulo della proiezione di ",n(Be.b,null,Oe(qe()))," su ",n(Be.b,null,Oe(Ee())),".")),n(Se.a,{title:"Prodotto vettoriale"},n("p",null,"Si chiama vettoriale perchè il risultato è un altro vettore."),n("ul",null,n("li",null,n(Be.b,null,Oe(Le()))),n("li",null,n(Be.b,null,Oe(De()))),n("li",null,n("a",{href:"https://it.wikipedia.org/wiki/Regola_della_mano_destra"},"Regola della mano destra"))),n("p",null,"Non è commutativo!"))),n(Ne.a,{title:"Leggi di Newton"},n(Se.a,{title:"1ᵃ: Inerzia"},n("p",null,"Se un corpo puntiforme ha forza risultante nulla, allora la sua velocità non cambia."),n("p",null,n(Be.b,null,Oe(ze())))),n(Se.a,{title:"2ᵃ: Proporzionalità"},n("p",null,"La forza risultante di un corpo è direttamente proporzionale alla sua accelerazione, e la costante di proporzionalità è la ",n("i",null,"massa"),"."),n("p",null,n(Be.b,null,Oe(be())))),n(Se.a,{title:"3ᵃ: Azione e reazione"},n("p",null,"Due corpi esercitano forze uguali e opposte uno sull'altro."),n("p",null,n(Be.b,null,Oe(he()))))),n(Ne.a,{title:"Forza di gravità"},n(Se.a,{title:"Tra due corpi"},n("p",null,"Due corpi puntiformi si attirano uno verso l'altro con forza:"),n("p",null,n(Be.b,null,Oe(ge()))),n("p",null,n(Be.b,null,"G")," è la ",n("i",null,"costante di gravitazione universale")," e vale:"),n("p",null,n(Be.b,null,Oe(_e())))),n(Se.a,{title:"Verso la Terra"},n("p",null,"Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo è attratto verso la Terra con forza ",n("i",null,"peso")," uguale a:"),n("p",null,n(Be.b,null,Oe(me()))),n("p",null,n(Be.b,null,"g")," è la ",n("i",null,"costante di gravità")," della Terra, e vale:"),n("p",null,n(Be.b,null,Oe(ve())))),n(Se.a,{title:"Su pianeti diversi"},n("p",null,"Per pianeti diversi dalla Terra vale la stessa regola:"),n("p",null,n(Be.b,null,Oe(fe()))),n("p",null,"L'unica differenza è che cambia la ",n("i",null,"costante di gravità"),":"),n("p",null,n(Be.b,null,Oe(de()))),n("p",null,n(Be.b,null,Oe(pe()))))),n(Ne.a,{title:"Forze di contatto"},n(Se.a,{title:"Normale"},n("p",null,"Si oppone alle forze applicate alla superficie di contatto."),n("p",null,"Un libro appoggiato su un tavolo ha la ",n("b",null,"forza di gravità")," che lo attira verso il terreno e la ",n("b",null,"forza normale")," che lo trattiene dal cadere.")),n(Se.a,{title:"Attrito statico"},n("p",null,"Impedisce a un corpo di muoversi se non viene spinto da una forza che supera una certa soglia:"),n("p",null,n(Be.b,null,Oe(se())))),n(Se.a,{title:"Attrito dinamico"},n("p",null,"Rallenta i corpi che si stanno muovendo finchè essi non si fermano:"),n("p",null,n(Be.b,null,Oe(ce())))),n(Se.a,{title:"Tensione"},n("p",null,"E' forza trasmessa tra due estremi di una fune."),n("p",null,"Può essere redirezionata per mezzo di carrucole.")),n(Se.a,{title:"Elastica"},n("p",null,"Una molla cerca sempre di tornare alla sua posizione indeformata con forza:"),n("p",null,n(Be.b,null,Oe(ue()))),n("p",null,"(E' negativa perchè la forza è opposta a quella applicata per deformarla.)"))),n(Ne.a,{title:"Cinematica"},n(Se.a,{title:"Spostamento"},n("p",null,"È un vettore che indica la posizione di un corpo rispetto a un'origine."),n("p",null,n(Be.b,null,Oe(re())))),n(Se.a,{title:"Velocità"},n("p",null,"È un vettore che misura la variazione di posizione nel tempo."),n("p",null,n(Be.b,null,Oe(oe()))),n("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",n("i",null,"velocità istantanea"),":"),n("p",null,n(Be.b,null,Oe(ie())))),n(Se.a,{title:"Accelerazione"},n("p",null,"È un vettore che misura la variazione di velocità nel tempo."),n("p",null,n(Be.b,null,Oe(ae()))),n("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",n("i",null,"accelerazione istantanea"),":"),n("p",null,n(Be.b,null,Oe(le())))),n(Se.a,{title:n("span",null,"Quantità di moto ",n("small",null,"(momento lineare)"))},n("p",null,"La quantità di moto è una proprietà vettoriale dei corpi:"),n("p",null,n(Be.b,null,Oe(te()))),n("p",null,"Se la forza risultante è nulla, la quantità di moto non cambia."),n("p",null,n(Be.b,null,Oe(ee()))))),n(Ne.a,{title:"Moto rettilineo uniforme"},n(Se.a,{title:"Spostamento"},n("p",null,"La ",n("i",null,"legge oraria")," è:"),n("p",null,n(Be.b,null,Oe(ne())))),n(Se.a,{title:"Velocità"},n("p",null,"È costante:"),n("p",null,n(Be.b,null,Oe($n())))),n(Se.a,{title:"Accelerazione"},n("p",null,"La velocità non varia:"),n("p",null,n(Be.b,null,Oe(Zn())))),n(Se.a,{title:"Forze"},n("p",null,"Si applica la prima legge di Newton:"),n("p",null,n(Be.b,null,"f(t) = 0")))),n(Ne.a,{title:"Moto rettilineo uniformemente accelerato"},n(Se.a,{title:"Spostamento"},n("p",null,"La ",n("i",null,"legge oraria")," è:"),n("p",null,n(Be.b,null,Oe(Xn())))),n(Se.a,{title:"Velocità"},n("p",null,"È una retta:"),n("p",null,n(Be.b,null,Oe(Kn())))),n(Se.a,{title:"Accelerazione"},n("p",null,"È costante:"),n("p",null,n(Be.b,null,Oe(Yn())))),n(Se.a,{title:"Forze"},n("p",null,"Si applica la prima legge di Newton:"),n("p",null,n(Be.b,null,"f(t) = m a")))),n(Ne.a,{title:"Moto armonico semplice"},n(Se.a,{title:"Ampiezza"},n("p",null,"E' la distanza dal centro massima che raggiunge il corpo."),n("p",null,"(L'ampiezza di una sinusoide.)")),n(Se.a,{title:"Velocità angolare"},n("p",null,"Indica quanto in fretta cambia la posizione del corpo."),n("p",null,"Dipende dal periodo:"),n("p",null,n(Be.b,null,Oe(Jn())))),n(Se.a,{title:"Spostamento"},n("p",null,"E' una sinusoide:"),n("p",null,n(Be.b,null,Oe(jn())))),n(Se.a,{title:"Velocità"},n("p",null,"E' la sinusoide dello spostamento, sfasata di ",n(Be.b,null,Oe(Wn())),":"),n("p",null,n(Be.b,null,Oe(Gn())))),n(Se.a,{title:"Accelerazione"},n("p",null,"E' la sinusoide della velocità, sfasata di ",n(Be.b,null,Oe(Qn())),":"),n("p",null,n(Be.b,null,Oe(Mn())))),n(Se.a,{title:"Forze"},n("p",null,"Si applica la prima legge di Newton:"),n("p",null,n(Be.b,null,"f(t) = m a")))),n(Ne.a,{title:"Moti composti"},n(Se.a,{title:"Moto parabolico"},n("p",null,"Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.")),n(Se.a,{title:"Moto circolare uniforme"},n("p",null,"Il moto parabolico è dato sommando due moti armonici semplici: uno sull'asse X, e l'altro, sfasato di ",n(Be.b,null,Oe(Hn())),", sull'asse Y."))),n(Ne.a,{title:"Moto circolare uniforme"},n(Se.a,null,n("h3",null,"Velocità angolare"),n("p",null,"Quanto cambia la fase nel tempo."),n("p",null,n(Be.b,null,Oe(Un())))),n(Se.a,{title:"Fase"},n("p",null,"E' l'angolo percorso dal corpo rispetto alla posizione iniziale."),n("p",null,"Si indica con ",n(Be.b,null,Oe(On())),", e generalmente si usa in radianti.")),n(Se.a,{title:"Velocità"},n("p",null,"Si applicano le formule per la circonferenza:"),n("p",null,n(Be.b,null,Oe(Rn())))),n(Se.a,{title:"Accelerazione"},n("p",null,"Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto:"),n("p",null,n(Be.b,null,Oe(yn())))),n(Se.a,{title:"Forza centripeta"},n("p",null,"È verso il centro e si calcola con:"),n("p",null,n(Be.b,null,Oe(Tn()))))),n(Ne.a,{title:"Lavoro ed energia"},n(Se.a,{title:"Lavoro"},n("p",null,"E' compiuto da una forza che sposta un corpo."),n("p",null,n(Be.b,null,Oe(Vn()))),n("p",null,"(Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)")),n(Se.a,{title:"Energia cinetica"},n("p",null,"Un corpo ha energia cinetica in ogni momento uguale a:"),n("p",null,n(Be.b,null,Oe(xn()))),n("p",null,"Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:"),n("p",null,n(Be.b,null,Oe(Nn())))),n(Se.a,{title:"Energia potenziale gravitazionale"},n("p",null,"Un corpo ha energia potenziale in ogni momento pari a:"),n("p",null,n(Be.b,null,Oe(Sn()))),n("p",null,"(Con ",n(Be.b,null,"h")," uguale a un altezza scelta come punto di riferimento.)")),n(Se.a,{title:"Energia potenziale elastica"},n("p",null,"Una molla ha sempre energia potenziale elastica pari a:"),n("p",null,n(Be.b,null,Oe(Bn())))),n(Se.a,{title:"Forze conservative"},n("p",null,"Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo."),n("p",null,"Ad esempio, è conservativa la ",n("i",null,"forza di gravità"),", ma ",n("b",null,"non")," è conservativa la forza di attrito."),n("p",null,"Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:"),n("p",null,n(Be.b,null,Oe(kn())))),n(Se.a,{title:"Potenza"},n("p",null,"È la velocità di trasferimento di energia:"),n("p",null,n(Be.b,null,Oe(wn()))))),n(Ne.a,{title:"Elettrostatica"},n(Se.a,{title:"Carica elettrica"},n("p",null,"È una proprietà dei corpi che può essere ",n(xe.a,null,"positiva")," o ",n(Ve.a,null,"negativa"),"."),n("p",null,"Si conserva: in un sistema chiuso la carica totale è costante."),n("p",null,"Esiste un'unità elementare: ",n(Be.b,null,Oe(In())),"."),n("p",null,"Cariche ",n(xe.a,null,"opp"),n(Ve.a,null,"oste")," si attraggono; cariche ",n(xe.a,null,"uguali")," si respingono.")),n(Se.a,{title:"Conduttori e isolanti"},n("p",null,"Più ",n("a",{href:"https://it.wikipedia.org/wiki/Ione"},"ioni")," ha un corpo, meglio la carica si muove attraverso di esso."),n("p",null,"I corpi in cui la carica si muove bene sono ",n("i",null,"conduttori"),", mentre quelli in cui si muove difficilmente sono ",n("i",null,"isolanti"),"."),n("p",null,n("i",null,"Il corpo umano è un buon conduttore.")))),n(Ne.a,{title:"Polarizzazione"},n(Se.a,{title:"Polarizzazione"},n("p",null,"E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona."))),n(Ne.a,null,n(Se.a,{title:"Messa a terra"},n("p",null,"Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno ",n("i",null,"equilibrate")," e il corpo diventerà elettricamente neutro (con stesso numero di ",n(xe.a,null,"cariche positive")," e ",n(Ve.a,null,"negative")," all'interno)."))),n(Ne.a,null,n(Se.a,{title:"Polarizzazione per strofinio"},n("p",null,"Strofinando tra loro due corpi isolanti, essi si ",n("i",null,"polarizzeranno per strofinio"),".")),n(Se.a,{title:"Polarizzazione per contatto"},n("p",null,"Toccando un conduttore con un corpo carico, il conduttore potrà ",n("i",null,"polarizzarsi per contatto"),".")),n(Se.a,{title:"Polarizzazione per induzione"},n("p",null,'Se un corpo conduttore ha cariche "esterne" di un ',n(xe.a,null,"certo segno")," vicino, esso avrà tutte le cariche del ",n(Ve.a,null,"segno opposto")," in equilibrio vicino alle cariche esterne, e tutte le cariche dello ",n(xe.a,null,"stesso segno")," più lontano possibile da esse."),n("p",null,"Mettendo a terra il conduttore, nuove cariche del ",n(Ve.a,null,"segno opposto")," saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate."),n("p",null,"Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà ",n(Ve.a,null,"caricato del segno opposto")," rispetto alle cariche esterne."))),n(Ne.a,{title:"Forza elettrica"},n(Se.a,{title:"Legge di Coulomb"},n("p",null,"Due corpi carichi si attraggono tra loro con forza:"),n("p",null,n(Be.b,null,Oe(Cn()))),n("p",null,n(Be.b,null,Oe(Pn()))," è la ",n("i",null,"costante di Coulomb"),", e vale ",n(Be.b,null,Oe(An())),".")),n(Se.a,{title:"Permeabilità dello spazio vuoto"},n("p",null,"La costante ",n(Be.b,null,Oe(Fn()))," è in realtà dipendente da un altra costante, ",n(Be.b,null,Oe(qn())),", la ",n("i",null,"permeabilità del vuoto"),"."),n("p",null,n(Be.b,null,Oe(En()))),n("p",null,n(Be.b,null,Oe(Ln())))),n(Se.a,{title:"Campo elettrico"},n("p",null,"Misura che forza viene applicata in ogni punto su una carica unitaria:"),n("p",null,n(Be.b,null,Oe(Dn())))),n(Se.a,{title:"Flusso elettrico"},n("p",null,'È la differenza tra "quanto" campo elettrico ',n(xe.a,null,"entra")," e quanto campo elettrico ",n(Ve.a,null,"esce")," da una certa area."),n("p",null,"In qualsiasi superficie chiusa, il flusso elettrico è uguale alla componente perpendicolare del campo elettrico moltiplicato per l'area."),n("p",null,n(Be.b,null,Oe(zn()))),n("p",null,"Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:"),n("p",null,n(Be.b,null,Oe(bn()))),n("p",null,n(Te.a,null,"Circa. E' una specie di integrale..."))),n(Se.a,{title:"Legge di Gauss per i campi elettrostatici"},n("p",null,"Il flusso elettrico è direttamente proporzionale alla carica presente all'interno della superficie."),n("p",null,n(Be.b,null,Oe(hn()))),n("p",null,"Ovvero, i campi elettrostatici sono generati dalle cariche elettriche."))),n(Ne.a,{title:"Energia elettrica"},n(Se.a,{title:"Energia potenziale elettrica"},n("p",null,"Un corpo carico vicino ad altre cariche possiede un'",n("i",null,"energia potenziale elettrica")," ",n(Be.b,null,Oe(gn())),"."))),n(Ne.a,{title:"Circuiti elettrici"},n(Se.a,{title:n("span",null,"Potenziale elettrico ",n("small",null,"(tensione)"))},n("p",null,"È il valore dell'energia potenziale elettrica per una carica unitaria."),n("p",null,n(Be.b,null,Oe(_n()))),n("p",null,"La sua unità di misura è il Volt (",n(Be.b,null,Oe(mn())),")."),n("p",null,"In una batteria è detto ",n("i",null,"forza elettromotrice"),", e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli.")),n(Se.a,{title:n("span",null,"Corrente elettrica ",n("small",null,"(intensità)"))},n("p",null,"Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo."),n("p",null,n(Be.b,null,Oe(vn()))),n("p",null,"Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla."),n("p",null,"La sua unità di misura è l'Ampere (",n(Be.b,null,Oe(fn())),").")),n(Se.a,{title:n("span",null,"Corrente continua ",n("small",null,"(",n("abbr",{title:"Direct Current"},"DC"),")"))},n("p",null,"Quando in un circuito la direzione della corrente è costante.")),n(Se.a,{title:n("span",null,"Corrente alternata ",n("small",null,"(",n("abbr",{title:"Alternate Current"},"AC"),")"))},n("p",null,"Quando in un circuito la direzione della corrente si alterna periodicamente.")),n(Se.a,{title:"Potenza elettrica"},n("p",null,"Possiamo calcolare la potenza di un circuito:"),n("p",null,n(Be.b,null,Oe(dn()))))),n(Ne.a,{title:"Elementi di un circuito"},n(Se.a,{title:"Resistore"},n("p",null,"Riduce l'intensità di corrente, e converte parte del potenziale in calore."),n("p",null,"Il potenziale utilizzato è pari a:"),n("p",null,n(Be.b,null,Oe(pn()))),n("p",null,"Dove ",n(Be.b,null,Oe(sn()))," è una costante detta ",n("i",null,"resistenza")," con unità di misura Ohm (",n(Be.b,null,Oe(cn())),")."),n("p",null,"La resistenza di un conduttore vale:"),n("p",null,n(Be.b,null,Oe(un()))),n("p",null,n(Be.b,null,Oe(rn()))," è la ",n("i",null,"resistività")," del materiale, e varia in base alla temperatura:"),n("p",null,n(Be.b,null,Oe(on())))),n(Se.a,{title:"Condensatore"},n("p",null,"Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito."),n("p",null,"Per farlo, cattura cariche ",n(xe.a,null,"positive")," e ",n(Ve.a,null,"negative")," sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro."),n("p",null,"Ha una ",n("b",null,"capacità")," caratteristica, che in un condensatore a facce piane parallele è:"),n("p",null,n(Be.b,null,Oe(an()))),n("p",null,"Condensatori di capacità maggiore immagazzinano più potenziale con meno carica."),n("p",null,"La capacità aumenta se viene messo qualcosa tra le armature:"),n("p",null,n(Be.b,null,Oe(ln()))),n("p",null,"Dove ",n(Be.b,null,Oe(tn()))," è la ",n("i",null,"costante dielettrica relativa")," del materiale inserito, ",n(Be.b,null,Oe(en()))," l'area di una armatura e ",n(Be.b,null,Oe(nn()))," la distanza tra le due armature."),n("p",null,"Se il campo elettrico creatosi tra le due armature supera la ",n("i",null,"rigidità dielettrica")," del condensatore, la carica immagazzinata viene persa e ha luogo un ",n("i",null,"breakdown"),"."),n("p",null,"La sua unità di misura è il Farad (",n(Be.b,null,Oe($())),")")),n(Se.a,{title:"Amperometro"},n("p",null,"Misura la corrente elettrica se messo in serie."),n("p",null,"(Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)")),n(Se.a,{title:"Voltmetro"},n("p",null,"Misura la differenza di potenziale se messo in parallelo."),n("p",null,"(Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)"))),n(Ne.a,{title:"Principi di Kirchhoff"},n(Se.a,{title:"Legge dei nodi"},n("p",null,"Per nodo si intende un qualsiasi punto del circuito."),n("p",null,"Da un nodo entra ed esce la stessa corrente.")),n(Se.a,{title:"Legge delle maglie"},n("p",null,"Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito."),n("p",null,"In una maglia chiusa, la somma delle differenze di potenziale è 0."))),n(Ne.a,{title:"Serie e Parallelo"},n(Se.a,{title:"Circuito in serie"},n("p",null,"Più parti di circuito sono ",n("i",null,"in serie")," se sono consecutive e senza biforcazioni."),n("p",null,"Parti di circuito in serie sono attraversate dalla stessa corrente.")),n(Se.a,{title:"Circuito in parallelo"},n("p",null,"Più parti di circuito sono ",n("i",null,"in parallelo")," tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo."),n("p",null,"Parti di circuito in parallelo hanno la stessa differenza di potenziale."))),n(Ne.a,{title:"Resistenze equivalenti"},n(Se.a,{title:"Circuiti in serie"},n("p",null,"Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:"),n("p",null,n(Be.b,null,Oe(Z())))),n(Se.a,{title:"Circuiti in parallelo"},n("p",null,"Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:"),n("p",null,n(Be.b,null,Oe(X()))))),n(Ne.a,{title:"Condensatori equivalenti"},n(Se.a,{title:"Circuiti in serie"},n("p",null,"Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacità di:"),n("p",null,n(Be.b,null,Oe(K())))),n(Se.a,{title:"Circuiti in parallelo"},n("p",null,"Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacità della somma di tutti quelli sostituiti:"),n("p",null,n(Be.b,null,Oe(Y()))))),n(Ne.a,{title:"Magnetismo"},n(Se.a,{title:"Permeabilità magnetica dello spazio vuoto"},n("p",null,"E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente."),n("p",null,n(Be.b,null,Oe(J()))," (",n(Be.b,null,Oe(j())),")")),n(Se.a,{title:"Campo magnetico"},n("p",null,"Come un campo elettrico, ma per i magneti."),n("p",null,"Il suo simbolo è ",n(Be.b,null,Oe(W())),", e la sua unità di misura è il Tesla (",n(Be.b,null,"T"),").")),n(Se.a,{title:"Flusso magnetico"},n("p",null,'È "quanto" campo magnetico ',n("b",null,"attraversa")," un percorso chiuso."),n("p",null,'Per qualsiasi percorso chiuso, il flusso magnetico è uguale alla somma di tutti i "sottoflussi" magnetici calcolati sui suoi lati.'),n("p",null,n(Be.b,null,Oe(G()))),n("p",null,n(Be.b,null,Oe(Q()))),n("p",null,"La sua unità di misura è il Weber (",n(Be.b,null,Oe(M())),").")),n(Se.a,{title:"Legge di Gauss per i campi magnetici"},n("p",null,"Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo."),n("p",null,"Ovvero, non esistono monopoli magnetici.")),n(Se.a,{title:"Legge di Ampère"},n("p",null,"L'intensità di corrente che attraversa un percorso chiuso è direttamente proporzionale al flusso magnetico dello stesso percorso."),n("p",null,n(Be.b,null,Oe(H()))))),n(Ne.a,{title:"Forze magnetiche"},n(Se.a,{title:n("span",null,"Forza magnetica su carica puntiforme ",n("small",null,"(Forza di Lorentz)"))},n("p",null,"I campi magnetici applicano una forza sulle cariche vicine:"),n("p",null,n(Be.b,null,Oe(U()))),n("p",null,"Dove ",n(Be.b,null,Oe(O()))," è l'intensità del campo magnetico e ",n(Be.b,null,Oe(R()))," la velocità della carica considerata."),n("p",null,"Si ha una forza massima se la velocità è perpendicolare al campo magnetico."),n("p",null,"In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme.")),n(Se.a,{title:"Forza magnetica in un filo"},n("p",null,"I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:"),n("p",null,n(Be.b,null,Oe(y()))," ",n("a",{href:"https://it.openprof.com/wb/forza_di_lorentz_su_un_filo_percorso_da_corrente?ch=360"},"[1]")),n("p",null,"Dove ",n(Be.b,null,Oe(T()))," è la corrente elettrica, ",n(Be.b,null,Oe(V()))," è un vettore che punta nella direzione di scorrimento della corrente e ha come modulo la lunghezza del conduttore."))),n(Ne.a,{title:"Campi magnetici"},n(Se.a,{title:"Campo magnetico in una spira"},n("p",null,"Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.")),n(Se.a,{title:"Campo magnetico di un solenoide"},n("p",null,"Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro."),n("p",null,"All'interno del solenoide si crea un campo (quasi) uniforme:"),n("p",null,n(Be.b,null,Oe(x())))),n(Se.a,{title:"Legge di Oersted"},n("p",null,n("i",null,"Caso particolare della ",n("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Amp%C3%A8re"},"Legge di Ampère"),".")),n("p",null,"Il modulo del campo magnetico ",n(Be.b,null,"B")," prodotto da un filo in cui passa una corrente continua ",n(Be.b,null,"I")," alla distanza ",n(Be.b,null,"s")," è:"),n("p",null,n(Be.b,null,Oe(N()))),n("p",null,"Il campo magnetico così creato gira attorno al filo in senso antiorario."),n("p",null,"Due fili attraversati dalla ",n(xe.a,null,"stessa corrente")," si attraggono, due fili attraversati da ",n(xe.a,null,"corr"),n(Ve.a,null,"enti")," ",n(xe.a,null,"opp"),n(Ve.a,null,"oste")," si respingono."))),n(Ne.a,{title:"Induzione elettromagnetica"},n(Se.a,{title:"Forza elettromotrice indotta"},n("p",null,"Un conduttore perpendicolare ad un campo magnetico può ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo."),n("p",null,"La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore."),n("p",null,"Essa vale:"),n("p",null,n(Be.b,null,Oe(S()))),n("p",null,"Dove ",n(Be.b,null,"v")," è la velocità del conduttore, ",n(Be.b,null,"B")," è l'intensità del campo magnetico ed ",n(Be.b,null,"L")," è la lunghezza del conduttore.")),n(Se.a,{title:"Flusso magnetico in una spira"},n("p",null,"In un campo magnetico ",n(Be.b,null,Oe(B()))," uniforme e perpendicolare al piano di una spira di area ",n(Be.b,null,Oe(k())),", il flusso magnetico si può determinare con la ",n("i",null,"Legge di Faraday-Neumann-Lenz"),":"),n("p",null,n(Be.b,null,Oe(w()))))),n(Ne.a,null,n(Se.a,{title:"Legge di Faraday-Neumann-Lenz"},n("p",null,"Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso."),n("p",null,n(Be.b,null,Oe(I()))),n("p",null,"Il meno è dovuto alla ",n("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Lenz"},"Legge di Lenz"),", che specifica qualitativamente il verso della forza elettromotrice indotta.")),n(Se.a,{title:"Faraday in un solenoide"},n("p",null,"In un solenoide, la forza elettromotrice indotta è uguale a:"),n("p",null,n(Be.b,null,Oe(C()))),n("p",null,"Dove ",n(Be.b,null,Oe(P()))," è il numero delle spire del solenoide.")),n(Se.a,{title:"Legge di Ampère-Maxwell"},n("p",null,"Correnti o campi elettrici variabili creano un campo magnetico."))),n(Ne.a,{title:"Elettromagnetismo"},n(Se.a,{title:"Onde elettromagnetiche"},n("p",null,"Nel vuoto, il campo elettrico ",n(Be.b,null,Oe(A()))," e il campo magnetico ",n(Be.b,null,Oe(F()))," sono perpendicolari tra loro e la direzione di propagazione, e sono entrambe funzioni del tempo."),n("p",null,"Si dice quindi che sono ",n("i",null,"onde elettromagnetiche"),"."),n("p",null,"Esse sono legate dalla relazione:"),n("p",null,n(Be.b,null,Oe(q()))),n("p",null,"Dove ",n(Be.b,null,Oe(E()))," è la velocità delle onde (luce) nel vuoto, e a sua volta è uguale a:"),n("p",null,n(Be.b,null,Oe(L())))),n(Se.a,{title:"Formula delle onde"},n("p",null,n(Be.b,null,Oe(D()))),n("p",null,"Dove ",n(Be.b,null,Oe(z()))," è l'ampiezza massima che può avere l'onda, ",n(Be.b,null,Oe(b()))," è il vettore d'onda, ",n(Be.b,null,Oe(h()))," la frequenza angolare e ",n(Be.b,null,Oe(g()))," la fase."))),n(Ne.a,{title:"Spettroscopia"},n(Se.a,{title:"Emissione"},n("p",null,"I solidi, se portati ad alta temperatura, emettono luce con uno ",n("a",{href:"https://it.wikipedia.org/wiki/Spettro_continuo"},"spettro continuo"),"."),n("p",null,"I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d'onda."),n("p",null,"In un gas di idrogeno, le lunghezze d'onda emesse sono ricavabili con:"),n("p",null,n(Be.b,null,Oe(_()))),n("p",null,"Con ",n(Be.b,null,Oe(m())),", detta costante di Rydberg, e ",n(Be.b,null,Oe(v()))," un numero intero.")),n(Se.a,{title:"Grandezza quantizzata"},n("p",null,"Una grandezza si dice quantizzata (o discreta) se può assumere solo determinati valori."),n("p",null,"Una grandezza si dice continua se può assumere qualsiasi valore e quindi se non è quantizzata."),n("p",null,"Energia, momento angolare e raggio sono quantizzati."),n("p",null,"Nota costante quantica è ",n(Be.b,null,Oe(f())),", la costante di Planck, ovvero il valore minimo possibile per la carica (talvolta espressa come ",n(Be.b,null,Oe(d())),"."))),n(Ne.a,null,n(Se.a,{title:"Modello di Bohr"},n("p",null,"L'energia degli elettroni è quantizzata."),n("p",null,"Inoltre, per essi è valido che:"),n("p",null,n(Be.b,null,Oe(p()))),n("p",null,"Ancora, il raggio delle orbite è uguale a:"),n("p",null,n(Be.b,null,Oe(s()))),n("p",null,"Con ",n(Be.b,null,Oe(c())),"."),n("p",null,"Infine, in ogni stato, l'energia è pari a:"),n("p",null,n(Be.b,null,Oe(u()))),n("p",null,"Due elettroni non possono occupare lo stesso stato."),n("p",null,"Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di"))),n(Ne.a,null,n(Se.a,{title:"Nei solidi"},n("p",null,"Nei solidi, le lunghezze d'onda sono talmente tanto vicine da poter essere considerate una banda."),n("p",null,"Possono però comunque avere dei gap dovuti agli intervalli di energia non ammessi."))),n(Ne.a,{title:"Semiconduttori"},n(Se.a,{title:"Semiconduttori"},n("p",null,n(Te.a,null,"Refactor this")),n("p",null,"Se la banda di emissione con energia più alta di un corpo è assente o è separata da un gap dell'ordine di grandezza maggiore di ",n(Be.b,null,Oe(r())),", allora il corpo è un isolante."),n("p",null,"Se invece la banda di emissione si sovrappone a un altra, allora il corpo è un conduttore."),n("p",null,"Se il gap è invece dell'ordine di grandezza di ",n(Be.b,null,Oe(o())),", allora il corpo è un semiconduttore.")),n(Se.a,{title:"Lacune"},n("p",null,"Legami in cui ",n(xe.a,null,"mancano elettroni"),"."),n("p",null,n(Ve.a,null,"Elettroni")," di altri legami possono spostarsi per colmare le ",n(xe.a,null,"lacune"),", creandone altre, e spostandole in direzione opposta a quella della corrente.")),n(Se.a,{title:"Accettori e donori"},n("p",null,"Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterrà:"),n("ul",null,n("li",null,"Con numero atomico maggiore, un semiconduttore di ",n(Ve.a,null,"tipo N")," con ",n(Ve.a,null,"elettroni in eccesso")," liberi di scorrere."),n("li",null,"Con numero atomico minore, un semiconduttore di ",n(xe.a,null,"tipo P")," con ",n(xe.a,null,"lacune in eccesso")," libere di catturare elettroni da altri legami.")),n("p",null,"Maggiore impurezza porta a maggiore conduttività.")),n(Se.a,{title:"Temperatura"},n("p",null,"Aumentando la temperatura di un semiconduttore si aumenta la conduttività, perchè eccita le particelle e favorisce il movimento di ",n(Ve.a,null,"elettroni")," e ",n(xe.a,null,"lacune"),"."))),n(Ne.a,{title:n("span",null,"Ottica ",n("small",null,"(non l'abbiamo fatta)"))},n(Se.a,{title:"Assorbimento e riflessione"},n("p",null,"I corpi possono assorbire o riflettere le onde elettromagnetiche che li colpiscono.")),n(Se.a,{title:"Corpo nero"},n("p",null,"Un corpo nero è un corpo che assorbe tutte le onde elettromagnetiche che riceve senza rifletterne nessuna."),n("p",null,"Le onde assorbite vengono poi riemesse sotto forma di un onda di ",n(Be.b,null,Oe(i()))," variabile in base alla temperatura."),n("p",null,n(Be.b,null,Oe(a()))," è costante.")),n(Se.a,{title:"Teoria di Planck per il corpo nero"},n("p",null,"L'energia assorbita e emessa dai corpi neri è quantizzata.")),n(Se.a,{title:"Fotone"},n("p",null,"Un onda magnetica con un quanto di energia è detta ",n("i",null,"fotone"),":"),n("p",null,n(Be.b,null,Oe(l())))),n(Se.a,{title:"Effetto fotoelettrico"},n("p",null,"A volte, i fotoni che colpiscono un metallo possono estrarvi degli elettroni e creare una differenza di potenziale."),n("p",null,"Perchè avvenga, la frequenza deve essere maggiore di una certa soglia."),n("p",null,"Il numero di elettroni estratti dipende dall'intensità dell'onda, mentre l'energia cinetica degli elettroni dipende dalla frequenza."),n("p",null,"Non c'è nessun ritardo tra l'assorbimento del fotone e l'estrazione di elettroni."))))))}}.call(this,t("hosL").h)},"4v1N":function(n,e,t){"use strict";(function(n){var l=t("T9fO"),a=t.n(l);e.a=function(e){return n("span",{class:a.a.minus},e.children)}}).call(this,t("hosL").h)},"8uYk":function(n){n.exports={box:"box__3cKyY",default:"default__v-emJ",red:"red__339Cz",orange:"orange__24_8v",yellow:"yellow__1Jo9W",lime:"lime__34yV5",cyan:"cyan__3RqLr",blue:"blue__13Wnj",magenta:"magenta__2tkzq"}},CfuJ:function(n,e,t){"use strict";(function(n){var l=t("U2NH"),a=t.n(l);t("hosL");e.a=function(e){return 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k"]);return Yn=function(){return n},n}function Kn(){var n=ke(["v(t) = a Delta t + v(0)"],["v(t) = a \\Delta t + v(0)"]);return Kn=function(){return n},n}function Xn(){var n=ke(["s(t) = \frac{1}{2} a cdot (Delta t)^2 + v(0) cdot (Delta t) + s(0)"],["s(t) = \\frac{1}{2} a \\cdot (\\Delta t)^2 + v(0) \\cdot (\\Delta t) + s(0)"]);return Xn=function(){return n},n}function Zn(){var n=ke(["a(t) = 0"]);return Zn=function(){return n},n}function $n(){var n=ke(["v(t) = k"]);return $n=function(){return n},n}function ne(){var n=ke(["s(t) = v cdot Delta t + s(0)"],["s(t) = v \\cdot \\Delta t + s(0)"]);return ne=function(){return n},n}function ee(){var n=ke(["Sigma \vec{F} = 0 Longleftrightarrow Delta \vec{p} = 0"],["\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta \\vec{p} = 0"]);return ee=function(){return n},n}function te(){var n=ke(["\vec{p} = m \vec{v}"],["\\vec{p} = m \\vec{v}"]);return te=function(){return n},n}function le(){var n=ke(["\vec{a} = lim_{Delta v \to 0} \frac{Delta \vec{v}}{Delta t} = \frac{d \vec{v}}{d t} = \frac{d^2 \vec{s}}{d t^2}"],["\\vec{a} = \\lim_{\\Delta v \\to 0} \\frac{\\Delta \\vec{v}}{\\Delta t} = \\frac{d \\vec{v}}{d t} = \\frac{d^2 \\vec{s}}{d t^2}"]);return le=function(){return n},n}function ae(){var n=ke(["\vec{a} = \frac{Delta \vec{v}}{Delta t}"],["\\vec{a} = \\frac{\\Delta \\vec{v}}{\\Delta t}"]);return ae=function(){return n},n}function ie(){var n=ke(["\vec{v} = lim_{Delta t \to 0} \frac{Delta \vec{s}}{Delta t} = \frac{d \vec{s}}{dt}"],["\\vec{v} = \\lim_{\\Delta t \\to 0} \\frac{\\Delta \\vec{s}}{\\Delta t} = \\frac{d \\vec{s}}{dt}"]);return ie=function(){return n},n}function oe(){var n=ke(["\vec{v} = \frac{Delta \vec{s}}{Delta t}"],["\\vec{v} = \\frac{\\Delta \\vec{s}}{\\Delta t}"]);return oe=function(){return n},n}function re(){var n=ke(["Delta \vec{s} = \vec{s}(fine) - \vec{s}(inizio)"],["\\Delta \\vec{s} = \\vec{s}(fine) - \\vec{s}(inizio)"]);return re=function(){return n},n}function ue(){var n=ke(["F = -k x"]);return ue=function(){return n},n}function ce(){var n=ke(["left | \vec{F} \right | leq mu_{d} left | \vec{F}_{normale} \right |"],["\\left | \\vec{F} \\right | \\leq \\mu_{d} \\left | \\vec{F}_{normale} \\right |"]);return ce=function(){return n},n}function se(){var n=ke(["left | \vec{F} \right | leq mu_{s} left | \vec{F}_{normale} \right |"],["\\left | \\vec{F} \\right | \\leq \\mu_{s} \\left | \\vec{F}_{normale} \\right |"]);return se=function(){return n},n}function pe(){var n=ke(["g_{marte} = 3.71 \frac{m}{s^2}"],["g_{marte} = 3.71 \\frac{m}{s^2}"]);return pe=function(){return n},n}function de(){var n=ke(["g_{luna} = 1.62 \frac{m}{s^2}"],["g_{luna} = 1.62 \\frac{m}{s^2}"]);return de=function(){return n},n}function fe(){var n=ke(["left | \vec{F} \right | = g m"],["\\left | \\vec{F} \\right | = g m"]);return fe=function(){return n},n}function ve(){var n=ke(["g = 9.81 \frac{m}{s^2}"],["g = 9.81 \\frac{m}{s^2}"]);return ve=function(){return n},n}function me(){var n=ke(["left | \vec{F} \right | = g m"],["\\left | \\vec{F} \\right | = g m"]);return me=function(){return n},n}function _e(){var n=ke(["G = 6.67 cdot 10^{-11} \frac{N m^2}{{kg}^2}"],["G = 6.67 \\cdot 10^{-11} \\frac{N m^2}{{kg}^2}"]);return _e=function(){return n},n}function ge(){var n=ke(["left | \vec{F} \right | = G \frac{m_1 m_2}{s^2}"],["\\left | \\vec{F} \\right | = G \\frac{m_1 m_2}{s^2}"]);return ge=function(){return n},n}function he(){var n=ke(["\vec{F}_{21} = -\vec{F}_{12}"],["\\vec{F}_{21} = -\\vec{F}_{12}"]);return he=function(){return n},n}function be(){var n=ke(["Sigma \vec{F} = m \vec{a}"],["\\Sigma \\vec{F} = m \\vec{a}"]);return be=function(){return n},n}function ze(){var n=ke(["Sigma \vec{F} = 0 Longleftrightarrow Delta v = 0"],["\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta v = 0"]);return ze=function(){return n},n}function De(){var n=ke(["left | \vec{c} \right | = left | \vec{a} \right | cdot left | \vec{b} \right | cdot sin(alpha)"],["\\left | \\vec{c} \\right | = \\left | \\vec{a} \\right | \\cdot \\left | \\vec{b} \\right | \\cdot \\sin(\\alpha)"]);return De=function(){return n},n}function Le(){var n=ke(["\vec{c} = \vec{a} \times \vec{b}"],["\\vec{c} = \\vec{a} \\times \\vec{b}"]);return Le=function(){return n},n}function Ee(){var n=ke(["\vec{b}"],["\\vec{b}"]);return Ee=function(){return n},n}function qe(){var n=ke(["\vec{a}"],["\\vec{a}"]);return qe=function(){return n},n}function Fe(){var n=ke(["\vec{v} cdot \vec{w} = left | \vec{v} \right | left | \vec{w} \right | cos alpha"],["\\vec{v} \\cdot \\vec{w} = \\left | \\vec{v} \\right | \\left | \\vec{w} \\right | \\cos \\alpha"]);return Fe=function(){return n},n}function Ae(){var n=ke(["\vec{v} - \vec{w} = (\vec{v}_x - \vec{w}_x) + (\vec{v}_y - \vec{w}_y)"],["\\vec{v} - \\vec{w} = (\\vec{v}_x - \\vec{w}_x) + (\\vec{v}_y - \\vec{w}_y)"]);return Ae=function(){return n},n}function Pe(){var n=ke(["\vec{v} + \vec{w} = (\vec{v}_x + \vec{w}_x) + (\vec{v}_y + \vec{w}_y)"],["\\vec{v} + \\vec{w} = (\\vec{v}_x + \\vec{w}_x) + (\\vec{v}_y + \\vec{w}_y)"]);return Pe=function(){return n},n}function Ce(){var n=ke(["left | \vec{v}_y \right | = left | \vec{v} \right | cos alpha"],["\\left | \\vec{v}_y \\right | = \\left | \\vec{v} \\right | \\cos \\alpha"]);return Ce=function(){return n},n}function Ie(){var n=ke(["left | \vec{v}_x \right | = left | \vec{v} \right | sin alpha"],["\\left | \\vec{v}_x \\right | = \\left | \\vec{v} \\right | \\sin \\alpha"]);return Ie=function(){return n},n}function we(){var n=ke(["\vec{v} = \vec{v}_x + \vec{v}_y"],["\\vec{v} = \\vec{v}_x + \\vec{v}_y"]);return we=function(){return n},n}function ke(n,e){return e||(e=n.slice(0)),n.raw=e,n}t("hosL");var Be=t("Q7TX"),Se=t("imVn"),Ne=t("OPqz"),xe=t("CfuJ"),Ve=t("4v1N"),Te=t("RMzO"),ye=t("wQ73"),Re=t("PGF6"),Oe=String.raw;e.default=function(){return n(ye.a.Provider,{value:!1},n(Re.a.Provider,{value:Be.a.INLINE},n("div",null,n("h1",null,"Fisica"),n(Ne.a,{title:"Vettori"},n(Se.a,{title:"Componenti cartesiane"},n("p",null,"Usa le regole base della trigonometria:"),n("p",null,n(Be.b,null,Oe(we()))),n("p",null,n(Be.b,null,Oe(Ie()))),n("p",null,n(Be.b,null,Oe(Ce())))),n(Se.a,{title:"Somma"},n("p",null,"Scomponi in componenti, poi sommali:"),n("p",null,n(Be.b,null,Oe(Pe()))),n("p",null,"Produce il vettore risultante dall'applicazione della regola del parallelogramma.")),n(Se.a,{title:"Differenza"},n("p",null,"Alla fine è sempre una somma:"),n("p",null,n(Be.b,null,Oe(Ae()))),n("p",null,"Produce il vettore che parte da ",n(Be.b,null,"w")," e arriva a ",n(Be.b,null,"v"),".")),n(Se.a,{title:"Prodotto scalare"},n("p",null,"Si chiama scalare perchè il risultato è uno scalare, non un vettore."),n("p",null,n(Be.b,null,Oe(Fe()))),n("p",null,"Produce il modulo della proiezione di ",n(Be.b,null,Oe(qe()))," su ",n(Be.b,null,Oe(Ee())),".")),n(Se.a,{title:"Prodotto vettoriale"},n("p",null,"Si chiama vettoriale perchè il risultato è un altro vettore."),n("ul",null,n("li",null,n(Be.b,null,Oe(Le()))),n("li",null,n(Be.b,null,Oe(De()))),n("li",null,n("a",{href:"https://it.wikipedia.org/wiki/Regola_della_mano_destra"},"Regola della mano destra"))),n("p",null,"Non è commutativo!"))),n(Ne.a,{title:"Leggi di Newton"},n(Se.a,{title:"1ᵃ: Inerzia"},n("p",null,"Se un corpo puntiforme ha forza risultante nulla, allora la sua velocità non cambia."),n("p",null,n(Be.b,null,Oe(ze())))),n(Se.a,{title:"2ᵃ: Proporzionalità"},n("p",null,"La forza risultante di un corpo è direttamente proporzionale alla sua accelerazione, e la costante di proporzionalità è la ",n("i",null,"massa"),"."),n("p",null,n(Be.b,null,Oe(be())))),n(Se.a,{title:"3ᵃ: Azione e reazione"},n("p",null,"Due corpi esercitano forze uguali e opposte uno sull'altro."),n("p",null,n(Be.b,null,Oe(he()))))),n(Ne.a,{title:"Forza di gravità"},n(Se.a,{title:"Tra due corpi"},n("p",null,"Due corpi puntiformi si attirano uno verso l'altro con forza:"),n("p",null,n(Be.b,null,Oe(ge()))),n("p",null,n(Be.b,null,"G")," è la ",n("i",null,"costante di gravitazione universale")," e vale:"),n("p",null,n(Be.b,null,Oe(_e())))),n(Se.a,{title:"Verso la Terra"},n("p",null,"Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo è attratto verso la Terra con forza ",n("i",null,"peso")," uguale a:"),n("p",null,n(Be.b,null,Oe(me()))),n("p",null,n(Be.b,null,"g")," è la ",n("i",null,"costante di gravità")," della Terra, e vale:"),n("p",null,n(Be.b,null,Oe(ve())))),n(Se.a,{title:"Su pianeti diversi"},n("p",null,"Per pianeti diversi dalla Terra vale la stessa regola:"),n("p",null,n(Be.b,null,Oe(fe()))),n("p",null,"L'unica differenza è che cambia la ",n("i",null,"costante di gravità"),":"),n("p",null,n(Be.b,null,Oe(de()))),n("p",null,n(Be.b,null,Oe(pe()))))),n(Ne.a,{title:"Forze di contatto"},n(Se.a,{title:"Normale"},n("p",null,"Si oppone alle forze applicate alla superficie di contatto."),n("p",null,"Un libro appoggiato su un tavolo ha la ",n("b",null,"forza di gravità")," che lo attira verso il terreno e la ",n("b",null,"forza normale")," che lo trattiene dal cadere.")),n(Se.a,{title:"Attrito statico"},n("p",null,"Impedisce a un corpo di muoversi se non viene spinto da una forza che supera una certa soglia:"),n("p",null,n(Be.b,null,Oe(se())))),n(Se.a,{title:"Attrito dinamico"},n("p",null,"Rallenta i corpi che si stanno muovendo finchè essi non si fermano:"),n("p",null,n(Be.b,null,Oe(ce())))),n(Se.a,{title:"Tensione"},n("p",null,"E' forza trasmessa tra due estremi di una fune."),n("p",null,"Può essere redirezionata per mezzo di carrucole.")),n(Se.a,{title:"Elastica"},n("p",null,"Una molla cerca sempre di tornare alla sua posizione indeformata con forza:"),n("p",null,n(Be.b,null,Oe(ue()))),n("p",null,"(E' negativa perchè la forza è opposta a quella applicata per deformarla.)"))),n(Ne.a,{title:"Cinematica"},n(Se.a,{title:"Spostamento"},n("p",null,"È un vettore che indica la posizione di un corpo rispetto a un'origine."),n("p",null,n(Be.b,null,Oe(re())))),n(Se.a,{title:"Velocità"},n("p",null,"È un vettore che misura la variazione di posizione nel tempo."),n("p",null,n(Be.b,null,Oe(oe()))),n("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",n("i",null,"velocità istantanea"),":"),n("p",null,n(Be.b,null,Oe(ie())))),n(Se.a,{title:"Accelerazione"},n("p",null,"È un vettore che misura la variazione di velocità nel tempo."),n("p",null,n(Be.b,null,Oe(ae()))),n("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",n("i",null,"accelerazione istantanea"),":"),n("p",null,n(Be.b,null,Oe(le())))),n(Se.a,{title:n("span",null,"Quantità di moto ",n("small",null,"(momento lineare)"))},n("p",null,"La quantità di moto è una proprietà vettoriale dei corpi:"),n("p",null,n(Be.b,null,Oe(te()))),n("p",null,"Se la forza risultante è nulla, la quantità di moto non cambia."),n("p",null,n(Be.b,null,Oe(ee()))))),n(Ne.a,{title:"Moto rettilineo uniforme"},n(Se.a,{title:"Spostamento"},n("p",null,"La ",n("i",null,"legge oraria")," è:"),n("p",null,n(Be.b,null,Oe(ne())))),n(Se.a,{title:"Velocità"},n("p",null,"È costante:"),n("p",null,n(Be.b,null,Oe($n())))),n(Se.a,{title:"Accelerazione"},n("p",null,"La velocità non varia:"),n("p",null,n(Be.b,null,Oe(Zn())))),n(Se.a,{title:"Forze"},n("p",null,"Si applica la prima legge di Newton:"),n("p",null,n(Be.b,null,"f(t) = 0")))),n(Ne.a,{title:"Moto rettilineo uniformemente accelerato"},n(Se.a,{title:"Spostamento"},n("p",null,"La ",n("i",null,"legge oraria")," è:"),n("p",null,n(Be.b,null,Oe(Xn())))),n(Se.a,{title:"Velocità"},n("p",null,"È una retta:"),n("p",null,n(Be.b,null,Oe(Kn())))),n(Se.a,{title:"Accelerazione"},n("p",null,"È costante:"),n("p",null,n(Be.b,null,Oe(Yn())))),n(Se.a,{title:"Forze"},n("p",null,"Si applica la prima legge di Newton:"),n("p",null,n(Be.b,null,"f(t) = m a")))),n(Ne.a,{title:"Moto armonico semplice"},n(Se.a,{title:"Ampiezza"},n("p",null,"E' la distanza dal centro massima che raggiunge il corpo."),n("p",null,"(L'ampiezza di una sinusoide.)")),n(Se.a,{title:"Velocità angolare"},n("p",null,"Indica quanto in fretta cambia la posizione del corpo."),n("p",null,"Dipende dal periodo:"),n("p",null,n(Be.b,null,Oe(Jn())))),n(Se.a,{title:"Spostamento"},n("p",null,"E' una sinusoide:"),n("p",null,n(Be.b,null,Oe(jn())))),n(Se.a,{title:"Velocità"},n("p",null,"E' la sinusoide dello spostamento, sfasata di ",n(Be.b,null,Oe(Wn())),":"),n("p",null,n(Be.b,null,Oe(Gn())))),n(Se.a,{title:"Accelerazione"},n("p",null,"E' la sinusoide della velocità, sfasata di ",n(Be.b,null,Oe(Qn())),":"),n("p",null,n(Be.b,null,Oe(Mn())))),n(Se.a,{title:"Forze"},n("p",null,"Si applica la prima legge di Newton:"),n("p",null,n(Be.b,null,"f(t) = m a")))),n(Ne.a,{title:"Moti composti"},n(Se.a,{title:"Moto parabolico"},n("p",null,"Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.")),n(Se.a,{title:"Moto circolare uniforme"},n("p",null,"Il moto parabolico è dato sommando due moti armonici semplici: uno sull'asse X, e l'altro, sfasato di ",n(Be.b,null,Oe(Hn())),", sull'asse Y."))),n(Ne.a,{title:"Moto circolare uniforme"},n(Se.a,null,n("h3",null,"Velocità angolare"),n("p",null,"Quanto cambia la fase nel tempo."),n("p",null,n(Be.b,null,Oe(Un())))),n(Se.a,{title:"Fase"},n("p",null,"E' l'angolo percorso dal corpo rispetto alla posizione iniziale."),n("p",null,"Si indica con ",n(Be.b,null,Oe(On())),", e generalmente si usa in radianti.")),n(Se.a,{title:"Velocità"},n("p",null,"Si applicano le formule per la circonferenza:"),n("p",null,n(Be.b,null,Oe(Rn())))),n(Se.a,{title:"Accelerazione"},n("p",null,"Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto:"),n("p",null,n(Be.b,null,Oe(yn())))),n(Se.a,{title:"Forza centripeta"},n("p",null,"È verso il centro e si calcola con:"),n("p",null,n(Be.b,null,Oe(Tn()))))),n(Ne.a,{title:"Lavoro ed energia"},n(Se.a,{title:"Lavoro"},n("p",null,"E' compiuto da una forza che sposta un corpo."),n("p",null,n(Be.b,null,Oe(Vn()))),n("p",null,"(Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)")),n(Se.a,{title:"Energia cinetica"},n("p",null,"Un corpo ha energia cinetica in ogni momento uguale a:"),n("p",null,n(Be.b,null,Oe(xn()))),n("p",null,"Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:"),n("p",null,n(Be.b,null,Oe(Nn())))),n(Se.a,{title:"Energia potenziale gravitazionale"},n("p",null,"Un corpo ha energia potenziale in ogni momento pari a:"),n("p",null,n(Be.b,null,Oe(Sn()))),n("p",null,"(Con ",n(Be.b,null,"h")," uguale a un altezza scelta come punto di riferimento.)")),n(Se.a,{title:"Energia potenziale elastica"},n("p",null,"Una molla ha sempre energia potenziale elastica pari a:"),n("p",null,n(Be.b,null,Oe(Bn())))),n(Se.a,{title:"Forze conservative"},n("p",null,"Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo."),n("p",null,"Ad esempio, è conservativa la ",n("i",null,"forza di gravità"),", ma ",n("b",null,"non")," è conservativa la forza di attrito."),n("p",null,"Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:"),n("p",null,n(Be.b,null,Oe(kn())))),n(Se.a,{title:"Potenza"},n("p",null,"È la velocità di trasferimento di energia:"),n("p",null,n(Be.b,null,Oe(wn()))))),n(Ne.a,{title:"Elettrostatica"},n(Se.a,{title:"Carica elettrica"},n("p",null,"È una proprietà dei corpi che può essere ",n(xe.a,null,"positiva")," o ",n(Ve.a,null,"negativa"),"."),n("p",null,"Si conserva: in un sistema chiuso la carica totale è costante."),n("p",null,"Esiste un'unità elementare: ",n(Be.b,null,Oe(In())),"."),n("p",null,"Cariche ",n(xe.a,null,"opp"),n(Ve.a,null,"oste")," si attraggono; cariche ",n(xe.a,null,"uguali")," si respingono.")),n(Se.a,{title:"Conduttori e isolanti"},n("p",null,"Più ",n("a",{href:"https://it.wikipedia.org/wiki/Ione"},"ioni")," ha un corpo, meglio la carica si muove attraverso di esso."),n("p",null,"I corpi in cui la carica si muove bene sono ",n("i",null,"conduttori"),", mentre quelli in cui si muove difficilmente sono ",n("i",null,"isolanti"),"."),n("p",null,n("i",null,"Il corpo umano è un buon conduttore.")))),n(Ne.a,{title:"Polarizzazione"},n(Se.a,{title:"Polarizzazione"},n("p",null,"E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona."))),n(Ne.a,null,n(Se.a,{title:"Messa a terra"},n("p",null,"Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno ",n("i",null,"equilibrate")," e il corpo diventerà elettricamente neutro (con stesso numero di ",n(xe.a,null,"cariche positive")," e ",n(Ve.a,null,"negative")," all'interno)."))),n(Ne.a,null,n(Se.a,{title:"Polarizzazione per strofinio"},n("p",null,"Strofinando tra loro due corpi isolanti, essi si ",n("i",null,"polarizzeranno per strofinio"),".")),n(Se.a,{title:"Polarizzazione per contatto"},n("p",null,"Toccando un conduttore con un corpo carico, il conduttore potrà ",n("i",null,"polarizzarsi per contatto"),".")),n(Se.a,{title:"Polarizzazione per induzione"},n("p",null,'Se un corpo conduttore ha cariche "esterne" di un ',n(xe.a,null,"certo segno")," vicino, esso avrà tutte le cariche del ",n(Ve.a,null,"segno opposto")," in equilibrio vicino alle cariche esterne, e tutte le cariche dello ",n(xe.a,null,"stesso segno")," più lontano possibile da esse."),n("p",null,"Mettendo a terra il conduttore, nuove cariche del ",n(Ve.a,null,"segno opposto")," saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate."),n("p",null,"Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà ",n(Ve.a,null,"caricato del segno opposto")," rispetto alle cariche esterne."))),n(Ne.a,{title:"Forza elettrica"},n(Se.a,{title:"Legge di Coulomb"},n("p",null,"Due corpi carichi si attraggono tra loro con forza:"),n("p",null,n(Be.b,null,Oe(Cn()))),n("p",null,n(Be.b,null,Oe(Pn()))," è la ",n("i",null,"costante di Coulomb"),", e vale ",n(Be.b,null,Oe(An())),".")),n(Se.a,{title:"Permeabilità dello spazio vuoto"},n("p",null,"La costante ",n(Be.b,null,Oe(Fn()))," è in realtà dipendente da un altra costante, ",n(Be.b,null,Oe(qn())),", la ",n("i",null,"permeabilità del vuoto"),"."),n("p",null,n(Be.b,null,Oe(En()))),n("p",null,n(Be.b,null,Oe(Ln())))),n(Se.a,{title:"Campo elettrico"},n("p",null,"Misura che forza viene applicata in ogni punto su una carica unitaria:"),n("p",null,n(Be.b,null,Oe(Dn())))),n(Se.a,{title:"Flusso elettrico"},n("p",null,'È la differenza tra "quanto" campo elettrico ',n(xe.a,null,"entra")," e quanto campo elettrico ",n(Ve.a,null,"esce")," da una certa area."),n("p",null,"In qualsiasi superficie chiusa, il flusso elettrico è uguale alla componente perpendicolare del campo elettrico moltiplicato per l'area."),n("p",null,n(Be.b,null,Oe(zn()))),n("p",null,"Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:"),n("p",null,n(Be.b,null,Oe(bn()))),n("p",null,n(Te.a,null,"Circa. E' una specie di integrale..."))),n(Se.a,{title:"Legge di Gauss per i campi elettrostatici"},n("p",null,"Il flusso elettrico è direttamente proporzionale alla carica presente all'interno della superficie."),n("p",null,n(Be.b,null,Oe(hn()))),n("p",null,"Ovvero, i campi elettrostatici sono generati dalle cariche elettriche."))),n(Ne.a,{title:"Energia elettrica"},n(Se.a,{title:"Energia potenziale elettrica"},n("p",null,"Un corpo carico vicino ad altre cariche possiede un'",n("i",null,"energia potenziale elettrica")," ",n(Be.b,null,Oe(gn())),"."))),n(Ne.a,{title:"Circuiti elettrici"},n(Se.a,{title:n("span",null,"Potenziale elettrico ",n("small",null,"(tensione)"))},n("p",null,"È il valore dell'energia potenziale elettrica per una carica unitaria."),n("p",null,n(Be.b,null,Oe(_n()))),n("p",null,"La sua unità di misura è il Volt (",n(Be.b,null,Oe(mn())),")."),n("p",null,"In una batteria è detto ",n("i",null,"forza elettromotrice"),", e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli.")),n(Se.a,{title:n("span",null,"Corrente elettrica ",n("small",null,"(intensità)"))},n("p",null,"Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo."),n("p",null,n(Be.b,null,Oe(vn()))),n("p",null,"Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla."),n("p",null,"La sua unità di misura è l'Ampere (",n(Be.b,null,Oe(fn())),").")),n(Se.a,{title:n("span",null,"Corrente continua ",n("small",null,"(",n("abbr",{title:"Direct Current"},"DC"),")"))},n("p",null,"Quando in un circuito la direzione della corrente è costante.")),n(Se.a,{title:n("span",null,"Corrente alternata ",n("small",null,"(",n("abbr",{title:"Alternate Current"},"AC"),")"))},n("p",null,"Quando in un circuito la direzione della corrente si alterna periodicamente.")),n(Se.a,{title:"Potenza elettrica"},n("p",null,"Possiamo calcolare la potenza di un circuito:"),n("p",null,n(Be.b,null,Oe(dn()))))),n(Ne.a,{title:"Elementi di un circuito"},n(Se.a,{title:"Resistore"},n("p",null,"Riduce l'intensità di corrente, e converte parte del potenziale in calore."),n("p",null,"Il potenziale utilizzato è pari a:"),n("p",null,n(Be.b,null,Oe(pn()))),n("p",null,"Dove ",n(Be.b,null,Oe(sn()))," è una costante detta ",n("i",null,"resistenza")," con unità di misura Ohm (",n(Be.b,null,Oe(cn())),")."),n("p",null,"La resistenza di un conduttore vale:"),n("p",null,n(Be.b,null,Oe(un()))),n("p",null,n(Be.b,null,Oe(rn()))," è la ",n("i",null,"resistività")," del materiale, e varia in base alla temperatura:"),n("p",null,n(Be.b,null,Oe(on())))),n(Se.a,{title:"Condensatore"},n("p",null,"Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito."),n("p",null,"Per farlo, cattura cariche ",n(xe.a,null,"positive")," e ",n(Ve.a,null,"negative")," sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro."),n("p",null,"Ha una ",n("b",null,"capacità")," caratteristica, che in un condensatore a facce piane parallele è:"),n("p",null,n(Be.b,null,Oe(an()))),n("p",null,"Condensatori di capacità maggiore immagazzinano più potenziale con meno carica."),n("p",null,"La capacità aumenta se viene messo qualcosa tra le armature:"),n("p",null,n(Be.b,null,Oe(ln()))),n("p",null,"Dove ",n(Be.b,null,Oe(tn()))," è la ",n("i",null,"costante dielettrica relativa")," del materiale inserito, ",n(Be.b,null,Oe(en()))," l'area di una armatura e ",n(Be.b,null,Oe(nn()))," la distanza tra le due armature."),n("p",null,"Se il campo elettrico creatosi tra le due armature supera la ",n("i",null,"rigidità dielettrica")," del condensatore, la carica immagazzinata viene persa e ha luogo un ",n("i",null,"breakdown"),"."),n("p",null,"La sua unità di misura è il Farad (",n(Be.b,null,Oe($())),")")),n(Se.a,{title:"Amperometro"},n("p",null,"Misura la corrente elettrica se messo in serie."),n("p",null,"(Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)")),n(Se.a,{title:"Voltmetro"},n("p",null,"Misura la differenza di potenziale se messo in parallelo."),n("p",null,"(Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)"))),n(Ne.a,{title:"Principi di Kirchhoff"},n(Se.a,{title:"Legge dei nodi"},n("p",null,"Per nodo si intende un qualsiasi punto del circuito."),n("p",null,"Da un nodo entra ed esce la stessa corrente.")),n(Se.a,{title:"Legge delle maglie"},n("p",null,"Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito."),n("p",null,"In una maglia chiusa, la somma delle differenze di potenziale è 0."))),n(Ne.a,{title:"Serie e Parallelo"},n(Se.a,{title:"Circuito in serie"},n("p",null,"Più parti di circuito sono ",n("i",null,"in serie")," se sono consecutive e senza biforcazioni."),n("p",null,"Parti di circuito in serie sono attraversate dalla stessa corrente.")),n(Se.a,{title:"Circuito in parallelo"},n("p",null,"Più parti di circuito sono ",n("i",null,"in parallelo")," tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo."),n("p",null,"Parti di circuito in parallelo hanno la stessa differenza di potenziale."))),n(Ne.a,{title:"Resistenze equivalenti"},n(Se.a,{title:"Circuiti in serie"},n("p",null,"Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:"),n("p",null,n(Be.b,null,Oe(Z())))),n(Se.a,{title:"Circuiti in parallelo"},n("p",null,"Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:"),n("p",null,n(Be.b,null,Oe(X()))))),n(Ne.a,{title:"Condensatori equivalenti"},n(Se.a,{title:"Circuiti in serie"},n("p",null,"Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacità di:"),n("p",null,n(Be.b,null,Oe(K())))),n(Se.a,{title:"Circuiti in parallelo"},n("p",null,"Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacità della somma di tutti quelli sostituiti:"),n("p",null,n(Be.b,null,Oe(Y()))))),n(Ne.a,{title:"Magnetismo"},n(Se.a,{title:"Permeabilità magnetica dello spazio vuoto"},n("p",null,"E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente."),n("p",null,n(Be.b,null,Oe(J()))," (",n(Be.b,null,Oe(j())),")")),n(Se.a,{title:"Campo magnetico"},n("p",null,"Come un campo elettrico, ma per i magneti."),n("p",null,"Il suo simbolo è ",n(Be.b,null,Oe(W())),", e la sua unità di misura è il Tesla (",n(Be.b,null,"T"),").")),n(Se.a,{title:"Flusso magnetico"},n("p",null,'È "quanto" campo magnetico ',n("b",null,"attraversa")," un percorso chiuso."),n("p",null,'Per qualsiasi percorso chiuso, il flusso magnetico è uguale alla somma di tutti i "sottoflussi" magnetici calcolati sui suoi lati.'),n("p",null,n(Be.b,null,Oe(G()))),n("p",null,n(Be.b,null,Oe(Q()))),n("p",null,"La sua unità di misura è il Weber (",n(Be.b,null,Oe(M())),").")),n(Se.a,{title:"Legge di Gauss per i campi magnetici"},n("p",null,"Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo."),n("p",null,"Ovvero, non esistono monopoli magnetici.")),n(Se.a,{title:"Legge di Ampère"},n("p",null,"L'intensità di corrente che attraversa un percorso chiuso è direttamente proporzionale al flusso magnetico dello stesso percorso."),n("p",null,n(Be.b,null,Oe(H()))))),n(Ne.a,{title:"Forze magnetiche"},n(Se.a,{title:n("span",null,"Forza magnetica su carica puntiforme ",n("small",null,"(Forza di Lorentz)"))},n("p",null,"I campi magnetici applicano una forza sulle cariche vicine:"),n("p",null,n(Be.b,null,Oe(U()))),n("p",null,"Dove ",n(Be.b,null,Oe(O()))," è l'intensità del campo magnetico e ",n(Be.b,null,Oe(R()))," la velocità della carica considerata."),n("p",null,"Si ha una forza massima se la velocità è perpendicolare al campo magnetico."),n("p",null,"In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme.")),n(Se.a,{title:"Forza magnetica in un filo"},n("p",null,"I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:"),n("p",null,n(Be.b,null,Oe(y()))," ",n("a",{href:"https://it.openprof.com/wb/forza_di_lorentz_su_un_filo_percorso_da_corrente?ch=360"},"[1]")),n("p",null,"Dove ",n(Be.b,null,Oe(T()))," è la corrente elettrica, ",n(Be.b,null,Oe(V()))," è un vettore che punta nella direzione di scorrimento della corrente e ha come modulo la lunghezza del conduttore."))),n(Ne.a,{title:"Campi magnetici"},n(Se.a,{title:"Campo magnetico in una spira"},n("p",null,"Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.")),n(Se.a,{title:"Campo magnetico di un solenoide"},n("p",null,"Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro."),n("p",null,"All'interno del solenoide si crea un campo (quasi) uniforme:"),n("p",null,n(Be.b,null,Oe(x())))),n(Se.a,{title:"Legge di Oersted"},n("p",null,n("i",null,"Caso particolare della ",n("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Amp%C3%A8re"},"Legge di Ampère"),".")),n("p",null,"Il modulo del campo magnetico ",n(Be.b,null,"B")," prodotto da un filo in cui passa una corrente continua ",n(Be.b,null,"I")," alla distanza ",n(Be.b,null,"s")," è:"),n("p",null,n(Be.b,null,Oe(N()))),n("p",null,"Il campo magnetico così creato gira attorno al filo in senso antiorario."),n("p",null,"Due fili attraversati dalla ",n(xe.a,null,"stessa corrente")," si attraggono, due fili attraversati da ",n(xe.a,null,"corr"),n(Ve.a,null,"enti")," ",n(xe.a,null,"opp"),n(Ve.a,null,"oste")," si respingono."))),n(Ne.a,{title:"Induzione elettromagnetica"},n(Se.a,{title:"Forza elettromotrice indotta"},n("p",null,"Un conduttore perpendicolare ad un campo magnetico può ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo."),n("p",null,"La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore."),n("p",null,"Essa vale:"),n("p",null,n(Be.b,null,Oe(S()))),n("p",null,"Dove ",n(Be.b,null,"v")," è la velocità del conduttore, ",n(Be.b,null,"B")," è l'intensità del campo magnetico ed ",n(Be.b,null,"L")," è la lunghezza del conduttore.")),n(Se.a,{title:"Flusso magnetico in una spira"},n("p",null,"In un campo magnetico ",n(Be.b,null,Oe(B()))," uniforme e perpendicolare al piano di una spira di area ",n(Be.b,null,Oe(k())),", il flusso magnetico si può determinare con la ",n("i",null,"Legge di Faraday-Neumann-Lenz"),":"),n("p",null,n(Be.b,null,Oe(w()))))),n(Ne.a,null,n(Se.a,{title:"Legge di Faraday-Neumann-Lenz"},n("p",null,"Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso."),n("p",null,n(Be.b,null,Oe(I()))),n("p",null,"Il meno è dovuto alla ",n("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Lenz"},"Legge di Lenz"),", che specifica qualitativamente il verso della forza elettromotrice indotta.")),n(Se.a,{title:"Faraday in un solenoide"},n("p",null,"In un solenoide, la forza elettromotrice indotta è uguale a:"),n("p",null,n(Be.b,null,Oe(C()))),n("p",null,"Dove ",n(Be.b,null,Oe(P()))," è il numero delle spire del solenoide.")),n(Se.a,{title:"Legge di Ampère-Maxwell"},n("p",null,"Correnti o campi elettrici variabili creano un campo magnetico."))),n(Ne.a,{title:"Elettromagnetismo"},n(Se.a,{title:"Onde elettromagnetiche"},n("p",null,"Nel vuoto, il campo elettrico ",n(Be.b,null,Oe(A()))," e il campo magnetico ",n(Be.b,null,Oe(F()))," sono perpendicolari tra loro e la direzione di propagazione, e sono entrambe funzioni del tempo."),n("p",null,"Si dice quindi che sono ",n("i",null,"onde elettromagnetiche"),"."),n("p",null,"Esse sono legate dalla relazione:"),n("p",null,n(Be.b,null,Oe(q()))),n("p",null,"Dove ",n(Be.b,null,Oe(E()))," è la velocità delle onde (luce) nel vuoto, e a sua volta è uguale a:"),n("p",null,n(Be.b,null,Oe(L())))),n(Se.a,{title:"Formula delle onde"},n("p",null,n(Be.b,null,Oe(D()))),n("p",null,"Dove ",n(Be.b,null,Oe(z()))," è l'ampiezza massima che può avere l'onda, ",n(Be.b,null,Oe(b()))," è il vettore d'onda, ",n(Be.b,null,Oe(h()))," la frequenza angolare e ",n(Be.b,null,Oe(g()))," la fase."))),n(Ne.a,{title:"Spettroscopia"},n(Se.a,{title:"Emissione"},n("p",null,"I solidi, se portati ad alta temperatura, emettono luce con uno ",n("a",{href:"https://it.wikipedia.org/wiki/Spettro_continuo"},"spettro continuo"),"."),n("p",null,"I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d'onda."),n("p",null,"In un gas di idrogeno, le lunghezze d'onda emesse sono ricavabili con:"),n("p",null,n(Be.b,null,Oe(_()))),n("p",null,"Con ",n(Be.b,null,Oe(m())),", detta costante di Rydberg, e ",n(Be.b,null,Oe(v()))," un numero intero.")),n(Se.a,{title:"Grandezza quantizzata"},n("p",null,"Una grandezza si dice quantizzata (o discreta) se può assumere solo determinati valori."),n("p",null,"Una grandezza si dice continua se può assumere qualsiasi valore e quindi se non è quantizzata."),n("p",null,"Energia, momento angolare e raggio sono quantizzati."),n("p",null,"Nota costante quantica è ",n(Be.b,null,Oe(f())),", la costante di Planck, ovvero il valore minimo possibile per la carica (talvolta espressa come ",n(Be.b,null,Oe(d())),"."))),n(Ne.a,null,n(Se.a,{title:"Modello di Bohr"},n("p",null,"L'energia degli elettroni è quantizzata."),n("p",null,"Inoltre, per essi è valido che:"),n("p",null,n(Be.b,null,Oe(p()))),n("p",null,"Ancora, il raggio delle orbite è uguale a:"),n("p",null,n(Be.b,null,Oe(s()))),n("p",null,"Con ",n(Be.b,null,Oe(c())),"."),n("p",null,"Infine, in ogni stato, l'energia è pari a:"),n("p",null,n(Be.b,null,Oe(u()))),n("p",null,"Due elettroni non possono occupare lo stesso stato."),n("p",null,"Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di"))),n(Ne.a,null,n(Se.a,{title:"Nei solidi"},n("p",null,"Nei solidi, le lunghezze d'onda sono talmente tanto vicine da poter essere considerate una banda."),n("p",null,"Possono però comunque avere dei gap dovuti agli intervalli di energia non ammessi."))),n(Ne.a,{title:"Semiconduttori"},n(Se.a,{title:"Semiconduttori"},n("p",null,n(Te.a,null,"Refactor this")),n("p",null,"Se la banda di emissione con energia più alta di un corpo è assente o è separata da un gap dell'ordine di grandezza maggiore di ",n(Be.b,null,Oe(r())),", allora il corpo è un isolante."),n("p",null,"Se invece la banda di emissione si sovrappone a un altra, allora il corpo è un conduttore."),n("p",null,"Se il gap è invece dell'ordine di grandezza di ",n(Be.b,null,Oe(o())),", allora il corpo è un semiconduttore.")),n(Se.a,{title:"Lacune"},n("p",null,"Legami in cui ",n(xe.a,null,"mancano elettroni"),"."),n("p",null,n(Ve.a,null,"Elettroni")," di altri legami possono spostarsi per colmare le ",n(xe.a,null,"lacune"),", creandone altre, e spostandole in direzione opposta a quella della corrente.")),n(Se.a,{title:"Accettori e donori"},n("p",null,"Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterrà:"),n("ul",null,n("li",null,"Con numero atomico maggiore, un semiconduttore di ",n(Ve.a,null,"tipo N")," con ",n(Ve.a,null,"elettroni in eccesso")," liberi di scorrere."),n("li",null,"Con numero atomico minore, un semiconduttore di ",n(xe.a,null,"tipo P")," con ",n(xe.a,null,"lacune in eccesso")," libere di catturare elettroni da altri legami.")),n("p",null,"Maggiore impurezza porta a maggiore conduttività.")),n(Se.a,{title:"Temperatura"},n("p",null,"Aumentando la temperatura di un semiconduttore si aumenta la conduttività, perchè eccita le particelle e favorisce il movimento di ",n(Ve.a,null,"elettroni")," e ",n(xe.a,null,"lacune"),"."))),n(Ne.a,{title:n("span",null,"Ottica ",n("small",null,"(non l'abbiamo fatta)"))},n(Se.a,{title:"Assorbimento e riflessione"},n("p",null,"I corpi possono assorbire o riflettere le onde elettromagnetiche che li colpiscono.")),n(Se.a,{title:"Corpo nero"},n("p",null,"Un corpo nero è un corpo che assorbe tutte le onde elettromagnetiche che riceve senza rifletterne nessuna."),n("p",null,"Le onde assorbite vengono poi riemesse sotto forma di un onda di ",n(Be.b,null,Oe(i()))," variabile in base alla temperatura."),n("p",null,n(Be.b,null,Oe(a()))," è costante.")),n(Se.a,{title:"Teoria di Planck per il corpo nero"},n("p",null,"L'energia assorbita e emessa dai corpi neri è quantizzata.")),n(Se.a,{title:"Fotone"},n("p",null,"Un onda magnetica con un quanto di energia è detta ",n("i",null,"fotone"),":"),n("p",null,n(Be.b,null,Oe(l())))),n(Se.a,{title:"Effetto fotoelettrico"},n("p",null,"A volte, i fotoni che colpiscono un metallo possono estrarvi degli elettroni e creare una differenza di potenziale."),n("p",null,"Perchè avvenga, la 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{ Component } from 'preact';\nimport Latex, {LatexDisplay} from '../components/Rendering/Latex';\nimport Panel from '../components/Elements/Panel';\nimport Section from \"../components/Elements/Section\";\nimport Plus from '../components/PageSpecific/Fisica/Plus';\nimport Minus from '../components/PageSpecific/Fisica/Minus';\nimport Todo from \"../components/Elements/Todo\";\nimport LatexDefaultInline from \"../contexts/LatexDefaultInline\";\nimport LatexDefaultDisplay from \"../contexts/LatexDefaultDisplay\";\n\nconst r = String.raw;\n\nexport default function(props) {\n    return (\n        \n        \n            
    \n                
    Fisica
    \n                
    \n                    \n                        
    \n                            Usa le regole base della trigonometria:\n                        
    \n                        
    \n                            {r`\\vec{v} = \\vec{v}_x + \\vec{v}_y`}\n                        
    \n                        
    \n                            {r`\\left | \\vec{v}_x \\right | = \\left | \\vec{v} \\right | \\sin \\alpha`}\n                        
    \n                        
    \n                            {r`\\left | \\vec{v}_y \\right | = \\left | \\vec{v} \\right | \\cos \\alpha`}\n                        
    \n                        \n                    \n                        
    \n                            Scomponi in componenti, poi sommali:\n                        
    \n                        
    \n                            {r`\\vec{v} + \\vec{w} = (\\vec{v}_x + \\vec{w}_x) + (\\vec{v}_y + \\vec{w}_y)`}\n                        
    \n                        
    \n                            Produce il vettore risultante dall'applicazione della regola del parallelogramma.\n                        
    \n                        \n                    \n                        
    \n                            Alla fine è sempre una somma:\n                        
    \n                        
    \n                            {r`\\vec{v} - \\vec{w} = (\\vec{v}_x - \\vec{w}_x) + (\\vec{v}_y - \\vec{w}_y)`}\n                        
    \n                        
    \n                            Produce il vettore che parte da w e arriva a v.\n                        
    \n                        \n                    \n                        
    \n                            Si chiama scalare perchè il risultato è uno scalare, non un vettore.\n                        
    \n                        
    \n                            {r`\\vec{v} \\cdot \\vec{w} = \\left | \\vec{v} \\right | \\left | \\vec{w} \\right | \\cos \\alpha`}\n                        
    \n                        
    \n                            Produce il modulo della proiezione di {r`\\vec{a}`} su {r`\\vec{b}`}.\n                        
    \n                        \n                    \n                        
    \n                            Si chiama vettoriale perchè il risultato è un altro vettore.\n                        
    \n                        
      \n                            
    • {r`\\vec{c} = \\vec{a} \\times \\vec{b}`}
      • \n                            
    • {r`\\left | \\vec{c} \\right | = \\left | \\vec{a} \\right | \\cdot \\left | \\vec{b} \\right | \\cdot \\sin(\\alpha)`}
      • \n                            
    • Regola della mano destra
      • \n                        
    \n                        
    \n                            Non è commutativo!\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Se un corpo puntiforme ha forza risultante nulla, allora la sua velocità non cambia.\n                        
    \n                        
    \n                            {r`\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta v = 0`}\n                        
    \n                        \n                    \n                        
    \n                            La forza risultante di un corpo è direttamente proporzionale alla sua accelerazione, e la costante di proporzionalità è la massa.\n                        
    \n                        
    \n                            {r`\\Sigma \\vec{F} = m \\vec{a}`}\n                        
    \n                        \n                    \n                        
    \n                            Due corpi esercitano forze uguali e opposte uno sull'altro.\n                        
    \n                        
    \n                            {r`\\vec{F}_{21} = -\\vec{F}_{12}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Due corpi puntiformi si attirano uno verso l'altro con forza:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | = G \\frac{m_1 m_2}{s^2}`}\n                        
    \n                        
    \n                            G è la costante di gravitazione universale e vale:\n                        
    \n                        
    \n                            {r`G = 6.67 \\cdot 10^{-11} \\frac{N m^2}{{kg}^2}`}\n                        
    \n                        \n                    \n                        
    \n                            Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo è attratto verso la Terra con forza peso uguale a:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | = g m`}\n                        
    \n                        
    \n                            g è la costante di gravità della Terra, e vale:\n                        
    \n                        
    \n                            {r`g = 9.81 \\frac{m}{s^2}`}\n                        
    \n                        \n                    \n                        
    \n                            Per pianeti diversi dalla Terra vale la stessa regola:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | = g m`}\n                        
    \n                        
    \n                            L'unica differenza è che cambia la costante di gravità:\n                        
    \n                        
    \n                            {r`g_{luna} = 1.62 \\frac{m}{s^2}`}\n                        
    \n                        
    \n                            {r`g_{marte} = 3.71 \\frac{m}{s^2}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Si oppone alle forze applicate alla superficie di contatto.\n                        
    \n                        
    \n                            Un libro appoggiato su un tavolo ha la forza di gravità che lo attira verso il terreno e la forza normale che lo trattiene dal cadere.\n                        
    \n                        \n                    \n                        
    \n                            Impedisce a un corpo di muoversi se non viene spinto da una forza che supera una certa soglia:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | \\leq \\mu_{s} \\left | \\vec{F}_{normale} \\right |`}\n                        
    \n                        \n                    \n                        
    \n                            Rallenta i corpi che si stanno muovendo finchè essi non si fermano:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | \\leq \\mu_{d} \\left | \\vec{F}_{normale} \\right |`}\n                        
    \n                        \n                    \n                        
    \n                            E' forza trasmessa tra due estremi di una fune.\n                        
    \n                        
    \n                            Può essere redirezionata per mezzo di carrucole.\n                        
    \n                        \n                    \n                        
    \n                            Una molla cerca sempre di tornare alla sua posizione indeformata con forza:\n                        
    \n                        
    \n                            {r`F = -k x`}\n                        
    \n                        
    \n                            (E' negativa perchè la forza è opposta a quella applicata per deformarla.)\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            È un vettore che indica la posizione di un corpo rispetto a un'origine.\n                        
    \n                        
    \n                            {r`\\Delta \\vec{s} = \\vec{s}(fine) - \\vec{s}(inizio)`}\n                        
    \n                        \n                    \n                        
    \n                            È un vettore che misura la variazione di posizione nel tempo.\n                        
    \n                        
    \n                            {r`\\vec{v} = \\frac{\\Delta \\vec{s}}{\\Delta t}`}\n                        
    \n                        
    \n                            Se si considera un intervallo di tempo infinitesimale si dice velocità istantanea:\n                        
    \n                        
    \n                            {r`\\vec{v} = \\lim_{\\Delta t \\to 0} \\frac{\\Delta \\vec{s}}{\\Delta t} = \\frac{d \\vec{s}}{dt}`}\n                        
    \n                        \n                    \n                        
    \n                            È un vettore che misura la variazione di velocità nel tempo.\n                        
    \n                        
    \n                            {r`\\vec{a} = \\frac{\\Delta \\vec{v}}{\\Delta t}`}\n                        
    \n                        
    \n                            Se si considera un intervallo di tempo infinitesimale si dice accelerazione istantanea:\n                        
    \n                        
    \n                            {r`\\vec{a} = \\lim_{\\Delta v \\to 0} \\frac{\\Delta \\vec{v}}{\\Delta t} = \\frac{d \\vec{v}}{d t} = \\frac{d^2 \\vec{s}}{d t^2}`}\n                        
    \n                        \n                    Quantità di moto (momento lineare)}>\n                        
    \n                            La quantità di moto è una proprietà vettoriale dei corpi:\n                        
    \n                        
    \n                            {r`\\vec{p} = m \\vec{v}`}\n                        
    \n                        
    \n                            Se la forza risultante è nulla, la quantità di moto non cambia.\n                        
    \n                        
    \n                            {r`\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta \\vec{p} = 0`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            La legge oraria è:\n                        
    \n                        
    \n                            {r`s(t) = v \\cdot \\Delta t + s(0)`}\n                        
    \n                        \n                    \n                        
    \n                            È costante:\n                        
    \n                        
    \n                            {r`v(t) = k`}\n                        
    \n                        \n                    \n                        
    \n                            La velocità non varia:\n                        
    \n                        
    \n                            {r`a(t) = 0`}\n                        
    \n                        \n                    \n                        
    \n                            Si applica la prima legge di Newton:\n                        
    \n                        
    \n                            f(t) = 0\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            La legge oraria è:\n                        
    \n                        
    \n                            {r`s(t) = \\frac{1}{2} a \\cdot (\\Delta t)^2 + v(0) \\cdot (\\Delta t) + s(0)`}\n                        
    \n                        \n                    \n                        
    \n                            È una retta:\n                        
    \n                        
    \n                            {r`v(t) = a \\Delta t + v(0)`}\n                        
    \n                        \n                    \n                        
    \n                            È costante:\n                        
    \n                        
    \n                            {r`a(t) = k`}\n                        
    \n                        \n                    \n                        
    \n                            Si applica la prima legge di Newton:\n                        
    \n                        
    \n                            f(t) = m a\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            E' la distanza dal centro massima che raggiunge il corpo.\n                        
    \n                        
    \n                            (L'ampiezza di una sinusoide.)\n                        
    \n                        \n                    \n                        
    \n                            Indica quanto in fretta cambia la posizione del corpo.\n                        
    \n                        
    \n                            Dipende dal periodo:\n                        
    \n                        
    \n                            {r`\\omega = \\frac{2 \\pi}{T}`}\n                        
    \n                        \n                    \n                        
    \n                            E' una sinusoide:\n                        
    \n                        
    \n                            {r`s(t) = A \\sin (\\omega \\cdot t + \\phi)`}\n                        
    \n                        \n                    \n                        
    \n                            E' la sinusoide dello spostamento, sfasata di {r`\\frac{\\pi}{2}`}:\n                        
    \n                        
    \n                            {r`v(t) = A \\sin (\\omega \\cdot t + \\phi + \\frac{\\pi}{2})`}\n                        
    \n                        \n                    \n                        
    \n                            E' la sinusoide della velocità, sfasata di {r`\\pi`}:\n                        
    \n                        
    \n                            {r`a(t) = A \\sin (\\omega \\cdot t + \\phi + \\pi)`}\n                        
    \n                        \n                    \n                        
    \n                            Si applica la prima legge di Newton:\n                        
    \n                        
    \n                            f(t) = m a\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.\n                        
    \n                        \n                    \n                        
    \n                            Il moto parabolico è dato sommando due moti armonici semplici: uno sull'asse X, e l'altro, sfasato di {r`\\frac{\\pi}{2}`}, sull'asse Y.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Velocità angolare\n                        
    \n                        
    \n                            Quanto cambia la fase nel tempo.\n                        
    \n                        
    \n                            {r`\\omega = \\frac{2 \\pi}{T}`}\n                        
    \n                        \n                    \n                        
    \n                            E' l'angolo percorso dal corpo rispetto alla posizione iniziale.\n                        
    \n                        
    \n                            Si indica con {r`\\phi`}, e generalmente si usa in radianti.\n                        
    \n                        \n                    \n                        
    \n                            Si applicano le formule per la circonferenza:\n                        
    \n                        
    \n                            {r`v = \\frac{\\Delta s}{t} = \\frac{2 \\pi \\cdot r}{T} = \\omega r`}\n                        
    \n                        \n                    \n                        
    \n                            Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto:\n                        
    \n                        
    \n                            {r`a = \\frac{v^2}{r} = r \\cdot \\omega^2 = v \\cdot \\omega`}\n                        
    \n                        \n                    \n                        
    \n                            È verso il centro e si calcola con:\n                        
    \n                        
    \n                            {r`F = m \\cdot a`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            E' compiuto da una forza che sposta un corpo.\n                        
    \n                        
    \n                            {r`W = \\vec{F} \\cdot \\vec{s} = F \\cdot \\Delta s \\cdot cos(\\alpha )`}\n                        
    \n                        
    \n                            (Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)\n                        
    \n                        \n                    \n                        
    \n                            Un corpo ha energia cinetica in ogni momento uguale a:\n                        
    \n                        
    \n                            {r`E_c = \\frac{1}{2} m v^2`}\n                        
    \n                        
    \n                            Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:\n                        
    \n                        
    \n                            {r`\\Delta E_c = W`}\n                        
    \n                        \n                    \n                        
    \n                            Un corpo ha energia potenziale in ogni momento pari a:\n                        
    \n                        
    \n                            {r`E_{p_g} = m \\cdot g \\cdot h`}\n                        
    \n                        
    \n                            (Con h uguale a un altezza scelta come punto di riferimento.)\n                        
    \n                        \n                    \n                        
    \n                            Una molla ha sempre energia potenziale elastica pari a:\n                        
    \n                        
    \n                            {r`E_{p_e} = \\frac{1}{2} k x^2`}\n                        
    \n                        \n                    \n                        
    \n                            Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo.\n                        
    \n                        
    \n                            Ad esempio, è conservativa la forza di gravità, ma non è conservativa la forza di attrito.\n                        
    \n                        
    \n                            Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:\n                        
    \n                        
    \n                            {r`E = E_k + E_p`}\n                        
    \n                        \n                    \n                        
    \n                            È la velocità di trasferimento di energia:\n                        
    \n                        
    \n                            {r`P = \\frac{\\Delta E}{\\Delta t}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            È una proprietà dei corpi che può essere positiva o negativa.\n                        
    \n                        
    \n                            Si conserva: in un sistema chiuso la carica totale è costante.\n                        
    \n                        
    \n                            Esiste un'unità elementare: {r`C_{elettrone} = 1.602 \\cdot 10^{-19}`}.\n                        
    \n                        
    \n                            Cariche opposte si attraggono; cariche uguali si respingono.\n                        
    \n                        \n                    \n                        
    \n                            Più ioni ha un corpo, meglio la carica si muove attraverso di esso.\n                        
    \n                        
    \n                            I corpi in cui la carica si muove bene sono conduttori, mentre quelli in cui si muove difficilmente sono isolanti.\n                        
    \n                        
    \n                            Il corpo umano è un buon conduttore.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno equilibrate e il corpo diventerà elettricamente neutro (con stesso numero di cariche positive e negative all'interno).\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Strofinando tra loro due corpi isolanti, essi si polarizzeranno per strofinio.\n                        
    \n                        \n                    \n                        
    \n                            Toccando un conduttore con un corpo carico, il conduttore potrà polarizzarsi per contatto.\n                        
    \n                        \n                    \n                        
    \n                            Se un corpo conduttore ha cariche \"esterne\" di un certo segno vicino, esso avrà tutte le cariche del segno opposto in equilibrio vicino alle cariche esterne, e tutte le cariche dello stesso segno più lontano possibile da esse.\n                        
    \n                        
    \n                            Mettendo a terra il conduttore, nuove cariche del segno opposto saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate.\n                        
    \n                        
    \n                            Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà caricato del segno opposto rispetto alle cariche esterne.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Due corpi carichi si attraggono tra loro con forza:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F}_{elettrica} \\right | = \\frac{-k \\cdot q_1 \\cdot q_2}{s^2}`}\n                        
    \n                        
    \n                            {r`k`} è la costante di Coulomb, e vale {r`k = 8.99 \\cdot 10^9 \\frac{N \\cdot m^2}{C^2}`}.\n                        
    \n                        \n                    \n                        
    \n                            La costante {r`k`} è in realtà dipendente da un altra costante, {r`\\epsilon_0`}, la permeabilità del vuoto.\n                        
    \n                        
    \n                            {r`k = \\frac{1}{4 \\pi \\cdot \\epsilon_0}`}\n                        
    \n                        
    \n                            {r`\\left | \\vec{F}_{elettrica} \\right | = \\frac{q_1 \\cdot q_2}{4 \\pi \\cdot \\epsilon_0 \\cdot s^2}`}\n                        
    \n                        \n                    \n                        
    \n                            Misura che forza viene applicata in ogni punto su una carica unitaria:\n                        
    \n                        
    \n                            {r`\\vec{E} = \\frac{\\vec{F}_{elettrica}}{q} = \\frac{-k \\cdot q}{s^2}`}\n                        
    \n                        \n                    \n                        
    \n                            È la differenza tra \"quanto\" campo elettrico entra e quanto campo elettrico esce da una certa area.\n                        
    \n                        
    \n                            In qualsiasi superficie chiusa, il flusso elettrico è uguale alla componente perpendicolare del campo elettrico moltiplicato per l'area.\n                        
    \n                        
    \n                            {r`\\Phi_E = \\vec{E} \\cdot \\vec{A}`}\n                        
    \n                        
    \n                            Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:\n                        
    \n                        
    \n                            {r`\\Phi_E = \\vec{E} \\cdot \\vec{A} = E_\\perp \\cdot A \\cdot \\cos(\\alpha)`}\n                        
    \n                        
    \n                            Circa. E' una specie di integrale...\n                        
    \n                        \n                    \n                        
    \n                            Il flusso elettrico è direttamente proporzionale alla carica presente all'interno della superficie.\n                        
    \n                        
    \n                            {r`\\Phi_E = 4 \\pi \\cdot k \\cdot q = \\frac{q}{\\epsilon_0}`}\n                        
    \n                        
    \n                            Ovvero, i campi elettrostatici sono generati dalle cariche elettriche.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Un corpo carico vicino ad altre cariche possiede un'energia potenziale elettrica {r`U_e`}.\n                        
    \n                        \n                
    \n                
    \n                    Potenziale elettrico (tensione)}>\n                        
    \n                            È il valore dell'energia potenziale elettrica per una carica unitaria.\n                        
    \n                        
    \n                            {r`V = \\frac{U_e}{q}`}\n                        
    \n                        
    \n                            La sua unità di misura è il Volt ({r`V`}).\n                        
    \n                        
    \n                            In una batteria è detto forza elettromotrice, e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli.\n                        
    \n                        \n                    Corrente elettrica (intensità)}>\n                        
    \n                            Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo.\n                        
    \n                        
    \n                            {r`I = \\frac{\\Delta q}{\\Delta t}`}\n                        
    \n                        
    \n                            Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla.\n                        
    \n                        
    \n                            La sua unità di misura è l'Ampere ({r`A`}).\n                        
    \n                        \n                    Corrente continua (DC)}>\n                        
    \n                            Quando in un circuito la direzione della corrente è costante.\n                        
    \n                        \n                    Corrente alternata (AC)}>\n                        
    \n                            Quando in un circuito la direzione della corrente si alterna periodicamente.\n                        
    \n                        \n                    \n                        
    \n                            Possiamo calcolare la potenza di un circuito:\n                        
    \n                        
    \n                            {r`P = \\frac{\\Delta U_e}{\\Delta t} = I \\cdot \\Delta V = I^2 \\cdot R = \\frac{(\\Delta V)^2}{R}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Riduce l'intensità di corrente, e converte parte del potenziale in calore.\n                        
    \n                        
    \n                            Il potenziale utilizzato è pari a:\n                        
    \n                        
    \n                            {r`V = R \\cdot I`}\n                        
    \n                        
    \n                            Dove {r`R`} è una costante detta resistenza con unità di misura Ohm ({r`\\Omega`}).\n                        
    \n                        
    \n                            La resistenza di un conduttore vale:\n                        
    \n                        
    \n                            {r`R = \\rho \\frac{L_{unghezza}}{A_{rea}}`}\n                        
    \n                        
    \n                            {r`\\rho`} è la resistività del materiale, e varia in base alla temperatura:\n                        
    \n                        
    \n                            {r`\\rho = \\rho_0 (1 + \\alpha(T - T_0))`}\n                        
    \n                        \n                    \n                        
    \n                            Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito.\n                        
    \n                        
    \n                            Per farlo, cattura cariche positive e negative sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro.\n                        
    \n                        
    \n                            Ha una capacità caratteristica, che in un condensatore a facce piane parallele è:\n                        
    \n                        
    \n                            {r`C = \\frac{q_{massima}}{\\Delta V}`}\n                        
    \n                        
    \n                            Condensatori di capacità maggiore immagazzinano più potenziale con meno carica.\n                        
    \n                        
    \n                            La capacità aumenta se viene messo qualcosa tra le armature:\n                        
    \n                        
    \n                            {r`C_{nuova} = \\kappa \\cdot \\frac{\\epsilon_0 \\cdot A}{s}`}\n                        
    \n                        
    \n                            Dove {r`\\kappa`} è la costante dielettrica relativa del materiale inserito, {r`A`} l'area di una armatura e {r`s`} la distanza tra le due armature.\n                        
    \n                        
    \n                            Se il campo elettrico creatosi tra le due armature supera la rigidità dielettrica del condensatore, la carica immagazzinata viene persa e ha luogo un breakdown.\n                        
    \n                        
    \n                            La sua unità di misura è il Farad ({r`Fa`})\n                        
    \n                        \n                    \n                        
    \n                            Misura la corrente elettrica se messo in serie.\n                        
    \n                        
    \n                            (Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)\n                        
    \n                        \n                    \n                        
    \n                            Misura la differenza di potenziale se messo in parallelo.\n                        
    \n                        
    \n                            (Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Per nodo si intende un qualsiasi punto del circuito.\n                        
    \n                        
    \n                            Da un nodo entra ed esce la stessa corrente.\n                        
    \n                        \n                    \n                        
    \n                            Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito.\n                        
    \n                        
    \n                            In una maglia chiusa, la somma delle differenze di potenziale è 0.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Più parti di circuito sono in serie se sono consecutive e senza biforcazioni.\n                        
    \n                        
    \n                            Parti di circuito in serie sono attraversate dalla stessa corrente.\n                        
    \n                        \n                    \n                        
    \n                            Più parti di circuito sono in parallelo tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo.\n                        
    \n                        
    \n                            Parti di circuito in parallelo hanno la stessa differenza di potenziale.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:\n                        
    \n                        
    \n                            {r`R_{serie} = \\sum_{i=1}^{n} R_i`}\n                        
    \n                        \n                    \n                        
    \n                            Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:\n                        
    \n                        
    \n                            {r`R_{parallelo} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{R_i}}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacità di:\n                        
    \n                        
    \n                            {r`C_{serie} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{C_i}}`}\n                        
    \n                        \n                    \n                        
    \n                            Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacità della somma di tutti quelli sostituiti:\n                        
    \n                        
    \n                            {r`C_{parallelo} = \\sum_{i=1}^{n} C_n`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente.\n                        
    \n                        
    \n                            {r`\\mu_0 = 4 \\pi \\cdot 10^{-7} \\frac{H}{m}`} ({r`\\frac{N}{A^2}`})\n                        
    \n                        \n                    \n                        
    \n                            Come un campo elettrico, ma per i magneti.\n                        
    \n                        
    \n                            Il suo simbolo è {r`B`}, e la sua unità di misura è il Tesla (T).\n                        
    \n                        \n                    \n                        
    \n                            È \"quanto\" campo magnetico attraversa un percorso chiuso.\n                        
    \n                        
    \n                            Per qualsiasi percorso chiuso, il flusso magnetico è uguale alla somma di tutti i \"sottoflussi\" magnetici calcolati sui suoi lati.\n                        
    \n                        
    \n                            {r`\\Phi_{B_{i}} = \\vec{B} \\cdot \\vec{L}_n = B \\cdot L_i \\cdot \\sin(\\alpha) = B_\\parallel \\cdot L_i`}\n                        
    \n                        
    \n                            {r`\\Phi_{B} = \\sum_{i=0}^{n_{lati}} \\Phi_{Bn}`}\n                        
    \n                        
    \n                            La sua unità di misura è il Weber ({r`Wb = T \\cdot m^2`}).\n                        
    \n                        \n                    \n                        
    \n                            Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo.\n                        
    \n                        
    \n                            Ovvero, non esistono monopoli magnetici.\n                        
    \n                        \n                    \n                        
    \n                            L'intensità di corrente che attraversa un percorso chiuso è direttamente proporzionale al flusso magnetico dello stesso percorso.\n                        
    \n                        
    \n                            {r`\\Phi_B = \\mu_0 \\cdot I`}\n                        
    \n                        \n                
    \n                
    \n                    Forza magnetica su carica puntiforme (Forza di Lorentz)}>\n                        
    \n                            I campi magnetici applicano una forza sulle cariche vicine:\n                        
    \n                        
    \n                            {r`\\vec{F}_{B} = q \\cdot (\\vec{v} \\times \\vec{B})`}\n                        
    \n                        
    \n                            Dove {r`\\vec{B}`} è l'intensità del campo magnetico e {r`\\vec{v}`} la velocità della carica considerata.\n                        
    \n                        
    \n                            Si ha una forza massima se la velocità è perpendicolare al campo magnetico.\n                        
    \n                        
    \n                            In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme.\n                        
    \n                        \n                    \n                        
    \n                            I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:\n                        
    \n                        
    \n                            {r`\\vec{F}_{magnetica} = I \\cdot (\\vec{L} \\times \\vec{B})`} [1]\n                        
    \n                        
    \n                            Dove {r`I`} è la corrente elettrica, {r`\\vec{L}`} è un vettore che punta nella direzione di scorrimento della corrente e ha come modulo la lunghezza del conduttore.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.\n                        
    \n                        \n                    \n                        
    \n                            Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro.\n                        
    \n                        
    \n                            All'interno del solenoide si crea un campo (quasi) uniforme:\n                        
    \n                        
    \n                            {r`\\left | \\vec{B} \\right | = \\mu_0 \\cdot I \\cdot \\frac{A_{vvolgimenti}}{L_{unghezzafilo}}`}\n                        
    \n                        \n                    \n                        
    \n                            Caso particolare della Legge di Ampère.\n                        
    \n                        
    \n                            Il modulo del campo magnetico B prodotto da un filo in cui passa una corrente continua I alla distanza s è:\n                        
    \n                        
    \n                            {r`\\left | \\vec{B} \\right | = \\frac{\\mu \\cdot I}{2 \\pi r}`}\n                        
    \n                        
    \n                            Il campo magnetico così creato gira attorno al filo in senso antiorario.\n                        
    \n                        
    \n                            Due fili attraversati dalla stessa corrente si attraggono, due fili attraversati da correnti opposte si respingono.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Un conduttore perpendicolare ad un campo magnetico può ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo.\n                        
    \n                        
    \n                            La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore.\n                        
    \n                        
    \n                            Essa vale:\n                        
    \n                        
    \n                            {r`\\Delta V_{indotta} = v \\cdot B \\cdot L`}\n                        
    \n                        
    \n                            Dove v è la velocità del conduttore, B è l'intensità del campo magnetico ed L è la lunghezza del conduttore.\n                        
    \n                        \n                    \n                        
    \n                            In un campo magnetico {r`B`} uniforme e perpendicolare al piano di una spira di area {r`A`}, il flusso magnetico si può determinare con la Legge di Faraday-Neumann-Lenz:\n                        
    \n                        
    \n                            {r`\\Phi_B = \\vec{B} \\cdot \\vec{A} = B \\cdot A \\cdot \\cos(\\alpha)`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso.\n                        
    \n                        
    \n                            {r`\\Delta V_{indotta} = - \\frac{\\Delta \\Phi_B}{\\Delta t}`}\n                        
    \n                        
    \n                            Il meno è dovuto alla Legge di Lenz, che specifica qualitativamente il verso della forza elettromotrice indotta.\n                        
    \n                        \n                    \n                        
    \n                            In un solenoide, la forza elettromotrice indotta è uguale a:\n                        
    \n                        
    \n                            {r`\\Delta V_{indotta} = - \\frac{N \\cdot \\Delta \\Phi_{B_{spira}}}{\\Delta t} = - \\frac{N \\cdot B \\cdot A \\cdot cos(\\alpha)}{\\Delta t}`}\n                        
    \n                        
    \n                            Dove {r`N`} è il numero delle spire del solenoide.\n                        
    \n                        \n                    \n                        
    \n                            Correnti o campi elettrici variabili creano un campo magnetico.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Nel vuoto, il campo elettrico {r`E`} e il campo magnetico {r`B`} sono perpendicolari tra loro e la direzione di propagazione, e sono entrambe funzioni del tempo.\n                        
    \n                        
    \n                            Si dice quindi che sono onde elettromagnetiche.\n                        
    \n                        
    \n                            Esse sono legate dalla relazione:\n                        
    \n                        
    \n                            {r`E = c \\cdot B`}\n                        
    \n                        
    \n                            Dove {r`c`} è la velocità delle onde (luce) nel vuoto, e a sua volta è uguale a:\n                        
    \n                        
    \n                            {r`c = \\frac{1}{\\sqrt{\\epsilon_0 \\cdot \\mu_0}} = 3.00 \\cdot 10^8 \\frac{m}{s}`}\n                        
    \n                        \n                    \n                        
    \n                            {r`A(t) = A_{max} \\cdot \\sin \\left ( \\frac{2 \\pi}{\\lambda} - \\omega t + \\phi \\right )`}\n                        
    \n                        
    \n                            Dove {r`A_{max}`} è l'ampiezza massima che può avere l'onda, {r`\\frac{2 \\pi}{\\lambda} = \\left | \\vec{k} \\right |`} è il vettore d'onda, {r`\\omega`} la frequenza angolare e {r`\\phi`} la fase.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            I solidi, se portati ad alta temperatura, emettono luce con uno spettro continuo.\n                        
    \n                        
    \n                            I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d'onda.\n                        
    \n                        
    \n                            In un gas di idrogeno, le lunghezze d'onda emesse sono ricavabili con:\n                        
    \n                        
    \n                            {r`\\frac{1}{\\lambda} = R \\left ( \\frac{1}{4} - \\frac{1}{n^2} \\right )`}\n                        
    \n                        
    \n                            Con {r`R = 1.097 \\cdot 10^7 \\frac{1}{m}`}, detta costante di Rydberg, e {r`n`} un numero intero.\n                        
    \n                        \n                    \n                        
    \n                            Una grandezza si dice quantizzata (o discreta) se può assumere solo determinati valori.\n                        
    \n                        
    \n                            Una grandezza si dice continua se può assumere qualsiasi valore e quindi se non è quantizzata.\n                        
    \n                        
    \n                            Energia, momento angolare e raggio sono quantizzati.\n                        
    \n                        
    \n                            Nota costante quantica è {r`h`}, la costante di Planck, ovvero il valore minimo possibile per la carica (talvolta espressa come {r`\\hbar = \\left ( \\frac{h}{2 \\pi} \\right )`}.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            L'energia degli elettroni è quantizzata.\n                        
    \n                        
    \n                            Inoltre, per essi è valido che:\n                        
    \n                        
    \n                            {r`m \\cdot v_n \\cdot 2 \\pi \\cdot r = n \\cdot h`}\n                        
    \n                        
    \n                            Ancora, il raggio delle orbite è uguale a:\n                        
    \n                        
    \n                            {r`r_n = n^2 \\cdot a_0 = n^2 \\cdot \\frac{\\hbar}{m_{elettrone} \\cdot k \\cdot e^2} `}\n                        
    \n                        
    \n                            Con {r`a_0 = \\left ( \\frac{h}{2 \\pi} \\right )^2 \\cdot \\frac{1}{m_{elettrone} \\cdot k \\cdot e^2} = 5.29 \\cdot 10^{-11} m`}.\n                        
    \n                        
    \n                            Infine, in ogni stato, l'energia è pari a:\n                        
    \n                        
    \n                            {r`E_n = \\frac{1}{n^2} \\cdot E_1 = - \\frac{1}{n^2} \\cdot \\frac{a_0^2}{2 \\cdot m \\cdot \\hbar^4} = - \\frac{1}{n^2} \\cdot \\frac{m_{elettrone} \\cdot k^2 \\cdot e^4}{2 \\cdot \\hbar^2}`}\n                        
    \n                        
    \n                            Due elettroni non possono occupare lo stesso stato.\n                        
    \n                        
    \n                            Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Nei solidi, le lunghezze d'onda sono talmente tanto vicine da poter essere considerate una banda.\n                        
    \n                        
    \n                            Possono però comunque avere dei gap dovuti agli intervalli di energia non ammessi.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Refactor this\n                        
    \n                        
    \n                            Se la banda di emissione con energia più alta di un corpo è assente o è separata da un gap dell'ordine di grandezza maggiore di {r`10^1 eV`}, allora il corpo è un isolante.\n                        
    \n                        
    \n                            Se invece la banda di emissione si sovrappone a un altra, allora il corpo è un conduttore.\n                        
    \n                        
    \n                            Se il gap è invece dell'ordine di grandezza di {r`1 eV`}, allora il corpo è un semiconduttore.\n                        
    \n                        \n                    \n                        
    \n                            Legami in cui mancano elettroni.\n                        
    \n                        
    \n                            Elettroni di altri legami possono spostarsi per colmare le lacune, creandone altre, e spostandole in direzione opposta a quella della corrente.\n                        
    \n                        \n                    \n                        
    \n                            Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterrà:\n                        
    \n                        
      \n                            
    • Con numero atomico maggiore, un semiconduttore di tipo N con elettroni in eccesso liberi di scorrere.
      • \n                            
    • Con numero atomico minore, un semiconduttore di tipo P con lacune in eccesso libere di catturare elettroni da altri legami.
      • \n                        
    \n                        
    \n                            Maggiore impurezza porta a maggiore conduttività.\n                        
    \n                        \n                    \n                        
    \n                            Aumentando la temperatura di un semiconduttore si aumenta la conduttività, perchè eccita le particelle e favorisce il movimento di elettroni e lacune.\n                        
    \n                        \n                
    \n                
    Ottica (non l'abbiamo fatta)}>\n                    \n                        
    \n                            I corpi possono assorbire o riflettere le onde elettromagnetiche che li colpiscono.\n                        
    \n                        \n                    \n                        
    \n                            Un corpo nero è un corpo che assorbe tutte le onde elettromagnetiche che riceve senza rifletterne nessuna.\n                        
    \n                        
    \n                            Le onde assorbite vengono poi riemesse sotto forma di un onda di {r`\\lambda`} variabile in base alla temperatura.\n                        
    \n                        
    \n                            {r`\\lambda_{max} \\cdot T`} è costante.\n                        
    \n                        \n                    \n                        
    \n                            L'energia assorbita e emessa dai corpi neri è quantizzata.\n                        
    \n                        \n                    \n                        
    \n                            Un onda magnetica con un quanto di energia è detta fotone:\n                        
    \n                        
    \n                            {r`E_{fotone} = h \\cdot f`}\n                        
    \n                        \n                    \n                        
    \n                            A volte, i fotoni che colpiscono un metallo possono estrarvi degli elettroni e creare una differenza di potenziale.\n                        
    \n                        
    \n                            Perchè avvenga, la frequenza deve essere maggiore di una certa soglia.\n                        
    \n                        
    \n                            Il numero di elettroni estratti dipende dall'intensità dell'onda, mentre l'energia cinetica degli elettroni dipende dalla frequenza.\n                        
    \n                        
    \n                            Non c'è nessun ritardo tra l'assorbimento del fotone e l'estrazione di elettroni.\n                        
    \n                        \n                
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    \n                {props.title}\n            
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invokeOrReturn(undefined, initialState) : init(initialState),\n\n\t\t\taction => {\n\t\t\t\tconst nextValue = hookState._reducer(hookState._value[0], action);\n\t\t\t\tif (hookState._value[0] !== nextValue) {\n\t\t\t\t\thookState._value[0] = nextValue;\n\t\t\t\t\thookState._component.setState({});\n\t\t\t\t}\n\t\t\t}\n\t\t];\n\t}\n\n\treturn hookState._value;\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++, 3);\n\tif (!options._skipEffects && argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent.__hooks._pendingEffects.push(state);\n\t}\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useLayoutEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++, 4);\n\tif (!options._skipEffects && argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent._renderCallbacks.push(state);\n\t}\n}\n\nexport function useRef(initialValue) {\n\tcurrentHook = 5;\n\treturn useMemo(() => ({ current: initialValue }), []);\n}\n\n/**\n * @param {object} ref\n * @param {() => object} createHandle\n * @param {any[]} args\n */\nexport function useImperativeHandle(ref, createHandle, args) {\n\tcurrentHook = 6;\n\tuseLayoutEffect(\n\t\t() => {\n\t\t\tif (typeof ref == 'function') ref(createHandle());\n\t\t\telse if (ref) ref.current = createHandle();\n\t\t},\n\t\targs == null ? 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{ Component } from 'preact';\nimport Latex, {LatexDisplay} from '../components/Rendering/Latex';\nimport Panel from '../components/Elements/Panel';\nimport Section from \"../components/Elements/Section\";\nimport Plus from '../components/PageSpecific/Fisica/Plus';\nimport Minus from '../components/PageSpecific/Fisica/Minus';\nimport Todo from \"../components/Elements/Todo\";\nimport LatexDefaultInline from \"../contexts/LatexDefaultInline\";\nimport LatexDefaultDisplay from \"../contexts/LatexDefaultDisplay\";\n\nconst r = String.raw;\n\nexport default function(props) {\n    return (\n        \n        \n            
    \n                
    Fisica
    \n                
    \n                    \n                        
    \n                            Usa le regole base della trigonometria:\n                        
    \n                        
    \n                            {r`\\vec{v} = \\vec{v}_x + \\vec{v}_y`}\n                        
    \n                        
    \n                            {r`\\left | \\vec{v}_x \\right | = \\left | \\vec{v} \\right | \\sin \\alpha`}\n                        
    \n                        
    \n                            {r`\\left | \\vec{v}_y \\right | = \\left | \\vec{v} \\right | \\cos \\alpha`}\n                        
    \n                        \n                    \n                        
    \n                            Scomponi in componenti, poi sommali:\n                        
    \n                        
    \n                            {r`\\vec{v} + \\vec{w} = (\\vec{v}_x + \\vec{w}_x) + (\\vec{v}_y + \\vec{w}_y)`}\n                        
    \n                        
    \n                            Produce il vettore risultante dall'applicazione della regola del parallelogramma.\n                        
    \n                        \n                    \n                        
    \n                            Alla fine è sempre una somma:\n                        
    \n                        
    \n                            {r`\\vec{v} - \\vec{w} = (\\vec{v}_x - \\vec{w}_x) + (\\vec{v}_y - \\vec{w}_y)`}\n                        
    \n                        
    \n                            Produce il vettore che parte da w e arriva a v.\n                        
    \n                        \n                    \n                        
    \n                            Si chiama scalare perchè il risultato è uno scalare, non un vettore.\n                        
    \n                        
    \n                            {r`\\vec{v} \\cdot \\vec{w} = \\left | \\vec{v} \\right | \\left | \\vec{w} \\right | \\cos \\alpha`}\n                        
    \n                        
    \n                            Produce il modulo della proiezione di {r`\\vec{a}`} su {r`\\vec{b}`}.\n                        
    \n                        \n                    \n                        
    \n                            Si chiama vettoriale perchè il risultato è un altro vettore.\n                        
    \n                        
      \n                            
    • {r`\\vec{c} = \\vec{a} \\times \\vec{b}`}
      • \n                            
    • {r`\\left | \\vec{c} \\right | = \\left | \\vec{a} \\right | \\cdot \\left | \\vec{b} \\right | \\cdot \\sin(\\alpha)`}
      • \n                            
    • Regola della mano destra
      • \n                        
    \n                        
    \n                            Non è commutativo!\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Se un corpo puntiforme ha forza risultante nulla, allora la sua velocità non cambia.\n                        
    \n                        
    \n                            {r`\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta v = 0`}\n                        
    \n                        \n                    \n                        
    \n                            La forza risultante di un corpo è direttamente proporzionale alla sua accelerazione, e la costante di proporzionalità è la massa.\n                        
    \n                        
    \n                            {r`\\Sigma \\vec{F} = m \\vec{a}`}\n                        
    \n                        \n                    \n                        
    \n                            Due corpi esercitano forze uguali e opposte uno sull'altro.\n                        
    \n                        
    \n                            {r`\\vec{F}_{21} = -\\vec{F}_{12}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Due corpi puntiformi si attirano uno verso l'altro con forza:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | = G \\frac{m_1 m_2}{s^2}`}\n                        
    \n                        
    \n                            G è la costante di gravitazione universale e vale:\n                        
    \n                        
    \n                            {r`G = 6.67 \\cdot 10^{-11} \\frac{N m^2}{{kg}^2}`}\n                        
    \n                        \n                    \n                        
    \n                            Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo è attratto verso la Terra con forza peso uguale a:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | = g m`}\n                        
    \n                        
    \n                            g è la costante di gravità della Terra, e vale:\n                        
    \n                        
    \n                            {r`g = 9.81 \\frac{m}{s^2}`}\n                        
    \n                        \n                    \n                        
    \n                            Per pianeti diversi dalla Terra vale la stessa regola:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | = g m`}\n                        
    \n                        
    \n                            L'unica differenza è che cambia la costante di gravità:\n                        
    \n                        
    \n                            {r`g_{luna} = 1.62 \\frac{m}{s^2}`}\n                        
    \n                        
    \n                            {r`g_{marte} = 3.71 \\frac{m}{s^2}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Si oppone alle forze applicate alla superficie di contatto.\n                        
    \n                        
    \n                            Un libro appoggiato su un tavolo ha la forza di gravità che lo attira verso il terreno e la forza normale che lo trattiene dal cadere.\n                        
    \n                        \n                    \n                        
    \n                            Impedisce a un corpo di muoversi se non viene spinto da una forza che supera una certa soglia:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | \\leq \\mu_{s} \\left | \\vec{F}_{normale} \\right |`}\n                        
    \n                        \n                    \n                        
    \n                            Rallenta i corpi che si stanno muovendo finchè essi non si fermano:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | \\leq \\mu_{d} \\left | \\vec{F}_{normale} \\right |`}\n                        
    \n                        \n                    \n                        
    \n                            E' forza trasmessa tra due estremi di una fune.\n                        
    \n                        
    \n                            Può essere redirezionata per mezzo di carrucole.\n                        
    \n                        \n                    \n                        
    \n                            Una molla cerca sempre di tornare alla sua posizione indeformata con forza:\n                        
    \n                        
    \n                            {r`F = -k x`}\n                        
    \n                        
    \n                            (E' negativa perchè la forza è opposta a quella applicata per deformarla.)\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            È un vettore che indica la posizione di un corpo rispetto a un'origine.\n                        
    \n                        
    \n                            {r`\\Delta \\vec{s} = \\vec{s}(fine) - \\vec{s}(inizio)`}\n                        
    \n                        \n                    \n                        
    \n                            È un vettore che misura la variazione di posizione nel tempo.\n                        
    \n                        
    \n                            {r`\\vec{v} = \\frac{\\Delta \\vec{s}}{\\Delta t}`}\n                        
    \n                        
    \n                            Se si considera un intervallo di tempo infinitesimale si dice velocità istantanea:\n                        
    \n                        
    \n                            {r`\\vec{v} = \\lim_{\\Delta t \\to 0} \\frac{\\Delta \\vec{s}}{\\Delta t} = \\frac{d \\vec{s}}{dt}`}\n                        
    \n                        \n                    \n                        
    \n                            È un vettore che misura la variazione di velocità nel tempo.\n                        
    \n                        
    \n                            {r`\\vec{a} = \\frac{\\Delta \\vec{v}}{\\Delta t}`}\n                        
    \n                        
    \n                            Se si considera un intervallo di tempo infinitesimale si dice accelerazione istantanea:\n                        
    \n                        
    \n                            {r`\\vec{a} = \\lim_{\\Delta v \\to 0} \\frac{\\Delta \\vec{v}}{\\Delta t} = \\frac{d \\vec{v}}{d t} = \\frac{d^2 \\vec{s}}{d t^2}`}\n                        
    \n                        \n                    Quantità di moto (momento lineare)}>\n                        
    \n                            La quantità di moto è una proprietà vettoriale dei corpi:\n                        
    \n                        
    \n                            {r`\\vec{p} = m \\vec{v}`}\n                        
    \n                        
    \n                            Se la forza risultante è nulla, la quantità di moto non cambia.\n                        
    \n                        
    \n                            {r`\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta \\vec{p} = 0`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            La legge oraria è:\n                        
    \n                        
    \n                            {r`s(t) = v \\cdot \\Delta t + s(0)`}\n                        
    \n                        \n                    \n                        
    \n                            È costante:\n                        
    \n                        
    \n                            {r`v(t) = k`}\n                        
    \n                        \n                    \n                        
    \n                            La velocità non varia:\n                        
    \n                        
    \n                            {r`a(t) = 0`}\n                        
    \n                        \n                    \n                        
    \n                            Si applica la prima legge di Newton:\n                        
    \n                        
    \n                            f(t) = 0\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            La legge oraria è:\n                        
    \n                        
    \n                            {r`s(t) = \\frac{1}{2} a \\cdot (\\Delta t)^2 + v(0) \\cdot (\\Delta t) + s(0)`}\n                        
    \n                        \n                    \n                        
    \n                            È una retta:\n                        
    \n                        
    \n                            {r`v(t) = a \\Delta t + v(0)`}\n                        
    \n                        \n                    \n                        
    \n                            È costante:\n                        
    \n                        
    \n                            {r`a(t) = k`}\n                        
    \n                        \n                    \n                        
    \n                            Si applica la prima legge di Newton:\n                        
    \n                        
    \n                            f(t) = m a\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            E' la distanza dal centro massima che raggiunge il corpo.\n                        
    \n                        
    \n                            (L'ampiezza di una sinusoide.)\n                        
    \n                        \n                    \n                        
    \n                            Indica quanto in fretta cambia la posizione del corpo.\n                        
    \n                        
    \n                            Dipende dal periodo:\n                        
    \n                        
    \n                            {r`\\omega = \\frac{2 \\pi}{T}`}\n                        
    \n                        \n                    \n                        
    \n                            E' una sinusoide:\n                        
    \n                        
    \n                            {r`s(t) = A \\sin (\\omega \\cdot t + \\phi)`}\n                        
    \n                        \n                    \n                        
    \n                            E' la sinusoide dello spostamento, sfasata di {r`\\frac{\\pi}{2}`}:\n                        
    \n                        
    \n                            {r`v(t) = A \\sin (\\omega \\cdot t + \\phi + \\frac{\\pi}{2})`}\n                        
    \n                        \n                    \n                        
    \n                            E' la sinusoide della velocità, sfasata di {r`\\pi`}:\n                        
    \n                        
    \n                            {r`a(t) = A \\sin (\\omega \\cdot t + \\phi + \\pi)`}\n                        
    \n                        \n                    \n                        
    \n                            Si applica la prima legge di Newton:\n                        
    \n                        
    \n                            f(t) = m a\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.\n                        
    \n                        \n                    \n                        
    \n                            Il moto parabolico è dato sommando due moti armonici semplici: uno sull'asse X, e l'altro, sfasato di {r`\\frac{\\pi}{2}`}, sull'asse Y.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Velocità angolare\n                        
    \n                        
    \n                            Quanto cambia la fase nel tempo.\n                        
    \n                        
    \n                            {r`\\omega = \\frac{2 \\pi}{T}`}\n                        
    \n                        \n                    \n                        
    \n                            E' l'angolo percorso dal corpo rispetto alla posizione iniziale.\n                        
    \n                        
    \n                            Si indica con {r`\\phi`}, e generalmente si usa in radianti.\n                        
    \n                        \n                    \n                        
    \n                            Si applicano le formule per la circonferenza:\n                        
    \n                        
    \n                            {r`v = \\frac{\\Delta s}{t} = \\frac{2 \\pi \\cdot r}{T} = \\omega r`}\n                        
    \n                        \n                    \n                        
    \n                            Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto:\n                        
    \n                        
    \n                            {r`a = \\frac{v^2}{r} = r \\cdot \\omega^2 = v \\cdot \\omega`}\n                        
    \n                        \n                    \n                        
    \n                            È verso il centro e si calcola con:\n                        
    \n                        
    \n                            {r`F = m \\cdot a`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            E' compiuto da una forza che sposta un corpo.\n                        
    \n                        
    \n                            {r`W = \\vec{F} \\cdot \\vec{s} = F \\cdot \\Delta s \\cdot cos(\\alpha )`}\n                        
    \n                        
    \n                            (Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)\n                        
    \n                        \n                    \n                        
    \n                            Un corpo ha energia cinetica in ogni momento uguale a:\n                        
    \n                        
    \n                            {r`E_c = \\frac{1}{2} m v^2`}\n                        
    \n                        
    \n                            Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:\n                        
    \n                        
    \n                            {r`\\Delta E_c = W`}\n                        
    \n                        \n                    \n                        
    \n                            Un corpo ha energia potenziale in ogni momento pari a:\n                        
    \n                        
    \n                            {r`E_{p_g} = m \\cdot g \\cdot h`}\n                        
    \n                        
    \n                            (Con h uguale a un altezza scelta come punto di riferimento.)\n                        
    \n                        \n                    \n                        
    \n                            Una molla ha sempre energia potenziale elastica pari a:\n                        
    \n                        
    \n                            {r`E_{p_e} = \\frac{1}{2} k x^2`}\n                        
    \n                        \n                    \n                        
    \n                            Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo.\n                        
    \n                        
    \n                            Ad esempio, è conservativa la forza di gravità, ma non è conservativa la forza di attrito.\n                        
    \n                        
    \n                            Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:\n                        
    \n                        
    \n                            {r`E = E_k + E_p`}\n                        
    \n                        \n                    \n                        
    \n                            È la velocità di trasferimento di energia:\n                        
    \n                        
    \n                            {r`P = \\frac{\\Delta E}{\\Delta t}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            È una proprietà dei corpi che può essere positiva o negativa.\n                        
    \n                        
    \n                            Si conserva: in un sistema chiuso la carica totale è costante.\n                        
    \n                        
    \n                            Esiste un'unità elementare: {r`C_{elettrone} = 1.602 \\cdot 10^{-19}`}.\n                        
    \n                        
    \n                            Cariche opposte si attraggono; cariche uguali si respingono.\n                        
    \n                        \n                    \n                        
    \n                            Più ioni ha un corpo, meglio la carica si muove attraverso di esso.\n                        
    \n                        
    \n                            I corpi in cui la carica si muove bene sono conduttori, mentre quelli in cui si muove difficilmente sono isolanti.\n                        
    \n                        
    \n                            Il corpo umano è un buon conduttore.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno equilibrate e il corpo diventerà elettricamente neutro (con stesso numero di cariche positive e negative all'interno).\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Strofinando tra loro due corpi isolanti, essi si polarizzeranno per strofinio.\n                        
    \n                        \n                    \n                        
    \n                            Toccando un conduttore con un corpo carico, il conduttore potrà polarizzarsi per contatto.\n                        
    \n                        \n                    \n                        
    \n                            Se un corpo conduttore ha cariche \"esterne\" di un certo segno vicino, esso avrà tutte le cariche del segno opposto in equilibrio vicino alle cariche esterne, e tutte le cariche dello stesso segno più lontano possibile da esse.\n                        
    \n                        
    \n                            Mettendo a terra il conduttore, nuove cariche del segno opposto saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate.\n                        
    \n                        
    \n                            Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà caricato del segno opposto rispetto alle cariche esterne.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Due corpi carichi si attraggono tra loro con forza:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F}_{elettrica} \\right | = \\frac{-k \\cdot q_1 \\cdot q_2}{s^2}`}\n                        
    \n                        
    \n                            {r`k`} è la costante di Coulomb, e vale {r`k = 8.99 \\cdot 10^9 \\frac{N \\cdot m^2}{C^2}`}.\n                        
    \n                        \n                    \n                        
    \n                            La costante {r`k`} è in realtà dipendente da un altra costante, {r`\\epsilon_0`}, la permeabilità del vuoto.\n                        
    \n                        
    \n                            {r`k = \\frac{1}{4 \\pi \\cdot \\epsilon_0}`}\n                        
    \n                        
    \n                            {r`\\left | \\vec{F}_{elettrica} \\right | = \\frac{q_1 \\cdot q_2}{4 \\pi \\cdot \\epsilon_0 \\cdot s^2}`}\n                        
    \n                        \n                    \n                        
    \n                            Misura che forza viene applicata in ogni punto su una carica unitaria:\n                        
    \n                        
    \n                            {r`\\vec{E} = \\frac{\\vec{F}_{elettrica}}{q} = \\frac{-k \\cdot q}{s^2}`}\n                        
    \n                        \n                    \n                        
    \n                            È la differenza tra \"quanto\" campo elettrico entra e quanto campo elettrico esce da una certa area.\n                        
    \n                        
    \n                            In qualsiasi superficie chiusa, il flusso elettrico è uguale alla componente perpendicolare del campo elettrico moltiplicato per l'area.\n                        
    \n                        
    \n                            {r`\\Phi_E = \\vec{E} \\cdot \\vec{A}`}\n                        
    \n                        
    \n                            Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:\n                        
    \n                        
    \n                            {r`\\Phi_E = \\vec{E} \\cdot \\vec{A} = E_\\perp \\cdot A \\cdot \\cos(\\alpha)`}\n                        
    \n                        
    \n                            Circa. E' una specie di integrale...\n                        
    \n                        \n                    \n                        
    \n                            Il flusso elettrico è direttamente proporzionale alla carica presente all'interno della superficie.\n                        
    \n                        
    \n                            {r`\\Phi_E = 4 \\pi \\cdot k \\cdot q = \\frac{q}{\\epsilon_0}`}\n                        
    \n                        
    \n                            Ovvero, i campi elettrostatici sono generati dalle cariche elettriche.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Un corpo carico vicino ad altre cariche possiede un'energia potenziale elettrica {r`U_e`}.\n                        
    \n                        \n                
    \n                
    \n                    Potenziale elettrico (tensione)}>\n                        
    \n                            È il valore dell'energia potenziale elettrica per una carica unitaria.\n                        
    \n                        
    \n                            {r`V = \\frac{U_e}{q}`}\n                        
    \n                        
    \n                            La sua unità di misura è il Volt ({r`V`}).\n                        
    \n                        
    \n                            In una batteria è detto forza elettromotrice, e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli.\n                        
    \n                        \n                    Corrente elettrica (intensità)}>\n                        
    \n                            Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo.\n                        
    \n                        
    \n                            {r`I = \\frac{\\Delta q}{\\Delta t}`}\n                        
    \n                        
    \n                            Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla.\n                        
    \n                        
    \n                            La sua unità di misura è l'Ampere ({r`A`}).\n                        
    \n                        \n                    Corrente continua (DC)}>\n                        
    \n                            Quando in un circuito la direzione della corrente è costante.\n                        
    \n                        \n                    Corrente alternata (AC)}>\n                        
    \n                            Quando in un circuito la direzione della corrente si alterna periodicamente.\n                        
    \n                        \n                    \n                        
    \n                            Possiamo calcolare la potenza di un circuito:\n                        
    \n                        
    \n                            {r`P = \\frac{\\Delta U_e}{\\Delta t} = I \\cdot \\Delta V = I^2 \\cdot R = \\frac{(\\Delta V)^2}{R}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Riduce l'intensità di corrente, e converte parte del potenziale in calore.\n                        
    \n                        
    \n                            Il potenziale utilizzato è pari a:\n                        
    \n                        
    \n                            {r`V = R \\cdot I`}\n                        
    \n                        
    \n                            Dove {r`R`} è una costante detta resistenza con unità di misura Ohm ({r`\\Omega`}).\n                        
    \n                        
    \n                            La resistenza di un conduttore vale:\n                        
    \n                        
    \n                            {r`R = \\rho \\frac{L_{unghezza}}{A_{rea}}`}\n                        
    \n                        
    \n                            {r`\\rho`} è la resistività del materiale, e varia in base alla temperatura:\n                        
    \n                        
    \n                            {r`\\rho = \\rho_0 (1 + \\alpha(T - T_0))`}\n                        
    \n                        \n                    \n                        
    \n                            Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito.\n                        
    \n                        
    \n                            Per farlo, cattura cariche positive e negative sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro.\n                        
    \n                        
    \n                            Ha una capacità caratteristica, che in un condensatore a facce piane parallele è:\n                        
    \n                        
    \n                            {r`C = \\frac{q_{massima}}{\\Delta V}`}\n                        
    \n                        
    \n                            Condensatori di capacità maggiore immagazzinano più potenziale con meno carica.\n                        
    \n                        
    \n                            La capacità aumenta se viene messo qualcosa tra le armature:\n                        
    \n                        
    \n                            {r`C_{nuova} = \\kappa \\cdot \\frac{\\epsilon_0 \\cdot A}{s}`}\n                        
    \n                        
    \n                            Dove {r`\\kappa`} è la costante dielettrica relativa del materiale inserito, {r`A`} l'area di una armatura e {r`s`} la distanza tra le due armature.\n                        
    \n                        
    \n                            Se il campo elettrico creatosi tra le due armature supera la rigidità dielettrica del condensatore, la carica immagazzinata viene persa e ha luogo un breakdown.\n                        
    \n                        
    \n                            La sua unità di misura è il Farad ({r`Fa`})\n                        
    \n                        \n                    \n                        
    \n                            Misura la corrente elettrica se messo in serie.\n                        
    \n                        
    \n                            (Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)\n                        
    \n                        \n                    \n                        
    \n                            Misura la differenza di potenziale se messo in parallelo.\n                        
    \n                        
    \n                            (Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Per nodo si intende un qualsiasi punto del circuito.\n                        
    \n                        
    \n                            Da un nodo entra ed esce la stessa corrente.\n                        
    \n                        \n                    \n                        
    \n                            Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito.\n                        
    \n                        
    \n                            In una maglia chiusa, la somma delle differenze di potenziale è 0.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Più parti di circuito sono in serie se sono consecutive e senza biforcazioni.\n                        
    \n                        
    \n                            Parti di circuito in serie sono attraversate dalla stessa corrente.\n                        
    \n                        \n                    \n                        
    \n                            Più parti di circuito sono in parallelo tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo.\n                        
    \n                        
    \n                            Parti di circuito in parallelo hanno la stessa differenza di potenziale.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:\n                        
    \n                        
    \n                            {r`R_{serie} = \\sum_{i=1}^{n} R_i`}\n                        
    \n                        \n                    \n                        
    \n                            Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:\n                        
    \n                        
    \n                            {r`R_{parallelo} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{R_i}}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacità di:\n                        
    \n                        
    \n                            {r`C_{serie} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{C_i}}`}\n                        
    \n                        \n                    \n                        
    \n                            Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacità della somma di tutti quelli sostituiti:\n                        
    \n                        
    \n                            {r`C_{parallelo} = \\sum_{i=1}^{n} C_n`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente.\n                        
    \n                        
    \n                            {r`\\mu_0 = 4 \\pi \\cdot 10^{-7} \\frac{H}{m}`} ({r`\\frac{N}{A^2}`})\n                        
    \n                        \n                    \n                        
    \n                            Come un campo elettrico, ma per i magneti.\n                        
    \n                        
    \n                            Il suo simbolo è {r`B`}, e la sua unità di misura è il Tesla (T).\n                        
    \n                        \n                    \n                        
    \n                            È \"quanto\" campo magnetico attraversa un percorso chiuso.\n                        
    \n                        
    \n                            Per qualsiasi percorso chiuso, il flusso magnetico è uguale alla somma di tutti i \"sottoflussi\" magnetici calcolati sui suoi lati.\n                        
    \n                        
    \n                            {r`\\Phi_{B_{i}} = \\vec{B} \\cdot \\vec{L}_n = B \\cdot L_i \\cdot \\sin(\\alpha) = B_\\parallel \\cdot L_i`}\n                        
    \n                        
    \n                            {r`\\Phi_{B} = \\sum_{i=0}^{n_{lati}} \\Phi_{Bn}`}\n                        
    \n                        
    \n                            La sua unità di misura è il Weber ({r`Wb = T \\cdot m^2`}).\n                        
    \n                        \n                    \n                        
    \n                            Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo.\n                        
    \n                        
    \n                            Ovvero, non esistono monopoli magnetici.\n                        
    \n                        \n                    \n                        
    \n                            L'intensità di corrente che attraversa un percorso chiuso è direttamente proporzionale al flusso magnetico dello stesso percorso.\n                        
    \n                        
    \n                            {r`\\Phi_B = \\mu_0 \\cdot I`}\n                        
    \n                        \n                
    \n                
    \n                    Forza magnetica su carica puntiforme (Forza di Lorentz)}>\n                        
    \n                            I campi magnetici applicano una forza sulle cariche vicine:\n                        
    \n                        
    \n                            {r`\\vec{F}_{B} = q \\cdot (\\vec{v} \\times \\vec{B})`}\n                        
    \n                        
    \n                            Dove {r`\\vec{B}`} è l'intensità del campo magnetico e {r`\\vec{v}`} la velocità della carica considerata.\n                        
    \n                        
    \n                            Si ha una forza massima se la velocità è perpendicolare al campo magnetico.\n                        
    \n                        
    \n                            In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme.\n                        
    \n                        \n                    \n                        
    \n                            I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:\n                        
    \n                        
    \n                            {r`\\vec{F}_{magnetica} = I \\cdot (\\vec{L} \\times \\vec{B})`} [1]\n                        
    \n                        
    \n                            Dove {r`I`} è la corrente elettrica, {r`\\vec{L}`} è un vettore che punta nella direzione di scorrimento della corrente e ha come modulo la lunghezza del conduttore.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.\n                        
    \n                        \n                    \n                        
    \n                            Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro.\n                        
    \n                        
    \n                            All'interno del solenoide si crea un campo (quasi) uniforme:\n                        
    \n                        
    \n                            {r`\\left | \\vec{B} \\right | = \\mu_0 \\cdot I \\cdot \\frac{A_{vvolgimenti}}{L_{unghezzafilo}}`}\n                        
    \n                        \n                    \n                        
    \n                            Caso particolare della Legge di Ampère.\n                        
    \n                        
    \n                            Il modulo del campo magnetico B prodotto da un filo in cui passa una corrente continua I alla distanza s è:\n                        
    \n                        
    \n                            {r`\\left | \\vec{B} \\right | = \\frac{\\mu \\cdot I}{2 \\pi r}`}\n                        
    \n                        
    \n                            Il campo magnetico così creato gira attorno al filo in senso antiorario.\n                        
    \n                        
    \n                            Due fili attraversati dalla stessa corrente si attraggono, due fili attraversati da correnti opposte si respingono.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Un conduttore perpendicolare ad un campo magnetico può ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo.\n                        
    \n                        
    \n                            La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore.\n                        
    \n                        
    \n                            Essa vale:\n                        
    \n                        
    \n                            {r`\\Delta V_{indotta} = v \\cdot B \\cdot L`}\n                        
    \n                        
    \n                            Dove v è la velocità del conduttore, B è l'intensità del campo magnetico ed L è la lunghezza del conduttore.\n                        
    \n                        \n                    \n                        
    \n                            In un campo magnetico {r`B`} uniforme e perpendicolare al piano di una spira di area {r`A`}, il flusso magnetico si può determinare con la Legge di Faraday-Neumann-Lenz:\n                        
    \n                        
    \n                            {r`\\Phi_B = \\vec{B} \\cdot \\vec{A} = B \\cdot A \\cdot \\cos(\\alpha)`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso.\n                        
    \n                        
    \n                            {r`\\Delta V_{indotta} = - \\frac{\\Delta \\Phi_B}{\\Delta t}`}\n                        
    \n                        
    \n                            Il meno è dovuto alla Legge di Lenz, che specifica qualitativamente il verso della forza elettromotrice indotta.\n                        
    \n                        \n                    \n                        
    \n                            In un solenoide, la forza elettromotrice indotta è uguale a:\n                        
    \n                        
    \n                            {r`\\Delta V_{indotta} = - \\frac{N \\cdot \\Delta \\Phi_{B_{spira}}}{\\Delta t} = - \\frac{N \\cdot B \\cdot A \\cdot cos(\\alpha)}{\\Delta t}`}\n                        
    \n                        
    \n                            Dove {r`N`} è il numero delle spire del solenoide.\n                        
    \n                        \n                    \n                        
    \n                            Correnti o campi elettrici variabili creano un campo magnetico.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Nel vuoto, il campo elettrico {r`E`} e il campo magnetico {r`B`} sono perpendicolari tra loro e la direzione di propagazione, e sono entrambe funzioni del tempo.\n                        
    \n                        
    \n                            Si dice quindi che sono onde elettromagnetiche.\n                        
    \n                        
    \n                            Esse sono legate dalla relazione:\n                        
    \n                        
    \n                            {r`E = c \\cdot B`}\n                        
    \n                        
    \n                            Dove {r`c`} è la velocità delle onde (luce) nel vuoto, e a sua volta è uguale a:\n                        
    \n                        
    \n                            {r`c = \\frac{1}{\\sqrt{\\epsilon_0 \\cdot \\mu_0}} = 3.00 \\cdot 10^8 \\frac{m}{s}`}\n                        
    \n                        \n                    \n                        
    \n                            {r`A(t) = A_{max} \\cdot \\sin \\left ( \\frac{2 \\pi}{\\lambda} - \\omega t + \\phi \\right )`}\n                        
    \n                        
    \n                            Dove {r`A_{max}`} è l'ampiezza massima che può avere l'onda, {r`\\frac{2 \\pi}{\\lambda} = \\left | \\vec{k} \\right |`} è il vettore d'onda, {r`\\omega`} la frequenza angolare e {r`\\phi`} la fase.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            I solidi, se portati ad alta temperatura, emettono luce con uno spettro continuo.\n                        
    \n                        
    \n                            I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d'onda.\n                        
    \n                        
    \n                            In un gas di idrogeno, le lunghezze d'onda emesse sono ricavabili con:\n                        
    \n                        
    \n                            {r`\\frac{1}{\\lambda} = R \\left ( \\frac{1}{4} - \\frac{1}{n^2} \\right )`}\n                        
    \n                        
    \n                            Con {r`R = 1.097 \\cdot 10^7 \\frac{1}{m}`}, detta costante di Rydberg, e {r`n`} un numero intero.\n                        
    \n                        \n                    \n                        
    \n                            Una grandezza si dice quantizzata (o discreta) se può assumere solo determinati valori.\n                        
    \n                        
    \n                            Una grandezza si dice continua se può assumere qualsiasi valore e quindi se non è quantizzata.\n                        
    \n                        
    \n                            Energia, momento angolare e raggio sono quantizzati.\n                        
    \n                        
    \n                            Nota costante quantica è {r`h`}, la costante di Planck, ovvero il valore minimo possibile per la carica (talvolta espressa come {r`\\hbar = \\left ( \\frac{h}{2 \\pi} \\right )`}.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            L'energia degli elettroni è quantizzata.\n                        
    \n                        
    \n                            Inoltre, per essi è valido che:\n                        
    \n                        
    \n                            {r`m \\cdot v_n \\cdot 2 \\pi \\cdot r = n \\cdot h`}\n                        
    \n                        
    \n                            Ancora, il raggio delle orbite è uguale a:\n                        
    \n                        
    \n                            {r`r_n = n^2 \\cdot a_0 = n^2 \\cdot \\frac{\\hbar}{m_{elettrone} \\cdot k \\cdot e^2} `}\n                        
    \n                        
    \n                            Con {r`a_0 = \\left ( \\frac{h}{2 \\pi} \\right )^2 \\cdot \\frac{1}{m_{elettrone} \\cdot k \\cdot e^2} = 5.29 \\cdot 10^{-11} m`}.\n                        
    \n                        
    \n                            Infine, in ogni stato, l'energia è pari a:\n                        
    \n                        
    \n                            {r`E_n = \\frac{1}{n^2} \\cdot E_1 = - \\frac{1}{n^2} \\cdot \\frac{a_0^2}{2 \\cdot m \\cdot \\hbar^4} = - \\frac{1}{n^2} \\cdot \\frac{m_{elettrone} \\cdot k^2 \\cdot e^4}{2 \\cdot \\hbar^2}`}\n                        
    \n                        
    \n                            Due elettroni non possono occupare lo stesso stato.\n                        
    \n                        
    \n                            Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Nei solidi, le lunghezze d'onda sono talmente tanto vicine da poter essere considerate una banda.\n                        
    \n                        
    \n                            Possono però comunque avere dei gap dovuti agli intervalli di energia non ammessi.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Refactor this\n                        
    \n                        
    \n                            Se la banda di emissione con energia più alta di un corpo è assente o è separata da un gap dell'ordine di grandezza maggiore di {r`10^1 eV`}, allora il corpo è un isolante.\n                        
    \n                        
    \n                            Se invece la banda di emissione si sovrappone a un altra, allora il corpo è un conduttore.\n                        
    \n                        
    \n                            Se il gap è invece dell'ordine di grandezza di {r`1 eV`}, allora il corpo è un semiconduttore.\n                        
    \n                        \n                    \n                        
    \n                            Legami in cui mancano elettroni.\n                        
    \n                        
    \n                            Elettroni di altri legami possono spostarsi per colmare le lacune, creandone altre, e spostandole in direzione opposta a quella della corrente.\n                        
    \n                        \n                    \n                        
    \n                            Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterrà:\n                        
    \n                        
      \n                            
    • Con numero atomico maggiore, un semiconduttore di tipo N con elettroni in eccesso liberi di scorrere.
      • \n                            
    • Con numero atomico minore, un semiconduttore di tipo P con lacune in eccesso libere di catturare elettroni da altri legami.
      • \n                        
    \n                        
    \n                            Maggiore impurezza porta a maggiore conduttività.\n                        
    \n                        \n                    \n                        
    \n                            Aumentando la temperatura di un semiconduttore si aumenta la conduttività, perchè eccita le particelle e favorisce il movimento di elettroni e lacune.\n                        
    \n                        \n                
    \n                
    Ottica (non l'abbiamo fatta)}>\n                    \n                        
    \n                            I corpi possono assorbire o riflettere le onde elettromagnetiche che li colpiscono.\n                        
    \n                        \n                    \n                        
    \n                            Un corpo nero è un corpo che assorbe tutte le onde elettromagnetiche che riceve senza rifletterne nessuna.\n                        
    \n                        
    \n                            Le onde assorbite vengono poi riemesse sotto forma di un onda di {r`\\lambda`} variabile in base alla temperatura.\n                        
    \n                        
    \n                            {r`\\lambda_{max} \\cdot T`} è costante.\n                        
    \n                        \n                    \n                        
    \n                            L'energia assorbita e emessa dai corpi neri è quantizzata.\n                        
    \n                        \n                    \n                        
    \n                            Un onda magnetica con un quanto di energia è detta fotone:\n                        
    \n                        
    \n                            {r`E_{fotone} = h \\cdot f`}\n                        
    \n                        \n                    \n                        
    \n                            A volte, i fotoni che colpiscono un metallo possono estrarvi degli elettroni e creare una differenza di potenziale.\n                        
    \n                        
    \n                            Perchè avvenga, la frequenza deve essere maggiore di una certa soglia.\n                        
    \n                        
    \n                            Il numero di elettroni estratti dipende dall'intensità dell'onda, mentre l'energia cinetica degli elettroni dipende dalla frequenza.\n                        
    \n                        
    \n                            Non c'è nessun ritardo tra l'assorbimento del fotone e l'estrazione di elettroni.\n                        
    \n                        \n                
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    \n                {props.title}\n            
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invokeOrReturn(undefined, initialState) : init(initialState),\n\n\t\t\taction => {\n\t\t\t\tconst nextValue = hookState._reducer(hookState._value[0], action);\n\t\t\t\tif (hookState._value[0] !== nextValue) {\n\t\t\t\t\thookState._value[0] = nextValue;\n\t\t\t\t\thookState._component.setState({});\n\t\t\t\t}\n\t\t\t}\n\t\t];\n\t}\n\n\treturn hookState._value;\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++, 3);\n\tif (!options._skipEffects && argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent.__hooks._pendingEffects.push(state);\n\t}\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useLayoutEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++, 4);\n\tif (!options._skipEffects && argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent._renderCallbacks.push(state);\n\t}\n}\n\nexport function useRef(initialValue) {\n\tcurrentHook = 5;\n\treturn useMemo(() => ({ current: initialValue }), []);\n}\n\n/**\n * @param {object} ref\n * @param {() => object} createHandle\n * @param {any[]} args\n */\nexport function useImperativeHandle(ref, createHandle, args) {\n\tcurrentHook = 6;\n\tuseLayoutEffect(\n\t\t() => {\n\t\t\tif (typeof ref == 'function') ref(createHandle());\n\t\t\telse if (ref) ref.current = createHandle();\n\t\t},\n\t\targs == null ? args : args.concat(ref)\n\t);\n}\n\n/**\n * @param {() => any} factory\n * @param {any[]} args\n */\nexport function useMemo(factory, args) {\n\t/** @type {import('./internal').MemoHookState} */\n\tconst state = getHookState(currentIndex++, 7);\n\tif (argsChanged(state._args, args)) {\n\t\tstate._args = args;\n\t\tstate._factory = factory;\n\t\treturn (state._value = factory());\n\t}\n\n\treturn state._value;\n}\n\n/**\n * @param {() => void} callback\n * @param {any[]} args\n */\nexport function useCallback(callback, args) {\n\tcurrentHook = 8;\n\treturn useMemo(() => callback, args);\n}\n\n/**\n * @param {import('./internal').PreactContext} context\n */\nexport function useContext(context) {\n\tconst provider = currentComponent.context[context._id];\n\t// We could skip this call here, but than we'd not call\n\t// `options._hook`. We need to do that in order to make\n\t// the devtools aware of this hook.\n\tconst state = getHookState(currentIndex++, 9);\n\t// The devtools needs access to the context object to\n\t// be able to pull of the default value when no provider\n\t// is present in the tree.\n\tstate._context = context;\n\tif (!provider) return context._defaultValue;\n\t// This is probably not safe to convert to \"!\"\n\tif (state._value == null) {\n\t\tstate._value = true;\n\t\tprovider.sub(currentComponent);\n\t}\n\treturn provider.props.value;\n}\n\n/**\n * Display a custom label for a custom hook for the devtools panel\n * @type {(value: T, cb?: (value: T) => string | number) => void}\n */\nexport function useDebugValue(value, formatter) {\n\tif (options.useDebugValue) {\n\t\toptions.useDebugValue(formatter ? formatter(value) : value);\n\t}\n}\n\nexport function useErrorBoundary(cb) {\n\tconst state = getHookState(currentIndex++, 10);\n\tconst errState = useState();\n\tstate._value = cb;\n\tif (!currentComponent.componentDidCatch) {\n\t\tcurrentComponent.componentDidCatch = err => {\n\t\t\tif (state._value) state._value(err);\n\t\t\terrState[1](err);\n\t\t};\n\t}\n\treturn [\n\t\terrState[0],\n\t\t() => {\n\t\t\terrState[1](undefined);\n\t\t}\n\t];\n}\n\n/**\n * After paint effects consumer.\n */\nfunction flushAfterPaintEffects() {\n\tafterPaintEffects.some(component => {\n\t\tif (component._parentDom) {\n\t\t\ttry {\n\t\t\t\tcomponent.__hooks._pendingEffects.forEach(invokeCleanup);\n\t\t\t\tcomponent.__hooks._pendingEffects.forEach(invokeEffect);\n\t\t\t\tcomponent.__hooks._pendingEffects = [];\n\t\t\t} catch (e) {\n\t\t\t\tcomponent.__hooks._pendingEffects = [];\n\t\t\t\toptions._catchError(e, component._vnode);\n\t\t\t\treturn true;\n\t\t\t}\n\t\t}\n\t});\n\tafterPaintEffects = [];\n}\n\n/**\n * Schedule a callback to be invoked after the browser has a chance to paint a new frame.\n * Do this by combining requestAnimationFrame (rAF) + setTimeout to invoke a callback after\n * the next browser frame.\n *\n * Also, schedule a timeout in parallel to the the rAF to ensure the callback is invoked\n * even if RAF doesn't fire (for example if the browser tab is not visible)\n *\n * @param {() => void} callback\n */\nfunction afterNextFrame(callback) {\n\tconst done = () => {\n\t\tclearTimeout(timeout);\n\t\tcancelAnimationFrame(raf);\n\t\tsetTimeout(callback);\n\t};\n\tconst timeout = setTimeout(done, RAF_TIMEOUT);\n\n\tlet raf;\n\tif (typeof window != 'undefined') {\n\t\traf = requestAnimationFrame(done);\n\t}\n}\n\n// Note: if someone used options.debounceRendering = requestAnimationFrame,\n// then effects will ALWAYS run on the NEXT frame instead of the current one, incurring a ~16ms delay.\n// Perhaps this is not such a big deal.\n/**\n * Schedule afterPaintEffects flush after the browser paints\n * @param {number} newQueueLength\n */\nfunction afterPaint(newQueueLength) {\n\tif (newQueueLength === 1 || prevRaf !== options.requestAnimationFrame) {\n\t\tprevRaf = options.requestAnimationFrame;\n\t\t(prevRaf || afterNextFrame)(flushAfterPaintEffects);\n\t}\n}\n\n/**\n * @param {import('./internal').EffectHookState} hook\n */\nfunction invokeCleanup(hook) {\n\tif (typeof hook._cleanup == 'function') hook._cleanup();\n}\n\n/**\n * Invoke a Hook's effect\n * @param {import('./internal').EffectHookState} hook\n */\nfunction invokeEffect(hook) {\n\thook._cleanup = hook._value();\n}\n\n/**\n * @param {any[]} oldArgs\n * @param {any[]} newArgs\n */\nfunction argsChanged(oldArgs, newArgs) {\n\treturn !oldArgs || newArgs.some((arg, index) => arg !== oldArgs[index]);\n}\n\nfunction invokeOrReturn(arg, f) {\n\treturn typeof f == 'function' ? f(arg) : f;\n}\n","import style from \"./Todo.less\";\n\nexport default function (props) {\n\tif(process.env.NODE_ENV === \"development\") {\n\t\treturn {props.children};\n\t}\n\telse {\n\t\treturn null;\n\t}\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"minus\":\"minus__VM3UF\"};","import style from \"./Split.less\";\n\nexport default function (props) {\n    let children;\n\n    if(Array.isArray(props.children)) {\n        children = props.children.map(element => {\n            return (\n                
    \n                    {element}\n                
    \n            );\n        });\n    }\n\n    else {\n        children = (\n            
    \n                {props.children}\n            
    \n        );\n    }\n    return (\n        
    \n            
    {children}
    \n        
    \n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"plus\":\"plus__5AywL\"};","import style from \"./Box.less\";\n\nexport const BoxColors = Object.freeze({\n    RED: style.red,\n    ORANGE: style.orange,\n    YELLOW: style.yellow,\n    LIME: style.lime,\n    CYAN: style.cyan,\n    BLUE: style.blue,\n    MAGENTA: style.magenta,\n    DEFAULT: style.default\n})\n\nexport default function (props) {\n    let color = BoxColors.DEFAULT;\n    if(props.color) {\n        color = props.color;\n    }\n\n    return (\n        
    \n            {props.children}\n        
    \n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"splitparent\":\"splitparent__3-wBs\",\"splitchild\":\"splitchild__begkX\"};","import style from \"./Panel.less\";\nimport Box from \"./Box\";\n\nexport default function(props) {\n\treturn (\n\t\t\n\t\t\t
    \n\t\t\t\t{props.title}\n\t\t\t
    \n\t\t\t
    \n\t\t\t\t{props.children}\n\t\t\t
    \n\t\t    \n\t);\n}\n","import {createContext} from \"preact\";\n\nexport default createContext(true);\n"],"sourceRoot":""}
\ No newline at end of file
diff --git a/docs/route-Fisica.chunk.52a73.esm.js b/docs/route-Fisica.chunk.ae8e3.esm.js
similarity index 99%
rename from docs/route-Fisica.chunk.52a73.esm.js
rename to docs/route-Fisica.chunk.ae8e3.esm.js
index 5197020..1a69b82 100644
--- a/docs/route-Fisica.chunk.52a73.esm.js
+++ b/docs/route-Fisica.chunk.ae8e3.esm.js
@@ -1,2 +1,2 @@
-(window.webpackJsonp=window.webpackJsonp||[]).push([[7],{"2QOB":function(e,l,a){"use strict";a.r(l),function(e){a("hosL");var n=a("Q7TX"),i=a("imVn"),t=a("OPqz"),o=a("CfuJ"),r=a("4v1N"),u=a("RMzO"),c=a("wQ73"),s=a("PGF6");let p,d,m,f,v,_,g,h,b,z,L,q,E,D,A,F,C,P,I,S,w,k,N,B,T,V,x,y,O,R,M,U,H,Q,G,W,j,J,Y,K,X,$,Z,ee,le,ae,ne,ie,te,oe,re,ue,ce,se,pe,de,me,fe,ve,_e,ge,he,be,ze,Le,qe,Ee,De,Ae,Fe,Ce,Pe,Ie,Se,we,ke,Ne,Be,Te,Ve,xe,ye,Oe,Re,Me,Ue,He,Qe,Ge,We,je,Je,Ye,Ke,Xe,$e,Ze,el,ll,al,nl,il,tl,ol,rl,ul,cl,sl,pl,dl,ml,fl,vl,_l,gl,hl,bl,zl,Ll,ql,El,Dl,Al,Fl,Cl,Pl,Il,Sl,wl,kl,Nl,Bl,Tl,Vl,xl,yl=e=>e;const Ol=String.raw;l.default=function(){return e(c.a.Provider,{value:!1},e(s.a.Provider,{value:n.a.INLINE},e("div",null,e("h1",null,"Fisica"),e(t.a,{title:"Vettori"},e(i.a,{title:"Componenti cartesiane"},e("p",null,"Usa le regole base della trigonometria:"),e("p",null,e(n.b,null,Ol(p||(p=yl`\vec{v} = \vec{v}_x + \vec{v}_y`)))),e("p",null,e(n.b,null,Ol(d||(d=yl`\left | \vec{v}_x \right | = \left | \vec{v} \right | \sin \alpha`)))),e("p",null,e(n.b,null,Ol(m||(m=yl`\left | \vec{v}_y \right | = \left | \vec{v} \right | \cos \alpha`))))),e(i.a,{title:"Somma"},e("p",null,"Scomponi in componenti, poi sommali:"),e("p",null,e(n.b,null,Ol(f||(f=yl`\vec{v} + \vec{w} = (\vec{v}_x + \vec{w}_x) + (\vec{v}_y + \vec{w}_y)`)))),e("p",null,"Produce il vettore risultante dall'applicazione della regola del parallelogramma.")),e(i.a,{title:"Differenza"},e("p",null,"Alla fine è sempre una somma:"),e("p",null,e(n.b,null,Ol(v||(v=yl`\vec{v} - \vec{w} = (\vec{v}_x - \vec{w}_x) + (\vec{v}_y - \vec{w}_y)`)))),e("p",null,"Produce il vettore che parte da ",e(n.b,null,"w")," e arriva a ",e(n.b,null,"v"),".")),e(i.a,{title:"Prodotto scalare"},e("p",null,"Si chiama scalare perchè il risultato è uno scalare, non un vettore."),e("p",null,e(n.b,null,Ol(_||(_=yl`\vec{v} \cdot \vec{w} = \left | \vec{v} \right | \left | \vec{w} \right | \cos \alpha`)))),e("p",null,"Produce il modulo della proiezione di ",e(n.b,null,Ol(g||(g=yl`\vec{a}`)))," su ",e(n.b,null,Ol(h||(h=yl`\vec{b}`))),".")),e(i.a,{title:"Prodotto vettoriale"},e("p",null,"Si chiama vettoriale perchè il risultato è un altro vettore."),e("ul",null,e("li",null,e(n.b,null,Ol(b||(b=yl`\vec{c} = \vec{a} \times \vec{b}`)))),e("li",null,e(n.b,null,Ol(z||(z=yl`\left | \vec{c} \right | = \left | \vec{a} \right | \cdot \left | \vec{b} \right | \cdot \sin(\alpha)`)))),e("li",null,e("a",{href:"https://it.wikipedia.org/wiki/Regola_della_mano_destra"},"Regola della mano destra"))),e("p",null,"Non è commutativo!"))),e(t.a,{title:"Leggi di Newton"},e(i.a,{title:"1ᵃ: Inerzia"},e("p",null,"Se un corpo puntiforme ha forza risultante nulla, allora la sua velocità non cambia."),e("p",null,e(n.b,null,Ol(L||(L=yl`\Sigma \vec{F} = 0 \Longleftrightarrow \Delta v = 0`))))),e(i.a,{title:"2ᵃ: Proporzionalità"},e("p",null,"La forza risultante di un corpo è direttamente proporzionale alla sua accelerazione, e la costante di proporzionalità è la ",e("i",null,"massa"),"."),e("p",null,e(n.b,null,Ol(q||(q=yl`\Sigma \vec{F} = m \vec{a}`))))),e(i.a,{title:"3ᵃ: Azione e reazione"},e("p",null,"Due corpi esercitano forze uguali e opposte uno sull'altro."),e("p",null,e(n.b,null,Ol(E||(E=yl`\vec{F}_{21} = -\vec{F}_{12}`)))))),e(t.a,{title:"Forza di gravità"},e(i.a,{title:"Tra due corpi"},e("p",null,"Due corpi puntiformi si attirano uno verso l'altro con forza:"),e("p",null,e(n.b,null,Ol(D||(D=yl`\left | \vec{F} \right | = G \frac{m_1 m_2}{s^2}`)))),e("p",null,e(n.b,null,"G")," è la ",e("i",null,"costante di gravitazione universale")," e vale:"),e("p",null,e(n.b,null,Ol(A||(A=yl`G = 6.67 \cdot 10^{-11} \frac{N m^2}{{kg}^2}`))))),e(i.a,{title:"Verso la Terra"},e("p",null,"Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo è attratto verso la Terra con forza ",e("i",null,"peso")," uguale a:"),e("p",null,e(n.b,null,Ol(F||(F=yl`\left | \vec{F} \right | = g m`)))),e("p",null,e(n.b,null,"g")," è la ",e("i",null,"costante di gravità")," della Terra, e vale:"),e("p",null,e(n.b,null,Ol(C||(C=yl`g = 9.81 \frac{m}{s^2}`))))),e(i.a,{title:"Su pianeti diversi"},e("p",null,"Per pianeti diversi dalla Terra vale la stessa regola:"),e("p",null,e(n.b,null,Ol(P||(P=yl`\left | \vec{F} \right | = g m`)))),e("p",null,"L'unica differenza è che cambia la ",e("i",null,"costante di gravità"),":"),e("p",null,e(n.b,null,Ol(I||(I=yl`g_{luna} = 1.62 \frac{m}{s^2}`)))),e("p",null,e(n.b,null,Ol(S||(S=yl`g_{marte} = 3.71 \frac{m}{s^2}`)))))),e(t.a,{title:"Forze di contatto"},e(i.a,{title:"Normale"},e("p",null,"Si oppone alle forze applicate alla superficie di contatto."),e("p",null,"Un libro appoggiato su un tavolo ha la ",e("b",null,"forza di gravità")," che lo attira verso il terreno e la ",e("b",null,"forza normale")," che lo trattiene dal cadere.")),e(i.a,{title:"Attrito statico"},e("p",null,"Impedisce a un corpo di muoversi se non viene spinto da una forza che supera una certa soglia:"),e("p",null,e(n.b,null,Ol(w||(w=yl`\left | \vec{F} \right | \leq \mu_{s} \left | \vec{F}_{normale} \right |`))))),e(i.a,{title:"Attrito dinamico"},e("p",null,"Rallenta i corpi che si stanno muovendo finchè essi non si fermano:"),e("p",null,e(n.b,null,Ol(k||(k=yl`\left | \vec{F} \right | \leq \mu_{d} \left | \vec{F}_{normale} \right |`))))),e(i.a,{title:"Tensione"},e("p",null,"E' forza trasmessa tra due estremi di una fune."),e("p",null,"Può essere redirezionata per mezzo di carrucole.")),e(i.a,{title:"Elastica"},e("p",null,"Una molla cerca sempre di tornare alla sua posizione indeformata con forza:"),e("p",null,e(n.b,null,Ol(N||(N=yl`F = -k x`)))),e("p",null,"(E' negativa perchè la forza è opposta a quella applicata per deformarla.)"))),e(t.a,{title:"Cinematica"},e(i.a,{title:"Spostamento"},e("p",null,"È un vettore che indica la posizione di un corpo rispetto a un'origine."),e("p",null,e(n.b,null,Ol(B||(B=yl`\Delta \vec{s} = \vec{s}(fine) - \vec{s}(inizio)`))))),e(i.a,{title:"Velocità"},e("p",null,"È un vettore che misura la variazione di posizione nel tempo."),e("p",null,e(n.b,null,Ol(T||(T=yl`\vec{v} = \frac{\Delta \vec{s}}{\Delta t}`)))),e("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",e("i",null,"velocità istantanea"),":"),e("p",null,e(n.b,null,Ol(V||(V=yl`\vec{v} = \lim_{\Delta t \to 0} \frac{\Delta \vec{s}}{\Delta t} = \frac{d \vec{s}}{dt}`))))),e(i.a,{title:"Accelerazione"},e("p",null,"È un vettore che misura la variazione di velocità nel tempo."),e("p",null,e(n.b,null,Ol(x||(x=yl`\vec{a} = \frac{\Delta \vec{v}}{\Delta t}`)))),e("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",e("i",null,"accelerazione istantanea"),":"),e("p",null,e(n.b,null,Ol(y||(y=yl`\vec{a} = \lim_{\Delta v \to 0} \frac{\Delta \vec{v}}{\Delta t} = \frac{d \vec{v}}{d t} = \frac{d^2 \vec{s}}{d t^2}`))))),e(i.a,{title:e("span",null,"Quantità di moto ",e("small",null,"(momento lineare)"))},e("p",null,"La quantità di moto è una proprietà vettoriale dei corpi:"),e("p",null,e(n.b,null,Ol(O||(O=yl`\vec{p} = m \vec{v}`)))),e("p",null,"Se la forza risultante è nulla, la quantità di moto non cambia."),e("p",null,e(n.b,null,Ol(R||(R=yl`\Sigma \vec{F} = 0 \Longleftrightarrow \Delta \vec{p} = 0`)))))),e(t.a,{title:"Moto rettilineo uniforme"},e(i.a,{title:"Spostamento"},e("p",null,"La ",e("i",null,"legge oraria")," è:"),e("p",null,e(n.b,null,Ol(M||(M=yl`s(t) = v \cdot \Delta t + s(0)`))))),e(i.a,{title:"Velocità"},e("p",null,"È costante:"),e("p",null,e(n.b,null,Ol(U||(U=yl`v(t) = k`))))),e(i.a,{title:"Accelerazione"},e("p",null,"La velocità non varia:"),e("p",null,e(n.b,null,Ol(H||(H=yl`a(t) = 0`))))),e(i.a,{title:"Forze"},e("p",null,"Si applica la prima legge di Newton:"),e("p",null,e(n.b,null,"f(t) = 0")))),e(t.a,{title:"Moto rettilineo uniformemente accelerato"},e(i.a,{title:"Spostamento"},e("p",null,"La ",e("i",null,"legge oraria")," è:"),e("p",null,e(n.b,null,Ol(Q||(Q=yl`s(t) = \frac{1}{2} a \cdot (\Delta t)^2 + v(0) \cdot (\Delta t) + s(0)`))))),e(i.a,{title:"Velocità"},e("p",null,"È una retta:"),e("p",null,e(n.b,null,Ol(G||(G=yl`v(t) = a \Delta t + v(0)`))))),e(i.a,{title:"Accelerazione"},e("p",null,"È costante:"),e("p",null,e(n.b,null,Ol(W||(W=yl`a(t) = k`))))),e(i.a,{title:"Forze"},e("p",null,"Si applica la prima legge di Newton:"),e("p",null,e(n.b,null,"f(t) = m a")))),e(t.a,{title:"Moto armonico semplice"},e(i.a,{title:"Ampiezza"},e("p",null,"E' la distanza dal centro massima che raggiunge il corpo."),e("p",null,"(L'ampiezza di una sinusoide.)")),e(i.a,{title:"Velocità angolare"},e("p",null,"Indica quanto in fretta cambia la posizione del corpo."),e("p",null,"Dipende dal periodo:"),e("p",null,e(n.b,null,Ol(j||(j=yl`\omega = \frac{2 \pi}{T}`))))),e(i.a,{title:"Spostamento"},e("p",null,"E' una sinusoide:"),e("p",null,e(n.b,null,Ol(J||(J=yl`s(t) = A \sin (\omega \cdot t + \phi)`))))),e(i.a,{title:"Velocità"},e("p",null,"E' la sinusoide dello spostamento, sfasata di ",e(n.b,null,Ol(Y||(Y=yl`\frac{\pi}{2}`))),":"),e("p",null,e(n.b,null,Ol(K||(K=yl`v(t) = A \sin (\omega \cdot t + \phi + \frac{\pi}{2})`))))),e(i.a,{title:"Accelerazione"},e("p",null,"E' la sinusoide della velocità, sfasata di ",e(n.b,null,Ol(X||(X=yl`\pi`))),":"),e("p",null,e(n.b,null,Ol($||($=yl`a(t) = A \sin (\omega \cdot t + \phi + \pi)`))))),e(i.a,{title:"Forze"},e("p",null,"Si applica la prima legge di Newton:"),e("p",null,e(n.b,null,"f(t) = m a")))),e(t.a,{title:"Moti composti"},e(i.a,{title:"Moto parabolico"},e("p",null,"Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.")),e(i.a,{title:"Moto circolare uniforme"},e("p",null,"Il moto parabolico è dato sommando due moti armonici semplici: uno sull'asse X, e l'altro, sfasato di ",e(n.b,null,Ol(Z||(Z=yl`\frac{\pi}{2}`))),", sull'asse Y."))),e(t.a,{title:"Moto circolare uniforme"},e(i.a,null,e("h3",null,"Velocità angolare"),e("p",null,"Quanto cambia la fase nel tempo."),e("p",null,e(n.b,null,Ol(ee||(ee=yl`\omega = \frac{2 \pi}{T}`))))),e(i.a,{title:"Fase"},e("p",null,"E' l'angolo percorso dal corpo rispetto alla posizione iniziale."),e("p",null,"Si indica con ",e(n.b,null,Ol(le||(le=yl`\phi`))),", e generalmente si usa in radianti.")),e(i.a,{title:"Velocità"},e("p",null,"Si applicano le formule per la circonferenza:"),e("p",null,e(n.b,null,Ol(ae||(ae=yl`v = \frac{\Delta s}{t} = \frac{2 \pi \cdot r}{T} = \omega r`))))),e(i.a,{title:"Accelerazione"},e("p",null,"Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto:"),e("p",null,e(n.b,null,Ol(ne||(ne=yl`a = \frac{v^2}{r} = r \cdot \omega^2 = v \cdot \omega`))))),e(i.a,{title:"Forza centripeta"},e("p",null,"È verso il centro e si calcola con:"),e("p",null,e(n.b,null,Ol(ie||(ie=yl`F = m \cdot a`)))))),e(t.a,{title:"Lavoro ed energia"},e(i.a,{title:"Lavoro"},e("p",null,"E' compiuto da una forza che sposta un corpo."),e("p",null,e(n.b,null,Ol(te||(te=yl`W = \vec{F} \cdot \vec{s} = F \cdot \Delta s \cdot cos(\alpha )`)))),e("p",null,"(Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)")),e(i.a,{title:"Energia cinetica"},e("p",null,"Un corpo ha energia cinetica in ogni momento uguale a:"),e("p",null,e(n.b,null,Ol(oe||(oe=yl`E_c = \frac{1}{2} m v^2`)))),e("p",null,"Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:"),e("p",null,e(n.b,null,Ol(re||(re=yl`\Delta E_c = W`))))),e(i.a,{title:"Energia potenziale gravitazionale"},e("p",null,"Un corpo ha energia potenziale in ogni momento pari a:"),e("p",null,e(n.b,null,Ol(ue||(ue=yl`E_{p_g} = m \cdot g \cdot h`)))),e("p",null,"(Con ",e(n.b,null,"h")," uguale a un altezza scelta come punto di riferimento.)")),e(i.a,{title:"Energia potenziale elastica"},e("p",null,"Una molla ha sempre energia potenziale elastica pari a:"),e("p",null,e(n.b,null,Ol(ce||(ce=yl`E_{p_e} = \frac{1}{2} k x^2`))))),e(i.a,{title:"Forze conservative"},e("p",null,"Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo."),e("p",null,"Ad esempio, è conservativa la ",e("i",null,"forza di gravità"),", ma ",e("b",null,"non")," è conservativa la forza di attrito."),e("p",null,"Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:"),e("p",null,e(n.b,null,Ol(se||(se=yl`E = E_k + E_p`))))),e(i.a,{title:"Potenza"},e("p",null,"È la velocità di trasferimento di energia:"),e("p",null,e(n.b,null,Ol(pe||(pe=yl`P = \frac{\Delta E}{\Delta t}`)))))),e(t.a,{title:"Elettrostatica"},e(i.a,{title:"Carica elettrica"},e("p",null,"È una proprietà dei corpi che può essere ",e(o.a,null,"positiva")," o ",e(r.a,null,"negativa"),"."),e("p",null,"Si conserva: in un sistema chiuso la carica totale è costante."),e("p",null,"Esiste un'unità elementare: ",e(n.b,null,Ol(de||(de=yl`C_{elettrone} = 1.602 \cdot 10^{-19}`))),"."),e("p",null,"Cariche ",e(o.a,null,"opp"),e(r.a,null,"oste")," si attraggono; cariche ",e(o.a,null,"uguali")," si respingono.")),e(i.a,{title:"Conduttori e isolanti"},e("p",null,"Più ",e("a",{href:"https://it.wikipedia.org/wiki/Ione"},"ioni")," ha un corpo, meglio la carica si muove attraverso di esso."),e("p",null,"I corpi in cui la carica si muove bene sono ",e("i",null,"conduttori"),", mentre quelli in cui si muove difficilmente sono ",e("i",null,"isolanti"),"."),e("p",null,e("i",null,"Il corpo umano è un buon conduttore.")))),e(t.a,{title:"Polarizzazione"},e(i.a,{title:"Polarizzazione"},e("p",null,"E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona."))),e(t.a,null,e(i.a,{title:"Messa a terra"},e("p",null,"Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno ",e("i",null,"equilibrate")," e il corpo diventerà elettricamente neutro (con stesso numero di ",e(o.a,null,"cariche positive")," e ",e(r.a,null,"negative")," all'interno)."))),e(t.a,null,e(i.a,{title:"Polarizzazione per strofinio"},e("p",null,"Strofinando tra loro due corpi isolanti, essi si ",e("i",null,"polarizzeranno per strofinio"),".")),e(i.a,{title:"Polarizzazione per contatto"},e("p",null,"Toccando un conduttore con un corpo carico, il conduttore potrà ",e("i",null,"polarizzarsi per contatto"),".")),e(i.a,{title:"Polarizzazione per induzione"},e("p",null,'Se un corpo conduttore ha cariche "esterne" di un ',e(o.a,null,"certo segno")," vicino, esso avrà tutte le cariche del ",e(r.a,null,"segno opposto")," in equilibrio vicino alle cariche esterne, e tutte le cariche dello ",e(o.a,null,"stesso segno")," più lontano possibile da esse."),e("p",null,"Mettendo a terra il conduttore, nuove cariche del ",e(r.a,null,"segno opposto")," saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate."),e("p",null,"Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà ",e(r.a,null,"caricato del segno opposto")," rispetto alle cariche esterne."))),e(t.a,{title:"Forza elettrica"},e(i.a,{title:"Legge di Coulomb"},e("p",null,"Due corpi carichi si attraggono tra loro con forza:"),e("p",null,e(n.b,null,Ol(me||(me=yl`\left | \vec{F}_{elettrica} \right | = \frac{-k \cdot q_1 \cdot q_2}{s^2}`)))),e("p",null,e(n.b,null,Ol(fe||(fe=yl`k`)))," è la ",e("i",null,"costante di Coulomb"),", e vale ",e(n.b,null,Ol(ve||(ve=yl`k = 8.99 \cdot 10^9 \frac{N \cdot m^2}{C^2}`))),".")),e(i.a,{title:"Permeabilità dello spazio vuoto"},e("p",null,"La costante ",e(n.b,null,Ol(_e||(_e=yl`k`)))," è in realtà dipendente da un altra costante, ",e(n.b,null,Ol(ge||(ge=yl`\epsilon_0`))),", la ",e("i",null,"permeabilità del vuoto"),"."),e("p",null,e(n.b,null,Ol(he||(he=yl`k = \frac{1}{4 \pi \cdot \epsilon_0}`)))),e("p",null,e(n.b,null,Ol(be||(be=yl`\left | \vec{F}_{elettrica} \right | = \frac{q_1 \cdot q_2}{4 \pi \cdot \epsilon_0 \cdot s^2}`))))),e(i.a,{title:"Campo elettrico"},e("p",null,"Misura che forza viene applicata in ogni punto su una carica unitaria:"),e("p",null,e(n.b,null,Ol(ze||(ze=yl`\vec{E} = \frac{\vec{F}_{elettrica}}{q} = \frac{-k \cdot q}{s^2}`))))),e(i.a,{title:"Flusso elettrico"},e("p",null,'È la differenza tra "quanto" campo elettrico ',e(o.a,null,"entra")," e quanto campo elettrico ",e(r.a,null,"esce")," da una certa area."),e("p",null,"In qualsiasi superficie chiusa, il flusso elettrico è uguale alla componente perpendicolare del campo elettrico moltiplicato per l'area."),e("p",null,e(n.b,null,Ol(Le||(Le=yl`\Phi_E = \vec{E} \cdot \vec{A}`)))),e("p",null,"Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:"),e("p",null,e(n.b,null,Ol(qe||(qe=yl`\Phi_E = \vec{E} \cdot \vec{A} = E_\perp \cdot A \cdot \cos(\alpha)`)))),e("p",null,e(u.a,null,"Circa. E' una specie di integrale..."))),e(i.a,{title:"Legge di Gauss per i campi elettrostatici"},e("p",null,"Il flusso elettrico è direttamente proporzionale alla carica presente all'interno della superficie."),e("p",null,e(n.b,null,Ol(Ee||(Ee=yl`\Phi_E = 4 \pi \cdot k \cdot q = \frac{q}{\epsilon_0}`)))),e("p",null,"Ovvero, i campi elettrostatici sono generati dalle cariche elettriche."))),e(t.a,{title:"Energia elettrica"},e(i.a,{title:"Energia potenziale elettrica"},e("p",null,"Un corpo carico vicino ad altre cariche possiede un'",e("i",null,"energia potenziale elettrica")," ",e(n.b,null,Ol(De||(De=yl`U_e`))),"."))),e(t.a,{title:"Circuiti elettrici"},e(i.a,{title:e("span",null,"Potenziale elettrico ",e("small",null,"(tensione)"))},e("p",null,"È il valore dell'energia potenziale elettrica per una carica unitaria."),e("p",null,e(n.b,null,Ol(Ae||(Ae=yl`V = \frac{U_e}{q}`)))),e("p",null,"La sua unità di misura è il Volt (",e(n.b,null,Ol(Fe||(Fe=yl`V`))),")."),e("p",null,"In una batteria è detto ",e("i",null,"forza elettromotrice"),", e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli.")),e(i.a,{title:e("span",null,"Corrente elettrica ",e("small",null,"(intensità)"))},e("p",null,"Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo."),e("p",null,e(n.b,null,Ol(Ce||(Ce=yl`I = \frac{\Delta q}{\Delta t}`)))),e("p",null,"Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla."),e("p",null,"La sua unità di misura è l'Ampere (",e(n.b,null,Ol(Pe||(Pe=yl`A`))),").")),e(i.a,{title:e("span",null,"Corrente continua ",e("small",null,"(",e("abbr",{title:"Direct Current"},"DC"),")"))},e("p",null,"Quando in un circuito la direzione della corrente è costante.")),e(i.a,{title:e("span",null,"Corrente alternata ",e("small",null,"(",e("abbr",{title:"Alternate Current"},"AC"),")"))},e("p",null,"Quando in un circuito la direzione della corrente si alterna periodicamente.")),e(i.a,{title:"Potenza elettrica"},e("p",null,"Possiamo calcolare la potenza di un circuito:"),e("p",null,e(n.b,null,Ol(Ie||(Ie=yl`P = \frac{\Delta U_e}{\Delta t} = I \cdot \Delta V = I^2 \cdot R = \frac{(\Delta V)^2}{R}`)))))),e(t.a,{title:"Elementi di un circuito"},e(i.a,{title:"Resistore"},e("p",null,"Riduce l'intensità di corrente, e converte parte del potenziale in calore."),e("p",null,"Il potenziale utilizzato è pari a:"),e("p",null,e(n.b,null,Ol(Se||(Se=yl`V = R \cdot I`)))),e("p",null,"Dove ",e(n.b,null,Ol(we||(we=yl`R`)))," è una costante detta ",e("i",null,"resistenza")," con unità di misura Ohm (",e(n.b,null,Ol(ke||(ke=yl`\Omega`))),")."),e("p",null,"La resistenza di un conduttore vale:"),e("p",null,e(n.b,null,Ol(Ne||(Ne=yl`R = \rho \frac{L_{unghezza}}{A_{rea}}`)))),e("p",null,e(n.b,null,Ol(Be||(Be=yl`\rho`)))," è la ",e("i",null,"resistività")," del materiale, e varia in base alla temperatura:"),e("p",null,e(n.b,null,Ol(Te||(Te=yl`\rho = \rho_0 (1 + \alpha(T - T_0))`))))),e(i.a,{title:"Condensatore"},e("p",null,"Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito."),e("p",null,"Per farlo, cattura cariche ",e(o.a,null,"positive")," e ",e(r.a,null,"negative")," sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro."),e("p",null,"Ha una ",e("b",null,"capacità")," caratteristica, che in un condensatore a facce piane parallele è:"),e("p",null,e(n.b,null,Ol(Ve||(Ve=yl`C = \frac{q_{massima}}{\Delta V}`)))),e("p",null,"Condensatori di capacità maggiore immagazzinano più potenziale con meno carica."),e("p",null,"La capacità aumenta se viene messo qualcosa tra le armature:"),e("p",null,e(n.b,null,Ol(xe||(xe=yl`C_{nuova} = \kappa \cdot \frac{\epsilon_0 \cdot A}{s}`)))),e("p",null,"Dove ",e(n.b,null,Ol(ye||(ye=yl`\kappa`)))," è la ",e("i",null,"costante dielettrica relativa")," del materiale inserito, ",e(n.b,null,Ol(Oe||(Oe=yl`A`)))," l'area di una armatura e ",e(n.b,null,Ol(Re||(Re=yl`s`)))," la distanza tra le due armature."),e("p",null,"Se il campo elettrico creatosi tra le due armature supera la ",e("i",null,"rigidità dielettrica")," del condensatore, la carica immagazzinata viene persa e ha luogo un ",e("i",null,"breakdown"),"."),e("p",null,"La sua unità di misura è il Farad (",e(n.b,null,Ol(Me||(Me=yl`Fa`))),")")),e(i.a,{title:"Amperometro"},e("p",null,"Misura la corrente elettrica se messo in serie."),e("p",null,"(Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)")),e(i.a,{title:"Voltmetro"},e("p",null,"Misura la differenza di potenziale se messo in parallelo."),e("p",null,"(Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)"))),e(t.a,{title:"Principi di Kirchhoff"},e(i.a,{title:"Legge dei nodi"},e("p",null,"Per nodo si intende un qualsiasi punto del circuito."),e("p",null,"Da un nodo entra ed esce la stessa corrente.")),e(i.a,{title:"Legge delle maglie"},e("p",null,"Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito."),e("p",null,"In una maglia chiusa, la somma delle differenze di potenziale è 0."))),e(t.a,{title:"Serie e Parallelo"},e(i.a,{title:"Circuito in serie"},e("p",null,"Più parti di circuito sono ",e("i",null,"in serie")," se sono consecutive e senza biforcazioni."),e("p",null,"Parti di circuito in serie sono attraversate dalla stessa corrente.")),e(i.a,{title:"Circuito in parallelo"},e("p",null,"Più parti di circuito sono ",e("i",null,"in parallelo")," tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo."),e("p",null,"Parti di circuito in parallelo hanno la stessa differenza di potenziale."))),e(t.a,{title:"Resistenze equivalenti"},e(i.a,{title:"Circuiti in serie"},e("p",null,"Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:"),e("p",null,e(n.b,null,Ol(Ue||(Ue=yl`R_{serie} = \sum_{i=1}^{n} R_i`))))),e(i.a,{title:"Circuiti in parallelo"},e("p",null,"Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:"),e("p",null,e(n.b,null,Ol(He||(He=yl`R_{parallelo} = \frac{1}{\sum_{i=1}^{n} \frac{1}{R_i}}`)))))),e(t.a,{title:"Condensatori equivalenti"},e(i.a,{title:"Circuiti in serie"},e("p",null,"Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacità di:"),e("p",null,e(n.b,null,Ol(Qe||(Qe=yl`C_{serie} = \frac{1}{\sum_{i=1}^{n} \frac{1}{C_i}}`))))),e(i.a,{title:"Circuiti in parallelo"},e("p",null,"Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacità della somma di tutti quelli sostituiti:"),e("p",null,e(n.b,null,Ol(Ge||(Ge=yl`C_{parallelo} = \sum_{i=1}^{n} C_n`)))))),e(t.a,{title:"Magnetismo"},e(i.a,{title:"Permeabilità magnetica dello spazio vuoto"},e("p",null,"E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente."),e("p",null,e(n.b,null,Ol(We||(We=yl`\mu_0 = 4 \pi \cdot 10^{-7} \frac{H}{m}`)))," (",e(n.b,null,Ol(je||(je=yl`\frac{N}{A^2}`))),")")),e(i.a,{title:"Campo magnetico"},e("p",null,"Come un campo elettrico, ma per i magneti."),e("p",null,"Il suo simbolo è ",e(n.b,null,Ol(Je||(Je=yl`B`))),", e la sua unità di misura è il Tesla (",e(n.b,null,"T"),").")),e(i.a,{title:"Flusso magnetico"},e("p",null,'È "quanto" campo magnetico ',e("b",null,"attraversa")," un percorso chiuso."),e("p",null,'Per qualsiasi percorso chiuso, il flusso magnetico è uguale alla somma di tutti i "sottoflussi" magnetici calcolati sui suoi lati.'),e("p",null,e(n.b,null,Ol(Ye||(Ye=yl`\Phi_{B_{i}} = \vec{B} \cdot \vec{L}_n = B \cdot L_i \cdot \sin(\alpha) = B_\parallel \cdot L_i`)))),e("p",null,e(n.b,null,Ol(Ke||(Ke=yl`\Phi_{B} = \sum_{i=0}^{n_{lati}} \Phi_{Bn}`)))),e("p",null,"La sua unità di misura è il Weber (",e(n.b,null,Ol(Xe||(Xe=yl`Wb = T \cdot m^2`))),").")),e(i.a,{title:"Legge di Gauss per i campi magnetici"},e("p",null,"Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo."),e("p",null,"Ovvero, non esistono monopoli magnetici.")),e(i.a,{title:"Legge di Ampère"},e("p",null,"L'intensità di corrente che attraversa un percorso chiuso è direttamente proporzionale al flusso magnetico dello stesso percorso."),e("p",null,e(n.b,null,Ol($e||($e=yl`\Phi_B = \mu_0 \cdot I`)))))),e(t.a,{title:"Forze magnetiche"},e(i.a,{title:e("span",null,"Forza magnetica su carica puntiforme ",e("small",null,"(Forza di Lorentz)"))},e("p",null,"I campi magnetici applicano una forza sulle cariche vicine:"),e("p",null,e(n.b,null,Ol(Ze||(Ze=yl`\vec{F}_{B} = q \cdot (\vec{v} \times \vec{B})`)))),e("p",null,"Dove ",e(n.b,null,Ol(el||(el=yl`\vec{B}`)))," è l'intensità del campo magnetico e ",e(n.b,null,Ol(ll||(ll=yl`\vec{v}`)))," la velocità della carica considerata."),e("p",null,"Si ha una forza massima se la velocità è perpendicolare al campo magnetico."),e("p",null,"In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme.")),e(i.a,{title:"Forza magnetica in un filo"},e("p",null,"I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:"),e("p",null,e(n.b,null,Ol(al||(al=yl`\vec{F}_{magnetica} = I \cdot (\vec{L} \times \vec{B})`)))," ",e("a",{href:"https://it.openprof.com/wb/forza_di_lorentz_su_un_filo_percorso_da_corrente?ch=360"},"[1]")),e("p",null,"Dove ",e(n.b,null,Ol(nl||(nl=yl`I`)))," è la corrente elettrica, ",e(n.b,null,Ol(il||(il=yl`\vec{L}`)))," è un vettore che punta nella direzione di scorrimento della corrente e ha come modulo la lunghezza del conduttore."))),e(t.a,{title:"Campi magnetici"},e(i.a,{title:"Campo magnetico in una spira"},e("p",null,"Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.")),e(i.a,{title:"Campo magnetico di un solenoide"},e("p",null,"Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro."),e("p",null,"All'interno del solenoide si crea un campo (quasi) uniforme:"),e("p",null,e(n.b,null,Ol(tl||(tl=yl`\left | \vec{B} \right | = \mu_0 \cdot I \cdot \frac{A_{vvolgimenti}}{L_{unghezzafilo}}`))))),e(i.a,{title:"Legge di Oersted"},e("p",null,e("i",null,"Caso particolare della ",e("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Amp%C3%A8re"},"Legge di Ampère"),".")),e("p",null,"Il modulo del campo magnetico ",e(n.b,null,"B")," prodotto da un filo in cui passa una corrente continua ",e(n.b,null,"I")," alla distanza ",e(n.b,null,"s")," è:"),e("p",null,e(n.b,null,Ol(ol||(ol=yl`\left | \vec{B} \right | = \frac{\mu \cdot I}{2 \pi r}`)))),e("p",null,"Il campo magnetico così creato gira attorno al filo in senso antiorario."),e("p",null,"Due fili attraversati dalla ",e(o.a,null,"stessa corrente")," si attraggono, due fili attraversati da ",e(o.a,null,"corr"),e(r.a,null,"enti")," ",e(o.a,null,"opp"),e(r.a,null,"oste")," si respingono."))),e(t.a,{title:"Induzione elettromagnetica"},e(i.a,{title:"Forza elettromotrice indotta"},e("p",null,"Un conduttore perpendicolare ad un campo magnetico può ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo."),e("p",null,"La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore."),e("p",null,"Essa vale:"),e("p",null,e(n.b,null,Ol(rl||(rl=yl`\Delta V_{indotta} = v \cdot B \cdot L`)))),e("p",null,"Dove ",e(n.b,null,"v")," è la velocità del conduttore, ",e(n.b,null,"B")," è l'intensità del campo magnetico ed ",e(n.b,null,"L")," è la lunghezza del conduttore.")),e(i.a,{title:"Flusso magnetico in una spira"},e("p",null,"In un campo magnetico ",e(n.b,null,Ol(ul||(ul=yl`B`)))," uniforme e perpendicolare al piano di una spira di area ",e(n.b,null,Ol(cl||(cl=yl`A`))),", il flusso magnetico si può determinare con la ",e("i",null,"Legge di Faraday-Neumann-Lenz"),":"),e("p",null,e(n.b,null,Ol(sl||(sl=yl`\Phi_B = \vec{B} \cdot \vec{A} = B \cdot A \cdot \cos(\alpha)`)))))),e(t.a,null,e(i.a,{title:"Legge di Faraday-Neumann-Lenz"},e("p",null,"Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso."),e("p",null,e(n.b,null,Ol(pl||(pl=yl`\Delta V_{indotta} = - \frac{\Delta \Phi_B}{\Delta t}`)))),e("p",null,"Il meno è dovuto alla ",e("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Lenz"},"Legge di Lenz"),", che specifica qualitativamente il verso della forza elettromotrice indotta.")),e(i.a,{title:"Faraday in un solenoide"},e("p",null,"In un solenoide, la forza elettromotrice indotta è uguale a:"),e("p",null,e(n.b,null,Ol(dl||(dl=yl`\Delta V_{indotta} = - \frac{N \cdot \Delta \Phi_{B_{spira}}}{\Delta t} = - \frac{N \cdot B \cdot A \cdot cos(\alpha)}{\Delta t}`)))),e("p",null,"Dove ",e(n.b,null,Ol(ml||(ml=yl`N`)))," è il numero delle spire del solenoide.")),e(i.a,{title:"Legge di Ampère-Maxwell"},e("p",null,"Correnti o campi elettrici variabili creano un campo magnetico."))),e(t.a,{title:"Elettromagnetismo"},e(i.a,{title:"Onde elettromagnetiche"},e("p",null,"Nel vuoto, il campo elettrico ",e(n.b,null,Ol(fl||(fl=yl`E`)))," e il campo magnetico ",e(n.b,null,Ol(vl||(vl=yl`B`)))," sono perpendicolari tra loro e la direzione di propagazione, e sono entrambe funzioni del tempo."),e("p",null,"Si dice quindi che sono ",e("i",null,"onde elettromagnetiche"),"."),e("p",null,"Esse sono legate dalla relazione:"),e("p",null,e(n.b,null,Ol(_l||(_l=yl`E = c \cdot B`)))),e("p",null,"Dove ",e(n.b,null,Ol(gl||(gl=yl`c`)))," è la velocità delle onde (luce) nel vuoto, e a sua volta è uguale a:"),e("p",null,e(n.b,null,Ol(hl||(hl=yl`c = \frac{1}{\sqrt{\epsilon_0 \cdot \mu_0}} = 3.00 \cdot 10^8 \frac{m}{s}`))))),e(i.a,{title:"Formula delle onde"},e("p",null,e(n.b,null,Ol(bl||(bl=yl`A(t) = A_{max} \cdot \sin \left ( \frac{2 \pi}{\lambda} - \omega t + \phi \right )`)))),e("p",null,"Dove ",e(n.b,null,Ol(zl||(zl=yl`A_{max}`)))," è l'ampiezza massima che può avere l'onda, ",e(n.b,null,Ol(Ll||(Ll=yl`\frac{2 \pi}{\lambda} = \left | \vec{k} \right |`)))," è il vettore d'onda, ",e(n.b,null,Ol(ql||(ql=yl`\omega`)))," la frequenza angolare e ",e(n.b,null,Ol(El||(El=yl`\phi`)))," la fase."))),e(t.a,{title:"Spettroscopia"},e(i.a,{title:"Emissione"},e("p",null,"I solidi, se portati ad alta temperatura, emettono luce con uno ",e("a",{href:"https://it.wikipedia.org/wiki/Spettro_continuo"},"spettro continuo"),"."),e("p",null,"I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d'onda."),e("p",null,"In un gas di idrogeno, le lunghezze d'onda emesse sono ricavabili con:"),e("p",null,e(n.b,null,Ol(Dl||(Dl=yl`\frac{1}{\lambda} = R \left ( \frac{1}{4} - \frac{1}{n^2} \right )`)))),e("p",null,"Con ",e(n.b,null,Ol(Al||(Al=yl`R = 1.097 \cdot 10^7 \frac{1}{m}`))),", detta costante di Rydberg, e ",e(n.b,null,Ol(Fl||(Fl=yl`n`)))," un numero intero.")),e(i.a,{title:"Grandezza quantizzata"},e("p",null,"Una grandezza si dice quantizzata (o discreta) se può assumere solo determinati valori."),e("p",null,"Una grandezza si dice continua se può assumere qualsiasi valore e quindi se non è quantizzata."),e("p",null,"Energia, momento angolare e raggio sono quantizzati."),e("p",null,"Nota costante quantica è ",e(n.b,null,Ol(Cl||(Cl=yl`h`))),", la costante di Planck, ovvero il valore minimo possibile per la carica (talvolta espressa come ",e(n.b,null,Ol(Pl||(Pl=yl`\hbar = \left ( \frac{h}{2 \pi} \right )`))),"."))),e(t.a,null,e(i.a,{title:"Modello di Bohr"},e("p",null,"L'energia degli elettroni è quantizzata."),e("p",null,"Inoltre, per essi è valido che:"),e("p",null,e(n.b,null,Ol(Il||(Il=yl`m \cdot v_n \cdot 2 \pi \cdot r = n \cdot h`)))),e("p",null,"Ancora, il raggio delle orbite è uguale a:"),e("p",null,e(n.b,null,Ol(Sl||(Sl=yl`r_n = n^2 \cdot a_0 = n^2 \cdot \frac{\hbar}{m_{elettrone} \cdot k \cdot e^2} `)))),e("p",null,"Con ",e(n.b,null,Ol(wl||(wl=yl`a_0 = \left ( \frac{h}{2 \pi} \right )^2 \cdot \frac{1}{m_{elettrone} \cdot k \cdot e^2} = 5.29 \cdot 10^{-11} m`))),"."),e("p",null,"Infine, in ogni stato, l'energia è pari a:"),e("p",null,e(n.b,null,Ol(kl||(kl=yl`E_n = \frac{1}{n^2} \cdot E_1 = - \frac{1}{n^2} \cdot \frac{a_0^2}{2 \cdot m \cdot \hbar^4} = - \frac{1}{n^2} \cdot \frac{m_{elettrone} \cdot k^2 \cdot e^4}{2 \cdot \hbar^2}`)))),e("p",null,"Due elettroni non possono occupare lo stesso stato."),e("p",null,"Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di"))),e(t.a,null,e(i.a,{title:"Nei solidi"},e("p",null,"Nei solidi, le lunghezze d'onda sono talmente tanto vicine da poter essere considerate una banda."),e("p",null,"Possono però comunque avere dei gap dovuti agli intervalli di energia non ammessi."))),e(t.a,{title:"Semiconduttori"},e(i.a,{title:"Semiconduttori"},e("p",null,e(u.a,null,"Refactor this")),e("p",null,"Se la banda di emissione con energia più alta di un corpo è assente o è separata da un gap dell'ordine di grandezza maggiore di ",e(n.b,null,Ol(Nl||(Nl=yl`10^1 eV`))),", allora il corpo è un isolante."),e("p",null,"Se invece la banda di emissione si sovrappone a un altra, allora il corpo è un conduttore."),e("p",null,"Se il gap è invece dell'ordine di grandezza di ",e(n.b,null,Ol(Bl||(Bl=yl`1 eV`))),", allora il corpo è un semiconduttore.")),e(i.a,{title:"Lacune"},e("p",null,"Legami in cui ",e(o.a,null,"mancano elettroni"),"."),e("p",null,e(r.a,null,"Elettroni")," di altri legami possono spostarsi per colmare le ",e(o.a,null,"lacune"),", creandone altre, e spostandole in direzione opposta a quella della corrente.")),e(i.a,{title:"Accettori e donori"},e("p",null,"Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterrà:"),e("ul",null,e("li",null,"Con numero atomico maggiore, un semiconduttore di ",e(r.a,null,"tipo N")," con ",e(r.a,null,"elettroni in eccesso")," liberi di scorrere."),e("li",null,"Con numero atomico minore, un semiconduttore di ",e(o.a,null,"tipo P")," con ",e(o.a,null,"lacune in eccesso")," libere di catturare elettroni da altri legami.")),e("p",null,"Maggiore impurezza porta a maggiore conduttività.")),e(i.a,{title:"Temperatura"},e("p",null,"Aumentando la temperatura di un semiconduttore si aumenta la conduttività, perchè eccita le particelle e favorisce il movimento di ",e(r.a,null,"elettroni")," e 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\vec{v} \right | \sin \alpha`)))),e("p",null,e(n.b,null,Ol(m||(m=yl`\left | \vec{v}_y \right | = \left | \vec{v} \right | \cos \alpha`))))),e(i.a,{title:"Somma"},e("p",null,"Scomponi in componenti, poi sommali:"),e("p",null,e(n.b,null,Ol(f||(f=yl`\vec{v} + \vec{w} = (\vec{v}_x + \vec{w}_x) + (\vec{v}_y + \vec{w}_y)`)))),e("p",null,"Produce il vettore risultante dall'applicazione della regola del parallelogramma.")),e(i.a,{title:"Differenza"},e("p",null,"Alla fine è sempre una somma:"),e("p",null,e(n.b,null,Ol(v||(v=yl`\vec{v} - \vec{w} = (\vec{v}_x - \vec{w}_x) + (\vec{v}_y - \vec{w}_y)`)))),e("p",null,"Produce il vettore che parte da ",e(n.b,null,"w")," e arriva a ",e(n.b,null,"v"),".")),e(i.a,{title:"Prodotto scalare"},e("p",null,"Si chiama scalare perchè il risultato è uno scalare, non un vettore."),e("p",null,e(n.b,null,Ol(_||(_=yl`\vec{v} \cdot \vec{w} = \left | \vec{v} \right | \left | \vec{w} \right | \cos \alpha`)))),e("p",null,"Produce il modulo della proiezione di ",e(n.b,null,Ol(g||(g=yl`\vec{a}`)))," su ",e(n.b,null,Ol(h||(h=yl`\vec{b}`))),".")),e(i.a,{title:"Prodotto vettoriale"},e("p",null,"Si chiama vettoriale perchè il risultato è un altro vettore."),e("ul",null,e("li",null,e(n.b,null,Ol(b||(b=yl`\vec{c} = \vec{a} \times \vec{b}`)))),e("li",null,e(n.b,null,Ol(z||(z=yl`\left | \vec{c} \right | = \left | \vec{a} \right | \cdot \left | \vec{b} \right | \cdot \sin(\alpha)`)))),e("li",null,e("a",{href:"https://it.wikipedia.org/wiki/Regola_della_mano_destra"},"Regola della mano destra"))),e("p",null,"Non è commutativo!"))),e(t.a,{title:"Leggi di Newton"},e(i.a,{title:"1ᵃ: Inerzia"},e("p",null,"Se un corpo puntiforme ha forza risultante nulla, allora la sua velocità non cambia."),e("p",null,e(n.b,null,Ol(L||(L=yl`\Sigma \vec{F} = 0 \Longleftrightarrow \Delta v = 0`))))),e(i.a,{title:"2ᵃ: Proporzionalità"},e("p",null,"La forza risultante di un corpo è direttamente proporzionale alla sua accelerazione, e la costante di proporzionalità è la ",e("i",null,"massa"),"."),e("p",null,e(n.b,null,Ol(q||(q=yl`\Sigma \vec{F} = m \vec{a}`))))),e(i.a,{title:"3ᵃ: Azione e reazione"},e("p",null,"Due corpi esercitano forze uguali e opposte uno sull'altro."),e("p",null,e(n.b,null,Ol(E||(E=yl`\vec{F}_{21} = -\vec{F}_{12}`)))))),e(t.a,{title:"Forza di gravità"},e(i.a,{title:"Tra due corpi"},e("p",null,"Due corpi puntiformi si attirano uno verso l'altro con forza:"),e("p",null,e(n.b,null,Ol(D||(D=yl`\left | \vec{F} \right | = G \frac{m_1 m_2}{s^2}`)))),e("p",null,e(n.b,null,"G")," è la ",e("i",null,"costante di gravitazione universale")," e vale:"),e("p",null,e(n.b,null,Ol(A||(A=yl`G = 6.67 \cdot 10^{-11} \frac{N m^2}{{kg}^2}`))))),e(i.a,{title:"Verso la Terra"},e("p",null,"Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo è attratto verso la Terra con forza ",e("i",null,"peso")," uguale a:"),e("p",null,e(n.b,null,Ol(F||(F=yl`\left | \vec{F} \right | = g m`)))),e("p",null,e(n.b,null,"g")," è la ",e("i",null,"costante di gravità")," della Terra, e vale:"),e("p",null,e(n.b,null,Ol(C||(C=yl`g = 9.81 \frac{m}{s^2}`))))),e(i.a,{title:"Su pianeti diversi"},e("p",null,"Per pianeti diversi dalla Terra vale la stessa regola:"),e("p",null,e(n.b,null,Ol(P||(P=yl`\left | \vec{F} \right | = g m`)))),e("p",null,"L'unica differenza è che cambia la ",e("i",null,"costante di gravità"),":"),e("p",null,e(n.b,null,Ol(I||(I=yl`g_{luna} = 1.62 \frac{m}{s^2}`)))),e("p",null,e(n.b,null,Ol(S||(S=yl`g_{marte} = 3.71 \frac{m}{s^2}`)))))),e(t.a,{title:"Forze di contatto"},e(i.a,{title:"Normale"},e("p",null,"Si oppone alle forze applicate alla superficie di contatto."),e("p",null,"Un libro appoggiato su un tavolo ha la ",e("b",null,"forza di gravità")," che lo attira verso il terreno e la ",e("b",null,"forza normale")," che lo trattiene dal cadere.")),e(i.a,{title:"Attrito statico"},e("p",null,"Impedisce a un corpo di muoversi se non viene spinto da una forza che supera una certa soglia:"),e("p",null,e(n.b,null,Ol(w||(w=yl`\left | \vec{F} \right | \leq \mu_{s} \left | \vec{F}_{normale} \right |`))))),e(i.a,{title:"Attrito dinamico"},e("p",null,"Rallenta i corpi che si stanno muovendo finchè essi non si fermano:"),e("p",null,e(n.b,null,Ol(k||(k=yl`\left | \vec{F} \right | \leq \mu_{d} \left | \vec{F}_{normale} \right |`))))),e(i.a,{title:"Tensione"},e("p",null,"E' forza trasmessa tra due estremi di una fune."),e("p",null,"Può essere redirezionata per mezzo di carrucole.")),e(i.a,{title:"Elastica"},e("p",null,"Una molla cerca sempre di tornare alla sua posizione indeformata con forza:"),e("p",null,e(n.b,null,Ol(N||(N=yl`F = -k x`)))),e("p",null,"(E' negativa perchè la forza è opposta a quella applicata per deformarla.)"))),e(t.a,{title:"Cinematica"},e(i.a,{title:"Spostamento"},e("p",null,"È un vettore che indica la posizione di un corpo rispetto a un'origine."),e("p",null,e(n.b,null,Ol(B||(B=yl`\Delta \vec{s} = \vec{s}(fine) - \vec{s}(inizio)`))))),e(i.a,{title:"Velocità"},e("p",null,"È un vettore che misura la variazione di posizione nel tempo."),e("p",null,e(n.b,null,Ol(T||(T=yl`\vec{v} = \frac{\Delta \vec{s}}{\Delta t}`)))),e("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",e("i",null,"velocità istantanea"),":"),e("p",null,e(n.b,null,Ol(V||(V=yl`\vec{v} = \lim_{\Delta t \to 0} \frac{\Delta \vec{s}}{\Delta t} = \frac{d \vec{s}}{dt}`))))),e(i.a,{title:"Accelerazione"},e("p",null,"È un vettore che misura la variazione di velocità nel tempo."),e("p",null,e(n.b,null,Ol(x||(x=yl`\vec{a} = \frac{\Delta \vec{v}}{\Delta t}`)))),e("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",e("i",null,"accelerazione istantanea"),":"),e("p",null,e(n.b,null,Ol(y||(y=yl`\vec{a} = \lim_{\Delta v \to 0} \frac{\Delta \vec{v}}{\Delta t} = \frac{d \vec{v}}{d t} = \frac{d^2 \vec{s}}{d t^2}`))))),e(i.a,{title:e("span",null,"Quantità di moto ",e("small",null,"(momento lineare)"))},e("p",null,"La quantità di moto è una proprietà vettoriale dei corpi:"),e("p",null,e(n.b,null,Ol(O||(O=yl`\vec{p} = m \vec{v}`)))),e("p",null,"Se la forza risultante è nulla, la quantità di moto non cambia."),e("p",null,e(n.b,null,Ol(R||(R=yl`\Sigma \vec{F} = 0 \Longleftrightarrow \Delta \vec{p} = 0`)))))),e(t.a,{title:"Moto rettilineo uniforme"},e(i.a,{title:"Spostamento"},e("p",null,"La ",e("i",null,"legge oraria")," è:"),e("p",null,e(n.b,null,Ol(M||(M=yl`s(t) = v \cdot \Delta t + s(0)`))))),e(i.a,{title:"Velocità"},e("p",null,"È costante:"),e("p",null,e(n.b,null,Ol(U||(U=yl`v(t) = k`))))),e(i.a,{title:"Accelerazione"},e("p",null,"La velocità non varia:"),e("p",null,e(n.b,null,Ol(H||(H=yl`a(t) = 0`))))),e(i.a,{title:"Forze"},e("p",null,"Si applica la prima legge di Newton:"),e("p",null,e(n.b,null,"f(t) = 0")))),e(t.a,{title:"Moto rettilineo uniformemente accelerato"},e(i.a,{title:"Spostamento"},e("p",null,"La ",e("i",null,"legge oraria")," è:"),e("p",null,e(n.b,null,Ol(Q||(Q=yl`s(t) = \frac{1}{2} a \cdot (\Delta t)^2 + v(0) \cdot (\Delta t) + s(0)`))))),e(i.a,{title:"Velocità"},e("p",null,"È una retta:"),e("p",null,e(n.b,null,Ol(G||(G=yl`v(t) = a \Delta t + v(0)`))))),e(i.a,{title:"Accelerazione"},e("p",null,"È costante:"),e("p",null,e(n.b,null,Ol(W||(W=yl`a(t) = k`))))),e(i.a,{title:"Forze"},e("p",null,"Si applica la prima legge di Newton:"),e("p",null,e(n.b,null,"f(t) = m a")))),e(t.a,{title:"Moto armonico semplice"},e(i.a,{title:"Ampiezza"},e("p",null,"E' la distanza dal centro massima che raggiunge il corpo."),e("p",null,"(L'ampiezza di una sinusoide.)")),e(i.a,{title:"Velocità angolare"},e("p",null,"Indica quanto in fretta cambia la posizione del corpo."),e("p",null,"Dipende dal periodo:"),e("p",null,e(n.b,null,Ol(j||(j=yl`\omega = \frac{2 \pi}{T}`))))),e(i.a,{title:"Spostamento"},e("p",null,"E' una sinusoide:"),e("p",null,e(n.b,null,Ol(J||(J=yl`s(t) = A \sin (\omega \cdot t + \phi)`))))),e(i.a,{title:"Velocità"},e("p",null,"E' la sinusoide dello spostamento, sfasata di ",e(n.b,null,Ol(Y||(Y=yl`\frac{\pi}{2}`))),":"),e("p",null,e(n.b,null,Ol(K||(K=yl`v(t) = A \sin (\omega \cdot t + \phi + \frac{\pi}{2})`))))),e(i.a,{title:"Accelerazione"},e("p",null,"E' la sinusoide della velocità, sfasata di ",e(n.b,null,Ol(X||(X=yl`\pi`))),":"),e("p",null,e(n.b,null,Ol($||($=yl`a(t) = A \sin (\omega \cdot t + \phi + \pi)`))))),e(i.a,{title:"Forze"},e("p",null,"Si applica la prima legge di Newton:"),e("p",null,e(n.b,null,"f(t) = m a")))),e(t.a,{title:"Moti composti"},e(i.a,{title:"Moto parabolico"},e("p",null,"Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.")),e(i.a,{title:"Moto circolare uniforme"},e("p",null,"Il moto parabolico è dato sommando due moti armonici semplici: uno sull'asse X, e l'altro, sfasato di ",e(n.b,null,Ol(Z||(Z=yl`\frac{\pi}{2}`))),", sull'asse Y."))),e(t.a,{title:"Moto circolare uniforme"},e(i.a,null,e("h3",null,"Velocità angolare"),e("p",null,"Quanto cambia la fase nel tempo."),e("p",null,e(n.b,null,Ol(ee||(ee=yl`\omega = \frac{2 \pi}{T}`))))),e(i.a,{title:"Fase"},e("p",null,"E' l'angolo percorso dal corpo rispetto alla posizione iniziale."),e("p",null,"Si indica con ",e(n.b,null,Ol(le||(le=yl`\phi`))),", e generalmente si usa in radianti.")),e(i.a,{title:"Velocità"},e("p",null,"Si applicano le formule per la circonferenza:"),e("p",null,e(n.b,null,Ol(ae||(ae=yl`v = \frac{\Delta s}{t} = \frac{2 \pi \cdot r}{T} = \omega r`))))),e(i.a,{title:"Accelerazione"},e("p",null,"Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto:"),e("p",null,e(n.b,null,Ol(ne||(ne=yl`a = \frac{v^2}{r} = r \cdot \omega^2 = v \cdot \omega`))))),e(i.a,{title:"Forza centripeta"},e("p",null,"È verso il centro e si calcola con:"),e("p",null,e(n.b,null,Ol(ie||(ie=yl`F = m \cdot a`)))))),e(t.a,{title:"Lavoro ed energia"},e(i.a,{title:"Lavoro"},e("p",null,"E' compiuto da una forza che sposta un corpo."),e("p",null,e(n.b,null,Ol(te||(te=yl`W = \vec{F} \cdot \vec{s} = F \cdot \Delta s \cdot cos(\alpha )`)))),e("p",null,"(Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)")),e(i.a,{title:"Energia cinetica"},e("p",null,"Un corpo ha energia cinetica in ogni momento uguale a:"),e("p",null,e(n.b,null,Ol(oe||(oe=yl`E_c = \frac{1}{2} m v^2`)))),e("p",null,"Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:"),e("p",null,e(n.b,null,Ol(re||(re=yl`\Delta E_c = W`))))),e(i.a,{title:"Energia potenziale gravitazionale"},e("p",null,"Un corpo ha energia potenziale in ogni momento pari a:"),e("p",null,e(n.b,null,Ol(ue||(ue=yl`E_{p_g} = m \cdot g \cdot h`)))),e("p",null,"(Con ",e(n.b,null,"h")," uguale a un altezza scelta come punto di riferimento.)")),e(i.a,{title:"Energia potenziale elastica"},e("p",null,"Una molla ha sempre energia potenziale elastica pari a:"),e("p",null,e(n.b,null,Ol(ce||(ce=yl`E_{p_e} = \frac{1}{2} k x^2`))))),e(i.a,{title:"Forze conservative"},e("p",null,"Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo."),e("p",null,"Ad esempio, è conservativa la ",e("i",null,"forza di gravità"),", ma ",e("b",null,"non")," è conservativa la forza di attrito."),e("p",null,"Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:"),e("p",null,e(n.b,null,Ol(se||(se=yl`E = E_k + E_p`))))),e(i.a,{title:"Potenza"},e("p",null,"È la velocità di trasferimento di energia:"),e("p",null,e(n.b,null,Ol(pe||(pe=yl`P = \frac{\Delta E}{\Delta t}`)))))),e(t.a,{title:"Elettrostatica"},e(i.a,{title:"Carica elettrica"},e("p",null,"È una proprietà dei corpi che può essere ",e(o.a,null,"positiva")," o ",e(r.a,null,"negativa"),"."),e("p",null,"Si conserva: in un sistema chiuso la carica totale è costante."),e("p",null,"Esiste un'unità elementare: ",e(n.b,null,Ol(de||(de=yl`C_{elettrone} = 1.602 \cdot 10^{-19}`))),"."),e("p",null,"Cariche ",e(o.a,null,"opp"),e(r.a,null,"oste")," si attraggono; cariche ",e(o.a,null,"uguali")," si respingono.")),e(i.a,{title:"Conduttori e isolanti"},e("p",null,"Più ",e("a",{href:"https://it.wikipedia.org/wiki/Ione"},"ioni")," ha un corpo, meglio la carica si muove attraverso di esso."),e("p",null,"I corpi in cui la carica si muove bene sono ",e("i",null,"conduttori"),", mentre quelli in cui si muove difficilmente sono ",e("i",null,"isolanti"),"."),e("p",null,e("i",null,"Il corpo umano è un buon conduttore.")))),e(t.a,{title:"Polarizzazione"},e(i.a,{title:"Polarizzazione"},e("p",null,"E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona."))),e(t.a,null,e(i.a,{title:"Messa a terra"},e("p",null,"Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno ",e("i",null,"equilibrate")," e il corpo diventerà elettricamente neutro (con stesso numero di ",e(o.a,null,"cariche positive")," e ",e(r.a,null,"negative")," all'interno)."))),e(t.a,null,e(i.a,{title:"Polarizzazione per strofinio"},e("p",null,"Strofinando tra loro due corpi isolanti, essi si ",e("i",null,"polarizzeranno per strofinio"),".")),e(i.a,{title:"Polarizzazione per contatto"},e("p",null,"Toccando un conduttore con un corpo carico, il conduttore potrà ",e("i",null,"polarizzarsi per contatto"),".")),e(i.a,{title:"Polarizzazione per induzione"},e("p",null,'Se un corpo conduttore ha cariche "esterne" di un ',e(o.a,null,"certo segno")," vicino, esso avrà tutte le cariche del ",e(r.a,null,"segno opposto")," in equilibrio vicino alle cariche esterne, e tutte le cariche dello ",e(o.a,null,"stesso segno")," più lontano possibile da esse."),e("p",null,"Mettendo a terra il conduttore, nuove cariche del ",e(r.a,null,"segno opposto")," saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate."),e("p",null,"Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà ",e(r.a,null,"caricato del segno opposto")," rispetto alle cariche esterne."))),e(t.a,{title:"Forza elettrica"},e(i.a,{title:"Legge di Coulomb"},e("p",null,"Due corpi carichi si attraggono tra loro con forza:"),e("p",null,e(n.b,null,Ol(me||(me=yl`\left | \vec{F}_{elettrica} \right | = \frac{-k \cdot q_1 \cdot q_2}{s^2}`)))),e("p",null,e(n.b,null,Ol(fe||(fe=yl`k`)))," è la ",e("i",null,"costante di Coulomb"),", e vale ",e(n.b,null,Ol(ve||(ve=yl`k = 8.99 \cdot 10^9 \frac{N \cdot m^2}{C^2}`))),".")),e(i.a,{title:"Permeabilità dello spazio vuoto"},e("p",null,"La costante ",e(n.b,null,Ol(_e||(_e=yl`k`)))," è in realtà dipendente da un altra costante, ",e(n.b,null,Ol(ge||(ge=yl`\epsilon_0`))),", la ",e("i",null,"permeabilità del vuoto"),"."),e("p",null,e(n.b,null,Ol(he||(he=yl`k = \frac{1}{4 \pi \cdot \epsilon_0}`)))),e("p",null,e(n.b,null,Ol(be||(be=yl`\left | \vec{F}_{elettrica} \right | = \frac{q_1 \cdot q_2}{4 \pi \cdot \epsilon_0 \cdot s^2}`))))),e(i.a,{title:"Campo elettrico"},e("p",null,"Misura che forza viene applicata in ogni punto su una carica unitaria:"),e("p",null,e(n.b,null,Ol(ze||(ze=yl`\vec{E} = \frac{\vec{F}_{elettrica}}{q} = \frac{-k \cdot q}{s^2}`))))),e(i.a,{title:"Flusso elettrico"},e("p",null,'È la differenza tra "quanto" campo elettrico ',e(o.a,null,"entra")," e quanto campo elettrico ",e(r.a,null,"esce")," da una certa area."),e("p",null,"In qualsiasi superficie chiusa, il flusso elettrico è uguale alla componente perpendicolare del campo elettrico moltiplicato per l'area."),e("p",null,e(n.b,null,Ol(Le||(Le=yl`\Phi_E = \vec{E} \cdot \vec{A}`)))),e("p",null,"Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:"),e("p",null,e(n.b,null,Ol(qe||(qe=yl`\Phi_E = \vec{E} \cdot \vec{A} = E_\perp \cdot A \cdot \cos(\alpha)`)))),e("p",null,e(u.a,null,"Circa. E' una specie di integrale..."))),e(i.a,{title:"Legge di Gauss per i campi elettrostatici"},e("p",null,"Il flusso elettrico è direttamente proporzionale alla carica presente all'interno della superficie."),e("p",null,e(n.b,null,Ol(Ee||(Ee=yl`\Phi_E = 4 \pi \cdot k \cdot q = \frac{q}{\epsilon_0}`)))),e("p",null,"Ovvero, i campi elettrostatici sono generati dalle cariche elettriche."))),e(t.a,{title:"Energia elettrica"},e(i.a,{title:"Energia potenziale elettrica"},e("p",null,"Un corpo carico vicino ad altre cariche possiede un'",e("i",null,"energia potenziale elettrica")," ",e(n.b,null,Ol(De||(De=yl`U_e`))),"."))),e(t.a,{title:"Circuiti elettrici"},e(i.a,{title:e("span",null,"Potenziale elettrico ",e("small",null,"(tensione)"))},e("p",null,"È il valore dell'energia potenziale elettrica per una carica unitaria."),e("p",null,e(n.b,null,Ol(Ae||(Ae=yl`V = \frac{U_e}{q}`)))),e("p",null,"La sua unità di misura è il Volt (",e(n.b,null,Ol(Fe||(Fe=yl`V`))),")."),e("p",null,"In una batteria è detto ",e("i",null,"forza elettromotrice"),", e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli.")),e(i.a,{title:e("span",null,"Corrente elettrica ",e("small",null,"(intensità)"))},e("p",null,"Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo."),e("p",null,e(n.b,null,Ol(Ce||(Ce=yl`I = \frac{\Delta q}{\Delta t}`)))),e("p",null,"Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla."),e("p",null,"La sua unità di misura è l'Ampere (",e(n.b,null,Ol(Pe||(Pe=yl`A`))),").")),e(i.a,{title:e("span",null,"Corrente continua ",e("small",null,"(",e("abbr",{title:"Direct Current"},"DC"),")"))},e("p",null,"Quando in un circuito la direzione della corrente è costante.")),e(i.a,{title:e("span",null,"Corrente alternata ",e("small",null,"(",e("abbr",{title:"Alternate Current"},"AC"),")"))},e("p",null,"Quando in un circuito la direzione della corrente si alterna periodicamente.")),e(i.a,{title:"Potenza elettrica"},e("p",null,"Possiamo calcolare la potenza di un circuito:"),e("p",null,e(n.b,null,Ol(Ie||(Ie=yl`P = \frac{\Delta U_e}{\Delta t} = I \cdot \Delta V = I^2 \cdot R = \frac{(\Delta V)^2}{R}`)))))),e(t.a,{title:"Elementi di un circuito"},e(i.a,{title:"Resistore"},e("p",null,"Riduce l'intensità di corrente, e converte parte del potenziale in calore."),e("p",null,"Il potenziale utilizzato è pari a:"),e("p",null,e(n.b,null,Ol(Se||(Se=yl`V = R \cdot I`)))),e("p",null,"Dove ",e(n.b,null,Ol(we||(we=yl`R`)))," è una costante detta ",e("i",null,"resistenza")," con unità di misura Ohm (",e(n.b,null,Ol(ke||(ke=yl`\Omega`))),")."),e("p",null,"La resistenza di un conduttore vale:"),e("p",null,e(n.b,null,Ol(Ne||(Ne=yl`R = \rho \frac{L_{unghezza}}{A_{rea}}`)))),e("p",null,e(n.b,null,Ol(Be||(Be=yl`\rho`)))," è la ",e("i",null,"resistività")," del materiale, e varia in base alla temperatura:"),e("p",null,e(n.b,null,Ol(Te||(Te=yl`\rho = \rho_0 (1 + \alpha(T - T_0))`))))),e(i.a,{title:"Condensatore"},e("p",null,"Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito."),e("p",null,"Per farlo, cattura cariche ",e(o.a,null,"positive")," e ",e(r.a,null,"negative")," sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro."),e("p",null,"Ha una ",e("b",null,"capacità")," caratteristica, che in un condensatore a facce piane parallele è:"),e("p",null,e(n.b,null,Ol(Ve||(Ve=yl`C = \frac{q_{massima}}{\Delta V}`)))),e("p",null,"Condensatori di capacità maggiore immagazzinano più potenziale con meno carica."),e("p",null,"La capacità aumenta se viene messo qualcosa tra le armature:"),e("p",null,e(n.b,null,Ol(xe||(xe=yl`C_{nuova} = \kappa \cdot \frac{\epsilon_0 \cdot A}{s}`)))),e("p",null,"Dove ",e(n.b,null,Ol(ye||(ye=yl`\kappa`)))," è la ",e("i",null,"costante dielettrica relativa")," del materiale inserito, ",e(n.b,null,Ol(Oe||(Oe=yl`A`)))," l'area di una armatura e ",e(n.b,null,Ol(Re||(Re=yl`s`)))," la distanza tra le due armature."),e("p",null,"Se il campo elettrico creatosi tra le due armature supera la ",e("i",null,"rigidità dielettrica")," del condensatore, la carica immagazzinata viene persa e ha luogo un ",e("i",null,"breakdown"),"."),e("p",null,"La sua unità di misura è il Farad (",e(n.b,null,Ol(Me||(Me=yl`Fa`))),")")),e(i.a,{title:"Amperometro"},e("p",null,"Misura la corrente elettrica se messo in serie."),e("p",null,"(Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)")),e(i.a,{title:"Voltmetro"},e("p",null,"Misura la differenza di potenziale se messo in parallelo."),e("p",null,"(Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)"))),e(t.a,{title:"Principi di Kirchhoff"},e(i.a,{title:"Legge dei nodi"},e("p",null,"Per nodo si intende un qualsiasi punto del circuito."),e("p",null,"Da un nodo entra ed esce la stessa corrente.")),e(i.a,{title:"Legge delle maglie"},e("p",null,"Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito."),e("p",null,"In una maglia chiusa, la somma delle differenze di potenziale è 0."))),e(t.a,{title:"Serie e Parallelo"},e(i.a,{title:"Circuito in serie"},e("p",null,"Più parti di circuito sono ",e("i",null,"in serie")," se sono consecutive e senza biforcazioni."),e("p",null,"Parti di circuito in serie sono attraversate dalla stessa corrente.")),e(i.a,{title:"Circuito in parallelo"},e("p",null,"Più parti di circuito sono ",e("i",null,"in parallelo")," tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo."),e("p",null,"Parti di circuito in parallelo hanno la stessa differenza di potenziale."))),e(t.a,{title:"Resistenze equivalenti"},e(i.a,{title:"Circuiti in serie"},e("p",null,"Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:"),e("p",null,e(n.b,null,Ol(Ue||(Ue=yl`R_{serie} = \sum_{i=1}^{n} R_i`))))),e(i.a,{title:"Circuiti in parallelo"},e("p",null,"Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:"),e("p",null,e(n.b,null,Ol(He||(He=yl`R_{parallelo} = \frac{1}{\sum_{i=1}^{n} \frac{1}{R_i}}`)))))),e(t.a,{title:"Condensatori equivalenti"},e(i.a,{title:"Circuiti in serie"},e("p",null,"Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacità di:"),e("p",null,e(n.b,null,Ol(Qe||(Qe=yl`C_{serie} = \frac{1}{\sum_{i=1}^{n} \frac{1}{C_i}}`))))),e(i.a,{title:"Circuiti in parallelo"},e("p",null,"Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacità della somma di tutti quelli sostituiti:"),e("p",null,e(n.b,null,Ol(Ge||(Ge=yl`C_{parallelo} = \sum_{i=1}^{n} C_n`)))))),e(t.a,{title:"Magnetismo"},e(i.a,{title:"Permeabilità magnetica dello spazio vuoto"},e("p",null,"E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente."),e("p",null,e(n.b,null,Ol(We||(We=yl`\mu_0 = 4 \pi \cdot 10^{-7} \frac{H}{m}`)))," (",e(n.b,null,Ol(je||(je=yl`\frac{N}{A^2}`))),")")),e(i.a,{title:"Campo magnetico"},e("p",null,"Come un campo elettrico, ma per i magneti."),e("p",null,"Il suo simbolo è ",e(n.b,null,Ol(Je||(Je=yl`B`))),", e la sua unità di misura è il Tesla (",e(n.b,null,"T"),").")),e(i.a,{title:"Flusso magnetico"},e("p",null,'È "quanto" campo magnetico ',e("b",null,"attraversa")," un percorso chiuso."),e("p",null,'Per qualsiasi percorso chiuso, il flusso magnetico è uguale alla somma di tutti i "sottoflussi" magnetici calcolati sui suoi lati.'),e("p",null,e(n.b,null,Ol(Ye||(Ye=yl`\Phi_{B_{i}} = \vec{B} \cdot \vec{L}_n = B \cdot L_i \cdot \sin(\alpha) = B_\parallel \cdot L_i`)))),e("p",null,e(n.b,null,Ol(Ke||(Ke=yl`\Phi_{B} = \sum_{i=0}^{n_{lati}} \Phi_{Bn}`)))),e("p",null,"La sua unità di misura è il Weber (",e(n.b,null,Ol(Xe||(Xe=yl`Wb = T \cdot m^2`))),").")),e(i.a,{title:"Legge di Gauss per i campi magnetici"},e("p",null,"Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo."),e("p",null,"Ovvero, non esistono monopoli magnetici.")),e(i.a,{title:"Legge di Ampère"},e("p",null,"L'intensità di corrente che attraversa un percorso chiuso è direttamente proporzionale al flusso magnetico dello stesso percorso."),e("p",null,e(n.b,null,Ol($e||($e=yl`\Phi_B = \mu_0 \cdot I`)))))),e(t.a,{title:"Forze magnetiche"},e(i.a,{title:e("span",null,"Forza magnetica su carica puntiforme ",e("small",null,"(Forza di Lorentz)"))},e("p",null,"I campi magnetici applicano una forza sulle cariche vicine:"),e("p",null,e(n.b,null,Ol(Ze||(Ze=yl`\vec{F}_{B} = q \cdot (\vec{v} \times \vec{B})`)))),e("p",null,"Dove ",e(n.b,null,Ol(el||(el=yl`\vec{B}`)))," è l'intensità del campo magnetico e ",e(n.b,null,Ol(ll||(ll=yl`\vec{v}`)))," la velocità della carica considerata."),e("p",null,"Si ha una forza massima se la velocità è perpendicolare al campo magnetico."),e("p",null,"In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme.")),e(i.a,{title:"Forza magnetica in un filo"},e("p",null,"I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:"),e("p",null,e(n.b,null,Ol(al||(al=yl`\vec{F}_{magnetica} = I \cdot (\vec{L} \times \vec{B})`)))," ",e("a",{href:"https://it.openprof.com/wb/forza_di_lorentz_su_un_filo_percorso_da_corrente?ch=360"},"[1]")),e("p",null,"Dove ",e(n.b,null,Ol(nl||(nl=yl`I`)))," è la corrente elettrica, ",e(n.b,null,Ol(il||(il=yl`\vec{L}`)))," è un vettore che punta nella direzione di scorrimento della corrente e ha come modulo la lunghezza del conduttore."))),e(t.a,{title:"Campi magnetici"},e(i.a,{title:"Campo magnetico in una spira"},e("p",null,"Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.")),e(i.a,{title:"Campo magnetico di un solenoide"},e("p",null,"Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro."),e("p",null,"All'interno del solenoide si crea un campo (quasi) uniforme:"),e("p",null,e(n.b,null,Ol(tl||(tl=yl`\left | \vec{B} \right | = \mu_0 \cdot I \cdot \frac{A_{vvolgimenti}}{L_{unghezzafilo}}`))))),e(i.a,{title:"Legge di Oersted"},e("p",null,e("i",null,"Caso particolare della ",e("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Amp%C3%A8re"},"Legge di Ampère"),".")),e("p",null,"Il modulo del campo magnetico ",e(n.b,null,"B")," prodotto da un filo in cui passa una corrente continua ",e(n.b,null,"I")," alla distanza ",e(n.b,null,"s")," è:"),e("p",null,e(n.b,null,Ol(ol||(ol=yl`\left | \vec{B} \right | = \frac{\mu \cdot I}{2 \pi r}`)))),e("p",null,"Il campo magnetico così creato gira attorno al filo in senso antiorario."),e("p",null,"Due fili attraversati dalla ",e(o.a,null,"stessa corrente")," si attraggono, due fili attraversati da ",e(o.a,null,"corr"),e(r.a,null,"enti")," ",e(o.a,null,"opp"),e(r.a,null,"oste")," si respingono."))),e(t.a,{title:"Induzione elettromagnetica"},e(i.a,{title:"Forza elettromotrice indotta"},e("p",null,"Un conduttore perpendicolare ad un campo magnetico può ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo."),e("p",null,"La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore."),e("p",null,"Essa vale:"),e("p",null,e(n.b,null,Ol(rl||(rl=yl`\Delta V_{indotta} = v \cdot B \cdot L`)))),e("p",null,"Dove ",e(n.b,null,"v")," è la velocità del conduttore, ",e(n.b,null,"B")," è l'intensità del campo magnetico ed ",e(n.b,null,"L")," è la lunghezza del conduttore.")),e(i.a,{title:"Flusso magnetico in una spira"},e("p",null,"In un campo magnetico ",e(n.b,null,Ol(ul||(ul=yl`B`)))," uniforme e perpendicolare al piano di una spira di area ",e(n.b,null,Ol(cl||(cl=yl`A`))),", il flusso magnetico si può determinare con la ",e("i",null,"Legge di Faraday-Neumann-Lenz"),":"),e("p",null,e(n.b,null,Ol(sl||(sl=yl`\Phi_B = \vec{B} \cdot \vec{A} = B \cdot A \cdot \cos(\alpha)`)))))),e(t.a,null,e(i.a,{title:"Legge di Faraday-Neumann-Lenz"},e("p",null,"Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso."),e("p",null,e(n.b,null,Ol(pl||(pl=yl`\Delta V_{indotta} = - \frac{\Delta \Phi_B}{\Delta t}`)))),e("p",null,"Il meno è dovuto alla ",e("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Lenz"},"Legge di Lenz"),", che specifica qualitativamente il verso della forza elettromotrice indotta.")),e(i.a,{title:"Faraday in un solenoide"},e("p",null,"In un solenoide, la forza elettromotrice indotta è uguale a:"),e("p",null,e(n.b,null,Ol(dl||(dl=yl`\Delta V_{indotta} = - \frac{N \cdot \Delta \Phi_{B_{spira}}}{\Delta t} = - \frac{N \cdot B \cdot A \cdot cos(\alpha)}{\Delta t}`)))),e("p",null,"Dove ",e(n.b,null,Ol(ml||(ml=yl`N`)))," è il numero delle spire del solenoide.")),e(i.a,{title:"Legge di Ampère-Maxwell"},e("p",null,"Correnti o campi elettrici variabili creano un campo magnetico."))),e(t.a,{title:"Elettromagnetismo"},e(i.a,{title:"Onde elettromagnetiche"},e("p",null,"Nel vuoto, il campo elettrico ",e(n.b,null,Ol(fl||(fl=yl`E`)))," e il campo magnetico ",e(n.b,null,Ol(vl||(vl=yl`B`)))," sono perpendicolari tra loro e la direzione di propagazione, e sono entrambe funzioni del tempo."),e("p",null,"Si dice quindi che sono ",e("i",null,"onde elettromagnetiche"),"."),e("p",null,"Esse sono legate dalla relazione:"),e("p",null,e(n.b,null,Ol(_l||(_l=yl`E = c \cdot B`)))),e("p",null,"Dove ",e(n.b,null,Ol(gl||(gl=yl`c`)))," è la velocità delle onde (luce) nel vuoto, e a sua volta è uguale a:"),e("p",null,e(n.b,null,Ol(hl||(hl=yl`c = \frac{1}{\sqrt{\epsilon_0 \cdot \mu_0}} = 3.00 \cdot 10^8 \frac{m}{s}`))))),e(i.a,{title:"Formula delle onde"},e("p",null,e(n.b,null,Ol(bl||(bl=yl`A(t) = A_{max} \cdot \sin \left ( \frac{2 \pi}{\lambda} - \omega t + \phi \right )`)))),e("p",null,"Dove ",e(n.b,null,Ol(zl||(zl=yl`A_{max}`)))," è l'ampiezza massima che può avere l'onda, ",e(n.b,null,Ol(Ll||(Ll=yl`\frac{2 \pi}{\lambda} = \left | \vec{k} \right |`)))," è il vettore d'onda, ",e(n.b,null,Ol(ql||(ql=yl`\omega`)))," la frequenza angolare e ",e(n.b,null,Ol(El||(El=yl`\phi`)))," la fase."))),e(t.a,{title:"Spettroscopia"},e(i.a,{title:"Emissione"},e("p",null,"I solidi, se portati ad alta temperatura, emettono luce con uno ",e("a",{href:"https://it.wikipedia.org/wiki/Spettro_continuo"},"spettro continuo"),"."),e("p",null,"I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d'onda."),e("p",null,"In un gas di idrogeno, le lunghezze d'onda emesse sono ricavabili con:"),e("p",null,e(n.b,null,Ol(Dl||(Dl=yl`\frac{1}{\lambda} = R \left ( \frac{1}{4} - \frac{1}{n^2} \right )`)))),e("p",null,"Con ",e(n.b,null,Ol(Al||(Al=yl`R = 1.097 \cdot 10^7 \frac{1}{m}`))),", detta costante di Rydberg, e ",e(n.b,null,Ol(Fl||(Fl=yl`n`)))," un numero intero.")),e(i.a,{title:"Grandezza quantizzata"},e("p",null,"Una grandezza si dice quantizzata (o discreta) se può assumere solo determinati valori."),e("p",null,"Una grandezza si dice continua se può assumere qualsiasi valore e quindi se non è quantizzata."),e("p",null,"Energia, momento angolare e raggio sono quantizzati."),e("p",null,"Nota costante quantica è ",e(n.b,null,Ol(Cl||(Cl=yl`h`))),", la costante di Planck, ovvero il valore minimo possibile per la carica (talvolta espressa come ",e(n.b,null,Ol(Pl||(Pl=yl`\hbar = \left ( \frac{h}{2 \pi} \right )`))),"."))),e(t.a,null,e(i.a,{title:"Modello di Bohr"},e("p",null,"L'energia degli elettroni è quantizzata."),e("p",null,"Inoltre, per essi è valido che:"),e("p",null,e(n.b,null,Ol(Il||(Il=yl`m \cdot v_n \cdot 2 \pi \cdot r = n \cdot h`)))),e("p",null,"Ancora, il raggio delle orbite è uguale a:"),e("p",null,e(n.b,null,Ol(Sl||(Sl=yl`r_n = n^2 \cdot a_0 = n^2 \cdot \frac{\hbar}{m_{elettrone} \cdot k \cdot e^2} `)))),e("p",null,"Con ",e(n.b,null,Ol(wl||(wl=yl`a_0 = \left ( \frac{h}{2 \pi} \right )^2 \cdot \frac{1}{m_{elettrone} \cdot k \cdot e^2} = 5.29 \cdot 10^{-11} m`))),"."),e("p",null,"Infine, in ogni stato, l'energia è pari a:"),e("p",null,e(n.b,null,Ol(kl||(kl=yl`E_n = \frac{1}{n^2} \cdot E_1 = - \frac{1}{n^2} \cdot \frac{a_0^2}{2 \cdot m \cdot \hbar^4} = - \frac{1}{n^2} \cdot \frac{m_{elettrone} \cdot k^2 \cdot e^4}{2 \cdot \hbar^2}`)))),e("p",null,"Due elettroni non possono occupare lo stesso stato."),e("p",null,"Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di"))),e(t.a,null,e(i.a,{title:"Nei solidi"},e("p",null,"Nei solidi, le lunghezze d'onda sono talmente tanto vicine da poter essere considerate una banda."),e("p",null,"Possono però comunque avere dei gap dovuti agli intervalli di energia non ammessi."))),e(t.a,{title:"Semiconduttori"},e(i.a,{title:"Semiconduttori"},e("p",null,e(u.a,null,"Refactor this")),e("p",null,"Se la banda di emissione con energia più alta di un corpo è assente o è separata da un gap dell'ordine di grandezza maggiore di ",e(n.b,null,Ol(Nl||(Nl=yl`10^1 eV`))),", allora il corpo è un isolante."),e("p",null,"Se invece la banda di emissione si sovrappone a un altra, allora il corpo è un conduttore."),e("p",null,"Se il gap è invece dell'ordine di grandezza di ",e(n.b,null,Ol(Bl||(Bl=yl`1 eV`))),", allora il corpo è un semiconduttore.")),e(i.a,{title:"Lacune"},e("p",null,"Legami in cui ",e(o.a,null,"mancano elettroni"),"."),e("p",null,e(r.a,null,"Elettroni")," di altri legami possono spostarsi per colmare le ",e(o.a,null,"lacune"),", creandone altre, e spostandole in direzione opposta a quella della corrente.")),e(i.a,{title:"Accettori e donori"},e("p",null,"Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterrà:"),e("ul",null,e("li",null,"Con numero atomico maggiore, un semiconduttore di ",e(r.a,null,"tipo N")," con ",e(r.a,null,"elettroni in eccesso")," liberi di scorrere."),e("li",null,"Con numero atomico minore, un semiconduttore di ",e(o.a,null,"tipo P")," con ",e(o.a,null,"lacune in eccesso")," libere di catturare elettroni da altri legami.")),e("p",null,"Maggiore impurezza porta a maggiore conduttività.")),e(i.a,{title:"Temperatura"},e("p",null,"Aumentando la temperatura di un semiconduttore si aumenta la conduttività, perchè eccita le particelle e favorisce il movimento di ",e(r.a,null,"elettroni")," e ",e(o.a,null,"lacune"),"."))),e(t.a,{title:e("span",null,"Ottica ",e("small",null,"(non l'abbiamo fatta)"))},e(i.a,{title:"Assorbimento e riflessione"},e("p",null,"I corpi possono assorbire o riflettere le onde elettromagnetiche che li colpiscono.")),e(i.a,{title:"Corpo nero"},e("p",null,"Un corpo nero è un corpo che assorbe tutte le onde elettromagnetiche che riceve senza rifletterne nessuna."),e("p",null,"Le onde assorbite vengono poi riemesse sotto forma di un onda di ",e(n.b,null,Ol(Tl||(Tl=yl`\lambda`)))," variabile in base alla temperatura."),e("p",null,e(n.b,null,Ol(Vl||(Vl=yl`\lambda_{max} \cdot T`)))," è costante.")),e(i.a,{title:"Teoria di Planck per il corpo nero"},e("p",null,"L'energia assorbita e emessa dai corpi neri è quantizzata.")),e(i.a,{title:"Fotone"},e("p",null,"Un onda magnetica con un quanto di energia è detta ",e("i",null,"fotone"),":"),e("p",null,e(n.b,null,Ol(xl||(xl=yl`E_{fotone} = h \cdot f`))))),e(i.a,{title:"Effetto fotoelettrico"},e("p",null,"A volte, i 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",t("a",{href:"http://personale.unimore.it/rubrica/dettaglio/llarocca"},"Luca La Rocca"),".")),t(r.a,{title:t("a",{href:"https://github.com/Steffo99/cleaver"},t(a.a,{icon:c.a})," Cleaver")},t("p",null,"Progetto in Java sviluppato per l'esame di ",t("a",{href:"http://personale.unimore.it/rubrica/contenutiad/gcabri/2019/58026/N0/N0/9999"},"Programmazione ad Oggetti")," del ",t("a",{href:"https://www.unimore.it/didattica/mlaurea.html?ID=54"},"corso triennale di Informatica")," all'",t("a",{href:"https://www.unimore.it/"},"Unimore"),", tenuto dai Prof. ",t("a",{href:"http://personale.unimore.it/rubrica/dettaglio/gcabri"},"Giacomo Cabri")," e ",t("a",{href:"http://personale.unimore.it/Rubrica/Dettaglio/n.capodieci"},"Nicola Capodieci"),".")),t(r.a,{title:t("a",{href:"/fisica"},"Fisica")},t("p",null,"Appunti delle ",t("a",{href:"http://personale.unimore.it/rubrica/contenutiad/brunetti/2019/58025/N0/N0/9999"},"lezioni di Fisica")," del ",t("a",{href:"https://www.unimore.it/didattica/mlaurea.html?ID=54"},"corso triennale di Informatica")," all'",t("a",{href:"https://www.unimore.it/"},"Unimore"),", tenute dalla ",t("a",{href:"https://personale.unimore.it/rubrica/dettaglio/brunetti"},"Prof.ssa Rossella Brunetti")," nel primo semestre dell'Anno Accademico 2019/2020.")),t(r.a,{title:t("a",{href:"https://github.com/Steffo99/appunti-universitari/tree/master/2019_SistemiOperativi/Arzigogoli"},t(a.a,{icon:c.a})," Sistemi Operativi")},t("p",null,"Soluzioni agli ",t("a",{href:"https://weblab.ing.unimore.it/people/andreolini/didattica/sistemi-operativi/index.html#arzigogoli"},"Arzigogoli")," proposti dal ",t("a",{href:"https://personale.unimore.it/rubrica/dettaglio/andreolini"},"Prof. Mauro Andreolini")," durante le ",t("a",{href:"https://personale.unimore.it/rubrica/contenutiad/andreolini/2019/58027/N0/N0/9999"},"lezioni di Sistemi Operativi")," del ",t("a",{href:"https://www.unimore.it/didattica/mlaurea.html?ID=54"},"corso triennale di Informatica")," all'",t("a",{href:"https://www.unimore.it/"},"Unimore")," tenutesi nel primo semestre dell'Anno Accademico 2019/2020.")),t(r.a,{title:t("a",{href:"/algoritmiestrutturedati"},"Algoritmi e Strutture Dati")},t("p",null,"Appunti delle ",t("a",{href:"https://personale.unimore.it/rubrica/contenutiad/mmontangero/2018/58133/N0/N0/9999"},"lezioni di Algoritmi e Strutture Dati")," del ",t("a",{href:"https://www.unimore.it/didattica/mlaurea.html?ID=54"},"corso triennale di Informatica")," all'",t("a",{href:"https://www.unimore.it/"},"Unimore"),", tenute dalla ",t("a",{href:"https://personale.unimore.it/rubrica/dettaglio/mmontangero"},"Prof.ssa Manuela Montangero")," nel secondo semestre dell'Anno Accademico 2018/2019."),t("p",null,t(o.a,null,"TODO: finisci di migrare da GitHub!"))),t(r.a,{title:t("a",{href:"/vldigeometria"},"Videolezioni di Geometria")},t("p",null,"Ottime videolezioni di Geometria con licenza 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faBattleNet: faBattleNet,\n  faBehance: faBehance,\n  faBehanceSquare: faBehanceSquare,\n  faBimobject: faBimobject,\n  faBitbucket: faBitbucket,\n  faBitcoin: faBitcoin,\n  faBity: faBity,\n  faBlackTie: faBlackTie,\n  faBlackberry: faBlackberry,\n  faBlogger: faBlogger,\n  faBloggerB: faBloggerB,\n  faBluetooth: faBluetooth,\n  faBluetoothB: faBluetoothB,\n  faBootstrap: faBootstrap,\n  faBtc: faBtc,\n  faBuffer: faBuffer,\n  faBuromobelexperte: faBuromobelexperte,\n  faBuyNLarge: faBuyNLarge,\n  faBuysellads: faBuysellads,\n  faCanadianMapleLeaf: faCanadianMapleLeaf,\n  faCcAmazonPay: faCcAmazonPay,\n  faCcAmex: faCcAmex,\n  faCcApplePay: faCcApplePay,\n  faCcDinersClub: faCcDinersClub,\n  faCcDiscover: faCcDiscover,\n  faCcJcb: faCcJcb,\n  faCcMastercard: faCcMastercard,\n  faCcPaypal: faCcPaypal,\n  faCcStripe: faCcStripe,\n  faCcVisa: faCcVisa,\n  faCentercode: faCentercode,\n  faCentos: faCentos,\n  faChrome: faChrome,\n  faChromecast: faChromecast,\n  faCloudscale: 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faCriticalRole,\n  faCss3: faCss3,\n  faCss3Alt: faCss3Alt,\n  faCuttlefish: faCuttlefish,\n  faDAndD: faDAndD,\n  faDAndDBeyond: faDAndDBeyond,\n  faDailymotion: faDailymotion,\n  faDashcube: faDashcube,\n  faDelicious: faDelicious,\n  faDeploydog: faDeploydog,\n  faDeskpro: faDeskpro,\n  faDev: faDev,\n  faDeviantart: faDeviantart,\n  faDhl: faDhl,\n  faDiaspora: faDiaspora,\n  faDigg: faDigg,\n  faDigitalOcean: faDigitalOcean,\n  faDiscord: faDiscord,\n  faDiscourse: faDiscourse,\n  faDochub: faDochub,\n  faDocker: faDocker,\n  faDraft2digital: faDraft2digital,\n  faDribbble: faDribbble,\n  faDribbbleSquare: faDribbbleSquare,\n  faDropbox: faDropbox,\n  faDrupal: faDrupal,\n  faDyalog: faDyalog,\n  faEarlybirds: faEarlybirds,\n  faEbay: faEbay,\n  faEdge: faEdge,\n  faElementor: faElementor,\n  faEllo: faEllo,\n  faEmber: faEmber,\n  faEmpire: faEmpire,\n  faEnvira: faEnvira,\n  faErlang: faErlang,\n  faEthereum: faEthereum,\n  faEtsy: faEtsy,\n  faEvernote: faEvernote,\n  faExpeditedssl: faExpeditedssl,\n  faFacebook: faFacebook,\n  faFacebookF: faFacebookF,\n  faFacebookMessenger: faFacebookMessenger,\n  faFacebookSquare: faFacebookSquare,\n  faFantasyFlightGames: faFantasyFlightGames,\n  faFedex: faFedex,\n  faFedora: faFedora,\n  faFigma: faFigma,\n  faFirefox: faFirefox,\n  faFirefoxBrowser: faFirefoxBrowser,\n  faFirstOrder: faFirstOrder,\n  faFirstOrderAlt: faFirstOrderAlt,\n  faFirstdraft: faFirstdraft,\n  faFlickr: faFlickr,\n  faFlipboard: faFlipboard,\n  faFly: faFly,\n  faFontAwesome: faFontAwesome,\n  faFontAwesomeAlt: faFontAwesomeAlt,\n  faFontAwesomeFlag: faFontAwesomeFlag,\n  faFontAwesomeLogoFull: faFontAwesomeLogoFull,\n  faFonticons: faFonticons,\n  faFonticonsFi: faFonticonsFi,\n  faFortAwesome: faFortAwesome,\n  faFortAwesomeAlt: faFortAwesomeAlt,\n  faForumbee: faForumbee,\n  faFoursquare: faFoursquare,\n  faFreeCodeCamp: faFreeCodeCamp,\n  faFreebsd: faFreebsd,\n  faFulcrum: faFulcrum,\n  faGalacticRepublic: faGalacticRepublic,\n  faGalacticSenate: faGalacticSenate,\n  faGetPocket: faGetPocket,\n  faGg: faGg,\n  faGgCircle: faGgCircle,\n  faGit: faGit,\n  faGitAlt: faGitAlt,\n  faGitSquare: faGitSquare,\n  faGithub: faGithub,\n  faGithubAlt: faGithubAlt,\n  faGithubSquare: faGithubSquare,\n  faGitkraken: faGitkraken,\n  faGitlab: faGitlab,\n  faGitter: faGitter,\n  faGlide: faGlide,\n  faGlideG: faGlideG,\n  faGofore: faGofore,\n  faGoodreads: faGoodreads,\n  faGoodreadsG: faGoodreadsG,\n  faGoogle: faGoogle,\n  faGoogleDrive: faGoogleDrive,\n  faGooglePlay: faGooglePlay,\n  faGooglePlus: faGooglePlus,\n  faGooglePlusG: faGooglePlusG,\n  faGooglePlusSquare: faGooglePlusSquare,\n  faGoogleWallet: faGoogleWallet,\n  faGratipay: faGratipay,\n  faGrav: faGrav,\n  faGripfire: faGripfire,\n  faGrunt: faGrunt,\n  faGulp: faGulp,\n  faHackerNews: faHackerNews,\n  faHackerNewsSquare: faHackerNewsSquare,\n  faHackerrank: faHackerrank,\n  faHips: faHips,\n  faHireAHelper: faHireAHelper,\n  faHooli: faHooli,\n  faHornbill: faHornbill,\n  faHotjar: faHotjar,\n  faHouzz: faHouzz,\n  faHtml5: faHtml5,\n  faHubspot: faHubspot,\n  faIdeal: faIdeal,\n  faImdb: faImdb,\n  faInstagram: faInstagram,\n  faInstagramSquare: faInstagramSquare,\n  faIntercom: faIntercom,\n  faInternetExplorer: faInternetExplorer,\n  faInvision: faInvision,\n  faIoxhost: faIoxhost,\n  faItchIo: faItchIo,\n  faItunes: faItunes,\n  faItunesNote: faItunesNote,\n  faJava: faJava,\n  faJediOrder: faJediOrder,\n  faJenkins: faJenkins,\n  faJira: faJira,\n  faJoget: faJoget,\n  faJoomla: faJoomla,\n  faJs: faJs,\n  faJsSquare: faJsSquare,\n  faJsfiddle: faJsfiddle,\n  faKaggle: faKaggle,\n  faKeybase: faKeybase,\n  faKeycdn: faKeycdn,\n  faKickstarter: faKickstarter,\n  faKickstarterK: faKickstarterK,\n  faKorvue: faKorvue,\n  faLaravel: faLaravel,\n  faLastfm: faLastfm,\n  faLastfmSquare: faLastfmSquare,\n  faLeanpub: faLeanpub,\n  faLess: faLess,\n  faLine: faLine,\n  faLinkedin: faLinkedin,\n  faLinkedinIn: faLinkedinIn,\n  faLinode: faLinode,\n  faLinux: faLinux,\n  faLyft: faLyft,\n  faMagento: faMagento,\n  faMailchimp: faMailchimp,\n  faMandalorian: faMandalorian,\n  faMarkdown: faMarkdown,\n  faMastodon: faMastodon,\n  faMaxcdn: faMaxcdn,\n  faMdb: faMdb,\n  faMedapps: faMedapps,\n  faMedium: faMedium,\n  faMediumM: faMediumM,\n  faMedrt: faMedrt,\n  faMeetup: faMeetup,\n  faMegaport: faMegaport,\n  faMendeley: faMendeley,\n  faMicroblog: faMicroblog,\n  faMicrosoft: faMicrosoft,\n  faMix: faMix,\n  faMixcloud: faMixcloud,\n  faMixer: faMixer,\n  faMizuni: faMizuni,\n  faModx: faModx,\n  faMonero: faMonero,\n  faNapster: faNapster,\n  faNeos: faNeos,\n  faNimblr: faNimblr,\n  faNode: faNode,\n  faNodeJs: faNodeJs,\n  faNpm: faNpm,\n  faNs8: faNs8,\n  faNutritionix: faNutritionix,\n  faOdnoklassniki: faOdnoklassniki,\n  faOdnoklassnikiSquare: faOdnoklassnikiSquare,\n  faOldRepublic: faOldRepublic,\n  faOpencart: faOpencart,\n  faOpenid: faOpenid,\n  faOpera: faOpera,\n  faOptinMonster: faOptinMonster,\n  faOrcid: faOrcid,\n  faOsi: faOsi,\n  faPage4: faPage4,\n  faPagelines: faPagelines,\n  faPalfed: faPalfed,\n  faPatreon: faPatreon,\n  faPaypal: faPaypal,\n  faPennyArcade: faPennyArcade,\n  faPeriscope: faPeriscope,\n  faPhabricator: faPhabricator,\n  faPhoenixFramework: faPhoenixFramework,\n  faPhoenixSquadron: faPhoenixSquadron,\n  faPhp: faPhp,\n  faPiedPiper: faPiedPiper,\n  faPiedPiperAlt: faPiedPiperAlt,\n  faPiedPiperHat: faPiedPiperHat,\n  faPiedPiperPp: faPiedPiperPp,\n  faPiedPiperSquare: faPiedPiperSquare,\n  faPinterest: faPinterest,\n  faPinterestP: faPinterestP,\n  faPinterestSquare: faPinterestSquare,\n  faPlaystation: faPlaystation,\n  faProductHunt: faProductHunt,\n  faPushed: faPushed,\n  faPython: faPython,\n  faQq: faQq,\n  faQuinscape: faQuinscape,\n  faQuora: faQuora,\n  faRProject: faRProject,\n  faRaspberryPi: faRaspberryPi,\n  faRavelry: faRavelry,\n  faReact: faReact,\n  faReacteurope: faReacteurope,\n  faReadme: faReadme,\n  faRebel: faRebel,\n  faRedRiver: faRedRiver,\n  faReddit: faReddit,\n  faRedditAlien: faRedditAlien,\n  faRedditSquare: faRedditSquare,\n  faRedhat: faRedhat,\n  faRenren: faRenren,\n  faReplyd: faReplyd,\n  faResearchgate: faResearchgate,\n  faResolving: faResolving,\n  faRev: faRev,\n  faRocketchat: faRocketchat,\n  faRockrms: faRockrms,\n  faSafari: faSafari,\n  faSalesforce: faSalesforce,\n  faSass: faSass,\n  faSchlix: faSchlix,\n  faScribd: faScribd,\n  faSearchengin: faSearchengin,\n  faSellcast: faSellcast,\n  faSellsy: faSellsy,\n  faServicestack: faServicestack,\n  faShirtsinbulk: faShirtsinbulk,\n  faShopify: faShopify,\n  faShopware: faShopware,\n  faSimplybuilt: faSimplybuilt,\n  faSistrix: faSistrix,\n  faSith: faSith,\n  faSketch: faSketch,\n  faSkyatlas: faSkyatlas,\n  faSkype: faSkype,\n  faSlack: faSlack,\n  faSlackHash: faSlackHash,\n  faSlideshare: faSlideshare,\n  faSnapchat: faSnapchat,\n  faSnapchatGhost: faSnapchatGhost,\n  faSnapchatSquare: faSnapchatSquare,\n  faSoundcloud: faSoundcloud,\n  faSourcetree: faSourcetree,\n  faSpeakap: faSpeakap,\n  faSpeakerDeck: faSpeakerDeck,\n  faSpotify: faSpotify,\n  faSquarespace: faSquarespace,\n  faStackExchange: faStackExchange,\n  faStackOverflow: faStackOverflow,\n  faStackpath: faStackpath,\n  faStaylinked: faStaylinked,\n  faSteam: faSteam,\n  faSteamSquare: faSteamSquare,\n  faSteamSymbol: faSteamSymbol,\n  faStickerMule: faStickerMule,\n  faStrava: faStrava,\n  faStripe: faStripe,\n  faStripeS: faStripeS,\n  faStudiovinari: faStudiovinari,\n  faStumbleupon: faStumbleupon,\n  faStumbleuponCircle: faStumbleuponCircle,\n  faSuperpowers: faSuperpowers,\n  faSupple: faSupple,\n  faSuse: faSuse,\n  faSwift: faSwift,\n  faSymfony: faSymfony,\n  faTeamspeak: faTeamspeak,\n  faTelegram: faTelegram,\n  faTelegramPlane: faTelegramPlane,\n  faTencentWeibo: faTencentWeibo,\n  faTheRedYeti: faTheRedYeti,\n  faThemeco: faThemeco,\n  faThemeisle: faThemeisle,\n  faThinkPeaks: faThinkPeaks,\n  faTradeFederation: faTradeFederation,\n  faTrello: faTrello,\n  faTripadvisor: faTripadvisor,\n  faTumblr: faTumblr,\n  faTumblrSquare: faTumblrSquare,\n  faTwitch: faTwitch,\n  faTwitter: faTwitter,\n  faTwitterSquare: faTwitterSquare,\n  faTypo3: faTypo3,\n  faUber: faUber,\n  faUbuntu: faUbuntu,\n  faUikit: faUikit,\n  faUmbraco: faUmbraco,\n  faUniregistry: faUniregistry,\n  faUnity: faUnity,\n  faUntappd: faUntappd,\n  faUps: faUps,\n  faUsb: faUsb,\n  faUsps: faUsps,\n  faUssunnah: faUssunnah,\n  faVaadin: faVaadin,\n  faViacoin: faViacoin,\n  faViadeo: faViadeo,\n  faViadeoSquare: faViadeoSquare,\n  faViber: faViber,\n  faVimeo: faVimeo,\n  faVimeoSquare: faVimeoSquare,\n  faVimeoV: faVimeoV,\n  faVine: faVine,\n  faVk: faVk,\n  faVnv: faVnv,\n  faVuejs: faVuejs,\n  faWaze: faWaze,\n  faWeebly: faWeebly,\n  faWeibo: faWeibo,\n  faWeixin: faWeixin,\n  faWhatsapp: faWhatsapp,\n  faWhatsappSquare: faWhatsappSquare,\n  faWhmcs: faWhmcs,\n  faWikipediaW: faWikipediaW,\n  faWindows: faWindows,\n  faWix: faWix,\n  faWizardsOfTheCoast: faWizardsOfTheCoast,\n  faWolfPackBattalion: faWolfPackBattalion,\n  faWordpress: faWordpress,\n  faWordpressSimple: faWordpressSimple,\n  faWpbeginner: faWpbeginner,\n  faWpexplorer: faWpexplorer,\n  faWpforms: faWpforms,\n  faWpressr: faWpressr,\n  faXbox: faXbox,\n  faXing: faXing,\n  faXingSquare: faXingSquare,\n  faYCombinator: faYCombinator,\n  faYahoo: faYahoo,\n  faYammer: faYammer,\n  faYandex: faYandex,\n  faYandexInternational: faYandexInternational,\n  faYarn: faYarn,\n  faYelp: faYelp,\n  faYoast: faYoast,\n  faYoutube: faYoutube,\n  faYoutubeSquare: faYoutubeSquare,\n  faZhihu: faZhihu\n};\n\nexport { _iconsCache as fab, prefix, fa500px, faAccessibleIcon, faAccusoft, faAcquisitionsIncorporated, faAdn, faAdobe, faAdversal, faAffiliatetheme, faAirbnb, faAlgolia, faAlipay, faAmazon, faAmazonPay, faAmilia, faAndroid, faAngellist, faAngrycreative, faAngular, faAppStore, faAppStoreIos, faApper, faApple, faApplePay, faArtstation, faAsymmetrik, faAtlassian, faAudible, faAutoprefixer, faAvianex, faAviato, faAws, faBandcamp, faBattleNet, faBehance, faBehanceSquare, faBimobject, faBitbucket, faBitcoin, faBity, faBlackTie, faBlackberry, faBlogger, faBloggerB, faBluetooth, faBluetoothB, faBootstrap, faBtc, faBuffer, faBuromobelexperte, faBuyNLarge, faBuysellads, faCanadianMapleLeaf, faCcAmazonPay, faCcAmex, faCcApplePay, faCcDinersClub, faCcDiscover, faCcJcb, faCcMastercard, faCcPaypal, faCcStripe, faCcVisa, faCentercode, faCentos, faChrome, faChromecast, faCloudscale, faCloudsmith, faCloudversify, faCodepen, faCodiepie, faConfluence, faConnectdevelop, faContao, faCottonBureau, faCpanel, faCreativeCommons, faCreativeCommonsBy, faCreativeCommonsNc, faCreativeCommonsNcEu, faCreativeCommonsNcJp, faCreativeCommonsNd, faCreativeCommonsPd, faCreativeCommonsPdAlt, faCreativeCommonsRemix, faCreativeCommonsSa, faCreativeCommonsSampling, faCreativeCommonsSamplingPlus, faCreativeCommonsShare, faCreativeCommonsZero, faCriticalRole, faCss3, faCss3Alt, faCuttlefish, faDAndD, faDAndDBeyond, faDailymotion, faDashcube, faDelicious, faDeploydog, faDeskpro, faDev, faDeviantart, faDhl, faDiaspora, faDigg, faDigitalOcean, faDiscord, faDiscourse, faDochub, faDocker, faDraft2digital, faDribbble, faDribbbleSquare, faDropbox, faDrupal, faDyalog, faEarlybirds, faEbay, faEdge, faElementor, faEllo, faEmber, faEmpire, faEnvira, faErlang, faEthereum, faEtsy, faEvernote, faExpeditedssl, faFacebook, faFacebookF, faFacebookMessenger, faFacebookSquare, faFantasyFlightGames, faFedex, faFedora, faFigma, faFirefox, faFirefoxBrowser, faFirstOrder, faFirstOrderAlt, faFirstdraft, faFlickr, faFlipboard, faFly, faFontAwesome, faFontAwesomeAlt, faFontAwesomeFlag, faFontAwesomeLogoFull, faFonticons, faFonticonsFi, faFortAwesome, faFortAwesomeAlt, faForumbee, faFoursquare, faFreeCodeCamp, faFreebsd, faFulcrum, faGalacticRepublic, faGalacticSenate, faGetPocket, faGg, faGgCircle, faGit, faGitAlt, faGitSquare, faGithub, faGithubAlt, faGithubSquare, faGitkraken, faGitlab, faGitter, faGlide, faGlideG, faGofore, faGoodreads, faGoodreadsG, faGoogle, faGoogleDrive, faGooglePlay, faGooglePlus, faGooglePlusG, faGooglePlusSquare, faGoogleWallet, faGratipay, faGrav, faGripfire, faGrunt, faGulp, faHackerNews, faHackerNewsSquare, faHackerrank, faHips, faHireAHelper, faHooli, faHornbill, faHotjar, faHouzz, faHtml5, faHubspot, faIdeal, faImdb, faInstagram, faInstagramSquare, faIntercom, faInternetExplorer, faInvision, faIoxhost, faItchIo, faItunes, faItunesNote, faJava, faJediOrder, faJenkins, faJira, faJoget, faJoomla, faJs, faJsSquare, faJsfiddle, faKaggle, faKeybase, faKeycdn, faKickstarter, faKickstarterK, faKorvue, faLaravel, faLastfm, faLastfmSquare, faLeanpub, faLess, faLine, faLinkedin, faLinkedinIn, faLinode, faLinux, faLyft, faMagento, faMailchimp, faMandalorian, faMarkdown, faMastodon, faMaxcdn, faMdb, faMedapps, faMedium, faMediumM, faMedrt, faMeetup, faMegaport, faMendeley, faMicroblog, faMicrosoft, faMix, faMixcloud, faMixer, faMizuni, faModx, faMonero, faNapster, faNeos, faNimblr, faNode, faNodeJs, faNpm, faNs8, faNutritionix, faOdnoklassniki, faOdnoklassnikiSquare, faOldRepublic, faOpencart, faOpenid, faOpera, faOptinMonster, faOrcid, faOsi, faPage4, faPagelines, faPalfed, faPatreon, faPaypal, faPennyArcade, faPeriscope, faPhabricator, faPhoenixFramework, faPhoenixSquadron, faPhp, faPiedPiper, faPiedPiperAlt, faPiedPiperHat, faPiedPiperPp, faPiedPiperSquare, faPinterest, faPinterestP, faPinterestSquare, faPlaystation, faProductHunt, faPushed, faPython, faQq, faQuinscape, faQuora, faRProject, faRaspberryPi, faRavelry, faReact, faReacteurope, faReadme, faRebel, faRedRiver, faReddit, faRedditAlien, faRedditSquare, faRedhat, faRenren, faReplyd, faResearchgate, faResolving, faRev, faRocketchat, faRockrms, faSafari, faSalesforce, faSass, faSchlix, faScribd, faSearchengin, faSellcast, faSellsy, faServicestack, faShirtsinbulk, faShopify, faShopware, faSimplybuilt, faSistrix, faSith, faSketch, faSkyatlas, faSkype, faSlack, faSlackHash, faSlideshare, faSnapchat, faSnapchatGhost, faSnapchatSquare, faSoundcloud, faSourcetree, faSpeakap, faSpeakerDeck, faSpotify, faSquarespace, faStackExchange, faStackOverflow, faStackpath, faStaylinked, faSteam, faSteamSquare, faSteamSymbol, faStickerMule, faStrava, faStripe, faStripeS, faStudiovinari, faStumbleupon, faStumbleuponCircle, faSuperpowers, faSupple, faSuse, faSwift, faSymfony, faTeamspeak, faTelegram, faTelegramPlane, faTencentWeibo, faTheRedYeti, faThemeco, faThemeisle, faThinkPeaks, faTradeFederation, faTrello, faTripadvisor, faTumblr, faTumblrSquare, faTwitch, faTwitter, faTwitterSquare, faTypo3, faUber, faUbuntu, faUikit, faUmbraco, faUniregistry, faUnity, faUntappd, faUps, faUsb, faUsps, faUssunnah, faVaadin, faViacoin, faViadeo, faViadeoSquare, faViber, faVimeo, faVimeoSquare, faVimeoV, faVine, faVk, faVnv, faVuejs, faWaze, faWeebly, faWeibo, faWeixin, faWhatsapp, faWhatsappSquare, faWhmcs, faWikipediaW, faWindows, faWix, faWizardsOfTheCoast, faWolfPackBattalion, faWordpress, faWordpressSimple, faWpbeginner, faWpexplorer, faWpforms, faWpressr, faXbox, faXing, faXingSquare, faYCombinator, faYahoo, faYammer, faYandex, faYandexInternational, faYarn, faYelp, faYoast, faYoutube, faYoutubeSquare, faZhihu };\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"todo\":\"todo__2IWIS\"};","/**\n * Copyright (c) 2013-present, Facebook, Inc.\n *\n * This source code is licensed under the MIT license found in the\n * LICENSE file in the root directory of this source tree.\n */\n\n'use strict';\n\nvar ReactPropTypesSecret = require('./lib/ReactPropTypesSecret');\n\nfunction emptyFunction() {}\nfunction emptyFunctionWithReset() {}\nemptyFunctionWithReset.resetWarningCache = emptyFunction;\n\nmodule.exports = function() {\n  function shim(props, propName, componentName, location, propFullName, secret) {\n    if (secret === ReactPropTypesSecret) {\n      // It is still safe when called from React.\n      return;\n    }\n    var err = new Error(\n      'Calling PropTypes validators directly is not supported by the `prop-types` package. ' +\n      'Use PropTypes.checkPropTypes() to call them. ' +\n      'Read more at http://fb.me/use-check-prop-types'\n    );\n    err.name = 'Invariant Violation';\n    throw err;\n  };\n  shim.isRequired = shim;\n  function getShim() {\n    return shim;\n  };\n  // Important!\n  // Keep this list in sync with production version in `./factoryWithTypeCheckers.js`.\n  var ReactPropTypes = {\n    array: shim,\n    bool: shim,\n    func: shim,\n    number: shim,\n    object: shim,\n    string: shim,\n    symbol: shim,\n\n    any: shim,\n    arrayOf: getShim,\n    element: shim,\n    elementType: shim,\n    instanceOf: getShim,\n    node: shim,\n    objectOf: getShim,\n    oneOf: getShim,\n    oneOfType: getShim,\n    shape: getShim,\n    exact: getShim,\n\n    checkPropTypes: emptyFunctionWithReset,\n    resetWarningCache: emptyFunction\n  };\n\n  ReactPropTypes.PropTypes = ReactPropTypes;\n\n  return ReactPropTypes;\n};\n","import Split from \"../Layout/Split\";\nimport {Fragment} from \"preact\";\n\nexport default function (props) {\n    return (\n        \n            
    \n                {props.title}\n            
    \n            \n                {props.children}\n            \n            \n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"title\":\"title__3ZVpg\",\"contents\":\"contents__20_NI\"};","import {\n\tcreateElement,\n\trender as preactRender,\n\tcloneElement as preactCloneElement,\n\tcreateRef,\n\tComponent,\n\tcreateContext,\n\tFragment\n} from 'preact';\nimport {\n\tuseState,\n\tuseReducer,\n\tuseEffect,\n\tuseLayoutEffect,\n\tuseRef,\n\tuseImperativeHandle,\n\tuseMemo,\n\tuseCallback,\n\tuseContext,\n\tuseDebugValue\n} from 'preact/hooks';\nimport { PureComponent } from './PureComponent';\nimport { memo } from './memo';\nimport { forwardRef } from './forwardRef';\nimport { Children } from './Children';\nimport { Suspense, lazy } from './suspense';\nimport { SuspenseList } from './suspense-list';\nimport { createPortal } from './portals';\nimport { hydrate, render, REACT_ELEMENT_TYPE } from './render';\n\nconst version = '16.8.0'; // trick libraries to think we are react\n\n/**\n * Legacy version of createElement.\n * @param {import('./internal').VNode[\"type\"]} type The node name or Component constructor\n */\nfunction createFactory(type) {\n\treturn createElement.bind(null, type);\n}\n\n/**\n * Check if the passed element is a valid (p)react node.\n * @param {*} element The element to check\n * @returns {boolean}\n */\nfunction isValidElement(element) {\n\treturn !!element && element.$$typeof === REACT_ELEMENT_TYPE;\n}\n\n/**\n * Wrap `cloneElement` to abort if the passed element is not a valid element and apply\n * all vnode normalizations.\n * @param {import('./internal').VNode} element The vnode to clone\n * @param {object} props Props to add when cloning\n * @param {Array} rest Optional component children\n */\nfunction cloneElement(element) {\n\tif (!isValidElement(element)) return element;\n\treturn preactCloneElement.apply(null, arguments);\n}\n\n/**\n * Remove a component tree from the DOM, including state and event handlers.\n * @param {import('./internal').PreactElement} container\n * @returns {boolean}\n */\nfunction unmountComponentAtNode(container) {\n\tif (container._children) {\n\t\tpreactRender(null, container);\n\t\treturn true;\n\t}\n\treturn false;\n}\n\n/**\n * Get the matching DOM node for a component\n * @param {import('./internal').Component} component\n * @returns {import('./internal').PreactElement | null}\n */\nfunction findDOMNode(component) {\n\treturn (\n\t\t(component &&\n\t\t\t(component.base || (component.nodeType === 1 && component))) ||\n\t\tnull\n\t);\n}\n\n/**\n * Deprecated way to control batched rendering inside the reconciler, but we\n * already schedule in batches inside our rendering code\n * @template Arg\n * @param {(arg: Arg) => void} callback function that triggers the updated\n * @param {Arg} [arg] Optional argument that can be passed to the callback\n */\n// eslint-disable-next-line camelcase\nconst unstable_batchedUpdates = (callback, arg) => callback(arg);\n\n/**\n * Strict Mode is not implemented in Preact, so we provide a stand-in for it\n * that just renders its children without imposing any restrictions.\n */\nconst StrictMode = Fragment;\n\nexport * from 'preact/hooks';\nexport {\n\tversion,\n\tChildren,\n\trender,\n\thydrate,\n\tunmountComponentAtNode,\n\tcreatePortal,\n\tcreateElement,\n\tcreateContext,\n\tcreateFactory,\n\tcloneElement,\n\tcreateRef,\n\tFragment,\n\tisValidElement,\n\tfindDOMNode,\n\tComponent,\n\tPureComponent,\n\tmemo,\n\tforwardRef,\n\t// eslint-disable-next-line camelcase\n\tunstable_batchedUpdates,\n\tStrictMode,\n\tSuspense,\n\tSuspenseList,\n\tlazy\n};\n\n// React copies the named exports to the default one.\nexport default {\n\tuseState,\n\tuseReducer,\n\tuseEffect,\n\tuseLayoutEffect,\n\tuseRef,\n\tuseImperativeHandle,\n\tuseMemo,\n\tuseCallback,\n\tuseContext,\n\tuseDebugValue,\n\tversion,\n\tChildren,\n\trender,\n\thydrate,\n\tunmountComponentAtNode,\n\tcreatePortal,\n\tcreateElement,\n\tcreateContext,\n\tcreateFactory,\n\tcloneElement,\n\tcreateRef,\n\tFragment,\n\tisValidElement,\n\tfindDOMNode,\n\tComponent,\n\tPureComponent,\n\tmemo,\n\tforwardRef,\n\tunstable_batchedUpdates,\n\tStrictMode,\n\tSuspense,\n\tSuspenseList,\n\tlazy\n};\n","import style from \"./Todo.less\";\n\nexport default function (props) {\n\tif(process.env.NODE_ENV === \"development\") {\n\t\treturn {props.children};\n\t}\n\telse {\n\t\treturn null;\n\t}\n}\n","import style from \"./Split.less\";\n\nexport default function (props) {\n    let children;\n\n    if(Array.isArray(props.children)) {\n        children = props.children.map(element => {\n            return (\n                
    \n                    {element}\n                
    \n            );\n        });\n    }\n\n    else {\n        children = (\n            
    \n                {props.children}\n            
    \n        );\n    }\n    return (\n        
    \n            
    {children}
    \n        
    \n    );\n}\n","/**\n * Copyright (c) 2013-present, Facebook, Inc.\n *\n * This source code is licensed under the MIT license found in the\n * LICENSE file in the root directory of this source tree.\n */\n\nif (process.env.NODE_ENV !== 'production') {\n  var ReactIs = require('react-is');\n\n  // By explicitly using `prop-types` you are opting into new development behavior.\n  // http://fb.me/prop-types-in-prod\n  var throwOnDirectAccess = true;\n  module.exports = require('./factoryWithTypeCheckers')(ReactIs.isElement, throwOnDirectAccess);\n} else {\n  // By explicitly using `prop-types` you are opting into new production behavior.\n  // http://fb.me/prop-types-in-prod\n  module.exports = require('./factoryWithThrowingShims')();\n}\n","var prefix = \"fas\";\nvar faAd = {\n  prefix: 'fas',\n  iconName: 'ad',\n  icon: [512, 512, [], \"f641\", \"M157.52 272h36.96L176 218.78 157.52 272zM352 256c-13.23 0-24 10.77-24 24s10.77 24 24 24 24-10.77 24-24-10.77-24-24-24zM464 64H48C21.5 64 0 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2.7 6 6v20c0 3.3-2.7 6-6 6H134c-3.3 0-6-2.7-6-6v-20zm0 64c0-3.3 2.7-6 6-6h212c3.3 0 6 2.7 6 6v20c0 3.3-2.7 6-6 6H134c-3.3 0-6-2.7-6-6v-20zm253.4 250H96c-17.7 0-32-14.3-32-32 0-17.6 14.4-32 32-32h285.4c-1.9 17.1-1.9 46.9 0 64z\"]\n};\nvar faBookDead = {\n  prefix: 'fas',\n  iconName: 'book-dead',\n  icon: [448, 512, [], \"f6b7\", \"M272 136c8.8 0 16-7.2 16-16s-7.2-16-16-16-16 7.2-16 16 7.2 16 16 16zm176 222.4V25.6c0-16-9.6-25.6-25.6-25.6H96C41.6 0 0 41.6 0 96v320c0 54.4 41.6 96 96 96h326.4c12.8 0 25.6-9.6 25.6-25.6v-16c0-6.4-3.2-12.8-9.6-19.2-3.2-16-3.2-60.8 0-73.6 6.4-3.2 9.6-9.6 9.6-19.2zM240 56c44.2 0 80 28.7 80 64 0 20.9-12.7 39.2-32 50.9V184c0 8.8-7.2 16-16 16h-64c-8.8 0-16-7.2-16-16v-13.1c-19.3-11.7-32-30-32-50.9 0-35.3 35.8-64 80-64zM124.8 223.3l6.3-14.7c1.7-4.1 6.4-5.9 10.5-4.2l98.3 42.1 98.4-42.1c4.1-1.7 8.8.1 10.5 4.2l6.3 14.7c1.7 4.1-.1 8.8-4.2 10.5L280.6 264l70.3 30.1c4.1 1.7 5.9 6.4 4.2 10.5l-6.3 14.7c-1.7 4.1-6.4 5.9-10.5 4.2L240 281.4l-98.3 42.2c-4.1 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iconName: 'bookmark',\n  icon: [384, 512, [], \"f02e\", \"M0 512V48C0 21.49 21.49 0 48 0h288c26.51 0 48 21.49 48 48v464L192 400 0 512z\"]\n};\nvar faBorderAll = {\n  prefix: 'fas',\n  iconName: 'border-all',\n  icon: [448, 512, [], \"f84c\", \"M416 32H32A32 32 0 0 0 0 64v384a32 32 0 0 0 32 32h384a32 32 0 0 0 32-32V64a32 32 0 0 0-32-32zm-32 64v128H256V96zm-192 0v128H64V96zM64 416V288h128v128zm192 0V288h128v128z\"]\n};\nvar faBorderNone = {\n  prefix: 'fas',\n  iconName: 'border-none',\n  icon: [448, 512, [], \"f850\", \"M240 224h-32a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h32a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zm96 0h-32a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h32a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zm96 0h-32a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h32a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zm-288 0h-32a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h32a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zm96 192h-32a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h32a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zm96 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0 16 16h32a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zm0 96h-32a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h32a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zm0-288h-32a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h32a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zm0-96H32A32 32 0 0 0 0 64v400a16 16 0 0 0 16 16h32a16 16 0 0 0 16-16V96h368a16 16 0 0 0 16-16V48a16 16 0 0 0-16-16z\"]\n};\nvar faBowlingBall = {\n  prefix: 'fas',\n  iconName: 'bowling-ball',\n  icon: [496, 512, [], \"f436\", \"M248 8C111 8 0 119 0 256s111 248 248 248 248-111 248-248S385 8 248 8zM120 192c-17.7 0-32-14.3-32-32s14.3-32 32-32 32 14.3 32 32-14.3 32-32 32zm64-96c0-17.7 14.3-32 32-32s32 14.3 32 32-14.3 32-32 32-32-14.3-32-32zm48 144c-17.7 0-32-14.3-32-32s14.3-32 32-32 32 14.3 32 32-14.3 32-32 32z\"]\n};\nvar faBox = {\n  prefix: 'fas',\n  iconName: 'box',\n  icon: [512, 512, [], \"f466\", \"M509.5 184.6L458.9 32.8C452.4 13.2 434.1 0 413.4 0H272v192h238.7c-.4-2.5-.4-5-1.2-7.4zM240 0H98.6c-20.7 0-39 13.2-45.5 32.8L2.5 184.6c-.8 2.4-.8 4.9-1.2 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0-12-5.4-12-12v-40zM192 268c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v40c0 6.6-5.4 12-12 12h-40c-6.6 0-12-5.4-12-12v-40zm0 128c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v40c0 6.6-5.4 12-12 12h-40c-6.6 0-12-5.4-12-12v-40zM64 268c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v40c0 6.6-5.4 12-12 12H76c-6.6 0-12-5.4-12-12v-40zm0 128c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v40c0 6.6-5.4 12-12 12H76c-6.6 0-12-5.4-12-12v-40zM400 64h-48V16c0-8.8-7.2-16-16-16h-32c-8.8 0-16 7.2-16 16v48H160V16c0-8.8-7.2-16-16-16h-32c-8.8 0-16 7.2-16 16v48H48C21.5 64 0 85.5 0 112v48h448v-48c0-26.5-21.5-48-48-48z\"]\n};\nvar faCalendarCheck = {\n  prefix: 'fas',\n  iconName: 'calendar-check',\n  icon: [448, 512, [], \"f274\", \"M436 160H12c-6.627 0-12-5.373-12-12v-36c0-26.51 21.49-48 48-48h48V12c0-6.627 5.373-12 12-12h40c6.627 0 12 5.373 12 12v52h128V12c0-6.627 5.373-12 12-12h40c6.627 0 12 5.373 12 12v52h48c26.51 0 48 21.49 48 48v36c0 6.627-5.373 12-12 12zM12 192h424c6.627 0 12 5.373 12 12v260c0 26.51-21.49 48-48 48H48c-26.51 0-48-21.49-48-48V204c0-6.627 5.373-12 12-12zm333.296 95.947l-28.169-28.398c-4.667-4.705-12.265-4.736-16.97-.068L194.12 364.665l-45.98-46.352c-4.667-4.705-12.266-4.736-16.971-.068l-28.397 28.17c-4.705 4.667-4.736 12.265-.068 16.97l82.601 83.269c4.667 4.705 12.265 4.736 16.97.068l142.953-141.805c4.705-4.667 4.736-12.265.068-16.97z\"]\n};\nvar faCalendarDay = {\n  prefix: 'fas',\n  iconName: 'calendar-day',\n  icon: [448, 512, [], \"f783\", \"M0 464c0 26.5 21.5 48 48 48h352c26.5 0 48-21.5 48-48V192H0v272zm64-192c0-8.8 7.2-16 16-16h96c8.8 0 16 7.2 16 16v96c0 8.8-7.2 16-16 16H80c-8.8 0-16-7.2-16-16v-96zM400 64h-48V16c0-8.8-7.2-16-16-16h-32c-8.8 0-16 7.2-16 16v48H160V16c0-8.8-7.2-16-16-16h-32c-8.8 0-16 7.2-16 16v48H48C21.5 64 0 85.5 0 112v48h448v-48c0-26.5-21.5-48-48-48z\"]\n};\nvar faCalendarMinus = {\n  prefix: 'fas',\n  iconName: 'calendar-minus',\n  icon: [448, 512, [], \"f272\", \"M436 160H12c-6.6 0-12-5.4-12-12v-36c0-26.5 21.5-48 48-48h48V12c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v52h128V12c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v52h48c26.5 0 48 21.5 48 48v36c0 6.6-5.4 12-12 12zM12 192h424c6.6 0 12 5.4 12 12v260c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V204c0-6.6 5.4-12 12-12zm304 192c6.6 0 12-5.4 12-12v-40c0-6.6-5.4-12-12-12H132c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12h184z\"]\n};\nvar faCalendarPlus = {\n  prefix: 'fas',\n  iconName: 'calendar-plus',\n  icon: [448, 512, [], \"f271\", \"M436 160H12c-6.6 0-12-5.4-12-12v-36c0-26.5 21.5-48 48-48h48V12c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v52h128V12c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v52h48c26.5 0 48 21.5 48 48v36c0 6.6-5.4 12-12 12zM12 192h424c6.6 0 12 5.4 12 12v260c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V204c0-6.6 5.4-12 12-12zm316 140c0-6.6-5.4-12-12-12h-60v-60c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v60h-60c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12h60v60c0 6.6 5.4 12 12 12h40c6.6 0 12-5.4 12-12v-60h60c6.6 0 12-5.4 12-12v-40z\"]\n};\nvar faCalendarTimes = {\n  prefix: 'fas',\n  iconName: 'calendar-times',\n  icon: [448, 512, [], \"f273\", \"M436 160H12c-6.6 0-12-5.4-12-12v-36c0-26.5 21.5-48 48-48h48V12c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v52h128V12c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v52h48c26.5 0 48 21.5 48 48v36c0 6.6-5.4 12-12 12zM12 192h424c6.6 0 12 5.4 12 12v260c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V204c0-6.6 5.4-12 12-12zm257.3 160l48.1-48.1c4.7-4.7 4.7-12.3 0-17l-28.3-28.3c-4.7-4.7-12.3-4.7-17 0L224 306.7l-48.1-48.1c-4.7-4.7-12.3-4.7-17 0l-28.3 28.3c-4.7 4.7-4.7 12.3 0 17l48.1 48.1-48.1 48.1c-4.7 4.7-4.7 12.3 0 17l28.3 28.3c4.7 4.7 12.3 4.7 17 0l48.1-48.1 48.1 48.1c4.7 4.7 12.3 4.7 17 0l28.3-28.3c4.7-4.7 4.7-12.3 0-17L269.3 352z\"]\n};\nvar faCalendarWeek = {\n  prefix: 'fas',\n  iconName: 'calendar-week',\n  icon: [448, 512, [], \"f784\", \"M0 464c0 26.5 21.5 48 48 48h352c26.5 0 48-21.5 48-48V192H0v272zm64-192c0-8.8 7.2-16 16-16h288c8.8 0 16 7.2 16 16v64c0 8.8-7.2 16-16 16H80c-8.8 0-16-7.2-16-16v-64zM400 64h-48V16c0-8.8-7.2-16-16-16h-32c-8.8 0-16 7.2-16 16v48H160V16c0-8.8-7.2-16-16-16h-32c-8.8 0-16 7.2-16 16v48H48C21.5 64 0 85.5 0 112v48h448v-48c0-26.5-21.5-48-48-48z\"]\n};\nvar faCamera = {\n  prefix: 'fas',\n  iconName: 'camera',\n  icon: [512, 512, [], \"f030\", \"M512 144v288c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V144c0-26.5 21.5-48 48-48h88l12.3-32.9c7-18.7 24.9-31.1 44.9-31.1h125.5c20 0 37.9 12.4 44.9 31.1L376 96h88c26.5 0 48 21.5 48 48zM376 288c0-66.2-53.8-120-120-120s-120 53.8-120 120 53.8 120 120 120 120-53.8 120-120zm-32 0c0 48.5-39.5 88-88 88s-88-39.5-88-88 39.5-88 88-88 88 39.5 88 88z\"]\n};\nvar faCameraRetro = {\n  prefix: 'fas',\n  iconName: 'camera-retro',\n  icon: [512, 512, [], \"f083\", \"M48 32C21.5 32 0 53.5 0 80v352c0 26.5 21.5 48 48 48h416c26.5 0 48-21.5 48-48V80c0-26.5-21.5-48-48-48H48zm0 32h106c3.3 0 6 2.7 6 6v20c0 3.3-2.7 6-6 6H38c-3.3 0-6-2.7-6-6V80c0-8.8 7.2-16 16-16zm426 96H38c-3.3 0-6-2.7-6-6v-36c0-3.3 2.7-6 6-6h138l30.2-45.3c1.1-1.7 3-2.7 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faCapsules = {\n  prefix: 'fas',\n  iconName: 'capsules',\n  icon: [576, 512, [], \"f46b\", \"M555.3 300.1L424.2 112.8C401.9 81 366.4 64 330.4 64c-22.6 0-45.5 6.7-65.5 20.7-19.7 13.8-33.7 32.8-41.5 53.8C220.5 79.2 172 32 112 32 50.1 32 0 82.1 0 144v224c0 61.9 50.1 112 112 112s112-50.1 112-112V218.9c3.3 8.6 7.3 17.1 12.8 25L368 431.2c22.2 31.8 57.7 48.8 93.8 48.8 22.7 0 45.5-6.7 65.5-20.7 51.7-36.2 64.2-107.5 28-159.2zM160 256H64V144c0-26.5 21.5-48 48-48s48 21.5 48 48v112zm194.8 44.9l-65.6-93.7c-7.7-11-10.7-24.4-8.3-37.6 2.3-13.2 9.7-24.8 20.7-32.5 8.5-6 18.5-9.1 28.8-9.1 16.5 0 31.9 8 41.3 21.5l65.6 93.7-82.5 57.7z\"]\n};\nvar faCar = {\n  prefix: 'fas',\n  iconName: 'car',\n  icon: [512, 512, [], \"f1b9\", \"M499.99 176h-59.87l-16.64-41.6C406.38 91.63 365.57 64 319.5 64h-127c-46.06 0-86.88 27.63-103.99 70.4L71.87 176H12.01C4.2 176-1.53 183.34.37 190.91l6 24C7.7 220.25 12.5 224 18.01 224h20.07C24.65 235.73 16 252.78 16 272v48c0 16.12 6.16 30.67 16 41.93V416c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32v-32h256v32c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32v-54.07c9.84-11.25 16-25.8 16-41.93v-48c0-19.22-8.65-36.27-22.07-48H494c5.51 0 10.31-3.75 11.64-9.09l6-24c1.89-7.57-3.84-14.91-11.65-14.91zm-352.06-17.83c7.29-18.22 24.94-30.17 44.57-30.17h127c19.63 0 37.28 11.95 44.57 30.17L384 208H128l19.93-49.83zM96 319.8c-19.2 0-32-12.76-32-31.9S76.8 256 96 256s48 28.71 48 47.85-28.8 15.95-48 15.95zm320 0c-19.2 0-48 3.19-48-15.95S396.8 256 416 256s32 12.76 32 31.9-12.8 31.9-32 31.9z\"]\n};\nvar faCarAlt = {\n  prefix: 'fas',\n  iconName: 'car-alt',\n  icon: [480, 512, [], \"f5de\", \"M438.66 212.33l-11.24-28.1-19.93-49.83C390.38 91.63 349.57 64 303.5 64h-127c-46.06 0-86.88 27.63-103.99 70.4l-19.93 49.83-11.24 28.1C17.22 221.5 0 244.66 0 272v48c0 16.12 6.16 30.67 16 41.93V416c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32v-32h256v32c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32v-54.07c9.84-11.25 16-25.8 16-41.93v-48c0-27.34-17.22-50.5-41.34-59.67zm-306.73-54.16c7.29-18.22 24.94-30.17 44.57-30.17h127c19.63 0 37.28 11.95 44.57 30.17L368 208H112l19.93-49.83zM80 319.8c-19.2 0-32-12.76-32-31.9S60.8 256 80 256s48 28.71 48 47.85-28.8 15.95-48 15.95zm320 0c-19.2 0-48 3.19-48-15.95S380.8 256 400 256s32 12.76 32 31.9-12.8 31.9-32 31.9z\"]\n};\nvar faCarBattery = {\n  prefix: 'fas',\n  iconName: 'car-battery',\n  icon: [512, 512, [], \"f5df\", \"M480 128h-32V80c0-8.84-7.16-16-16-16h-96c-8.84 0-16 7.16-16 16v48H192V80c0-8.84-7.16-16-16-16H80c-8.84 0-16 7.16-16 16v48H32c-17.67 0-32 14.33-32 32v256c0 17.67 14.33 32 32 32h448c17.67 0 32-14.33 32-32V160c0-17.67-14.33-32-32-32zM192 264c0 4.42-3.58 8-8 8H72c-4.42 0-8-3.58-8-8v-16c0-4.42 3.58-8 8-8h112c4.42 0 8 3.58 8 8v16zm256 0c0 4.42-3.58 8-8 8h-40v40c0 4.42-3.58 8-8 8h-16c-4.42 0-8-3.58-8-8v-40h-40c-4.42 0-8-3.58-8-8v-16c0-4.42 3.58-8 8-8h40v-40c0-4.42 3.58-8 8-8h16c4.42 0 8 3.58 8 8v40h40c4.42 0 8 3.58 8 8v16z\"]\n};\nvar faCarCrash = {\n  prefix: 'fas',\n  iconName: 'car-crash',\n  icon: [640, 512, [], \"f5e1\", \"M143.25 220.81l-12.42 46.37c-3.01 11.25-3.63 22.89-2.41 34.39l-35.2 28.98c-6.57 5.41-16.31-.43-14.62-8.77l15.44-76.68c1.06-5.26-2.66-10.28-8-10.79l-77.86-7.55c-8.47-.82-11.23-11.83-4.14-16.54l65.15-43.3c4.46-2.97 5.38-9.15 1.98-13.29L21.46 93.22c-5.41-6.57.43-16.3 8.78-14.62l76.68 15.44c5.26 1.06 10.28-2.66 10.8-8l7.55-77.86c.82-8.48 11.83-11.23 16.55-4.14l43.3 65.14c2.97 4.46 9.15 5.38 13.29 1.98l60.4-49.71c6.57-5.41 16.3.43 14.62 8.77L262.1 86.38c-2.71 3.05-5.43 6.09-7.91 9.4l-32.15 42.97-10.71 14.32c-32.73 8.76-59.18 34.53-68.08 67.74zm494.57 132.51l-12.42 46.36c-3.13 11.68-9.38 21.61-17.55 29.36a66.876 66.876 0 0 1-8.76 7l-13.99 52.23c-1.14 4.27-3.1 8.1-5.65 11.38-7.67 9.84-20.74 14.68-33.54 11.25L515 502.62c-17.07-4.57-27.2-22.12-22.63-39.19l8.28-30.91-247.28-66.26-8.28 30.91c-4.57 17.07-22.12 27.2-39.19 22.63l-30.91-8.28c-12.8-3.43-21.7-14.16-23.42-26.51-.57-4.12-.35-8.42.79-12.68l13.99-52.23a66.62 66.62 0 0 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 prefix: 'fas',\n  iconName: 'car-side',\n  icon: [640, 512, [], \"f5e4\", \"M544 192h-16L419.22 56.02A64.025 64.025 0 0 0 369.24 32H155.33c-26.17 0-49.7 15.93-59.42 40.23L48 194.26C20.44 201.4 0 226.21 0 256v112c0 8.84 7.16 16 16 16h48c0 53.02 42.98 96 96 96s96-42.98 96-96h128c0 53.02 42.98 96 96 96s96-42.98 96-96h48c8.84 0 16-7.16 16-16v-80c0-53.02-42.98-96-96-96zM160 432c-26.47 0-48-21.53-48-48s21.53-48 48-48 48 21.53 48 48-21.53 48-48 48zm72-240H116.93l38.4-96H232v96zm48 0V96h89.24l76.8 96H280zm200 240c-26.47 0-48-21.53-48-48s21.53-48 48-48 48 21.53 48 48-21.53 48-48 48z\"]\n};\nvar faCaravan = {\n  prefix: 'fas',\n  iconName: 'caravan',\n  icon: [640, 512, [], \"f8ff\", \"M416,208a16,16,0,1,0,16,16A16,16,0,0,0,416,208ZM624,320H576V160A160,160,0,0,0,416,0H64A64,64,0,0,0,0,64V320a64,64,0,0,0,64,64H96a96,96,0,0,0,192,0H624a16,16,0,0,0,16-16V336A16,16,0,0,0,624,320ZM192,432a48,48,0,1,1,48-48A48.05,48.05,0,0,1,192,432Zm64-240a32,32,0,0,1-32,32H96a32,32,0,0,1-32-32V128A32,32,0,0,1,96,96H224a32,32,0,0,1,32,32ZM448,320H320V128a32,32,0,0,1,32-32h64a32,32,0,0,1,32,32Z\"]\n};\nvar faCaretDown = {\n  prefix: 'fas',\n  iconName: 'caret-down',\n  icon: [320, 512, [], \"f0d7\", \"M31.3 192h257.3c17.8 0 26.7 21.5 14.1 34.1L174.1 354.8c-7.8 7.8-20.5 7.8-28.3 0L17.2 226.1C4.6 213.5 13.5 192 31.3 192z\"]\n};\nvar faCaretLeft = {\n  prefix: 'fas',\n  iconName: 'caret-left',\n  icon: [192, 512, [], \"f0d9\", \"M192 127.338v257.324c0 17.818-21.543 26.741-34.142 14.142L29.196 270.142c-7.81-7.81-7.81-20.474 0-28.284l128.662-128.662c12.599-12.6 34.142-3.676 34.142 14.142z\"]\n};\nvar faCaretRight = {\n  prefix: 'fas',\n  iconName: 'caret-right',\n  icon: [192, 512, [], \"f0da\", \"M0 384.662V127.338c0-17.818 21.543-26.741 34.142-14.142l128.662 128.662c7.81 7.81 7.81 20.474 0 28.284L34.142 398.804C21.543 411.404 0 402.48 0 384.662z\"]\n};\nvar faCaretSquareDown = {\n  prefix: 'fas',\n  iconName: 'caret-square-down',\n  icon: [448, 512, [], \"f150\", \"M448 80v352c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V80c0-26.5 21.5-48 48-48h352c26.5 0 48 21.5 48 48zM92.5 220.5l123 123c4.7 4.7 12.3 4.7 17 0l123-123c7.6-7.6 2.2-20.5-8.5-20.5H101c-10.7 0-16.1 12.9-8.5 20.5z\"]\n};\nvar faCaretSquareLeft = {\n  prefix: 'fas',\n  iconName: 'caret-square-left',\n  icon: [448, 512, [], \"f191\", \"M400 480H48c-26.51 0-48-21.49-48-48V80c0-26.51 21.49-48 48-48h352c26.51 0 48 21.49 48 48v352c0 26.51-21.49 48-48 48zM259.515 124.485l-123.03 123.03c-4.686 4.686-4.686 12.284 0 16.971l123.029 123.029c7.56 7.56 20.485 2.206 20.485-8.485V132.971c.001-10.691-12.925-16.045-20.484-8.486z\"]\n};\nvar faCaretSquareRight = {\n  prefix: 'fas',\n  iconName: 'caret-square-right',\n  icon: [448, 512, [], \"f152\", \"M48 32h352c26.51 0 48 21.49 48 48v352c0 26.51-21.49 48-48 48H48c-26.51 0-48-21.49-48-48V80c0-26.51 21.49-48 48-48zm140.485 355.515l123.029-123.029c4.686-4.686 4.686-12.284 0-16.971l-123.029-123.03c-7.56-7.56-20.485-2.206-20.485 8.485v246.059c0 10.691 12.926 16.045 20.485 8.486z\"]\n};\nvar faCaretSquareUp = {\n  prefix: 'fas',\n  iconName: 'caret-square-up',\n  icon: [448, 512, [], \"f151\", \"M0 432V80c0-26.51 21.49-48 48-48h352c26.51 0 48 21.49 48 48v352c0 26.51-21.49 48-48 48H48c-26.51 0-48-21.49-48-48zm355.515-140.485l-123.03-123.03c-4.686-4.686-12.284-4.686-16.971 0L92.485 291.515c-7.56 7.56-2.206 20.485 8.485 20.485h246.059c10.691 0 16.045-12.926 8.486-20.485z\"]\n};\nvar faCaretUp = {\n  prefix: 'fas',\n  iconName: 'caret-up',\n  icon: [320, 512, [], \"f0d8\", \"M288.662 352H31.338c-17.818 0-26.741-21.543-14.142-34.142l128.662-128.662c7.81-7.81 20.474-7.81 28.284 0l128.662 128.662c12.6 12.599 3.676 34.142-14.142 34.142z\"]\n};\nvar faCarrot = {\n  prefix: 'fas',\n  iconName: 'carrot',\n  icon: [512, 512, [], \"f787\", \"M298.2 156.6c-52.7-25.7-114.5-10.5-150.2 32.8l55.2 55.2c6.3 6.3 6.3 16.4 0 22.6-3.1 3.1-7.2 4.7-11.3 4.7s-8.2-1.6-11.3-4.7L130.4 217 2.3 479.7c-2.9 6-3.1 13.3 0 19.7 5.4 11.1 18.9 15.7 30 10.3l133.6-65.2-49.2-49.2c-6.3-6.2-6.3-16.4 0-22.6 6.3-6.2 16.4-6.2 22.6 0l57 57 102-49.8c24-11.7 44.5-31.3 57.1-57.1 30.1-61.7 4.5-136.1-57.2-166.2zm92.1-34.9C409.8 81 399.7 32.9 360 0c-50.3 41.7-52.5 107.5-7.9 151.9l8 8c44.4 44.6 110.3 42.4 151.9-7.9-32.9-39.7-81-49.8-121.7-30.3z\"]\n};\nvar faCartArrowDown = {\n  prefix: 'fas',\n  iconName: 'cart-arrow-down',\n  icon: [576, 512, [], \"f218\", \"M504.717 320H211.572l6.545 32h268.418c15.401 0 26.816 14.301 23.403 29.319l-5.517 24.276C523.112 414.668 536 433.828 536 456c0 31.202-25.519 56.444-56.824 55.994-29.823-.429-54.35-24.631-55.155-54.447-.44-16.287 6.085-31.049 16.803-41.548H231.176C241.553 426.165 248 440.326 248 456c0 31.813-26.528 57.431-58.67 55.938-28.54-1.325-51.751-24.385-53.251-52.917-1.158-22.034 10.436-41.455 28.051-51.586L93.883 64H24C10.745 64 0 53.255 0 40V24C0 10.745 10.745 0 24 0h102.529c11.401 0 21.228 8.021 23.513 19.19L159.208 64H551.99c15.401 0 26.816 14.301 23.403 29.319l-47.273 208C525.637 312.246 515.923 320 504.717 320zM403.029 192H360v-60c0-6.627-5.373-12-12-12h-24c-6.627 0-12 5.373-12 12v60h-43.029c-10.691 0-16.045 12.926-8.485 20.485l67.029 67.029c4.686 4.686 12.284 4.686 16.971 0l67.029-67.029c7.559-7.559 2.205-20.485-8.486-20.485z\"]\n};\nvar faCartPlus = {\n  prefix: 'fas',\n  iconName: 'cart-plus',\n  icon: [576, 512, [], \"f217\", \"M504.717 320H211.572l6.545 32h268.418c15.401 0 26.816 14.301 23.403 29.319l-5.517 24.276C523.112 414.668 536 433.828 536 456c0 31.202-25.519 56.444-56.824 55.994-29.823-.429-54.35-24.631-55.155-54.447-.44-16.287 6.085-31.049 16.803-41.548H231.176C241.553 426.165 248 440.326 248 456c0 31.813-26.528 57.431-58.67 55.938-28.54-1.325-51.751-24.385-53.251-52.917-1.158-22.034 10.436-41.455 28.051-51.586L93.883 64H24C10.745 64 0 53.255 0 40V24C0 10.745 10.745 0 24 0h102.529c11.401 0 21.228 8.021 23.513 19.19L159.208 64H551.99c15.401 0 26.816 14.301 23.403 29.319l-47.273 208C525.637 312.246 515.923 320 504.717 320zM408 168h-48v-40c0-8.837-7.163-16-16-16h-16c-8.837 0-16 7.163-16 16v40h-48c-8.837 0-16 7.163-16 16v16c0 8.837 7.163 16 16 16h48v40c0 8.837 7.163 16 16 16h16c8.837 0 16-7.163 16-16v-40h48c8.837 0 16-7.163 16-16v-16c0-8.837-7.163-16-16-16z\"]\n};\nvar faCashRegister = {\n  prefix: 'fas',\n  iconName: 'cash-register',\n  icon: [512, 512, [], \"f788\", \"M511.1 378.8l-26.7-160c-2.6-15.4-15.9-26.7-31.6-26.7H208v-64h96c8.8 0 16-7.2 16-16V16c0-8.8-7.2-16-16-16H48c-8.8 0-16 7.2-16 16v96c0 8.8 7.2 16 16 16h96v64H59.1c-15.6 0-29 11.3-31.6 26.7L.8 378.7c-.6 3.5-.9 7-.9 10.5V480c0 17.7 14.3 32 32 32h448c17.7 0 32-14.3 32-32v-90.7c.1-3.5-.2-7-.8-10.5zM280 248c0-8.8 7.2-16 16-16h16c8.8 0 16 7.2 16 16v16c0 8.8-7.2 16-16 16h-16c-8.8 0-16-7.2-16-16v-16zm-32 64h16c8.8 0 16 7.2 16 16v16c0 8.8-7.2 16-16 16h-16c-8.8 0-16-7.2-16-16v-16c0-8.8 7.2-16 16-16zm-32-80c8.8 0 16 7.2 16 16v16c0 8.8-7.2 16-16 16h-16c-8.8 0-16-7.2-16-16v-16c0-8.8 7.2-16 16-16h16zM80 80V48h192v32H80zm40 200h-16c-8.8 0-16-7.2-16-16v-16c0-8.8 7.2-16 16-16h16c8.8 0 16 7.2 16 16v16c0 8.8-7.2 16-16 16zm16 64v-16c0-8.8 7.2-16 16-16h16c8.8 0 16 7.2 16 16v16c0 8.8-7.2 16-16 16h-16c-8.8 0-16-7.2-16-16zm216 112c0 4.4-3.6 8-8 8H168c-4.4 0-8-3.6-8-8v-16c0-4.4 3.6-8 8-8h176c4.4 0 8 3.6 8 8v16zm24-112c0 8.8-7.2 16-16 16h-16c-8.8 0-16-7.2-16-16v-16c0-8.8 7.2-16 16-16h16c8.8 0 16 7.2 16 16v16zm48-80c0 8.8-7.2 16-16 16h-16c-8.8 0-16-7.2-16-16v-16c0-8.8 7.2-16 16-16h16c8.8 0 16 7.2 16 16v16z\"]\n};\nvar faCat = {\n  prefix: 'fas',\n  iconName: 'cat',\n  icon: [512, 512, [], \"f6be\", \"M290.59 192c-20.18 0-106.82 1.98-162.59 85.95V192c0-52.94-43.06-96-96-96-17.67 0-32 14.33-32 32s14.33 32 32 32c17.64 0 32 14.36 32 32v256c0 35.3 28.7 64 64 64h176c8.84 0 16-7.16 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faChessQueen = {\n  prefix: 'fas',\n  iconName: 'chess-queen',\n  icon: [512, 512, [], \"f445\", \"M256 112a56 56 0 1 0-56-56 56 56 0 0 0 56 56zm176 336H80a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h352a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zm72.87-263.84l-28.51-15.92c-7.44-5-16.91-2.46-22.29 4.68a47.59 47.59 0 0 1-47.23 18.23C383.7 186.86 368 164.93 368 141.4a13.4 13.4 0 0 0-13.4-13.4h-38.77c-6 0-11.61 4-12.86 9.91a48 48 0 0 1-93.94 0c-1.25-5.92-6.82-9.91-12.86-9.91H157.4a13.4 13.4 0 0 0-13.4 13.4c0 25.69-19 48.75-44.67 50.49a47.5 47.5 0 0 1-41.54-19.15c-5.28-7.09-14.73-9.45-22.09-4.54l-28.57 16a16 16 0 0 0-5.44 20.47L104.24 416h303.52l102.55-211.37a16 16 0 0 0-5.44-20.47z\"]\n};\nvar faChessRook = {\n  prefix: 'fas',\n  iconName: 'chess-rook',\n  icon: [384, 512, [], \"f447\", \"M368 32h-56a16 16 0 0 0-16 16v48h-48V48a16 16 0 0 0-16-16h-80a16 16 0 0 0-16 16v48H88.1V48a16 16 0 0 0-16-16H16A16 16 0 0 0 0 48v176l64 32c0 48.33-1.54 95-13.21 160h282.42C321.54 351 320 303.72 320 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iconName: 'chevron-circle-right',\n  icon: [512, 512, [], \"f138\", \"M256 8c137 0 248 111 248 248S393 504 256 504 8 393 8 256 119 8 256 8zm113.9 231L234.4 103.5c-9.4-9.4-24.6-9.4-33.9 0l-17 17c-9.4 9.4-9.4 24.6 0 33.9L285.1 256 183.5 357.6c-9.4 9.4-9.4 24.6 0 33.9l17 17c9.4 9.4 24.6 9.4 33.9 0L369.9 273c9.4-9.4 9.4-24.6 0-34z\"]\n};\nvar faChevronCircleUp = {\n  prefix: 'fas',\n  iconName: 'chevron-circle-up',\n  icon: [512, 512, [], \"f139\", \"M8 256C8 119 119 8 256 8s248 111 248 248-111 248-248 248S8 393 8 256zm231-113.9L103.5 277.6c-9.4 9.4-9.4 24.6 0 33.9l17 17c9.4 9.4 24.6 9.4 33.9 0L256 226.9l101.6 101.6c9.4 9.4 24.6 9.4 33.9 0l17-17c9.4-9.4 9.4-24.6 0-33.9L273 142.1c-9.4-9.4-24.6-9.4-34 0z\"]\n};\nvar faChevronDown = {\n  prefix: 'fas',\n  iconName: 'chevron-down',\n  icon: [448, 512, [], \"f078\", \"M207.029 381.476L12.686 187.132c-9.373-9.373-9.373-24.569 0-33.941l22.667-22.667c9.357-9.357 24.522-9.375 33.901-.04L224 284.505l154.745-154.021c9.379-9.335 24.544-9.317 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17.7-178.5-53.7-178.5-147.7 0-54.2 29-104 76.1-130.8 7.3-4.1 5.4-15.1-2.8-16.7C448.4 1.1 436.7 0 425 0 319.1 0 233.1 85.9 233.1 192c0 8.5.7 16.8 1.8 25 5.9 4.3 11.6 8.9 16.7 14.2 11.4-4.7 23.7-7.2 36.4-7.2 52.9 0 96 43.1 96 96 0 3.6-.2 7.2-.6 10.7 23.6 10.8 42.4 29.5 53.5 52.6 54.4-3.4 103.7-29.3 137.1-70.4 5.3-6.5-.5-16.1-8.7-14.5z\"]\n};\nvar faCloudMoonRain = {\n  prefix: 'fas',\n  iconName: 'cloud-moon-rain',\n  icon: [576, 512, [], \"f73c\", \"M350.5 225.5c-6.9-37.2-39.3-65.5-78.5-65.5-12.3 0-23.9 3-34.3 8-17.4-24.1-45.6-40-77.7-40-53 0-96 43-96 96 0 .5.2 1.1.2 1.6C27.6 232.9 0 265.2 0 304c0 44.2 35.8 80 80 80h256c44.2 0 80-35.8 80-80 0-39.2-28.2-71.7-65.5-78.5zm217.4-1.7c-70.4 13.3-135-40.3-135-110.8 0-40.6 21.9-78 57.5-98.1 5.5-3.1 4.1-11.4-2.1-12.5C479.6.8 470.7 0 461.8 0c-77.9 0-141.1 61.2-144.4 137.9 26.7 11.9 48.2 33.8 58.9 61.7 37.1 14.3 64 47.4 70.2 86.8 5.1.5 10 1.5 15.2 1.5 44.7 0 85.6-20.2 112.6-53.3 4.2-4.8-.2-12-6.4-10.8zM364.5 418.1c-7.6-4.3-17.4-1.8-21.8 6l-36.6 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0-38.1 6-53.3 16.2C367 64.2 315.3 32 256 32c-88.4 0-160 71.6-160 160 0 2.7.1 5.4.2 8.1C40.2 219.8 0 273.2 0 336c0 79.5 64.5 144 144 144h368c70.7 0 128-57.3 128-128 0-61.9-44-113.6-102.4-125.4zM393.4 288H328v112c0 8.8-7.2 16-16 16h-48c-8.8 0-16-7.2-16-16V288h-65.4c-14.3 0-21.4-17.2-11.3-27.3l105.4-105.4c6.2-6.2 16.4-6.2 22.6 0l105.4 105.4c10.1 10.1 2.9 27.3-11.3 27.3z\"]\n};\nvar faCocktail = {\n  prefix: 'fas',\n  iconName: 'cocktail',\n  icon: [576, 512, [], \"f561\", \"M296 464h-56V338.78l168.74-168.73c15.52-15.52 4.53-42.05-17.42-42.05H24.68c-21.95 0-32.94 26.53-17.42 42.05L176 338.78V464h-56c-22.09 0-40 17.91-40 40 0 4.42 3.58 8 8 8h240c4.42 0 8-3.58 8-8 0-22.09-17.91-40-40-40zM432 0c-62.61 0-115.35 40.2-135.18 96h52.54c16.65-28.55 47.27-48 82.64-48 52.93 0 96 43.06 96 96s-43.07 96-96 96c-14.04 0-27.29-3.2-39.32-8.64l-35.26 35.26C379.23 279.92 404.59 288 432 288c79.53 0 144-64.47 144-144S511.53 0 432 0z\"]\n};\nvar faCode = {\n  prefix: 'fas',\n  iconName: 'code',\n  icon: [640, 512, [], \"f121\", \"M278.9 511.5l-61-17.7c-6.4-1.8-10-8.5-8.2-14.9L346.2 8.7c1.8-6.4 8.5-10 14.9-8.2l61 17.7c6.4 1.8 10 8.5 8.2 14.9L293.8 503.3c-1.9 6.4-8.5 10.1-14.9 8.2zm-114-112.2l43.5-46.4c4.6-4.9 4.3-12.7-.8-17.2L117 256l90.6-79.7c5.1-4.5 5.5-12.3.8-17.2l-43.5-46.4c-4.5-4.8-12.1-5.1-17-.5L3.8 247.2c-5.1 4.7-5.1 12.8 0 17.5l144.1 135.1c4.9 4.6 12.5 4.4 17-.5zm327.2.6l144.1-135.1c5.1-4.7 5.1-12.8 0-17.5L492.1 112.1c-4.8-4.5-12.4-4.3-17 .5L431.6 159c-4.6 4.9-4.3 12.7.8 17.2L523 256l-90.6 79.7c-5.1 4.5-5.5 12.3-.8 17.2l43.5 46.4c4.5 4.9 12.1 5.1 17 .6z\"]\n};\nvar faCodeBranch = {\n  prefix: 'fas',\n  iconName: 'code-branch',\n  icon: [384, 512, [], \"f126\", \"M384 144c0-44.2-35.8-80-80-80s-80 35.8-80 80c0 36.4 24.3 67.1 57.5 76.8-.6 16.1-4.2 28.5-11 36.9-15.4 19.2-49.3 22.4-85.2 25.7-28.2 2.6-57.4 5.4-81.3 16.9v-144c32.5-10.2 56-40.5 56-76.3 0-44.2-35.8-80-80-80S0 35.8 0 80c0 35.8 23.5 66.1 56 76.3v199.3C23.5 365.9 0 396.2 0 432c0 44.2 35.8 80 80 80s80-35.8 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'glass-cheers',\n  icon: [640, 512, [], \"f79f\", \"M639.4 433.6c-8.4-20.4-31.8-30.1-52.2-21.6l-22.1 9.2-38.7-101.9c47.9-35 64.8-100.3 34.5-152.8L474.3 16c-8-13.9-25.1-19.7-40-13.6L320 49.8 205.7 2.4c-14.9-6.2-32-.3-40 13.6L79.1 166.5C48.9 219 65.7 284.3 113.6 319.2L74.9 421.1l-22.1-9.2c-20.4-8.5-43.7 1.2-52.2 21.6-1.7 4.1.2 8.8 4.3 10.5l162.3 67.4c4.1 1.7 8.7-.2 10.4-4.3 8.4-20.4-1.2-43.8-21.6-52.3l-22.1-9.2L173.3 342c4.4.5 8.8 1.3 13.1 1.3 51.7 0 99.4-33.1 113.4-85.3l20.2-75.4 20.2 75.4c14 52.2 61.7 85.3 113.4 85.3 4.3 0 8.7-.8 13.1-1.3L506 445.6l-22.1 9.2c-20.4 8.5-30.1 31.9-21.6 52.3 1.7 4.1 6.4 6 10.4 4.3L635.1 444c4-1.7 6-6.3 4.3-10.4zM275.9 162.1l-112.1-46.5 36.5-63.4 94.5 39.2-18.9 70.7zm88.2 0l-18.9-70.7 94.5-39.2 36.5 63.4-112.1 46.5z\"]\n};\nvar faGlassMartini = {\n  prefix: 'fas',\n  iconName: 'glass-martini',\n  icon: [512, 512, [], \"f000\", \"M502.05 57.6C523.3 36.34 508.25 0 478.2 0H33.8C3.75 0-11.3 36.34 9.95 57.6L224 271.64V464h-56c-22.09 0-40 17.91-40 40 0 4.42 3.58 8 8 8h240c4.42 0 8-3.58 8-8 0-22.09-17.91-40-40-40h-56V271.64L502.05 57.6z\"]\n};\nvar faGlassMartiniAlt = {\n  prefix: 'fas',\n  iconName: 'glass-martini-alt',\n  icon: [512, 512, [], \"f57b\", \"M502.05 57.6C523.3 36.34 508.25 0 478.2 0H33.8C3.75 0-11.3 36.34 9.95 57.6L224 271.64V464h-56c-22.09 0-40 17.91-40 40 0 4.42 3.58 8 8 8h240c4.42 0 8-3.58 8-8 0-22.09-17.91-40-40-40h-56V271.64L502.05 57.6zM443.77 48l-48 48H116.24l-48-48h375.53z\"]\n};\nvar faGlassWhiskey = {\n  prefix: 'fas',\n  iconName: 'glass-whiskey',\n  icon: [512, 512, [], \"f7a0\", \"M480 32H32C12.5 32-2.4 49.2.3 68.5l56 356.5c4.5 31.5 31.5 54.9 63.4 54.9h273c31.8 0 58.9-23.4 63.4-54.9l55.6-356.5C514.4 49.2 499.5 32 480 32zm-37.4 64l-30 192h-313L69.4 96h373.2z\"]\n};\nvar faGlasses = {\n  prefix: 'fas',\n  iconName: 'glasses',\n  icon: [576, 512, [], \"f530\", \"M574.1 280.37L528.75 98.66c-5.91-23.7-21.59-44.05-43-55.81-21.44-11.73-46.97-14.11-70.19-6.33l-15.25 5.08c-8.39 2.79-12.92 11.86-10.12 20.24l5.06 15.18c2.79 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iconName: 'globe-africa',\n  icon: [496, 512, [], \"f57c\", \"M248 8C111.03 8 0 119.03 0 256s111.03 248 248 248 248-111.03 248-248S384.97 8 248 8zm160 215.5v6.93c0 5.87-3.32 11.24-8.57 13.86l-15.39 7.7a15.485 15.485 0 0 1-15.53-.97l-18.21-12.14a15.52 15.52 0 0 0-13.5-1.81l-2.65.88c-9.7 3.23-13.66 14.79-7.99 23.3l13.24 19.86c2.87 4.31 7.71 6.9 12.89 6.9h8.21c8.56 0 15.5 6.94 15.5 15.5v11.34c0 3.35-1.09 6.62-3.1 9.3l-18.74 24.98c-1.42 1.9-2.39 4.1-2.83 6.43l-4.3 22.83c-.62 3.29-2.29 6.29-4.76 8.56a159.608 159.608 0 0 0-25 29.16l-13.03 19.55a27.756 27.756 0 0 1-23.09 12.36c-10.51 0-20.12-5.94-24.82-15.34a78.902 78.902 0 0 1-8.33-35.29V367.5c0-8.56-6.94-15.5-15.5-15.5h-25.88c-14.49 0-28.38-5.76-38.63-16a54.659 54.659 0 0 1-16-38.63v-14.06c0-17.19 8.1-33.38 21.85-43.7l27.58-20.69a54.663 54.663 0 0 1 32.78-10.93h.89c8.48 0 16.85 1.97 24.43 5.77l14.72 7.36c3.68 1.84 7.93 2.14 11.83.84l47.31-15.77c6.33-2.11 10.6-8.03 10.6-14.7 0-8.56-6.94-15.5-15.5-15.5h-10.09c-4.11 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\"M271.06,144.3l54.27,14.3a8.59,8.59,0,0,1,6.63,8.1c0,4.6-4.09,8.4-9.12,8.4h-35.6a30,30,0,0,1-11.19-2.2c-5.24-2.2-11.28-1.7-15.3,2l-19,17.5a11.68,11.68,0,0,0-2.25,2.66,11.42,11.42,0,0,0,3.88,15.74,83.77,83.77,0,0,0,34.51,11.5V240c0,8.8,7.83,16,17.37,16h17.37c9.55,0,17.38-7.2,17.38-16V222.4c32.93-3.6,57.84-31,53.5-63-3.15-23-22.46-41.3-46.56-47.7L282.68,97.4a8.59,8.59,0,0,1-6.63-8.1c0-4.6,4.09-8.4,9.12-8.4h35.6A30,30,0,0,1,332,83.1c5.23,2.2,11.28,1.7,15.3-2l19-17.5A11.31,11.31,0,0,0,368.47,61a11.43,11.43,0,0,0-3.84-15.78,83.82,83.82,0,0,0-34.52-11.5V16c0-8.8-7.82-16-17.37-16H295.37C285.82,0,278,7.2,278,16V33.6c-32.89,3.6-57.85,31-53.51,63C227.63,119.6,247,137.9,271.06,144.3ZM565.27,328.1c-11.8-10.7-30.2-10-42.6,0L430.27,402a63.64,63.64,0,0,1-40,14H272a16,16,0,0,1,0-32h78.29c15.9,0,30.71-10.9,33.25-26.6a31.2,31.2,0,0,0,.46-5.46A32,32,0,0,0,352,320H192a117.66,117.66,0,0,0-74.1,26.29L71.4,384H16A16,16,0,0,0,0,400v96a16,16,0,0,0,16,16H372.77a64,64,0,0,0,40-14L564,377a32,32,0,0,0,1.28-48.9Z\"]\n};\nvar faHandHoldingWater = {\n  prefix: 'fas',\n  iconName: 'hand-holding-water',\n  icon: [576, 512, [], \"f4c1\", \"M288 256c53 0 96-42.1 96-94 0-40-57.1-120.7-83.2-155.6-6.4-8.5-19.2-8.5-25.6 0C249.1 41.3 192 122 192 162c0 51.9 43 94 96 94zm277.3 72.1c-11.8-10.7-30.2-10-42.6 0L430.3 402c-11.3 9.1-25.4 14-40 14H272c-8.8 0-16-7.2-16-16s7.2-16 16-16h78.3c15.9 0 30.7-10.9 33.3-26.6 3.3-20-12.1-37.4-31.6-37.4H192c-27 0-53.1 9.3-74.1 26.3L71.4 384H16c-8.8 0-16 7.2-16 16v96c0 8.8 7.2 16 16 16h356.8c14.5 0 28.6-4.9 40-14L564 377c15.2-12.1 16.4-35.3 1.3-48.9z\"]\n};\nvar faHandLizard = {\n  prefix: 'fas',\n  iconName: 'hand-lizard',\n  icon: [576, 512, [], \"f258\", \"M384 480h192V363.778a95.998 95.998 0 0 0-14.833-51.263L398.127 54.368A48 48 0 0 0 357.544 32H24C10.745 32 0 42.745 0 56v16c0 30.928 25.072 56 56 56h229.981c12.844 0 21.556 13.067 16.615 24.923l-21.41 51.385A32 32 0 0 1 251.648 224H128c-35.346 0-64 28.654-64 64v8c0 13.255 10.745 24 24 24h147.406a47.995 47.995 0 0 1 25.692 7.455l111.748 70.811A24.001 24.001 0 0 1 384 418.539V480z\"]\n};\nvar faHandMiddleFinger = {\n  prefix: 'fas',\n  iconName: 'hand-middle-finger',\n  icon: [512, 512, [], \"f806\", \"M479.93 317.12a37.33 37.33 0 0 0-28.28-36.19L416 272v-49.59c0-11.44-9.69-21.29-23.15-23.54l-38.4-6.4C336.63 189.5 320 200.86 320 216v32a8 8 0 0 1-16 0V50c0-26.28-20.25-49.2-46.52-50A48 48 0 0 0 208 48v200a8 8 0 0 1-16 0v-32c0-15.15-16.63-26.51-34.45-23.54l-30.68 5.12c-18 3-30.87 16.12-30.87 31.38V376a8 8 0 0 1-16 0v-76l-27.36 15A37.34 37.34 0 0 0 32 348.4v73.47a37.31 37.31 0 0 0 10.93 26.39l30.93 30.93A112 112 0 0 0 153.05 512h215A112 112 0 0 0 480 400z\"]\n};\nvar faHandPaper = {\n  prefix: 'fas',\n  iconName: 'hand-paper',\n  icon: [448, 512, [], \"f256\", \"M408.781 128.007C386.356 127.578 368 146.36 368 168.79V256h-8V79.79c0-22.43-18.356-41.212-40.781-40.783C297.488 39.423 280 57.169 280 79v177h-8V40.79C272 18.36 253.644-.422 231.219.007 209.488.423 192 18.169 192 40v216h-8V80.79c0-22.43-18.356-41.212-40.781-40.783C121.488 40.423 104 58.169 104 80v235.992l-31.648-43.519c-12.993-17.866-38.009-21.817-55.877-8.823-17.865 12.994-21.815 38.01-8.822 55.877l125.601 172.705A48 48 0 0 0 172.073 512h197.59c22.274 0 41.622-15.324 46.724-37.006l26.508-112.66a192.011 192.011 0 0 0 5.104-43.975V168c.001-21.831-17.487-39.577-39.218-39.993z\"]\n};\nvar faHandPeace = {\n  prefix: 'fas',\n  iconName: 'hand-peace',\n  icon: [448, 512, [], \"f25b\", \"M408 216c-22.092 0-40 17.909-40 40h-8v-32c0-22.091-17.908-40-40-40s-40 17.909-40 40v32h-8V48c0-26.51-21.49-48-48-48s-48 21.49-48 48v208h-13.572L92.688 78.449C82.994 53.774 55.134 41.63 30.461 51.324 5.787 61.017-6.356 88.877 3.337 113.551l74.765 190.342-31.09 24.872c-15.381 12.306-19.515 33.978-9.741 51.081l64 112A39.998 39.998 0 0 0 136 512h240c18.562 0 34.686-12.77 38.937-30.838l32-136A39.97 39.97 0 0 0 448 336v-80c0-22.091-17.908-40-40-40z\"]\n};\nvar faHandPointDown = {\n  prefix: 'fas',\n  iconName: 'hand-point-down',\n  icon: [384, 512, [], \"f0a7\", \"M91.826 467.2V317.966c-8.248 5.841-16.558 10.57-24.918 14.153C35.098 345.752-.014 322.222 0 288c.008-18.616 10.897-32.203 29.092-40 28.286-12.122 64.329-78.648 77.323-107.534 7.956-17.857 25.479-28.453 43.845-28.464l.001-.002h171.526c11.812 0 21.897 8.596 23.703 20.269 7.25 46.837 38.483 61.76 38.315 123.731-.007 2.724.195 13.254.195 16 0 50.654-22.122 81.574-71.263 72.6-9.297 18.597-39.486 30.738-62.315 16.45-21.177 24.645-53.896 22.639-70.944 6.299V467.2c0 24.15-20.201 44.8-43.826 44.8-23.283 0-43.826-21.35-43.826-44.8zM112 72V24c0-13.255 10.745-24 24-24h192c13.255 0 24 10.745 24 24v48c0 13.255-10.745 24-24 24H136c-13.255 0-24-10.745-24-24zm212-24c0-11.046-8.954-20-20-20s-20 8.954-20 20 8.954 20 20 20 20-8.954 20-20z\"]\n};\nvar faHandPointLeft = {\n  prefix: 'fas',\n  iconName: 'hand-point-left',\n  icon: [512, 512, [], \"f0a5\", \"M44.8 155.826h149.234c-5.841-8.248-10.57-16.558-14.153-24.918C166.248 99.098 189.778 63.986 224 64c18.616.008 32.203 10.897 40 29.092 12.122 28.286 78.648 64.329 107.534 77.323 17.857 7.956 28.453 25.479 28.464 43.845l.002.001v171.526c0 11.812-8.596 21.897-20.269 23.703-46.837 7.25-61.76 38.483-123.731 38.315-2.724-.007-13.254.195-16 .195-50.654 0-81.574-22.122-72.6-71.263-18.597-9.297-30.738-39.486-16.45-62.315-24.645-21.177-22.639-53.896-6.299-70.944H44.8c-24.15 0-44.8-20.201-44.8-43.826 0-23.283 21.35-43.826 44.8-43.826zM440 176h48c13.255 0 24 10.745 24 24v192c0 13.255-10.745 24-24 24h-48c-13.255 0-24-10.745-24-24V200c0-13.255 10.745-24 24-24zm24 212c11.046 0 20-8.954 20-20s-8.954-20-20-20-20 8.954-20 20 8.954 20 20 20z\"]\n};\nvar faHandPointRight = {\n  prefix: 'fas',\n  iconName: 'hand-point-right',\n  icon: [512, 512, [], \"f0a4\", \"M512 199.652c0 23.625-20.65 43.826-44.8 43.826h-99.851c16.34 17.048 18.346 49.766-6.299 70.944 14.288 22.829 2.147 53.017-16.45 62.315C353.574 425.878 322.654 448 272 448c-2.746 0-13.276-.203-16-.195-61.971.168-76.894-31.065-123.731-38.315C120.596 407.683 112 397.599 112 385.786V214.261l.002-.001c.011-18.366 10.607-35.889 28.464-43.845 28.886-12.994 95.413-49.038 107.534-77.323 7.797-18.194 21.384-29.084 40-29.092 34.222-.014 57.752 35.098 44.119 66.908-3.583 8.359-8.312 16.67-14.153 24.918H467.2c23.45 0 44.8 20.543 44.8 43.826zM96 200v192c0 13.255-10.745 24-24 24H24c-13.255 0-24-10.745-24-24V200c0-13.255 10.745-24 24-24h48c13.255 0 24 10.745 24 24zM68 368c0-11.046-8.954-20-20-20s-20 8.954-20 20 8.954 20 20 20 20-8.954 20-20z\"]\n};\nvar faHandPointUp = {\n  prefix: 'fas',\n  iconName: 'hand-point-up',\n  icon: [384, 512, [], \"f0a6\", \"M135.652 0c23.625 0 43.826 20.65 43.826 44.8v99.851c17.048-16.34 49.766-18.346 70.944 6.299 22.829-14.288 53.017-2.147 62.315 16.45C361.878 158.426 384 189.346 384 240c0 2.746-.203 13.276-.195 16 .168 61.971-31.065 76.894-38.315 123.731C343.683 391.404 333.599 400 321.786 400H150.261l-.001-.002c-18.366-.011-35.889-10.607-43.845-28.464C93.421 342.648 57.377 276.122 29.092 264 10.897 256.203.008 242.616 0 224c-.014-34.222 35.098-57.752 66.908-44.119 8.359 3.583 16.67 8.312 24.918 14.153V44.8c0-23.45 20.543-44.8 43.826-44.8zM136 416h192c13.255 0 24 10.745 24 24v48c0 13.255-10.745 24-24 24H136c-13.255 0-24-10.745-24-24v-48c0-13.255 10.745-24 24-24zm168 28c-11.046 0-20 8.954-20 20s8.954 20 20 20 20-8.954 20-20-8.954-20-20-20z\"]\n};\nvar faHandPointer = {\n  prefix: 'fas',\n  iconName: 'hand-pointer',\n  icon: [448, 512, [], \"f25a\", \"M448 240v96c0 3.084-.356 6.159-1.063 9.162l-32 136C410.686 499.23 394.562 512 376 512H168a40.004 40.004 0 0 1-32.35-16.473l-127.997-176c-12.993-17.866-9.043-42.883 8.822-55.876 17.867-12.994 42.884-9.043 55.877 8.823L104 315.992V40c0-22.091 17.908-40 40-40s40 17.909 40 40v200h8v-40c0-22.091 17.908-40 40-40s40 17.909 40 40v40h8v-24c0-22.091 17.908-40 40-40s40 17.909 40 40v24h8c0-22.091 17.908-40 40-40s40 17.909 40 40zm-256 80h-8v96h8v-96zm88 0h-8v96h8v-96zm88 0h-8v96h8v-96z\"]\n};\nvar faHandRock = {\n  prefix: 'fas',\n  iconName: 'hand-rock',\n  icon: [512, 512, [], \"f255\", \"M464.8 80c-26.9-.4-48.8 21.2-48.8 48h-8V96.8c0-26.3-20.9-48.3-47.2-48.8-26.9-.4-48.8 21.2-48.8 48v32h-8V80.8c0-26.3-20.9-48.3-47.2-48.8-26.9-.4-48.8 21.2-48.8 48v48h-8V96.8c0-26.3-20.9-48.3-47.2-48.8-26.9-.4-48.8 21.2-48.8 48v136l-8-7.1v-48.1c0-26.3-20.9-48.3-47.2-48.8C21.9 127.6 0 149.2 0 176v66.4c0 27.4 11.7 53.5 32.2 71.8l111.7 99.3c10.2 9.1 16.1 22.2 16.1 35.9v6.7c0 13.3 10.7 24 24 24h240c13.3 0 24-10.7 24-24v-2.9c0-12.8 2.6-25.5 7.5-37.3l49-116.3c5-11.8 7.5-24.5 7.5-37.3V128.8c0-26.3-20.9-48.4-47.2-48.8z\"]\n};\nvar faHandScissors = {\n  prefix: 'fas',\n  iconName: 'hand-scissors',\n  icon: [512, 512, [], \"f257\", \"M216 440c0-22.092 17.909-40 40-40v-8h-32c-22.091 0-40-17.908-40-40s17.909-40 40-40h32v-8H48c-26.51 0-48-21.49-48-48s21.49-48 48-48h208v-13.572l-177.551-69.74c-24.674-9.694-36.818-37.555-27.125-62.228 9.693-24.674 37.554-36.817 62.228-27.124l190.342 74.765 24.872-31.09c12.306-15.381 33.978-19.515 51.081-9.741l112 64A40.002 40.002 0 0 1 512 168v240c0 18.562-12.77 34.686-30.838 38.937l-136 32A39.982 39.982 0 0 1 336 480h-80c-22.091 0-40-17.908-40-40z\"]\n};\nvar faHandSparkles = {\n  prefix: 'fas',\n  iconName: 'hand-sparkles',\n  icon: [640, 512, [], \"f95d\", \"M106.66,170.64l.09,0,49.55-20.65a7.32,7.32,0,0,0,3.68-6h0a7.29,7.29,0,0,0-3.68-6l-49.57-20.67-.07,0L86,67.68a6.66,6.66,0,0,0-11.92,0l-20.7,49.63-.05,0L3.7,138A7.29,7.29,0,0,0,0,144H0a7.32,7.32,0,0,0,3.68,6L53.27,170.6l.07,0L74,220.26a6.65,6.65,0,0,0,11.92,0l20.69-49.62ZM471.38,467.41l-1-.42-1-.5a38.67,38.67,0,0,1,0-69.14l1-.49,1-.43,37.49-15.63,15.63-37.48.41-1,.47-.95c3.85-7.74,10.58-13.63,18.35-17.34,0-1.33.25-2.69.27-4V144a32,32,0,0,0-64,0v72a8,8,0,0,1-8,8H456a8,8,0,0,1-8-8V64a32,32,0,0,0-64,0V216a8,8,0,0,1-8,8H360a8,8,0,0,1-8-8V32a32,32,0,0,0-64,0V216a8,8,0,0,1-8,8H264a8,8,0,0,1-8-8V64a32,32,0,0,0-64,0v241l-23.59-32.49a40,40,0,0,0-64.71,47.09L229.3,492.21A48.07,48.07,0,0,0,268.09,512H465.7c19.24,0,35.65-11.73,43.24-28.79l-.07-.17ZM349.79,339.52,320,351.93l-12.42,29.78a4,4,0,0,1-7.15,0L288,351.93l-29.79-12.41a4,4,0,0,1,0-7.16L288,319.94l12.42-29.78a4,4,0,0,1,7.15,0L320,319.94l29.79,12.42a4,4,0,0,1,0,7.16ZM640,431.91a7.28,7.28,0,0,0-3.68-6l-49.57-20.67-.07,0L566,355.63a6.66,6.66,0,0,0-11.92,0l-20.7,49.63-.05,0L483.7,426a7.28,7.28,0,0,0-3.68,6h0a7.29,7.29,0,0,0,3.68,5.95l49.57,20.67.07,0L554,508.21a6.65,6.65,0,0,0,11.92,0l20.69-49.62h0l.09,0,49.55-20.66a7.29,7.29,0,0,0,3.68-5.95h0Z\"]\n};\nvar faHandSpock = {\n  prefix: 'fas',\n  iconName: 'hand-spock',\n  icon: [512, 512, [], \"f259\", \"M510.9005,145.27027,442.604,432.09391A103.99507,103.99507,0,0,1,341.43745,512H214.074a135.96968,135.96968,0,0,1-93.18489-36.95291L12.59072,373.12723a39.992,39.992,0,0,1,54.8122-58.24988l60.59342,57.02528v0a283.24849,283.24849,0,0,0-11.6703-80.46734L73.63726,147.36011a40.00575,40.00575,0,1,1,76.71833-22.7187l37.15458,125.39477a8.33113,8.33113,0,0,0,16.05656-4.4414L153.26183,49.95406A39.99638,39.99638,0,1,1,230.73015,30.0166l56.09491,218.15825a10.42047,10.42047,0,0,0,20.30018-.501L344.80766,63.96966a40.052,40.052,0,0,1,51.30245-30.0893c19.86073,6.2998,30.86262,27.67378,26.67564,48.08487l-33.83869,164.966a7.55172,7.55172,0,0,0,14.74406,3.2666l29.3973-123.45874a39.99414,39.99414,0,1,1,77.81208,18.53121Z\"]\n};\nvar faHands = {\n  prefix: 'fas',\n  iconName: 'hands',\n  icon: [640, 512, [], \"f4c2\", \"M204.8 230.4c-10.6-14.1-30.7-17-44.8-6.4-14.1 10.6-17 30.7-6.4 44.8l38.1 50.8c4.8 6.4 4.1 15.3-1.5 20.9l-12.8 12.8c-6.7 6.7-17.6 6.2-23.6-1.1L64 244.4V96c0-17.7-14.3-32-32-32S0 78.3 0 96v218.4c0 10.9 3.7 21.5 10.5 30l104.1 134.3c5 6.5 8.4 13.9 10.4 21.7 1.8 6.9 8.1 11.6 15.3 11.6H272c8.8 0 16-7.2 16-16V384c0-27.7-9-54.6-25.6-76.8l-57.6-76.8zM608 64c-17.7 0-32 14.3-32 32v148.4l-89.8 107.8c-6 7.2-17 7.7-23.6 1.1l-12.8-12.8c-5.6-5.6-6.3-14.5-1.5-20.9l38.1-50.8c10.6-14.1 7.7-34.2-6.4-44.8-14.1-10.6-34.2-7.7-44.8 6.4l-57.6 76.8C361 329.4 352 356.3 352 384v112c0 8.8 7.2 16 16 16h131.7c7.1 0 13.5-4.7 15.3-11.6 2-7.8 5.4-15.2 10.4-21.7l104.1-134.3c6.8-8.5 10.5-19.1 10.5-30V96c0-17.7-14.3-32-32-32z\"]\n};\nvar faHandsHelping = {\n  prefix: 'fas',\n  iconName: 'hands-helping',\n  icon: [640, 512, [], \"f4c4\", \"M488 192H336v56c0 39.7-32.3 72-72 72s-72-32.3-72-72V126.4l-64.9 39C107.8 176.9 96 197.8 96 220.2v47.3l-80 46.2C.7 322.5-4.6 342.1 4.3 357.4l80 138.6c8.8 15.3 28.4 20.5 43.7 11.7L231.4 448H368c35.3 0 64-28.7 64-64h16c17.7 0 32-14.3 32-32v-64h8c13.3 0 24-10.7 24-24v-48c0-13.3-10.7-24-24-24zm147.7-37.4L555.7 16C546.9.7 527.3-4.5 512 4.3L408.6 64H306.4c-12 0-23.7 3.4-33.9 9.7L239 94.6c-9.4 5.8-15 16.1-15 27.1V248c0 22.1 17.9 40 40 40s40-17.9 40-40v-88h184c30.9 0 56 25.1 56 56v28.5l80-46.2c15.3-8.9 20.5-28.4 11.7-43.7z\"]\n};\nvar faHandsWash = {\n  prefix: 'fas',\n  iconName: 'hands-wash',\n  icon: [576, 512, [], \"f95e\", \"M496,224a48,48,0,1,0-48-48A48,48,0,0,0,496,224ZM311.47,178.45A56.77,56.77,0,0,1,328,176a56,56,0,0,1,19,3.49l15.35-48.61A24,24,0,0,0,342,99.74c-11.53-1.35-22.21,6.44-25.71,17.51l-20.9,66.17ZM93.65,386.33c.8-.19,1.54-.54,2.35-.71V359.93a156,156,0,0,1,107.06-148l73.7-22.76L310.92,81.05a24,24,0,0,0-20.33-31.11c-11.53-1.34-22.22,6.45-25.72,17.52L231.42,173.88a8,8,0,0,1-15.26-4.83L259.53,31.26A24,24,0,0,0,239.2.15C227.67-1.19,217,6.6,213.49,17.66L165.56,169.37a8,8,0,1,1-15.26-4.82l38.56-122a24,24,0,0,0-20.33-31.11C157,10,146.32,17.83,142.82,28.9l-60,189.85L80.76,168.7A24,24,0,0,0,56.9,144.55c-13.23-.05-24.72,10.54-24.9,23.86V281.14A123.69,123.69,0,0,0,93.65,386.33ZM519.1,336H360a8,8,0,0,1,0-16H488a24,24,0,0,0,23.54-28.76C509.35,279.84,498.71,272,487.1,272H288l47.09-17.06a24,24,0,0,0-14.18-45.88L213.19,242.31A123.88,123.88,0,0,0,128,360v25.65a79.78,79.78,0,0,1,58,108.63A118.9,118.9,0,0,0,248,512H456a24,24,0,0,0,23.54-28.76C477.35,471.84,466.71,464,455.1,464H360a8,8,0,0,1,0-16H488a24,24,0,0,0,23.54-28.76C509.35,407.84,498.71,400,487.1,400H360a8,8,0,0,1,0-16H520a24,24,0,0,0,23.54-28.76C541.35,343.84,530.71,336,519.1,336ZM416,64a32,32,0,1,0-32-32A32,32,0,0,0,416,64ZM112,416a48,48,0,1,0,48,48A48,48,0,0,0,112,416Z\"]\n};\nvar faHandshake = {\n  prefix: 'fas',\n  iconName: 'handshake',\n  icon: [640, 512, [], \"f2b5\", \"M434.7 64h-85.9c-8 0-15.7 3-21.6 8.4l-98.3 90c-.1.1-.2.3-.3.4-16.6 15.6-16.3 40.5-2.1 56 12.7 13.9 39.4 17.6 56.1 2.7.1-.1.3-.1.4-.2l79.9-73.2c6.5-5.9 16.7-5.5 22.6 1 6 6.5 5.5 16.6-1 22.6l-26.1 23.9L504 313.8c2.9 2.4 5.5 5 7.9 7.7V128l-54.6-54.6c-5.9-6-14.1-9.4-22.6-9.4zM544 128.2v223.9c0 17.7 14.3 32 32 32h64V128.2h-96zm48 223.9c-8.8 0-16-7.2-16-16s7.2-16 16-16 16 7.2 16 16-7.2 16-16 16zM0 384h64c17.7 0 32-14.3 32-32V128.2H0V384zm48-63.9c8.8 0 16 7.2 16 16s-7.2 16-16 16-16-7.2-16-16c0-8.9 7.2-16 16-16zm435.9 18.6L334.6 217.5l-30 27.5c-29.7 27.1-75.2 24.5-101.7-4.4-26.9-29.4-24.8-74.9 4.4-101.7L289.1 64h-83.8c-8.5 0-16.6 3.4-22.6 9.4L128 128v223.9h18.3l90.5 81.9c27.4 22.3 67.7 18.1 90-9.3l.2-.2 17.9 15.5c15.9 13 39.4 10.5 52.3-5.4l31.4-38.6 5.4 4.4c13.7 11.1 33.9 9.1 45-4.7l9.5-11.7c11.2-13.8 9.1-33.9-4.6-45.1z\"]\n};\nvar faHandshakeAltSlash = {\n  prefix: 'fas',\n  iconName: 'handshake-alt-slash',\n  icon: [640, 512, [], \"f95f\", \"M358.59,195.6,504.2,313.8a63.4,63.4,0,0,1,22.21,37.91H624a16.05,16.05,0,0,0,16-16V143.91A16,16,0,0,0,624,128H512L457.41,73.41A32,32,0,0,0,434.8,64H348.91a32,32,0,0,0-21.61,8.41l-88.12,80.68-25.69-19.85L289.09,64H205.3a32,32,0,0,0-22.6,9.41l-20.34,20.3L45.47,3.38A16,16,0,0,0,23,6.19L3.38,31.46A16,16,0,0,0,6.19,53.91L594.54,508.63A16,16,0,0,0,617,505.82l19.64-25.27a16,16,0,0,0-2.81-22.45L303.4,202.72l32.69-29.92,27-24.7a16,16,0,0,1,21.61,23.61ZM16,128A16.05,16.05,0,0,0,0,144V335.91a16,16,0,0,0,16,16H146.3l90.5,81.89a64,64,0,0,0,90-9.3l.2-.2,17.91,15.5a37.16,37.16,0,0,0,52.29-5.39l8.8-10.82L23.56,128Z\"]\n};\nvar faHandshakeSlash = {\n  prefix: 'fas',\n  iconName: 'handshake-slash',\n  icon: [640, 512, [], \"f960\", \"M0,128.21V384H64a32,32,0,0,0,32-32V184L23.83,128.21ZM48,320.1a16,16,0,1,1-16,16A16,16,0,0,1,48,320.1Zm80,31.81h18.3l90.5,81.89a64,64,0,0,0,90-9.3l.2-.2,17.91,15.5a37.16,37.16,0,0,0,52.29-5.39l8.8-10.82L128,208.72Zm416-223.7V352.1a32,32,0,0,0,32,32h64V128.21ZM592,352.1a16,16,0,1,1,16-16A16,16,0,0,1,592,352.1ZM303.33,202.67l59.58-54.57a16,16,0,0,1,21.59,23.61L358.41,195.6,504,313.8a73.08,73.08,0,0,1,7.91,7.7V128L457.3,73.41A31.76,31.76,0,0,0,434.7,64H348.8a31.93,31.93,0,0,0-21.6,8.41l-88.07,80.64-25.64-19.81L289.09,64H205.3a32,32,0,0,0-22.6,9.41L162.36,93.72,45.47,3.38A16,16,0,0,0,23,6.19L3.38,31.46A16,16,0,0,0,6.19,53.91L594.53,508.63A16,16,0,0,0,617,505.82l19.65-25.27a16,16,0,0,0-2.82-22.45Z\"]\n};\nvar faHanukiah = {\n  prefix: 'fas',\n  iconName: 'hanukiah',\n  icon: [640, 512, [], \"f6e6\", \"M232 160c-4.42 0-8 3.58-8 8v120h32V168c0-4.42-3.58-8-8-8h-16zm-64 0c-4.42 0-8 3.58-8 8v120h32V168c0-4.42-3.58-8-8-8h-16zm224 0c-4.42 0-8 3.58-8 8v120h32V168c0-4.42-3.58-8-8-8h-16zm64 0c-4.42 0-8 3.58-8 8v120h32V168c0-4.42-3.58-8-8-8h-16zm88 8c0-4.42-3.58-8-8-8h-16c-4.42 0-8 3.58-8 8v120h32V168zm-440-8c-4.42 0-8 3.58-8 8v120h32V168c0-4.42-3.58-8-8-8h-16zm520 0h-32c-8.84 0-16 7.16-16 16v112c0 17.67-14.33 32-32 32H352V128c0-8.84-7.16-16-16-16h-32c-8.84 0-16 7.16-16 16v192H96c-17.67 0-32-14.33-32-32V176c0-8.84-7.16-16-16-16H16c-8.84 0-16 7.16-16 16v112c0 53.02 42.98 96 96 96h192v64H112c-8.84 0-16 7.16-16 16v32c0 8.84 7.16 16 16 16h416c8.84 0 16-7.16 16-16v-32c0-8.84-7.16-16-16-16H352v-64h192c53.02 0 96-42.98 96-96V176c0-8.84-7.16-16-16-16zm-16-32c13.25 0 24-11.94 24-26.67S608 48 608 48s-24 38.61-24 53.33S594.75 128 608 128zm-576 0c13.25 0 24-11.94 24-26.67S32 48 32 48 8 86.61 8 101.33 18.75 128 32 128zm288-48c13.25 0 24-11.94 24-26.67S320 0 320 0s-24 38.61-24 53.33S306.75 80 320 80zm-208 48c13.25 0 24-11.94 24-26.67S112 48 112 48s-24 38.61-24 53.33S98.75 128 112 128zm64 0c13.25 0 24-11.94 24-26.67S176 48 176 48s-24 38.61-24 53.33S162.75 128 176 128zm64 0c13.25 0 24-11.94 24-26.67S240 48 240 48s-24 38.61-24 53.33S226.75 128 240 128zm160 0c13.25 0 24-11.94 24-26.67S400 48 400 48s-24 38.61-24 53.33S386.75 128 400 128zm64 0c13.25 0 24-11.94 24-26.67S464 48 464 48s-24 38.61-24 53.33S450.75 128 464 128zm64 0c13.25 0 24-11.94 24-26.67S528 48 528 48s-24 38.61-24 53.33S514.75 128 528 128z\"]\n};\nvar faHardHat = {\n  prefix: 'fas',\n  iconName: 'hard-hat',\n  icon: [512, 512, [], \"f807\", \"M480 288c0-80.25-49.28-148.92-119.19-177.62L320 192V80a16 16 0 0 0-16-16h-96a16 16 0 0 0-16 16v112l-40.81-81.62C81.28 139.08 32 207.75 32 288v64h448zm16 96H16a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h480a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16z\"]\n};\nvar faHashtag = {\n  prefix: 'fas',\n  iconName: 'hashtag',\n  icon: [448, 512, [], \"f292\", \"M440.667 182.109l7.143-40c1.313-7.355-4.342-14.109-11.813-14.109h-74.81l14.623-81.891C377.123 38.754 371.468 32 363.997 32h-40.632a12 12 0 0 0-11.813 9.891L296.175 128H197.54l14.623-81.891C213.477 38.754 207.822 32 200.35 32h-40.632a12 12 0 0 0-11.813 9.891L132.528 128H53.432a12 12 0 0 0-11.813 9.891l-7.143 40C33.163 185.246 38.818 192 46.289 192h74.81L98.242 320H19.146a12 12 0 0 0-11.813 9.891l-7.143 40C-1.123 377.246 4.532 384 12.003 384h74.81L72.19 465.891C70.877 473.246 76.532 480 84.003 480h40.632a12 12 0 0 0 11.813-9.891L151.826 384h98.634l-14.623 81.891C234.523 473.246 240.178 480 247.65 480h40.632a12 12 0 0 0 11.813-9.891L315.472 384h79.096a12 12 0 0 0 11.813-9.891l7.143-40c1.313-7.355-4.342-14.109-11.813-14.109h-74.81l22.857-128h79.096a12 12 0 0 0 11.813-9.891zM261.889 320h-98.634l22.857-128h98.634l-22.857 128z\"]\n};\nvar faHatCowboy = {\n  prefix: 'fas',\n  iconName: 'hat-cowboy',\n  icon: [640, 512, [], \"f8c0\", \"M490 296.9C480.51 239.51 450.51 64 392.3 64c-14 0-26.49 5.93-37 14a58.21 58.21 0 0 1-70.58 0c-10.51-8-23-14-37-14-58.2 0-88.2 175.47-97.71 232.88C188.81 309.47 243.73 320 320 320s131.23-10.51 170-23.1zm142.9-37.18a16 16 0 0 0-19.75 1.5c-1 .9-101.27 90.78-293.16 90.78-190.82 0-292.22-89.94-293.24-90.84A16 16 0 0 0 1 278.53C1.73 280.55 78.32 480 320 480s318.27-199.45 319-201.47a16 16 0 0 0-6.09-18.81z\"]\n};\nvar faHatCowboySide = {\n  prefix: 'fas',\n  iconName: 'hat-cowboy-side',\n  icon: [640, 512, [], \"f8c1\", \"M260.8 291.06c-28.63-22.94-62-35.06-96.4-35.06C87 256 21.47 318.72 1.43 412.06c-3.55 16.6-.43 33.83 8.57 47.3C18.75 472.47 31.83 480 45.88 480H592c-103.21 0-155-37.07-233.19-104.46zm234.65-18.29L468.4 116.2A64 64 0 0 0 392 64.41L200.85 105a64 64 0 0 0-50.35 55.79L143.61 226c6.9-.83 13.7-2 20.79-2 41.79 0 82 14.55 117.29 42.82l98 84.48C450.76 412.54 494.9 448 592 448a48 48 0 0 0 48-48c0-25.39-29.6-119.33-144.55-127.23z\"]\n};\nvar faHatWizard = {\n  prefix: 'fas',\n  iconName: 'hat-wizard',\n  icon: [512, 512, [], \"f6e8\", \"M496 448H16c-8.84 0-16 7.16-16 16v32c0 8.84 7.16 16 16 16h480c8.84 0 16-7.16 16-16v-32c0-8.84-7.16-16-16-16zm-304-64l-64-32 64-32 32-64 32 64 64 32-64 32-16 32h208l-86.41-201.63a63.955 63.955 0 0 1-1.89-45.45L416 0 228.42 107.19a127.989 127.989 0 0 0-53.46 59.15L64 416h144l-16-32zm64-224l16-32 16 32 32 16-32 16-16 32-16-32-32-16 32-16z\"]\n};\nvar faHdd = {\n  prefix: 'fas',\n  iconName: 'hdd',\n  icon: [576, 512, [], \"f0a0\", \"M576 304v96c0 26.51-21.49 48-48 48H48c-26.51 0-48-21.49-48-48v-96c0-26.51 21.49-48 48-48h480c26.51 0 48 21.49 48 48zm-48-80a79.557 79.557 0 0 1 30.777 6.165L462.25 85.374A48.003 48.003 0 0 0 422.311 64H153.689a48 48 0 0 0-39.938 21.374L17.223 230.165A79.557 79.557 0 0 1 48 224h480zm-48 96c-17.673 0-32 14.327-32 32s14.327 32 32 32 32-14.327 32-32-14.327-32-32-32zm-96 0c-17.673 0-32 14.327-32 32s14.327 32 32 32 32-14.327 32-32-14.327-32-32-32z\"]\n};\nvar faHeadSideCough = {\n  prefix: 'fas',\n  iconName: 'head-side-cough',\n  icon: [640, 512, [], \"f961\", \"M616,304a24,24,0,1,0-24-24A24,24,0,0,0,616,304ZM552,416a24,24,0,1,0,24,24A24,24,0,0,0,552,416Zm-64-56a24,24,0,1,0,24,24A24,24,0,0,0,488,360ZM616,464a24,24,0,1,0,24,24A24,24,0,0,0,616,464Zm0-104a24,24,0,1,0,24,24A24,24,0,0,0,616,360Zm-64-40a24,24,0,1,0,24,24A24,24,0,0,0,552,320Zm-74.78-45c-21-47.12-48.5-151.75-73.12-186.75A208.13,208.13,0,0,0,234.1,0H192C86,0,0,86,0,192c0,56.75,24.75,107.62,64,142.88V512H288V480h64a64,64,0,0,0,64-64H320a32,32,0,0,1,0-64h96V320h32A32,32,0,0,0,477.22,275ZM288,224a32,32,0,1,1,32-32A32.07,32.07,0,0,1,288,224Z\"]\n};\nvar faHeadSideCoughSlash = {\n  prefix: 'fas',\n  iconName: 'head-side-cough-slash',\n  icon: [640, 512, [], \"f962\", \"M454.11,319.21c19.56-3.81,31.62-25,23.11-44.21-21-47.12-48.5-151.75-73.12-186.75A208.13,208.13,0,0,0,234.1,0H192A190.64,190.64,0,0,0,84.18,33.3L45.46,3.38A16,16,0,0,0,23,6.19L3.37,31.46A16,16,0,0,0,6.18,53.91L594.53,508.63A16,16,0,0,0,617,505.82l19.64-25.27a16,16,0,0,0-2.81-22.45ZM313.39,210.45,263.61,172c5.88-7.14,14.43-12,24.36-12a32.06,32.06,0,0,1,32,32C320,199,317.24,205.17,313.39,210.45ZM616,304a24,24,0,1,0-24-24A24,24,0,0,0,616,304Zm-64,64a24,24,0,1,0-24-24A24,24,0,0,0,552,368ZM288,384a32,32,0,0,1,32-32h19.54L20.73,105.59A190.86,190.86,0,0,0,0,192c0,56.75,24.75,107.62,64,142.88V512H288V480h64a64,64,0,0,0,64-64H320A32,32,0,0,1,288,384Zm328-24a24,24,0,1,0,24,24A24,24,0,0,0,616,360Z\"]\n};\nvar faHeadSideMask = {\n  prefix: 'fas',\n  iconName: 'head-side-mask',\n  icon: [512, 512, [], \"f963\", \"M.15,184.42C-2.17,244.21,23,298.06,64,334.88V512H224V316.51L3.67,156.25A182.28,182.28,0,0,0,.15,184.42ZM509.22,275c-21-47.12-48.5-151.75-73.12-186.75A208.11,208.11,0,0,0,266.11,0H200C117,0,42.48,50.57,13.25,123.65L239.21,288H511.76A31.35,31.35,0,0,0,509.22,275ZM320,224a32,32,0,1,1,32-32A32.07,32.07,0,0,1,320,224Zm16,144H496l16-48H256V512H401.88a64,64,0,0,0,60.71-43.76L464,464H336a16,16,0,0,1,0-32H474.67l10.67-32H336a16,16,0,0,1,0-32Z\"]\n};\nvar faHeadSideVirus = {\n  prefix: 'fas',\n  iconName: 'head-side-virus',\n  icon: [512, 512, [], \"f964\", \"M272,240a16,16,0,1,0,16,16A16,16,0,0,0,272,240Zm-64-64a16,16,0,1,0,16,16A16,16,0,0,0,208,176Zm301.2,99c-20.93-47.12-48.43-151.73-73.07-186.75A207.9,207.9,0,0,0,266.09,0H192C86,0,0,86,0,192A191.23,191.23,0,0,0,64,334.81V512H320V448h64a64,64,0,0,0,64-64V320H480A32,32,0,0,0,509.2,275ZM368,240H355.88c-28.51,0-42.79,34.47-22.63,54.63l8.58,8.57a16,16,0,1,1-22.63,22.63l-8.57-8.58C290.47,297.09,256,311.37,256,339.88V352a16,16,0,0,1-32,0V339.88c0-28.51-34.47-42.79-54.63-22.63l-8.57,8.58a16,16,0,0,1-22.63-22.63l8.58-8.57c20.16-20.16,5.88-54.63-22.63-54.63H112a16,16,0,0,1,0-32h12.12c28.51,0,42.79-34.47,22.63-54.63l-8.58-8.57a16,16,0,0,1,22.63-22.63l8.57,8.58c20.16,20.16,54.63,5.88,54.63-22.63V96a16,16,0,0,1,32,0v12.12c0,28.51,34.47,42.79,54.63,22.63l8.57-8.58a16,16,0,0,1,22.63,22.63l-8.58,8.57C313.09,173.53,327.37,208,355.88,208H368a16,16,0,0,1,0,32Z\"]\n};\nvar faHeading = {\n  prefix: 'fas',\n  iconName: 'heading',\n  icon: [512, 512, [], \"f1dc\", \"M448 96v320h32a16 16 0 0 1 16 16v32a16 16 0 0 1-16 16H320a16 16 0 0 1-16-16v-32a16 16 0 0 1 16-16h32V288H160v128h32a16 16 0 0 1 16 16v32a16 16 0 0 1-16 16H32a16 16 0 0 1-16-16v-32a16 16 0 0 1 16-16h32V96H32a16 16 0 0 1-16-16V48a16 16 0 0 1 16-16h160a16 16 0 0 1 16 16v32a16 16 0 0 1-16 16h-32v128h192V96h-32a16 16 0 0 1-16-16V48a16 16 0 0 1 16-16h160a16 16 0 0 1 16 16v32a16 16 0 0 1-16 16z\"]\n};\nvar faHeadphones = {\n  prefix: 'fas',\n  iconName: 'headphones',\n  icon: [512, 512, [], \"f025\", \"M256 32C114.52 32 0 146.496 0 288v48a32 32 0 0 0 17.689 28.622l14.383 7.191C34.083 431.903 83.421 480 144 480h24c13.255 0 24-10.745 24-24V280c0-13.255-10.745-24-24-24h-24c-31.342 0-59.671 12.879-80 33.627V288c0-105.869 86.131-192 192-192s192 86.131 192 192v1.627C427.671 268.879 399.342 256 368 256h-24c-13.255 0-24 10.745-24 24v176c0 13.255 10.745 24 24 24h24c60.579 0 109.917-48.098 111.928-108.187l14.382-7.191A32 32 0 0 0 512 336v-48c0-141.479-114.496-256-256-256z\"]\n};\nvar faHeadphonesAlt = {\n  prefix: 'fas',\n  iconName: 'headphones-alt',\n  icon: [512, 512, [], \"f58f\", \"M160 288h-16c-35.35 0-64 28.7-64 64.12v63.76c0 35.41 28.65 64.12 64 64.12h16c17.67 0 32-14.36 32-32.06V320.06c0-17.71-14.33-32.06-32-32.06zm208 0h-16c-17.67 0-32 14.35-32 32.06v127.88c0 17.7 14.33 32.06 32 32.06h16c35.35 0 64-28.71 64-64.12v-63.76c0-35.41-28.65-64.12-64-64.12zM256 32C112.91 32 4.57 151.13 0 288v112c0 8.84 7.16 16 16 16h16c8.84 0 16-7.16 16-16V288c0-114.67 93.33-207.8 208-207.82 114.67.02 208 93.15 208 207.82v112c0 8.84 7.16 16 16 16h16c8.84 0 16-7.16 16-16V288C507.43 151.13 399.09 32 256 32z\"]\n};\nvar faHeadset = {\n  prefix: 'fas',\n  iconName: 'headset',\n  icon: [512, 512, [], \"f590\", \"M192 208c0-17.67-14.33-32-32-32h-16c-35.35 0-64 28.65-64 64v48c0 35.35 28.65 64 64 64h16c17.67 0 32-14.33 32-32V208zm176 144c35.35 0 64-28.65 64-64v-48c0-35.35-28.65-64-64-64h-16c-17.67 0-32 14.33-32 32v112c0 17.67 14.33 32 32 32h16zM256 0C113.18 0 4.58 118.83 0 256v16c0 8.84 7.16 16 16 16h16c8.84 0 16-7.16 16-16v-16c0-114.69 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\"f21e\", \"M320.2 243.8l-49.7 99.4c-6 12.1-23.4 11.7-28.9-.6l-56.9-126.3-30 71.7H60.6l182.5 186.5c7.1 7.3 18.6 7.3 25.7 0L451.4 288H342.3l-22.1-44.2zM473.7 73.9l-2.4-2.5c-51.5-52.6-135.8-52.6-187.4 0L256 100l-27.9-28.5c-51.5-52.7-135.9-52.7-187.4 0l-2.4 2.4C-10.4 123.7-12.5 203 31 256h102.4l35.9-86.2c5.4-12.9 23.6-13.2 29.4-.4l58.2 129.3 49-97.9c5.9-11.8 22.7-11.8 28.6 0l27.6 55.2H481c43.5-53 41.4-132.3-7.3-182.1z\"]\n};\nvar faHelicopter = {\n  prefix: 'fas',\n  iconName: 'helicopter',\n  icon: [640, 512, [], \"f533\", \"M304 384h272c17.67 0 32-14.33 32-32 0-123.71-100.29-224-224-224V64h176c8.84 0 16-7.16 16-16V16c0-8.84-7.16-16-16-16H144c-8.84 0-16 7.16-16 16v32c0 8.84 7.16 16 16 16h176v64H112L68.8 70.4C65.78 66.37 61.03 64 56 64H16.01C5.6 64-2.04 73.78.49 83.88L32 192l160 64 86.4 115.2A31.992 31.992 0 0 0 304 384zm112-188.49C478.55 208.3 528.03 257.44 540.79 320H416V195.51zm219.37 263.3l-22.15-22.2c-6.25-6.26-16.24-6.1-22.64.01-7.09 6.77-13.84 11.25-24.64 11.25H240c-8.84 0-16 7.18-16 16.03v32.06c0 8.85 7.16 16.03 16 16.03h325.94c14.88 0 35.3-.47 68.45-29.52 7.02-6.14 7.57-17.05.98-23.66z\"]\n};\nvar faHighlighter = {\n  prefix: 'fas',\n  iconName: 'highlighter',\n  icon: [544, 512, [], \"f591\", \"M0 479.98L99.92 512l35.45-35.45-67.04-67.04L0 479.98zm124.61-240.01a36.592 36.592 0 0 0-10.79 38.1l13.05 42.83-50.93 50.94 96.23 96.23 50.86-50.86 42.74 13.08c13.73 4.2 28.65-.01 38.15-10.78l35.55-41.64-173.34-173.34-41.52 35.44zm403.31-160.7l-63.2-63.2c-20.49-20.49-53.38-21.52-75.12-2.35L190.55 183.68l169.77 169.78L530.27 154.4c19.18-21.74 18.15-54.63-2.35-75.13z\"]\n};\nvar faHiking = {\n  prefix: 'fas',\n  iconName: 'hiking',\n  icon: [384, 512, [], \"f6ec\", \"M80.95 472.23c-4.28 17.16 6.14 34.53 23.28 38.81 2.61.66 5.22.95 7.8.95 14.33 0 27.37-9.7 31.02-24.23l25.24-100.97-52.78-52.78-34.56 138.22zm14.89-196.12L137 117c2.19-8.42-3.14-16.95-11.92-19.06-43.88-10.52-88.35 15.07-99.32 57.17L.49 253.24c-2.19 8.42 3.14 16.95 11.92 19.06l63.56 15.25c8.79 2.1 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16.9l25.5 31A12 12 0 0 0 45.15 301l235.22-193.74a12.19 12.19 0 0 1 15.3 0L530.9 301a12 12 0 0 0 16.9-1.6l25.5-31a12 12 0 0 0-1.7-16.93z\"]\n};\nvar faHorse = {\n  prefix: 'fas',\n  iconName: 'horse',\n  icon: [576, 512, [], \"f6f0\", \"M575.92 76.6c-.01-8.13-3.02-15.87-8.58-21.8-3.78-4.03-8.58-9.12-13.69-14.5 11.06-6.84 19.5-17.49 22.18-30.66C576.85 4.68 572.96 0 567.9 0H447.92c-70.69 0-128 57.31-128 128H160c-28.84 0-54.4 12.98-72 33.11V160c-48.53 0-88 39.47-88 88v56c0 8.84 7.16 16 16 16h16c8.84 0 16-7.16 16-16v-56c0-13.22 6.87-24.39 16.78-31.68-.21 2.58-.78 5.05-.78 7.68 0 27.64 11.84 52.36 30.54 69.88l-25.72 68.6a63.945 63.945 0 0 0-2.16 37.99l24.85 99.41A15.982 15.982 0 0 0 107.02 512h65.96c10.41 0 18.05-9.78 15.52-19.88l-26.31-105.26 23.84-63.59L320 345.6V496c0 8.84 7.16 16 16 16h64c8.84 0 16-7.16 16-16V318.22c19.74-20.19 32-47.75 32-78.22 0-.22-.07-.42-.08-.64V136.89l16 7.11 18.9 37.7c7.45 14.87 25.05 21.55 40.49 15.37l32.55-13.02a31.997 31.997 0 0 0 20.12-29.74l-.06-77.71zm-64 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12zM308 192h-40c-6.627 0-12 5.373-12 12v40c0 6.627 5.373 12 12 12h40c6.627 0 12-5.373 12-12v-40c0-6.627-5.373-12-12-12zm-168 64h40c6.627 0 12-5.373 12-12v-40c0-6.627-5.373-12-12-12h-40c-6.627 0-12 5.373-12 12v40c0 6.627 5.373 12 12 12zm104 128h-40c-6.627 0-12 5.373-12 12v84h64v-84c0-6.627-5.373-12-12-12zm64-96h-40c-6.627 0-12 5.373-12 12v40c0 6.627 5.373 12 12 12h40c6.627 0 12-5.373 12-12v-40c0-6.627-5.373-12-12-12zm-116 12c0-6.627-5.373-12-12-12h-40c-6.627 0-12 5.373-12 12v40c0 6.627 5.373 12 12 12h40c6.627 0 12-5.373 12-12v-40zM182 96h26v26a6 6 0 0 0 6 6h20a6 6 0 0 0 6-6V96h26a6 6 0 0 0 6-6V70a6 6 0 0 0-6-6h-26V38a6 6 0 0 0-6-6h-20a6 6 0 0 0-6 6v26h-26a6 6 0 0 0-6 6v20a6 6 0 0 0 6 6z\"]\n};\nvar faHospitalAlt = {\n  prefix: 'fas',\n  iconName: 'hospital-alt',\n  icon: [576, 512, [], \"f47d\", \"M544 96H416V32c0-17.7-14.3-32-32-32H192c-17.7 0-32 14.3-32 32v64H32c-17.7 0-32 14.3-32 32v368c0 8.8 7.2 16 16 16h544c8.8 0 16-7.2 16-16V128c0-17.7-14.3-32-32-32zM160 436c0 6.6-5.4 12-12 12h-40c-6.6 0-12-5.4-12-12v-40c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v40zm0-128c0 6.6-5.4 12-12 12h-40c-6.6 0-12-5.4-12-12v-40c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v40zm160 128c0 6.6-5.4 12-12 12h-40c-6.6 0-12-5.4-12-12v-40c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v40zm0-128c0 6.6-5.4 12-12 12h-40c-6.6 0-12-5.4-12-12v-40c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v40zm16-170c0 3.3-2.7 6-6 6h-26v26c0 3.3-2.7 6-6 6h-20c-3.3 0-6-2.7-6-6v-26h-26c-3.3 0-6-2.7-6-6v-20c0-3.3 2.7-6 6-6h26V86c0-3.3 2.7-6 6-6h20c3.3 0 6 2.7 6 6v26h26c3.3 0 6 2.7 6 6v20zm144 298c0 6.6-5.4 12-12 12h-40c-6.6 0-12-5.4-12-12v-40c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v40zm0-128c0 6.6-5.4 12-12 12h-40c-6.6 0-12-5.4-12-12v-40c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v40z\"]\n};\nvar faHospitalSymbol = {\n  prefix: 'fas',\n  iconName: 'hospital-symbol',\n  icon: [512, 512, [], \"f47e\", \"M256 0C114.6 0 0 114.6 0 256s114.6 256 256 256 256-114.6 256-256S397.4 0 256 0zm112 376c0 4.4-3.6 8-8 8h-48c-4.4 0-8-3.6-8-8v-88h-96v88c0 4.4-3.6 8-8 8h-48c-4.4 0-8-3.6-8-8V136c0-4.4 3.6-8 8-8h48c4.4 0 8 3.6 8 8v88h96v-88c0-4.4 3.6-8 8-8h48c4.4 0 8 3.6 8 8v240z\"]\n};\nvar faHospitalUser = {\n  prefix: 'fas',\n  iconName: 'hospital-user',\n  icon: [640, 512, [], \"f80d\", \"M480 320a96 96 0 1 0-96-96 96 96 0 0 0 96 96zm48 32a22.88 22.88 0 0 0-7.06 1.09 124.76 124.76 0 0 1-81.89 0A22.82 22.82 0 0 0 432 352a112 112 0 0 0-112 112.62c.14 26.26 21.73 47.38 48 47.38h224c26.27 0 47.86-21.12 48-47.38A112 112 0 0 0 528 352zm-198.09 10.45A145.19 145.19 0 0 1 352 344.62V128a32 32 0 0 0-32-32h-32V32a32 32 0 0 0-32-32H96a32 32 0 0 0-32 32v64H32a32 32 0 0 0-32 32v368a16 16 0 0 0 16 16h288.31A78.62 78.62 0 0 1 288 464.79a143.06 143.06 0 0 1 41.91-102.34zM144 404a12 12 0 0 1-12 12H92a12 12 0 0 1-12-12v-40a12 12 0 0 1 12-12h40a12 12 0 0 1 12 12zm0-128a12 12 0 0 1-12 12H92a12 12 0 0 1-12-12v-40a12 12 0 0 1 12-12h40a12 12 0 0 1 12 12zm48-122a6 6 0 0 1-6 6h-20a6 6 0 0 1-6-6v-26h-26a6 6 0 0 1-6-6v-20a6 6 0 0 1 6-6h26V70a6 6 0 0 1 6-6h20a6 6 0 0 1 6 6v26h26a6 6 0 0 1 6 6v20a6 6 0 0 1-6 6h-26zm80 250a12 12 0 0 1-12 12h-40a12 12 0 0 1-12-12v-40a12 12 0 0 1 12-12h40a12 12 0 0 1 12 12zm0-128a12 12 0 0 1-12 12h-40a12 12 0 0 1-12-12v-40a12 12 0 0 1 12-12h40a12 12 0 0 1 12 12z\"]\n};\nvar faHotTub = {\n  prefix: 'fas',\n  iconName: 'hot-tub',\n  icon: [512, 512, [], \"f593\", \"M414.21 177.65c1.02 8.21 7.75 14.35 15.75 14.35h16.12c9.51 0 17.08-8.57 16-18.35-4.34-39.11-22.4-74.53-50.13-97.16-17.37-14.17-28.82-36.75-31.98-62.15C378.96 6.14 372.22 0 364.23 0h-16.12c-9.51 0-17.09 8.57-16 18.35 4.34 39.11 22.4 74.53 50.13 97.16 17.36 14.17 28.82 36.75 31.97 62.14zm-108 0c1.02 8.21 7.75 14.35 15.75 14.35h16.12c9.51 0 17.08-8.57 16-18.35-4.34-39.11-22.4-74.53-50.13-97.16-17.37-14.17-28.82-36.75-31.98-62.15C270.96 6.14 264.22 0 256.23 0h-16.12c-9.51 0-17.09 8.57-16 18.35 4.34 39.11 22.4 74.53 50.13 97.16 17.36 14.17 28.82 36.75 31.97 62.14zM480 256H256l-110.93-83.2a63.99 63.99 0 0 0-38.4-12.8H64c-35.35 0-64 28.65-64 64v224c0 35.35 28.65 64 64 64h384c35.35 0 64-28.65 64-64V288c0-17.67-14.33-32-32-32zM128 440c0 4.42-3.58 8-8 8h-16c-4.42 0-8-3.58-8-8V328c0-4.42 3.58-8 8-8h16c4.42 0 8 3.58 8 8v112zm96 0c0 4.42-3.58 8-8 8h-16c-4.42 0-8-3.58-8-8V328c0-4.42 3.58-8 8-8h16c4.42 0 8 3.58 8 8v112zm96 0c0 4.42-3.58 8-8 8h-16c-4.42 0-8-3.58-8-8V328c0-4.42 3.58-8 8-8h16c4.42 0 8 3.58 8 8v112zm96 0c0 4.42-3.58 8-8 8h-16c-4.42 0-8-3.58-8-8V328c0-4.42 3.58-8 8-8h16c4.42 0 8 3.58 8 8v112zM64 128c35.35 0 64-28.65 64-64S99.35 0 64 0 0 28.65 0 64s28.65 64 64 64z\"]\n};\nvar faHotdog = {\n  prefix: 'fas',\n  iconName: 'hotdog',\n  icon: [512, 512, [], \"f80f\", \"M488.56 23.44a80 80 0 0 0-113.12 0l-352 352a80 80 0 1 0 113.12 113.12l352-352a80 80 0 0 0 0-113.12zm-49.93 95.19c-19.6 19.59-37.52 22.67-51.93 25.14C373.76 146 364.4 147.6 352 160s-14 21.76-16.23 34.71c-2.48 14.4-5.55 32.33-25.15 51.92s-37.52 22.67-51.92 25.15C245.75 274 236.4 275.6 224 288s-14 21.75-16.23 34.7c-2.47 14.4-5.54 32.33-25.14 51.92s-37.53 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44.8c0-6.4 6.4-12.8 12.8-12.8h38.4c6.4 0 12.8 6.4 12.8 12.8v38.4c0 6.4-6.4 12.8-12.8 12.8h-38.4c-6.4 0-12.8-6.4-12.8-12.8v-38.4zm0 96c0-6.4 6.4-12.8 12.8-12.8h38.4c6.4 0 12.8 6.4 12.8 12.8v38.4c0 6.4-6.4 12.8-12.8 12.8h-38.4c-6.4 0-12.8-6.4-12.8-12.8v-38.4zm-128-96c0-6.4 6.4-12.8 12.8-12.8h38.4c6.4 0 12.8 6.4 12.8 12.8v38.4c0 6.4-6.4 12.8-12.8 12.8h-38.4c-6.4 0-12.8-6.4-12.8-12.8v-38.4zM179.2 256h-38.4c-6.4 0-12.8-6.4-12.8-12.8v-38.4c0-6.4 6.4-12.8 12.8-12.8h38.4c6.4 0 12.8 6.4 12.8 12.8v38.4c0 6.4-6.4 12.8-12.8 12.8zM192 384c0-53.02 42.98-96 96-96s96 42.98 96 96H192zm256-140.8c0 6.4-6.4 12.8-12.8 12.8h-38.4c-6.4 0-12.8-6.4-12.8-12.8v-38.4c0-6.4 6.4-12.8 12.8-12.8h38.4c6.4 0 12.8 6.4 12.8 12.8v38.4zm0-96c0 6.4-6.4 12.8-12.8 12.8h-38.4c-6.4 0-12.8-6.4-12.8-12.8v-38.4c0-6.4 6.4-12.8 12.8-12.8h38.4c6.4 0 12.8 6.4 12.8 12.8v38.4z\"]\n};\nvar faHourglass = {\n  prefix: 'fas',\n  iconName: 'hourglass',\n  icon: [384, 512, [], \"f254\", \"M360 64c13.255 0 24-10.745 24-24V24c0-13.255-10.745-24-24-24H24C10.745 0 0 10.745 0 24v16c0 13.255 10.745 24 24 24 0 90.965 51.016 167.734 120.842 192C75.016 280.266 24 357.035 24 448c-13.255 0-24 10.745-24 24v16c0 13.255 10.745 24 24 24h336c13.255 0 24-10.745 24-24v-16c0-13.255-10.745-24-24-24 0-90.965-51.016-167.734-120.842-192C308.984 231.734 360 154.965 360 64z\"]\n};\nvar faHourglassEnd = {\n  prefix: 'fas',\n  iconName: 'hourglass-end',\n  icon: [384, 512, [], \"f253\", \"M360 64c13.255 0 24-10.745 24-24V24c0-13.255-10.745-24-24-24H24C10.745 0 0 10.745 0 24v16c0 13.255 10.745 24 24 24 0 90.965 51.016 167.734 120.842 192C75.016 280.266 24 357.035 24 448c-13.255 0-24 10.745-24 24v16c0 13.255 10.745 24 24 24h336c13.255 0 24-10.745 24-24v-16c0-13.255-10.745-24-24-24 0-90.965-51.016-167.734-120.842-192C308.984 231.734 360 154.965 360 64zM192 208c-57.787 0-104-66.518-104-144h208c0 77.945-46.51 144-104 144z\"]\n};\nvar faHourglassHalf = {\n  prefix: 'fas',\n  iconName: 'hourglass-half',\n  icon: [384, 512, [], \"f252\", \"M360 0H24C10.745 0 0 10.745 0 24v16c0 13.255 10.745 24 24 24 0 90.965 51.016 167.734 120.842 192C75.016 280.266 24 357.035 24 448c-13.255 0-24 10.745-24 24v16c0 13.255 10.745 24 24 24h336c13.255 0 24-10.745 24-24v-16c0-13.255-10.745-24-24-24 0-90.965-51.016-167.734-120.842-192C308.984 231.734 360 154.965 360 64c13.255 0 24-10.745 24-24V24c0-13.255-10.745-24-24-24zm-75.078 384H99.08c17.059-46.797 52.096-80 92.92-80 40.821 0 75.862 33.196 92.922 80zm.019-256H99.078C91.988 108.548 88 86.748 88 64h208c0 22.805-3.987 44.587-11.059 64z\"]\n};\nvar faHourglassStart = {\n  prefix: 'fas',\n  iconName: 'hourglass-start',\n  icon: [384, 512, [], \"f251\", \"M360 0H24C10.745 0 0 10.745 0 24v16c0 13.255 10.745 24 24 24 0 90.965 51.016 167.734 120.842 192C75.016 280.266 24 357.035 24 448c-13.255 0-24 10.745-24 24v16c0 13.255 10.745 24 24 24h336c13.255 0 24-10.745 24-24v-16c0-13.255-10.745-24-24-24 0-90.965-51.016-167.734-120.842-192C308.984 231.734 360 154.965 360 64c13.255 0 24-10.745 24-24V24c0-13.255-10.745-24-24-24zm-64 448H88c0-77.458 46.204-144 104-144 57.786 0 104 66.517 104 144z\"]\n};\nvar faHouseDamage = {\n  prefix: 'fas',\n  iconName: 'house-damage',\n  icon: [576, 512, [], \"f6f1\", \"M288 114.96L69.47 307.71c-1.62 1.46-3.69 2.14-5.47 3.35V496c0 8.84 7.16 16 16 16h149.23L192 439.19l104.11-64-60.16-119.22L384 392.75l-104.11 64L319.81 512H496c8.84 0 16-7.16 16-16V311.1c-1.7-1.16-3.72-1.82-5.26-3.2L288 114.96zm282.69 121.32L512 184.45V48c0-8.84-7.16-16-16-16h-64c-8.84 0-16 7.16-16 16v51.69L314.75 10.31C307.12 3.45 297.56.01 288 0s-19.1 3.41-26.7 10.27L5.31 236.28c-6.57 5.91-7.12 16.02-1.21 22.6l21.4 23.82c5.9 6.57 16.02 7.12 22.6 1.21L277.42 81.63c6.05-5.33 15.12-5.33 21.17 0L527.91 283.9c6.57 5.9 16.69 5.36 22.6-1.21l21.4-23.82c5.9-6.57 5.36-16.69-1.22-22.59z\"]\n};\nvar faHouseUser = {\n  prefix: 'fas',\n  iconName: 'house-user',\n  icon: [576, 512, [], \"f965\", 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0 0 8-8v-16a8 8 0 0 0-8-8H64V40a8 8 0 0 0-8-8H32a8 8 0 0 0-7.14 4.42l-8 16A8 8 0 0 0 24 64h8v64H16a8 8 0 0 0-8 8v16a8 8 0 0 0 8 8zm-3.91 160H80a8 8 0 0 0 8-8v-16a8 8 0 0 0-8-8H41.32c3.29-10.29 48.34-18.68 48.34-56.44 0-29.06-25-39.56-44.47-39.56-21.36 0-33.8 10-40.46 18.75-4.37 5.59-3 10.84 2.8 15.37l8.58 6.88c5.61 4.56 11 2.47 16.12-2.44a13.44 13.44 0 0 1 9.46-3.84c3.33 0 9.28 1.56 9.28 8.75C51 248.19 0 257.31 0 304.59v4C0 316 5.08 320 12.09 320z\"]\n};\nvar faListUl = {\n  prefix: 'fas',\n  iconName: 'list-ul',\n  icon: [512, 512, [], \"f0ca\", \"M48 48a48 48 0 1 0 48 48 48 48 0 0 0-48-48zm0 160a48 48 0 1 0 48 48 48 48 0 0 0-48-48zm0 160a48 48 0 1 0 48 48 48 48 0 0 0-48-48zm448 16H176a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h320a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zm0-320H176a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h320a16 16 0 0 0 16-16V80a16 16 0 0 0-16-16zm0 160H176a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h320a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16z\"]\n};\nvar faLocationArrow = {\n  prefix: 'fas',\n  iconName: 'location-arrow',\n  icon: [512, 512, [], \"f124\", \"M444.52 3.52L28.74 195.42c-47.97 22.39-31.98 92.75 19.19 92.75h175.91v175.91c0 51.17 70.36 67.17 92.75 19.19l191.9-415.78c15.99-38.39-25.59-79.97-63.97-63.97z\"]\n};\nvar faLock = {\n  prefix: 'fas',\n  iconName: 'lock',\n  icon: [448, 512, [], \"f023\", \"M400 224h-24v-72C376 68.2 307.8 0 224 0S72 68.2 72 152v72H48c-26.5 0-48 21.5-48 48v192c0 26.5 21.5 48 48 48h352c26.5 0 48-21.5 48-48V272c0-26.5-21.5-48-48-48zm-104 0H152v-72c0-39.7 32.3-72 72-72s72 32.3 72 72v72z\"]\n};\nvar faLockOpen = {\n  prefix: 'fas',\n  iconName: 'lock-open',\n  icon: [576, 512, [], \"f3c1\", \"M423.5 0C339.5.3 272 69.5 272 153.5V224H48c-26.5 0-48 21.5-48 48v192c0 26.5 21.5 48 48 48h352c26.5 0 48-21.5 48-48V272c0-26.5-21.5-48-48-48h-48v-71.1c0-39.6 31.7-72.5 71.3-72.9 40-.4 72.7 32.1 72.7 72v80c0 13.3 10.7 24 24 24h32c13.3 0 24-10.7 24-24v-80C576 68 507.5-.3 423.5 0z\"]\n};\nvar faLongArrowAltDown = {\n  prefix: 'fas',\n  iconName: 'long-arrow-alt-down',\n  icon: [256, 512, [], \"f309\", \"M168 345.941V44c0-6.627-5.373-12-12-12h-56c-6.627 0-12 5.373-12 12v301.941H41.941c-21.382 0-32.09 25.851-16.971 40.971l86.059 86.059c9.373 9.373 24.569 9.373 33.941 0l86.059-86.059c15.119-15.119 4.411-40.971-16.971-40.971H168z\"]\n};\nvar faLongArrowAltLeft = {\n  prefix: 'fas',\n  iconName: 'long-arrow-alt-left',\n  icon: [448, 512, [], \"f30a\", \"M134.059 296H436c6.627 0 12-5.373 12-12v-56c0-6.627-5.373-12-12-12H134.059v-46.059c0-21.382-25.851-32.09-40.971-16.971L7.029 239.029c-9.373 9.373-9.373 24.569 0 33.941l86.059 86.059c15.119 15.119 40.971 4.411 40.971-16.971V296z\"]\n};\nvar faLongArrowAltRight = {\n  prefix: 'fas',\n  iconName: 'long-arrow-alt-right',\n  icon: [448, 512, [], \"f30b\", \"M313.941 216H12c-6.627 0-12 5.373-12 12v56c0 6.627 5.373 12 12 12h301.941v46.059c0 21.382 25.851 32.09 40.971 16.971l86.059-86.059c9.373-9.373 9.373-24.569 0-33.941l-86.059-86.059c-15.119-15.119-40.971-4.411-40.971 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faMagic = {\n  prefix: 'fas',\n  iconName: 'magic',\n  icon: [512, 512, [], \"f0d0\", \"M224 96l16-32 32-16-32-16-16-32-16 32-32 16 32 16 16 32zM80 160l26.66-53.33L160 80l-53.34-26.67L80 0 53.34 53.33 0 80l53.34 26.67L80 160zm352 128l-26.66 53.33L352 368l53.34 26.67L432 448l26.66-53.33L512 368l-53.34-26.67L432 288zm70.62-193.77L417.77 9.38C411.53 3.12 403.34 0 395.15 0c-8.19 0-16.38 3.12-22.63 9.38L9.38 372.52c-12.5 12.5-12.5 32.76 0 45.25l84.85 84.85c6.25 6.25 14.44 9.37 22.62 9.37 8.19 0 16.38-3.12 22.63-9.37l363.14-363.15c12.5-12.48 12.5-32.75 0-45.24zM359.45 203.46l-50.91-50.91 86.6-86.6 50.91 50.91-86.6 86.6z\"]\n};\nvar faMagnet = {\n  prefix: 'fas',\n  iconName: 'magnet',\n  icon: [512, 512, [], \"f076\", \"M164.07 148.1H12a12 12 0 0 1-12-12v-80a36 36 0 0 1 36-36h104a36 36 0 0 1 36 36v80a11.89 11.89 0 0 1-11.93 12zm347.93-12V56a36 36 0 0 0-36-36H372a36 36 0 0 0-36 36v80a12 12 0 0 0 12 12h152a11.89 11.89 0 0 0 12-11.9zm-164 44a12 12 0 0 0-12 12v52c0 128.1-160 127.9-160 0v-52a12 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'microscope',\n  icon: [512, 512, [], \"f610\", \"M160 320h12v16c0 8.84 7.16 16 16 16h40c8.84 0 16-7.16 16-16v-16h12c17.67 0 32-14.33 32-32V64c0-17.67-14.33-32-32-32V16c0-8.84-7.16-16-16-16h-64c-8.84 0-16 7.16-16 16v16c-17.67 0-32 14.33-32 32v224c0 17.67 14.33 32 32 32zm304 128h-1.29C493.24 413.99 512 369.2 512 320c0-105.88-86.12-192-192-192v64c70.58 0 128 57.42 128 128s-57.42 128-128 128H48c-26.51 0-48 21.49-48 48 0 8.84 7.16 16 16 16h480c8.84 0 16-7.16 16-16 0-26.51-21.49-48-48-48zm-360-32h208c4.42 0 8-3.58 8-8v-16c0-4.42-3.58-8-8-8H104c-4.42 0-8 3.58-8 8v16c0 4.42 3.58 8 8 8z\"]\n};\nvar faMinus = {\n  prefix: 'fas',\n  iconName: 'minus',\n  icon: [448, 512, [], \"f068\", \"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"]\n};\nvar faMinusCircle = {\n  prefix: 'fas',\n  iconName: 'minus-circle',\n  icon: [512, 512, [], \"f056\", \"M256 8C119 8 8 119 8 256s111 248 248 248 248-111 248-248S393 8 256 8zM124 296c-6.6 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22.5-2.8l19.6-25.3c5.4-6.8 4.1-16.9-2.9-22.3z\"]\n};\nvar faPhoneSquare = {\n  prefix: 'fas',\n  iconName: 'phone-square',\n  icon: [448, 512, [], \"f098\", \"M400 32H48C21.49 32 0 53.49 0 80v352c0 26.51 21.49 48 48 48h352c26.51 0 48-21.49 48-48V80c0-26.51-21.49-48-48-48zM94 416c-7.033 0-13.057-4.873-14.616-11.627l-14.998-65a15 15 0 0 1 8.707-17.16l69.998-29.999a15 15 0 0 1 17.518 4.289l30.997 37.885c48.944-22.963 88.297-62.858 110.781-110.78l-37.886-30.997a15.001 15.001 0 0 1-4.289-17.518l30-69.998a15 15 0 0 1 17.16-8.707l65 14.998A14.997 14.997 0 0 1 384 126c0 160.292-129.945 290-290 290z\"]\n};\nvar faPhoneSquareAlt = {\n  prefix: 'fas',\n  iconName: 'phone-square-alt',\n  icon: [448, 512, [], \"f87b\", \"M400 32H48A48 48 0 0 0 0 80v352a48 48 0 0 0 48 48h352a48 48 0 0 0 48-48V80a48 48 0 0 0-48-48zm-16.39 307.37l-15 65A15 15 0 0 1 354 416C194 416 64 286.29 64 126a15.7 15.7 0 0 1 11.63-14.61l65-15A18.23 18.23 0 0 1 144 96a16.27 16.27 0 0 1 13.79 9.09l30 70A17.9 17.9 0 0 1 189 181a17 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5.327-12.53 5.746-17.552.933l-5.798-5.557c-4.56-4.371-4.977-11.529-.93-16.379 49.687-59.538 49.646-145.933 0-205.422-4.047-4.85-3.631-12.008.93-16.379l5.798-5.557c5.022-4.813 13.078-4.394 17.552.933zm-45.972 44.941c36.05 46.322 36.108 111.149 0 157.546-4.39 5.641-12.697 6.251-17.856 1.304l-5.818-5.579c-4.4-4.219-4.998-11.095-1.285-15.931 26.536-34.564 26.534-82.572 0-117.134-3.713-4.836-3.115-11.711 1.285-15.931l5.818-5.579c5.159-4.947 13.466-4.337 17.856 1.304z\"]\n};\nvar faPhotoVideo = {\n  prefix: 'fas',\n  iconName: 'photo-video',\n  icon: [640, 512, [], \"f87c\", \"M608 0H160a32 32 0 0 0-32 32v96h160V64h192v320h128a32 32 0 0 0 32-32V32a32 32 0 0 0-32-32zM232 103a9 9 0 0 1-9 9h-30a9 9 0 0 1-9-9V73a9 9 0 0 1 9-9h30a9 9 0 0 1 9 9zm352 208a9 9 0 0 1-9 9h-30a9 9 0 0 1-9-9v-30a9 9 0 0 1 9-9h30a9 9 0 0 1 9 9zm0-104a9 9 0 0 1-9 9h-30a9 9 0 0 1-9-9v-30a9 9 0 0 1 9-9h30a9 9 0 0 1 9 9zm0-104a9 9 0 0 1-9 9h-30a9 9 0 0 1-9-9V73a9 9 0 0 1 9-9h30a9 9 0 0 1 9 9zm-168 57H32a32 32 0 0 0-32 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[448, 512, [], \"f681\", \"M400 32H48C21.5 32 0 53.5 0 80v352c0 26.5 21.5 48 48 48h352c26.5 0 48-21.5 48-48V80c0-26.5-21.5-48-48-48zM160 368c0 8.84-7.16 16-16 16h-32c-8.84 0-16-7.16-16-16V240c0-8.84 7.16-16 16-16h32c8.84 0 16 7.16 16 16v128zm96 0c0 8.84-7.16 16-16 16h-32c-8.84 0-16-7.16-16-16V144c0-8.84 7.16-16 16-16h32c8.84 0 16 7.16 16 16v224zm96 0c0 8.84-7.16 16-16 16h-32c-8.84 0-16-7.16-16-16v-64c0-8.84 7.16-16 16-16h32c8.84 0 16 7.16 16 16v64z\"]\n};\nvar faPollH = {\n  prefix: 'fas',\n  iconName: 'poll-h',\n  icon: [448, 512, [], \"f682\", \"M448 432V80c0-26.5-21.5-48-48-48H48C21.5 32 0 53.5 0 80v352c0 26.5 21.5 48 48 48h352c26.5 0 48-21.5 48-48zM112 192c-8.84 0-16-7.16-16-16v-32c0-8.84 7.16-16 16-16h128c8.84 0 16 7.16 16 16v32c0 8.84-7.16 16-16 16H112zm0 96c-8.84 0-16-7.16-16-16v-32c0-8.84 7.16-16 16-16h224c8.84 0 16 7.16 16 16v32c0 8.84-7.16 16-16 16H112zm0 96c-8.84 0-16-7.16-16-16v-32c0-8.84 7.16-16 16-16h64c8.84 0 16 7.16 16 16v32c0 8.84-7.16 16-16 16h-64z\"]\n};\nvar faPoo = {\n  prefix: 'fas',\n  iconName: 'poo',\n  icon: [512, 512, [], \"f2fe\", \"M451.4 369.1C468.7 356 480 335.4 480 312c0-39.8-32.2-72-72-72h-14.1c13.4-11.7 22.1-28.8 22.1-48 0-35.3-28.7-64-64-64h-5.9c3.6-10.1 5.9-20.7 5.9-32 0-53-43-96-96-96-5.2 0-10.2.7-15.1 1.5C250.3 14.6 256 30.6 256 48c0 44.2-35.8 80-80 80h-16c-35.3 0-64 28.7-64 64 0 19.2 8.7 36.3 22.1 48H104c-39.8 0-72 32.2-72 72 0 23.4 11.3 44 28.6 57.1C26.3 374.6 0 404.1 0 440c0 39.8 32.2 72 72 72h368c39.8 0 72-32.2 72-72 0-35.9-26.3-65.4-60.6-70.9zM192 256c17.7 0 32 14.3 32 32s-14.3 32-32 32-32-14.3-32-32 14.3-32 32-32zm159.5 139C341 422.9 293 448 256 448s-85-25.1-95.5-53c-2-5.3 2-11 7.8-11h175.4c5.8 0 9.8 5.7 7.8 11zM320 320c-17.7 0-32-14.3-32-32s14.3-32 32-32 32 14.3 32 32-14.3 32-32 32z\"]\n};\nvar faPooStorm = {\n  prefix: 'fas',\n  iconName: 'poo-storm',\n  icon: [448, 512, [], \"f75a\", \"M308 336h-57.7l17.3-64.9c2-7.6-3.7-15.1-11.6-15.1h-68c-6 0-11.1 4.5-11.9 10.4l-16 120c-1 7.2 4.6 13.6 11.9 13.6h59.3l-23 97.2c-1.8 7.6 4 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faShieldVirus = {\n  prefix: 'fas',\n  iconName: 'shield-virus',\n  icon: [512, 512, [], \"f96c\", \"M224,192a16,16,0,1,0,16,16A16,16,0,0,0,224,192ZM466.5,83.68l-192-80A57.4,57.4,0,0,0,256.05,0a57.4,57.4,0,0,0-18.46,3.67l-192,80A47.93,47.93,0,0,0,16,128C16,326.5,130.5,463.72,237.5,508.32a48.09,48.09,0,0,0,36.91,0C360.09,472.61,496,349.3,496,128A48,48,0,0,0,466.5,83.68ZM384,256H371.88c-28.51,0-42.79,34.47-22.63,54.63l8.58,8.57a16,16,0,1,1-22.63,22.63l-8.57-8.58C306.47,313.09,272,327.37,272,355.88V368a16,16,0,0,1-32,0V355.88c0-28.51-34.47-42.79-54.63-22.63l-8.57,8.58a16,16,0,0,1-22.63-22.63l8.58-8.57c20.16-20.16,5.88-54.63-22.63-54.63H128a16,16,0,0,1,0-32h12.12c28.51,0,42.79-34.47,22.63-54.63l-8.58-8.57a16,16,0,0,1,22.63-22.63l8.57,8.58c20.16,20.16,54.63,5.88,54.63-22.63V112a16,16,0,0,1,32,0v12.12c0,28.51,34.47,42.79,54.63,22.63l8.57-8.58a16,16,0,0,1,22.63,22.63l-8.58,8.57C329.09,189.53,343.37,224,371.88,224H384a16,16,0,0,1,0,32Zm-96,0a16,16,0,1,0,16,16A16,16,0,0,0,288,256Z\"]\n};\nvar faShip = {\n  prefix: 'fas',\n  iconName: 'ship',\n  icon: [640, 512, [], \"f21a\", \"M496.616 372.639l70.012-70.012c16.899-16.9 9.942-45.771-12.836-53.092L512 236.102V96c0-17.673-14.327-32-32-32h-64V24c0-13.255-10.745-24-24-24H248c-13.255 0-24 10.745-24 24v40h-64c-17.673 0-32 14.327-32 32v140.102l-41.792 13.433c-22.753 7.313-29.754 36.173-12.836 53.092l70.012 70.012C125.828 416.287 85.587 448 24 448c-13.255 0-24 10.745-24 24v16c0 13.255 10.745 24 24 24 61.023 0 107.499-20.61 143.258-59.396C181.677 487.432 216.021 512 256 512h128c39.979 0 74.323-24.568 88.742-59.396C508.495 491.384 554.968 512 616 512c13.255 0 24-10.745 24-24v-16c0-13.255-10.745-24-24-24-60.817 0-101.542-31.001-119.384-75.361zM192 128h256v87.531l-118.208-37.995a31.995 31.995 0 0 0-19.584 0L192 215.531V128z\"]\n};\nvar faShippingFast = {\n  prefix: 'fas',\n  iconName: 'shipping-fast',\n  icon: [640, 512, [], \"f48b\", \"M624 352h-16V243.9c0-12.7-5.1-24.9-14.1-33.9L494 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faShuttleVan = {\n  prefix: 'fas',\n  iconName: 'shuttle-van',\n  icon: [640, 512, [], \"f5b6\", \"M628.88 210.65L494.39 49.27A48.01 48.01 0 0 0 457.52 32H32C14.33 32 0 46.33 0 64v288c0 17.67 14.33 32 32 32h32c0 53.02 42.98 96 96 96s96-42.98 96-96h128c0 53.02 42.98 96 96 96s96-42.98 96-96h32c17.67 0 32-14.33 32-32V241.38c0-11.23-3.94-22.1-11.12-30.73zM64 192V96h96v96H64zm96 240c-26.51 0-48-21.49-48-48s21.49-48 48-48 48 21.49 48 48-21.49 48-48 48zm160-240h-96V96h96v96zm160 240c-26.51 0-48-21.49-48-48s21.49-48 48-48 48 21.49 48 48-21.49 48-48 48zm-96-240V96h66.02l80 96H384z\"]\n};\nvar faSign = {\n  prefix: 'fas',\n  iconName: 'sign',\n  icon: [512, 512, [], \"f4d9\", \"M496 64H128V16c0-8.8-7.2-16-16-16H80c-8.8 0-16 7.2-16 16v48H16C7.2 64 0 71.2 0 80v32c0 8.8 7.2 16 16 16h48v368c0 8.8 7.2 16 16 16h32c8.8 0 16-7.2 16-16V128h368c8.8 0 16-7.2 16-16V80c0-8.8-7.2-16-16-16zM160 384h320V160H160v224z\"]\n};\nvar faSignInAlt = {\n  prefix: 'fas',\n  iconName: 'sign-in-alt',\n  icon: [512, 512, [], \"f2f6\", \"M416 448h-84c-6.6 0-12-5.4-12-12v-40c0-6.6 5.4-12 12-12h84c17.7 0 32-14.3 32-32V160c0-17.7-14.3-32-32-32h-84c-6.6 0-12-5.4-12-12V76c0-6.6 5.4-12 12-12h84c53 0 96 43 96 96v192c0 53-43 96-96 96zm-47-201L201 79c-15-15-41-4.5-41 17v96H24c-13.3 0-24 10.7-24 24v96c0 13.3 10.7 24 24 24h136v96c0 21.5 26 32 41 17l168-168c9.3-9.4 9.3-24.6 0-34z\"]\n};\nvar faSignLanguage = {\n  prefix: 'fas',\n  iconName: 'sign-language',\n  icon: [448, 512, [], \"f2a7\", \"M91.434 483.987c-.307-16.018 13.109-29.129 29.13-29.129h62.293v-5.714H56.993c-16.021 0-29.437-13.111-29.13-29.129C28.16 404.491 40.835 392 56.428 392h126.429v-5.714H29.136c-16.021 0-29.437-13.111-29.13-29.129.297-15.522 12.973-28.013 28.566-28.013h154.286v-5.714H57.707c-16.021 0-29.437-13.111-29.13-29.129.297-15.522 12.973-28.013 28.566-28.013h168.566l-31.085-22.606c-12.762-9.281-15.583-27.149-6.302-39.912 9.281-12.761 27.15-15.582 39.912-6.302l123.361 89.715a34.287 34.287 0 0 1 14.12 27.728v141.136c0 15.91-10.946 29.73-26.433 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\"f2f5\", \"M497 273L329 441c-15 15-41 4.5-41-17v-96H152c-13.3 0-24-10.7-24-24v-96c0-13.3 10.7-24 24-24h136V88c0-21.4 25.9-32 41-17l168 168c9.3 9.4 9.3 24.6 0 34zM192 436v-40c0-6.6-5.4-12-12-12H96c-17.7 0-32-14.3-32-32V160c0-17.7 14.3-32 32-32h84c6.6 0 12-5.4 12-12V76c0-6.6-5.4-12-12-12H96c-53 0-96 43-96 96v192c0 53 43 96 96 96h84c6.6 0 12-5.4 12-12z\"]\n};\nvar faSignal = {\n  prefix: 'fas',\n  iconName: 'signal',\n  icon: [640, 512, [], \"f012\", \"M216 288h-48c-8.84 0-16 7.16-16 16v192c0 8.84 7.16 16 16 16h48c8.84 0 16-7.16 16-16V304c0-8.84-7.16-16-16-16zM88 384H40c-8.84 0-16 7.16-16 16v96c0 8.84 7.16 16 16 16h48c8.84 0 16-7.16 16-16v-96c0-8.84-7.16-16-16-16zm256-192h-48c-8.84 0-16 7.16-16 16v288c0 8.84 7.16 16 16 16h48c8.84 0 16-7.16 16-16V208c0-8.84-7.16-16-16-16zm128-96h-48c-8.84 0-16 7.16-16 16v384c0 8.84 7.16 16 16 16h48c8.84 0 16-7.16 16-16V112c0-8.84-7.16-16-16-16zM600 0h-48c-8.84 0-16 7.16-16 16v480c0 8.84 7.16 16 16 16h48c8.84 0 16-7.16 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iconName: 'slash',\n  icon: [640, 512, [], \"f715\", \"M594.53 508.63L6.18 53.9c-6.97-5.42-8.23-15.47-2.81-22.45L23.01 6.18C28.43-.8 38.49-2.06 45.47 3.37L633.82 458.1c6.97 5.42 8.23 15.47 2.81 22.45l-19.64 25.27c-5.42 6.98-15.48 8.23-22.46 2.81z\"]\n};\nvar faSleigh = {\n  prefix: 'fas',\n  iconName: 'sleigh',\n  icon: [640, 512, [], \"f7cc\", \"M612.7 350.7l-9.3-7.4c-6.9-5.5-17-4.4-22.5 2.5l-10 12.5c-5.5 6.9-4.4 17 2.5 22.5l9.3 7.4c5.9 4.7 9.2 11.7 9.2 19.2 0 13.6-11 24.6-24.6 24.6H48c-8.8 0-16 7.2-16 16v16c0 8.8 7.2 16 16 16h516c39 0 73.7-29.3 75.9-68.3 1.4-23.8-8.7-46.3-27.2-61zM32 224c0 59.6 40.9 109.2 96 123.5V400h64v-48h192v48h64v-48c53 0 96-43 96-96v-96c17.7 0 32-14.3 32-32s-14.3-32-32-32h-96v64c0 35.3-28.7 64-64 64h-20.7c-65.8 0-125.9-37.2-155.3-96-29.4-58.8-89.6-96-155.3-96H32C14.3 32 0 46.3 0 64s14.3 32 32 32v128z\"]\n};\nvar faSlidersH = {\n  prefix: 'fas',\n  iconName: 'sliders-h',\n  icon: [512, 512, [], \"f1de\", \"M496 384H160v-16c0-8.8-7.2-16-16-16h-32c-8.8 0-16 7.2-16 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90.2-42.2c13.4-16.2 38.1 4.2 24.6 20.5z\"]\n};\nvar faSmileBeam = {\n  prefix: 'fas',\n  iconName: 'smile-beam',\n  icon: [496, 512, [], \"f5b8\", \"M248 8C111 8 0 119 0 256s111 248 248 248 248-111 248-248S385 8 248 8zM112 223.4c3.3-42.1 32.2-71.4 56-71.4s52.7 29.3 56 71.4c.7 8.6-10.8 11.9-14.9 4.5l-9.5-17c-7.7-13.7-19.2-21.6-31.5-21.6s-23.8 7.9-31.5 21.6l-9.5 17c-4.3 7.4-15.8 4-15.1-4.5zm250.8 122.8C334.3 380.4 292.5 400 248 400s-86.3-19.6-114.8-53.8c-13.5-16.3 11-36.7 24.6-20.5 22.4 26.9 55.2 42.2 90.2 42.2s67.8-15.4 90.2-42.2c13.6-16.2 38.1 4.3 24.6 20.5zm6.2-118.3l-9.5-17c-7.7-13.7-19.2-21.6-31.5-21.6s-23.8 7.9-31.5 21.6l-9.5 17c-4.1 7.3-15.6 4-14.9-4.5 3.3-42.1 32.2-71.4 56-71.4s52.7 29.3 56 71.4c.6 8.6-11 11.9-15.1 4.5z\"]\n};\nvar faSmileWink = {\n  prefix: 'fas',\n  iconName: 'smile-wink',\n  icon: [496, 512, [], \"f4da\", \"M0 256c0 137 111 248 248 248s248-111 248-248S385 8 248 8 0 119 0 256zm200-48c0 17.7-14.3 32-32 32s-32-14.3-32-32 14.3-32 32-32 32 14.3 32 32zm158.5 16.5c-14.8-13.2-46.2-13.2-61 0L288 233c-8.3 7.4-21.6.4-19.8-10.8 4-25.2 34.2-42.1 59.9-42.1S384 197 388 222.2c1.7 11.1-11.4 18.3-19.8 10.8l-9.7-8.5zM157.8 325.8C180.2 352.7 213 368 248 368s67.8-15.4 90.2-42.2c13.6-16.2 38.1 4.2 24.6 20.5C334.3 380.4 292.5 400 248 400s-86.3-19.6-114.8-53.8c-13.5-16.3 11.2-36.7 24.6-20.4z\"]\n};\nvar faSmog = {\n  prefix: 'fas',\n  iconName: 'smog',\n  icon: [640, 512, [], \"f75f\", \"M624 368H80c-8.8 0-16 7.2-16 16v16c0 8.8 7.2 16 16 16h544c8.8 0 16-7.2 16-16v-16c0-8.8-7.2-16-16-16zm-480 96H16c-8.8 0-16 7.2-16 16v16c0 8.8 7.2 16 16 16h128c8.8 0 16-7.2 16-16v-16c0-8.8-7.2-16-16-16zm416 0H224c-8.8 0-16 7.2-16 16v16c0 8.8 7.2 16 16 16h336c8.8 0 16-7.2 16-16v-16c0-8.8-7.2-16-16-16zM144 288h156.1c22.5 19.7 51.6 32 83.9 32s61.3-12.3 83.9-32H528c61.9 0 112-50.1 112-112S589.9 64 528 64c-18 0-34.7 4.6-49.7 12.1C454 31 406.8 0 352 0c-41 0-77.8 17.3-104 44.8C221.8 17.3 185 0 144 0 64.5 0 0 64.5 0 144s64.5 144 144 144z\"]\n};\nvar faSmoking = {\n  prefix: 'fas',\n  iconName: 'smoking',\n  icon: [640, 512, [], \"f48d\", \"M632 352h-48c-4.4 0-8 3.6-8 8v144c0 4.4 3.6 8 8 8h48c4.4 0 8-3.6 8-8V360c0-4.4-3.6-8-8-8zM553.3 87.1c-5.7-3.8-9.3-10-9.3-16.8V8c0-4.4-3.6-8-8-8h-48c-4.4 0-8 3.6-8 8v62.3c0 22 10.2 43.4 28.6 55.4 42.2 27.3 67.4 73.8 67.4 124V280c0 4.4 3.6 8 8 8h48c4.4 0 8-3.6 8-8v-30.3c0-65.5-32.4-126.2-86.7-162.6zM432 352H48c-26.5 0-48 21.5-48 48v64c0 26.5 21.5 48 48 48h384c8.8 0 16-7.2 16-16V368c0-8.8-7.2-16-16-16zm-32 112H224v-64h176v64zm87.7-322.4C463.8 125 448 99.3 448 70.3V8c0-4.4-3.6-8-8-8h-48c-4.4 0-8 3.6-8 8v66.4c0 43.7 24.6 81.6 60.3 106.7 22.4 15.7 35.7 41.2 35.7 68.6V280c0 4.4 3.6 8 8 8h48c4.4 0 8-3.6 8-8v-30.3c0-43.3-21-83.4-56.3-108.1zM536 352h-48c-4.4 0-8 3.6-8 8v144c0 4.4 3.6 8 8 8h48c4.4 0 8-3.6 8-8V360c0-4.4-3.6-8-8-8z\"]\n};\nvar faSmokingBan = {\n  prefix: 'fas',\n  iconName: 'smoking-ban',\n  icon: [512, 512, [], \"f54d\", \"M96 304c0 8.8 7.2 16 16 16h117.5l-96-96H112c-8.8 0-16 7.2-16 16v64zM256 0C114.6 0 0 114.6 0 256s114.6 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13.1-10.7 10.9-18.9l-4-14.9c-2.2-8.2-10.7-13.1-18.9-10.9l-70.8 19-63.9-37 63.8-36.9 70.8 19c8.2 2.2 16.7-2.7 18.9-10.9l4-14.9c2.2-8.2-2.7-16.7-10.9-18.9l-26-7 33.8-19.5c7.4-4.3 9.9-13.7 5.7-21.1L430.4 119c-4.3-7.4-13.7-9.9-21.1-5.7l-33.8 19.5 7-26c2.2-8.2-2.7-16.7-10.9-18.9l-14.9-4c-8.2-2.2-16.7 2.7-18.9 10.9l-19 70.8-62.8 36.2v-77.5l53.7-53.7c6.2-6.2 6.2-16.4 0-22.6l-11.3-11.3c-6.2-6.2-16.4-6.2-22.6 0L256 56.4V16c0-8.8-7.2-16-16-16h-32c-8.8 0-16 7.2-16 16v40.4l-19.7-19.7c-6.2-6.2-16.4-6.2-22.6 0L138.3 48c-6.3 6.2-6.3 16.4 0 22.6l53.7 53.7v77.5l-62.8-36.2-19-70.8c-2.2-8.2-10.7-13.1-18.9-10.9l-14.9 4c-8.2 2.2-13.1 10.7-10.9 18.9l7 26-33.8-19.5c-7.4-4.3-16.8-1.7-21.1 5.7L2.1 145.7c-4.3 7.4-1.7 16.8 5.7 21.1l33.8 19.5-26 7c-8.3 2.2-13.2 10.7-11 19l4 14.9c2.2 8.2 10.7 13.1 18.9 10.9l70.8-19 63.8 36.9-63.8 36.9-70.8-19c-8.2-2.2-16.7 2.7-18.9 10.9l-4 14.9c-2.2 8.2 2.7 16.7 10.9 18.9l26 7-33.8 19.6c-7.4 4.3-9.9 13.7-5.7 21.1l15.5 26.8c4.3 7.4 13.7 9.9 21.1 5.7l33.8-19.5-7 26c-2.2 8.2 2.7 16.7 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\"M416,192a95.42,95.42,0,0,1-30.94,70.21A95.8,95.8,0,0,1,352,448H160a96,96,0,0,1,0-192h88.91A95.3,95.3,0,0,1,224,192H96A96,96,0,0,0,0,288V416a96,96,0,0,0,96,96H416a96,96,0,0,0,96-96V288A96,96,0,0,0,416,192Zm-96,64a64,64,0,1,0-64-64A64,64,0,0,0,320,256ZM208,96a48,48,0,1,0-48-48A48,48,0,0,0,208,96ZM384,64a32,32,0,1,0-32-32A32,32,0,0,0,384,64ZM160,288a64,64,0,0,0,0,128H352a64,64,0,0,0,0-128Z\"]\n};\nvar faSocks = {\n  prefix: 'fas',\n  iconName: 'socks',\n  icon: [512, 512, [], \"f696\", \"M214.66 311.01L288 256V96H128v176l-86.65 64.61c-39.4 29.56-53.86 84.42-29.21 127.06C30.39 495.25 63.27 512 96.08 512c20.03 0 40.25-6.25 57.52-19.2l21.86-16.39c-29.85-55.38-13.54-125.84 39.2-165.4zM288 32c0-11.05 3.07-21.3 8.02-30.38C293.4.92 290.85 0 288 0H160c-17.67 0-32 14.33-32 32v32h160V32zM480 0H352c-17.67 0-32 14.33-32 32v32h192V32c0-17.67-14.33-32-32-32zM320 272l-86.13 64.61c-39.4 29.56-53.86 84.42-29.21 127.06 18.25 31.58 50.61 48.33 83.42 48.33 20.03 0 40.25-6.25 57.52-19.2l115.2-86.4A127.997 127.997 0 0 0 512 304V96H320v176z\"]\n};\nvar faSolarPanel = {\n  prefix: 'fas',\n  iconName: 'solar-panel',\n  icon: [640, 512, [], \"f5ba\", \"M431.98 448.01l-47.97.05V416h-128v32.21l-47.98.05c-8.82.01-15.97 7.16-15.98 15.99l-.05 31.73c-.01 8.85 7.17 16.03 16.02 16.02l223.96-.26c8.82-.01 15.97-7.16 15.98-15.98l.04-31.73c.01-8.85-7.17-16.03-16.02-16.02zM585.2 26.74C582.58 11.31 568.99 0 553.06 0H86.93C71 0 57.41 11.31 54.79 26.74-3.32 369.16.04 348.08.03 352c-.03 17.32 14.29 32 32.6 32h574.74c18.23 0 32.51-14.56 32.59-31.79.02-4.08 3.35 16.95-54.76-325.47zM259.83 64h120.33l9.77 96H250.06l9.77-96zm-75.17 256H71.09L90.1 208h105.97l-11.41 112zm16.29-160H98.24l16.29-96h96.19l-9.77 96zm32.82 160l11.4-112h149.65l11.4 112H233.77zm195.5-256h96.19l16.29 96H439.04l-9.77-96zm26.06 256l-11.4-112H549.9l19.01 112H455.33z\"]\n};\nvar faSort = {\n  prefix: 'fas',\n  iconName: 'sort',\n  icon: [320, 512, [], \"f0dc\", \"M41 288h238c21.4 0 32.1 25.9 17 41L177 448c-9.4 9.4-24.6 9.4-33.9 0L24 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352h-48V48a16 16 0 0 0-16-16H80a16 16 0 0 0-16 16v304H16c-14.19 0-21.36 17.24-11.29 27.31l80 96a16 16 0 0 0 22.62 0l80-96C197.35 369.26 190.22 352 176 352zm112-128h128a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16h-56l61.26-70.45A32 32 0 0 0 432 65.63V48a16 16 0 0 0-16-16H288a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h56l-61.26 70.45A32 32 0 0 0 272 190.37V208a16 16 0 0 0 16 16zm159.06 234.62l-59.27-160A16 16 0 0 0 372.72 288h-41.44a16 16 0 0 0-15.07 10.62l-59.27 160A16 16 0 0 0 272 480h24.83a16 16 0 0 0 15.23-11.08l4.42-12.92h71l4.41 12.92A16 16 0 0 0 407.16 480H432a16 16 0 0 0 15.06-21.38zM335.61 400L352 352l16.39 48z\"]\n};\nvar faSortAlphaUp = {\n  prefix: 'fas',\n  iconName: 'sort-alpha-up',\n  icon: [448, 512, [], \"f15e\", \"M16 160h48v304a16 16 0 0 0 16 16h32a16 16 0 0 0 16-16V160h48c14.21 0 21.38-17.24 11.31-27.31l-80-96a16 16 0 0 0-22.62 0l-80 96C-5.35 142.74 1.78 160 16 160zm400 128H288a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h56l-61.26 70.45A32 32 0 0 0 272 446.37V464a16 16 0 0 0 16 16h128a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16h-56l61.26-70.45A32 32 0 0 0 432 321.63V304a16 16 0 0 0-16-16zm31.06-85.38l-59.27-160A16 16 0 0 0 372.72 32h-41.44a16 16 0 0 0-15.07 10.62l-59.27 160A16 16 0 0 0 272 224h24.83a16 16 0 0 0 15.23-11.08l4.42-12.92h71l4.41 12.92A16 16 0 0 0 407.16 224H432a16 16 0 0 0 15.06-21.38zM335.61 144L352 96l16.39 48z\"]\n};\nvar faSortAlphaUpAlt = {\n  prefix: 'fas',\n  iconName: 'sort-alpha-up-alt',\n  icon: [448, 512, [], \"f882\", \"M16 160h48v304a16 16 0 0 0 16 16h32a16 16 0 0 0 16-16V160h48c14.21 0 21.38-17.24 11.31-27.31l-80-96a16 16 0 0 0-22.62 0l-80 96C-5.35 142.74 1.78 160 16 160zm272 64h128a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16h-56l61.26-70.45A32 32 0 0 0 432 65.63V48a16 16 0 0 0-16-16H288a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h56l-61.26 70.45A32 32 0 0 0 272 190.37V208a16 16 0 0 0 16 16zm159.06 234.62l-59.27-160A16 16 0 0 0 372.72 288h-41.44a16 16 0 0 0-15.07 10.62l-59.27 160A16 16 0 0 0 272 480h24.83a16 16 0 0 0 15.23-11.08l4.42-12.92h71l4.41 12.92A16 16 0 0 0 407.16 480H432a16 16 0 0 0 15.06-21.38zM335.61 400L352 352l16.39 48z\"]\n};\nvar faSortAmountDown = {\n  prefix: 'fas',\n  iconName: 'sort-amount-down',\n  icon: [512, 512, [], \"f160\", \"M304 416h-64a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h64a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zm-128-64h-48V48a16 16 0 0 0-16-16H80a16 16 0 0 0-16 16v304H16c-14.19 0-21.37 17.24-11.29 27.31l80 96a16 16 0 0 0 22.62 0l80-96C197.35 369.26 190.22 352 176 352zm256-192H240a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h192a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zm-64 128H240a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h128a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zM496 32H240a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h256a16 16 0 0 0 16-16V48a16 16 0 0 0-16-16z\"]\n};\nvar faSortAmountDownAlt = {\n  prefix: 'fas',\n  iconName: 'sort-amount-down-alt',\n  icon: [512, 512, [], \"f884\", \"M240 96h64a16 16 0 0 0 16-16V48a16 16 0 0 0-16-16h-64a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16zm0 128h128a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16H240a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16zm256 192H240a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h256a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zm-256-64h192a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16H240a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16zm-64 0h-48V48a16 16 0 0 0-16-16H80a16 16 0 0 0-16 16v304H16c-14.19 0-21.37 17.24-11.29 27.31l80 96a16 16 0 0 0 22.62 0l80-96C197.35 369.26 190.22 352 176 352z\"]\n};\nvar faSortAmountUp = {\n  prefix: 'fas',\n  iconName: 'sort-amount-up',\n  icon: [512, 512, [], \"f161\", \"M304 416h-64a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h64a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zM16 160h48v304a16 16 0 0 0 16 16h32a16 16 0 0 0 16-16V160h48c14.21 0 21.38-17.24 11.31-27.31l-80-96a16 16 0 0 0-22.62 0l-80 96C-5.35 142.74 1.77 160 16 160zm416 0H240a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h192a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zm-64 128H240a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h128a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zM496 32H240a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h256a16 16 0 0 0 16-16V48a16 16 0 0 0-16-16z\"]\n};\nvar faSortAmountUpAlt = {\n  prefix: 'fas',\n  iconName: 'sort-amount-up-alt',\n  icon: [512, 512, [], \"f885\", \"M240 96h64a16 16 0 0 0 16-16V48a16 16 0 0 0-16-16h-64a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16zm0 128h128a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16H240a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16zm256 192H240a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h256a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zm-256-64h192a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16H240a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16zM16 160h48v304a16 16 0 0 0 16 16h32a16 16 0 0 0 16-16V160h48c14.21 0 21.39-17.24 11.31-27.31l-80-96a16 16 0 0 0-22.62 0l-80 96C-5.35 142.74 1.78 160 16 160z\"]\n};\nvar faSortDown = {\n  prefix: 'fas',\n  iconName: 'sort-down',\n  icon: [320, 512, [], \"f0dd\", \"M41 288h238c21.4 0 32.1 25.9 17 41L177 448c-9.4 9.4-24.6 9.4-33.9 0L24 329c-15.1-15.1-4.4-41 17-41z\"]\n};\nvar faSortNumericDown = {\n  prefix: 'fas',\n  iconName: 'sort-numeric-down',\n  icon: [448, 512, [], \"f162\", \"M304 96h16v64h-16a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h96a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16h-16V48a16 16 0 0 0-16-16h-48a16 16 0 0 0-14.29 8.83l-16 32A16 16 0 0 0 304 96zm26.15 162.91a79 79 0 0 0-55 54.17c-14.25 51.05 21.21 97.77 68.85 102.53a84.07 84.07 0 0 1-20.85 12.91c-7.57 3.4-10.8 12.47-8.18 20.34l9.9 20c2.87 8.63 12.53 13.49 20.9 9.91 58-24.76 86.25-61.61 86.25-132V336c-.02-51.21-48.4-91.34-101.85-77.09zM352 356a20 20 0 1 1 20-20 20 20 0 0 1-20 20zm-176-4h-48V48a16 16 0 0 0-16-16H80a16 16 0 0 0-16 16v304H16c-14.19 0-21.36 17.24-11.29 27.31l80 96a16 16 0 0 0 22.62 0l80-96C197.35 369.26 190.22 352 176 352z\"]\n};\nvar faSortNumericDownAlt = {\n  prefix: 'fas',\n  iconName: 'sort-numeric-down-alt',\n  icon: [448, 512, [], \"f886\", \"M176 352h-48V48a16 16 0 0 0-16-16H80a16 16 0 0 0-16 16v304H16c-14.19 0-21.36 17.24-11.29 27.31l80 96a16 16 0 0 0 22.62 0l80-96C197.35 369.26 190.22 352 176 352zm224 64h-16V304a16 16 0 0 0-16-16h-48a16 16 0 0 0-14.29 8.83l-16 32A16 16 0 0 0 304 352h16v64h-16a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h96a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zM330.17 34.91a79 79 0 0 0-55 54.17c-14.27 51.05 21.19 97.77 68.83 102.53a84.07 84.07 0 0 1-20.85 12.91c-7.57 3.4-10.8 12.47-8.18 20.34l9.9 20c2.87 8.63 12.53 13.49 20.9 9.91 58-24.77 86.25-61.61 86.25-132V112c-.02-51.21-48.4-91.34-101.85-77.09zM352 132a20 20 0 1 1 20-20 20 20 0 0 1-20 20z\"]\n};\nvar faSortNumericUp = {\n  prefix: 'fas',\n  iconName: 'sort-numeric-up',\n  icon: [448, 512, [], \"f163\", \"M330.17 258.91a79 79 0 0 0-55 54.17c-14.27 51.05 21.19 97.77 68.83 102.53a84.07 84.07 0 0 1-20.85 12.91c-7.57 3.4-10.8 12.47-8.18 20.34l9.9 20c2.87 8.63 12.53 13.49 20.9 9.91 58-24.76 86.25-61.61 86.25-132V336c-.02-51.21-48.4-91.34-101.85-77.09zM352 356a20 20 0 1 1 20-20 20 20 0 0 1-20 20zM304 96h16v64h-16a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h96a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16h-16V48a16 16 0 0 0-16-16h-48a16 16 0 0 0-14.29 8.83l-16 32A16 16 0 0 0 304 96zM107.31 36.69a16 16 0 0 0-22.62 0l-80 96C-5.35 142.74 1.78 160 16 160h48v304a16 16 0 0 0 16 16h32a16 16 0 0 0 16-16V160h48c14.21 0 21.38-17.24 11.31-27.31z\"]\n};\nvar faSortNumericUpAlt = {\n  prefix: 'fas',\n  iconName: 'sort-numeric-up-alt',\n  icon: [448, 512, [], \"f887\", \"M107.31 36.69a16 16 0 0 0-22.62 0l-80 96C-5.35 142.74 1.78 160 16 160h48v304a16 16 0 0 0 16 16h32a16 16 0 0 0 16-16V160h48c14.21 0 21.38-17.24 11.31-27.31zM400 416h-16V304a16 16 0 0 0-16-16h-48a16 16 0 0 0-14.29 8.83l-16 32A16 16 0 0 0 304 352h16v64h-16a16 16 0 0 0-16 16v32a16 16 0 0 0 16 16h96a16 16 0 0 0 16-16v-32a16 16 0 0 0-16-16zM330.17 34.91a79 79 0 0 0-55 54.17c-14.27 51.05 21.19 97.77 68.83 102.53a84.07 84.07 0 0 1-20.85 12.91c-7.57 3.4-10.8 12.47-8.18 20.34l9.9 20c2.87 8.63 12.53 13.49 20.9 9.91 58-24.77 86.25-61.61 86.25-132V112c-.02-51.21-48.4-91.34-101.85-77.09zM352 132a20 20 0 1 1 20-20 20 20 0 0 1-20 20z\"]\n};\nvar faSortUp = {\n  prefix: 'fas',\n  iconName: 'sort-up',\n  icon: [320, 512, [], \"f0de\", \"M279 224H41c-21.4 0-32.1-25.9-17-41L143 64c9.4-9.4 24.6-9.4 33.9 0l119 119c15.2 15.1 4.5 41-16.9 41z\"]\n};\nvar faSpa = {\n  prefix: 'fas',\n  iconName: 'spa',\n  icon: [576, 512, [], \"f5bb\", \"M568.25 192c-29.04.13-135.01 6.16-213.84 83-33.12 29.63-53.36 63.3-66.41 94.86-13.05-31.56-33.29-65.23-66.41-94.86-78.83-76.84-184.8-82.87-213.84-83-4.41-.02-7.79 3.4-7.75 7.82.23 27.92 7.14 126.14 88.77 199.3C172.79 480.94 256 480 288 480s115.19.95 199.23-80.88c81.64-73.17 88.54-171.38 88.77-199.3.04-4.42-3.34-7.84-7.75-7.82zM287.98 302.6c12.82-18.85 27.6-35.78 44.09-50.52 19.09-18.61 39.58-33.3 60.26-45.18-16.44-70.5-51.72-133.05-96.73-172.22-4.11-3.58-11.02-3.58-15.14 0-44.99 39.14-80.27 101.63-96.74 172.07 20.37 11.7 40.5 26.14 59.22 44.39a282.768 282.768 0 0 1 45.04 51.46z\"]\n};\nvar faSpaceShuttle = {\n  prefix: 'fas',\n  iconName: 'space-shuttle',\n  icon: [640, 512, [], \"f197\", \"M592.604 208.244C559.735 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\"f110\", \"M304 48c0 26.51-21.49 48-48 48s-48-21.49-48-48 21.49-48 48-48 48 21.49 48 48zm-48 368c-26.51 0-48 21.49-48 48s21.49 48 48 48 48-21.49 48-48-21.49-48-48-48zm208-208c-26.51 0-48 21.49-48 48s21.49 48 48 48 48-21.49 48-48-21.49-48-48-48zM96 256c0-26.51-21.49-48-48-48S0 229.49 0 256s21.49 48 48 48 48-21.49 48-48zm12.922 99.078c-26.51 0-48 21.49-48 48s21.49 48 48 48 48-21.49 48-48c0-26.509-21.491-48-48-48zm294.156 0c-26.51 0-48 21.49-48 48s21.49 48 48 48 48-21.49 48-48c0-26.509-21.49-48-48-48zM108.922 60.922c-26.51 0-48 21.49-48 48s21.49 48 48 48 48-21.49 48-48-21.491-48-48-48z\"]\n};\nvar faSplotch = {\n  prefix: 'fas',\n  iconName: 'splotch',\n  icon: [512, 512, [], \"f5bc\", \"M472.29 195.89l-67.06-22.95c-19.28-6.6-33.54-20.92-38.14-38.3L351.1 74.19c-11.58-43.77-76.57-57.13-109.98-22.62l-46.14 47.67c-13.26 13.71-33.54 20.93-54.2 19.31l-71.88-5.62c-52.05-4.07-86.93 44.88-59.03 82.83l38.54 52.42c11.08 15.07 12.82 33.86 4.64 50.24L24.62 355.4c-20.59 41.25 22.84 84.87 73.49 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\"f96f\", 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faStore = {\n  prefix: 'fas',\n  iconName: 'store',\n  icon: [616, 512, [], \"f54e\", \"M602 118.6L537.1 15C531.3 5.7 521 0 510 0H106C95 0 84.7 5.7 78.9 15L14 118.6c-33.5 53.5-3.8 127.9 58.8 136.4 4.5.6 9.1.9 13.7.9 29.6 0 55.8-13 73.8-33.1 18 20.1 44.3 33.1 73.8 33.1 29.6 0 55.8-13 73.8-33.1 18 20.1 44.3 33.1 73.8 33.1 29.6 0 55.8-13 73.8-33.1 18.1 20.1 44.3 33.1 73.8 33.1 4.7 0 9.2-.3 13.7-.9 62.8-8.4 92.6-82.8 59-136.4zM529.5 288c-10 0-19.9-1.5-29.5-3.8V384H116v-99.8c-9.6 2.2-19.5 3.8-29.5 3.8-6 0-12.1-.4-18-1.2-5.6-.8-11.1-2.1-16.4-3.6V480c0 17.7 14.3 32 32 32h448c17.7 0 32-14.3 32-32V283.2c-5.4 1.6-10.8 2.9-16.4 3.6-6.1.8-12.1 1.2-18.2 1.2z\"]\n};\nvar faStoreAlt = {\n  prefix: 'fas',\n  iconName: 'store-alt',\n  icon: [640, 512, [], \"f54f\", \"M320 384H128V224H64v256c0 17.7 14.3 32 32 32h256c17.7 0 32-14.3 32-32V224h-64v160zm314.6-241.8l-85.3-128c-6-8.9-16-14.2-26.7-14.2H117.4c-10.7 0-20.7 5.3-26.6 14.2l-85.3 128c-14.2 21.3 1 49.8 26.6 49.8H608c25.5 0 40.7-28.5 26.6-49.8zM512 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faThermometerFull = {\n  prefix: 'fas',\n  iconName: 'thermometer-full',\n  icon: [256, 512, [], \"f2c7\", \"M224 96c0-53.019-42.981-96-96-96S32 42.981 32 96v203.347C12.225 321.756.166 351.136.002 383.333c-.359 70.303 56.787 128.176 127.089 128.664.299.002.61.003.909.003 70.698 0 128-57.304 128-128 0-32.459-12.088-62.09-32-84.653V96zm-96 368l-.576-.002c-43.86-.304-79.647-36.544-79.423-80.42.173-33.98 19.266-51.652 31.999-66.08V96c0-26.467 21.533-48 48-48s48 21.533 48 48v221.498c12.63 14.312 32 32.164 32 66.502 0 44.112-35.888 80-80 80zm64-80c0 35.346-28.654 64-64 64s-64-28.654-64-64c0-23.685 12.876-44.349 32-55.417V96c0-17.673 14.327-32 32-32s32 14.327 32 32v232.583c19.124 11.068 32 31.732 32 55.417z\"]\n};\nvar faThermometerHalf = {\n  prefix: 'fas',\n  iconName: 'thermometer-half',\n  icon: [256, 512, [], \"f2c9\", \"M192 384c0 35.346-28.654 64-64 64s-64-28.654-64-64c0-23.685 12.876-44.349 32-55.417V224c0-17.673 14.327-32 32-32s32 14.327 32 32v104.583c19.124 11.068 32 31.732 32 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384c0-34.339-19.37-52.19-32-66.502V96c0-26.467-21.533-48-48-48S80 69.533 80 96v221.498c-12.732 14.428-31.825 32.1-31.999 66.08-.224 43.876 35.563 80.116 79.423 80.42L128 464c44.112 0 80-35.888 80-80z\"]\n};\nvar faThermometerThreeQuarters = {\n  prefix: 'fas',\n  iconName: 'thermometer-three-quarters',\n  icon: [256, 512, [], \"f2c8\", \"M192 384c0 35.346-28.654 64-64 64-35.346 0-64-28.654-64-64 0-23.685 12.876-44.349 32-55.417V160c0-17.673 14.327-32 32-32s32 14.327 32 32v168.583c19.124 11.068 32 31.732 32 55.417zm32-84.653c19.912 22.563 32 52.194 32 84.653 0 70.696-57.303 128-128 128-.299 0-.609-.001-.909-.003C56.789 511.509-.357 453.636.002 383.333.166 351.135 12.225 321.755 32 299.347V96c0-53.019 42.981-96 96-96s96 42.981 96 96v203.347zM208 384c0-34.339-19.37-52.19-32-66.502V96c0-26.467-21.533-48-48-48S80 69.533 80 96v221.498c-12.732 14.428-31.825 32.1-31.999 66.08-.224 43.876 35.563 80.116 79.423 80.42L128 464c44.112 0 80-35.888 80-80z\"]\n};\nvar faThumbsDown = {\n  prefix: 'fas',\n  iconName: 'thumbs-down',\n  icon: [512, 512, [], \"f165\", \"M0 56v240c0 13.255 10.745 24 24 24h80c13.255 0 24-10.745 24-24V56c0-13.255-10.745-24-24-24H24C10.745 32 0 42.745 0 56zm40 200c0-13.255 10.745-24 24-24s24 10.745 24 24-10.745 24-24 24-24-10.745-24-24zm272 256c-20.183 0-29.485-39.293-33.931-57.795-5.206-21.666-10.589-44.07-25.393-58.902-32.469-32.524-49.503-73.967-89.117-113.111a11.98 11.98 0 0 1-3.558-8.521V59.901c0-6.541 5.243-11.878 11.783-11.998 15.831-.29 36.694-9.079 52.651-16.178C256.189 17.598 295.709.017 343.995 0h2.844c42.777 0 93.363.413 113.774 29.737 8.392 12.057 10.446 27.034 6.148 44.632 16.312 17.053 25.063 48.863 16.382 74.757 17.544 23.432 19.143 56.132 9.308 79.469l.11.11c11.893 11.949 19.523 31.259 19.439 49.197-.156 30.352-26.157 58.098-59.553 58.098H350.723C358.03 364.34 384 388.132 384 430.548 384 504 336 512 312 512z\"]\n};\nvar faThumbsUp = {\n  prefix: 'fas',\n  iconName: 'thumbs-up',\n  icon: [512, 512, [], \"f164\", \"M104 224H24c-13.255 0-24 10.745-24 24v240c0 13.255 10.745 24 24 24h80c13.255 0 24-10.745 24-24V248c0-13.255-10.745-24-24-24zM64 472c-13.255 0-24-10.745-24-24s10.745-24 24-24 24 10.745 24 24-10.745 24-24 24zM384 81.452c0 42.416-25.97 66.208-33.277 94.548h101.723c33.397 0 59.397 27.746 59.553 58.098.084 17.938-7.546 37.249-19.439 49.197l-.11.11c9.836 23.337 8.237 56.037-9.308 79.469 8.681 25.895-.069 57.704-16.382 74.757 4.298 17.598 2.244 32.575-6.148 44.632C440.202 511.587 389.616 512 346.839 512l-2.845-.001c-48.287-.017-87.806-17.598-119.56-31.725-15.957-7.099-36.821-15.887-52.651-16.178-6.54-.12-11.783-5.457-11.783-11.998v-213.77c0-3.2 1.282-6.271 3.558-8.521 39.614-39.144 56.648-80.587 89.117-113.111 14.804-14.832 20.188-37.236 25.393-58.902C282.515 39.293 291.817 0 312 0c24 0 72 8 72 81.452z\"]\n};\nvar faThumbtack = {\n  prefix: 'fas',\n  iconName: 'thumbtack',\n  icon: [384, 512, [], \"f08d\", \"M298.028 214.267L285.793 96H328c13.255 0 24-10.745 24-24V24c0-13.255-10.745-24-24-24H56C42.745 0 32 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0 0 1 32 0v224a16 16 0 0 1-32 0zm-96 0a16 16 0 0 1 32 0v224a16 16 0 0 1-32 0zm-96 0a16 16 0 0 1 32 0v224a16 16 0 0 1-32 0zM432 32H312l-9.4-18.7A24 24 0 0 0 281.1 0H166.8a23.72 23.72 0 0 0-21.4 13.3L136 32H16A16 16 0 0 0 0 48v32a16 16 0 0 0 16 16h416a16 16 0 0 0 16-16V48a16 16 0 0 0-16-16z\"]\n};\nvar faTrashRestore = {\n  prefix: 'fas',\n  iconName: 'trash-restore',\n  icon: [448, 512, [], \"f829\", \"M53.2 467a48 48 0 0 0 47.9 45h245.8a48 48 0 0 0 47.9-45L416 128H32zm70.11-175.8l89.38-94.26a15.41 15.41 0 0 1 22.62 0l89.38 94.26c10.08 10.62 2.94 28.8-11.32 28.8H256v112a16 16 0 0 1-16 16h-32a16 16 0 0 1-16-16V320h-57.37c-14.26 0-21.4-18.18-11.32-28.8zM432 32H312l-9.4-18.7A24 24 0 0 0 281.1 0H166.8a23.72 23.72 0 0 0-21.4 13.3L136 32H16A16 16 0 0 0 0 48v32a16 16 0 0 0 16 16h416a16 16 0 0 0 16-16V48a16 16 0 0 0-16-16z\"]\n};\nvar faTrashRestoreAlt = {\n  prefix: 'fas',\n  iconName: 'trash-restore-alt',\n  icon: [448, 512, [], \"f82a\", \"M32 464a48 48 0 0 0 48 48h288a48 48 0 0 0 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faVoicemail = {\n  prefix: 'fas',\n  iconName: 'voicemail',\n  icon: [640, 512, [], \"f897\", \"M496 128a144 144 0 0 0-119.74 224H263.74A144 144 0 1 0 144 416h352a144 144 0 0 0 0-288zM64 272a80 80 0 1 1 80 80 80 80 0 0 1-80-80zm432 80a80 80 0 1 1 80-80 80 80 0 0 1-80 80z\"]\n};\nvar faVolleyballBall = {\n  prefix: 'fas',\n  iconName: 'volleyball-ball',\n  icon: [512, 512, [], \"f45f\", \"M231.39 243.48a285.56 285.56 0 0 0-22.7-105.7c-90.8 42.4-157.5 122.4-180.3 216.8a249 249 0 0 0 56.9 81.1 333.87 333.87 0 0 1 146.1-192.2zm-36.9-134.4a284.23 284.23 0 0 0-57.4-70.7c-91 49.8-144.8 152.9-125 262.2 33.4-83.1 98.4-152 182.4-191.5zm187.6 165.1c8.6-99.8-27.3-197.5-97.5-264.4-14.7-1.7-51.6-5.5-98.9 8.5A333.87 333.87 0 0 1 279.19 241a285 285 0 0 0 102.9 33.18zm-124.7 9.5a286.33 286.33 0 0 0-80.2 72.6c82 57.3 184.5 75.1 277.5 47.8a247.15 247.15 0 0 0 42.2-89.9 336.1 336.1 0 0 1-80.9 10.4c-54.6-.1-108.9-14.1-158.6-40.9zm-98.3 99.7c-15.2 26-25.7 54.4-32.1 84.2a247.07 247.07 0 0 0 289-22.1c-112.9 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faAngleDoubleRight,\n  faAngleDoubleUp: faAngleDoubleUp,\n  faAngleDown: faAngleDown,\n  faAngleLeft: faAngleLeft,\n  faAngleRight: faAngleRight,\n  faAngleUp: faAngleUp,\n  faAngry: faAngry,\n  faAnkh: faAnkh,\n  faAppleAlt: faAppleAlt,\n  faArchive: faArchive,\n  faArchway: faArchway,\n  faArrowAltCircleDown: faArrowAltCircleDown,\n  faArrowAltCircleLeft: faArrowAltCircleLeft,\n  faArrowAltCircleRight: faArrowAltCircleRight,\n  faArrowAltCircleUp: faArrowAltCircleUp,\n  faArrowCircleDown: faArrowCircleDown,\n  faArrowCircleLeft: faArrowCircleLeft,\n  faArrowCircleRight: faArrowCircleRight,\n  faArrowCircleUp: faArrowCircleUp,\n  faArrowDown: faArrowDown,\n  faArrowLeft: faArrowLeft,\n  faArrowRight: faArrowRight,\n  faArrowUp: faArrowUp,\n  faArrowsAlt: faArrowsAlt,\n  faArrowsAltH: faArrowsAltH,\n  faArrowsAltV: faArrowsAltV,\n  faAssistiveListeningSystems: faAssistiveListeningSystems,\n  faAsterisk: faAsterisk,\n  faAt: faAt,\n  faAtlas: faAtlas,\n  faAtom: faAtom,\n  faAudioDescription: faAudioDescription,\n  faAward: faAward,\n  faBaby: faBaby,\n  faBabyCarriage: faBabyCarriage,\n  faBackspace: faBackspace,\n  faBackward: faBackward,\n  faBacon: faBacon,\n  faBahai: faBahai,\n  faBalanceScale: faBalanceScale,\n  faBalanceScaleLeft: faBalanceScaleLeft,\n  faBalanceScaleRight: faBalanceScaleRight,\n  faBan: faBan,\n  faBandAid: faBandAid,\n  faBarcode: faBarcode,\n  faBars: faBars,\n  faBaseballBall: faBaseballBall,\n  faBasketballBall: faBasketballBall,\n  faBath: faBath,\n  faBatteryEmpty: faBatteryEmpty,\n  faBatteryFull: faBatteryFull,\n  faBatteryHalf: faBatteryHalf,\n  faBatteryQuarter: faBatteryQuarter,\n  faBatteryThreeQuarters: faBatteryThreeQuarters,\n  faBed: faBed,\n  faBeer: faBeer,\n  faBell: faBell,\n  faBellSlash: faBellSlash,\n  faBezierCurve: faBezierCurve,\n  faBible: faBible,\n  faBicycle: faBicycle,\n  faBiking: faBiking,\n  faBinoculars: faBinoculars,\n  faBiohazard: faBiohazard,\n  faBirthdayCake: faBirthdayCake,\n  faBlender: faBlender,\n  faBlenderPhone: faBlenderPhone,\n  faBlind: faBlind,\n  faBlog: faBlog,\n  faBold: faBold,\n  faBolt: faBolt,\n  faBomb: faBomb,\n  faBone: faBone,\n  faBong: faBong,\n  faBook: faBook,\n  faBookDead: faBookDead,\n  faBookMedical: faBookMedical,\n  faBookOpen: faBookOpen,\n  faBookReader: faBookReader,\n  faBookmark: faBookmark,\n  faBorderAll: faBorderAll,\n  faBorderNone: faBorderNone,\n  faBorderStyle: faBorderStyle,\n  faBowlingBall: faBowlingBall,\n  faBox: faBox,\n  faBoxOpen: faBoxOpen,\n  faBoxTissue: faBoxTissue,\n  faBoxes: faBoxes,\n  faBraille: faBraille,\n  faBrain: faBrain,\n  faBreadSlice: faBreadSlice,\n  faBriefcase: faBriefcase,\n  faBriefcaseMedical: faBriefcaseMedical,\n  faBroadcastTower: faBroadcastTower,\n  faBroom: faBroom,\n  faBrush: faBrush,\n  faBug: faBug,\n  faBuilding: faBuilding,\n  faBullhorn: faBullhorn,\n  faBullseye: faBullseye,\n  faBurn: faBurn,\n  faBus: faBus,\n  faBusAlt: faBusAlt,\n  faBusinessTime: faBusinessTime,\n  faCalculator: faCalculator,\n  faCalendar: faCalendar,\n  faCalendarAlt: faCalendarAlt,\n  faCalendarCheck: faCalendarCheck,\n  faCalendarDay: faCalendarDay,\n  faCalendarMinus: faCalendarMinus,\n  faCalendarPlus: faCalendarPlus,\n  faCalendarTimes: faCalendarTimes,\n  faCalendarWeek: faCalendarWeek,\n  faCamera: faCamera,\n  faCameraRetro: faCameraRetro,\n  faCampground: faCampground,\n  faCandyCane: faCandyCane,\n  faCannabis: faCannabis,\n  faCapsules: faCapsules,\n  faCar: faCar,\n  faCarAlt: faCarAlt,\n  faCarBattery: faCarBattery,\n  faCarCrash: faCarCrash,\n  faCarSide: faCarSide,\n  faCaravan: faCaravan,\n  faCaretDown: faCaretDown,\n  faCaretLeft: faCaretLeft,\n  faCaretRight: faCaretRight,\n  faCaretSquareDown: faCaretSquareDown,\n  faCaretSquareLeft: faCaretSquareLeft,\n  faCaretSquareRight: faCaretSquareRight,\n  faCaretSquareUp: faCaretSquareUp,\n  faCaretUp: faCaretUp,\n  faCarrot: faCarrot,\n  faCartArrowDown: faCartArrowDown,\n  faCartPlus: faCartPlus,\n  faCashRegister: faCashRegister,\n  faCat: faCat,\n  faCertificate: faCertificate,\n  faChair: faChair,\n  faChalkboard: faChalkboard,\n  faChalkboardTeacher: faChalkboardTeacher,\n  faChargingStation: faChargingStation,\n  faChartArea: faChartArea,\n  faChartBar: faChartBar,\n  faChartLine: faChartLine,\n  faChartPie: faChartPie,\n  faCheck: faCheck,\n  faCheckCircle: faCheckCircle,\n  faCheckDouble: faCheckDouble,\n  faCheckSquare: faCheckSquare,\n  faCheese: faCheese,\n  faChess: faChess,\n  faChessBishop: faChessBishop,\n  faChessBoard: faChessBoard,\n  faChessKing: faChessKing,\n  faChessKnight: faChessKnight,\n  faChessPawn: faChessPawn,\n  faChessQueen: faChessQueen,\n  faChessRook: faChessRook,\n  faChevronCircleDown: faChevronCircleDown,\n  faChevronCircleLeft: faChevronCircleLeft,\n  faChevronCircleRight: faChevronCircleRight,\n  faChevronCircleUp: faChevronCircleUp,\n  faChevronDown: faChevronDown,\n  faChevronLeft: faChevronLeft,\n  faChevronRight: faChevronRight,\n  faChevronUp: faChevronUp,\n  faChild: faChild,\n  faChurch: faChurch,\n  faCircle: faCircle,\n  faCircleNotch: faCircleNotch,\n  faCity: faCity,\n  faClinicMedical: faClinicMedical,\n  faClipboard: faClipboard,\n  faClipboardCheck: faClipboardCheck,\n  faClipboardList: faClipboardList,\n  faClock: faClock,\n  faClone: faClone,\n  faClosedCaptioning: faClosedCaptioning,\n  faCloud: faCloud,\n  faCloudDownloadAlt: faCloudDownloadAlt,\n  faCloudMeatball: faCloudMeatball,\n  faCloudMoon: faCloudMoon,\n  faCloudMoonRain: faCloudMoonRain,\n  faCloudRain: faCloudRain,\n  faCloudShowersHeavy: faCloudShowersHeavy,\n  faCloudSun: faCloudSun,\n  faCloudSunRain: faCloudSunRain,\n  faCloudUploadAlt: faCloudUploadAlt,\n  faCocktail: faCocktail,\n  faCode: faCode,\n  faCodeBranch: faCodeBranch,\n  faCoffee: faCoffee,\n  faCog: faCog,\n  faCogs: faCogs,\n  faCoins: faCoins,\n  faColumns: faColumns,\n  faComment: faComment,\n  faCommentAlt: faCommentAlt,\n  faCommentDollar: faCommentDollar,\n  faCommentDots: faCommentDots,\n  faCommentMedical: faCommentMedical,\n  faCommentSlash: faCommentSlash,\n  faComments: faComments,\n  faCommentsDollar: faCommentsDollar,\n  faCompactDisc: faCompactDisc,\n  faCompass: faCompass,\n  faCompress: faCompress,\n  faCompressAlt: faCompressAlt,\n  faCompressArrowsAlt: faCompressArrowsAlt,\n  faConciergeBell: faConciergeBell,\n  faCookie: faCookie,\n  faCookieBite: faCookieBite,\n  faCopy: faCopy,\n  faCopyright: faCopyright,\n  faCouch: faCouch,\n  faCreditCard: faCreditCard,\n  faCrop: faCrop,\n  faCropAlt: faCropAlt,\n  faCross: faCross,\n  faCrosshairs: faCrosshairs,\n  faCrow: faCrow,\n  faCrown: faCrown,\n  faCrutch: faCrutch,\n  faCube: faCube,\n  faCubes: faCubes,\n  faCut: faCut,\n  faDatabase: faDatabase,\n  faDeaf: faDeaf,\n  faDemocrat: faDemocrat,\n  faDesktop: faDesktop,\n  faDharmachakra: faDharmachakra,\n  faDiagnoses: faDiagnoses,\n  faDice: faDice,\n  faDiceD20: faDiceD20,\n  faDiceD6: faDiceD6,\n  faDiceFive: faDiceFive,\n  faDiceFour: faDiceFour,\n  faDiceOne: faDiceOne,\n  faDiceSix: faDiceSix,\n  faDiceThree: faDiceThree,\n  faDiceTwo: faDiceTwo,\n  faDigitalTachograph: faDigitalTachograph,\n  faDirections: faDirections,\n  faDisease: faDisease,\n  faDivide: faDivide,\n  faDizzy: faDizzy,\n  faDna: faDna,\n  faDog: faDog,\n  faDollarSign: faDollarSign,\n  faDolly: faDolly,\n  faDollyFlatbed: faDollyFlatbed,\n  faDonate: faDonate,\n  faDoorClosed: faDoorClosed,\n  faDoorOpen: faDoorOpen,\n  faDotCircle: faDotCircle,\n  faDove: faDove,\n  faDownload: faDownload,\n  faDraftingCompass: faDraftingCompass,\n  faDragon: faDragon,\n  faDrawPolygon: faDrawPolygon,\n  faDrum: faDrum,\n  faDrumSteelpan: faDrumSteelpan,\n  faDrumstickBite: faDrumstickBite,\n  faDumbbell: faDumbbell,\n  faDumpster: faDumpster,\n  faDumpsterFire: faDumpsterFire,\n  faDungeon: faDungeon,\n  faEdit: faEdit,\n  faEgg: faEgg,\n  faEject: faEject,\n  faEllipsisH: faEllipsisH,\n  faEllipsisV: faEllipsisV,\n  faEnvelope: faEnvelope,\n  faEnvelopeOpen: faEnvelopeOpen,\n  faEnvelopeOpenText: faEnvelopeOpenText,\n  faEnvelopeSquare: faEnvelopeSquare,\n  faEquals: faEquals,\n  faEraser: faEraser,\n  faEthernet: faEthernet,\n  faEuroSign: faEuroSign,\n  faExchangeAlt: faExchangeAlt,\n  faExclamation: faExclamation,\n  faExclamationCircle: faExclamationCircle,\n  faExclamationTriangle: faExclamationTriangle,\n  faExpand: faExpand,\n  faExpandAlt: faExpandAlt,\n  faExpandArrowsAlt: faExpandArrowsAlt,\n  faExternalLinkAlt: faExternalLinkAlt,\n  faExternalLinkSquareAlt: faExternalLinkSquareAlt,\n  faEye: faEye,\n  faEyeDropper: faEyeDropper,\n  faEyeSlash: faEyeSlash,\n  faFan: faFan,\n  faFastBackward: faFastBackward,\n  faFastForward: faFastForward,\n  faFaucet: faFaucet,\n  faFax: faFax,\n  faFeather: faFeather,\n  faFeatherAlt: faFeatherAlt,\n  faFemale: faFemale,\n  faFighterJet: faFighterJet,\n  faFile: faFile,\n  faFileAlt: faFileAlt,\n  faFileArchive: faFileArchive,\n  faFileAudio: faFileAudio,\n  faFileCode: faFileCode,\n  faFileContract: faFileContract,\n  faFileCsv: faFileCsv,\n  faFileDownload: faFileDownload,\n  faFileExcel: faFileExcel,\n  faFileExport: faFileExport,\n  faFileImage: faFileImage,\n  faFileImport: faFileImport,\n  faFileInvoice: faFileInvoice,\n  faFileInvoiceDollar: faFileInvoiceDollar,\n  faFileMedical: faFileMedical,\n  faFileMedicalAlt: faFileMedicalAlt,\n  faFilePdf: faFilePdf,\n  faFilePowerpoint: faFilePowerpoint,\n  faFilePrescription: faFilePrescription,\n  faFileSignature: faFileSignature,\n  faFileUpload: faFileUpload,\n  faFileVideo: faFileVideo,\n  faFileWord: faFileWord,\n  faFill: faFill,\n  faFillDrip: faFillDrip,\n  faFilm: faFilm,\n  faFilter: faFilter,\n  faFingerprint: faFingerprint,\n  faFire: faFire,\n  faFireAlt: faFireAlt,\n  faFireExtinguisher: faFireExtinguisher,\n  faFirstAid: faFirstAid,\n  faFish: faFish,\n  faFistRaised: faFistRaised,\n  faFlag: faFlag,\n  faFlagCheckered: faFlagCheckered,\n  faFlagUsa: faFlagUsa,\n  faFlask: faFlask,\n  faFlushed: faFlushed,\n  faFolder: faFolder,\n  faFolderMinus: faFolderMinus,\n  faFolderOpen: faFolderOpen,\n  faFolderPlus: faFolderPlus,\n  faFont: faFont,\n  faFontAwesomeLogoFull: faFontAwesomeLogoFull,\n  faFootballBall: faFootballBall,\n  faForward: faForward,\n  faFrog: faFrog,\n  faFrown: faFrown,\n  faFrownOpen: faFrownOpen,\n  faFunnelDollar: faFunnelDollar,\n  faFutbol: faFutbol,\n  faGamepad: faGamepad,\n  faGasPump: faGasPump,\n  faGavel: faGavel,\n  faGem: faGem,\n  faGenderless: faGenderless,\n  faGhost: faGhost,\n  faGift: faGift,\n  faGifts: faGifts,\n  faGlassCheers: faGlassCheers,\n  faGlassMartini: faGlassMartini,\n  faGlassMartiniAlt: faGlassMartiniAlt,\n  faGlassWhiskey: faGlassWhiskey,\n  faGlasses: faGlasses,\n  faGlobe: faGlobe,\n  faGlobeAfrica: faGlobeAfrica,\n  faGlobeAmericas: faGlobeAmericas,\n  faGlobeAsia: faGlobeAsia,\n  faGlobeEurope: faGlobeEurope,\n  faGolfBall: faGolfBall,\n  faGopuram: faGopuram,\n  faGraduationCap: faGraduationCap,\n  faGreaterThan: faGreaterThan,\n  faGreaterThanEqual: faGreaterThanEqual,\n  faGrimace: faGrimace,\n  faGrin: faGrin,\n  faGrinAlt: faGrinAlt,\n  faGrinBeam: faGrinBeam,\n  faGrinBeamSweat: faGrinBeamSweat,\n  faGrinHearts: faGrinHearts,\n  faGrinSquint: faGrinSquint,\n  faGrinSquintTears: faGrinSquintTears,\n  faGrinStars: faGrinStars,\n  faGrinTears: faGrinTears,\n  faGrinTongue: faGrinTongue,\n  faGrinTongueSquint: faGrinTongueSquint,\n  faGrinTongueWink: faGrinTongueWink,\n  faGrinWink: faGrinWink,\n  faGripHorizontal: faGripHorizontal,\n  faGripLines: faGripLines,\n  faGripLinesVertical: faGripLinesVertical,\n  faGripVertical: faGripVertical,\n  faGuitar: faGuitar,\n  faHSquare: faHSquare,\n  faHamburger: faHamburger,\n  faHammer: faHammer,\n  faHamsa: faHamsa,\n  faHandHolding: faHandHolding,\n  faHandHoldingHeart: faHandHoldingHeart,\n  faHandHoldingMedical: faHandHoldingMedical,\n  faHandHoldingUsd: faHandHoldingUsd,\n  faHandHoldingWater: faHandHoldingWater,\n  faHandLizard: faHandLizard,\n  faHandMiddleFinger: faHandMiddleFinger,\n  faHandPaper: faHandPaper,\n  faHandPeace: faHandPeace,\n  faHandPointDown: faHandPointDown,\n  faHandPointLeft: faHandPointLeft,\n  faHandPointRight: faHandPointRight,\n  faHandPointUp: faHandPointUp,\n  faHandPointer: faHandPointer,\n  faHandRock: faHandRock,\n  faHandScissors: faHandScissors,\n  faHandSparkles: faHandSparkles,\n  faHandSpock: faHandSpock,\n  faHands: faHands,\n  faHandsHelping: faHandsHelping,\n  faHandsWash: faHandsWash,\n  faHandshake: faHandshake,\n  faHandshakeAltSlash: faHandshakeAltSlash,\n  faHandshakeSlash: faHandshakeSlash,\n  faHanukiah: faHanukiah,\n  faHardHat: faHardHat,\n  faHashtag: faHashtag,\n  faHatCowboy: faHatCowboy,\n  faHatCowboySide: faHatCowboySide,\n  faHatWizard: faHatWizard,\n  faHdd: faHdd,\n  faHeadSideCough: faHeadSideCough,\n  faHeadSideCoughSlash: faHeadSideCoughSlash,\n  faHeadSideMask: faHeadSideMask,\n  faHeadSideVirus: faHeadSideVirus,\n  faHeading: faHeading,\n  faHeadphones: faHeadphones,\n  faHeadphonesAlt: faHeadphonesAlt,\n  faHeadset: faHeadset,\n  faHeart: faHeart,\n  faHeartBroken: faHeartBroken,\n  faHeartbeat: faHeartbeat,\n  faHelicopter: faHelicopter,\n  faHighlighter: faHighlighter,\n  faHiking: faHiking,\n  faHippo: faHippo,\n  faHistory: faHistory,\n  faHockeyPuck: faHockeyPuck,\n  faHollyBerry: faHollyBerry,\n  faHome: faHome,\n  faHorse: faHorse,\n  faHorseHead: faHorseHead,\n  faHospital: faHospital,\n  faHospitalAlt: faHospitalAlt,\n  faHospitalSymbol: faHospitalSymbol,\n  faHospitalUser: faHospitalUser,\n  faHotTub: faHotTub,\n  faHotdog: faHotdog,\n  faHotel: faHotel,\n  faHourglass: faHourglass,\n  faHourglassEnd: faHourglassEnd,\n  faHourglassHalf: faHourglassHalf,\n  faHourglassStart: faHourglassStart,\n  faHouseDamage: faHouseDamage,\n  faHouseUser: faHouseUser,\n  faHryvnia: faHryvnia,\n  faICursor: faICursor,\n  faIceCream: faIceCream,\n  faIcicles: faIcicles,\n  faIcons: faIcons,\n  faIdBadge: faIdBadge,\n  faIdCard: faIdCard,\n  faIdCardAlt: faIdCardAlt,\n  faIgloo: faIgloo,\n  faImage: faImage,\n  faImages: faImages,\n  faInbox: faInbox,\n  faIndent: faIndent,\n  faIndustry: faIndustry,\n  faInfinity: faInfinity,\n  faInfo: faInfo,\n  faInfoCircle: faInfoCircle,\n  faItalic: faItalic,\n  faJedi: faJedi,\n  faJoint: faJoint,\n  faJournalWhills: faJournalWhills,\n  faKaaba: faKaaba,\n  faKey: faKey,\n  faKeyboard: faKeyboard,\n  faKhanda: faKhanda,\n  faKiss: faKiss,\n  faKissBeam: faKissBeam,\n  faKissWinkHeart: faKissWinkHeart,\n  faKiwiBird: faKiwiBird,\n  faLandmark: faLandmark,\n  faLanguage: faLanguage,\n  faLaptop: faLaptop,\n  faLaptopCode: faLaptopCode,\n  faLaptopHouse: faLaptopHouse,\n  faLaptopMedical: faLaptopMedical,\n  faLaugh: faLaugh,\n  faLaughBeam: faLaughBeam,\n  faLaughSquint: faLaughSquint,\n  faLaughWink: faLaughWink,\n  faLayerGroup: faLayerGroup,\n  faLeaf: faLeaf,\n  faLemon: faLemon,\n  faLessThan: faLessThan,\n  faLessThanEqual: faLessThanEqual,\n  faLevelDownAlt: faLevelDownAlt,\n  faLevelUpAlt: faLevelUpAlt,\n  faLifeRing: faLifeRing,\n  faLightbulb: faLightbulb,\n  faLink: faLink,\n  faLiraSign: faLiraSign,\n  faList: faList,\n  faListAlt: faListAlt,\n  faListOl: faListOl,\n  faListUl: faListUl,\n  faLocationArrow: faLocationArrow,\n  faLock: faLock,\n  faLockOpen: faLockOpen,\n  faLongArrowAltDown: faLongArrowAltDown,\n  faLongArrowAltLeft: faLongArrowAltLeft,\n  faLongArrowAltRight: faLongArrowAltRight,\n  faLongArrowAltUp: faLongArrowAltUp,\n  faLowVision: faLowVision,\n  faLuggageCart: faLuggageCart,\n  faLungs: faLungs,\n  faLungsVirus: faLungsVirus,\n  faMagic: faMagic,\n  faMagnet: faMagnet,\n  faMailBulk: faMailBulk,\n  faMale: faMale,\n  faMap: faMap,\n  faMapMarked: faMapMarked,\n  faMapMarkedAlt: faMapMarkedAlt,\n  faMapMarker: faMapMarker,\n  faMapMarkerAlt: faMapMarkerAlt,\n  faMapPin: faMapPin,\n  faMapSigns: faMapSigns,\n  faMarker: faMarker,\n  faMars: faMars,\n  faMarsDouble: faMarsDouble,\n  faMarsStroke: faMarsStroke,\n  faMarsStrokeH: faMarsStrokeH,\n  faMarsStrokeV: faMarsStrokeV,\n  faMask: faMask,\n  faMedal: faMedal,\n  faMedkit: faMedkit,\n  faMeh: faMeh,\n  faMehBlank: faMehBlank,\n  faMehRollingEyes: faMehRollingEyes,\n  faMemory: faMemory,\n  faMenorah: faMenorah,\n  faMercury: faMercury,\n  faMeteor: faMeteor,\n  faMicrochip: faMicrochip,\n  faMicrophone: faMicrophone,\n  faMicrophoneAlt: faMicrophoneAlt,\n  faMicrophoneAltSlash: faMicrophoneAltSlash,\n  faMicrophoneSlash: faMicrophoneSlash,\n  faMicroscope: faMicroscope,\n  faMinus: faMinus,\n  faMinusCircle: faMinusCircle,\n  faMinusSquare: faMinusSquare,\n  faMitten: faMitten,\n  faMobile: faMobile,\n  faMobileAlt: faMobileAlt,\n  faMoneyBill: faMoneyBill,\n  faMoneyBillAlt: faMoneyBillAlt,\n  faMoneyBillWave: faMoneyBillWave,\n  faMoneyBillWaveAlt: faMoneyBillWaveAlt,\n  faMoneyCheck: faMoneyCheck,\n  faMoneyCheckAlt: faMoneyCheckAlt,\n  faMonument: faMonument,\n  faMoon: faMoon,\n  faMortarPestle: faMortarPestle,\n  faMosque: faMosque,\n  faMotorcycle: faMotorcycle,\n  faMountain: faMountain,\n  faMouse: faMouse,\n  faMousePointer: faMousePointer,\n  faMugHot: faMugHot,\n  faMusic: faMusic,\n  faNetworkWired: faNetworkWired,\n  faNeuter: faNeuter,\n  faNewspaper: faNewspaper,\n  faNotEqual: faNotEqual,\n  faNotesMedical: faNotesMedical,\n  faObjectGroup: faObjectGroup,\n  faObjectUngroup: faObjectUngroup,\n  faOilCan: faOilCan,\n  faOm: faOm,\n  faOtter: faOtter,\n  faOutdent: faOutdent,\n  faPager: faPager,\n  faPaintBrush: faPaintBrush,\n  faPaintRoller: faPaintRoller,\n  faPalette: faPalette,\n  faPallet: faPallet,\n  faPaperPlane: faPaperPlane,\n  faPaperclip: faPaperclip,\n  faParachuteBox: faParachuteBox,\n  faParagraph: faParagraph,\n  faParking: faParking,\n  faPassport: faPassport,\n  faPastafarianism: faPastafarianism,\n  faPaste: faPaste,\n  faPause: faPause,\n  faPauseCircle: faPauseCircle,\n  faPaw: faPaw,\n  faPeace: faPeace,\n  faPen: faPen,\n  faPenAlt: faPenAlt,\n  faPenFancy: faPenFancy,\n  faPenNib: faPenNib,\n  faPenSquare: faPenSquare,\n  faPencilAlt: faPencilAlt,\n  faPencilRuler: faPencilRuler,\n  faPeopleArrows: faPeopleArrows,\n  faPeopleCarry: faPeopleCarry,\n  faPepperHot: faPepperHot,\n  faPercent: faPercent,\n  faPercentage: faPercentage,\n  faPersonBooth: faPersonBooth,\n  faPhone: faPhone,\n  faPhoneAlt: faPhoneAlt,\n  faPhoneSlash: faPhoneSlash,\n  faPhoneSquare: faPhoneSquare,\n  faPhoneSquareAlt: faPhoneSquareAlt,\n  faPhoneVolume: faPhoneVolume,\n  faPhotoVideo: faPhotoVideo,\n  faPiggyBank: faPiggyBank,\n  faPills: faPills,\n  faPizzaSlice: faPizzaSlice,\n  faPlaceOfWorship: faPlaceOfWorship,\n  faPlane: faPlane,\n  faPlaneArrival: faPlaneArrival,\n  faPlaneDeparture: faPlaneDeparture,\n  faPlaneSlash: faPlaneSlash,\n  faPlay: faPlay,\n  faPlayCircle: faPlayCircle,\n  faPlug: faPlug,\n  faPlus: faPlus,\n  faPlusCircle: faPlusCircle,\n  faPlusSquare: faPlusSquare,\n  faPodcast: faPodcast,\n  faPoll: faPoll,\n  faPollH: faPollH,\n  faPoo: faPoo,\n  faPooStorm: faPooStorm,\n  faPoop: faPoop,\n  faPortrait: faPortrait,\n  faPoundSign: faPoundSign,\n  faPowerOff: faPowerOff,\n  faPray: faPray,\n  faPrayingHands: faPrayingHands,\n  faPrescription: faPrescription,\n  faPrescriptionBottle: faPrescriptionBottle,\n  faPrescriptionBottleAlt: faPrescriptionBottleAlt,\n  faPrint: faPrint,\n  faProcedures: faProcedures,\n  faProjectDiagram: faProjectDiagram,\n  faPumpMedical: faPumpMedical,\n  faPumpSoap: faPumpSoap,\n  faPuzzlePiece: faPuzzlePiece,\n  faQrcode: faQrcode,\n  faQuestion: faQuestion,\n  faQuestionCircle: faQuestionCircle,\n  faQuidditch: faQuidditch,\n  faQuoteLeft: faQuoteLeft,\n  faQuoteRight: faQuoteRight,\n  faQuran: faQuran,\n  faRadiation: faRadiation,\n  faRadiationAlt: faRadiationAlt,\n  faRainbow: faRainbow,\n  faRandom: faRandom,\n  faReceipt: faReceipt,\n  faRecordVinyl: faRecordVinyl,\n  faRecycle: faRecycle,\n  faRedo: faRedo,\n  faRedoAlt: faRedoAlt,\n  faRegistered: faRegistered,\n  faRemoveFormat: faRemoveFormat,\n  faReply: faReply,\n  faReplyAll: faReplyAll,\n  faRepublican: faRepublican,\n  faRestroom: faRestroom,\n  faRetweet: faRetweet,\n  faRibbon: faRibbon,\n  faRing: faRing,\n  faRoad: faRoad,\n  faRobot: faRobot,\n  faRocket: faRocket,\n  faRoute: faRoute,\n  faRss: faRss,\n  faRssSquare: faRssSquare,\n  faRubleSign: faRubleSign,\n  faRuler: faRuler,\n  faRulerCombined: faRulerCombined,\n  faRulerHorizontal: faRulerHorizontal,\n  faRulerVertical: faRulerVertical,\n  faRunning: faRunning,\n  faRupeeSign: faRupeeSign,\n  faSadCry: faSadCry,\n  faSadTear: faSadTear,\n  faSatellite: faSatellite,\n  faSatelliteDish: faSatelliteDish,\n  faSave: faSave,\n  faSchool: faSchool,\n  faScrewdriver: faScrewdriver,\n  faScroll: faScroll,\n  faSdCard: faSdCard,\n  faSearch: faSearch,\n  faSearchDollar: faSearchDollar,\n  faSearchLocation: faSearchLocation,\n  faSearchMinus: faSearchMinus,\n  faSearchPlus: faSearchPlus,\n  faSeedling: faSeedling,\n  faServer: faServer,\n  faShapes: faShapes,\n  faShare: faShare,\n  faShareAlt: faShareAlt,\n  faShareAltSquare: faShareAltSquare,\n  faShareSquare: faShareSquare,\n  faShekelSign: faShekelSign,\n  faShieldAlt: faShieldAlt,\n  faShieldVirus: faShieldVirus,\n  faShip: faShip,\n  faShippingFast: faShippingFast,\n  faShoePrints: faShoePrints,\n  faShoppingBag: faShoppingBag,\n  faShoppingBasket: faShoppingBasket,\n  faShoppingCart: faShoppingCart,\n  faShower: faShower,\n  faShuttleVan: faShuttleVan,\n  faSign: faSign,\n  faSignInAlt: faSignInAlt,\n  faSignLanguage: faSignLanguage,\n  faSignOutAlt: faSignOutAlt,\n  faSignal: faSignal,\n  faSignature: faSignature,\n  faSimCard: faSimCard,\n  faSitemap: faSitemap,\n  faSkating: faSkating,\n  faSkiing: faSkiing,\n  faSkiingNordic: faSkiingNordic,\n  faSkull: faSkull,\n  faSkullCrossbones: faSkullCrossbones,\n  faSlash: faSlash,\n  faSleigh: faSleigh,\n  faSlidersH: faSlidersH,\n  faSmile: faSmile,\n  faSmileBeam: faSmileBeam,\n  faSmileWink: faSmileWink,\n  faSmog: faSmog,\n  faSmoking: faSmoking,\n  faSmokingBan: faSmokingBan,\n  faSms: faSms,\n  faSnowboarding: faSnowboarding,\n  faSnowflake: faSnowflake,\n  faSnowman: faSnowman,\n  faSnowplow: faSnowplow,\n  faSoap: faSoap,\n  faSocks: faSocks,\n  faSolarPanel: faSolarPanel,\n  faSort: faSort,\n  faSortAlphaDown: faSortAlphaDown,\n  faSortAlphaDownAlt: faSortAlphaDownAlt,\n  faSortAlphaUp: faSortAlphaUp,\n  faSortAlphaUpAlt: faSortAlphaUpAlt,\n  faSortAmountDown: faSortAmountDown,\n  faSortAmountDownAlt: faSortAmountDownAlt,\n  faSortAmountUp: faSortAmountUp,\n  faSortAmountUpAlt: faSortAmountUpAlt,\n  faSortDown: faSortDown,\n  faSortNumericDown: faSortNumericDown,\n  faSortNumericDownAlt: faSortNumericDownAlt,\n  faSortNumericUp: faSortNumericUp,\n  faSortNumericUpAlt: faSortNumericUpAlt,\n  faSortUp: faSortUp,\n  faSpa: faSpa,\n  faSpaceShuttle: faSpaceShuttle,\n  faSpellCheck: faSpellCheck,\n  faSpider: faSpider,\n  faSpinner: faSpinner,\n  faSplotch: faSplotch,\n  faSprayCan: faSprayCan,\n  faSquare: faSquare,\n  faSquareFull: faSquareFull,\n  faSquareRootAlt: faSquareRootAlt,\n  faStamp: faStamp,\n  faStar: faStar,\n  faStarAndCrescent: faStarAndCrescent,\n  faStarHalf: faStarHalf,\n  faStarHalfAlt: faStarHalfAlt,\n  faStarOfDavid: faStarOfDavid,\n  faStarOfLife: faStarOfLife,\n  faStepBackward: faStepBackward,\n  faStepForward: faStepForward,\n  faStethoscope: faStethoscope,\n  faStickyNote: faStickyNote,\n  faStop: faStop,\n  faStopCircle: faStopCircle,\n  faStopwatch: faStopwatch,\n  faStopwatch20: faStopwatch20,\n  faStore: faStore,\n  faStoreAlt: faStoreAlt,\n  faStoreAltSlash: faStoreAltSlash,\n  faStoreSlash: faStoreSlash,\n  faStream: faStream,\n  faStreetView: faStreetView,\n  faStrikethrough: faStrikethrough,\n  faStroopwafel: faStroopwafel,\n  faSubscript: faSubscript,\n  faSubway: faSubway,\n  faSuitcase: faSuitcase,\n  faSuitcaseRolling: faSuitcaseRolling,\n  faSun: faSun,\n  faSuperscript: faSuperscript,\n  faSurprise: faSurprise,\n  faSwatchbook: faSwatchbook,\n  faSwimmer: faSwimmer,\n  faSwimmingPool: faSwimmingPool,\n  faSynagogue: faSynagogue,\n  faSync: faSync,\n  faSyncAlt: faSyncAlt,\n  faSyringe: faSyringe,\n  faTable: faTable,\n  faTableTennis: faTableTennis,\n  faTablet: faTablet,\n  faTabletAlt: faTabletAlt,\n  faTablets: faTablets,\n  faTachometerAlt: faTachometerAlt,\n  faTag: faTag,\n  faTags: faTags,\n  faTape: faTape,\n  faTasks: faTasks,\n  faTaxi: faTaxi,\n  faTeeth: faTeeth,\n  faTeethOpen: faTeethOpen,\n  faTemperatureHigh: faTemperatureHigh,\n  faTemperatureLow: faTemperatureLow,\n  faTenge: faTenge,\n  faTerminal: faTerminal,\n  faTextHeight: faTextHeight,\n  faTextWidth: faTextWidth,\n  faTh: faTh,\n  faThLarge: faThLarge,\n  faThList: faThList,\n  faTheaterMasks: faTheaterMasks,\n  faThermometer: faThermometer,\n  faThermometerEmpty: faThermometerEmpty,\n  faThermometerFull: faThermometerFull,\n  faThermometerHalf: faThermometerHalf,\n  faThermometerQuarter: faThermometerQuarter,\n  faThermometerThreeQuarters: faThermometerThreeQuarters,\n  faThumbsDown: faThumbsDown,\n  faThumbsUp: faThumbsUp,\n  faThumbtack: faThumbtack,\n  faTicketAlt: faTicketAlt,\n  faTimes: faTimes,\n  faTimesCircle: faTimesCircle,\n  faTint: faTint,\n  faTintSlash: faTintSlash,\n  faTired: faTired,\n  faToggleOff: faToggleOff,\n  faToggleOn: faToggleOn,\n  faToilet: faToilet,\n  faToiletPaper: faToiletPaper,\n  faToiletPaperSlash: faToiletPaperSlash,\n  faToolbox: faToolbox,\n  faTools: faTools,\n  faTooth: faTooth,\n  faTorah: faTorah,\n  faToriiGate: faToriiGate,\n  faTractor: faTractor,\n  faTrademark: faTrademark,\n  faTrafficLight: faTrafficLight,\n  faTrailer: faTrailer,\n  faTrain: faTrain,\n  faTram: faTram,\n  faTransgender: faTransgender,\n  faTransgenderAlt: faTransgenderAlt,\n  faTrash: faTrash,\n  faTrashAlt: faTrashAlt,\n  faTrashRestore: faTrashRestore,\n  faTrashRestoreAlt: faTrashRestoreAlt,\n  faTree: faTree,\n  faTrophy: faTrophy,\n  faTruck: faTruck,\n  faTruckLoading: faTruckLoading,\n  faTruckMonster: faTruckMonster,\n  faTruckMoving: faTruckMoving,\n  faTruckPickup: faTruckPickup,\n  faTshirt: faTshirt,\n  faTty: faTty,\n  faTv: faTv,\n  faUmbrella: faUmbrella,\n  faUmbrellaBeach: faUmbrellaBeach,\n  faUnderline: faUnderline,\n  faUndo: faUndo,\n  faUndoAlt: faUndoAlt,\n  faUniversalAccess: faUniversalAccess,\n  faUniversity: faUniversity,\n  faUnlink: faUnlink,\n  faUnlock: faUnlock,\n  faUnlockAlt: faUnlockAlt,\n  faUpload: faUpload,\n  faUser: faUser,\n  faUserAlt: faUserAlt,\n  faUserAltSlash: faUserAltSlash,\n  faUserAstronaut: faUserAstronaut,\n  faUserCheck: faUserCheck,\n  faUserCircle: faUserCircle,\n  faUserClock: faUserClock,\n  faUserCog: faUserCog,\n  faUserEdit: faUserEdit,\n  faUserFriends: faUserFriends,\n  faUserGraduate: faUserGraduate,\n  faUserInjured: faUserInjured,\n  faUserLock: faUserLock,\n  faUserMd: faUserMd,\n  faUserMinus: faUserMinus,\n  faUserNinja: faUserNinja,\n  faUserNurse: faUserNurse,\n  faUserPlus: faUserPlus,\n  faUserSecret: faUserSecret,\n  faUserShield: faUserShield,\n  faUserSlash: faUserSlash,\n  faUserTag: faUserTag,\n  faUserTie: faUserTie,\n  faUserTimes: faUserTimes,\n  faUsers: faUsers,\n  faUsersCog: faUsersCog,\n  faUtensilSpoon: faUtensilSpoon,\n  faUtensils: faUtensils,\n  faVectorSquare: faVectorSquare,\n  faVenus: faVenus,\n  faVenusDouble: faVenusDouble,\n  faVenusMars: faVenusMars,\n  faVial: faVial,\n  faVials: faVials,\n  faVideo: faVideo,\n  faVideoSlash: faVideoSlash,\n  faVihara: faVihara,\n  faVirus: faVirus,\n  faVirusSlash: faVirusSlash,\n  faViruses: faViruses,\n  faVoicemail: faVoicemail,\n  faVolleyballBall: faVolleyballBall,\n  faVolumeDown: faVolumeDown,\n  faVolumeMute: faVolumeMute,\n  faVolumeOff: faVolumeOff,\n  faVolumeUp: faVolumeUp,\n  faVoteYea: faVoteYea,\n  faVrCardboard: faVrCardboard,\n  faWalking: faWalking,\n  faWallet: faWallet,\n  faWarehouse: faWarehouse,\n  faWater: faWater,\n  faWaveSquare: faWaveSquare,\n  faWeight: faWeight,\n  faWeightHanging: faWeightHanging,\n  faWheelchair: faWheelchair,\n  faWifi: faWifi,\n  faWind: faWind,\n  faWindowClose: faWindowClose,\n  faWindowMaximize: faWindowMaximize,\n  faWindowMinimize: faWindowMinimize,\n  faWindowRestore: faWindowRestore,\n  faWineBottle: faWineBottle,\n  faWineGlass: faWineGlass,\n  faWineGlassAlt: faWineGlassAlt,\n  faWonSign: faWonSign,\n  faWrench: faWrench,\n  faXRay: faXRay,\n  faYenSign: faYenSign,\n  faYinYang: faYinYang\n};\n\nexport { _iconsCache as fas, prefix, faAd, faAddressBook, faAddressCard, faAdjust, faAirFreshener, faAlignCenter, faAlignJustify, faAlignLeft, faAlignRight, faAllergies, faAmbulance, faAmericanSignLanguageInterpreting, faAnchor, faAngleDoubleDown, faAngleDoubleLeft, faAngleDoubleRight, faAngleDoubleUp, faAngleDown, faAngleLeft, faAngleRight, faAngleUp, faAngry, faAnkh, faAppleAlt, faArchive, faArchway, faArrowAltCircleDown, faArrowAltCircleLeft, faArrowAltCircleRight, faArrowAltCircleUp, faArrowCircleDown, faArrowCircleLeft, faArrowCircleRight, faArrowCircleUp, faArrowDown, faArrowLeft, faArrowRight, faArrowUp, faArrowsAlt, faArrowsAltH, faArrowsAltV, faAssistiveListeningSystems, faAsterisk, faAt, faAtlas, faAtom, faAudioDescription, faAward, faBaby, faBabyCarriage, faBackspace, faBackward, faBacon, faBahai, faBalanceScale, faBalanceScaleLeft, faBalanceScaleRight, faBan, faBandAid, faBarcode, faBars, faBaseballBall, faBasketballBall, faBath, faBatteryEmpty, faBatteryFull, faBatteryHalf, faBatteryQuarter, faBatteryThreeQuarters, faBed, faBeer, faBell, faBellSlash, faBezierCurve, faBible, faBicycle, faBiking, faBinoculars, faBiohazard, faBirthdayCake, faBlender, faBlenderPhone, faBlind, faBlog, faBold, faBolt, faBomb, faBone, faBong, faBook, faBookDead, faBookMedical, faBookOpen, faBookReader, faBookmark, faBorderAll, faBorderNone, faBorderStyle, faBowlingBall, faBox, faBoxOpen, faBoxTissue, faBoxes, faBraille, faBrain, faBreadSlice, faBriefcase, faBriefcaseMedical, faBroadcastTower, faBroom, faBrush, faBug, faBuilding, faBullhorn, faBullseye, faBurn, faBus, faBusAlt, faBusinessTime, faCalculator, faCalendar, faCalendarAlt, faCalendarCheck, faCalendarDay, faCalendarMinus, faCalendarPlus, faCalendarTimes, faCalendarWeek, faCamera, faCameraRetro, faCampground, faCandyCane, faCannabis, faCapsules, faCar, faCarAlt, faCarBattery, faCarCrash, faCarSide, faCaravan, faCaretDown, faCaretLeft, faCaretRight, faCaretSquareDown, faCaretSquareLeft, faCaretSquareRight, faCaretSquareUp, faCaretUp, faCarrot, faCartArrowDown, faCartPlus, faCashRegister, faCat, faCertificate, faChair, faChalkboard, faChalkboardTeacher, faChargingStation, faChartArea, faChartBar, faChartLine, faChartPie, faCheck, faCheckCircle, faCheckDouble, faCheckSquare, faCheese, faChess, faChessBishop, faChessBoard, faChessKing, faChessKnight, faChessPawn, faChessQueen, faChessRook, faChevronCircleDown, faChevronCircleLeft, faChevronCircleRight, faChevronCircleUp, faChevronDown, faChevronLeft, faChevronRight, faChevronUp, faChild, faChurch, faCircle, faCircleNotch, faCity, faClinicMedical, faClipboard, faClipboardCheck, faClipboardList, faClock, faClone, faClosedCaptioning, faCloud, faCloudDownloadAlt, faCloudMeatball, faCloudMoon, faCloudMoonRain, faCloudRain, faCloudShowersHeavy, faCloudSun, faCloudSunRain, faCloudUploadAlt, faCocktail, faCode, faCodeBranch, faCoffee, faCog, faCogs, faCoins, faColumns, faComment, faCommentAlt, faCommentDollar, faCommentDots, faCommentMedical, faCommentSlash, faComments, faCommentsDollar, faCompactDisc, faCompass, faCompress, faCompressAlt, faCompressArrowsAlt, faConciergeBell, faCookie, faCookieBite, faCopy, faCopyright, faCouch, faCreditCard, faCrop, faCropAlt, faCross, faCrosshairs, faCrow, faCrown, faCrutch, faCube, faCubes, faCut, faDatabase, faDeaf, faDemocrat, faDesktop, faDharmachakra, faDiagnoses, faDice, faDiceD20, faDiceD6, faDiceFive, faDiceFour, faDiceOne, faDiceSix, faDiceThree, faDiceTwo, faDigitalTachograph, faDirections, faDisease, faDivide, faDizzy, faDna, faDog, faDollarSign, faDolly, faDollyFlatbed, faDonate, faDoorClosed, faDoorOpen, faDotCircle, faDove, faDownload, faDraftingCompass, faDragon, faDrawPolygon, faDrum, faDrumSteelpan, faDrumstickBite, faDumbbell, faDumpster, faDumpsterFire, faDungeon, faEdit, faEgg, faEject, faEllipsisH, faEllipsisV, faEnvelope, faEnvelopeOpen, faEnvelopeOpenText, faEnvelopeSquare, faEquals, faEraser, faEthernet, faEuroSign, faExchangeAlt, faExclamation, faExclamationCircle, faExclamationTriangle, faExpand, faExpandAlt, faExpandArrowsAlt, faExternalLinkAlt, faExternalLinkSquareAlt, faEye, faEyeDropper, faEyeSlash, faFan, faFastBackward, faFastForward, faFaucet, faFax, faFeather, faFeatherAlt, faFemale, faFighterJet, faFile, faFileAlt, faFileArchive, faFileAudio, faFileCode, faFileContract, faFileCsv, faFileDownload, faFileExcel, faFileExport, faFileImage, faFileImport, faFileInvoice, faFileInvoiceDollar, faFileMedical, faFileMedicalAlt, faFilePdf, faFilePowerpoint, faFilePrescription, faFileSignature, faFileUpload, faFileVideo, faFileWord, faFill, faFillDrip, faFilm, faFilter, faFingerprint, faFire, faFireAlt, faFireExtinguisher, faFirstAid, faFish, faFistRaised, faFlag, faFlagCheckered, faFlagUsa, faFlask, faFlushed, faFolder, faFolderMinus, faFolderOpen, faFolderPlus, faFont, faFontAwesomeLogoFull, faFootballBall, faForward, faFrog, faFrown, faFrownOpen, faFunnelDollar, faFutbol, faGamepad, faGasPump, faGavel, faGem, faGenderless, faGhost, faGift, faGifts, faGlassCheers, faGlassMartini, faGlassMartiniAlt, faGlassWhiskey, faGlasses, faGlobe, faGlobeAfrica, faGlobeAmericas, faGlobeAsia, faGlobeEurope, faGolfBall, faGopuram, faGraduationCap, faGreaterThan, faGreaterThanEqual, faGrimace, faGrin, faGrinAlt, faGrinBeam, faGrinBeamSweat, faGrinHearts, faGrinSquint, faGrinSquintTears, faGrinStars, faGrinTears, faGrinTongue, faGrinTongueSquint, faGrinTongueWink, faGrinWink, faGripHorizontal, faGripLines, faGripLinesVertical, faGripVertical, faGuitar, faHSquare, faHamburger, faHammer, faHamsa, faHandHolding, faHandHoldingHeart, faHandHoldingMedical, faHandHoldingUsd, faHandHoldingWater, faHandLizard, faHandMiddleFinger, faHandPaper, faHandPeace, faHandPointDown, faHandPointLeft, faHandPointRight, faHandPointUp, faHandPointer, faHandRock, faHandScissors, faHandSparkles, faHandSpock, faHands, faHandsHelping, faHandsWash, faHandshake, faHandshakeAltSlash, faHandshakeSlash, faHanukiah, faHardHat, faHashtag, faHatCowboy, faHatCowboySide, faHatWizard, faHdd, faHeadSideCough, faHeadSideCoughSlash, faHeadSideMask, faHeadSideVirus, faHeading, faHeadphones, faHeadphonesAlt, faHeadset, faHeart, faHeartBroken, faHeartbeat, faHelicopter, faHighlighter, faHiking, faHippo, faHistory, faHockeyPuck, faHollyBerry, faHome, faHorse, faHorseHead, faHospital, faHospitalAlt, faHospitalSymbol, faHospitalUser, faHotTub, faHotdog, faHotel, faHourglass, faHourglassEnd, faHourglassHalf, faHourglassStart, faHouseDamage, faHouseUser, faHryvnia, faICursor, faIceCream, faIcicles, faIcons, faIdBadge, faIdCard, faIdCardAlt, faIgloo, faImage, faImages, faInbox, faIndent, faIndustry, faInfinity, faInfo, faInfoCircle, faItalic, faJedi, faJoint, faJournalWhills, faKaaba, faKey, faKeyboard, faKhanda, faKiss, faKissBeam, faKissWinkHeart, faKiwiBird, faLandmark, faLanguage, faLaptop, faLaptopCode, faLaptopHouse, faLaptopMedical, faLaugh, faLaughBeam, faLaughSquint, faLaughWink, faLayerGroup, faLeaf, faLemon, faLessThan, faLessThanEqual, faLevelDownAlt, faLevelUpAlt, faLifeRing, faLightbulb, faLink, faLiraSign, faList, faListAlt, faListOl, faListUl, faLocationArrow, faLock, faLockOpen, faLongArrowAltDown, faLongArrowAltLeft, faLongArrowAltRight, faLongArrowAltUp, faLowVision, faLuggageCart, faLungs, faLungsVirus, faMagic, faMagnet, faMailBulk, faMale, faMap, faMapMarked, faMapMarkedAlt, faMapMarker, faMapMarkerAlt, faMapPin, faMapSigns, faMarker, faMars, faMarsDouble, faMarsStroke, faMarsStrokeH, faMarsStrokeV, faMask, faMedal, faMedkit, faMeh, faMehBlank, faMehRollingEyes, faMemory, faMenorah, faMercury, faMeteor, faMicrochip, faMicrophone, faMicrophoneAlt, faMicrophoneAltSlash, faMicrophoneSlash, faMicroscope, faMinus, faMinusCircle, faMinusSquare, faMitten, faMobile, faMobileAlt, faMoneyBill, faMoneyBillAlt, faMoneyBillWave, faMoneyBillWaveAlt, faMoneyCheck, faMoneyCheckAlt, faMonument, faMoon, faMortarPestle, faMosque, faMotorcycle, faMountain, faMouse, faMousePointer, faMugHot, faMusic, faNetworkWired, faNeuter, faNewspaper, faNotEqual, faNotesMedical, faObjectGroup, faObjectUngroup, faOilCan, faOm, faOtter, faOutdent, faPager, faPaintBrush, faPaintRoller, faPalette, faPallet, faPaperPlane, faPaperclip, faParachuteBox, faParagraph, faParking, faPassport, faPastafarianism, faPaste, faPause, faPauseCircle, faPaw, faPeace, faPen, faPenAlt, faPenFancy, faPenNib, faPenSquare, faPencilAlt, faPencilRuler, faPeopleArrows, faPeopleCarry, faPepperHot, faPercent, faPercentage, faPersonBooth, faPhone, faPhoneAlt, faPhoneSlash, faPhoneSquare, faPhoneSquareAlt, faPhoneVolume, faPhotoVideo, faPiggyBank, faPills, faPizzaSlice, faPlaceOfWorship, faPlane, faPlaneArrival, faPlaneDeparture, faPlaneSlash, faPlay, faPlayCircle, faPlug, faPlus, faPlusCircle, faPlusSquare, faPodcast, faPoll, faPollH, faPoo, faPooStorm, faPoop, faPortrait, faPoundSign, faPowerOff, faPray, faPrayingHands, faPrescription, faPrescriptionBottle, faPrescriptionBottleAlt, faPrint, faProcedures, faProjectDiagram, faPumpMedical, faPumpSoap, faPuzzlePiece, faQrcode, faQuestion, faQuestionCircle, faQuidditch, faQuoteLeft, faQuoteRight, faQuran, faRadiation, faRadiationAlt, faRainbow, faRandom, faReceipt, faRecordVinyl, faRecycle, faRedo, faRedoAlt, faRegistered, faRemoveFormat, faReply, faReplyAll, faRepublican, faRestroom, faRetweet, faRibbon, faRing, faRoad, faRobot, faRocket, faRoute, faRss, faRssSquare, faRubleSign, faRuler, faRulerCombined, faRulerHorizontal, faRulerVertical, faRunning, faRupeeSign, faSadCry, faSadTear, faSatellite, faSatelliteDish, faSave, faSchool, faScrewdriver, faScroll, faSdCard, faSearch, faSearchDollar, faSearchLocation, faSearchMinus, faSearchPlus, faSeedling, faServer, faShapes, faShare, faShareAlt, faShareAltSquare, faShareSquare, faShekelSign, faShieldAlt, faShieldVirus, faShip, faShippingFast, faShoePrints, faShoppingBag, faShoppingBasket, faShoppingCart, faShower, faShuttleVan, faSign, faSignInAlt, faSignLanguage, faSignOutAlt, faSignal, faSignature, faSimCard, faSitemap, faSkating, faSkiing, faSkiingNordic, faSkull, faSkullCrossbones, faSlash, faSleigh, faSlidersH, faSmile, faSmileBeam, faSmileWink, faSmog, faSmoking, faSmokingBan, faSms, faSnowboarding, faSnowflake, faSnowman, faSnowplow, faSoap, faSocks, faSolarPanel, faSort, faSortAlphaDown, faSortAlphaDownAlt, faSortAlphaUp, faSortAlphaUpAlt, faSortAmountDown, faSortAmountDownAlt, faSortAmountUp, faSortAmountUpAlt, faSortDown, faSortNumericDown, faSortNumericDownAlt, faSortNumericUp, faSortNumericUpAlt, faSortUp, faSpa, faSpaceShuttle, faSpellCheck, faSpider, faSpinner, faSplotch, faSprayCan, faSquare, faSquareFull, faSquareRootAlt, faStamp, faStar, faStarAndCrescent, faStarHalf, faStarHalfAlt, faStarOfDavid, faStarOfLife, faStepBackward, faStepForward, faStethoscope, faStickyNote, faStop, faStopCircle, faStopwatch, faStopwatch20, faStore, faStoreAlt, faStoreAltSlash, faStoreSlash, faStream, faStreetView, faStrikethrough, faStroopwafel, faSubscript, faSubway, faSuitcase, faSuitcaseRolling, faSun, faSuperscript, faSurprise, faSwatchbook, faSwimmer, faSwimmingPool, faSynagogue, faSync, faSyncAlt, faSyringe, faTable, faTableTennis, faTablet, faTabletAlt, faTablets, faTachometerAlt, faTag, faTags, faTape, faTasks, faTaxi, faTeeth, faTeethOpen, faTemperatureHigh, faTemperatureLow, faTenge, faTerminal, faTextHeight, faTextWidth, faTh, faThLarge, faThList, faTheaterMasks, faThermometer, faThermometerEmpty, faThermometerFull, faThermometerHalf, faThermometerQuarter, faThermometerThreeQuarters, faThumbsDown, faThumbsUp, faThumbtack, faTicketAlt, faTimes, faTimesCircle, faTint, faTintSlash, faTired, faToggleOff, faToggleOn, faToilet, faToiletPaper, faToiletPaperSlash, faToolbox, faTools, faTooth, faTorah, faToriiGate, faTractor, faTrademark, faTrafficLight, faTrailer, faTrain, faTram, faTransgender, faTransgenderAlt, faTrash, faTrashAlt, faTrashRestore, faTrashRestoreAlt, faTree, faTrophy, faTruck, faTruckLoading, faTruckMonster, faTruckMoving, faTruckPickup, faTshirt, faTty, faTv, faUmbrella, faUmbrellaBeach, faUnderline, faUndo, faUndoAlt, faUniversalAccess, faUniversity, faUnlink, faUnlock, faUnlockAlt, faUpload, faUser, faUserAlt, faUserAltSlash, faUserAstronaut, faUserCheck, faUserCircle, faUserClock, faUserCog, faUserEdit, faUserFriends, faUserGraduate, faUserInjured, faUserLock, faUserMd, faUserMinus, faUserNinja, faUserNurse, faUserPlus, faUserSecret, faUserShield, faUserSlash, faUserTag, faUserTie, faUserTimes, faUsers, faUsersCog, faUtensilSpoon, faUtensils, faVectorSquare, faVenus, faVenusDouble, faVenusMars, faVial, faVials, faVideo, faVideoSlash, faVihara, faVirus, faVirusSlash, faViruses, faVoicemail, faVolleyballBall, faVolumeDown, faVolumeMute, faVolumeOff, faVolumeUp, faVoteYea, faVrCardboard, faWalking, faWallet, faWarehouse, faWater, faWaveSquare, faWeight, faWeightHanging, faWheelchair, faWifi, faWind, faWindowClose, faWindowMaximize, faWindowMinimize, faWindowRestore, faWineBottle, faWineGlass, faWineGlassAlt, faWonSign, faWrench, faXRay, faYenSign, faYinYang };\n","function _typeof(obj) {\n  if (typeof Symbol === \"function\" && typeof Symbol.iterator === \"symbol\") {\n    _typeof = function (obj) {\n      return typeof obj;\n    };\n  } else {\n    _typeof = function (obj) {\n      return obj && typeof Symbol === \"function\" && obj.constructor === Symbol && obj !== Symbol.prototype ? \"symbol\" : typeof obj;\n    };\n  }\n\n  return _typeof(obj);\n}\n\nfunction _classCallCheck(instance, Constructor) {\n  if (!(instance instanceof Constructor)) {\n    throw new TypeError(\"Cannot call a class as a function\");\n  }\n}\n\nfunction _defineProperties(target, props) {\n  for (var i = 0; i < props.length; i++) {\n    var descriptor = props[i];\n    descriptor.enumerable = descriptor.enumerable || false;\n    descriptor.configurable = true;\n    if (\"value\" in descriptor) descriptor.writable = true;\n    Object.defineProperty(target, descriptor.key, descriptor);\n  }\n}\n\nfunction _createClass(Constructor, protoProps, staticProps) {\n  if (protoProps) _defineProperties(Constructor.prototype, protoProps);\n  if (staticProps) _defineProperties(Constructor, staticProps);\n  return Constructor;\n}\n\nfunction _defineProperty(obj, key, value) {\n  if (key in obj) {\n    Object.defineProperty(obj, key, {\n      value: value,\n      enumerable: true,\n      configurable: true,\n      writable: true\n    });\n  } else {\n    obj[key] = value;\n  }\n\n  return obj;\n}\n\nfunction _objectSpread(target) {\n  for (var i = 1; i < arguments.length; i++) {\n    var source = arguments[i] != null ? arguments[i] : {};\n    var ownKeys = Object.keys(source);\n\n    if (typeof Object.getOwnPropertySymbols === 'function') {\n      ownKeys = ownKeys.concat(Object.getOwnPropertySymbols(source).filter(function (sym) {\n        return Object.getOwnPropertyDescriptor(source, sym).enumerable;\n      }));\n    }\n\n    ownKeys.forEach(function (key) {\n      _defineProperty(target, key, source[key]);\n    });\n  }\n\n  return target;\n}\n\nfunction _slicedToArray(arr, i) {\n  return _arrayWithHoles(arr) || _iterableToArrayLimit(arr, i) || _nonIterableRest();\n}\n\nfunction _toConsumableArray(arr) {\n  return _arrayWithoutHoles(arr) || _iterableToArray(arr) || _nonIterableSpread();\n}\n\nfunction _arrayWithoutHoles(arr) {\n  if (Array.isArray(arr)) {\n    for (var i = 0, arr2 = new Array(arr.length); i < arr.length; i++) arr2[i] = arr[i];\n\n    return arr2;\n  }\n}\n\nfunction _arrayWithHoles(arr) {\n  if (Array.isArray(arr)) return arr;\n}\n\nfunction _iterableToArray(iter) {\n  if (Symbol.iterator in Object(iter) || Object.prototype.toString.call(iter) === \"[object Arguments]\") return Array.from(iter);\n}\n\nfunction _iterableToArrayLimit(arr, i) {\n  var _arr = [];\n  var _n = true;\n  var _d = false;\n  var _e = undefined;\n\n  try {\n    for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) {\n      _arr.push(_s.value);\n\n      if (i && _arr.length === i) break;\n    }\n  } catch (err) {\n    _d = true;\n    _e = err;\n  } finally {\n    try {\n      if (!_n && _i[\"return\"] != null) _i[\"return\"]();\n    } finally {\n      if (_d) throw _e;\n    }\n  }\n\n  return _arr;\n}\n\nfunction _nonIterableSpread() {\n  throw new TypeError(\"Invalid attempt to spread non-iterable instance\");\n}\n\nfunction _nonIterableRest() {\n  throw new TypeError(\"Invalid attempt to destructure non-iterable instance\");\n}\n\nvar noop = function noop() {};\n\nvar _WINDOW = {};\nvar _DOCUMENT = {};\nvar _MUTATION_OBSERVER = null;\nvar _PERFORMANCE = {\n  mark: noop,\n  measure: noop\n};\n\ntry {\n  if (typeof window !== 'undefined') _WINDOW = window;\n  if (typeof document !== 'undefined') _DOCUMENT = document;\n  if (typeof MutationObserver !== 'undefined') _MUTATION_OBSERVER = MutationObserver;\n  if (typeof performance !== 'undefined') _PERFORMANCE = performance;\n} catch (e) {}\n\nvar _ref = _WINDOW.navigator || {},\n    _ref$userAgent = _ref.userAgent,\n    userAgent = _ref$userAgent === void 0 ? '' : _ref$userAgent;\n\nvar WINDOW = _WINDOW;\nvar DOCUMENT = _DOCUMENT;\nvar MUTATION_OBSERVER = _MUTATION_OBSERVER;\nvar PERFORMANCE = _PERFORMANCE;\nvar IS_BROWSER = !!WINDOW.document;\nvar IS_DOM = !!DOCUMENT.documentElement && !!DOCUMENT.head && typeof DOCUMENT.addEventListener === 'function' && typeof DOCUMENT.createElement === 'function';\nvar IS_IE = ~userAgent.indexOf('MSIE') || ~userAgent.indexOf('Trident/');\n\nvar NAMESPACE_IDENTIFIER = '___FONT_AWESOME___';\nvar UNITS_IN_GRID = 16;\nvar DEFAULT_FAMILY_PREFIX = 'fa';\nvar DEFAULT_REPLACEMENT_CLASS = 'svg-inline--fa';\nvar DATA_FA_I2SVG = 'data-fa-i2svg';\nvar DATA_FA_PSEUDO_ELEMENT = 'data-fa-pseudo-element';\nvar DATA_FA_PSEUDO_ELEMENT_PENDING = 'data-fa-pseudo-element-pending';\nvar DATA_PREFIX = 'data-prefix';\nvar DATA_ICON = 'data-icon';\nvar HTML_CLASS_I2SVG_BASE_CLASS = 'fontawesome-i2svg';\nvar MUTATION_APPROACH_ASYNC = 'async';\nvar TAGNAMES_TO_SKIP_FOR_PSEUDOELEMENTS = ['HTML', 'HEAD', 'STYLE', 'SCRIPT'];\nvar PRODUCTION = function () {\n  try {\n    return process.env.NODE_ENV === 'production';\n  } catch (e) {\n    return false;\n  }\n}();\nvar PREFIX_TO_STYLE = {\n  'fas': 'solid',\n  'far': 'regular',\n  'fal': 'light',\n  'fad': 'duotone',\n  'fab': 'brands',\n  'fa': 'solid'\n};\nvar STYLE_TO_PREFIX = {\n  'solid': 'fas',\n  'regular': 'far',\n  'light': 'fal',\n  'duotone': 'fad',\n  'brands': 'fab'\n};\nvar LAYERS_TEXT_CLASSNAME = 'fa-layers-text';\nvar FONT_FAMILY_PATTERN = /Font Awesome 5 (Solid|Regular|Light|Duotone|Brands|Free|Pro)/;\nvar FONT_WEIGHT_TO_PREFIX = {\n  '900': 'fas',\n  '400': 'far',\n  'normal': 'far',\n  '300': 'fal'\n};\nvar oneToTen = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];\nvar oneToTwenty = oneToTen.concat([11, 12, 13, 14, 15, 16, 17, 18, 19, 20]);\nvar ATTRIBUTES_WATCHED_FOR_MUTATION = ['class', 'data-prefix', 'data-icon', 'data-fa-transform', 'data-fa-mask'];\nvar DUOTONE_CLASSES = {\n  GROUP: 'group',\n  SWAP_OPACITY: 'swap-opacity',\n  PRIMARY: 'primary',\n  SECONDARY: 'secondary'\n};\nvar RESERVED_CLASSES = ['xs', 'sm', 'lg', 'fw', 'ul', 'li', 'border', 'pull-left', 'pull-right', 'spin', 'pulse', 'rotate-90', 'rotate-180', 'rotate-270', 'flip-horizontal', 'flip-vertical', 'flip-both', 'stack', 'stack-1x', 'stack-2x', 'inverse', 'layers', 'layers-text', 'layers-counter', DUOTONE_CLASSES.GROUP, DUOTONE_CLASSES.SWAP_OPACITY, DUOTONE_CLASSES.PRIMARY, DUOTONE_CLASSES.SECONDARY].concat(oneToTen.map(function (n) {\n  return \"\".concat(n, \"x\");\n})).concat(oneToTwenty.map(function (n) {\n  return \"w-\".concat(n);\n}));\n\nvar initial = WINDOW.FontAwesomeConfig || {};\n\nfunction getAttrConfig(attr) {\n  var element = DOCUMENT.querySelector('script[' + attr + ']');\n\n  if (element) {\n    return element.getAttribute(attr);\n  }\n}\n\nfunction coerce(val) {\n  // Getting an empty string will occur if the attribute is set on the HTML tag but without a value\n  // We'll assume that this is an indication that it should be toggled to true\n  // For example \n  if (val === '') return true;\n  if (val === 'false') return false;\n  if (val === 'true') return true;\n  return val;\n}\n\nif (DOCUMENT && typeof DOCUMENT.querySelector === 'function') {\n  var attrs = [['data-family-prefix', 'familyPrefix'], ['data-replacement-class', 'replacementClass'], ['data-auto-replace-svg', 'autoReplaceSvg'], ['data-auto-add-css', 'autoAddCss'], ['data-auto-a11y', 'autoA11y'], ['data-search-pseudo-elements', 'searchPseudoElements'], ['data-observe-mutations', 'observeMutations'], ['data-mutate-approach', 'mutateApproach'], ['data-keep-original-source', 'keepOriginalSource'], ['data-measure-performance', 'measurePerformance'], ['data-show-missing-icons', 'showMissingIcons']];\n  attrs.forEach(function (_ref) {\n    var _ref2 = _slicedToArray(_ref, 2),\n        attr = _ref2[0],\n        key = _ref2[1];\n\n    var val = coerce(getAttrConfig(attr));\n\n    if (val !== undefined && val !== null) {\n      initial[key] = val;\n    }\n  });\n}\n\nvar _default = {\n  familyPrefix: DEFAULT_FAMILY_PREFIX,\n  replacementClass: DEFAULT_REPLACEMENT_CLASS,\n  autoReplaceSvg: true,\n  autoAddCss: true,\n  autoA11y: true,\n  searchPseudoElements: false,\n  observeMutations: true,\n  mutateApproach: 'async',\n  keepOriginalSource: true,\n  measurePerformance: false,\n  showMissingIcons: true\n};\n\nvar _config = _objectSpread({}, _default, initial);\n\nif (!_config.autoReplaceSvg) _config.observeMutations = false;\n\nvar config = _objectSpread({}, _config);\n\nWINDOW.FontAwesomeConfig = config;\n\nvar w = WINDOW || {};\nif (!w[NAMESPACE_IDENTIFIER]) w[NAMESPACE_IDENTIFIER] = {};\nif (!w[NAMESPACE_IDENTIFIER].styles) w[NAMESPACE_IDENTIFIER].styles = {};\nif (!w[NAMESPACE_IDENTIFIER].hooks) w[NAMESPACE_IDENTIFIER].hooks = {};\nif (!w[NAMESPACE_IDENTIFIER].shims) w[NAMESPACE_IDENTIFIER].shims = [];\nvar namespace = w[NAMESPACE_IDENTIFIER];\n\nvar functions = [];\n\nvar listener = function listener() {\n  DOCUMENT.removeEventListener('DOMContentLoaded', listener);\n  loaded = 1;\n  functions.map(function (fn) {\n    return fn();\n  });\n};\n\nvar loaded = false;\n\nif (IS_DOM) {\n  loaded = (DOCUMENT.documentElement.doScroll ? /^loaded|^c/ : /^loaded|^i|^c/).test(DOCUMENT.readyState);\n  if (!loaded) DOCUMENT.addEventListener('DOMContentLoaded', listener);\n}\n\nfunction domready (fn) {\n  if (!IS_DOM) return;\n  loaded ? setTimeout(fn, 0) : functions.push(fn);\n}\n\nvar PENDING = 'pending';\nvar SETTLED = 'settled';\nvar FULFILLED = 'fulfilled';\nvar REJECTED = 'rejected';\n\nvar NOOP = function NOOP() {};\n\nvar isNode = typeof global !== 'undefined' && typeof global.process !== 'undefined' && typeof global.process.emit === 'function';\nvar asyncSetTimer = typeof setImmediate === 'undefined' ? setTimeout : setImmediate;\nvar asyncQueue = [];\nvar asyncTimer;\n\nfunction asyncFlush() {\n  // run promise callbacks\n  for (var i = 0; i < asyncQueue.length; i++) {\n    asyncQueue[i][0](asyncQueue[i][1]);\n  } // reset async asyncQueue\n\n\n  asyncQueue = [];\n  asyncTimer = false;\n}\n\nfunction asyncCall(callback, arg) {\n  asyncQueue.push([callback, arg]);\n\n  if (!asyncTimer) {\n    asyncTimer = true;\n    asyncSetTimer(asyncFlush, 0);\n  }\n}\n\nfunction invokeResolver(resolver, promise) {\n  function resolvePromise(value) {\n    resolve(promise, value);\n  }\n\n  function rejectPromise(reason) {\n    reject(promise, reason);\n  }\n\n  try {\n    resolver(resolvePromise, rejectPromise);\n  } catch (e) {\n    rejectPromise(e);\n  }\n}\n\nfunction invokeCallback(subscriber) {\n  var owner = subscriber.owner;\n  var settled = owner._state;\n  var value = owner._data;\n  var callback = subscriber[settled];\n  var promise = subscriber.then;\n\n  if (typeof callback === 'function') {\n    settled = FULFILLED;\n\n    try {\n      value = callback(value);\n    } catch (e) {\n      reject(promise, e);\n    }\n  }\n\n  if (!handleThenable(promise, value)) {\n    if (settled === FULFILLED) {\n      resolve(promise, value);\n    }\n\n    if (settled === REJECTED) {\n      reject(promise, value);\n    }\n  }\n}\n\nfunction handleThenable(promise, value) {\n  var resolved;\n\n  try {\n    if (promise === value) {\n      throw new TypeError('A promises callback cannot return that same promise.');\n    }\n\n    if (value && (typeof value === 'function' || _typeof(value) === 'object')) {\n      // then should be retrieved only once\n      var then = value.then;\n\n      if (typeof then === 'function') {\n        then.call(value, function (val) {\n          if (!resolved) {\n            resolved = true;\n\n            if (value === val) {\n              fulfill(promise, val);\n            } else {\n              resolve(promise, val);\n            }\n          }\n        }, function (reason) {\n          if (!resolved) {\n            resolved = true;\n            reject(promise, reason);\n          }\n        });\n        return true;\n      }\n    }\n  } catch (e) {\n    if (!resolved) {\n      reject(promise, e);\n    }\n\n    return true;\n  }\n\n  return false;\n}\n\nfunction resolve(promise, value) {\n  if (promise === value || !handleThenable(promise, value)) {\n    fulfill(promise, value);\n  }\n}\n\nfunction fulfill(promise, value) {\n  if (promise._state === PENDING) {\n    promise._state = SETTLED;\n    promise._data = value;\n    asyncCall(publishFulfillment, promise);\n  }\n}\n\nfunction reject(promise, reason) {\n  if (promise._state === PENDING) {\n    promise._state = SETTLED;\n    promise._data = reason;\n    asyncCall(publishRejection, promise);\n  }\n}\n\nfunction publish(promise) {\n  promise._then = promise._then.forEach(invokeCallback);\n}\n\nfunction publishFulfillment(promise) {\n  promise._state = FULFILLED;\n  publish(promise);\n}\n\nfunction publishRejection(promise) {\n  promise._state = REJECTED;\n  publish(promise);\n\n  if (!promise._handled && isNode) {\n    global.process.emit('unhandledRejection', promise._data, promise);\n  }\n}\n\nfunction notifyRejectionHandled(promise) {\n  global.process.emit('rejectionHandled', promise);\n}\n/**\n * @class\n */\n\n\nfunction P(resolver) {\n  if (typeof resolver !== 'function') {\n    throw new TypeError('Promise resolver ' + resolver + ' is not a function');\n  }\n\n  if (this instanceof P === false) {\n    throw new TypeError('Failed to construct \\'Promise\\': Please use the \\'new\\' operator, this object constructor cannot be called as a function.');\n  }\n\n  this._then = [];\n  invokeResolver(resolver, this);\n}\n\nP.prototype = {\n  constructor: P,\n  _state: PENDING,\n  _then: null,\n  _data: undefined,\n  _handled: false,\n  then: function then(onFulfillment, onRejection) {\n    var subscriber = {\n      owner: this,\n      then: new this.constructor(NOOP),\n      fulfilled: onFulfillment,\n      rejected: onRejection\n    };\n\n    if ((onRejection || onFulfillment) && !this._handled) {\n      this._handled = true;\n\n      if (this._state === REJECTED && isNode) {\n        asyncCall(notifyRejectionHandled, this);\n      }\n    }\n\n    if (this._state === FULFILLED || this._state === REJECTED) {\n      // already resolved, call callback async\n      asyncCall(invokeCallback, subscriber);\n    } else {\n      // subscribe\n      this._then.push(subscriber);\n    }\n\n    return subscriber.then;\n  },\n  catch: function _catch(onRejection) {\n    return this.then(null, onRejection);\n  }\n};\n\nP.all = function (promises) {\n  if (!Array.isArray(promises)) {\n    throw new TypeError('You must pass an array to Promise.all().');\n  }\n\n  return new P(function (resolve, reject) {\n    var results = [];\n    var remaining = 0;\n\n    function resolver(index) {\n      remaining++;\n      return function (value) {\n        results[index] = value;\n\n        if (! --remaining) {\n          resolve(results);\n        }\n      };\n    }\n\n    for (var i = 0, promise; i < promises.length; i++) {\n      promise = promises[i];\n\n      if (promise && typeof promise.then === 'function') {\n        promise.then(resolver(i), reject);\n      } else {\n        results[i] = promise;\n      }\n    }\n\n    if (!remaining) {\n      resolve(results);\n    }\n  });\n};\n\nP.race = function (promises) {\n  if (!Array.isArray(promises)) {\n    throw new TypeError('You must pass an array to Promise.race().');\n  }\n\n  return new P(function (resolve, reject) {\n    for (var i = 0, promise; i < promises.length; i++) {\n      promise = promises[i];\n\n      if (promise && typeof promise.then === 'function') {\n        promise.then(resolve, reject);\n      } else {\n        resolve(promise);\n      }\n    }\n  });\n};\n\nP.resolve = function (value) {\n  if (value && _typeof(value) === 'object' && value.constructor === P) {\n    return value;\n  }\n\n  return new P(function (resolve) {\n    resolve(value);\n  });\n};\n\nP.reject = function (reason) {\n  return new P(function (resolve, reject) {\n    reject(reason);\n  });\n};\n\nvar picked = typeof Promise === 'function' ? Promise : P;\n\nvar d = UNITS_IN_GRID;\nvar meaninglessTransform = {\n  size: 16,\n  x: 0,\n  y: 0,\n  rotate: 0,\n  flipX: false,\n  flipY: false\n};\n\nfunction isReserved(name) {\n  return ~RESERVED_CLASSES.indexOf(name);\n}\nfunction insertCss(css) {\n  if (!css || !IS_DOM) {\n    return;\n  }\n\n  var style = DOCUMENT.createElement('style');\n  style.setAttribute('type', 'text/css');\n  style.innerHTML = css;\n  var headChildren = DOCUMENT.head.childNodes;\n  var beforeChild = null;\n\n  for (var i = headChildren.length - 1; i > -1; i--) {\n    var child = headChildren[i];\n    var tagName = (child.tagName || '').toUpperCase();\n\n    if (['STYLE', 'LINK'].indexOf(tagName) > -1) {\n      beforeChild = child;\n    }\n  }\n\n  DOCUMENT.head.insertBefore(style, beforeChild);\n  return css;\n}\nvar idPool = '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ';\nfunction nextUniqueId() {\n  var size = 12;\n  var id = '';\n\n  while (size-- > 0) {\n    id += idPool[Math.random() * 62 | 0];\n  }\n\n  return id;\n}\nfunction toArray(obj) {\n  var array = [];\n\n  for (var i = (obj || []).length >>> 0; i--;) {\n    array[i] = obj[i];\n  }\n\n  return array;\n}\nfunction classArray(node) {\n  if (node.classList) {\n    return toArray(node.classList);\n  } else {\n    return (node.getAttribute('class') || '').split(' ').filter(function (i) {\n      return i;\n    });\n  }\n}\nfunction getIconName(familyPrefix, cls) {\n  var parts = cls.split('-');\n  var prefix = parts[0];\n  var iconName = parts.slice(1).join('-');\n\n  if (prefix === familyPrefix && iconName !== '' && !isReserved(iconName)) {\n    return iconName;\n  } else {\n    return null;\n  }\n}\nfunction htmlEscape(str) {\n  return \"\".concat(str).replace(/&/g, '&').replace(/\"/g, '"').replace(/'/g, ''').replace(//g, '>');\n}\nfunction joinAttributes(attributes) {\n  return Object.keys(attributes || {}).reduce(function (acc, attributeName) {\n    return acc + \"\".concat(attributeName, \"=\\\"\").concat(htmlEscape(attributes[attributeName]), \"\\\" \");\n  }, '').trim();\n}\nfunction joinStyles(styles) {\n  return Object.keys(styles || {}).reduce(function (acc, styleName) {\n    return acc + \"\".concat(styleName, \": \").concat(styles[styleName], \";\");\n  }, '');\n}\nfunction transformIsMeaningful(transform) {\n  return transform.size !== meaninglessTransform.size || transform.x !== meaninglessTransform.x || transform.y !== meaninglessTransform.y || transform.rotate !== meaninglessTransform.rotate || transform.flipX || transform.flipY;\n}\nfunction transformForSvg(_ref) {\n  var transform = _ref.transform,\n      containerWidth = _ref.containerWidth,\n      iconWidth = _ref.iconWidth;\n  var outer = {\n    transform: \"translate(\".concat(containerWidth / 2, \" 256)\")\n  };\n  var innerTranslate = \"translate(\".concat(transform.x * 32, \", \").concat(transform.y * 32, \") \");\n  var innerScale = \"scale(\".concat(transform.size / 16 * (transform.flipX ? -1 : 1), \", \").concat(transform.size / 16 * (transform.flipY ? -1 : 1), \") \");\n  var innerRotate = \"rotate(\".concat(transform.rotate, \" 0 0)\");\n  var inner = {\n    transform: \"\".concat(innerTranslate, \" \").concat(innerScale, \" \").concat(innerRotate)\n  };\n  var path = {\n    transform: \"translate(\".concat(iconWidth / 2 * -1, \" -256)\")\n  };\n  return {\n    outer: outer,\n    inner: inner,\n    path: path\n  };\n}\nfunction transformForCss(_ref2) {\n  var transform = _ref2.transform,\n      _ref2$width = _ref2.width,\n      width = _ref2$width === void 0 ? UNITS_IN_GRID : _ref2$width,\n      _ref2$height = _ref2.height,\n      height = _ref2$height === void 0 ? UNITS_IN_GRID : _ref2$height,\n      _ref2$startCentered = _ref2.startCentered,\n      startCentered = _ref2$startCentered === void 0 ? false : _ref2$startCentered;\n  var val = '';\n\n  if (startCentered && IS_IE) {\n    val += \"translate(\".concat(transform.x / d - width / 2, \"em, \").concat(transform.y / d - height / 2, \"em) \");\n  } else if (startCentered) {\n    val += \"translate(calc(-50% + \".concat(transform.x / d, \"em), calc(-50% + \").concat(transform.y / d, \"em)) \");\n  } else {\n    val += \"translate(\".concat(transform.x / d, \"em, \").concat(transform.y / d, \"em) \");\n  }\n\n  val += \"scale(\".concat(transform.size / d * (transform.flipX ? -1 : 1), \", \").concat(transform.size / d * (transform.flipY ? -1 : 1), \") \");\n  val += \"rotate(\".concat(transform.rotate, \"deg) \");\n  return val;\n}\n\nvar ALL_SPACE = {\n  x: 0,\n  y: 0,\n  width: '100%',\n  height: '100%'\n};\n\nfunction fillBlack(abstract) {\n  var force = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : true;\n\n  if (abstract.attributes && (abstract.attributes.fill || force)) {\n    abstract.attributes.fill = 'black';\n  }\n\n  return abstract;\n}\n\nfunction deGroup(abstract) {\n  if (abstract.tag === 'g') {\n    return abstract.children;\n  } else {\n    return [abstract];\n  }\n}\n\nfunction makeIconMasking (_ref) {\n  var children = _ref.children,\n      attributes = _ref.attributes,\n      main = _ref.main,\n      mask = _ref.mask,\n      explicitMaskId = _ref.maskId,\n      transform = _ref.transform;\n  var mainWidth = main.width,\n      mainPath = main.icon;\n  var maskWidth = mask.width,\n      maskPath = mask.icon;\n  var trans = transformForSvg({\n    transform: transform,\n    containerWidth: maskWidth,\n    iconWidth: mainWidth\n  });\n  var maskRect = {\n    tag: 'rect',\n    attributes: _objectSpread({}, ALL_SPACE, {\n      fill: 'white'\n    })\n  };\n  var maskInnerGroupChildrenMixin = mainPath.children ? {\n    children: mainPath.children.map(fillBlack)\n  } : {};\n  var maskInnerGroup = {\n    tag: 'g',\n    attributes: _objectSpread({}, trans.inner),\n    children: [fillBlack(_objectSpread({\n      tag: mainPath.tag,\n      attributes: _objectSpread({}, mainPath.attributes, trans.path)\n    }, maskInnerGroupChildrenMixin))]\n  };\n  var maskOuterGroup = {\n    tag: 'g',\n    attributes: _objectSpread({}, trans.outer),\n    children: [maskInnerGroup]\n  };\n  var maskId = \"mask-\".concat(explicitMaskId || nextUniqueId());\n  var clipId = \"clip-\".concat(explicitMaskId || nextUniqueId());\n  var maskTag = {\n    tag: 'mask',\n    attributes: _objectSpread({}, ALL_SPACE, {\n      id: maskId,\n      maskUnits: 'userSpaceOnUse',\n      maskContentUnits: 'userSpaceOnUse'\n    }),\n    children: [maskRect, maskOuterGroup]\n  };\n  var defs = {\n    tag: 'defs',\n    children: [{\n      tag: 'clipPath',\n      attributes: {\n        id: clipId\n      },\n      children: deGroup(maskPath)\n    }, maskTag]\n  };\n  children.push(defs, {\n    tag: 'rect',\n    attributes: _objectSpread({\n      fill: 'currentColor',\n      'clip-path': \"url(#\".concat(clipId, \")\"),\n      mask: \"url(#\".concat(maskId, \")\")\n    }, ALL_SPACE)\n  });\n  return {\n    children: children,\n    attributes: attributes\n  };\n}\n\nfunction makeIconStandard (_ref) {\n  var children = _ref.children,\n      attributes = _ref.attributes,\n      main = _ref.main,\n      transform = _ref.transform,\n      styles = _ref.styles;\n  var styleString = joinStyles(styles);\n\n  if (styleString.length > 0) {\n    attributes['style'] = styleString;\n  }\n\n  if (transformIsMeaningful(transform)) {\n    var trans = transformForSvg({\n      transform: transform,\n      containerWidth: main.width,\n      iconWidth: main.width\n    });\n    children.push({\n      tag: 'g',\n      attributes: _objectSpread({}, trans.outer),\n      children: [{\n        tag: 'g',\n        attributes: _objectSpread({}, trans.inner),\n        children: [{\n          tag: main.icon.tag,\n          children: main.icon.children,\n          attributes: _objectSpread({}, main.icon.attributes, trans.path)\n        }]\n      }]\n    });\n  } else {\n    children.push(main.icon);\n  }\n\n  return {\n    children: children,\n    attributes: attributes\n  };\n}\n\nfunction asIcon (_ref) {\n  var children = _ref.children,\n      main = _ref.main,\n      mask = _ref.mask,\n      attributes = _ref.attributes,\n      styles = _ref.styles,\n      transform = _ref.transform;\n\n  if (transformIsMeaningful(transform) && main.found && !mask.found) {\n    var width = main.width,\n        height = main.height;\n    var offset = {\n      x: width / height / 2,\n      y: 0.5\n    };\n    attributes['style'] = joinStyles(_objectSpread({}, styles, {\n      'transform-origin': \"\".concat(offset.x + transform.x / 16, \"em \").concat(offset.y + transform.y / 16, \"em\")\n    }));\n  }\n\n  return [{\n    tag: 'svg',\n    attributes: attributes,\n    children: children\n  }];\n}\n\nfunction asSymbol (_ref) {\n  var prefix = _ref.prefix,\n      iconName = _ref.iconName,\n      children = _ref.children,\n      attributes = _ref.attributes,\n      symbol = _ref.symbol;\n  var id = symbol === true ? \"\".concat(prefix, \"-\").concat(config.familyPrefix, \"-\").concat(iconName) : symbol;\n  return [{\n    tag: 'svg',\n    attributes: {\n      style: 'display: none;'\n    },\n    children: [{\n      tag: 'symbol',\n      attributes: _objectSpread({}, attributes, {\n        id: id\n      }),\n      children: children\n    }]\n  }];\n}\n\nfunction makeInlineSvgAbstract(params) {\n  var _params$icons = params.icons,\n      main = _params$icons.main,\n      mask = _params$icons.mask,\n      prefix = params.prefix,\n      iconName = params.iconName,\n      transform = params.transform,\n      symbol = params.symbol,\n      title = params.title,\n      maskId = params.maskId,\n      titleId = params.titleId,\n      extra = params.extra,\n      _params$watchable = params.watchable,\n      watchable = _params$watchable === void 0 ? false : _params$watchable;\n\n  var _ref = mask.found ? mask : main,\n      width = _ref.width,\n      height = _ref.height;\n\n  var widthClass = \"fa-w-\".concat(Math.ceil(width / height * 16));\n  var attrClass = [config.replacementClass, iconName ? \"\".concat(config.familyPrefix, \"-\").concat(iconName) : '', widthClass].filter(function (c) {\n    return extra.classes.indexOf(c) === -1;\n  }).concat(extra.classes).join(' ');\n  var content = {\n    children: [],\n    attributes: _objectSpread({}, extra.attributes, {\n      'data-prefix': prefix,\n      'data-icon': iconName,\n      'class': attrClass,\n      'role': extra.attributes.role || 'img',\n      'xmlns': 'http://www.w3.org/2000/svg',\n      'viewBox': \"0 0 \".concat(width, \" \").concat(height)\n    })\n  };\n\n  if (watchable) {\n    content.attributes[DATA_FA_I2SVG] = '';\n  }\n\n  if (title) content.children.push({\n    tag: 'title',\n    attributes: {\n      id: content.attributes['aria-labelledby'] || \"title-\".concat(titleId || nextUniqueId())\n    },\n    children: [title]\n  });\n\n  var args = _objectSpread({}, content, {\n    prefix: prefix,\n    iconName: iconName,\n    main: main,\n    mask: mask,\n    maskId: maskId,\n    transform: transform,\n    symbol: symbol,\n    styles: extra.styles\n  });\n\n  var _ref2 = mask.found && main.found ? makeIconMasking(args) : makeIconStandard(args),\n      children = _ref2.children,\n      attributes = _ref2.attributes;\n\n  args.children = children;\n  args.attributes = attributes;\n\n  if (symbol) {\n    return asSymbol(args);\n  } else {\n    return asIcon(args);\n  }\n}\nfunction makeLayersTextAbstract(params) {\n  var content = params.content,\n      width = params.width,\n      height = params.height,\n      transform = params.transform,\n      title = params.title,\n      extra = params.extra,\n      _params$watchable2 = params.watchable,\n      watchable = _params$watchable2 === void 0 ? false : _params$watchable2;\n\n  var attributes = _objectSpread({}, extra.attributes, title ? {\n    'title': title\n  } : {}, {\n    'class': extra.classes.join(' ')\n  });\n\n  if (watchable) {\n    attributes[DATA_FA_I2SVG] = '';\n  }\n\n  var styles = _objectSpread({}, extra.styles);\n\n  if (transformIsMeaningful(transform)) {\n    styles['transform'] = transformForCss({\n      transform: transform,\n      startCentered: true,\n      width: width,\n      height: height\n    });\n    styles['-webkit-transform'] = styles['transform'];\n  }\n\n  var styleString = joinStyles(styles);\n\n  if (styleString.length > 0) {\n    attributes['style'] = styleString;\n  }\n\n  var val = [];\n  val.push({\n    tag: 'span',\n    attributes: attributes,\n    children: [content]\n  });\n\n  if (title) {\n    val.push({\n      tag: 'span',\n      attributes: {\n        class: 'sr-only'\n      },\n      children: [title]\n    });\n  }\n\n  return val;\n}\nfunction makeLayersCounterAbstract(params) {\n  var content = params.content,\n      title = params.title,\n      extra = params.extra;\n\n  var attributes = _objectSpread({}, extra.attributes, title ? {\n    'title': title\n  } : {}, {\n    'class': extra.classes.join(' ')\n  });\n\n  var styleString = joinStyles(extra.styles);\n\n  if (styleString.length > 0) {\n    attributes['style'] = styleString;\n  }\n\n  var val = [];\n  val.push({\n    tag: 'span',\n    attributes: attributes,\n    children: [content]\n  });\n\n  if (title) {\n    val.push({\n      tag: 'span',\n      attributes: {\n        class: 'sr-only'\n      },\n      children: [title]\n    });\n  }\n\n  return val;\n}\n\nvar noop$1 = function noop() {};\n\nvar p = config.measurePerformance && PERFORMANCE && PERFORMANCE.mark && PERFORMANCE.measure ? PERFORMANCE : {\n  mark: noop$1,\n  measure: noop$1\n};\nvar preamble = \"FA \\\"5.13.0\\\"\";\n\nvar begin = function begin(name) {\n  p.mark(\"\".concat(preamble, \" \").concat(name, \" begins\"));\n  return function () {\n    return end(name);\n  };\n};\n\nvar end = function end(name) {\n  p.mark(\"\".concat(preamble, \" \").concat(name, \" ends\"));\n  p.measure(\"\".concat(preamble, \" \").concat(name), \"\".concat(preamble, \" \").concat(name, \" begins\"), \"\".concat(preamble, \" \").concat(name, \" ends\"));\n};\n\nvar perf = {\n  begin: begin,\n  end: end\n};\n\n/**\n * Internal helper to bind a function known to have 4 arguments\n * to a given context.\n */\n\nvar bindInternal4 = function bindInternal4(func, thisContext) {\n  return function (a, b, c, d) {\n    return func.call(thisContext, a, b, c, d);\n  };\n};\n\n/**\n * # Reduce\n *\n * A fast object `.reduce()` implementation.\n *\n * @param  {Object}   subject      The object to reduce over.\n * @param  {Function} fn           The reducer function.\n * @param  {mixed}    initialValue The initial value for the reducer, defaults to subject[0].\n * @param  {Object}   thisContext  The context for the reducer.\n * @return {mixed}                 The final result.\n */\n\n\nvar reduce = function fastReduceObject(subject, fn, initialValue, thisContext) {\n  var keys = Object.keys(subject),\n      length = keys.length,\n      iterator = thisContext !== undefined ? bindInternal4(fn, thisContext) : fn,\n      i,\n      key,\n      result;\n\n  if (initialValue === undefined) {\n    i = 1;\n    result = subject[keys[0]];\n  } else {\n    i = 0;\n    result = initialValue;\n  }\n\n  for (; i < length; i++) {\n    key = keys[i];\n    result = iterator(result, subject[key], key, subject);\n  }\n\n  return result;\n};\n\nfunction toHex(unicode) {\n  var result = '';\n\n  for (var i = 0; i < unicode.length; i++) {\n    var hex = unicode.charCodeAt(i).toString(16);\n    result += ('000' + hex).slice(-4);\n  }\n\n  return result;\n}\n\nfunction defineIcons(prefix, icons) {\n  var params = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : {};\n  var _params$skipHooks = params.skipHooks,\n      skipHooks = _params$skipHooks === void 0 ? false : _params$skipHooks;\n  var normalized = Object.keys(icons).reduce(function (acc, iconName) {\n    var icon = icons[iconName];\n    var expanded = !!icon.icon;\n\n    if (expanded) {\n      acc[icon.iconName] = icon.icon;\n    } else {\n      acc[iconName] = icon;\n    }\n\n    return acc;\n  }, {});\n\n  if (typeof namespace.hooks.addPack === 'function' && !skipHooks) {\n    namespace.hooks.addPack(prefix, normalized);\n  } else {\n    namespace.styles[prefix] = _objectSpread({}, namespace.styles[prefix] || {}, normalized);\n  }\n  /**\n   * Font Awesome 4 used the prefix of `fa` for all icons. With the introduction\n   * of new styles we needed to differentiate between them. Prefix `fa` is now an alias\n   * for `fas` so we'll easy the upgrade process for our users by automatically defining\n   * this as well.\n   */\n\n\n  if (prefix === 'fas') {\n    defineIcons('fa', icons);\n  }\n}\n\nvar styles = namespace.styles,\n    shims = namespace.shims;\nvar _byUnicode = {};\nvar _byLigature = {};\nvar _byOldName = {};\nvar build = function build() {\n  var lookup = function lookup(reducer) {\n    return reduce(styles, function (o, style, prefix) {\n      o[prefix] = reduce(style, reducer, {});\n      return o;\n    }, {});\n  };\n\n  _byUnicode = lookup(function (acc, icon, iconName) {\n    if (icon[3]) {\n      acc[icon[3]] = iconName;\n    }\n\n    return acc;\n  });\n  _byLigature = lookup(function (acc, icon, iconName) {\n    var ligatures = icon[2];\n    acc[iconName] = iconName;\n    ligatures.forEach(function (ligature) {\n      acc[ligature] = iconName;\n    });\n    return acc;\n  });\n  var hasRegular = 'far' in styles;\n  _byOldName = reduce(shims, function (acc, shim) {\n    var oldName = shim[0];\n    var prefix = shim[1];\n    var iconName = shim[2];\n\n    if (prefix === 'far' && !hasRegular) {\n      prefix = 'fas';\n    }\n\n    acc[oldName] = {\n      prefix: prefix,\n      iconName: iconName\n    };\n    return acc;\n  }, {});\n};\nbuild();\nfunction byUnicode(prefix, unicode) {\n  return (_byUnicode[prefix] || {})[unicode];\n}\nfunction byLigature(prefix, ligature) {\n  return (_byLigature[prefix] || {})[ligature];\n}\nfunction byOldName(name) {\n  return _byOldName[name] || {\n    prefix: null,\n    iconName: null\n  };\n}\n\nvar styles$1 = namespace.styles;\nvar emptyCanonicalIcon = function emptyCanonicalIcon() {\n  return {\n    prefix: null,\n    iconName: null,\n    rest: []\n  };\n};\nfunction getCanonicalIcon(values) {\n  return values.reduce(function (acc, cls) {\n    var iconName = getIconName(config.familyPrefix, cls);\n\n    if (styles$1[cls]) {\n      acc.prefix = cls;\n    } else if (config.autoFetchSvg && ['fas', 'far', 'fal', 'fad', 'fab', 'fa'].indexOf(cls) > -1) {\n      acc.prefix = cls;\n    } else if (iconName) {\n      var shim = acc.prefix === 'fa' ? byOldName(iconName) : {};\n      acc.iconName = shim.iconName || iconName;\n      acc.prefix = shim.prefix || acc.prefix;\n    } else if (cls !== config.replacementClass && cls.indexOf('fa-w-') !== 0) {\n      acc.rest.push(cls);\n    }\n\n    return acc;\n  }, emptyCanonicalIcon());\n}\nfunction iconFromMapping(mapping, prefix, iconName) {\n  if (mapping && mapping[prefix] && mapping[prefix][iconName]) {\n    return {\n      prefix: prefix,\n      iconName: iconName,\n      icon: mapping[prefix][iconName]\n    };\n  }\n}\n\nfunction toHtml(abstractNodes) {\n  var tag = abstractNodes.tag,\n      _abstractNodes$attrib = abstractNodes.attributes,\n      attributes = _abstractNodes$attrib === void 0 ? {} : _abstractNodes$attrib,\n      _abstractNodes$childr = abstractNodes.children,\n      children = _abstractNodes$childr === void 0 ? [] : _abstractNodes$childr;\n\n  if (typeof abstractNodes === 'string') {\n    return htmlEscape(abstractNodes);\n  } else {\n    return \"<\".concat(tag, \" \").concat(joinAttributes(attributes), \">\").concat(children.map(toHtml).join(''), \"\");\n  }\n}\n\nvar noop$2 = function noop() {};\n\nfunction isWatched(node) {\n  var i2svg = node.getAttribute ? node.getAttribute(DATA_FA_I2SVG) : null;\n  return typeof i2svg === 'string';\n}\n\nfunction getMutator() {\n  if (config.autoReplaceSvg === true) {\n    return mutators.replace;\n  }\n\n  var mutator = mutators[config.autoReplaceSvg];\n  return mutator || mutators.replace;\n}\n\nvar mutators = {\n  replace: function replace(mutation) {\n    var node = mutation[0];\n    var abstract = mutation[1];\n    var newOuterHTML = abstract.map(function (a) {\n      return toHtml(a);\n    }).join('\\n');\n\n    if (node.parentNode && node.outerHTML) {\n      node.outerHTML = newOuterHTML + (config.keepOriginalSource && node.tagName.toLowerCase() !== 'svg' ? \"\") : '');\n    } else if (node.parentNode) {\n      var newNode = document.createElement('span');\n      node.parentNode.replaceChild(newNode, node);\n      newNode.outerHTML = newOuterHTML;\n    }\n  },\n  nest: function nest(mutation) {\n    var node = mutation[0];\n    var abstract = mutation[1]; // If we already have a replaced node we do not want to continue nesting within it.\n    // Short-circuit to the standard replacement\n\n    if (~classArray(node).indexOf(config.replacementClass)) {\n      return mutators.replace(mutation);\n    }\n\n    var forSvg = new RegExp(\"\".concat(config.familyPrefix, \"-.*\"));\n    delete abstract[0].attributes.style;\n    delete abstract[0].attributes.id;\n    var splitClasses = abstract[0].attributes.class.split(' ').reduce(function (acc, cls) {\n      if (cls === config.replacementClass || cls.match(forSvg)) {\n        acc.toSvg.push(cls);\n      } else {\n        acc.toNode.push(cls);\n      }\n\n      return acc;\n    }, {\n      toNode: [],\n      toSvg: []\n    });\n    abstract[0].attributes.class = splitClasses.toSvg.join(' ');\n    var newInnerHTML = abstract.map(function (a) {\n      return toHtml(a);\n    }).join('\\n');\n    node.setAttribute('class', splitClasses.toNode.join(' '));\n    node.setAttribute(DATA_FA_I2SVG, '');\n    node.innerHTML = newInnerHTML;\n  }\n};\n\nfunction performOperationSync(op) {\n  op();\n}\n\nfunction perform(mutations, callback) {\n  var callbackFunction = typeof callback === 'function' ? callback : noop$2;\n\n  if (mutations.length === 0) {\n    callbackFunction();\n  } else {\n    var frame = performOperationSync;\n\n    if (config.mutateApproach === MUTATION_APPROACH_ASYNC) {\n      frame = WINDOW.requestAnimationFrame || performOperationSync;\n    }\n\n    frame(function () {\n      var mutator = getMutator();\n      var mark = perf.begin('mutate');\n      mutations.map(mutator);\n      mark();\n      callbackFunction();\n    });\n  }\n}\nvar disabled = false;\nfunction disableObservation() {\n  disabled = true;\n}\nfunction enableObservation() {\n  disabled = false;\n}\nvar mo = null;\nfunction observe(options) {\n  if (!MUTATION_OBSERVER) {\n    return;\n  }\n\n  if (!config.observeMutations) {\n    return;\n  }\n\n  var treeCallback = options.treeCallback,\n      nodeCallback = options.nodeCallback,\n      pseudoElementsCallback = options.pseudoElementsCallback,\n      _options$observeMutat = options.observeMutationsRoot,\n      observeMutationsRoot = _options$observeMutat === void 0 ? DOCUMENT : _options$observeMutat;\n  mo = new MUTATION_OBSERVER(function (objects) {\n    if (disabled) return;\n    toArray(objects).forEach(function (mutationRecord) {\n      if (mutationRecord.type === 'childList' && mutationRecord.addedNodes.length > 0 && !isWatched(mutationRecord.addedNodes[0])) {\n        if (config.searchPseudoElements) {\n          pseudoElementsCallback(mutationRecord.target);\n        }\n\n        treeCallback(mutationRecord.target);\n      }\n\n      if (mutationRecord.type === 'attributes' && mutationRecord.target.parentNode && config.searchPseudoElements) {\n        pseudoElementsCallback(mutationRecord.target.parentNode);\n      }\n\n      if (mutationRecord.type === 'attributes' && isWatched(mutationRecord.target) && ~ATTRIBUTES_WATCHED_FOR_MUTATION.indexOf(mutationRecord.attributeName)) {\n        if (mutationRecord.attributeName === 'class') {\n          var _getCanonicalIcon = getCanonicalIcon(classArray(mutationRecord.target)),\n              prefix = _getCanonicalIcon.prefix,\n              iconName = _getCanonicalIcon.iconName;\n\n          if (prefix) mutationRecord.target.setAttribute('data-prefix', prefix);\n          if (iconName) mutationRecord.target.setAttribute('data-icon', iconName);\n        } else {\n          nodeCallback(mutationRecord.target);\n        }\n      }\n    });\n  });\n  if (!IS_DOM) return;\n  mo.observe(observeMutationsRoot, {\n    childList: true,\n    attributes: true,\n    characterData: true,\n    subtree: true\n  });\n}\nfunction disconnect() {\n  if (!mo) return;\n  mo.disconnect();\n}\n\nfunction styleParser (node) {\n  var style = node.getAttribute('style');\n  var val = [];\n\n  if (style) {\n    val = style.split(';').reduce(function (acc, style) {\n      var styles = style.split(':');\n      var prop = styles[0];\n      var value = styles.slice(1);\n\n      if (prop && value.length > 0) {\n        acc[prop] = value.join(':').trim();\n      }\n\n      return acc;\n    }, {});\n  }\n\n  return val;\n}\n\nfunction classParser (node) {\n  var existingPrefix = node.getAttribute('data-prefix');\n  var existingIconName = node.getAttribute('data-icon');\n  var innerText = node.innerText !== undefined ? node.innerText.trim() : '';\n  var val = getCanonicalIcon(classArray(node));\n\n  if (existingPrefix && existingIconName) {\n    val.prefix = existingPrefix;\n    val.iconName = existingIconName;\n  }\n\n  if (val.prefix && innerText.length > 1) {\n    val.iconName = byLigature(val.prefix, node.innerText);\n  } else if (val.prefix && innerText.length === 1) {\n    val.iconName = byUnicode(val.prefix, toHex(node.innerText));\n  }\n\n  return val;\n}\n\nvar parseTransformString = function parseTransformString(transformString) {\n  var transform = {\n    size: 16,\n    x: 0,\n    y: 0,\n    flipX: false,\n    flipY: false,\n    rotate: 0\n  };\n\n  if (!transformString) {\n    return transform;\n  } else {\n    return transformString.toLowerCase().split(' ').reduce(function (acc, n) {\n      var parts = n.toLowerCase().split('-');\n      var first = parts[0];\n      var rest = parts.slice(1).join('-');\n\n      if (first && rest === 'h') {\n        acc.flipX = true;\n        return acc;\n      }\n\n      if (first && rest === 'v') {\n        acc.flipY = true;\n        return acc;\n      }\n\n      rest = parseFloat(rest);\n\n      if (isNaN(rest)) {\n        return acc;\n      }\n\n      switch (first) {\n        case 'grow':\n          acc.size = acc.size + rest;\n          break;\n\n        case 'shrink':\n          acc.size = acc.size - rest;\n          break;\n\n        case 'left':\n          acc.x = acc.x - rest;\n          break;\n\n        case 'right':\n          acc.x = acc.x + rest;\n          break;\n\n        case 'up':\n          acc.y = acc.y - rest;\n          break;\n\n        case 'down':\n          acc.y = acc.y + rest;\n          break;\n\n        case 'rotate':\n          acc.rotate = acc.rotate + rest;\n          break;\n      }\n\n      return acc;\n    }, transform);\n  }\n};\nfunction transformParser (node) {\n  return parseTransformString(node.getAttribute('data-fa-transform'));\n}\n\nfunction symbolParser (node) {\n  var symbol = node.getAttribute('data-fa-symbol');\n  return symbol === null ? false : symbol === '' ? true : symbol;\n}\n\nfunction attributesParser (node) {\n  var extraAttributes = toArray(node.attributes).reduce(function (acc, attr) {\n    if (acc.name !== 'class' && acc.name !== 'style') {\n      acc[attr.name] = attr.value;\n    }\n\n    return acc;\n  }, {});\n  var title = node.getAttribute('title');\n  var titleId = node.getAttribute('data-fa-title-id');\n\n  if (config.autoA11y) {\n    if (title) {\n      extraAttributes['aria-labelledby'] = \"\".concat(config.replacementClass, \"-title-\").concat(titleId || nextUniqueId());\n    } else {\n      extraAttributes['aria-hidden'] = 'true';\n      extraAttributes['focusable'] = 'false';\n    }\n  }\n\n  return extraAttributes;\n}\n\nfunction maskParser (node) {\n  var mask = node.getAttribute('data-fa-mask');\n\n  if (!mask) {\n    return emptyCanonicalIcon();\n  } else {\n    return getCanonicalIcon(mask.split(' ').map(function (i) {\n      return i.trim();\n    }));\n  }\n}\n\nfunction blankMeta() {\n  return {\n    iconName: null,\n    title: null,\n    titleId: null,\n    prefix: null,\n    transform: meaninglessTransform,\n    symbol: false,\n    mask: null,\n    maskId: null,\n    extra: {\n      classes: [],\n      styles: {},\n      attributes: {}\n    }\n  };\n}\nfunction parseMeta(node) {\n  var _classParser = classParser(node),\n      iconName = _classParser.iconName,\n      prefix = _classParser.prefix,\n      extraClasses = _classParser.rest;\n\n  var extraStyles = styleParser(node);\n  var transform = transformParser(node);\n  var symbol = symbolParser(node);\n  var extraAttributes = attributesParser(node);\n  var mask = maskParser(node);\n  return {\n    iconName: iconName,\n    title: node.getAttribute('title'),\n    titleId: node.getAttribute('data-fa-title-id'),\n    prefix: prefix,\n    transform: transform,\n    symbol: symbol,\n    mask: mask,\n    maskId: node.getAttribute('data-fa-mask-id'),\n    extra: {\n      classes: extraClasses,\n      styles: extraStyles,\n      attributes: extraAttributes\n    }\n  };\n}\n\nfunction MissingIcon(error) {\n  this.name = 'MissingIcon';\n  this.message = error || 'Icon unavailable';\n  this.stack = new Error().stack;\n}\nMissingIcon.prototype = Object.create(Error.prototype);\nMissingIcon.prototype.constructor = MissingIcon;\n\nvar FILL = {\n  fill: 'currentColor'\n};\nvar ANIMATION_BASE = {\n  attributeType: 'XML',\n  repeatCount: 'indefinite',\n  dur: '2s'\n};\nvar RING = {\n  tag: 'path',\n  attributes: _objectSpread({}, FILL, {\n    d: 'M156.5,447.7l-12.6,29.5c-18.7-9.5-35.9-21.2-51.5-34.9l22.7-22.7C127.6,430.5,141.5,440,156.5,447.7z M40.6,272H8.5 c1.4,21.2,5.4,41.7,11.7,61.1L50,321.2C45.1,305.5,41.8,289,40.6,272z M40.6,240c1.4-18.8,5.2-37,11.1-54.1l-29.5-12.6 C14.7,194.3,10,216.7,8.5,240H40.6z M64.3,156.5c7.8-14.9,17.2-28.8,28.1-41.5L69.7,92.3c-13.7,15.6-25.5,32.8-34.9,51.5 L64.3,156.5z M397,419.6c-13.9,12-29.4,22.3-46.1,30.4l11.9,29.8c20.7-9.9,39.8-22.6,56.9-37.6L397,419.6z M115,92.4 c13.9-12,29.4-22.3,46.1-30.4l-11.9-29.8c-20.7,9.9-39.8,22.6-56.8,37.6L115,92.4z M447.7,355.5c-7.8,14.9-17.2,28.8-28.1,41.5 l22.7,22.7c13.7-15.6,25.5-32.9,34.9-51.5L447.7,355.5z M471.4,272c-1.4,18.8-5.2,37-11.1,54.1l29.5,12.6 c7.5-21.1,12.2-43.5,13.6-66.8H471.4z M321.2,462c-15.7,5-32.2,8.2-49.2,9.4v32.1c21.2-1.4,41.7-5.4,61.1-11.7L321.2,462z M240,471.4c-18.8-1.4-37-5.2-54.1-11.1l-12.6,29.5c21.1,7.5,43.5,12.2,66.8,13.6V471.4z M462,190.8c5,15.7,8.2,32.2,9.4,49.2h32.1 c-1.4-21.2-5.4-41.7-11.7-61.1L462,190.8z M92.4,397c-12-13.9-22.3-29.4-30.4-46.1l-29.8,11.9c9.9,20.7,22.6,39.8,37.6,56.9 L92.4,397z M272,40.6c18.8,1.4,36.9,5.2,54.1,11.1l12.6-29.5C317.7,14.7,295.3,10,272,8.5V40.6z M190.8,50 c15.7-5,32.2-8.2,49.2-9.4V8.5c-21.2,1.4-41.7,5.4-61.1,11.7L190.8,50z M442.3,92.3L419.6,115c12,13.9,22.3,29.4,30.5,46.1 l29.8-11.9C470,128.5,457.3,109.4,442.3,92.3z M397,92.4l22.7-22.7c-15.6-13.7-32.8-25.5-51.5-34.9l-12.6,29.5 C370.4,72.1,384.4,81.5,397,92.4z'\n  })\n};\n\nvar OPACITY_ANIMATE = _objectSpread({}, ANIMATION_BASE, {\n  attributeName: 'opacity'\n});\n\nvar DOT = {\n  tag: 'circle',\n  attributes: _objectSpread({}, FILL, {\n    cx: '256',\n    cy: '364',\n    r: '28'\n  }),\n  children: [{\n    tag: 'animate',\n    attributes: _objectSpread({}, ANIMATION_BASE, {\n      attributeName: 'r',\n      values: '28;14;28;28;14;28;'\n    })\n  }, {\n    tag: 'animate',\n    attributes: _objectSpread({}, OPACITY_ANIMATE, {\n      values: '1;0;1;1;0;1;'\n    })\n  }]\n};\nvar QUESTION = {\n  tag: 'path',\n  attributes: _objectSpread({}, FILL, {\n    opacity: '1',\n    d: 'M263.7,312h-16c-6.6,0-12-5.4-12-12c0-71,77.4-63.9,77.4-107.8c0-20-17.8-40.2-57.4-40.2c-29.1,0-44.3,9.6-59.2,28.7 c-3.9,5-11.1,6-16.2,2.4l-13.1-9.2c-5.6-3.9-6.9-11.8-2.6-17.2c21.2-27.2,46.4-44.7,91.2-44.7c52.3,0,97.4,29.8,97.4,80.2 c0,67.6-77.4,63.5-77.4,107.8C275.7,306.6,270.3,312,263.7,312z'\n  }),\n  children: [{\n    tag: 'animate',\n    attributes: _objectSpread({}, OPACITY_ANIMATE, {\n      values: '1;0;0;0;0;1;'\n    })\n  }]\n};\nvar EXCLAMATION = {\n  tag: 'path',\n  attributes: _objectSpread({}, FILL, {\n    opacity: '0',\n    d: 'M232.5,134.5l7,168c0.3,6.4,5.6,11.5,12,11.5h9c6.4,0,11.7-5.1,12-11.5l7-168c0.3-6.8-5.2-12.5-12-12.5h-23 C237.7,122,232.2,127.7,232.5,134.5z'\n  }),\n  children: [{\n    tag: 'animate',\n    attributes: _objectSpread({}, OPACITY_ANIMATE, {\n      values: '0;0;1;1;0;0;'\n    })\n  }]\n};\nvar missing = {\n  tag: 'g',\n  children: [RING, DOT, QUESTION, EXCLAMATION]\n};\n\nvar styles$2 = namespace.styles;\nfunction asFoundIcon(icon) {\n  var width = icon[0];\n  var height = icon[1];\n\n  var _icon$slice = icon.slice(4),\n      _icon$slice2 = _slicedToArray(_icon$slice, 1),\n      vectorData = _icon$slice2[0];\n\n  var element = null;\n\n  if (Array.isArray(vectorData)) {\n    element = {\n      tag: 'g',\n      attributes: {\n        class: \"\".concat(config.familyPrefix, \"-\").concat(DUOTONE_CLASSES.GROUP)\n      },\n      children: [{\n        tag: 'path',\n        attributes: {\n          class: \"\".concat(config.familyPrefix, \"-\").concat(DUOTONE_CLASSES.SECONDARY),\n          fill: 'currentColor',\n          d: vectorData[0]\n        }\n      }, {\n        tag: 'path',\n        attributes: {\n          class: \"\".concat(config.familyPrefix, \"-\").concat(DUOTONE_CLASSES.PRIMARY),\n          fill: 'currentColor',\n          d: vectorData[1]\n        }\n      }]\n    };\n  } else {\n    element = {\n      tag: 'path',\n      attributes: {\n        fill: 'currentColor',\n        d: vectorData\n      }\n    };\n  }\n\n  return {\n    found: true,\n    width: width,\n    height: height,\n    icon: element\n  };\n}\nfunction findIcon(iconName, prefix) {\n  return new picked(function (resolve, reject) {\n    var val = {\n      found: false,\n      width: 512,\n      height: 512,\n      icon: missing\n    };\n\n    if (iconName && prefix && styles$2[prefix] && styles$2[prefix][iconName]) {\n      var icon = styles$2[prefix][iconName];\n      return resolve(asFoundIcon(icon));\n    }\n\n    var headers = {};\n\n    if (_typeof(WINDOW.FontAwesomeKitConfig) === 'object' && typeof window.FontAwesomeKitConfig.token === 'string') {\n      headers['fa-kit-token'] = WINDOW.FontAwesomeKitConfig.token;\n    }\n\n    if (iconName && prefix && !config.showMissingIcons) {\n      reject(new MissingIcon(\"Icon is missing for prefix \".concat(prefix, \" with icon name \").concat(iconName)));\n    } else {\n      resolve(val);\n    }\n  });\n}\n\nvar styles$3 = namespace.styles;\n\nfunction generateSvgReplacementMutation(node, nodeMeta) {\n  var iconName = nodeMeta.iconName,\n      title = nodeMeta.title,\n      titleId = nodeMeta.titleId,\n      prefix = nodeMeta.prefix,\n      transform = nodeMeta.transform,\n      symbol = nodeMeta.symbol,\n      mask = nodeMeta.mask,\n      maskId = nodeMeta.maskId,\n      extra = nodeMeta.extra;\n  return new picked(function (resolve, reject) {\n    picked.all([findIcon(iconName, prefix), findIcon(mask.iconName, mask.prefix)]).then(function (_ref) {\n      var _ref2 = _slicedToArray(_ref, 2),\n          main = _ref2[0],\n          mask = _ref2[1];\n\n      resolve([node, makeInlineSvgAbstract({\n        icons: {\n          main: main,\n          mask: mask\n        },\n        prefix: prefix,\n        iconName: iconName,\n        transform: transform,\n        symbol: symbol,\n        mask: mask,\n        maskId: maskId,\n        title: title,\n        titleId: titleId,\n        extra: extra,\n        watchable: true\n      })]);\n    });\n  });\n}\n\nfunction generateLayersText(node, nodeMeta) {\n  var title = nodeMeta.title,\n      transform = nodeMeta.transform,\n      extra = nodeMeta.extra;\n  var width = null;\n  var height = null;\n\n  if (IS_IE) {\n    var computedFontSize = parseInt(getComputedStyle(node).fontSize, 10);\n    var boundingClientRect = node.getBoundingClientRect();\n    width = boundingClientRect.width / computedFontSize;\n    height = boundingClientRect.height / computedFontSize;\n  }\n\n  if (config.autoA11y && !title) {\n    extra.attributes['aria-hidden'] = 'true';\n  }\n\n  return picked.resolve([node, makeLayersTextAbstract({\n    content: node.innerHTML,\n    width: width,\n    height: height,\n    transform: transform,\n    title: title,\n    extra: extra,\n    watchable: true\n  })]);\n}\n\nfunction generateMutation(node) {\n  var nodeMeta = parseMeta(node);\n\n  if (~nodeMeta.extra.classes.indexOf(LAYERS_TEXT_CLASSNAME)) {\n    return generateLayersText(node, nodeMeta);\n  } else {\n    return generateSvgReplacementMutation(node, nodeMeta);\n  }\n}\n\nfunction onTree(root) {\n  var callback = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : null;\n  if (!IS_DOM) return;\n  var htmlClassList = DOCUMENT.documentElement.classList;\n\n  var hclAdd = function hclAdd(suffix) {\n    return htmlClassList.add(\"\".concat(HTML_CLASS_I2SVG_BASE_CLASS, \"-\").concat(suffix));\n  };\n\n  var hclRemove = function hclRemove(suffix) {\n    return htmlClassList.remove(\"\".concat(HTML_CLASS_I2SVG_BASE_CLASS, \"-\").concat(suffix));\n  };\n\n  var prefixes = config.autoFetchSvg ? Object.keys(PREFIX_TO_STYLE) : Object.keys(styles$3);\n  var prefixesDomQuery = [\".\".concat(LAYERS_TEXT_CLASSNAME, \":not([\").concat(DATA_FA_I2SVG, \"])\")].concat(prefixes.map(function (p) {\n    return \".\".concat(p, \":not([\").concat(DATA_FA_I2SVG, \"])\");\n  })).join(', ');\n\n  if (prefixesDomQuery.length === 0) {\n    return;\n  }\n\n  var candidates = [];\n\n  try {\n    candidates = toArray(root.querySelectorAll(prefixesDomQuery));\n  } catch (e) {// noop\n  }\n\n  if (candidates.length > 0) {\n    hclAdd('pending');\n    hclRemove('complete');\n  } else {\n    return;\n  }\n\n  var mark = perf.begin('onTree');\n  var mutations = candidates.reduce(function (acc, node) {\n    try {\n      var mutation = generateMutation(node);\n\n      if (mutation) {\n        acc.push(mutation);\n      }\n    } catch (e) {\n      if (!PRODUCTION) {\n        if (e instanceof MissingIcon) {\n          console.error(e);\n        }\n      }\n    }\n\n    return acc;\n  }, []);\n  return new picked(function (resolve, reject) {\n    picked.all(mutations).then(function (resolvedMutations) {\n      perform(resolvedMutations, function () {\n        hclAdd('active');\n        hclAdd('complete');\n        hclRemove('pending');\n        if (typeof callback === 'function') callback();\n        mark();\n        resolve();\n      });\n    }).catch(function () {\n      mark();\n      reject();\n    });\n  });\n}\nfunction onNode(node) {\n  var callback = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : null;\n  generateMutation(node).then(function (mutation) {\n    if (mutation) {\n      perform([mutation], callback);\n    }\n  });\n}\n\nfunction replaceForPosition(node, position) {\n  var pendingAttribute = \"\".concat(DATA_FA_PSEUDO_ELEMENT_PENDING).concat(position.replace(':', '-'));\n  return new picked(function (resolve, reject) {\n    if (node.getAttribute(pendingAttribute) !== null) {\n      // This node is already being processed\n      return resolve();\n    }\n\n    var children = toArray(node.children);\n    var alreadyProcessedPseudoElement = children.filter(function (c) {\n      return c.getAttribute(DATA_FA_PSEUDO_ELEMENT) === position;\n    })[0];\n    var styles = WINDOW.getComputedStyle(node, position);\n    var fontFamily = styles.getPropertyValue('font-family').match(FONT_FAMILY_PATTERN);\n    var fontWeight = styles.getPropertyValue('font-weight');\n    var content = styles.getPropertyValue('content');\n\n    if (alreadyProcessedPseudoElement && !fontFamily) {\n      // If we've already processed it but the current computed style does not result in a font-family,\n      // that probably means that a class name that was previously present to make the icon has been\n      // removed. So we now should delete the icon.\n      node.removeChild(alreadyProcessedPseudoElement);\n      return resolve();\n    } else if (fontFamily && content !== 'none' && content !== '') {\n      var prefix = ~['Solid', 'Regular', 'Light', 'Duotone', 'Brands'].indexOf(fontFamily[1]) ? STYLE_TO_PREFIX[fontFamily[1].toLowerCase()] : FONT_WEIGHT_TO_PREFIX[fontWeight];\n      var hexValue = toHex(content.length === 3 ? content.substr(1, 1) : content);\n      var iconName = byUnicode(prefix, hexValue);\n      var iconIdentifier = iconName; // Only convert the pseudo element in this :before/:after position into an icon if we haven't\n      // already done so with the same prefix and iconName\n\n      if (iconName && (!alreadyProcessedPseudoElement || alreadyProcessedPseudoElement.getAttribute(DATA_PREFIX) !== prefix || alreadyProcessedPseudoElement.getAttribute(DATA_ICON) !== iconIdentifier)) {\n        node.setAttribute(pendingAttribute, iconIdentifier);\n\n        if (alreadyProcessedPseudoElement) {\n          // Delete the old one, since we're replacing it with a new one\n          node.removeChild(alreadyProcessedPseudoElement);\n        }\n\n        var meta = blankMeta();\n        var extra = meta.extra;\n        extra.attributes[DATA_FA_PSEUDO_ELEMENT] = position;\n        findIcon(iconName, prefix).then(function (main) {\n          var abstract = makeInlineSvgAbstract(_objectSpread({}, meta, {\n            icons: {\n              main: main,\n              mask: emptyCanonicalIcon()\n            },\n            prefix: prefix,\n            iconName: iconIdentifier,\n            extra: extra,\n            watchable: true\n          }));\n          var element = DOCUMENT.createElement('svg');\n\n          if (position === ':before') {\n            node.insertBefore(element, node.firstChild);\n          } else {\n            node.appendChild(element);\n          }\n\n          element.outerHTML = abstract.map(function (a) {\n            return toHtml(a);\n          }).join('\\n');\n          node.removeAttribute(pendingAttribute);\n          resolve();\n        }).catch(reject);\n      } else {\n        resolve();\n      }\n    } else {\n      resolve();\n    }\n  });\n}\n\nfunction replace(node) {\n  return picked.all([replaceForPosition(node, ':before'), replaceForPosition(node, ':after')]);\n}\n\nfunction processable(node) {\n  return node.parentNode !== document.head && !~TAGNAMES_TO_SKIP_FOR_PSEUDOELEMENTS.indexOf(node.tagName.toUpperCase()) && !node.getAttribute(DATA_FA_PSEUDO_ELEMENT) && (!node.parentNode || node.parentNode.tagName !== 'svg');\n}\n\nfunction searchPseudoElements (root) {\n  if (!IS_DOM) return;\n  return new picked(function (resolve, reject) {\n    var operations = toArray(root.querySelectorAll('*')).filter(processable).map(replace);\n    var end = perf.begin('searchPseudoElements');\n    disableObservation();\n    picked.all(operations).then(function () {\n      end();\n      enableObservation();\n      resolve();\n    }).catch(function () {\n      end();\n      enableObservation();\n      reject();\n    });\n  });\n}\n\nvar baseStyles = \"svg:not(:root).svg-inline--fa {\\n  overflow: visible;\\n}\\n\\n.svg-inline--fa {\\n  display: inline-block;\\n  font-size: inherit;\\n  height: 1em;\\n  overflow: visible;\\n  vertical-align: -0.125em;\\n}\\n.svg-inline--fa.fa-lg {\\n  vertical-align: -0.225em;\\n}\\n.svg-inline--fa.fa-w-1 {\\n  width: 0.0625em;\\n}\\n.svg-inline--fa.fa-w-2 {\\n  width: 0.125em;\\n}\\n.svg-inline--fa.fa-w-3 {\\n  width: 0.1875em;\\n}\\n.svg-inline--fa.fa-w-4 {\\n  width: 0.25em;\\n}\\n.svg-inline--fa.fa-w-5 {\\n  width: 0.3125em;\\n}\\n.svg-inline--fa.fa-w-6 {\\n  width: 0.375em;\\n}\\n.svg-inline--fa.fa-w-7 {\\n  width: 0.4375em;\\n}\\n.svg-inline--fa.fa-w-8 {\\n  width: 0.5em;\\n}\\n.svg-inline--fa.fa-w-9 {\\n  width: 0.5625em;\\n}\\n.svg-inline--fa.fa-w-10 {\\n  width: 0.625em;\\n}\\n.svg-inline--fa.fa-w-11 {\\n  width: 0.6875em;\\n}\\n.svg-inline--fa.fa-w-12 {\\n  width: 0.75em;\\n}\\n.svg-inline--fa.fa-w-13 {\\n  width: 0.8125em;\\n}\\n.svg-inline--fa.fa-w-14 {\\n  width: 0.875em;\\n}\\n.svg-inline--fa.fa-w-15 {\\n  width: 0.9375em;\\n}\\n.svg-inline--fa.fa-w-16 {\\n  width: 1em;\\n}\\n.svg-inline--fa.fa-w-17 {\\n  width: 1.0625em;\\n}\\n.svg-inline--fa.fa-w-18 {\\n  width: 1.125em;\\n}\\n.svg-inline--fa.fa-w-19 {\\n  width: 1.1875em;\\n}\\n.svg-inline--fa.fa-w-20 {\\n  width: 1.25em;\\n}\\n.svg-inline--fa.fa-pull-left {\\n  margin-right: 0.3em;\\n  width: auto;\\n}\\n.svg-inline--fa.fa-pull-right {\\n  margin-left: 0.3em;\\n  width: auto;\\n}\\n.svg-inline--fa.fa-border {\\n  height: 1.5em;\\n}\\n.svg-inline--fa.fa-li {\\n  width: 2em;\\n}\\n.svg-inline--fa.fa-fw {\\n  width: 1.25em;\\n}\\n\\n.fa-layers svg.svg-inline--fa {\\n  bottom: 0;\\n  left: 0;\\n  margin: auto;\\n  position: absolute;\\n  right: 0;\\n  top: 0;\\n}\\n\\n.fa-layers {\\n  display: inline-block;\\n  height: 1em;\\n  position: relative;\\n  text-align: center;\\n  vertical-align: -0.125em;\\n  width: 1em;\\n}\\n.fa-layers svg.svg-inline--fa {\\n  -webkit-transform-origin: center center;\\n          transform-origin: center center;\\n}\\n\\n.fa-layers-counter, .fa-layers-text {\\n  display: inline-block;\\n  position: absolute;\\n  text-align: center;\\n}\\n\\n.fa-layers-text {\\n  left: 50%;\\n  top: 50%;\\n  -webkit-transform: translate(-50%, -50%);\\n          transform: translate(-50%, -50%);\\n  -webkit-transform-origin: center center;\\n          transform-origin: center center;\\n}\\n\\n.fa-layers-counter {\\n  background-color: #ff253a;\\n  border-radius: 1em;\\n  -webkit-box-sizing: border-box;\\n          box-sizing: border-box;\\n  color: #fff;\\n  height: 1.5em;\\n  line-height: 1;\\n  max-width: 5em;\\n  min-width: 1.5em;\\n  overflow: hidden;\\n  padding: 0.25em;\\n  right: 0;\\n  text-overflow: ellipsis;\\n  top: 0;\\n  -webkit-transform: scale(0.25);\\n          transform: scale(0.25);\\n  -webkit-transform-origin: top right;\\n          transform-origin: top right;\\n}\\n\\n.fa-layers-bottom-right {\\n  bottom: 0;\\n  right: 0;\\n  top: auto;\\n  -webkit-transform: scale(0.25);\\n          transform: scale(0.25);\\n  -webkit-transform-origin: bottom right;\\n          transform-origin: bottom right;\\n}\\n\\n.fa-layers-bottom-left {\\n  bottom: 0;\\n  left: 0;\\n  right: auto;\\n  top: auto;\\n  -webkit-transform: scale(0.25);\\n          transform: scale(0.25);\\n  -webkit-transform-origin: bottom left;\\n          transform-origin: bottom left;\\n}\\n\\n.fa-layers-top-right {\\n  right: 0;\\n  top: 0;\\n  -webkit-transform: scale(0.25);\\n          transform: scale(0.25);\\n  -webkit-transform-origin: top right;\\n          transform-origin: top right;\\n}\\n\\n.fa-layers-top-left {\\n  left: 0;\\n  right: auto;\\n  top: 0;\\n  -webkit-transform: scale(0.25);\\n          transform: scale(0.25);\\n  -webkit-transform-origin: top left;\\n          transform-origin: top left;\\n}\\n\\n.fa-lg {\\n  font-size: 1.3333333333em;\\n  line-height: 0.75em;\\n  vertical-align: -0.0667em;\\n}\\n\\n.fa-xs {\\n  font-size: 0.75em;\\n}\\n\\n.fa-sm {\\n  font-size: 0.875em;\\n}\\n\\n.fa-1x {\\n  font-size: 1em;\\n}\\n\\n.fa-2x {\\n  font-size: 2em;\\n}\\n\\n.fa-3x {\\n  font-size: 3em;\\n}\\n\\n.fa-4x {\\n  font-size: 4em;\\n}\\n\\n.fa-5x {\\n  font-size: 5em;\\n}\\n\\n.fa-6x {\\n  font-size: 6em;\\n}\\n\\n.fa-7x {\\n  font-size: 7em;\\n}\\n\\n.fa-8x {\\n  font-size: 8em;\\n}\\n\\n.fa-9x {\\n  font-size: 9em;\\n}\\n\\n.fa-10x {\\n  font-size: 10em;\\n}\\n\\n.fa-fw {\\n  text-align: center;\\n  width: 1.25em;\\n}\\n\\n.fa-ul {\\n  list-style-type: none;\\n  margin-left: 2.5em;\\n  padding-left: 0;\\n}\\n.fa-ul > li {\\n  position: relative;\\n}\\n\\n.fa-li {\\n  left: -2em;\\n  position: absolute;\\n  text-align: center;\\n  width: 2em;\\n  line-height: inherit;\\n}\\n\\n.fa-border {\\n  border: solid 0.08em #eee;\\n  border-radius: 0.1em;\\n  padding: 0.2em 0.25em 0.15em;\\n}\\n\\n.fa-pull-left {\\n  float: left;\\n}\\n\\n.fa-pull-right {\\n  float: right;\\n}\\n\\n.fa.fa-pull-left,\\n.fas.fa-pull-left,\\n.far.fa-pull-left,\\n.fal.fa-pull-left,\\n.fab.fa-pull-left {\\n  margin-right: 0.3em;\\n}\\n.fa.fa-pull-right,\\n.fas.fa-pull-right,\\n.far.fa-pull-right,\\n.fal.fa-pull-right,\\n.fab.fa-pull-right {\\n  margin-left: 0.3em;\\n}\\n\\n.fa-spin {\\n  -webkit-animation: fa-spin 2s infinite linear;\\n          animation: fa-spin 2s infinite linear;\\n}\\n\\n.fa-pulse {\\n  -webkit-animation: fa-spin 1s infinite steps(8);\\n          animation: fa-spin 1s infinite steps(8);\\n}\\n\\n@-webkit-keyframes fa-spin {\\n  0% {\\n    -webkit-transform: rotate(0deg);\\n            transform: rotate(0deg);\\n  }\\n  100% {\\n    -webkit-transform: rotate(360deg);\\n            transform: rotate(360deg);\\n  }\\n}\\n\\n@keyframes fa-spin {\\n  0% {\\n    -webkit-transform: rotate(0deg);\\n            transform: rotate(0deg);\\n  }\\n  100% {\\n    -webkit-transform: rotate(360deg);\\n            transform: rotate(360deg);\\n  }\\n}\\n.fa-rotate-90 {\\n  -ms-filter: \\\"progid:DXImageTransform.Microsoft.BasicImage(rotation=1)\\\";\\n  -webkit-transform: rotate(90deg);\\n          transform: rotate(90deg);\\n}\\n\\n.fa-rotate-180 {\\n  -ms-filter: \\\"progid:DXImageTransform.Microsoft.BasicImage(rotation=2)\\\";\\n  -webkit-transform: rotate(180deg);\\n          transform: rotate(180deg);\\n}\\n\\n.fa-rotate-270 {\\n  -ms-filter: \\\"progid:DXImageTransform.Microsoft.BasicImage(rotation=3)\\\";\\n  -webkit-transform: rotate(270deg);\\n          transform: rotate(270deg);\\n}\\n\\n.fa-flip-horizontal {\\n  -ms-filter: \\\"progid:DXImageTransform.Microsoft.BasicImage(rotation=0, mirror=1)\\\";\\n  -webkit-transform: scale(-1, 1);\\n          transform: scale(-1, 1);\\n}\\n\\n.fa-flip-vertical {\\n  -ms-filter: \\\"progid:DXImageTransform.Microsoft.BasicImage(rotation=2, mirror=1)\\\";\\n  -webkit-transform: scale(1, -1);\\n          transform: scale(1, -1);\\n}\\n\\n.fa-flip-both, .fa-flip-horizontal.fa-flip-vertical {\\n  -ms-filter: \\\"progid:DXImageTransform.Microsoft.BasicImage(rotation=2, mirror=1)\\\";\\n  -webkit-transform: scale(-1, -1);\\n          transform: scale(-1, -1);\\n}\\n\\n:root .fa-rotate-90,\\n:root .fa-rotate-180,\\n:root .fa-rotate-270,\\n:root .fa-flip-horizontal,\\n:root .fa-flip-vertical,\\n:root .fa-flip-both {\\n  -webkit-filter: none;\\n          filter: none;\\n}\\n\\n.fa-stack {\\n  display: inline-block;\\n  height: 2em;\\n  position: relative;\\n  width: 2.5em;\\n}\\n\\n.fa-stack-1x,\\n.fa-stack-2x {\\n  bottom: 0;\\n  left: 0;\\n  margin: auto;\\n  position: absolute;\\n  right: 0;\\n  top: 0;\\n}\\n\\n.svg-inline--fa.fa-stack-1x {\\n  height: 1em;\\n  width: 1.25em;\\n}\\n.svg-inline--fa.fa-stack-2x {\\n  height: 2em;\\n  width: 2.5em;\\n}\\n\\n.fa-inverse {\\n  color: #fff;\\n}\\n\\n.sr-only {\\n  border: 0;\\n  clip: rect(0, 0, 0, 0);\\n  height: 1px;\\n  margin: -1px;\\n  overflow: hidden;\\n  padding: 0;\\n  position: absolute;\\n  width: 1px;\\n}\\n\\n.sr-only-focusable:active, .sr-only-focusable:focus {\\n  clip: auto;\\n  height: auto;\\n  margin: 0;\\n  overflow: visible;\\n  position: static;\\n  width: auto;\\n}\\n\\n.svg-inline--fa .fa-primary {\\n  fill: var(--fa-primary-color, currentColor);\\n  opacity: 1;\\n  opacity: var(--fa-primary-opacity, 1);\\n}\\n\\n.svg-inline--fa .fa-secondary {\\n  fill: var(--fa-secondary-color, currentColor);\\n  opacity: 0.4;\\n  opacity: var(--fa-secondary-opacity, 0.4);\\n}\\n\\n.svg-inline--fa.fa-swap-opacity .fa-primary {\\n  opacity: 0.4;\\n  opacity: var(--fa-secondary-opacity, 0.4);\\n}\\n\\n.svg-inline--fa.fa-swap-opacity .fa-secondary {\\n  opacity: 1;\\n  opacity: var(--fa-primary-opacity, 1);\\n}\\n\\n.svg-inline--fa mask .fa-primary,\\n.svg-inline--fa mask .fa-secondary {\\n  fill: black;\\n}\\n\\n.fad.fa-inverse {\\n  color: #fff;\\n}\";\n\nfunction css () {\n  var dfp = DEFAULT_FAMILY_PREFIX;\n  var drc = DEFAULT_REPLACEMENT_CLASS;\n  var fp = config.familyPrefix;\n  var rc = config.replacementClass;\n  var s = baseStyles;\n\n  if (fp !== dfp || rc !== drc) {\n    var dPatt = new RegExp(\"\\\\.\".concat(dfp, \"\\\\-\"), 'g');\n    var customPropPatt = new RegExp(\"\\\\--\".concat(dfp, \"\\\\-\"), 'g');\n    var rPatt = new RegExp(\"\\\\.\".concat(drc), 'g');\n    s = s.replace(dPatt, \".\".concat(fp, \"-\")).replace(customPropPatt, \"--\".concat(fp, \"-\")).replace(rPatt, \".\".concat(rc));\n  }\n\n  return s;\n}\n\nvar Library =\n/*#__PURE__*/\nfunction () {\n  function Library() {\n    _classCallCheck(this, Library);\n\n    this.definitions = {};\n  }\n\n  _createClass(Library, [{\n    key: \"add\",\n    value: function add() {\n      var _this = this;\n\n      for (var _len = arguments.length, definitions = new Array(_len), _key = 0; _key < _len; _key++) {\n        definitions[_key] = arguments[_key];\n      }\n\n      var additions = definitions.reduce(this._pullDefinitions, {});\n      Object.keys(additions).forEach(function (key) {\n        _this.definitions[key] = _objectSpread({}, _this.definitions[key] || {}, additions[key]);\n        defineIcons(key, additions[key]);\n        build();\n      });\n    }\n  }, {\n    key: \"reset\",\n    value: function reset() {\n      this.definitions = {};\n    }\n  }, {\n    key: \"_pullDefinitions\",\n    value: function _pullDefinitions(additions, definition) {\n      var normalized = definition.prefix && definition.iconName && definition.icon ? {\n        0: definition\n      } : definition;\n      Object.keys(normalized).map(function (key) {\n        var _normalized$key = normalized[key],\n            prefix = _normalized$key.prefix,\n            iconName = _normalized$key.iconName,\n            icon = _normalized$key.icon;\n        if (!additions[prefix]) additions[prefix] = {};\n        additions[prefix][iconName] = icon;\n      });\n      return additions;\n    }\n  }]);\n\n  return Library;\n}();\n\nfunction ensureCss() {\n  if (config.autoAddCss && !_cssInserted) {\n    insertCss(css());\n\n    _cssInserted = true;\n  }\n}\n\nfunction apiObject(val, abstractCreator) {\n  Object.defineProperty(val, 'abstract', {\n    get: abstractCreator\n  });\n  Object.defineProperty(val, 'html', {\n    get: function get() {\n      return val.abstract.map(function (a) {\n        return toHtml(a);\n      });\n    }\n  });\n  Object.defineProperty(val, 'node', {\n    get: function get() {\n      if (!IS_DOM) return;\n      var container = DOCUMENT.createElement('div');\n      container.innerHTML = val.html;\n      return container.children;\n    }\n  });\n  return val;\n}\n\nfunction findIconDefinition(iconLookup) {\n  var _iconLookup$prefix = iconLookup.prefix,\n      prefix = _iconLookup$prefix === void 0 ? 'fa' : _iconLookup$prefix,\n      iconName = iconLookup.iconName;\n  if (!iconName) return;\n  return iconFromMapping(library.definitions, prefix, iconName) || iconFromMapping(namespace.styles, prefix, iconName);\n}\n\nfunction resolveIcons(next) {\n  return function (maybeIconDefinition) {\n    var params = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {};\n    var iconDefinition = (maybeIconDefinition || {}).icon ? maybeIconDefinition : findIconDefinition(maybeIconDefinition || {});\n    var mask = params.mask;\n\n    if (mask) {\n      mask = (mask || {}).icon ? mask : findIconDefinition(mask || {});\n    }\n\n    return next(iconDefinition, _objectSpread({}, params, {\n      mask: mask\n    }));\n  };\n}\n\nvar library = new Library();\nvar noAuto = function noAuto() {\n  config.autoReplaceSvg = false;\n  config.observeMutations = false;\n  disconnect();\n};\nvar _cssInserted = false;\nvar dom = {\n  i2svg: function i2svg() {\n    var params = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : {};\n\n    if (IS_DOM) {\n      ensureCss();\n      var _params$node = params.node,\n          node = _params$node === void 0 ? DOCUMENT : _params$node,\n          _params$callback = params.callback,\n          callback = _params$callback === void 0 ? function () {} : _params$callback;\n\n      if (config.searchPseudoElements) {\n        searchPseudoElements(node);\n      }\n\n      return onTree(node, callback);\n    } else {\n      return picked.reject('Operation requires a DOM of some kind.');\n    }\n  },\n  css: css,\n  insertCss: function insertCss$$1() {\n    if (!_cssInserted) {\n      insertCss(css());\n\n      _cssInserted = true;\n    }\n  },\n  watch: function watch() {\n    var params = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : {};\n    var autoReplaceSvgRoot = params.autoReplaceSvgRoot,\n        observeMutationsRoot = params.observeMutationsRoot;\n\n    if (config.autoReplaceSvg === false) {\n      config.autoReplaceSvg = true;\n    }\n\n    config.observeMutations = true;\n    domready(function () {\n      autoReplace({\n        autoReplaceSvgRoot: autoReplaceSvgRoot\n      });\n      observe({\n        treeCallback: onTree,\n        nodeCallback: onNode,\n        pseudoElementsCallback: searchPseudoElements,\n        observeMutationsRoot: observeMutationsRoot\n      });\n    });\n  }\n};\nvar parse = {\n  transform: function transform(transformString) {\n    return parseTransformString(transformString);\n  }\n};\nvar icon = resolveIcons(function (iconDefinition) {\n  var params = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {};\n  var _params$transform = params.transform,\n      transform = _params$transform === void 0 ? meaninglessTransform : _params$transform,\n      _params$symbol = params.symbol,\n      symbol = _params$symbol === void 0 ? false : _params$symbol,\n      _params$mask = params.mask,\n      mask = _params$mask === void 0 ? null : _params$mask,\n      _params$maskId = params.maskId,\n      maskId = _params$maskId === void 0 ? null : _params$maskId,\n      _params$title = params.title,\n      title = _params$title === void 0 ? null : _params$title,\n      _params$titleId = params.titleId,\n      titleId = _params$titleId === void 0 ? null : _params$titleId,\n      _params$classes = params.classes,\n      classes = _params$classes === void 0 ? [] : _params$classes,\n      _params$attributes = params.attributes,\n      attributes = _params$attributes === void 0 ? {} : _params$attributes,\n      _params$styles = params.styles,\n      styles = _params$styles === void 0 ? {} : _params$styles;\n  if (!iconDefinition) return;\n  var prefix = iconDefinition.prefix,\n      iconName = iconDefinition.iconName,\n      icon = iconDefinition.icon;\n  return apiObject(_objectSpread({\n    type: 'icon'\n  }, iconDefinition), function () {\n    ensureCss();\n\n    if (config.autoA11y) {\n      if (title) {\n        attributes['aria-labelledby'] = \"\".concat(config.replacementClass, \"-title-\").concat(titleId || nextUniqueId());\n      } else {\n        attributes['aria-hidden'] = 'true';\n        attributes['focusable'] = 'false';\n      }\n    }\n\n    return makeInlineSvgAbstract({\n      icons: {\n        main: asFoundIcon(icon),\n        mask: mask ? asFoundIcon(mask.icon) : {\n          found: false,\n          width: null,\n          height: null,\n          icon: {}\n        }\n      },\n      prefix: prefix,\n      iconName: iconName,\n      transform: _objectSpread({}, meaninglessTransform, transform),\n      symbol: symbol,\n      title: title,\n      maskId: maskId,\n      titleId: titleId,\n      extra: {\n        attributes: attributes,\n        styles: styles,\n        classes: classes\n      }\n    });\n  });\n});\nvar text = function text(content) {\n  var params = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {};\n  var _params$transform2 = params.transform,\n      transform = _params$transform2 === void 0 ? meaninglessTransform : _params$transform2,\n      _params$title2 = params.title,\n      title = _params$title2 === void 0 ? null : _params$title2,\n      _params$classes2 = params.classes,\n      classes = _params$classes2 === void 0 ? [] : _params$classes2,\n      _params$attributes2 = params.attributes,\n      attributes = _params$attributes2 === void 0 ? {} : _params$attributes2,\n      _params$styles2 = params.styles,\n      styles = _params$styles2 === void 0 ? {} : _params$styles2;\n  return apiObject({\n    type: 'text',\n    content: content\n  }, function () {\n    ensureCss();\n    return makeLayersTextAbstract({\n      content: content,\n      transform: _objectSpread({}, meaninglessTransform, transform),\n      title: title,\n      extra: {\n        attributes: attributes,\n        styles: styles,\n        classes: [\"\".concat(config.familyPrefix, \"-layers-text\")].concat(_toConsumableArray(classes))\n      }\n    });\n  });\n};\nvar counter = function counter(content) {\n  var params = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {};\n  var _params$title3 = params.title,\n      title = _params$title3 === void 0 ? null : _params$title3,\n      _params$classes3 = params.classes,\n      classes = _params$classes3 === void 0 ? [] : _params$classes3,\n      _params$attributes3 = params.attributes,\n      attributes = _params$attributes3 === void 0 ? {} : _params$attributes3,\n      _params$styles3 = params.styles,\n      styles = _params$styles3 === void 0 ? {} : _params$styles3;\n  return apiObject({\n    type: 'counter',\n    content: content\n  }, function () {\n    ensureCss();\n    return makeLayersCounterAbstract({\n      content: content.toString(),\n      title: title,\n      extra: {\n        attributes: attributes,\n        styles: styles,\n        classes: [\"\".concat(config.familyPrefix, \"-layers-counter\")].concat(_toConsumableArray(classes))\n      }\n    });\n  });\n};\nvar layer = function layer(assembler) {\n  var params = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {};\n  var _params$classes4 = params.classes,\n      classes = _params$classes4 === void 0 ? [] : _params$classes4;\n  return apiObject({\n    type: 'layer'\n  }, function () {\n    ensureCss();\n    var children = [];\n    assembler(function (args) {\n      Array.isArray(args) ? args.map(function (a) {\n        children = children.concat(a.abstract);\n      }) : children = children.concat(args.abstract);\n    });\n    return [{\n      tag: 'span',\n      attributes: {\n        class: [\"\".concat(config.familyPrefix, \"-layers\")].concat(_toConsumableArray(classes)).join(' ')\n      },\n      children: children\n    }];\n  });\n};\nvar api = {\n  noAuto: noAuto,\n  config: config,\n  dom: dom,\n  library: library,\n  parse: parse,\n  findIconDefinition: findIconDefinition,\n  icon: icon,\n  text: text,\n  counter: counter,\n  layer: layer,\n  toHtml: toHtml\n};\n\nvar autoReplace = function autoReplace() {\n  var params = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : {};\n  var _params$autoReplaceSv = params.autoReplaceSvgRoot,\n      autoReplaceSvgRoot = _params$autoReplaceSv === void 0 ? DOCUMENT : _params$autoReplaceSv;\n  if ((Object.keys(namespace.styles).length > 0 || config.autoFetchSvg) && IS_DOM && config.autoReplaceSvg) api.dom.i2svg({\n    node: autoReplaceSvgRoot\n  });\n};\n\nexport { icon, noAuto, config, toHtml, layer, text, counter, library, dom, parse, findIconDefinition };\n","import style from \"./Box.less\";\n\nexport const BoxColors = Object.freeze({\n    RED: style.red,\n    ORANGE: style.orange,\n    YELLOW: style.yellow,\n    LIME: style.lime,\n    CYAN: style.cyan,\n    BLUE: style.blue,\n    MAGENTA: style.magenta,\n    DEFAULT: style.default\n})\n\nexport default function (props) {\n    let color = BoxColors.DEFAULT;\n    if(props.color) {\n        color = props.color;\n    }\n\n    return (\n        
    \n            {props.children}\n        
    \n    );\n}\n","import Panel from '../components/Elements/Panel';\nimport Section from \"../components/Elements/Section\";\nimport Todo from \"../components/Elements/Todo\";\nimport { FontAwesomeIcon } from '@fortawesome/react-fontawesome'\nimport {faGithub, faTelegram} from \"@fortawesome/free-brands-svg-icons\";\nimport {faExternalLinkAlt} from \"@fortawesome/free-solid-svg-icons\";\n\n\nexport default function(props) {\n    return (\n        
    \n            
    Indice
    \n            
    \n                Apprendimento ed evoluzione in sistemi artificiali}>\n                    
    \n                        Appunti scritti mentre studiavo per l'esame di Apprendimento ed evoluzione in sistemi artificiali del corso triennale di Informatica all'Unimore.\n                    
    \n                    \n                Basi di dati}>\n                    
    \n                        Appunti scritti mentre studiavo per l'esame di Basi di dati del corso triennale di Informatica all'Unimore.\n                    
    \n                    \n                Calcolo Numerico}>\n                    
    \n                        Appunti scritti mentre studiavo per l'esame di Calcolo Numerico del corso triennale di Informatica all'Unimore.\n                    
    \n                    \n                Ottimizzazione lineare intera}>\n                    
    \n                        Appunti scritti mentre studiavo per l'esame di Ottimizzazione lineare intera del corso triennale di Informatica all'Unimore.\n                    
    \n                    \n            
    \n            
    \n                Statistica ed elementi di probabilità}>\n                    
    \n                        Appunti scritti mentre studiavo per l'esame di Statistica ed elementi di probabilità del corso triennale di Informatica all'Unimore del Prof. Luca La Rocca.\n                    
    \n                    \n                 Cleaver}>\n                    
    \n                        Progetto in Java sviluppato per l'esame di Programmazione ad Oggetti del corso triennale di Informatica all'Unimore, tenuto dai Prof. Giacomo Cabri e Nicola Capodieci.\n                    
    \n                    \n                Fisica}>\n                    
    \n                        Appunti delle lezioni di Fisica del corso triennale di Informatica all'Unimore, tenute dalla Prof.ssa Rossella Brunetti nel primo semestre dell'Anno Accademico 2019/2020.\n                    
    \n                    \n                 Sistemi Operativi}>\n                    
    \n                        Soluzioni agli Arzigogoli proposti dal Prof. Mauro Andreolini durante le lezioni di Sistemi Operativi del corso triennale di Informatica all'Unimore tenutesi nel primo semestre dell'Anno Accademico 2019/2020.\n                    
    \n                    \n                Algoritmi e Strutture Dati}>\n                    
    \n                        Appunti delle lezioni di Algoritmi e Strutture Dati del corso triennale di Informatica all'Unimore, tenute dalla Prof.ssa Manuela Montangero nel secondo semestre dell'Anno Accademico 2018/2019.\n                    
    \n                    
    \n                        TODO: finisci di migrare da GitHub!\n                    
    \n                    \n                Videolezioni di Geometria}>\n                    
    \n                        Ottime videolezioni di Geometria con licenza CC BY-NC-SA 4.0 che ho trovato sul portale Dolly 2018 dell'Unimore.\n                    
    \n                    \n                Come installare MinGW}>\n                    
    \n                        Un breve tutorial con immagini su come installare e configurare MinGW per compilare programmi C e C++ su Windows.\n                    
    \n                    \n            
    \n            
    \n                 Unimore Informatica}>\n                    
    \n                        Il gruppo Telegram del corso di Informatica dell'Unimore!\n                    
    \n                    \n                 Calendario Lezioni}>\n                    
    \n                        Calendario Google quasi sempre aggiornato delle lezioni e degli esami del secondo anno dell'Unimore durante l'Anno Accademico 2019/2020.\n                    
    \n                    \n                 Erre2}>\n                    
    \n                        Portale contenente appunti e riassunti mantenuto da Lorenzo Balugani.\n                    
    \n                    \n                 vezzalinistefano/Appunti-Algoritmi}>\n                    
    \n                        Appunti di Algoritmi e Strutture Dati mantenuti da Vezzalini Stefano.\n                    
    \n                    \n            
    \n        
    \n    )\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"splitparent\":\"splitparent__3-wBs\",\"splitchild\":\"splitchild__begkX\"};","import style from \"./Panel.less\";\nimport Box from \"./Box\";\n\nexport default function(props) {\n\treturn (\n\t\t\n\t\t\t
    \n\t\t\t\t{props.title}\n\t\t\t
    \n\t\t\t
    \n\t\t\t\t{props.children}\n\t\t\t
    \n\t\t    \n\t);\n}\n","/**\n * Assign properties from `props` to `obj`\n * @template O, P The obj and props types\n * @param {O} obj The object to copy properties to\n * @param {P} props The object to copy properties from\n * @returns {O & P}\n */\nexport function assign(obj, props) {\n\tfor (let i in props) obj[i] = props[i];\n\treturn /** @type {O & P} */ (obj);\n}\n\n/**\n * Check if two objects have a different shape\n * @param {object} a\n * @param {object} b\n * @returns {boolean}\n */\nexport function shallowDiffers(a, b) {\n\tfor (let i in a) if (i !== '__source' && !(i in b)) return true;\n\tfor (let i in b) if (i !== '__source' && a[i] !== b[i]) return true;\n\treturn false;\n}\n","import { Component, createElement, options } from 'preact';\nimport { assign } from './util';\n\nconst oldCatchError = options._catchError;\noptions._catchError = function(error, newVNode, oldVNode) {\n\tif (error.then) {\n\t\t/** @type {import('./internal').Component} */\n\t\tlet component;\n\t\tlet vnode = newVNode;\n\n\t\tfor (; (vnode = vnode._parent); ) {\n\t\t\tif ((component = vnode._component) && component._childDidSuspend) {\n\t\t\t\t// Don't call oldCatchError if we found a Suspense\n\t\t\t\treturn component._childDidSuspend(error, newVNode._component);\n\t\t\t}\n\t\t}\n\t}\n\toldCatchError(error, newVNode, oldVNode);\n};\n\nfunction detachedClone(vnode) {\n\tif (vnode) {\n\t\tvnode = assign({}, vnode);\n\t\tvnode._component = null;\n\t\tvnode._children = vnode._children && vnode._children.map(detachedClone);\n\t}\n\treturn vnode;\n}\n\n// having custom inheritance instead of a class here saves a lot of bytes\nexport function Suspense() {\n\t// we do not call super here to golf some bytes...\n\tthis._pendingSuspensionCount = 0;\n\tthis._suspenders = null;\n\tthis._detachOnNextRender = null;\n}\n\n// Things we do here to save some bytes but are not proper JS inheritance:\n// - call `new Component()` as the prototype\n// - do not set `Suspense.prototype.constructor` to `Suspense`\nSuspense.prototype = new Component();\n\n/**\n * @param {Promise} promise The thrown promise\n * @param {Component} suspendingComponent The suspending component\n */\nSuspense.prototype._childDidSuspend = function(promise, suspendingComponent) {\n\t/** @type {import('./internal').SuspenseComponent} */\n\tconst c = this;\n\n\tif (c._suspenders == null) {\n\t\tc._suspenders = [];\n\t}\n\tc._suspenders.push(suspendingComponent);\n\n\tconst resolve = suspended(c._vnode);\n\n\tlet resolved = false;\n\tconst onResolved = () => {\n\t\tif (resolved) return;\n\n\t\tresolved = true;\n\n\t\tif (resolve) {\n\t\t\tresolve(onSuspensionComplete);\n\t\t} else {\n\t\t\tonSuspensionComplete();\n\t\t}\n\t};\n\n\tsuspendingComponent._suspendedComponentWillUnmount =\n\t\tsuspendingComponent.componentWillUnmount;\n\tsuspendingComponent.componentWillUnmount = () => {\n\t\tonResolved();\n\n\t\tif (suspendingComponent._suspendedComponentWillUnmount) {\n\t\t\tsuspendingComponent._suspendedComponentWillUnmount();\n\t\t}\n\t};\n\n\tconst onSuspensionComplete = () => {\n\t\tif (!--c._pendingSuspensionCount) {\n\t\t\tc._vnode._children[0] = c.state._suspended;\n\t\t\tc.setState({ _suspended: (c._detachOnNextRender = null) });\n\n\t\t\tlet suspended;\n\t\t\twhile ((suspended = c._suspenders.pop())) {\n\t\t\t\tsuspended.forceUpdate();\n\t\t\t}\n\t\t}\n\t};\n\n\tif (!c._pendingSuspensionCount++) {\n\t\tc.setState({ _suspended: (c._detachOnNextRender = c._vnode._children[0]) });\n\t}\n\tpromise.then(onResolved, onResolved);\n};\n\nSuspense.prototype.render = function(props, state) {\n\tif (this._detachOnNextRender) {\n\t\tthis._vnode._children[0] = detachedClone(this._detachOnNextRender);\n\t\tthis._detachOnNextRender = null;\n\t}\n\n\treturn [\n\t\tcreateElement(Component, null, state._suspended ? null : props.children),\n\t\tstate._suspended && props.fallback\n\t];\n};\n\n/**\n * Checks and calls the parent component's _suspended method, passing in the\n * suspended vnode. This is a way for a parent (e.g. SuspenseList) to get notified\n * that one of its children/descendants suspended.\n *\n * The parent MAY return a callback. The callback will get called when the\n * suspension resolves, notifying the parent of the fact.\n * Moreover, the callback gets function `unsuspend` as a parameter. The resolved\n * child descendant will not actually get unsuspended until `unsuspend` gets called.\n * This is a way for the parent to delay unsuspending.\n *\n * If the parent does not return a callback then the resolved vnode\n * gets unsuspended immediately when it resolves.\n *\n * @param {import('../src/internal').VNode} vnode\n * @returns {((unsuspend: () => void) => void)?}\n */\nexport function suspended(vnode) {\n\tlet component = vnode._parent._component;\n\treturn component && component._suspended && component._suspended(vnode);\n}\n\nexport function lazy(loader) {\n\tlet prom;\n\tlet component;\n\tlet error;\n\n\tfunction Lazy(props) {\n\t\tif (!prom) {\n\t\t\tprom = loader();\n\t\t\tprom.then(\n\t\t\t\texports => {\n\t\t\t\t\tcomponent = exports.default || exports;\n\t\t\t\t},\n\t\t\t\te => {\n\t\t\t\t\terror = e;\n\t\t\t\t}\n\t\t\t);\n\t\t}\n\n\t\tif (error) {\n\t\t\tthrow error;\n\t\t}\n\n\t\tif (!component) {\n\t\t\tthrow prom;\n\t\t}\n\n\t\treturn createElement(component, props);\n\t}\n\n\tLazy.displayName = 'Lazy';\n\tLazy._forwarded = true;\n\treturn Lazy;\n}\n","import { Component, toChildArray } from 'preact';\nimport { suspended } from './suspense.js';\n\n// Indexes to linked list nodes (nodes are stored as arrays to save bytes).\nconst SUSPENDED_COUNT = 0;\nconst RESOLVED_COUNT = 1;\nconst NEXT_NODE = 2;\n\n// Having custom inheritance instead of a class here saves a lot of bytes.\nexport function SuspenseList() {\n\tthis._next = null;\n\tthis._map = null;\n}\n\n// Mark one of child's earlier suspensions as resolved.\n// Some pending callbacks may become callable due to this\n// (e.g. the last suspended descendant gets resolved when\n// revealOrder === 'together'). Process those callbacks as well.\nconst resolve = (list, child, node) => {\n\tif (++node[RESOLVED_COUNT] === node[SUSPENDED_COUNT]) {\n\t\t// The number a child (or any of its descendants) has been suspended\n\t\t// matches the number of times it's been resolved. Therefore we\n\t\t// mark the child as completely resolved by deleting it from ._map.\n\t\t// This is used to figure out when *all* children have been completely\n\t\t// resolved when revealOrder is 'together'.\n\t\tlist._map.delete(child);\n\t}\n\n\t// If revealOrder is falsy then we can do an early exit, as the\n\t// callbacks won't get queued in the node anyway.\n\t// If revealOrder is 'together' then also do an early exit\n\t// if all suspended descendants have not yet been resolved.\n\tif (\n\t\t!list.props.revealOrder ||\n\t\t(list.props.revealOrder[0] === 't' && list._map.size)\n\t) {\n\t\treturn;\n\t}\n\n\t// Walk the currently suspended children in order, calling their\n\t// stored callbacks on the way. Stop if we encounter a child that\n\t// has not been completely resolved yet.\n\tnode = list._next;\n\twhile (node) {\n\t\twhile (node.length > 3) {\n\t\t\tnode.pop()();\n\t\t}\n\t\tif (node[RESOLVED_COUNT] < node[SUSPENDED_COUNT]) {\n\t\t\tbreak;\n\t\t}\n\t\tlist._next = node = node[NEXT_NODE];\n\t}\n};\n\n// Things we do here to save some bytes but are not proper JS inheritance:\n// - call `new Component()` as the prototype\n// - do not set `Suspense.prototype.constructor` to `Suspense`\nSuspenseList.prototype = new Component();\n\nSuspenseList.prototype._suspended = function(child) {\n\tconst list = this;\n\tconst delegated = suspended(list._vnode);\n\n\tlet node = list._map.get(child);\n\tnode[SUSPENDED_COUNT]++;\n\n\treturn unsuspend => {\n\t\tconst wrappedUnsuspend = () => {\n\t\t\tif (!list.props.revealOrder) {\n\t\t\t\t// Special case the undefined (falsy) revealOrder, as there\n\t\t\t\t// is no need to coordinate a specific order or unsuspends.\n\t\t\t\tunsuspend();\n\t\t\t} else {\n\t\t\t\tnode.push(unsuspend);\n\t\t\t\tresolve(list, child, node);\n\t\t\t}\n\t\t};\n\t\tif (delegated) {\n\t\t\tdelegated(wrappedUnsuspend);\n\t\t} else {\n\t\t\twrappedUnsuspend();\n\t\t}\n\t};\n};\n\nSuspenseList.prototype.render = function(props) {\n\tthis._next = null;\n\tthis._map = new Map();\n\n\tconst children = toChildArray(props.children);\n\tif (props.revealOrder && props.revealOrder[0] === 'b') {\n\t\t// If order === 'backwards' (or, well, anything starting with a 'b')\n\t\t// then flip the child list around so that the last child will be\n\t\t// the first in the linked list.\n\t\tchildren.reverse();\n\t}\n\t// Build the linked list. Iterate through the children in reverse order\n\t// so that `_next` points to the first linked list node to be resolved.\n\tfor (let i = children.length; i--; ) {\n\t\t// Create a new linked list node as an array of form:\n\t\t// \t[suspended_count, resolved_count, next_node]\n\t\t// where suspended_count and resolved_count are numeric counters for\n\t\t// keeping track how many times a node has been suspended and resolved.\n\t\t//\n\t\t// Note that suspended_count starts from 1 instead of 0, so we can block\n\t\t// processing callbacks until componentDidMount has been called. In a sense\n\t\t// node is suspended at least until componentDidMount gets called!\n\t\t//\n\t\t// Pending callbacks are added to the end of the node:\n\t\t// \t[suspended_count, resolved_count, next_node, callback_0, callback_1, ...]\n\t\tthis._map.set(children[i], (this._next = [1, 0, this._next]));\n\t}\n\treturn props.children;\n};\n\nSuspenseList.prototype.componentDidUpdate = SuspenseList.prototype.componentDidMount = function() {\n\t// Iterate through all children after mounting for two reasons:\n\t// 1. As each node[SUSPENDED_COUNT] starts from 1, this iteration increases\n\t//    each node[RELEASED_COUNT] by 1, therefore balancing the counters.\n\t//    The nodes can now be completely consumed from the linked list.\n\t// 2. Handle nodes that might have gotten resolved between render and\n\t//    componentDidMount.\n\tconst list = this;\n\tlist._map.forEach((node, child) => {\n\t\tresolve(list, child, node);\n\t});\n};\n","import { createElement, hydrate, render, _unmount } from 'preact';\n\nclass ContextProvider {\n\tgetChildContext() {\n\t\treturn this.props.context;\n\t}\n\trender(props) {\n\t\treturn props.children;\n\t}\n}\n\n/**\n * Portal component\n * @param {object | null | undefined} props\n */\nfunction Portal(props) {\n\tlet _this = this;\n\tlet container = props.container;\n\tlet wrap = createElement(\n\t\tContextProvider,\n\t\t{ context: _this.context },\n\t\tprops.vnode\n\t);\n\n\t// When we change container we should clear our old container and\n\t// indicate a new mount.\n\tif (_this._container && _this._container !== container) {\n\t\tif (_this._temp.parentNode) _this._container.removeChild(_this._temp);\n\t\t_unmount(_this._wrap);\n\t\t_this._hasMounted = false;\n\t}\n\n\t// When props.vnode is undefined/false/null we are dealing with some kind of\n\t// conditional vnode. This should not trigger a render.\n\tif (props.vnode) {\n\t\tif (!_this._hasMounted) {\n\t\t\t// Create a placeholder that we can use to insert into.\n\t\t\t_this._temp = document.createTextNode('');\n\t\t\t// Hydrate existing nodes to keep the dom intact, when rendering\n\t\t\t// wrap into the container.\n\t\t\thydrate('', container);\n\t\t\t// Append to the container (this matches React's behavior)\n\t\t\tcontainer.appendChild(_this._temp);\n\t\t\t// At this point we have mounted and should set our container.\n\t\t\t_this._hasMounted = true;\n\t\t\t_this._container = container;\n\t\t\t// Render our wrapping element into temp.\n\t\t\trender(wrap, container, _this._temp);\n\t\t\t_this._children = _this._temp._children;\n\t\t} else {\n\t\t\t// When we have mounted and the vnode is present it means the\n\t\t\t// props have changed or a parent is triggering a rerender.\n\t\t\t// This implies we only need to call render. But we need to keep\n\t\t\t// the old tree around, otherwise will treat the vnodes as new and\n\t\t\t// will wrongly call `componentDidMount` on them\n\t\t\tcontainer._children = _this._children;\n\t\t\trender(wrap, container);\n\t\t\t_this._children = container._children;\n\t\t}\n\t}\n\t// When we come from a conditional render, on a mounted\n\t// portal we should clear the DOM.\n\telse if (_this._hasMounted) {\n\t\tif (_this._temp.parentNode) _this._container.removeChild(_this._temp);\n\t\t_unmount(_this._wrap);\n\t}\n\t// Set the wrapping element for future unmounting.\n\t_this._wrap = wrap;\n\n\t_this.componentWillUnmount = () => {\n\t\tif (_this._temp.parentNode) _this._container.removeChild(_this._temp);\n\t\t_unmount(_this._wrap);\n\t};\n\n\treturn null;\n}\n\n/**\n * Create a `Portal` to continue rendering the vnode tree at a different DOM node\n * @param {import('./internal').VNode} vnode The vnode to render\n * @param {import('./internal').PreactElement} container The DOM node to continue rendering in to.\n */\nexport function createPortal(vnode, container) {\n\treturn createElement(Portal, { vnode, container });\n}\n","import {\n\trender as preactRender,\n\thydrate as preactHydrate,\n\toptions,\n\ttoChildArray,\n\tComponent\n} from 'preact';\nimport { applyEventNormalization } from './events';\n\nconst CAMEL_PROPS = /^(?:accent|alignment|arabic|baseline|cap|clip(?!PathU)|color|fill|flood|font|glyph(?!R)|horiz|marker(?!H|W|U)|overline|paint|stop|strikethrough|stroke|text(?!L)|underline|unicode|units|v|vector|vert|word|writing|x(?!C))[A-Z]/;\n\n// Some libraries like `react-virtualized` explicitly check for this.\nComponent.prototype.isReactComponent = {};\n\nexport const REACT_ELEMENT_TYPE =\n\t(typeof Symbol != 'undefined' && Symbol.for && Symbol.for('react.element')) ||\n\t0xeac7;\n\n/**\n * Proxy render() since React returns a Component reference.\n * @param {import('./internal').VNode} vnode VNode tree to render\n * @param {import('./internal').PreactElement} parent DOM node to render vnode tree into\n * @param {() => void} [callback] Optional callback that will be called after rendering\n * @returns {import('./internal').Component | null} The root component reference or null\n */\nexport function render(vnode, parent, callback) {\n\t// React destroys any existing DOM nodes, see #1727\n\t// ...but only on the first render, see #1828\n\tif (parent._children == null) {\n\t\twhile (parent.firstChild) {\n\t\t\tparent.removeChild(parent.firstChild);\n\t\t}\n\t}\n\n\tpreactRender(vnode, parent);\n\tif (typeof callback == 'function') callback();\n\n\treturn vnode ? vnode._component : null;\n}\n\nexport function hydrate(vnode, parent, callback) {\n\tpreactHydrate(vnode, parent);\n\tif (typeof callback == 'function') callback();\n\n\treturn vnode ? vnode._component : null;\n}\n\nlet oldEventHook = options.event;\noptions.event = e => {\n\tif (oldEventHook) e = oldEventHook(e);\n\te.persist = () => {};\n\tlet stoppedPropagating = false,\n\t\tdefaultPrevented = false;\n\n\tconst origStopPropagation = e.stopPropagation;\n\te.stopPropagation = () => {\n\t\torigStopPropagation.call(e);\n\t\tstoppedPropagating = true;\n\t};\n\n\tconst origPreventDefault = e.preventDefault;\n\te.preventDefault = () => {\n\t\torigPreventDefault.call(e);\n\t\tdefaultPrevented = true;\n\t};\n\n\te.isPropagationStopped = () => stoppedPropagating;\n\te.isDefaultPrevented = () => defaultPrevented;\n\treturn (e.nativeEvent = e);\n};\n\n// Patch in `UNSAFE_*` lifecycle hooks\nfunction setSafeDescriptor(proto, key) {\n\tif (proto['UNSAFE_' + key] && !proto[key]) {\n\t\tObject.defineProperty(proto, key, {\n\t\t\tconfigurable: false,\n\t\t\tget() {\n\t\t\t\treturn this['UNSAFE_' + key];\n\t\t\t},\n\t\t\t// This `set` is only used if a user sets a lifecycle like cWU\n\t\t\t// after setting a lifecycle like UNSAFE_cWU. I doubt anyone\n\t\t\t// actually does this in practice so not testing it\n\t\t\t/* istanbul ignore next */\n\t\t\tset(v) {\n\t\t\t\tthis['UNSAFE_' + key] = v;\n\t\t\t}\n\t\t});\n\t}\n}\n\nlet classNameDescriptor = {\n\tconfigurable: true,\n\tget() {\n\t\treturn this.class;\n\t}\n};\n\nlet oldVNodeHook = options.vnode;\noptions.vnode = vnode => {\n\tvnode.$$typeof = REACT_ELEMENT_TYPE;\n\n\tlet type = vnode.type;\n\tlet props = vnode.props;\n\n\tif (type) {\n\t\t// Alias `class` prop to `className` if available\n\t\tif (props.class != props.className) {\n\t\t\tclassNameDescriptor.enumerable = 'className' in props;\n\t\t\tif (props.className != null) props.class = props.className;\n\t\t\tObject.defineProperty(props, 'className', classNameDescriptor);\n\t\t}\n\n\t\t// Apply DOM VNode compat\n\t\tif (typeof type != 'function') {\n\t\t\t// Apply defaultValue to value\n\t\t\tif (props.defaultValue && props.value !== undefined) {\n\t\t\t\tif (!props.value && props.value !== 0) {\n\t\t\t\t\tprops.value = props.defaultValue;\n\t\t\t\t}\n\t\t\t\tdelete props.defaultValue;\n\t\t\t}\n\n\t\t\t// Add support for array select values: \n\t\t\tif (Array.isArray(props.value) && props.multiple && type === 'select') {\n\t\t\t\ttoChildArray(props.children).forEach(child => {\n\t\t\t\t\tif (props.value.indexOf(child.props.value) != -1) {\n\t\t\t\t\t\tchild.props.selected = true;\n\t\t\t\t\t}\n\t\t\t\t});\n\t\t\t\tdelete props.value;\n\t\t\t}\n\n\t\t\t// Normalize DOM vnode properties.\n\t\t\tlet shouldSanitize, attrs, i;\n\t\t\tfor (i in props) if ((shouldSanitize = CAMEL_PROPS.test(i))) break;\n\t\t\tif (shouldSanitize) {\n\t\t\t\tattrs = vnode.props = {};\n\t\t\t\tfor (i in props) {\n\t\t\t\t\tattrs[\n\t\t\t\t\t\tCAMEL_PROPS.test(i) ? i.replace(/[A-Z0-9]/, '-$&').toLowerCase() : i\n\t\t\t\t\t] = props[i];\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t\t// Events\n\t\tapplyEventNormalization(vnode);\n\n\t\t// Component base class compat\n\t\t// We can't just patch the base component class, because components that use\n\t\t// inheritance and are transpiled down to ES5 will overwrite our patched\n\t\t// getters and setters. See #1941\n\t\tif (\n\t\t\ttypeof type == 'function' &&\n\t\t\t!type._patchedLifecycles &&\n\t\t\ttype.prototype\n\t\t) {\n\t\t\tsetSafeDescriptor(type.prototype, 'componentWillMount');\n\t\t\tsetSafeDescriptor(type.prototype, 'componentWillReceiveProps');\n\t\t\tsetSafeDescriptor(type.prototype, 'componentWillUpdate');\n\t\t\ttype._patchedLifecycles = true;\n\t\t}\n\t}\n\n\tif (oldVNodeHook) oldVNodeHook(vnode);\n};\n","import { Component } from 'preact';\nimport { shallowDiffers } from './util';\n\n/**\n * Component class with a predefined `shouldComponentUpdate` implementation\n */\nexport class PureComponent extends Component {\n\tconstructor(props) {\n\t\tsuper(props);\n\t\t// Some third-party libraries check if this property is present\n\t\tthis.isPureReactComponent = true;\n\t}\n\n\tshouldComponentUpdate(props, state) {\n\t\treturn (\n\t\t\tshallowDiffers(this.props, props) || shallowDiffers(this.state, state)\n\t\t);\n\t}\n}\n","import { options } from 'preact';\nimport { assign } from './util';\n\nlet oldDiffHook = options._diff;\noptions._diff = vnode => {\n\tif (vnode.type && vnode.type._forwarded && vnode.ref) {\n\t\tvnode.props.ref = vnode.ref;\n\t\tvnode.ref = null;\n\t}\n\tif (oldDiffHook) oldDiffHook(vnode);\n};\n\nexport const REACT_FORWARD_SYMBOL =\n\t(typeof Symbol != 'undefined' &&\n\t\tSymbol.for &&\n\t\tSymbol.for('react.forward_ref')) ||\n\t0xf47;\n\n/**\n * Pass ref down to a child. This is mainly used in libraries with HOCs that\n * wrap components. Using `forwardRef` there is an easy way to get a reference\n * of the wrapped component instead of one of the wrapper itself.\n * @param {import('./index').ForwardFn} fn\n * @returns {import('./internal').FunctionalComponent}\n */\nexport function forwardRef(fn) {\n\t// We always have ref in props.ref, except for\n\t// mobx-react. It will call this function directly\n\t// and always pass ref as the second argument.\n\tfunction Forwarded(props, ref) {\n\t\tlet clone = assign({}, props);\n\t\tdelete clone.ref;\n\t\treturn fn(clone, props.ref || ref);\n\t}\n\n\t// mobx-react checks for this being present\n\tForwarded.$$typeof = REACT_FORWARD_SYMBOL;\n\t// mobx-react heavily relies on implementation details.\n\t// It expects an object here with a `render` property,\n\t// and prototype.render will fail. Without this\n\t// mobx-react throws.\n\tForwarded.render = Forwarded;\n\n\tForwarded.prototype.isReactComponent = Forwarded._forwarded = true;\n\tForwarded.displayName = 'ForwardRef(' + (fn.displayName || fn.name) + ')';\n\treturn Forwarded;\n}\n","import { toChildArray } from 'preact';\n\nconst mapFn = (children, fn) => {\n\tif (!children) return null;\n\treturn toChildArray(children).reduce(\n\t\t(acc, value, index) => acc.concat(fn(value, index)),\n\t\t[]\n\t);\n};\n\n// This API is completely unnecessary for Preact, so it's basically passthrough.\nexport const Children = {\n\tmap: mapFn,\n\tforEach: mapFn,\n\tcount(children) {\n\t\treturn children ? toChildArray(children).length : 0;\n\t},\n\tonly(children) {\n\t\tchildren = toChildArray(children);\n\t\tif (children.length !== 1) {\n\t\t\tthrow new Error('Children.only() expects only one child.');\n\t\t}\n\t\treturn children[0];\n\t},\n\ttoArray: toChildArray\n};\n","/**\n * Normalize event handlers like react does. Most famously it uses `onChange` for any input element.\n * @param {import('./internal').VNode} vnode The vnode to normalize events on\n */\nexport function applyEventNormalization({ type, props }) {\n\tif (!props || typeof type != 'string') return;\n\tlet newProps = {};\n\n\tfor (let i in props) {\n\t\tif (/^on(Ani|Tra|Tou)/.test(i)) {\n\t\t\tprops[i.toLowerCase()] = props[i];\n\t\t\tdelete props[i];\n\t\t}\n\t\tnewProps[i.toLowerCase()] = i;\n\t}\n\tif (newProps.ondoubleclick) {\n\t\tprops.ondblclick = props[newProps.ondoubleclick];\n\t\tdelete props[newProps.ondoubleclick];\n\t}\n\tif (newProps.onbeforeinput) {\n\t\tprops.onbeforeinput = props[newProps.onbeforeinput];\n\t\tdelete props[newProps.onbeforeinput];\n\t}\n\t// for *textual inputs* (incl textarea), normalize `onChange` -> `onInput`:\n\tif (\n\t\tnewProps.onchange &&\n\t\t(type === 'textarea' ||\n\t\t\t(type.toLowerCase() === 'input' && !/^fil|che|ra/i.test(props.type)))\n\t) {\n\t\tlet normalized = newProps.oninput || 'oninput';\n\t\tif (!props[normalized]) {\n\t\t\tprops[normalized] = props[newProps.onchange];\n\t\t\tdelete props[newProps.onchange];\n\t\t}\n\t}\n}\n","import { createElement } from 'preact';\nimport { shallowDiffers } from './util';\n\n/**\n * Memoize a component, so that it only updates when the props actually have\n * changed. This was previously known as `React.pure`.\n * @param {import('./internal').FunctionalComponent} c functional component\n * @param {(prev: object, next: object) => boolean} [comparer] Custom equality function\n * @returns {import('./internal').FunctionalComponent}\n */\nexport function memo(c, comparer) {\n\tfunction shouldUpdate(nextProps) {\n\t\tlet ref = this.props.ref;\n\t\tlet updateRef = ref == nextProps.ref;\n\t\tif (!updateRef && ref) {\n\t\t\tref.call ? ref(null) : (ref.current = null);\n\t\t}\n\n\t\tif (!comparer) {\n\t\t\treturn shallowDiffers(this.props, nextProps);\n\t\t}\n\n\t\treturn !comparer(this.props, nextProps) || !updateRef;\n\t}\n\n\tfunction Memoed(props) {\n\t\tthis.shouldComponentUpdate = shouldUpdate;\n\t\treturn createElement(c, props);\n\t}\n\tMemoed.prototype.isReactComponent = true;\n\tMemoed.displayName = 'Memo(' + (c.displayName || c.name) + ')';\n\tMemoed._forwarded = true;\n\treturn Memoed;\n}\n"],"sourceRoot":""}
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+++ /dev/null
@@ -1,2 +0,0 @@
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    Come installare MinGW
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    \"\"/\n\t\t\t\t\t
     Aspettate che finisca il download. Pochi secondi dopo, dovrebbe finire e dovrebbe apparire un tasto\n\t\t\t\t\t\tContinue. Premetelo.
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     Dovrebbe apparirvi questa finestra. L'installer di MinGW è una specie di gestore pacchetti (tipo apt su\n\t\t\t\t\t\tUbuntu); potete scegliere quali pacchetti installare, e quindi quali funzionalità.
    \"\"/\n\t\t\t\t\t
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    \"\"/\n\t\t\t\t\t
     Ora, è il momento di installare i pacchetti. Aprite il menù Installation, poi premete\n\t\t\t\t\t\tApply Changes, e di nuovo Apply.
    \"\"/\n\t\t\t\t\t
     Lasciate che scarichi, ci vorrà un po'. Guardatevi un video nel frattempo, fatevi una partitina a qualcosa, tornate\n\t\t\t\t\t\tdopo circa 10 minuti.
    \"\"/\n\t\t\t\t\t
     Una volta installato, dobbiamo aggiungere g++ ai programmi eseguibili da Prompt dei Comandi: premete il\n\t\t\t\t\t\ttasto Windows, e scrivete PATH. Windows dovrebbe trovarvi automaticamente quell'opzione.
    \n\t\t\t\t\t\"\"/\n\t\t\t\t\t
     Dentro la finestra di Proprietà del Sistema, premete Variabili d'ambiente.
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     Trovate la variabile d'ambiente globale Path, e fateci doppio click per modificarla.
    \"\"/\n\t\t\t\t\t
     Ora dovreste vedere l'elenco di tutte le cartelle contenenti programmi eseguibili da terminale: dobbiamo aggiungere\n\t\t\t\t\t\tquella di MinGW! Premete Sfoglia.
    \"\"/\n\t\t\t\t\t
     Trovate la cartella in cui avete installato MinGW (vi avevo detto di ricordarvela!); entrateci, poi selezionate la\n\t\t\t\t\t\tsottocartella bin e premete OK su tutte le finestre che avete aperto fino ad ora,\n\t\t\t\t\t\tchiudendole.
    \n\t\t\t\t\t
     Complimenti! Avete installato MinGW e potete compilare programmi C e C++ da Windows! Avete a disposizione\n\t\t\t\t\t\tgcc e g++ sul Prompt dei Comandi, e potete finalmente creare dei file .exe! 
    \n\t\t\t\t    \n\t\t\t
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    \n    );\n}\n","import style from \"./Panel.less\";\nimport Box from \"./Box\";\n\nexport default function(props) {\n\treturn (\n\t\t\n\t\t\t
    \n\t\t\t\t{props.title}\n\t\t\t
    \n\t\t\t
    \n\t\t\t\t{props.children}\n\t\t\t
    \n\t\t    \n\t);\n}\n","import { Component } from 'preact';\nimport Panel from '../components/Elements/Panel';\n\nexport default class MingwInstall extends Component {\n\trender() {\n\t\t//Imported from unimore-info-wiki\n\t\treturn (\n\t\t\t
    \n                
    Come installare MinGW
    \n                \n\t\t\t\t\t
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    \"\"/\n\t\t\t\t\t
     Aspettate che finisca il download. Pochi secondi dopo, dovrebbe finire e dovrebbe apparire un tasto\n\t\t\t\t\t\tContinue. Premetelo.
    \"\"/\n\t\t\t\t\t
     Dovrebbe apparirvi questa finestra. L'installer di MinGW è una specie di gestore pacchetti (tipo apt su\n\t\t\t\t\t\tUbuntu); potete scegliere quali pacchetti installare, e quindi quali funzionalità.
    \"\"/\n\t\t\t\t\t
     Nel nostro caso, dovrebbero servirci mingw32-base-bin (per il C e alcune librerie C++) e\n\t\t\t\t\t\tmingw32-gcc-g++-bin (per il C++). Cliccate, quindi, sui due quadratini corrispondenti, e premete\n\t\t\t\t\t\tMark for Installation. Dovrebbe comparire una freccia gialla sul quadratino.
    \"\"/\n\t\t\t\t\t
     Ora, è il momento di installare i pacchetti. Aprite il menù Installation, poi premete\n\t\t\t\t\t\tApply Changes, e di nuovo Apply.
    \"\"/\n\t\t\t\t\t
     Lasciate che scarichi, ci vorrà un po'. Guardatevi un video nel frattempo, fatevi una partitina a qualcosa, tornate\n\t\t\t\t\t\tdopo circa 10 minuti.
    \"\"/\n\t\t\t\t\t
     Una volta installato, dobbiamo aggiungere g++ ai programmi eseguibili da Prompt dei Comandi: premete il\n\t\t\t\t\t\ttasto Windows, e scrivete PATH. Windows dovrebbe trovarvi automaticamente quell'opzione.
    \n\t\t\t\t\t\"\"/\n\t\t\t\t\t
     Dentro la finestra di Proprietà del Sistema, premete Variabili d'ambiente.
    \"\"/\n\t\t\t\t\t
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    \"\"/\n\t\t\t\t\t
     Ora dovreste vedere l'elenco di tutte le cartelle contenenti programmi eseguibili da terminale: dobbiamo aggiungere\n\t\t\t\t\t\tquella di MinGW! Premete Sfoglia.
    \"\"/\n\t\t\t\t\t
     Trovate la cartella in cui avete installato MinGW (vi avevo detto di ricordarvela!); entrateci, poi selezionate la\n\t\t\t\t\t\tsottocartella bin e premete OK su tutte le finestre che avete aperto fino ad ora,\n\t\t\t\t\t\tchiudendole.
    \n\t\t\t\t\t
     Complimenti! Avete installato MinGW e potete compilare programmi C e C++ da Windows! Avete a disposizione\n\t\t\t\t\t\tgcc e g++ sul Prompt dei Comandi, e potete finalmente creare dei file .exe! 
    \n\t\t\t\t    \n\t\t\t
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diff --git a/docs/route-NetLogo.chunk.6c63d.esm.js b/docs/route-NetLogo.chunk.6c63d.esm.js
new file mode 100644
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+                        back 10
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+                        right 10
+                    `))))))}}.call(this,a("hosL").h)}}]);
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similarity index 68%
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                             \end{cases}
-                        `)))),l(o.a,null,"Serve solo nella teoria per dimostrare che le forme sono equivalenti.")),l(a.a,{title:"Canonica e standard"},l("p",null,"Aggiungi una ",l("i",null,"variabile slack")," ",l(t.b,null,Sl(el||(el=Il`s`)))," ",l("b",null,"non-vincolata")," a ogni disequazione nel sistema:"),l("p",null,l(t.b,{inline:!1},Sl(tl||(tl=Il`
+                        `)))),l(o.a,null,"Serve solo nella teoria per dimostrare che le forme sono equivalenti.")),l(a.a,{title:"Canonica e standard"},l("p",null,"Aggiungi una ",l("i",null,"variabile slack")," ",l(t.b,null,yl(el||(el=Il`s`)))," ",l("b",null,"non-vincolata")," a ogni disequazione nel sistema:"),l("p",null,l(t.b,{inline:!1},yl(tl||(tl=Il`
                             a \leq b \Leftrightarrow a + s = b
-                        `)))),l("p",null,l(t.b,{inline:!1},Sl(al||(al=Il`
+                        `)))),l("p",null,l(t.b,{inline:!1},yl(al||(al=Il`
                             a \geq b \Leftrightarrow a - s = b
-                        `))))),l(a.a,{title:"Generale e canonica"},l("p",null,"Sdoppia ogni variabile non-vincolata in due variabili con vincolo di non-negatività:"),l("p",null,l(t.b,{inline:!1},Sl(ol||(ol=Il`\begin{cases}
+                        `))))),l(a.a,{title:"Generale e canonica"},l("p",null,"Sdoppia ogni variabile non-vincolata in due variabili con vincolo di non-negatività:"),l("p",null,l(t.b,{inline:!1},yl(ol||(ol=Il`\begin{cases}
                             a = a^+ - a^-\\
                             a^+ \geq 0\\
                             a^- \geq 0
-                        \end{cases}`)))))),l(e.a,{title:"La forma standard"},l(a.a,{title:"Tableau"},l("p",null,"Un modo per rappresentare sistemi in forma standard, anche noto come ",l("b",null,"matrice equivalente completa")," del sistema."),l(o.a,null,"Il sistema:",l("br",null),l("br",null),l(t.b,{inline:!1},Sl(ul||(ul=Il`
+                        \end{cases}`)))))),l(e.a,{title:"La forma standard"},l(a.a,{title:"Tableau"},l("p",null,"Un modo per rappresentare sistemi in forma standard, anche noto come ",l("b",null,"matrice equivalente completa")," del sistema."),l(o.a,null,"Il sistema:",l("br",null),l("br",null),l(t.b,{inline:!1},yl(ul||(ul=Il`
                             \begin{cases}
                             2000x_1 + 1000x_2 = z\\
                             1x_1 \leq 3\\
                             1x_2 \leq 3\\
                             2x_1 + 2x_2 \leq 7
                             \end{cases}
-                        `))),l("br",null),l("br",null),"Diventa il tableau:",l("br",null),l("br",null),l("table",{class:"right"},l("thead",null,l("tr",null,l("th",null,l("abbr",{title:"Termine noto"},"TN")),l("th",null,l(t.b,null,"x_1")),l("th",null,l(t.b,null,"x_2")),l("th",null,l(t.b,null,"s_1")),l("th",null,l(t.b,null,"s_2")))),l("tbody",null,l("tr",null,l("td",null,l(t.b,null,"z")),l("td",null,l(t.b,null,"2000")),l("td",null,l(t.b,null,"1000")),l("td",null,l(t.b,null,"0")),l("td",null,l(t.b,null,"0"))),l("tr",null,l("td",null,l(t.b,null,"3")),l("td",null,l(t.b,null,"1")),l("td",null,l(t.b,null,"0")),l("td",null,l(t.b,null,"1")),l("td",null,l(t.b,null,"0"))),l("tr",null,l("td",null,l(t.b,null,"3")),l("td",null,l(t.b,null,"0")),l("td",null,l(t.b,null,"1")),l("td",null,l(t.b,null,"0")),l("td",null,l(t.b,null,"1"))),l("tr",null,l("td",null,l(t.b,null,"7")),l("td",null,l(t.b,null,"2")),l("td",null,l(t.b,null,"2")),l("td",null,l(t.b,null,"0")),l("td",null,l(t.b,null,"0"))))))),l(a.a,{title:"Variabili nella base"},l("p",null,"Variabili che hanno ",l("b",null,"tutti 0 e un solo 1")," nella loro colonna del tableau."),l("p",null,"La loro controparte sono le ",l("i",null,"variabili fuori base"),", che hanno qualsiasi altro valore."))),l(e.a,{title:"Simplex primale"},l(a.a,{title:"Cos'è?"},l("p",null,"Un algoritmo per ",l(d.a,null,"minimizzare"),"/",l(b.a,null,"massimizzare")," trovare efficientemente ",l("b",null,"valore ottimo")," di problemi di ottimizzazione lineare, derivato da Gauss-Jordan."),l("p",null,"Da esso si può anche ricavare un ",l("b",null,"vertice ottimo ammissibile"),".",l("br",null),"C'è la possibilità che ne esistano anche altri: quello ottenuto dipende da come è stata effettuata la scelta delle variabili entranti."),l(o.a,null,"E' spiegato in modo semplice ",l("a",{href:"https://web.archive.org/web/20200523052252/https://www.cs.cmu.edu/~15451-f17/handouts/simplex.pdf"},"qui"),", e ci sono dei codici sorgenti di esempio ",l("a",{href:"https://www.cs.cmu.edu/~15451-f17/handouts/simplexcodes/"},"qui"),"."),l(o.a,{title:"Esempio"},l("p",null,l("a",{href:"https://i.imgur.com/1r405Mb.jpg"},"Questa")," è la soluzione passo per passo del problema 3 del file ",l("a",{href:"https://dolly.fim.unimore.it/2019/mod/resource/view.php?id=2716"},l("code",null,"Ex_LP_testo")),"."))),l(a.a,{title:"I passi"},l("ol",null,l("li",null,"Trasforma il sistema in ",l("b",null,"forma standard"),"."),l("li",null,"Trova tante variabili ",l("b",null,"linearmente indipendenti")," quante siano le righe: esse saranno la ",l("i",null,"base iniziale"),"."),l("li",null,"Finchè ci sono variabili con coefficienti ",l(d.a,null,"positivi"),"/",l(b.a,null,"negativi")," nella funzione obiettivo:",l("ol",null,l("li",null,l("b",null,"Scegli")," la prima variabile fuori base con coefficiente ",l(d.a,null,"positivo"),"/",l(b.a,null,"negativo")," nella funzione obiettivo: essa è la ",l("i",null,"variabile entrante"),".",l("br",null),l("aside",null,l("i",null,"Regola di Bland"),": Si potrebbe scegliere qualsiasi variabile come entrante, ma scegliendo sempre la prima ammissibile ci si assicura che l'algoritmo termini.")),l("li",null,l("b",null,"Scegli")," la variabile in base con il minor rapporto positivo ",l(t.b,null,Sl(rl||(rl=Il`\frac{termine\ noto}{coeff.\ variabile\ entrante}`))),".",l("aside",null,"Se non sei riuscito a trovare nessuna variabile con un rapporto positivo, significa che il poliedro è ",l(c.a,null),".")),l("li",null,l("u",null,"Pivot"),": ",l("b",null,"riscrivi")," tutte le funzioni del sistema in termini della variabile entrante."))),l("li",null,"Il poliedro è ",l(p.a,null),": i ",l("b",null,"termini noti dei vincoli")," sono le coordinate del suo vertice ottimo, mentre il ",l("b",null,"termine noto della funzione obiettivo")," è il valore ottimo.")),l(o.a,null,"È praticamente l'algoritmo di Gauss-Jordan applicato al tableau, con delle regole aggiuntive per la decisione delle variabili di pivot.")),l(a.a,{title:"Soluzioni di base degenerata"},l("p",null,"Una soluzione con almeno una variabile di valore ",l(t.b,null,"0"),", dovuta a uno o più ",l("b",null,"vincoli ridondanti"),"."),l("p",null,"Senza ",l("b",null,"Regola di Bland")," e in presenza di vincoli ridondanti si rischia di trovarsi a fare pivot infiniti."))),l(e.a,{title:"Metodo delle due fasi"},l(a.a,{title:"Metodo delle due fasi"},l("p",null,"Un estensione del Simplex per permettere la risoluzione di problemi la cui origine non è una soluzione ammissibile."),l("p",null,"Prevede l'introduzione di un ",l("i",null,"problema ausiliario"),", le cui incognite sono dette ",l("i",null,"artificiali"),"."),l("p",null,"Il vettore delle incognite artificiali è solitamente chiamato ",l(t.b,null,Sl(sl||(sl=Il`\mathbf{y}`))),"."),l(o.a,null,"E' spiegato in modo semplice ",l("a",{href:"https://web.archive.org/web/20200523052252/https://www.cs.cmu.edu/~15451-f17/handouts/simplex.pdf"},"qui"),".")),l(a.a,{title:"Procedimento"},l("ol",null,l("li",null,"Crea un nuovo tableau, ",l("b",null,"aggiungendo variabili artificiali")," in modo da avere una base ammissibile."),l("li",null,"Sostituisci la vecchia funzione obiettivo con una nuova che ",l("b",null,"minimizzi la somma")," di tutte le variabili artificiali."),l("li",null,l("u",null,"Fase 1"),": ",l("b",null,"Risolvi")," il nuovo problema con il simplex primale."),l("li",null,"Se il Simplex termina quando ci sono ancora ",l("b",null,"variabili artificiali nella base"),", allora il poliedro è ",l("b",null,l(s.a,null)),"."),l("li",null,"Una volta che le variabili artificiali sono fuori base, ",l("b",null,"elimina")," le loro colonne e la nuova funzione obiettivo.",l("br",null)),l("li",null,"Riporta il tableau in forma base compiendo operazioni per ",l("b",null,"azzerare i coefficienti")," delle variabili di base nella funzione obiettivo."),l("li",null,l("u",null,"Fase 2"),": ",l("b",null,"Risolvi")," il tableau con il simplex primale.")))),l(e.a,{title:"Rilassamento"},l(a.a,{title:"Cos'è?"},l("p",null,"Una versione semplificata di un problema nella quale si ",l("b",null,"ignora la violazione")," di uno o più vincoli.")),l(a.a,{title:"Rilassamento di Lagrange"},l("p",null,"Un rilassamento che permette di misurare ",l("b",null,"di quanto i vincoli vengono violati"),"."),l("p",null,"I vincoli, moltiplicati per ",l("b",null,"coefficienti di rilassamento"),", vengono inseriti nella funzione obiettivo."),l("p",null,"Il vettore dei coefficienti di rilassamento solitamente è indicato con ",l(t.b,null,Sl(cl||(cl=Il`\mathbf{u}`))),"."),l(o.a,null,l("p",null,"Il sistema:"),l(t.b,{inline:!1},Sl(dl||(dl=Il`
+                        `))),l("br",null),l("br",null),"Diventa il tableau:",l("br",null),l("br",null),l("table",{class:"right"},l("thead",null,l("tr",null,l("th",null,l("abbr",{title:"Termine noto"},"TN")),l("th",null,l(t.b,null,"x_1")),l("th",null,l(t.b,null,"x_2")),l("th",null,l(t.b,null,"s_1")),l("th",null,l(t.b,null,"s_2")))),l("tbody",null,l("tr",null,l("td",null,l(t.b,null,"z")),l("td",null,l(t.b,null,"2000")),l("td",null,l(t.b,null,"1000")),l("td",null,l(t.b,null,"0")),l("td",null,l(t.b,null,"0"))),l("tr",null,l("td",null,l(t.b,null,"3")),l("td",null,l(t.b,null,"1")),l("td",null,l(t.b,null,"0")),l("td",null,l(t.b,null,"1")),l("td",null,l(t.b,null,"0"))),l("tr",null,l("td",null,l(t.b,null,"3")),l("td",null,l(t.b,null,"0")),l("td",null,l(t.b,null,"1")),l("td",null,l(t.b,null,"0")),l("td",null,l(t.b,null,"1"))),l("tr",null,l("td",null,l(t.b,null,"7")),l("td",null,l(t.b,null,"2")),l("td",null,l(t.b,null,"2")),l("td",null,l(t.b,null,"0")),l("td",null,l(t.b,null,"0"))))))),l(a.a,{title:"Variabili nella base"},l("p",null,"Variabili che hanno ",l("b",null,"tutti 0 e un solo 1")," nella loro colonna del tableau."),l("p",null,"La loro controparte sono le ",l("i",null,"variabili fuori base"),", che hanno qualsiasi altro valore."))),l(e.a,{title:"Simplex primale"},l(a.a,{title:"Cos'è?"},l("p",null,"Un algoritmo per ",l(d.a,null,"minimizzare"),"/",l(b.a,null,"massimizzare")," trovare efficientemente ",l("b",null,"valore ottimo")," di problemi di ottimizzazione lineare, derivato da Gauss-Jordan."),l("p",null,"Da esso si può anche ricavare un ",l("b",null,"vertice ottimo ammissibile"),".",l("br",null),"C'è la possibilità che ne esistano anche altri: quello ottenuto dipende da come è stata effettuata la scelta delle variabili entranti."),l(o.a,null,"E' spiegato in modo semplice ",l("a",{href:"https://web.archive.org/web/20200523052252/https://www.cs.cmu.edu/~15451-f17/handouts/simplex.pdf"},"qui"),", e ci sono dei codici sorgenti di esempio ",l("a",{href:"https://www.cs.cmu.edu/~15451-f17/handouts/simplexcodes/"},"qui"),"."),l(o.a,{title:"Esempio"},l("p",null,l("a",{href:"https://i.imgur.com/1r405Mb.jpg"},"Questa")," è la soluzione passo per passo del problema 3 del file ",l("a",{href:"https://dolly.fim.unimore.it/2019/mod/resource/view.php?id=2716"},l("code",null,"Ex_LP_testo")),"."))),l(a.a,{title:"I passi"},l("ol",null,l("li",null,"Trasforma il sistema in ",l("b",null,"forma standard"),"."),l("li",null,"Trova tante variabili ",l("b",null,"linearmente indipendenti")," quante siano le righe: esse saranno la ",l("i",null,"base iniziale"),"."),l("li",null,"Finchè ci sono variabili con coefficienti ",l(d.a,null,"positivi"),"/",l(b.a,null,"negativi")," nella funzione obiettivo:",l("ol",null,l("li",null,l("b",null,"Scegli")," la prima variabile fuori base con coefficiente ",l(d.a,null,"positivo"),"/",l(b.a,null,"negativo")," nella funzione obiettivo: essa è la ",l("i",null,"variabile entrante"),".",l("br",null),l("aside",null,l("i",null,"Regola di Bland"),": Si potrebbe scegliere qualsiasi variabile come entrante, ma scegliendo sempre la prima ammissibile ci si assicura che l'algoritmo termini.")),l("li",null,l("b",null,"Scegli")," la variabile in base con il minor rapporto positivo ",l(t.b,null,yl(rl||(rl=Il`\frac{termine\ noto}{coeff.\ variabile\ entrante}`))),".",l("aside",null,"Se non sei riuscito a trovare nessuna variabile con un rapporto positivo, significa che il poliedro è ",l(c.a,null),".")),l("li",null,l("u",null,"Pivot"),": ",l("b",null,"riscrivi")," tutte le funzioni del sistema in termini della variabile entrante."))),l("li",null,"Il poliedro è ",l(p.a,null),": i ",l("b",null,"termini noti dei vincoli")," sono le coordinate del suo vertice ottimo, mentre il ",l("b",null,"termine noto della funzione obiettivo")," è il valore ottimo.")),l(o.a,null,"È praticamente l'algoritmo di Gauss-Jordan applicato al tableau, con delle regole aggiuntive per la decisione delle variabili di pivot.")),l(a.a,{title:"Soluzioni di base degenerata"},l("p",null,"Una soluzione con almeno una variabile di valore ",l(t.b,null,"0"),", dovuta a uno o più ",l("b",null,"vincoli ridondanti"),"."),l("p",null,"Senza ",l("b",null,"Regola di Bland")," e in presenza di vincoli ridondanti si rischia di trovarsi a fare pivot infiniti."))),l(e.a,{title:"Metodo delle due fasi"},l(a.a,{title:"Metodo delle due fasi"},l("p",null,"Un estensione del Simplex per permettere la risoluzione di problemi la cui origine non è una soluzione ammissibile."),l("p",null,"Prevede l'introduzione di un ",l("i",null,"problema ausiliario"),", le cui incognite sono dette ",l("i",null,"artificiali"),"."),l("p",null,"Il vettore delle incognite artificiali è solitamente chiamato ",l(t.b,null,yl(sl||(sl=Il`\mathbf{y}`))),"."),l(o.a,null,"E' spiegato in modo semplice ",l("a",{href:"https://web.archive.org/web/20200523052252/https://www.cs.cmu.edu/~15451-f17/handouts/simplex.pdf"},"qui"),".")),l(a.a,{title:"Procedimento"},l("ol",null,l("li",null,"Crea un nuovo tableau, ",l("b",null,"aggiungendo variabili artificiali")," in modo da avere una base ammissibile."),l("li",null,"Sostituisci la vecchia funzione obiettivo con una nuova che ",l("b",null,"minimizzi la somma")," di tutte le variabili artificiali."),l("li",null,l("u",null,"Fase 1"),": ",l("b",null,"Risolvi")," il nuovo problema con il simplex primale."),l("li",null,"Se il Simplex termina quando ci sono ancora ",l("b",null,"variabili artificiali nella base"),", allora il poliedro è ",l("b",null,l(s.a,null)),"."),l("li",null,"Una volta che le variabili artificiali sono fuori base, ",l("b",null,"elimina")," le loro colonne e la nuova funzione obiettivo.",l("br",null)),l("li",null,"Riporta il tableau in forma base compiendo operazioni per ",l("b",null,"azzerare i coefficienti")," delle variabili di base nella funzione obiettivo."),l("li",null,l("u",null,"Fase 2"),": ",l("b",null,"Risolvi")," il tableau con il simplex primale.")))),l(e.a,{title:"Rilassamento"},l(a.a,{title:"Cos'è?"},l("p",null,"Una versione semplificata di un problema nella quale si ",l("b",null,"ignora la violazione")," di uno o più vincoli.")),l(a.a,{title:"Rilassamento di Lagrange"},l("p",null,"Un rilassamento che permette di misurare ",l("b",null,"di quanto i vincoli vengono violati"),"."),l("p",null,"I vincoli, moltiplicati per ",l("b",null,"coefficienti di rilassamento"),", vengono inseriti nella funzione obiettivo."),l("p",null,"Il vettore dei coefficienti di rilassamento solitamente è indicato con ",l(t.b,null,yl(cl||(cl=Il`\mathbf{u}`))),"."),l(o.a,null,l("p",null,"Il sistema:"),l(t.b,{inline:!1},yl(dl||(dl=Il`
                             \begin{cases}
                             z = 3 x_1 + 5 x_2\\
                             2 x_1 + 3 x_2 \geq 12\\
@@ -26,11 +26,11 @@
                             x_1 \geq 0\\
                             x_2 \geq 0
                             \end{cases}
-                        `))),l("p",null,"diventa:"),l(t.b,{inline:!1},Sl(bl||(bl=Il`
+                        `))),l("p",null,"diventa:"),l(t.b,{inline:!1},yl(bl||(bl=Il`
                             \begin{cases}
                             z = 3 x_1 + 5 x_2 + u_1 ( 12 - 2 x_1 - 3 x_2 ) + u_2 ( 3 + x_1 - 3 x_2 )\\
                             x_1 \geq 0\\
                             x_2 \geq 0
                             \end{cases}
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le ",n("i",null,"variabili fuori base"),", che hanno qualsiasi altro valore."))),n(hn.a,{title:"Simplex primale"},n(pn.a,{title:"Cos'è?"},n("p",null,"Un algoritmo per ",n(Tn.a,null,"minimizzare"),"/",n(An.a,null,"massimizzare")," trovare efficientemente ",n("b",null,"valore ottimo")," di problemi di ottimizzazione lineare, derivato da Gauss-Jordan."),n("p",null,"Da esso si può anche ricavare un ",n("b",null,"vertice ottimo ammissibile"),".",n("br",null),"C'è la possibilità che ne esistano anche altri: quello ottenuto dipende da come è stata effettuata la scelta delle variabili entranti."),n(vn.a,null,"E' spiegato in modo semplice ",n("a",{href:"https://web.archive.org/web/20200523052252/https://www.cs.cmu.edu/~15451-f17/handouts/simplex.pdf"},"qui"),", e ci sono dei codici sorgenti di esempio ",n("a",{href:"https://www.cs.cmu.edu/~15451-f17/handouts/simplexcodes/"},"qui"),"."),n(vn.a,{title:"Esempio"},n("p",null,n("a",{href:"https://i.imgur.com/1r405Mb.jpg"},"Questa")," è la soluzione passo per passo del problema 3 del file ",n("a",{href:"https://dolly.fim.unimore.it/2019/mod/resource/view.php?id=2716"},n("code",null,"Ex_LP_testo")),"."))),n(pn.a,{title:"I passi"},n("ol",null,n("li",null,"Trasforma il sistema in ",n("b",null,"forma standard"),"."),n("li",null,"Trova tante variabili ",n("b",null,"linearmente indipendenti")," quante siano le righe: esse saranno la ",n("i",null,"base iniziale"),"."),n("li",null,"Finchè ci sono variabili con coefficienti ",n(Tn.a,null,"positivi"),"/",n(An.a,null,"negativi")," nella funzione obiettivo:",n("ol",null,n("li",null,n("b",null,"Scegli")," la prima variabile fuori base con coefficiente ",n(Tn.a,null,"positivo"),"/",n(An.a,null,"negativo")," nella funzione obiettivo: essa è la ",n("i",null,"variabile entrante"),".",n("br",null),n("aside",null,n("i",null,"Regola di Bland"),": Si potrebbe scegliere qualsiasi variabile come entrante, ma scegliendo sempre la prima ammissibile ci si assicura che l'algoritmo termini.")),n("li",null,n("b",null,"Scegli")," la variabile in base con il minor rapporto positivo ",n(_n.b,null,Sn(z())),".",n("aside",null,"Se non sei riuscito a trovare nessuna variabile con un rapporto positivo, significa che il poliedro è ",n(qn.a,null),".")),n("li",null,n("u",null,"Pivot"),": ",n("b",null,"riscrivi")," tutte le funzioni del sistema in termini della variabile entrante."))),n("li",null,"Il poliedro è ",n(In.a,null),": i ",n("b",null,"termini noti dei vincoli")," sono le coordinate del suo vertice ottimo, mentre il ",n("b",null,"termine noto della funzione obiettivo")," è il valore ottimo.")),n(vn.a,null,"È praticamente l'algoritmo di Gauss-Jordan applicato al tableau, con delle regole aggiuntive per la decisione delle variabili di pivot.")),n(pn.a,{title:"Soluzioni di base degenerata"},n("p",null,"Una soluzione con almeno una variabile di valore ",n(_n.b,null,"0"),", dovuta a uno o più ",n("b",null,"vincoli ridondanti"),"."),n("p",null,"Senza ",n("b",null,"Regola di Bland")," e in presenza di vincoli ridondanti si rischia di trovarsi a fare pivot infiniti."))),n(hn.a,{title:"Metodo delle due fasi"},n(pn.a,{title:"Metodo delle due fasi"},n("p",null,"Un estensione del Simplex per permettere la risoluzione di problemi la cui origine non è una soluzione ammissibile."),n("p",null,"Prevede l'introduzione di un ",n("i",null,"problema ausiliario"),", le cui incognite sono dette ",n("i",null,"artificiali"),"."),n("p",null,"Il vettore delle incognite artificiali è solitamente chiamato ",n(_n.b,null,Sn(x())),"."),n(vn.a,null,"E' spiegato in modo semplice ",n("a",{href:"https://web.archive.org/web/20200523052252/https://www.cs.cmu.edu/~15451-f17/handouts/simplex.pdf"},"qui"),".")),n(pn.a,{title:"Procedimento"},n("ol",null,n("li",null,"Crea un nuovo tableau, ",n("b",null,"aggiungendo variabili artificiali")," in modo da avere una base ammissibile."),n("li",null,"Sostituisci la vecchia funzione obiettivo con una nuova che ",n("b",null,"minimizzi la somma")," di tutte le variabili artificiali."),n("li",null,n("u",null,"Fase 1"),": ",n("b",null,"Risolvi")," il nuovo problema con il simplex primale."),n("li",null,"Se il Simplex termina quando ci sono ancora ",n("b",null,"variabili artificiali nella base"),", allora il poliedro è ",n("b",null,n(zn.a,null)),"."),n("li",null,"Una volta che le variabili artificiali sono fuori base, ",n("b",null,"elimina")," le loro colonne e la nuova funzione obiettivo.",n("br",null)),n("li",null,"Riporta il tableau in forma base compiendo operazioni per ",n("b",null,"azzerare i coefficienti")," delle variabili di base nella funzione obiettivo."),n("li",null,n("u",null,"Fase 2"),": ",n("b",null,"Risolvi")," il tableau con il simplex primale.")))),n(hn.a,{title:"Rilassamento"},n(pn.a,{title:"Cos'è?"},n("p",null,"Una versione semplificata di un problema nella quale si ",n("b",null,"ignora la violazione")," di uno o più vincoli.")),n(pn.a,{title:"Rilassamento di Lagrange"},n("p",null,"Un rilassamento che permette di misurare ",n("b",null,"di quanto i vincoli vengono violati"),"."),n("p",null,"I vincoli, moltiplicati per ",n("b",null,"coefficienti di rilassamento"),", vengono inseriti nella funzione obiettivo."),n("p",null,"Il vettore dei coefficienti di rilassamento solitamente è indicato con ",n(_n.b,null,Sn(g())),"."),n(vn.a,null,n("p",null,"Il sistema:"),n(_n.b,{inline:!1},Sn(v())),n("p",null,"diventa:"),n(_n.b,{inline:!1},Sn(p()))))),n(hn.a,{title:"Dualità"},n(pn.a,{title:"Duale"},n("p",null,"Il sistema che ",n("b",null,n(Tn.a,null,"massimizza"),"/",n(An.a,null,"minimizza")," i moltiplicatori di rilassamento")," di un problema detto ",n("i",null,"primale"),".")),n(pn.a,{title:"In termini matriciali"},n("p",null,"Possiamo ",n("b",null,"trasporre")," il tableau e sostituire le variabili ",n(_n.b,null,Sn(_()))," con variabili ",n(_n.b,null,Sn(h()))," per ottenere il sistema duale!"),n("p",null,"I maggiori e minori dei vincoli diventeranno maggiori e minori delle variabili e viceversa.")),n(pn.a,{title:"Feasibility del duale"},n("ul",null,n("li",null,"Se un problema ha una ",n("b",null,"soluzione finita"),", allora anche il suo duale la avrà."),n("li",null,"Se un problema è ",n("b",null,n(zn.a,null)),", allora il suo duale potrà essere ",n(zn.a,null)," oppure ",n(qn.a,null),"."),n("li",null,"Se un problema è ",n("b",null,n(qn.a,null)),", allora il suo duale sarà certamente ",n(zn.a,null),".")))),n(hn.a,{title:"Un po' di teoria"},n(pn.a,{title:"Lemma di Farkas"},n("p",null,"Una disuguaglianza lineare ",n(_n.b,null,Sn(m()))," è verificata da tutti i punti di un poliedro non-",n(zn.a,null)," se e solo se esiste un vettore ",n(_n.b,null,Sn(d()))," tale che:"),n(Ln.a,null,Sn(b())),n(Ln.a,null,Sn(f())),n("p",null,n(gn.a,null,"TODO: Cioè?"))),n(pn.a,{title:"Dualità forte"},n("p",null,"Il teorema che dimostra l'equivalenza tra primale e duale."),n("p",null,"Se uno dei due problemi è finito, la soluzione di uno coincide con la soluzione dell'altro."),n("p",null,n(_n.b,null,Sn(s()))),n("p",null,n(gn.a,null,"TODO: Anche qui c'è una lunga dimostrazione..."))),n(pn.a,{title:"Dualità debole"},n("p",null,"Il teorema che dimostra che il valore della funzione obiettivo del duale (di un qualsiasi tableau) è sempre ",n(Tn.a,null,"minore o uguale"),"/",n(An.a,null,"maggiore o uguale")," alla soluzione del corrispettivo primale."),n("p",null,n(gn.a,null,"TODO: Dimostrazione cortina, ma sembra complicata."))),n(pn.a,{title:"Condizioni di ottimalità"},n("p",null,"Il teorema che ci permette di passare dalla soluzione del duale alla soluzione del primale. ",n(gn.a,null,"TODO: credo?")),n("p",null,"Si deriva combinando le seguenti condizioni:"),n("ul",null,n("li",null,"Ammissibilità del primale: ",n(_n.b,null,Sn(c()))),n("li",null,"Ammissibilità del duale: ",n(_n.b,null,Sn(r()))),n("li",null,"Teorema della dualità forte: ",n(_n.b,null,Sn(o()))," (alla soluzione ottima)")),n("p",null,"Ne risulta che una soluzione è ottima se e solo se:"),n(Ln.a,null,Sn(u())),n(Ln.a,null,Sn(a())))),n(hn.a,{title:"Simplex duale"},n(pn.a,{title:"Cos'è?"},n("p",null,"Un'estensione al Simplex primale che opera sul problema duale.")),n(pn.a,{title:"Come funziona?"},n("p",null,"Funziona esattamente come il Simplex primale, ma opera sulle righe invece che sulle colonne, cercando di rendere ",n(Tn.a,null,"positivi"),"/",n(An.a,null,"negativi")," tutti i termini noti."),n(vn.a,null,"Significa che si possono moltiplicare tutti i valori di una riga per lo stesso numero e il risultato non cambia...?"))),n(hn.a,{title:"Analisi di sensibilità"},n(pn.a,{title:"Cos'è?"},n("p",null,"Un procedimento che misura di ",n("b",null,"quanto può variare")," il termine noto di un vincolo ",n(_n.b,null,Sn(e()))," o il coefficiente della funzione obiettivo ",n(_n.b,null,Sn(t()))," prima che la base degeneri. 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style from \"./TablePanel.less\";\n\nexport default function (props) {\n    return (\n        \n            {props.children}\n        
    \n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"example\":\"example__9acWs\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"box\":\"box__3cKyY\",\"default\":\"default__v-emJ\",\"red\":\"red__339Cz\",\"orange\":\"orange__24_8v\",\"yellow\":\"yellow__1Jo9W\",\"lime\":\"lime__34yV5\",\"cyan\":\"cyan__3RqLr\",\"blue\":\"blue__13Wnj\",\"magenta\":\"magenta__2tkzq\"};","import style from \"./Styles.less\";\n\nexport default function (props) {\n    return (\n        {props.children ? props.children : \"min\"}\n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"inline\":\"inline__1yl8V\",\"block\":\"block__fPiiB\"};","import style from \"./Styles.less\";\n\nexport default function (props) {\n    return (\n        {props.children ? props.children : \"finito\"}\n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"todo\":\"todo__2IWIS\"};","import Split from \"../Layout/Split\";\nimport {Fragment} from \"preact\";\n\nexport default function (props) {\n    return (\n        \n            
    \n                {props.title}\n            
    \n            \n                {props.children}\n            \n            \n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"title\":\"title__3ZVpg\",\"contents\":\"contents__20_NI\"};","import {createContext} from \"preact\";\n\nexport default createContext(null);\n","import style from './Latex.less';\nimport {useContext} from \"preact/hooks\";\nimport LatexRenderColor from \"../../contexts/LatexRenderColor\";\nimport LatexDefaultInline from \"../../contexts/LatexDefaultInline\";\nimport LatexDefaultDisplay from \"../../contexts/LatexDefaultDisplay\";\n\nexport const LatexDisplay = Object.freeze({\n    INLINE: style.inline,\n    BLOCK: style.block,\n})\n\nexport default function(props) {\n    // black, blue, brown, cyan, darkgray, gray, green, lightgray, lime, magenta, olive, orange, pink, purple, red, teal, violet, white, yellow\n    let renderColor = useContext(LatexRenderColor);\n    let defaultInline = useContext(LatexDefaultInline);\n    let defaultDisplay = useContext(LatexDefaultDisplay);\n\n    let inline;\n    if(props.inline === undefined) {\n        inline = defaultInline;\n    }\n    else {\n        inline = props.inline;\n    }\n\n    let display;\n    if(props.display === undefined) {\n        if(defaultDisplay === null) {\n            display = LatexDisplay.INLINE;\n        }\n        else {\n            display = defaultDisplay;\n        }\n    }\n    else {\n        display = props.display;\n    }\n\n    if(inline) {\n        let equation = `\\\\inline {\\\\color{${renderColor}} ${props.children} }`;\n        return (\n            {props.children}\n\n        );\n    }\n    else {\n        let equation = `{\\\\color{${renderColor}} ${props.children} }`;\n        return (\n            {props.children}\n\n        );\n    }\n}\n","import {Component} from 'preact'\nimport style from \"./Timer.less\"\n\n\nexport default class Timer extends Component {\n    constructor() {\n        super();\n        this.state = {\n            \"now\": Date.now()\n        };\n        this.timer = null;\n    }\n\n    componentDidMount() {\n        this.timer = setInterval(() => {\n            this.setState({\"now\": Date.now()})\n        }, 1000)\n    }\n\n    componentWillUnmount() {\n        if(this.timer !== null) {\n            clearInterval(this.timer)\n        }\n    }\n\n    render() {\n        let dateTo = \"Unknown date\";\n        let className = style.timer;\n\n        let parts = {\n            milliseconds: \"?\",\n            seconds: \"?\",\n            minutes: \"?\",\n            hours: \"?\",\n            days: \"?\",\n        };\n\n        if(this.props.to) {\n            dateTo = new Date(this.props.to);\n            let timeLeft = dateTo - this.state.now;\n\n            if(timeLeft > 0) {\n                parts = {\n                    milliseconds: timeLeft % 1000,\n                    seconds: Math.floor(timeLeft / 1000) % 60,\n                    minutes: Math.floor(timeLeft / 60000) % 60,\n                    hours: Math.floor(timeLeft / 3600000) % 24,\n                    days: Math.floor(timeLeft / 86400000),\n                };\n            }\n\n            else {\n                parts = {\n                    milliseconds: 0,\n                    seconds: 0,\n                    minutes: 0,\n                    hours: 0,\n                    days: 0,\n                };\n\n                className += \" \" + style.expired;\n            }\n        }\n        else {\n            className += \" \" + style.unknown;\n        }\n\n        return (\n            
    \n                
    \n                    {parts.days}\n                
    \n                
    \n                    giorni\n                
    \n                
    \n                    {parts.hours}\n                
    \n                
    \n                    ore\n                
    \n                
    \n                    {parts.minutes}\n                
    \n                
    \n                    minuti\n                
    \n                
    \n                    {parts.seconds}\n                
    \n                
    \n                    secondi\n                
    \n            
    \n        )\n    }\n}\n","import { options } from 'preact';\n\n/** @type {number} */\nlet currentIndex;\n\n/** @type {import('./internal').Component} */\nlet currentComponent;\n\n/** @type {number} */\nlet currentHook = 0;\n\n/** @type {Array} */\nlet afterPaintEffects = [];\n\nlet oldBeforeRender = options._render;\nlet oldAfterDiff = options.diffed;\nlet oldCommit = options._commit;\nlet oldBeforeUnmount = options.unmount;\n\nconst RAF_TIMEOUT = 100;\nlet prevRaf;\n\noptions._render = vnode => {\n\tif (oldBeforeRender) oldBeforeRender(vnode);\n\n\tcurrentComponent = vnode._component;\n\tcurrentIndex = 0;\n\n\tconst hooks = currentComponent.__hooks;\n\tif (hooks) {\n\t\thooks._pendingEffects.forEach(invokeCleanup);\n\t\thooks._pendingEffects.forEach(invokeEffect);\n\t\thooks._pendingEffects = [];\n\t}\n};\n\noptions.diffed = vnode => {\n\tif (oldAfterDiff) oldAfterDiff(vnode);\n\n\tconst c = vnode._component;\n\tif (c && c.__hooks && c.__hooks._pendingEffects.length) {\n\t\tafterPaint(afterPaintEffects.push(c));\n\t}\n};\n\noptions._commit = (vnode, commitQueue) => {\n\tcommitQueue.some(component => {\n\t\ttry {\n\t\t\tcomponent._renderCallbacks.forEach(invokeCleanup);\n\t\t\tcomponent._renderCallbacks = component._renderCallbacks.filter(cb =>\n\t\t\t\tcb._value ? invokeEffect(cb) : true\n\t\t\t);\n\t\t} catch (e) {\n\t\t\tcommitQueue.some(c => {\n\t\t\t\tif (c._renderCallbacks) c._renderCallbacks = [];\n\t\t\t});\n\t\t\tcommitQueue = [];\n\t\t\toptions._catchError(e, component._vnode);\n\t\t}\n\t});\n\n\tif (oldCommit) oldCommit(vnode, commitQueue);\n};\n\noptions.unmount = vnode => {\n\tif (oldBeforeUnmount) oldBeforeUnmount(vnode);\n\n\tconst c = vnode._component;\n\tif (c && c.__hooks) {\n\t\ttry {\n\t\t\tc.__hooks._list.forEach(invokeCleanup);\n\t\t} catch (e) {\n\t\t\toptions._catchError(e, c._vnode);\n\t\t}\n\t}\n};\n\n/**\n * Get a hook's state from the currentComponent\n * @param {number} index The index of the hook to get\n * @param {number} type The index of the hook to get\n * @returns {import('./internal').HookState}\n */\nfunction getHookState(index, type) {\n\tif (options._hook) {\n\t\toptions._hook(currentComponent, index, currentHook || type);\n\t}\n\tcurrentHook = 0;\n\n\t// Largely inspired by:\n\t// * https://github.com/michael-klein/funcy.js/blob/f6be73468e6ec46b0ff5aa3cc4c9baf72a29025a/src/hooks/core_hooks.mjs\n\t// * https://github.com/michael-klein/funcy.js/blob/650beaa58c43c33a74820a3c98b3c7079cf2e333/src/renderer.mjs\n\t// Other implementations to look at:\n\t// * https://codesandbox.io/s/mnox05qp8\n\tconst hooks =\n\t\tcurrentComponent.__hooks ||\n\t\t(currentComponent.__hooks = {\n\t\t\t_list: [],\n\t\t\t_pendingEffects: []\n\t\t});\n\n\tif (index >= hooks._list.length) {\n\t\thooks._list.push({});\n\t}\n\treturn hooks._list[index];\n}\n\n/**\n * @param {import('./index').StateUpdater} initialState\n */\nexport function useState(initialState) {\n\tcurrentHook = 1;\n\treturn useReducer(invokeOrReturn, initialState);\n}\n\n/**\n * @param {import('./index').Reducer} reducer\n * @param {import('./index').StateUpdater} initialState\n * @param {(initialState: any) => void} [init]\n * @returns {[ any, (state: any) => void ]}\n */\nexport function useReducer(reducer, initialState, init) {\n\t/** @type {import('./internal').ReducerHookState} */\n\tconst hookState = getHookState(currentIndex++, 2);\n\thookState._reducer = reducer;\n\tif (!hookState._component) {\n\t\thookState._component = currentComponent;\n\n\t\thookState._value = [\n\t\t\t!init ? invokeOrReturn(undefined, initialState) : init(initialState),\n\n\t\t\taction => {\n\t\t\t\tconst nextValue = hookState._reducer(hookState._value[0], action);\n\t\t\t\tif (hookState._value[0] !== nextValue) {\n\t\t\t\t\thookState._value[0] = nextValue;\n\t\t\t\t\thookState._component.setState({});\n\t\t\t\t}\n\t\t\t}\n\t\t];\n\t}\n\n\treturn hookState._value;\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++, 3);\n\tif (!options._skipEffects && argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent.__hooks._pendingEffects.push(state);\n\t}\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useLayoutEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++, 4);\n\tif (!options._skipEffects && argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent._renderCallbacks.push(state);\n\t}\n}\n\nexport function useRef(initialValue) {\n\tcurrentHook = 5;\n\treturn useMemo(() => ({ current: initialValue }), []);\n}\n\n/**\n * @param {object} ref\n * @param {() => object} createHandle\n * @param {any[]} args\n */\nexport function useImperativeHandle(ref, createHandle, args) {\n\tcurrentHook = 6;\n\tuseLayoutEffect(\n\t\t() => {\n\t\t\tif (typeof ref == 'function') ref(createHandle());\n\t\t\telse if (ref) ref.current = createHandle();\n\t\t},\n\t\targs == null ? args : args.concat(ref)\n\t);\n}\n\n/**\n * @param {() => any} factory\n * @param {any[]} args\n */\nexport function useMemo(factory, args) {\n\t/** @type {import('./internal').MemoHookState} */\n\tconst state = getHookState(currentIndex++, 7);\n\tif (argsChanged(state._args, args)) {\n\t\tstate._args = args;\n\t\tstate._factory = factory;\n\t\treturn (state._value = factory());\n\t}\n\n\treturn state._value;\n}\n\n/**\n * @param {() => void} callback\n * @param {any[]} args\n */\nexport function useCallback(callback, args) {\n\tcurrentHook = 8;\n\treturn useMemo(() => callback, args);\n}\n\n/**\n * @param {import('./internal').PreactContext} context\n */\nexport function useContext(context) {\n\tconst provider = currentComponent.context[context._id];\n\t// We could skip this call here, but than we'd not call\n\t// `options._hook`. We need to do that in order to make\n\t// the devtools aware of this hook.\n\tconst state = getHookState(currentIndex++, 9);\n\t// The devtools needs access to the context object to\n\t// be able to pull of the default value when no provider\n\t// is present in the tree.\n\tstate._context = context;\n\tif (!provider) return context._defaultValue;\n\t// This is probably not safe to convert to \"!\"\n\tif (state._value == null) {\n\t\tstate._value = true;\n\t\tprovider.sub(currentComponent);\n\t}\n\treturn provider.props.value;\n}\n\n/**\n * Display a custom label for a custom hook for the devtools panel\n * @type {(value: T, cb?: (value: T) => string | number) => void}\n */\nexport function useDebugValue(value, formatter) {\n\tif (options.useDebugValue) {\n\t\toptions.useDebugValue(formatter ? formatter(value) : value);\n\t}\n}\n\nexport function useErrorBoundary(cb) {\n\tconst state = getHookState(currentIndex++, 10);\n\tconst errState = useState();\n\tstate._value = cb;\n\tif (!currentComponent.componentDidCatch) {\n\t\tcurrentComponent.componentDidCatch = err => {\n\t\t\tif (state._value) state._value(err);\n\t\t\terrState[1](err);\n\t\t};\n\t}\n\treturn [\n\t\terrState[0],\n\t\t() => {\n\t\t\terrState[1](undefined);\n\t\t}\n\t];\n}\n\n/**\n * After paint effects consumer.\n */\nfunction flushAfterPaintEffects() {\n\tafterPaintEffects.some(component => {\n\t\tif (component._parentDom) {\n\t\t\ttry {\n\t\t\t\tcomponent.__hooks._pendingEffects.forEach(invokeCleanup);\n\t\t\t\tcomponent.__hooks._pendingEffects.forEach(invokeEffect);\n\t\t\t\tcomponent.__hooks._pendingEffects = [];\n\t\t\t} catch (e) {\n\t\t\t\tcomponent.__hooks._pendingEffects = [];\n\t\t\t\toptions._catchError(e, component._vnode);\n\t\t\t\treturn true;\n\t\t\t}\n\t\t}\n\t});\n\tafterPaintEffects = [];\n}\n\n/**\n * Schedule a callback to be invoked after the browser has a chance to paint a new frame.\n * Do this by combining requestAnimationFrame (rAF) + setTimeout to invoke a callback after\n * the next browser frame.\n *\n * Also, schedule a timeout in parallel to the the rAF to ensure the callback is invoked\n * even if RAF doesn't fire (for example if the browser tab is not visible)\n *\n * @param {() => void} callback\n */\nfunction afterNextFrame(callback) {\n\tconst done = () => {\n\t\tclearTimeout(timeout);\n\t\tcancelAnimationFrame(raf);\n\t\tsetTimeout(callback);\n\t};\n\tconst timeout = setTimeout(done, RAF_TIMEOUT);\n\n\tlet raf;\n\tif (typeof window != 'undefined') {\n\t\traf = requestAnimationFrame(done);\n\t}\n}\n\n// Note: if someone used options.debounceRendering = requestAnimationFrame,\n// then effects will ALWAYS run on the NEXT frame instead of the current one, incurring a ~16ms delay.\n// Perhaps this is not such a big deal.\n/**\n * Schedule afterPaintEffects flush after the browser paints\n * @param {number} newQueueLength\n */\nfunction afterPaint(newQueueLength) {\n\tif (newQueueLength === 1 || prevRaf !== options.requestAnimationFrame) {\n\t\tprevRaf = options.requestAnimationFrame;\n\t\t(prevRaf || afterNextFrame)(flushAfterPaintEffects);\n\t}\n}\n\n/**\n * @param {import('./internal').EffectHookState} hook\n */\nfunction invokeCleanup(hook) {\n\tif (typeof hook._cleanup == 'function') hook._cleanup();\n}\n\n/**\n * Invoke a Hook's effect\n * @param {import('./internal').EffectHookState} hook\n */\nfunction invokeEffect(hook) {\n\thook._cleanup = hook._value();\n}\n\n/**\n * @param {any[]} oldArgs\n * @param {any[]} newArgs\n */\nfunction argsChanged(oldArgs, newArgs) {\n\treturn !oldArgs || newArgs.some((arg, index) => arg !== oldArgs[index]);\n}\n\nfunction invokeOrReturn(arg, f) {\n\treturn typeof f == 'function' ? f(arg) : f;\n}\n","import style from \"./Todo.less\";\n\nexport default function (props) {\n\tif(process.env.NODE_ENV === \"development\") {\n\t\treturn {props.children};\n\t}\n\telse {\n\t\treturn null;\n\t}\n}\n","import style from \"./Styles.less\";\n\nexport default function (props) {\n    return (\n        {props.children ? props.children : \"max\"}\n    );\n}\n","import style from \"./Split.less\";\n\nexport default function (props) {\n    let children;\n\n    if(Array.isArray(props.children)) {\n        children = props.children.map(element => {\n            return (\n                
    \n                    {element}\n                
    \n            );\n        });\n    }\n\n    else {\n        children = (\n            
    \n                {props.children}\n            
    \n        );\n    }\n    return (\n        
    \n            
    {children}
    \n        
    \n    );\n}\n","import BLatex from \"./BLatex\";\n\nexport default function (props) {\n    return (\n        
    \n            {props.children}\n        
    \n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"tablepanel\":\"tablepanel__1Wil3\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"unbounded\":\"unbounded__KZ9A2\",\"unfeasible\":\"unfeasible__9LnzW\",\"finite\":\"finite__3_e9S\",\"min\":\"min__3VEkp\",\"max\":\"max__BtCuw\"};","import style from \"./Example.less\";\nimport {Component} from \"preact\";\n\nexport default function(props) {\n    return (\n        
    \n            {props.children}\n        
    \n    );\n}\n","import style from \"./Box.less\";\n\nexport const BoxColors = Object.freeze({\n    RED: style.red,\n    ORANGE: style.orange,\n    YELLOW: style.yellow,\n    LIME: style.lime,\n    CYAN: style.cyan,\n    BLUE: style.blue,\n    MAGENTA: style.magenta,\n    DEFAULT: style.default\n})\n\nexport default function (props) {\n    let color = BoxColors.DEFAULT;\n    if(props.color) {\n        color = props.color;\n    }\n\n    return (\n        
    \n            {props.children}\n        
    \n    );\n}\n","import style from \"./Styles.less\";\n\nexport default function (props) {\n    return (\n        {props.children ? props.children : \"vuoto\"}\n    );\n}\n","import style from \"./Styles.less\";\n\nexport default function (props) {\n    return (\n        {props.children ? props.children : \"illimitato\"}\n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"timer\":\"timer__3Z2pL\",\"days\":\"days__myhe2\",\"hours\":\"hours__3JUDn\",\"minutes\":\"minutes__24lD7\",\"seconds\":\"seconds__2vZ4f\",\"count\":\"count__chi9X\",\"text\":\"text__34ldC\",\"unknown\":\"unknown__3sT2P\",\"expired\":\"expired__zNiuP\"};","import Section from \"../components/Elements/Section\";\nimport Latex from \"../components/Rendering/Latex\";\nimport Panel from \"../components/Elements/Panel\";\nimport Example from \"../components/Elements/Example\";\nimport Todo from \"../components/Elements/Todo\";\nimport Timer from \"../components/Elements/Timer\";\nimport Empty from \"../components/PageSpecific/OttimizzazioneLineare/Empty\";\nimport Unbounded from \"../components/PageSpecific/OttimizzazioneLineare/Unbounded\";\nimport Min from \"../components/PageSpecific/OttimizzazioneLineare/Min\";\nimport Max from \"../components/PageSpecific/OttimizzazioneLineare/Max\";\nimport PLatex from \"../components/Rendering/PLatex\";\nimport LatexDefaultInline from \"../contexts/LatexDefaultInline\";\nimport TablePanel from \"../components/Elements/TablePanel\";\nimport Finite from \"../components/PageSpecific/OttimizzazioneLineare/Finite\";\n\nconst r = String.raw;\n\nexport default function(props) {\n    return (\n        
    \n            
    Ottimizzazione lineare intera
    \n            
    \n                \n                    \n                \n                \n                    
    \n                        Se sei uno studente dell'Unimore, puoi accedere all'archivio del corso su Google Drive.\n                    
    \n                    \n            
    \n            
    \n                \n                    
    \n                        Uno scritto con tre domande:\n                    
    \n                    
      \n                        
    • Progettazione concettuale e logica
      • \n                        
    • Formulazione interrogazione
      • \n                        
    • Una domanda tra:\n                            
        \n                                
      • Studio dato derivato
        • \n                                
      • Progettazione fisica
        • \n                                
      • Tecnologia database
        • \n                            
      \n                        
      • \n                    
    \n                    \n                \n                    
      \n                        
      2. \n                        
      3. \n                        
      4. \n                    
    \n                    \n            
    \n            \n                
    \n                    \n                        \n                            \n                                v\n                                s\n                                Significato\n                            \n                        \n                        \n                            \n                                {r`\\mathbf{x}`}\n                                {r`x_i`}\n                                Incognite\n                            \n                            \n                                {r`\\mathbf{s}`}\n                                {r`s_i`}\n                                Variabili slack\n                            \n                            \n                                {r`\\mathbf{c}`}\n                                {r`c_i`}\n                                Coefficienti della funzione obiettivo\n                            \n                            \n                                {r`\\mathbf{A}`}\n                                {r`a_{ij}`}\n                                Coefficienti dei vincoli\n                            \n                            \n                                {r`\\mathbf{b}`}\n                                {r`b_i`}\n                                Termini noti dei vincoli\n                            \n                            \n                                {r`\\mathbf{y}`}\n                                {r`y_i`}\n                                Incognite artificiali\n                            \n                            \n                                {r`\\mathbf{u}`}\n                                {r`u_i`}\n                                Coefficienti di rilassamento\n                            \n                            \n                                \n                                {r`c_0`}\n                                Valore ottimo di un problema\n                            \n                            \n                                {r`\\mathbf{x}_B`}\n                                \n                                Incognite in base\n                            \n                            \n                                {r`\\mathbf{c}_B`}\n                                \n                                Coefficienti della funzione obiettivo delle variabili in base\n                            \n                            \n                                {r`\\mathbf{B}`}\n                                \n                                Coefficienti dei vincoli delle variabili in base\n                            \n                            \n                                {r`\\mathbf{x}_F`}\n                                \n                                Incognite fuori base\n                            \n                            \n                                {r`\\mathbf{c}_F`}\n                                \n                                Coefficienti della funzione obiettivo delle variabili fuori base\n                            \n                            \n                                {r`\\mathbf{F}`}\n                                \n                                Coefficienti dei vincoli delle variabili fuori base\n                            \n                        \n                    \n                    \n                        \n                            \n                                Simboli\n                                Significato\n                            \n                        \n                        \n                            \n                                {r`\\mathbf{c}^T \\mathbf{x}`}\n                                Soluzione del problema\n                            \n                            \n                                {r`\\mathbf{A} \\mathbf{x} = \\mathbf{b}`}\n                                Vincoli in forma standard\n                            \n                            \n                                {r`z(\\dots)`}\n                                Funzione obiettivo\n                            \n                            \n                                {r`\\mathbf{u}^T \\mathbf{b}`}\n                                Soluzione del problema duale\n                            \n                            \n                                {r`\\mathbf{u}^T \\mathbf{A} = \\mathbf{c}^T`}\n                                Vincoli del problema duale in forma standard\n                            \n                        \n                    \n                
    \n                \n            
    \n                \n                    
    \n                        La funzione obiettivo è la funzione con valore noto sconosciuto:\n                    
    \n                    
    \n                        {r`z = C_1 \\cdot x_1 + C_2 \\cdot x_2 + C_n \\cdot x_n`}\n                    
    \n                    \n            
    \n            
    \n                \n                    
    \n                        I problemi di ottimizzazione lineare sono problemi che cercano di minimizzare/massimizzare il valore di una funzione obiettivo le cui incognite sono sottoposte a un sistema di vincoli.\n                    
    \n                    \n                \n                    
    \n                        La funzione da minimizzare/massimizzare.\n                    
    \n                    
    \n                        Il vettore dei suoi coefficienti è detto {r`\\mathbf{c}`}, mentre quello delle sue incognite {r`\\mathbf{x}`}.\n                    
    \n                    \n                \n                    
    \n                        Equazioni e disequazioni a cui devono sottostare le incognite perchè esse formino una soluzione valida.\n                    
    \n                    
    \n                        I loro coefficienti sono contenuti nella matrice {r`\\mathbf{A}`}, mentre i loro termini noti nel vettore {r`\\mathbf{b}`}.\n                    
    \n                    \n                \n                    
    \n                        La soluzione di un problema, ricavabile dal prodotto {r`\\mathbf{c}^T \\mathbf{x}`}.\n                    
    \n                    
    \n                        Spesso, la funzione obiettivo è indicata con il nome {r`z(\\dots)`}.\n                    
    \n                    \n                \n                    
    \n                        L'insieme che racchiunde tutte le soluzioni ammissibili di un problema.\n                    
    \n                    
    \n                        In particolare, il valore ottimo è un vertice del poliedro, detto vertice ottimo.\n                    
    \n                    
    \n                        Può essere ,  oppure .\n                    
    \n                    \n                \n                    
    \n                        Funzione della funzione obiettivo che restituisce la direzione del suo aumento più veloce.\n                    
    \n                    
    \n                        {r`\\nabla f = \\frac{\\delta f}{\\delta x_1} \\mathbf{I}_1 + \\frac{\\delta f}{\\delta x_2} \\mathbf{I}_2 + \\frac{\\delta f}{\\delta x_n} \\mathbf{I}_n`}\n                    
    \n                    \n                        La matrice {r`\\mathbf{I}`} è la matrice identità.\n                    \n                    \n                        Se la funzione obiettivo è z = 2w + 3x + 4y, il suo gradiente è {r`\\nabla z = (2, 3, 4)`}.\n                    \n                    \n            
    \n            
    \n                \n                    
    \n                        Un problema con:\n                    
    \n                    
      \n                        
    • Equazioni e disequazioni
      • \n                        
    • Variabili non vincolate
      • \n                    
    \n                    {r`min \\left\\{ \\mathbf{c}^T \\mathbf{x} : \\mathbf{A} \\mathbf{x} = b,\\quad \\mathbf{A'} \\mathbf{x} \\geq \\mathbf{b'} \\quad x_j \\geq 0,\\quad j = 1 \\dots n \\right\\}`}\n                    \n                \n                    
    \n                        Un problema con:\n                    
    \n                    
      \n                        
    • Solo disequazioni
      • \n                        
    • Vincoli di non-negatività sulle incognite
      • \n                    
    \n                    {r`min \\left\\{ \\mathbf{c}^T \\mathbf{x} : \\mathbf{A} \\mathbf{x} \\geq b,\\quad x_j \\geq 0,\\quad j = 1 \\dots n \\right\\}`}\n                    \n                \n                    
    \n                        Un problema con:\n                    
    \n                    
      \n                        
    • Solo equazioni
      • \n                        
    • Vincoli di non-negatività sulle incognite
      • \n                    
    \n                    {r`min \\left\\{ \\mathbf{c}^T \\mathbf{x} : \\mathbf{A} \\mathbf{x} = b,\\quad x_j \\geq 0,\\quad j = 1 \\dots n \\right\\}`}\n                    \n            
    \n            
    \n                \n                    
    \n                        Applica questa conversione a ogni equazione nel sistema:\n                    
    \n                    
    \n                        {r`a = b \\Leftrightarrow\n                            \\begin{cases}\n                                a \\leq b\\\\\n                                a \\geq b\n                            \\end{cases}\n                        `}\n                    
    \n                    Serve solo nella teoria per dimostrare che le forme sono equivalenti.\n                    \n                \n                    
    \n                        Aggiungi una variabile slack {r`s`} non-vincolata a ogni disequazione nel sistema:\n                    
    \n                    
    \n                        {r`\n                            a \\leq b \\Leftrightarrow a + s = b\n                        `}\n                    
    \n                    
    \n                        {r`\n                            a \\geq b \\Leftrightarrow a - s = b\n                        `}\n                    
    \n                    \n                \n                    
    \n                        Sdoppia ogni variabile non-vincolata in due variabili con vincolo di non-negatività:\n                    
    \n                    
    \n                        {r`\\begin{cases}\n                            a = a^+ - a^-\\\\\n                            a^+ \\geq 0\\\\\n                            a^- \\geq 0\n                        \\end{cases}`}\n                    
    \n                    \n            
    \n            
    \n                \n                    
    \n                        Un modo per rappresentare sistemi in forma standard, anche noto come matrice equivalente completa del sistema.\n                    
    \n                    \n                        Il sistema:

    \n                        {r`\n                            \\begin{cases}\n                            2000x_1 + 1000x_2 = z\\\\\n                            1x_1 \\leq 3\\\\\n                            1x_2 \\leq 3\\\\\n                            2x_1 + 2x_2 \\leq 7\n                            \\end{cases}\n                        `}

    \n                        Diventa il tableau:

    \n                        \n                            \n                                \n                                    \n                                    \n                                    \n                                    \n                                    \n                                \n                            \n                            \n                                \n                                    \n                                    \n                                    \n                                    \n                                    \n                                \n                                \n                                    \n                                    \n                                    \n                                    \n                                    \n                                \n                                \n                                    \n                                    \n                                    \n                                    \n                                    \n                                \n                                \n                                    \n                                    \n                                    \n                                    \n                                    \n                                \n                            \n                        
    TNx_1x_2s_1s_2
    z2000100000
    31010
    30101
    72200
    \n                        \n                    \n                \n                    
    \n                        Variabili che hanno tutti 0 e un solo 1 nella loro colonna del tableau.\n                    
    \n                    
    \n                        La loro controparte sono le variabili fuori base, che hanno qualsiasi altro valore.\n                    
    \n                    \n            
    \n            
    \n                \n                    
    \n                        Un algoritmo per minimizzare/massimizzare trovare efficientemente valore ottimo di problemi di ottimizzazione lineare, derivato da Gauss-Jordan.\n                    
    \n                    
    \n                        Da esso si può anche ricavare un vertice ottimo ammissibile.
    \n                        C'è la possibilità che ne esistano anche altri: quello ottenuto dipende da come è stata effettuata la scelta delle variabili entranti.\n                    
    \n                    \n                        E' spiegato in modo semplice qui, e ci sono dei codici sorgenti di esempio qui.\n                    \n                    \n                        
    \n                            Questa è la soluzione passo per passo del problema 3 del file Ex_LP_testo.\n                        
    \n                        \n                    \n                \n                    
      \n                        
    1. Trasforma il sistema in forma standard.
      2. \n                        
    2. Trova tante variabili linearmente indipendenti quante siano le righe: esse saranno la base iniziale.
      3. \n                        
    3. Finchè ci sono variabili con coefficienti positivi/negativi nella funzione obiettivo:\n                            
        \n                                
      1. \n                                    Scegli la prima variabile fuori base con coefficiente positivo/negativo nella funzione obiettivo: essa è la variabile entrante.
        \n                                    \n                                
        2. \n                                
      2. \n                                    Scegli la variabile in base con il minor rapporto positivo {r`\\frac{termine\\ noto}{coeff.\\ variabile\\ entrante}`}.\n                                    \n                                
        3. \n                                
      3. Pivot: riscrivi tutte le funzioni del sistema in termini della variabile entrante.
        4. \n                            
      \n                        
      4. \n                        
    4. Il poliedro è : i termini noti dei vincoli sono le coordinate del suo vertice ottimo, mentre il termine noto della funzione obiettivo è il valore ottimo.
      5. \n                    
    \n                    \n                        È praticamente l'algoritmo di Gauss-Jordan applicato al tableau, con delle regole aggiuntive per la decisione delle variabili di pivot.\n                    \n                    \n                \n                    
    \n                        Una soluzione con almeno una variabile di valore 0, dovuta a uno o più vincoli ridondanti.\n                    
    \n                    
    \n                        Senza Regola di Bland e in presenza di vincoli ridondanti si rischia di trovarsi a fare pivot infiniti.\n                    
    \n                    \n            
    \n            
    \n                \n                    
    \n                        Un estensione del Simplex per permettere la risoluzione di problemi la cui origine non è una soluzione ammissibile.\n                    
    \n                    
    \n                        Prevede l'introduzione di un problema ausiliario, le cui incognite sono dette artificiali.\n                    
    \n                    
    \n                        Il vettore delle incognite artificiali è solitamente chiamato {r`\\mathbf{y}`}.\n                    
    \n                    \n                        E' spiegato in modo semplice qui.\n                    \n                    \n                \n                    
      \n                        
    1. Crea un nuovo tableau, aggiungendo variabili artificiali in modo da avere una base ammissibile.
      2. \n                        
    2. Sostituisci la vecchia funzione obiettivo con una nuova che minimizzi la somma di tutte le variabili artificiali.
      3. \n                        
    3. Fase 1: Risolvi il nuovo problema con il simplex primale.
      4. \n                        
    4. Se il Simplex termina quando ci sono ancora variabili artificiali nella base, allora il poliedro è .
      5. \n                        
    5. Una volta che le variabili artificiali sono fuori base, elimina le loro colonne e la nuova funzione obiettivo.
      6. \n                        
    6. Riporta il tableau in forma base compiendo operazioni per azzerare i coefficienti delle variabili di base nella funzione obiettivo.
      7. \n                        
    7. Fase 2: Risolvi il tableau con il simplex primale.
      8. \n                    
    \n                    \n            
    \n            
    \n                \n                    
    \n                        Una versione semplificata di un problema nella quale si ignora la violazione di uno o più vincoli.\n                    
    \n                    \n                \n                    
    \n                        Un rilassamento che permette di misurare di quanto i vincoli vengono violati.\n                    
    \n                    
    \n                        I vincoli, moltiplicati per coefficienti di rilassamento, vengono inseriti nella funzione obiettivo.\n                    
    \n                    
    \n                        Il vettore dei coefficienti di rilassamento solitamente è indicato con {r`\\mathbf{u}`}.\n                    
    \n                    \n                        
    \n                            Il sistema:\n                        
    \n                        {r`\n                            \\begin{cases}\n                            z = 3 x_1 + 5 x_2\\\\\n                            2 x_1 + 3 x_2 \\geq 12\\\\\n                            - x_1 + 3 x_2 \\geq 3\\\\\n                            x_1 \\geq 0\\\\\n                            x_2 \\geq 0\n                            \\end{cases}\n                        `}\n                        
    \n                            diventa:\n                        
    \n                        {r`\n                            \\begin{cases}\n                            z = 3 x_1 + 5 x_2 + u_1 ( 12 - 2 x_1 - 3 x_2 ) + u_2 ( 3 + x_1 - 3 x_2 )\\\\\n                            x_1 \\geq 0\\\\\n                            x_2 \\geq 0\n                            \\end{cases}\n                        `}\n                        \n                    \n            
    \n            
    \n                \n                    
    \n                        Il sistema che massimizza/minimizza i moltiplicatori di rilassamento di un problema detto primale.\n                    
    \n                    \n                \n                    
    \n                        Possiamo trasporre il tableau e sostituire le variabili {r`x_n`} con variabili {r`u_n`} per ottenere il sistema duale!\n                    
    \n                    
    \n                        I maggiori e minori dei vincoli diventeranno maggiori e minori delle variabili e viceversa.\n                    
    \n                    \n                \n                    
      \n                        
    • Se un problema ha una soluzione finita, allora anche il suo duale la avrà.
      • \n                        
    • Se un problema è , allora il suo duale potrà essere  oppure .
      • \n                        
    • Se un problema è , allora il suo duale sarà certamente .
      • \n                    
    \n                    \n            
    \n            
    \n                \n                    
    \n                        Una disuguaglianza lineare {r`c_0 \\leq \\mathbf{c}^T \\mathbf{x}`} è verificata da tutti i punti di un poliedro non- se e solo se esiste un vettore {r`u \\in \\mathfrak{R}^m`} tale che:\n                    
    \n                    {r`\\mathbf{c}^T \\geq \\mathbf{u}^T \\mathbf{A}`}\n                    {r`c_0 \\leq \\mathbf{u}^T \\mathbf{b}`}\n                    
    \n                        TODO: Cioè?\n                    
    \n                    \n                \n                    
    \n                        Il teorema che dimostra l'equivalenza tra primale e duale.\n                    
    \n                    
    \n                        Se uno dei due problemi è finito, la soluzione di uno coincide con la soluzione dell'altro.\n                    
    \n                    
    \n                        {r`\\mathbf{c}^T \\mathbf{x} = \\mathbf{u}^T \\mathbf{b}`}\n                    
    \n                    
    \n                        TODO: Anche qui c'è una lunga dimostrazione...\n                    
    \n                    \n                \n                    
    \n                        Il teorema che dimostra che il valore della funzione obiettivo del duale (di un qualsiasi tableau) è sempre minore o uguale/maggiore o uguale alla soluzione del corrispettivo primale.\n                    
    \n                    
    \n                        TODO: Dimostrazione cortina, ma sembra complicata.\n                    
    \n                    \n                \n                    
    \n                        Il teorema che ci permette di passare dalla soluzione del duale alla soluzione del primale. TODO: credo?\n                    
    \n                    
    \n                        Si deriva combinando le seguenti condizioni:\n                    
    \n                    
      \n                        
    • Ammissibilità del primale: {r`\\mathbf{A} \\mathbf{X} \\geq \\mathbf{b}, \\quad \\mathbf{x} \\geq 0`}
      • \n                        
    • Ammissibilità del duale: {r`\\mathbf{u}^T \\mathbf{A} \\leq \\mathbf{c}^T, \\quad \\mathbf{u} \\geq 0`}
      • \n                        
    • Teorema della dualità forte: {r`\\mathbf{c}^T \\mathbf{x} = \\mathbf{u}^T \\mathbf{b}`} (alla soluzione ottima)
      • \n                    
    \n                    
    \n                        Ne risulta che una soluzione è ottima se e solo se:\n                    
    \n                    {r`\\left( \\mathbf{c}^T - \\mathbf{u}^T \\mathbf{A} \\right) \\mathbf{x} = 0`}\n                    {r`\\mathbf{u}^T \\left( \\mathbf{A} \\mathbf{x} - \\mathbf{b}  \\right) = 0`}\n                    \n            
    \n            
    \n                \n                    
    \n                        Un'estensione al Simplex primale che opera sul problema duale.\n                    
    \n                    \n                \n                    
    \n                        Funziona esattamente come il Simplex primale, ma opera sulle righe invece che sulle colonne, cercando di rendere positivi/negativi tutti i termini noti.\n                    
    \n                    \n                        Significa che si possono moltiplicare tutti i valori di una riga per lo stesso numero e il risultato non cambia...?\n                    \n                    \n            
    \n            
    \n                \n                    
    \n                        Un procedimento che misura di quanto può variare il termine noto di un vincolo {r`b_i`} o il coefficiente della funzione obiettivo {r`c_i`} prima che la base degeneri. TODO: verificare\n                    
    \n                    \n            
    \n        
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n},n}function dn(){var n=mn(["mathbf{x}"],["\\mathbf{x}"]);return dn=function(){return n},n}function mn(n,l){return l||(l=n.slice(0)),n.raw=l,n}var hn=i("OPqz"),_n=i("Q7TX"),pn=i("imVn"),vn=i("Wxxq"),gn=i("RMzO"),xn=i("QNda"),zn=i("Z395"),qn=i("e3h+"),Tn=i("FP0W"),wn=i("SgMg"),Ln=i("UEzA"),An=i("wQ73"),yn=i("2e/m"),In=i("JyGO"),Sn=String.raw;l.default=function(){return n("div",null,n("h1",null,"Ottimizzazione lineare intera"),n(hn.a,{title:"Unimore"},n(pn.a,{title:"Videolezioni su YouTube"},n("p",null,"Ho rimosso il rumore in sottofondo da tutti i video di Ricerca Operativa!"),n("p",null,n("b",null,n("a",{href:"https://www.youtube.com/playlist?list=PLh93e8qjTszffkHNn-19CqUOhHFbhBlBh"},"Guardate i video qui!")))),n(pn.a,{title:"Prossimi appelli"},n("ol",null,n("li",null,n(xn.a,{to:"2020-06-08"})),n("li",null,n(xn.a,{to:"2020-06-25"})),n("li",null,n(xn.a,{to:"2020-07-14"}))))),n(An.a.Provider,{value:!1},n(hn.a,{title:"Glossario"},n(yn.a,null,n("thead",null,n("tr",null,n("th",null,n("abbr",{title:"Vettore / matrice"},"v")),n("th",null,n("abbr",{title:"Elemento singolo"},"s")),n("th",null,"Significato"))),n("tbody",null,n("tr",null,n("td",null,n(_n.b,null,Sn(dn()))),n("td",null,n(_n.b,null,Sn(bn()))),n("td",null,"Incognite")),n("tr",null,n("td",null,n(_n.b,null,Sn(fn()))),n("td",null,n(_n.b,null,Sn(sn()))),n("td",null,"Variabili slack")),n("tr",null,n("td",null,n(_n.b,null,Sn(cn()))),n("td",null,n(_n.b,null,Sn(rn()))),n("td",null,"Coefficienti della funzione obiettivo")),n("tr",null,n("td",null,n(_n.b,null,Sn(on()))),n("td",null,n(_n.b,null,Sn(un()))),n("td",null,"Coefficienti dei vincoli")),n("tr",null,n("td",null,n(_n.b,null,Sn(an()))),n("td",null,n(_n.b,null,Sn(en()))),n("td",null,"Termini noti dei 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le ",n("i",null,"variabili fuori base"),", che hanno qualsiasi altro valore."))),n(hn.a,{title:"Simplex primale"},n(pn.a,{title:"Cos'è?"},n("p",null,"Un algoritmo per ",n(Tn.a,null,"minimizzare"),"/",n(wn.a,null,"massimizzare")," trovare efficientemente ",n("b",null,"valore ottimo")," di problemi di ottimizzazione lineare, derivato da Gauss-Jordan."),n("p",null,"Da esso si può anche ricavare un ",n("b",null,"vertice ottimo ammissibile"),".",n("br",null),"C'è la possibilità che ne esistano anche altri: quello ottenuto dipende da come è stata effettuata la scelta delle variabili entranti."),n(vn.a,null,"E' spiegato in modo semplice ",n("a",{href:"https://web.archive.org/web/20200523052252/https://www.cs.cmu.edu/~15451-f17/handouts/simplex.pdf"},"qui"),", e ci sono dei codici sorgenti di esempio ",n("a",{href:"https://www.cs.cmu.edu/~15451-f17/handouts/simplexcodes/"},"qui"),"."),n(vn.a,{title:"Esempio"},n("p",null,n("a",{href:"https://i.imgur.com/1r405Mb.jpg"},"Questa")," è la soluzione passo per passo del problema 3 del file ",n("a",{href:"https://dolly.fim.unimore.it/2019/mod/resource/view.php?id=2716"},n("code",null,"Ex_LP_testo")),"."))),n(pn.a,{title:"I passi"},n("ol",null,n("li",null,"Trasforma il sistema in ",n("b",null,"forma standard"),"."),n("li",null,"Trova tante variabili ",n("b",null,"linearmente indipendenti")," quante siano le righe: esse saranno la ",n("i",null,"base iniziale"),"."),n("li",null,"Finchè ci sono variabili con coefficienti ",n(Tn.a,null,"positivi"),"/",n(wn.a,null,"negativi")," nella funzione obiettivo:",n("ol",null,n("li",null,n("b",null,"Scegli")," la prima variabile fuori base con coefficiente ",n(Tn.a,null,"positivo"),"/",n(wn.a,null,"negativo")," nella funzione obiettivo: essa è la ",n("i",null,"variabile entrante"),".",n("br",null),n("aside",null,n("i",null,"Regola di Bland"),": Si potrebbe scegliere qualsiasi variabile come entrante, ma scegliendo sempre la prima ammissibile ci si assicura che l'algoritmo termini.")),n("li",null,n("b",null,"Scegli")," la variabile in base con il minor rapporto positivo ",n(_n.b,null,Sn(z())),".",n("aside",null,"Se non sei riuscito a trovare nessuna variabile con un rapporto positivo, significa che il poliedro è ",n(qn.a,null),".")),n("li",null,n("u",null,"Pivot"),": ",n("b",null,"riscrivi")," tutte le funzioni del sistema in termini della variabile entrante."))),n("li",null,"Il poliedro è ",n(In.a,null),": i ",n("b",null,"termini noti dei vincoli")," sono le coordinate del suo vertice ottimo, mentre il ",n("b",null,"termine noto della funzione obiettivo")," è il valore ottimo.")),n(vn.a,null,"È praticamente l'algoritmo di Gauss-Jordan applicato al tableau, con delle regole aggiuntive per la decisione delle variabili di pivot.")),n(pn.a,{title:"Soluzioni di base degenerata"},n("p",null,"Una soluzione con almeno una variabile di valore ",n(_n.b,null,"0"),", dovuta a uno o più ",n("b",null,"vincoli ridondanti"),"."),n("p",null,"Senza ",n("b",null,"Regola di Bland")," e in presenza di vincoli ridondanti si rischia di trovarsi a fare pivot infiniti."))),n(hn.a,{title:"Metodo delle due fasi"},n(pn.a,{title:"Metodo delle due fasi"},n("p",null,"Un estensione del Simplex per permettere la risoluzione di problemi la cui origine non è una soluzione ammissibile."),n("p",null,"Prevede l'introduzione di un ",n("i",null,"problema ausiliario"),", le cui incognite sono dette ",n("i",null,"artificiali"),"."),n("p",null,"Il vettore delle incognite artificiali è solitamente chiamato ",n(_n.b,null,Sn(x())),"."),n(vn.a,null,"E' spiegato in modo semplice ",n("a",{href:"https://web.archive.org/web/20200523052252/https://www.cs.cmu.edu/~15451-f17/handouts/simplex.pdf"},"qui"),".")),n(pn.a,{title:"Procedimento"},n("ol",null,n("li",null,"Crea un nuovo tableau, ",n("b",null,"aggiungendo variabili artificiali")," in modo da avere una base ammissibile."),n("li",null,"Sostituisci la vecchia funzione obiettivo con una nuova che ",n("b",null,"minimizzi la somma")," di tutte le variabili artificiali."),n("li",null,n("u",null,"Fase 1"),": ",n("b",null,"Risolvi")," il nuovo problema con il simplex primale."),n("li",null,"Se il Simplex termina quando ci sono ancora ",n("b",null,"variabili artificiali nella base"),", allora il poliedro è ",n("b",null,n(zn.a,null)),"."),n("li",null,"Una volta che le variabili artificiali sono fuori base, ",n("b",null,"elimina")," le loro colonne e la nuova funzione obiettivo.",n("br",null)),n("li",null,"Riporta il tableau in forma base compiendo operazioni per ",n("b",null,"azzerare i coefficienti")," delle variabili di base nella funzione obiettivo."),n("li",null,n("u",null,"Fase 2"),": ",n("b",null,"Risolvi")," il tableau con il simplex primale.")))),n(hn.a,{title:"Rilassamento"},n(pn.a,{title:"Cos'è?"},n("p",null,"Una versione semplificata di un problema nella quale si ",n("b",null,"ignora la violazione")," di uno o più vincoli.")),n(pn.a,{title:"Rilassamento di Lagrange"},n("p",null,"Un rilassamento che permette di misurare ",n("b",null,"di quanto i vincoli vengono violati"),"."),n("p",null,"I vincoli, moltiplicati per ",n("b",null,"coefficienti di rilassamento"),", vengono inseriti nella funzione obiettivo."),n("p",null,"Il vettore dei coefficienti di rilassamento solitamente è indicato con ",n(_n.b,null,Sn(g())),"."),n(vn.a,null,n("p",null,"Il sistema:"),n(_n.b,{inline:!1},Sn(v())),n("p",null,"diventa:"),n(_n.b,{inline:!1},Sn(p()))))),n(hn.a,{title:"Dualità"},n(pn.a,{title:"Duale"},n("p",null,"Il sistema che ",n("b",null,n(Tn.a,null,"massimizza"),"/",n(wn.a,null,"minimizza")," i moltiplicatori di rilassamento")," di un problema detto ",n("i",null,"primale"),".")),n(pn.a,{title:"In termini matriciali"},n("p",null,"Possiamo ",n("b",null,"trasporre")," il tableau e sostituire le variabili ",n(_n.b,null,Sn(_()))," con variabili ",n(_n.b,null,Sn(h()))," per ottenere il sistema duale!"),n("p",null,"I maggiori e minori dei vincoli diventeranno maggiori e minori delle variabili e viceversa.")),n(pn.a,{title:"Feasibility del duale"},n("ul",null,n("li",null,"Se un problema ha una ",n("b",null,"soluzione finita"),", allora anche il suo duale la avrà."),n("li",null,"Se un problema è ",n("b",null,n(zn.a,null)),", allora il suo duale potrà essere ",n(zn.a,null)," oppure ",n(qn.a,null),"."),n("li",null,"Se un problema è ",n("b",null,n(qn.a,null)),", allora il suo duale sarà certamente ",n(zn.a,null),".")))),n(hn.a,{title:"Un po' di teoria"},n(pn.a,{title:"Lemma di Farkas"},n("p",null,"Una disuguaglianza lineare ",n(_n.b,null,Sn(m()))," è verificata da tutti i punti di un poliedro non-",n(zn.a,null)," se e solo se esiste un vettore ",n(_n.b,null,Sn(d()))," tale che:"),n(Ln.a,null,Sn(b())),n(Ln.a,null,Sn(f())),n("p",null,n(gn.a,null,"TODO: Cioè?"))),n(pn.a,{title:"Dualità forte"},n("p",null,"Il teorema che dimostra l'equivalenza tra primale e duale."),n("p",null,"Se uno dei due problemi è finito, la soluzione di uno coincide con la soluzione dell'altro."),n("p",null,n(_n.b,null,Sn(s()))),n("p",null,n(gn.a,null,"TODO: Anche qui c'è una lunga dimostrazione..."))),n(pn.a,{title:"Dualità debole"},n("p",null,"Il teorema che dimostra che il valore della funzione obiettivo del duale (di un qualsiasi tableau) è sempre ",n(Tn.a,null,"minore o uguale"),"/",n(wn.a,null,"maggiore o uguale")," alla soluzione del corrispettivo primale."),n("p",null,n(gn.a,null,"TODO: Dimostrazione cortina, ma sembra complicata."))),n(pn.a,{title:"Condizioni di ottimalità"},n("p",null,"Il teorema che ci permette di passare dalla soluzione del duale alla soluzione del primale. ",n(gn.a,null,"TODO: credo?")),n("p",null,"Si deriva combinando le seguenti condizioni:"),n("ul",null,n("li",null,"Ammissibilità del primale: ",n(_n.b,null,Sn(c()))),n("li",null,"Ammissibilità del duale: ",n(_n.b,null,Sn(r()))),n("li",null,"Teorema della dualità forte: ",n(_n.b,null,Sn(o()))," (alla soluzione ottima)")),n("p",null,"Ne risulta che una soluzione è ottima se e solo se:"),n(Ln.a,null,Sn(u())),n(Ln.a,null,Sn(a())))),n(hn.a,{title:"Simplex duale"},n(pn.a,{title:"Cos'è?"},n("p",null,"Un'estensione al Simplex primale che opera sul problema duale.")),n(pn.a,{title:"Come funziona?"},n("p",null,"Funziona esattamente come il Simplex primale, ma opera sulle righe invece che sulle colonne, cercando di rendere ",n(Tn.a,null,"positivi"),"/",n(wn.a,null,"negativi")," tutti i termini noti."),n(vn.a,null,"Significa che si possono moltiplicare tutti i valori di una riga per lo stesso numero e il risultato non cambia...?"))),n(hn.a,{title:"Analisi di sensibilità"},n(pn.a,{title:"Cos'è?"},n("p",null,"Un procedimento che misura di ",n("b",null,"quanto può variare")," il termine noto di un vincolo ",n(_n.b,null,Sn(e()))," o il coefficiente della funzione obiettivo ",n(_n.b,null,Sn(t()))," prima che la base degeneri. 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style from \"./TablePanel.less\";\n\nexport default function (props) {\n    return (\n        \n            {props.children}\n        
    \n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"example\":\"example__9acWs\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"box\":\"box__3cKyY\",\"default\":\"default__v-emJ\",\"red\":\"red__339Cz\",\"orange\":\"orange__24_8v\",\"yellow\":\"yellow__1Jo9W\",\"lime\":\"lime__34yV5\",\"cyan\":\"cyan__3RqLr\",\"blue\":\"blue__13Wnj\",\"magenta\":\"magenta__2tkzq\"};","import style from \"./Styles.less\";\n\nexport default function (props) {\n    return (\n        {props.children ? props.children : \"min\"}\n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"inline\":\"inline__1yl8V\",\"block\":\"block__fPiiB\"};","import style from \"./Styles.less\";\n\nexport default function (props) {\n    return (\n        {props.children ? props.children : \"finito\"}\n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"todo\":\"todo__2IWIS\"};","import Split from \"../Layout/Split\";\nimport {Fragment} from \"preact\";\n\nexport default function (props) {\n    return (\n        \n            
    \n                {props.title}\n            
    \n            \n                {props.children}\n            \n            \n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"title\":\"title__3ZVpg\",\"contents\":\"contents__20_NI\"};","import {createContext} from \"preact\";\n\nexport default createContext(null);\n","import style from './Latex.less';\nimport {useContext} from \"preact/hooks\";\nimport LatexRenderColor from \"../../contexts/LatexRenderColor\";\nimport LatexDefaultInline from \"../../contexts/LatexDefaultInline\";\nimport LatexDefaultDisplay from \"../../contexts/LatexDefaultDisplay\";\n\nexport const LatexDisplay = Object.freeze({\n    INLINE: style.inline,\n    BLOCK: style.block,\n})\n\nexport default function(props) {\n    // black, blue, brown, cyan, darkgray, gray, green, lightgray, lime, magenta, olive, orange, pink, purple, red, teal, violet, white, yellow\n    let renderColor = useContext(LatexRenderColor);\n    let defaultInline = useContext(LatexDefaultInline);\n    let defaultDisplay = useContext(LatexDefaultDisplay);\n\n    let inline;\n    if(props.inline === undefined) {\n        inline = defaultInline;\n    }\n    else {\n        inline = props.inline;\n    }\n\n    let display;\n    if(props.display === undefined) {\n        if(defaultDisplay === null) {\n            display = LatexDisplay.INLINE;\n        }\n        else {\n            display = defaultDisplay;\n        }\n    }\n    else {\n        display = props.display;\n    }\n\n    if(inline) {\n        let equation = `\\\\inline {\\\\color{${renderColor}} ${props.children} }`;\n        return (\n            {props.children}\n\n        );\n    }\n    else {\n        let equation = `{\\\\color{${renderColor}} ${props.children} }`;\n        return (\n            {props.children}\n\n        );\n    }\n}\n","import {Component} from 'preact'\nimport style from \"./Timer.less\"\n\n\nexport default class Timer extends Component {\n    constructor() {\n        super();\n        this.state = {\n            \"now\": Date.now()\n        };\n        this.timer = null;\n    }\n\n    componentDidMount() {\n        this.timer = setInterval(() => {\n            this.setState({\"now\": Date.now()})\n        }, 1000)\n    }\n\n    componentWillUnmount() {\n        if(this.timer !== null) {\n            clearInterval(this.timer)\n        }\n    }\n\n    render() {\n        let dateTo = \"Unknown date\";\n        let className = style.timer;\n\n        let parts = {\n            milliseconds: \"?\",\n            seconds: \"?\",\n            minutes: \"?\",\n            hours: \"?\",\n            days: \"?\",\n        };\n\n        if(this.props.to) {\n            dateTo = new Date(this.props.to);\n            let timeLeft = dateTo - this.state.now;\n\n            if(timeLeft > 0) {\n                parts = {\n                    milliseconds: timeLeft % 1000,\n                    seconds: Math.floor(timeLeft / 1000) % 60,\n                    minutes: Math.floor(timeLeft / 60000) % 60,\n                    hours: Math.floor(timeLeft / 3600000) % 24,\n                    days: Math.floor(timeLeft / 86400000),\n                };\n            }\n\n            else {\n                parts = {\n                    milliseconds: 0,\n                    seconds: 0,\n                    minutes: 0,\n                    hours: 0,\n                    days: 0,\n                };\n\n                className += \" \" + style.expired;\n            }\n        }\n        else {\n            className += \" \" + style.unknown;\n        }\n\n        return (\n            
    \n                
    \n                    {parts.days}\n                
    \n                
    \n                    giorni\n                
    \n                
    \n                    {parts.hours}\n                
    \n                
    \n                    ore\n                
    \n                
    \n                    {parts.minutes}\n                
    \n                
    \n                    minuti\n                
    \n                
    \n                    {parts.seconds}\n                
    \n                
    \n                    secondi\n                
    \n            
    \n        )\n    }\n}\n","import { options } from 'preact';\n\n/** @type {number} */\nlet currentIndex;\n\n/** @type {import('./internal').Component} */\nlet currentComponent;\n\n/** @type {number} */\nlet currentHook = 0;\n\n/** @type {Array} */\nlet afterPaintEffects = [];\n\nlet oldBeforeRender = options._render;\nlet oldAfterDiff = options.diffed;\nlet oldCommit = options._commit;\nlet oldBeforeUnmount = options.unmount;\n\nconst RAF_TIMEOUT = 100;\nlet prevRaf;\n\noptions._render = vnode => {\n\tif (oldBeforeRender) oldBeforeRender(vnode);\n\n\tcurrentComponent = vnode._component;\n\tcurrentIndex = 0;\n\n\tconst hooks = currentComponent.__hooks;\n\tif (hooks) {\n\t\thooks._pendingEffects.forEach(invokeCleanup);\n\t\thooks._pendingEffects.forEach(invokeEffect);\n\t\thooks._pendingEffects = [];\n\t}\n};\n\noptions.diffed = vnode => {\n\tif (oldAfterDiff) oldAfterDiff(vnode);\n\n\tconst c = vnode._component;\n\tif (c && c.__hooks && c.__hooks._pendingEffects.length) {\n\t\tafterPaint(afterPaintEffects.push(c));\n\t}\n};\n\noptions._commit = (vnode, commitQueue) => {\n\tcommitQueue.some(component => {\n\t\ttry {\n\t\t\tcomponent._renderCallbacks.forEach(invokeCleanup);\n\t\t\tcomponent._renderCallbacks = component._renderCallbacks.filter(cb =>\n\t\t\t\tcb._value ? invokeEffect(cb) : true\n\t\t\t);\n\t\t} catch (e) {\n\t\t\tcommitQueue.some(c => {\n\t\t\t\tif (c._renderCallbacks) c._renderCallbacks = [];\n\t\t\t});\n\t\t\tcommitQueue = [];\n\t\t\toptions._catchError(e, component._vnode);\n\t\t}\n\t});\n\n\tif (oldCommit) oldCommit(vnode, commitQueue);\n};\n\noptions.unmount = vnode => {\n\tif (oldBeforeUnmount) oldBeforeUnmount(vnode);\n\n\tconst c = vnode._component;\n\tif (c && c.__hooks) {\n\t\ttry {\n\t\t\tc.__hooks._list.forEach(invokeCleanup);\n\t\t} catch (e) {\n\t\t\toptions._catchError(e, c._vnode);\n\t\t}\n\t}\n};\n\n/**\n * Get a hook's state from the currentComponent\n * @param {number} index The index of the hook to get\n * @param {number} type The index of the hook to get\n * @returns {import('./internal').HookState}\n */\nfunction getHookState(index, type) {\n\tif (options._hook) {\n\t\toptions._hook(currentComponent, index, currentHook || type);\n\t}\n\tcurrentHook = 0;\n\n\t// Largely inspired by:\n\t// * https://github.com/michael-klein/funcy.js/blob/f6be73468e6ec46b0ff5aa3cc4c9baf72a29025a/src/hooks/core_hooks.mjs\n\t// * https://github.com/michael-klein/funcy.js/blob/650beaa58c43c33a74820a3c98b3c7079cf2e333/src/renderer.mjs\n\t// Other implementations to look at:\n\t// * https://codesandbox.io/s/mnox05qp8\n\tconst hooks =\n\t\tcurrentComponent.__hooks ||\n\t\t(currentComponent.__hooks = {\n\t\t\t_list: [],\n\t\t\t_pendingEffects: []\n\t\t});\n\n\tif (index >= hooks._list.length) {\n\t\thooks._list.push({});\n\t}\n\treturn hooks._list[index];\n}\n\n/**\n * @param {import('./index').StateUpdater} initialState\n */\nexport function useState(initialState) {\n\tcurrentHook = 1;\n\treturn useReducer(invokeOrReturn, initialState);\n}\n\n/**\n * @param {import('./index').Reducer} reducer\n * @param {import('./index').StateUpdater} initialState\n * @param {(initialState: any) => void} [init]\n * @returns {[ any, (state: any) => void ]}\n */\nexport function useReducer(reducer, initialState, init) {\n\t/** @type {import('./internal').ReducerHookState} */\n\tconst hookState = getHookState(currentIndex++, 2);\n\thookState._reducer = reducer;\n\tif (!hookState._component) {\n\t\thookState._component = currentComponent;\n\n\t\thookState._value = [\n\t\t\t!init ? invokeOrReturn(undefined, initialState) : init(initialState),\n\n\t\t\taction => {\n\t\t\t\tconst nextValue = hookState._reducer(hookState._value[0], action);\n\t\t\t\tif (hookState._value[0] !== nextValue) {\n\t\t\t\t\thookState._value[0] = nextValue;\n\t\t\t\t\thookState._component.setState({});\n\t\t\t\t}\n\t\t\t}\n\t\t];\n\t}\n\n\treturn hookState._value;\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++, 3);\n\tif (!options._skipEffects && argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent.__hooks._pendingEffects.push(state);\n\t}\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useLayoutEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++, 4);\n\tif (!options._skipEffects && argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent._renderCallbacks.push(state);\n\t}\n}\n\nexport function useRef(initialValue) {\n\tcurrentHook = 5;\n\treturn useMemo(() => ({ current: initialValue }), []);\n}\n\n/**\n * @param {object} ref\n * @param {() => object} createHandle\n * @param {any[]} args\n */\nexport function useImperativeHandle(ref, createHandle, args) {\n\tcurrentHook = 6;\n\tuseLayoutEffect(\n\t\t() => {\n\t\t\tif (typeof ref == 'function') ref(createHandle());\n\t\t\telse if (ref) ref.current = createHandle();\n\t\t},\n\t\targs == null ? args : args.concat(ref)\n\t);\n}\n\n/**\n * @param {() => any} factory\n * @param {any[]} args\n */\nexport function useMemo(factory, args) {\n\t/** @type {import('./internal').MemoHookState} */\n\tconst state = getHookState(currentIndex++, 7);\n\tif (argsChanged(state._args, args)) {\n\t\tstate._args = args;\n\t\tstate._factory = factory;\n\t\treturn (state._value = factory());\n\t}\n\n\treturn state._value;\n}\n\n/**\n * @param {() => void} callback\n * @param {any[]} args\n */\nexport function useCallback(callback, args) {\n\tcurrentHook = 8;\n\treturn useMemo(() => callback, args);\n}\n\n/**\n * @param {import('./internal').PreactContext} context\n */\nexport function useContext(context) {\n\tconst provider = currentComponent.context[context._id];\n\t// We could skip this call here, but than we'd not call\n\t// `options._hook`. We need to do that in order to make\n\t// the devtools aware of this hook.\n\tconst state = getHookState(currentIndex++, 9);\n\t// The devtools needs access to the context object to\n\t// be able to pull of the default value when no provider\n\t// is present in the tree.\n\tstate._context = context;\n\tif (!provider) return context._defaultValue;\n\t// This is probably not safe to convert to \"!\"\n\tif (state._value == null) {\n\t\tstate._value = true;\n\t\tprovider.sub(currentComponent);\n\t}\n\treturn provider.props.value;\n}\n\n/**\n * Display a custom label for a custom hook for the devtools panel\n * @type {(value: T, cb?: (value: T) => string | number) => void}\n */\nexport function useDebugValue(value, formatter) {\n\tif (options.useDebugValue) {\n\t\toptions.useDebugValue(formatter ? formatter(value) : value);\n\t}\n}\n\nexport function useErrorBoundary(cb) {\n\tconst state = getHookState(currentIndex++, 10);\n\tconst errState = useState();\n\tstate._value = cb;\n\tif (!currentComponent.componentDidCatch) {\n\t\tcurrentComponent.componentDidCatch = err => {\n\t\t\tif (state._value) state._value(err);\n\t\t\terrState[1](err);\n\t\t};\n\t}\n\treturn [\n\t\terrState[0],\n\t\t() => {\n\t\t\terrState[1](undefined);\n\t\t}\n\t];\n}\n\n/**\n * After paint effects consumer.\n */\nfunction flushAfterPaintEffects() {\n\tafterPaintEffects.some(component => {\n\t\tif (component._parentDom) {\n\t\t\ttry {\n\t\t\t\tcomponent.__hooks._pendingEffects.forEach(invokeCleanup);\n\t\t\t\tcomponent.__hooks._pendingEffects.forEach(invokeEffect);\n\t\t\t\tcomponent.__hooks._pendingEffects = [];\n\t\t\t} catch (e) {\n\t\t\t\tcomponent.__hooks._pendingEffects = [];\n\t\t\t\toptions._catchError(e, component._vnode);\n\t\t\t\treturn true;\n\t\t\t}\n\t\t}\n\t});\n\tafterPaintEffects = [];\n}\n\n/**\n * Schedule a callback to be invoked after the browser has a chance to paint a new frame.\n * Do this by combining requestAnimationFrame (rAF) + setTimeout to invoke a callback after\n * the next browser frame.\n *\n * Also, schedule a timeout in parallel to the the rAF to ensure the callback is invoked\n * even if RAF doesn't fire (for example if the browser tab is not visible)\n *\n * @param {() => void} callback\n */\nfunction afterNextFrame(callback) {\n\tconst done = () => {\n\t\tclearTimeout(timeout);\n\t\tcancelAnimationFrame(raf);\n\t\tsetTimeout(callback);\n\t};\n\tconst timeout = setTimeout(done, RAF_TIMEOUT);\n\n\tlet raf;\n\tif (typeof window != 'undefined') {\n\t\traf = requestAnimationFrame(done);\n\t}\n}\n\n// Note: if someone used options.debounceRendering = requestAnimationFrame,\n// then effects will ALWAYS run on the NEXT frame instead of the current one, incurring a ~16ms delay.\n// Perhaps this is not such a big deal.\n/**\n * Schedule afterPaintEffects flush after the browser paints\n * @param {number} newQueueLength\n */\nfunction afterPaint(newQueueLength) {\n\tif (newQueueLength === 1 || prevRaf !== options.requestAnimationFrame) {\n\t\tprevRaf = options.requestAnimationFrame;\n\t\t(prevRaf || afterNextFrame)(flushAfterPaintEffects);\n\t}\n}\n\n/**\n * @param {import('./internal').EffectHookState} hook\n */\nfunction invokeCleanup(hook) {\n\tif (typeof hook._cleanup == 'function') hook._cleanup();\n}\n\n/**\n * Invoke a Hook's effect\n * @param {import('./internal').EffectHookState} hook\n */\nfunction invokeEffect(hook) {\n\thook._cleanup = hook._value();\n}\n\n/**\n * @param {any[]} oldArgs\n * @param {any[]} newArgs\n */\nfunction argsChanged(oldArgs, newArgs) {\n\treturn !oldArgs || newArgs.some((arg, index) => arg !== oldArgs[index]);\n}\n\nfunction invokeOrReturn(arg, f) {\n\treturn typeof f == 'function' ? f(arg) : f;\n}\n","import style from \"./Todo.less\";\n\nexport default function (props) {\n\tif(process.env.NODE_ENV === \"development\") {\n\t\treturn {props.children};\n\t}\n\telse {\n\t\treturn null;\n\t}\n}\n","import style from \"./Styles.less\";\n\nexport default function (props) {\n    return (\n        {props.children ? props.children : \"max\"}\n    );\n}\n","import style from \"./Split.less\";\n\nexport default function (props) {\n    let children;\n\n    if(Array.isArray(props.children)) {\n        children = props.children.map(element => {\n            return (\n                
    \n                    {element}\n                
    \n            );\n        });\n    }\n\n    else {\n        children = (\n            
    \n                {props.children}\n            
    \n        );\n    }\n    return (\n        
    \n            
    {children}
    \n        
    \n    );\n}\n","import BLatex from \"./BLatex\";\n\nexport default function (props) {\n    return (\n        
    \n            {props.children}\n        
    \n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"tablepanel\":\"tablepanel__1Wil3\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"unbounded\":\"unbounded__KZ9A2\",\"unfeasible\":\"unfeasible__9LnzW\",\"finite\":\"finite__3_e9S\",\"min\":\"min__3VEkp\",\"max\":\"max__BtCuw\"};","import style from \"./Example.less\";\nimport {Component} from \"preact\";\n\nexport default function(props) {\n    return (\n        
    \n            {props.children}\n        
    \n    );\n}\n","import style from \"./Box.less\";\n\nexport const BoxColors = Object.freeze({\n    RED: style.red,\n    ORANGE: style.orange,\n    YELLOW: style.yellow,\n    LIME: style.lime,\n    CYAN: style.cyan,\n    BLUE: style.blue,\n    MAGENTA: style.magenta,\n    DEFAULT: style.default\n})\n\nexport default function (props) {\n    let color = BoxColors.DEFAULT;\n    if(props.color) {\n        color = props.color;\n    }\n\n    return (\n        
    \n            {props.children}\n        
    \n    );\n}\n","import style from \"./Styles.less\";\n\nexport default function (props) {\n    return (\n        {props.children ? props.children : \"vuoto\"}\n    );\n}\n","import style from \"./Styles.less\";\n\nexport default function (props) {\n    return (\n        {props.children ? props.children : \"illimitato\"}\n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"timer\":\"timer__3Z2pL\",\"days\":\"days__myhe2\",\"hours\":\"hours__3JUDn\",\"minutes\":\"minutes__24lD7\",\"seconds\":\"seconds__2vZ4f\",\"count\":\"count__chi9X\",\"text\":\"text__34ldC\",\"unknown\":\"unknown__3sT2P\",\"expired\":\"expired__zNiuP\"};","import Section from \"../components/Elements/Section\";\nimport Latex from \"../components/Rendering/Latex\";\nimport Panel from \"../components/Elements/Panel\";\nimport Example from \"../components/Elements/Example\";\nimport Todo from \"../components/Elements/Todo\";\nimport Timer from \"../components/Elements/Timer\";\nimport Empty from \"../components/PageSpecific/OttimizzazioneLineare/Empty\";\nimport Unbounded from \"../components/PageSpecific/OttimizzazioneLineare/Unbounded\";\nimport Min from \"../components/PageSpecific/OttimizzazioneLineare/Min\";\nimport Max from \"../components/PageSpecific/OttimizzazioneLineare/Max\";\nimport PLatex from \"../components/Rendering/PLatex\";\nimport LatexDefaultInline from \"../contexts/LatexDefaultInline\";\nimport TablePanel from \"../components/Elements/TablePanel\";\nimport Finite from \"../components/PageSpecific/OttimizzazioneLineare/Finite\";\n\nconst r = String.raw;\n\nexport default function(props) {\n    return (\n        
    \n            
    Ottimizzazione lineare intera
    \n            
    \n                \n                    
    \n                        Ho rimosso il rumore in sottofondo da tutti i video di Ricerca Operativa!\n                    
    \n                    
    \n                        Guardate i video qui!\n                    
    \n                    \n                \n                    
      \n                        
      2. \n                        
      3. \n                        
      4. \n                    
    \n                    \n            
    \n            \n                
    \n                        \n                            \n                                \n                                    v\n                                    s\n                                    Significato\n                                \n                            \n                            \n                                \n                                    {r`\\mathbf{x}`}\n                                    {r`x_i`}\n                                    Incognite\n                                \n                                \n                                    {r`\\mathbf{s}`}\n                                    {r`s_i`}\n                                    Variabili slack\n                                \n                                \n                                    {r`\\mathbf{c}`}\n                                    {r`c_i`}\n                                    Coefficienti della funzione obiettivo\n                                \n                                \n                                    {r`\\mathbf{A}`}\n                                    {r`a_{ij}`}\n                                    Coefficienti dei vincoli\n                                \n                                \n                                    {r`\\mathbf{b}`}\n                                    {r`b_i`}\n                                    Termini noti dei vincoli\n                                \n                                \n                                    {r`\\mathbf{y}`}\n                                    {r`y_i`}\n                                    Incognite artificiali\n                                \n                                \n                                    {r`\\mathbf{u}`}\n                                    {r`u_i`}\n                                    Coefficienti di rilassamento\n                                \n                                \n                                    \n                                    {r`c_0`}\n                                    Valore ottimo di un problema\n                                \n                                \n                                    {r`\\mathbf{x}_B`}\n                                    \n                                    Incognite in base\n                                \n                                \n                                    {r`\\mathbf{c}_B`}\n                                    \n                                    Coefficienti della funzione obiettivo delle variabili in base\n                                \n                                \n                                    {r`\\mathbf{B}`}\n                                    \n                                    Coefficienti dei vincoli delle variabili in base\n                                \n                                \n                                    {r`\\mathbf{x}_F`}\n                                    \n                                    Incognite fuori base\n                                \n                                \n                                    {r`\\mathbf{c}_F`}\n                                    \n                                    Coefficienti della funzione obiettivo delle variabili fuori base\n                                \n                                \n                                    {r`\\mathbf{F}`}\n                                    \n                                    Coefficienti dei vincoli delle variabili fuori base\n                                \n                            \n                        \n                        \n                            \n                                \n                                    Simboli\n                                    Significato\n                                \n                            \n                            \n                                \n                                    {r`\\mathbf{c}^T \\mathbf{x}`}\n                                    Soluzione del problema\n                                \n                                \n                                    {r`\\mathbf{A} \\mathbf{x} = \\mathbf{b}`}\n                                    Vincoli in forma standard\n                                \n                                \n                                    {r`z(\\dots)`}\n                                    Funzione obiettivo\n                                \n                                \n                                    {r`\\mathbf{u}^T \\mathbf{b}`}\n                                    Soluzione del problema duale\n                                \n                                \n                                    {r`\\mathbf{u}^T \\mathbf{A} = \\mathbf{c}^T`}\n                                    Vincoli del problema duale in forma standard\n                                \n                            \n                        \n                
    \n                \n            
    \n                \n                    
    \n                        La funzione obiettivo è la funzione con valore noto sconosciuto:\n                    
    \n                    
    \n                        {r`z = C_1 \\cdot x_1 + C_2 \\cdot x_2 + C_n \\cdot x_n`}\n                    
    \n                    \n            
    \n            
    \n                \n                    
    \n                        I problemi di ottimizzazione lineare sono problemi che cercano di minimizzare/massimizzare il valore di una funzione obiettivo le cui incognite sono sottoposte a un sistema di vincoli.\n                    
    \n                    \n                \n                    
    \n                        La funzione da minimizzare/massimizzare.\n                    
    \n                    
    \n                        Il vettore dei suoi coefficienti è detto {r`\\mathbf{c}`}, mentre quello delle sue incognite {r`\\mathbf{x}`}.\n                    
    \n                    \n                \n                    
    \n                        Equazioni e disequazioni a cui devono sottostare le incognite perchè esse formino una soluzione valida.\n                    
    \n                    
    \n                        I loro coefficienti sono contenuti nella matrice {r`\\mathbf{A}`}, mentre i loro termini noti nel vettore {r`\\mathbf{b}`}.\n                    
    \n                    \n                \n                    
    \n                        La soluzione di un problema, ricavabile dal prodotto {r`\\mathbf{c}^T \\mathbf{x}`}.\n                    
    \n                    
    \n                        Spesso, la funzione obiettivo è indicata con il nome {r`z(\\dots)`}.\n                    
    \n                    \n                \n                    
    \n                        L'insieme che racchiunde tutte le soluzioni ammissibili di un problema.\n                    
    \n                    
    \n                        In particolare, il valore ottimo è un vertice del poliedro, detto vertice ottimo.\n                    
    \n                    
    \n                        Può essere ,  oppure .\n                    
    \n                    \n                \n                    
    \n                        Funzione della funzione obiettivo che restituisce la direzione del suo aumento più veloce.\n                    
    \n                    
    \n                        {r`\\nabla f = \\frac{\\delta f}{\\delta x_1} \\mathbf{I}_1 + \\frac{\\delta f}{\\delta x_2} \\mathbf{I}_2 + \\frac{\\delta f}{\\delta x_n} \\mathbf{I}_n`}\n                    
    \n                    \n                        La matrice {r`\\mathbf{I}`} è la matrice identità.\n                    \n                    \n                        Se la funzione obiettivo è z = 2w + 3x + 4y, il suo gradiente è {r`\\nabla z = (2, 3, 4)`}.\n                    \n                    \n            
    \n            
    \n                \n                    
    \n                        Un problema con:\n                    
    \n                    
      \n                        
    • Equazioni e disequazioni
      • \n                        
    • Variabili non vincolate
      • \n                    
    \n                    {r`min \\left\\{ \\mathbf{c}^T \\mathbf{x} : \\mathbf{A} \\mathbf{x} = b,\\quad \\mathbf{A'} \\mathbf{x} \\geq \\mathbf{b'} \\quad x_j \\geq 0,\\quad j = 1 \\dots n \\right\\}`}\n                    \n                \n                    
    \n                        Un problema con:\n                    
    \n                    
      \n                        
    • Solo disequazioni
      • \n                        
    • Vincoli di non-negatività sulle incognite
      • \n                    
    \n                    {r`min \\left\\{ \\mathbf{c}^T \\mathbf{x} : \\mathbf{A} \\mathbf{x} \\geq b,\\quad x_j \\geq 0,\\quad j = 1 \\dots n \\right\\}`}\n                    \n                \n                    
    \n                        Un problema con:\n                    
    \n                    
      \n                        
    • Solo equazioni
      • \n                        
    • Vincoli di non-negatività sulle incognite
      • \n                    
    \n                    {r`min \\left\\{ \\mathbf{c}^T \\mathbf{x} : \\mathbf{A} \\mathbf{x} = b,\\quad x_j \\geq 0,\\quad j = 1 \\dots n \\right\\}`}\n                    \n            
    \n            
    \n                \n                    
    \n                        Applica questa conversione a ogni equazione nel sistema:\n                    
    \n                    
    \n                        {r`a = b \\Leftrightarrow\n                            \\begin{cases}\n                                a \\leq b\\\\\n                                a \\geq b\n                            \\end{cases}\n                        `}\n                    
    \n                    Serve solo nella teoria per dimostrare che le forme sono equivalenti.\n                    \n                \n                    
    \n                        Aggiungi una variabile slack {r`s`} non-vincolata a ogni disequazione nel sistema:\n                    
    \n                    
    \n                        {r`\n                            a \\leq b \\Leftrightarrow a + s = b\n                        `}\n                    
    \n                    
    \n                        {r`\n                            a \\geq b \\Leftrightarrow a - s = b\n                        `}\n                    
    \n                    \n                \n                    
    \n                        Sdoppia ogni variabile non-vincolata in due variabili con vincolo di non-negatività:\n                    
    \n                    
    \n                        {r`\\begin{cases}\n                            a = a^+ - a^-\\\\\n                            a^+ \\geq 0\\\\\n                            a^- \\geq 0\n                        \\end{cases}`}\n                    
    \n                    \n            
    \n            
    \n                \n                    
    \n                        Un modo per rappresentare sistemi in forma standard, anche noto come matrice equivalente completa del sistema.\n                    
    \n                    \n                        Il sistema:

    \n                        {r`\n                            \\begin{cases}\n                            2000x_1 + 1000x_2 = z\\\\\n                            1x_1 \\leq 3\\\\\n                            1x_2 \\leq 3\\\\\n                            2x_1 + 2x_2 \\leq 7\n                            \\end{cases}\n                        `}

    \n                        Diventa il tableau:

    \n                        \n                            \n                                \n                                    \n                                    \n                                    \n                                    \n                                    \n                                \n                            \n                            \n                                \n                                    \n                                    \n                                    \n                                    \n                                    \n                                \n                                \n                                    \n                                    \n                                    \n                                    \n                                    \n                                \n                                \n                                    \n                                    \n                                    \n                                    \n                                    \n                                \n                                \n                                    \n                                    \n                                    \n                                    \n                                    \n                                \n                            \n                        
    TNx_1x_2s_1s_2
    z2000100000
    31010
    30101
    72200
    \n                        \n                    \n                \n                    
    \n                        Variabili che hanno tutti 0 e un solo 1 nella loro colonna del tableau.\n                    
    \n                    
    \n                        La loro controparte sono le variabili fuori base, che hanno qualsiasi altro valore.\n                    
    \n                    \n            
    \n            
    \n                \n                    
    \n                        Un algoritmo per minimizzare/massimizzare trovare efficientemente valore ottimo di problemi di ottimizzazione lineare, derivato da Gauss-Jordan.\n                    
    \n                    
    \n                        Da esso si può anche ricavare un vertice ottimo ammissibile.
    \n                        C'è la possibilità che ne esistano anche altri: quello ottenuto dipende da come è stata effettuata la scelta delle variabili entranti.\n                    
    \n                    \n                        E' spiegato in modo semplice qui, e ci sono dei codici sorgenti di esempio qui.\n                    \n                    \n                        
    \n                            Questa è la soluzione passo per passo del problema 3 del file Ex_LP_testo.\n                        
    \n                        \n                    \n                \n                    
      \n                        
    1. Trasforma il sistema in forma standard.
      2. \n                        
    2. Trova tante variabili linearmente indipendenti quante siano le righe: esse saranno la base iniziale.
      3. \n                        
    3. Finchè ci sono variabili con coefficienti positivi/negativi nella funzione obiettivo:\n                            
        \n                                
      1. \n                                    Scegli la prima variabile fuori base con coefficiente positivo/negativo nella funzione obiettivo: essa è la variabile entrante.
        \n                                    \n                                
        2. \n                                
      2. \n                                    Scegli la variabile in base con il minor rapporto positivo {r`\\frac{termine\\ noto}{coeff.\\ variabile\\ entrante}`}.\n                                    \n                                
        3. \n                                
      3. Pivot: riscrivi tutte le funzioni del sistema in termini della variabile entrante.
        4. \n                            
      \n                        
      4. \n                        
    4. Il poliedro è : i termini noti dei vincoli sono le coordinate del suo vertice ottimo, mentre il termine noto della funzione obiettivo è il valore ottimo.
      5. \n                    
    \n                    \n                        È praticamente l'algoritmo di Gauss-Jordan applicato al tableau, con delle regole aggiuntive per la decisione delle variabili di pivot.\n                    \n                    \n                \n                    
    \n                        Una soluzione con almeno una variabile di valore 0, dovuta a uno o più vincoli ridondanti.\n                    
    \n                    
    \n                        Senza Regola di Bland e in presenza di vincoli ridondanti si rischia di trovarsi a fare pivot infiniti.\n                    
    \n                    \n            
    \n            
    \n                \n                    
    \n                        Un estensione del Simplex per permettere la risoluzione di problemi la cui origine non è una soluzione ammissibile.\n                    
    \n                    
    \n                        Prevede l'introduzione di un problema ausiliario, le cui incognite sono dette artificiali.\n                    
    \n                    
    \n                        Il vettore delle incognite artificiali è solitamente chiamato {r`\\mathbf{y}`}.\n                    
    \n                    \n                        E' spiegato in modo semplice qui.\n                    \n                    \n                \n                    
      \n                        
    1. Crea un nuovo tableau, aggiungendo variabili artificiali in modo da avere una base ammissibile.
      2. \n                        
    2. Sostituisci la vecchia funzione obiettivo con una nuova che minimizzi la somma di tutte le variabili artificiali.
      3. \n                        
    3. Fase 1: Risolvi il nuovo problema con il simplex primale.
      4. \n                        
    4. Se il Simplex termina quando ci sono ancora variabili artificiali nella base, allora il poliedro è .
      5. \n                        
    5. Una volta che le variabili artificiali sono fuori base, elimina le loro colonne e la nuova funzione obiettivo.
      6. \n                        
    6. Riporta il tableau in forma base compiendo operazioni per azzerare i coefficienti delle variabili di base nella funzione obiettivo.
      7. \n                        
    7. Fase 2: Risolvi il tableau con il simplex primale.
      8. \n                    
    \n                    \n            
    \n            
    \n                \n                    
    \n                        Una versione semplificata di un problema nella quale si ignora la violazione di uno o più vincoli.\n                    
    \n                    \n                \n                    
    \n                        Un rilassamento che permette di misurare di quanto i vincoli vengono violati.\n                    
    \n                    
    \n                        I vincoli, moltiplicati per coefficienti di rilassamento, vengono inseriti nella funzione obiettivo.\n                    
    \n                    
    \n                        Il vettore dei coefficienti di rilassamento solitamente è indicato con {r`\\mathbf{u}`}.\n                    
    \n                    \n                        
    \n                            Il sistema:\n                        
    \n                        {r`\n                            \\begin{cases}\n                            z = 3 x_1 + 5 x_2\\\\\n                            2 x_1 + 3 x_2 \\geq 12\\\\\n                            - x_1 + 3 x_2 \\geq 3\\\\\n                            x_1 \\geq 0\\\\\n                            x_2 \\geq 0\n                            \\end{cases}\n                        `}\n                        
    \n                            diventa:\n                        
    \n                        {r`\n                            \\begin{cases}\n                            z = 3 x_1 + 5 x_2 + u_1 ( 12 - 2 x_1 - 3 x_2 ) + u_2 ( 3 + x_1 - 3 x_2 )\\\\\n                            x_1 \\geq 0\\\\\n                            x_2 \\geq 0\n                            \\end{cases}\n                        `}\n                        \n                    \n            
    \n            
    \n                \n                    
    \n                        Il sistema che massimizza/minimizza i moltiplicatori di rilassamento di un problema detto primale.\n                    
    \n                    \n                \n                    
    \n                        Possiamo trasporre il tableau e sostituire le variabili {r`x_n`} con variabili {r`u_n`} per ottenere il sistema duale!\n                    
    \n                    
    \n                        I maggiori e minori dei vincoli diventeranno maggiori e minori delle variabili e viceversa.\n                    
    \n                    \n                \n                    
      \n                        
    • Se un problema ha una soluzione finita, allora anche il suo duale la avrà.
      • \n                        
    • Se un problema è , allora il suo duale potrà essere  oppure .
      • \n                        
    • Se un problema è , allora il suo duale sarà certamente .
      • \n                    
    \n                    \n            
    \n            
    \n                \n                    
    \n                        Una disuguaglianza lineare {r`c_0 \\leq \\mathbf{c}^T \\mathbf{x}`} è verificata da tutti i punti di un poliedro non- se e solo se esiste un vettore {r`u \\in \\mathfrak{R}^m`} tale che:\n                    
    \n                    {r`\\mathbf{c}^T \\geq \\mathbf{u}^T \\mathbf{A}`}\n                    {r`c_0 \\leq \\mathbf{u}^T \\mathbf{b}`}\n                    
    \n                        TODO: Cioè?\n                    
    \n                    \n                \n                    
    \n                        Il teorema che dimostra l'equivalenza tra primale e duale.\n                    
    \n                    
    \n                        Se uno dei due problemi è finito, la soluzione di uno coincide con la soluzione dell'altro.\n                    
    \n                    
    \n                        {r`\\mathbf{c}^T \\mathbf{x} = \\mathbf{u}^T \\mathbf{b}`}\n                    
    \n                    
    \n                        TODO: Anche qui c'è una lunga dimostrazione...\n                    
    \n                    \n                \n                    
    \n                        Il teorema che dimostra che il valore della funzione obiettivo del duale (di un qualsiasi tableau) è sempre minore o uguale/maggiore o uguale alla soluzione del corrispettivo primale.\n                    
    \n                    
    \n                        TODO: Dimostrazione cortina, ma sembra complicata.\n                    
    \n                    \n                \n                    
    \n                        Il teorema che ci permette di passare dalla soluzione del duale alla soluzione del primale. TODO: credo?\n                    
    \n                    
    \n                        Si deriva combinando le seguenti condizioni:\n                    
    \n                    
      \n                        
    • Ammissibilità del primale: {r`\\mathbf{A} \\mathbf{X} \\geq \\mathbf{b}, \\quad \\mathbf{x} \\geq 0`}
      • \n                        
    • Ammissibilità del duale: {r`\\mathbf{u}^T \\mathbf{A} \\leq \\mathbf{c}^T, \\quad \\mathbf{u} \\geq 0`}
      • \n                        
    • Teorema della dualità forte: {r`\\mathbf{c}^T \\mathbf{x} = \\mathbf{u}^T \\mathbf{b}`} (alla soluzione ottima)
      • \n                    
    \n                    
    \n                        Ne risulta che una soluzione è ottima se e solo se:\n                    
    \n                    {r`\\left( \\mathbf{c}^T - \\mathbf{u}^T \\mathbf{A} \\right) \\mathbf{x} = 0`}\n                    {r`\\mathbf{u}^T \\left( \\mathbf{A} \\mathbf{x} - \\mathbf{b}  \\right) = 0`}\n                    \n            
    \n            
    \n                \n                    
    \n                        Un'estensione al Simplex primale che opera sul problema duale.\n                    
    \n                    \n                \n                    
    \n                        Funziona esattamente come il Simplex primale, ma opera sulle righe invece che sulle colonne, cercando di rendere positivi/negativi tutti i termini noti.\n                    
    \n                    \n                        Significa che si possono moltiplicare tutti i valori di una riga per lo stesso numero e il risultato non cambia...?\n                    \n                    \n            
    \n            
    \n                \n                    
    \n                        Un procedimento che misura di quanto può variare il termine noto di un vincolo {r`b_i`} o il coefficiente della funzione obiettivo {r`c_i`} prima che la base degeneri. TODO: verificare\n                    
    \n                    \n            
    \n        
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diff --git a/docs/route-Statistica.chunk.94f25.js b/docs/route-Statistica.chunk.6c374.js
similarity index 99%
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= \theta"],["\\lim_{n \\to +\\infty} E(T_n) = \\theta"]);return M=function(){return n},n}function A(){var n=We(["E(T_n) = \theta"],["E(T_n) = \\theta"]);return A=function(){return n},n}function T(){var n=We(["T(\boldsymbol{X}) = \boldsymbol{X}"],["T(\\boldsymbol{X}) = \\boldsymbol{X}"]);return T=function(){return n},n}function U(){var n=We(["T(\boldsymbol{X})"],["T(\\boldsymbol{X})"]);return U=function(){return n},n}function B(){var n=We(["Y = sum_{i=1}^{n} X_i"],["Y = \\sum_{i=1}^{n} X_i"]);return B=function(){return n},n}function O(){var n=We(["Gamma (alpha, lambda) approx Nor left( \frac{alpha}{lambda}, \frac{alpha}{lambda^2} \right)"],["\\Gamma (\\alpha, \\lambda) \\approx Nor \\left( \\frac{\\alpha}{\\lambda}, \\frac{\\alpha}{\\lambda^2} \\right)"]);return O=function(){return n},n}function G(){var n=We(["Poi(lambda) approx Nor(lambda, lambda)"],["Poi(\\lambda) \\approx Nor(\\lambda, \\lambda)"]);return G=function(){return n},n}function R(){var n=We(["overline{Bin} (n, p) approx Nor left( \frac{n}{p}, \frac{n cdot (1 - p)}{p^2} \right)"],["\\overline{Bin} (n, p) \\approx Nor \\left( \\frac{n}{p}, \\frac{n \\cdot (1 - p)}{p^2} \\right)"]);return R=function(){return n},n}function H(){var n=We(["Bin(n, p) approx Nor(n cdot p, n cdot p cdot q)"],["Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)"]);return H=function(){return n},n}function j(){var n=We(["\forall x in mathbb{R}, lim_{n \to +infty} P left( \frac{overline{X}_n - E(X)}{sqrt{\frac{Var(X)}{n}}} leq x \right) = Phi(x)"],["\\forall x \\in \\mathbb{R}, \\lim_{n \\to +\\infty} P \\left( \\frac{\\overline{X}_n - E(X)}{\\sqrt{\\frac{Var(X)}{n}}} \\leq x \\right) = \\Phi(x)"]);return j=function(){return n},n}function K(){var n=We(["overline{X}_n approx Nor left(E(X), \frac{Var(X)}{n} \right)"],["\\overline{X}_n \\approx Nor \\left(E(X), \\frac{Var(X)}{n} \\right)"]);return K=function(){return n},n}function Q(){var n=We(["Nor(0, 1) = Phi()"],["Nor(0, 1) = \\Phi()"]);return Q=function(){return n},n}function W(){var n=We(["overline{X}_n"],["\\overline{X}_n"]);return W=function(){return n},n}function J(){var n=We(["\forall epsilon > 0, P left( lim_{n \to +infty} | overline{X}_n - E(X) | < epsilon \right) = 1"],["\\forall \\epsilon > 0, P \\left( \\lim_{n \\to +\\infty} | \\overline{X}_n - E(X) | < \\epsilon \\right) = 1"]);return J=function(){return n},n}function Z(){var n=We(["E(X)"]);return Z=function(){return n},n}function $(){var n=We(["overline{X}_n"],["\\overline{X}_n"]);return $=function(){return n},n}function nn(){var n=We(["P( | overline{X}_n - E(X) | < epsilon) \to 1"],["P( | \\overline{X}_n - E(X) | < \\epsilon) \\to 1"]);return nn=function(){return n},n}function ln(){var n=We(["\forall epsilon > 0, lim_{n \to +infty} P( | overline{X}_n - E(X) | < epsilon) = 1"],["\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | \\overline{X}_n - E(X) | < \\epsilon) = 1"]);return ln=function(){return n},n}function en(){var n=We(["E(X)"]);return en=function(){return n},n}function an(){var n=We(["overline{X}_n"],["\\overline{X}_n"]);return an=function(){return n},n}function tn(){var n=We(["S_n^2 sim \frac{sigma^2}{n - 1} cdot chi^2 (n-1)"],["S_n^2 \\sim \\frac{\\sigma^2}{n - 1} \\cdot \\chi^2 (n-1)"]);return tn=function(){return n},n}function rn(){var n=We(["S_0^2 sim \frac{sigma^2}{n} cdot chi^2 (n)"],["S_0^2 \\sim \\frac{\\sigma^2}{n} \\cdot \\chi^2 (n)"]);return rn=function(){return n},n}function on(){var n=We(["overline{X}_n sim Nor left( mu, \frac{sigma^2}{n} \right)"],["\\overline{X}_n \\sim Nor \\left( \\mu, \\frac{\\sigma^2}{n} \\right)"]);return on=function(){return n},n}function un(){var n=We(["X sim Nor(mu, sigma^2)"],["X \\sim Nor(\\mu, \\sigma^2)"]);return un=function(){return n},n}function cn(){var n=We(["E(S_0^2) = E(S_n^2) = Var(X)"]);return cn=function(){return n},n}function sn(){var n=We(["Var(overline{X}_n) = \frac{Var(X)}{n}"],["Var(\\overline{X}_n) = \\frac{Var(X)}{n}"]);return sn=function(){return n},n}function pn(){var n=We(["E(overline{X}_n) = E(X)"],["E(\\overline{X}_n) = E(X)"]);return pn=function(){return n},n}function dn(){var n=We(["S_n^2 = \frac{1}{n - 1} cdot sum_{i = 1}^n (X_i - overline{X}_n)^2 = \frac{1}{n - 1} cdot ( n cdot M_2^{(2)} - n cdot overline{X}_n^2)"],["S_n^2 = \\frac{1}{n - 1} \\cdot \\sum_{i = 1}^n (X_i - \\overline{X}_n)^2 = \\frac{1}{n - 1} \\cdot ( n \\cdot M_2^{(2)} - n \\cdot \\overline{X}_n^2)"]);return dn=function(){return n},n}function mn(){var n=We(["S_0^2 = \frac{1}{n} cdot sum_{i = 1}^n (X_i - m)^2 = M_n^(2) - 2 cdot m cdot overline{X}_n + m^2"],["S_0^2 = \\frac{1}{n} \\cdot \\sum_{i = 1}^n (X_i - m)^2 = M_n^(2) - 2 \\cdot m \\cdot \\overline{X}_n + m^2"]);return mn=function(){return n},n}function fn(){var n=We(["m = E(X)"]);return fn=function(){return n},n}function bn(){var n=We(["overline{X}_n"],["\\overline{X}_n"]);return bn=function(){return n},n}function vn(){var n=We(["M^{(k)}_n = \frac{1}{n} cdot sum_{i = 1}^n X_i^k "],["M^{(k)}_n = \\frac{1}{n} \\cdot \\sum_{i = 1}^n X_i^k "]);return vn=function(){return n},n}function _n(){var n=We(["Var left( sum_i X_i \right) = sum_i Var(X_i)"],["Var \\left( \\sum_i X_i \\right) = \\sum_i Var(X_i)"]);return _n=function(){return n},n}function hn(){var n=We(["Cov(X, Y) = 0"]);return hn=function(){return n},n}function Xn(){var n=We(["Var(X + Y) = Var(X) + Var(Y) + 2 cdot Cov(X, Y)"],["Var(X + Y) = Var(X) + Var(Y) + 2 \\cdot Cov(X, Y)"]);return Xn=function(){return n},n}function gn(){var n=We(["Y = a X + b Longleftrightarrow | \rho_{X, Y} | = 1"],["Y = a X + b \\Longleftrightarrow | \\rho_{X, Y} | = 1"]);return gn=function(){return n},n}function qn(){var n=We(["-1 leq \rho_{X, Y} leq 1"],["-1 \\leq \\rho_{X, Y} \\leq 1"]);return qn=function(){return n},n}function zn(){var n=We(["\rho_{X, Y} = \frac{Cov(X, Y)}{sqrt{Var(X)} cdot sqrt{Var(Y)}}"],["\\rho_{X, Y} = \\frac{Cov(X, Y)}{\\sqrt{Var(X)} \\cdot \\sqrt{Var(Y)}}"]);return zn=function(){return n},n}function En(){var n=We(["\n                                \boldsymbol{C_X} = \n                                \begin{bmatrix}\n                                    Var(X_1) & Cov(X_1, X_2) & Cov(X_1, X_3)\\\n                                    Cov(X_2, X_1) & Var(X_2) & Cov(X_2, X_3)\\\n                                    Cov(X_3, X_1) & Cov(X_3, X_2) & Var(X_3)\n                                end{bmatrix}\n                            "],["\n                                \\boldsymbol{C_X} = \n                                \\begin{bmatrix}\n                                    Var(X_1) & Cov(X_1, X_2) & Cov(X_1, X_3)\\\\\n                                    Cov(X_2, X_1) & Var(X_2) & Cov(X_2, X_3)\\\\\n                                    Cov(X_3, X_1) & Cov(X_3, X_2) & Var(X_3)\n                                \\end{bmatrix}\n                            "]);return En=function(){return n},n}function Pn(){var n=We(["\boldsymbol{X}"],["\\boldsymbol{X}"]);return Pn=function(){return n},n}function xn(){var n=We(["\boldsymbol{C_X}"],["\\boldsymbol{C_X}"]);return xn=function(){return n},n}function kn(){var n=We(["Cov(X, Y) = 0"]);return kn=function(){return n},n}function Ln(){var n=We(["Cov(X + Y, V + W) = Cov(X, Y) + Cov(X, W) + Cov(Y, V) + Cov(Y, W)"]);return Ln=function(){return n},n}function Fn(){var n=We(["Cov(alpha X, \beta Y) = alpha cdot \beta cdot Cov(X, Y)"],["Cov(\\alpha X, \\beta Y) = \\alpha \\cdot \\beta \\cdot Cov(X, Y)"]);return Fn=function(){return n},n}function yn(){var n=We(["Cov(X, X) = Var(X)"]);return yn=function(){return n},n}function Nn(){var n=We(["Cov(X, Y) = Cov(Y, X)"]);return Nn=function(){return n},n}function Vn(){var n=We(["Cov(X, alpha) = 0"],["Cov(X, \\alpha) = 0"]);return Vn=function(){return n},n}function Yn(){var n=We(["Cov(X, Y) = E((X - E(X) cdot (Y - E(Y)) = E(XY) - E(X) cdot E(Y)"],["Cov(X, Y) = E((X - E(X) \\cdot (Y - E(Y)) = E(XY) - E(X) \\cdot E(Y)"]);return Yn=function(){return n},n}function Cn(){var n=We(["E(X + Y) = E(X) + E(Y)"]);return Cn=function(){return n},n}function Sn(){var n=We(["E(g(X, Y)) = sum_{i, j} g(x_i, y_i) cdot p_{X, Y} (x_i, y_i)"],["E(g(X, Y)) = \\sum_{i, j} g(x_i, y_i) \\cdot p_{X, Y} (x_i, y_i)"]);return Sn=function(){return n},n}function wn(){var n=We(["P(X_1 in A_1, dots, X_n in A_n) = P(X_1 in A_1) \times dots \times P(X_n in A_n)"],["P(X_1 \\in A_1, \\dots, X_n \\in A_n) = P(X_1 \\in A_1) \\times \\dots \\times P(X_n \\in A_n)"]);return wn=function(){return n},n}function In(){var n=We(["p_X (x) = sum_j p_{X, Y} (x_i, y_j)"],["p_X (x) = \\sum_j p_{X, Y} (x_i, y_j)"]);return In=function(){return n},n}function Dn(){var n=We(["p_{X, Y} (x, y) = P(X = x, Y = y)"]);return Dn=function(){return n},n}function Mn(){var n=We(["F_X (x) = P(X leq x) = lim_{y \to +infty} F_{X, Y} (x, y)"],["F_X (x) = P(X \\leq x) = \\lim_{y \\to +\\infty} F_{X, Y} (x, y)"]);return Mn=function(){return n},n}function An(){var n=We(["F_{X, Y} (x, y) = P(X leq x, Y leq y)"],["F_{X, Y} (x, y) = P(X \\leq x, Y \\leq y)"]);return An=function(){return n},n}function Tn(){var n=We(["X, Y"]);return Tn=function(){return n},n}function Un(){var n=We(["\boldsymbol{X}"],["\\boldsymbol{X}"]);return Un=function(){return n},n}function Bn(){var n=We(["P(X > k) simeq P(Y geq k + \frac{1}{2})"],["P(X > k) \\simeq P(Y \\geq k + \\frac{1}{2})"]);return Bn=function(){return n},n}function On(){var n=We(["P(X geq k) simeq P(Y geq k - \frac{1}{2})"],["P(X \\geq k) \\simeq P(Y \\geq k - \\frac{1}{2})"]);return On=function(){return n},n}function Gn(){var n=We(["P(X leq k) simeq P(Y leq k + \frac{1}{2})"],["P(X \\leq k) \\simeq P(Y \\leq k + \\frac{1}{2})"]);return Gn=function(){return n},n}function Rn(){var n=We(["P(X < k) simeq P(Y leq k - \frac{1}{2})"],["P(X < k) \\simeq P(Y \\leq k - \\frac{1}{2})"]);return Rn=function(){return n},n}function Hn(){var n=We(["(k - \frac{1}{2}, k + \frac{1}{2})"],["(k - \\frac{1}{2}, k + \\frac{1}{2})"]);return Hn=function(){return n},n}function jn(){var n=We(["Bin(n, p) approx Nor(n cdot p, n cdot p cdot q)"],["Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)"]);return jn=function(){return n},n}function Kn(){var n=We(["Bin(n, p) approx Poi(n cdot p)"],["Bin(n, p) \\approx Poi(n \\cdot p)"]);return Kn=function(){return n},n}function Qn(){var n=We(["Ipe(N, K, n) approx Bin(n, \frac{K}{N})"],["Ipe(N, K, n) \\approx Bin(n, \\frac{K}{N})"]);return Qn=function(){return n},n}function Wn(){var n=We(["T(v) = \frac{Nor(0, 1)}{sqrt{\frac{chi^2(v)}{v}}}"],["T(v) = \\frac{Nor(0, 1)}{\\sqrt{\\frac{\\chi^2(v)}{v}}}"]);return Wn=function(){return n},n}function Jn(){var n=We(["chi^2 (n) + chi^2 (m) = chi^2 (n + m)"],["\\chi^2 (n) + \\chi^2 (m) = \\chi^2 (n + m)"]);return Jn=function(){return n},n}function Zn(){var n=We(["Gamma left( \frac{1}{2}, \frac{1}{2} \right) = chi^2 (v = 1)"],["\\Gamma \\left( \\frac{1}{2}, \\frac{1}{2} \\right) = \\chi^2 (v = 1)"]);return Zn=function(){return n},n}function $n(){var n=We(["Z^2 sim chi^2 (v = 1)"],["Z^2 \\sim \\chi^2 (v = 1)"]);return $n=function(){return n},n}function nl(){var n=We(["x_alpha = mu + z_alpha cdot sqrt{sigma^2}"],["x_\\alpha = \\mu + z_\\alpha \\cdot \\sqrt{\\sigma^2}"]);return nl=function(){return n},n}function ll(){var n=We(["z_alpha"],["z_\\alpha"]);return ll=function(){return n},n}function il(){var n=We(["F_Z(z) = phi(z) = \frac{1}{sqrt{2 pi}} int_{-infty}^{z} e^{-\frac{x^2}{2}} dx"],["F_Z(z) = \\phi(z) = \\frac{1}{\\sqrt{2 \\pi}} \\int_{-\\infty}^{z} e^{-\\frac{x^2}{2}} dx"]);return il=function(){return n},n}function el(){var n=We(["phi(z)"],["\\phi(z)"]);return el=function(){return n},n}function al(){var n=We(["X sim Nor(m, v^2) implies alpha X + \beta sim Nor(alpha m + \beta, (alpha v)^2)"],["X \\sim Nor(m, v^2) \\implies \\alpha X + \\beta \\sim Nor(\\alpha m + \\beta, (\\alpha v)^2)"]);return al=function(){return n},n}function tl(){var n=We(["Var(X) = sigma^2"],["Var(X) = \\sigma^2"]);return tl=function(){return n},n}function rl(){var n=We(["E(X) = mu"],["E(X) = \\mu"]);return rl=function(){return n},n}function ol(){var n=We(["m_X (t) = e^{mu cdot t + \frac{sigma^2 cdot t^2}{2}}"],["m_X (t) = e^{\\mu \\cdot t + \\frac{\\sigma^2 \\cdot t^2}{2}}"]);return ol=function(){return n},n}function ul(){var n=We(["f_X (x) = \frac{e^{-\frac{(x - mu)^2}{2 sigma^2}}}{sqrt{2 pi cdot sigma^2}}"],["f_X (x) = \\frac{e^{-\\frac{(x - \\mu)^2}{2 \\sigma^2}}}{\\sqrt{2 \\pi \\cdot \\sigma^2}}"]);return ul=function(){return n},n}function cl(){var n=We(["Nor(mu, sigma^2)"],["Nor(\\mu, \\sigma^2)"]);return cl=function(){return n},n}function sl(){var n=We(["Var(X) = \frac{(b - a)^2}{12}"],["Var(X) = \\frac{(b - a)^2}{12}"]);return sl=function(){return n},n}function pl(){var n=We(["E(X) = \frac{a + b}{2}"],["E(X) = \\frac{a + b}{2}"]);return pl=function(){return n},n}function dl(){var n=We(["m_X (t) = \frac{e^{b cdot t} - e^{a cdot t}}{(b - a) cdot t}"],["m_X (t) = \\frac{e^{b \\cdot t} - e^{a \\cdot t}}{(b - a) \\cdot t}"]);return dl=function(){return n},n}function ml(){var n=We(["f_X (x) = \begin{cases}\n                                0 qquad quad x < a  \n                                \frac{1}{b - a} qquad a leq x leq b\\\n                                1 qquad quad x > b\n                            end{cases}"],["f_X (x) = \\begin{cases}\n                                0 \\qquad \\quad x < a  \n                                \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n                                1 \\qquad \\quad x > b\n                            \\end{cases}"]);return ml=function(){return n},n}function fl(){var n=We(["f_X (x) = \begin{cases}\n                                \frac{1}{b - a} qquad a leq x leq b\\\n                                0 qquad quad altrimenti    \n                            end{cases}"],["f_X (x) = \\begin{cases}\n                                \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n                                0 \\qquad \\quad altrimenti    \n                            \\end{cases}"]);return fl=function(){return n},n}function bl(){var n=We(["P(X in (c, d)) = \frac{d - c}{b - a}"],["P(X \\in (c, d)) = \\frac{d - c}{b - a}"]);return bl=function(){return n},n}function vl(){var n=We(["Uni(a, b)"]);return vl=function(){return n},n}function _l(){var n=We(["[a, b]"]);return _l=function(){return n},n}function hl(){var n=We(["Var(X) = \frac{alpha}{lambda^2}"],["Var(X) = \\frac{\\alpha}{\\lambda^2}"]);return hl=function(){return n},n}function Xl(){var n=We(["E(X) = \frac{alpha}{lambda}"],["E(X) = \\frac{\\alpha}{\\lambda}"]);return Xl=function(){return n},n}function gl(){var n=We(["m_X (t) : ( t < lambda ) in mathbb{R} = left( \frac{lambda}{lambda - t} \right) ^alpha"],["m_X (t) : ( t < \\lambda ) \\in \\mathbb{R} = \\left( \\frac{\\lambda}{\\lambda - t} \\right) ^\\alpha"]);return gl=function(){return n},n}function ql(){var n=We(["f_X (x) = \begin{cases}\n                            0 qquad qquad qquad qquad qquad x < 0\\\n                            \frac{1}{(n-1)!} cdot lambda^n cdot x^{n-1} cdot e^{-lambda cdot x} quad k > 0\n                            end{cases}"],["f_X (x) = \\begin{cases}\n                            0 \\qquad \\qquad \\qquad \\qquad \\qquad x < 0\\\\\n                            \\frac{1}{(n-1)!} \\cdot \\lambda^n \\cdot x^{n-1} \\cdot e^{-\\lambda \\cdot x} \\quad k > 0\n                            \\end{cases}"]);return ql=function(){return n},n}function zl(){var n=We(["Gamma(n, lambda)"],["\\Gamma(n, \\lambda)"]);return zl=function(){return n},n}function El(){var n=We(["lambda"],["\\lambda"]);return El=function(){return n},n}function Pl(){var n=We(["P([X > s + t | X > s]) = P([X > t])"]);return Pl=function(){return n},n}function xl(){var n=We(["Var(X) = \frac{1}{lambda^2}"],["Var(X) = \\frac{1}{\\lambda^2}"]);return xl=function(){return n},n}function kl(){var n=We(["E(X) = \frac{1}{lambda}"],["E(X) = \\frac{1}{\\lambda}"]);return kl=function(){return n},n}function Ll(){var n=We(["m_X (t) : { t | t < lambda } in mathbb{R} = \frac{lambda}{lambda - t}"],["m_X (t) : \\{ t | t < \\lambda \\} \\in \\mathbb{R} = \\frac{\\lambda}{\\lambda - t}"]);return Ll=function(){return n},n}function Fl(){var n=We(["F_X (t) = \begin{cases}\n                            0 qquad qquad t < 0\\\n                            1 - e^{-lambda cdot t} quad t geq 0\n                            end{cases}"],["F_X (t) = \\begin{cases}\n                            0 \\qquad \\qquad t < 0\\\\\n                            1 - e^{-\\lambda \\cdot t} \\quad t \\geq 0\n                            \\end{cases}"]);return Fl=function(){return n},n}function yl(){var n=We(["f_X (x) = \begin{cases}\n                            0 qquad qquad x < 0\\\n                            lambda cdot e^{-lambda cdot x} quad x > 0\n                            end{cases}"],["f_X (x) = \\begin{cases}\n                            0 \\qquad \\qquad x < 0\\\\\n                            \\lambda \\cdot e^{-\\lambda \\cdot x} \\quad x > 0\n                            \\end{cases}"]);return yl=function(){return n},n}function Nl(){var n=We(["Esp(lambda)"],["Esp(\\lambda)"]);return Nl=function(){return n},n}function Vl(){var n=We(["lambda"],["\\lambda"]);return Vl=function(){return n},n}function Yl(){var n=We(["Poi(t cdot lambda)"],["Poi(t \\cdot \\lambda)"]);return Yl=function(){return n},n}function Cl(){var n=We(["mu = t cdot lambda"],["\\mu = t \\cdot \\lambda"]);return Cl=function(){return n},n}function Sl(){var n=We(["lambda"],["\\lambda"]);return Sl=function(){return n},n}function wl(){var n=We(["lambda"],["\\lambda"]);return wl=function(){return n},n}function Il(){var n=We(["E(X^2) = mu^2 + mu"],["E(X^2) = \\mu^2 + \\mu"]);return Il=function(){return n},n}function Dl(){var n=We(["Var(X) = mu"],["Var(X) = \\mu"]);return Dl=function(){return n},n}function Ml(){var n=We(["E(X) = mu"],["E(X) = \\mu"]);return Ml=function(){return n},n}function Al(){var n=We(["m_X (t) = e^{mu cdot (e^t - 1)}"],["m_X (t) = e^{\\mu \\cdot (e^t - 1)}"]);return 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n=We(["\boldsymbol{D}^{r}_{n, k} = n^k"],["\\boldsymbol{D}^{r}_{n, k} = n^k"]);return ve=function(){return n},n}function _e(){var n=We(["\boldsymbol{D}_{n, k} = \frac{n!}{(n - k)!}"],["\\boldsymbol{D}_{n, k} = \\frac{n!}{(n - k)!}"]);return _e=function(){return n},n}function he(){var n=We(["P(E) = \frac{len(E)}{len(Omega)}"],["P(E) = \\frac{len(E)}{len(\\Omega)}"]);return he=function(){return n},n}function Xe(){var n=We(["P(E cup F) = P(E) + P(F) - P(E cap F)"],["P(E \\cup F) = P(E) + P(F) - P(E \\cap F)"]);return Xe=function(){return n},n}function ge(){var n=We(["F subseteq E implies P(F) leq P(E)"],["F \\subseteq E \\implies P(F) \\leq P(E)"]);return ge=function(){return n},n}function qe(){var n=We(["P(\bar{E}) = 1 - P({E})"],["P(\\bar{E}) = 1 - P({E})"]);return qe=function(){return n},n}function ze(){var n=We(["P left ( \bigcup_i E_i \right ) = sum_i P ( E_i )"],["P \\left ( \\bigcup_i E_i \\right ) = \\sum_i P ( E_i )"]);return ze=function(){return n},n}function Ee(){var 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n=We(["E in mathcal{F} implies \bar{E} in mathcal{F}"],["E \\in \\mathcal{F} \\implies \\bar{E} \\in \\mathcal{F}"]);return Ye=function(){return n},n}function Ce(){var n=We(["Omega in mathcal{F}"],["\\Omega \\in \\mathcal{F}"]);return Ce=function(){return n},n}function Se(){var n=We(["sigma"],["\\sigma"]);return Se=function(){return n},n}function we(){var n=We(["sigma"],["\\sigma"]);return we=function(){return n},n}function Ie(){var n=We(["mathcal{F}"],["\\mathcal{F}"]);return Ie=function(){return n},n}function De(){var n=We(["mathcal{F}"],["\\mathcal{F}"]);return De=function(){return n},n}function Me(){var n=We(["E cap F = emptyset"],["E \\cap F = \\emptyset"]);return Me=function(){return n},n}function Ae(){var n=We(["E = emptyset"],["E = \\emptyset"]);return Ae=function(){return n},n}function Te(){var n=We(["E subseteq F"],["E \\subseteq F"]);return Te=function(){return n},n}function Ue(){var n=We(["E setminus F = E cap \bar{F}"],["E \\setminus F = E \\cap \\bar{F}"]);return 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esiti possibili di un esperimento."),n("p",null,n(Je.b,null,ta(je())))),n(Ze.a,{title:"Esito"},n("blockquote",null,'"omeghino"'),n("p",null,"Un ",n("b",null,"elemento")," dello spazio campionario."),n("p",null,n(Je.b,null,ta(He())))),n(Ze.a,{title:"Evento"},n("blockquote",null,'"e"'),n("p",null,"Un ",n("b",null,"sottoinsieme")," dello spazio campionario."),n("p",null,n(Je.b,null,ta(Re()))),n("p",null,"Lo spazio campionario stesso è un ",n("b",null,"evento certo"),".")),n(Ze.a,{title:"Not"},n("blockquote",null,'"not e"'),n("p",null,"Il ",n("b",null,"complementare")," di un sottoinsieme."),n("p",null,n(Je.b,null,ta(Ge())))),n(Ze.a,{title:"And"},n("blockquote",null,'"e intersecato effe"'),n("p",null,"L'",n("b",null,"intersezione")," di più sottoinsiemi."),n("p",null,n(Je.b,null,ta(Oe())))),n(Ze.a,{title:"Or"},n("blockquote",null,'"e unito a effe"'),n("p",null,"L'",n("b",null,"unione")," di più 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",n("i",null,"famiglia degli eventi"),"."),n("p",null,n(Je.b,null,ta(De()))),n("p",null,"Qualsiasi sottoinsieme appartenente a ",n(Je.b,null,ta(Ie()))," è considerato un evento.")),n(Ze.a,{title:n("span",null,n(Je.b,null,ta(we())),"-algebra")},n("blockquote",null,'"sigma algebra"'),n("p",null,"Se la famiglia degli eventi soddisfa questi tre requisiti, allora viene detta ",n("i",null,n(Je.b,null,ta(Se())),"-algebra"),":"),n("ol",null,n("li",null,"Lo spazio campionario è un evento: ",n(Je.b,null,ta(Ce()))),n("li",null,"Se un sottoinsieme è un evento, allora anche il suo complementare lo è: ",n(Je.b,null,ta(Ye()))),n("li",null,"Se due sottoinsiemi sono eventi, allora lo sono anche la loro unione e intersezione: ",n(Je.b,null,ta(Ve())))),n("p",null,"Un esempio: ",n(Je.b,null,ta(Ne()))))),n($e.a,null,n(Ze.a,{title:"Partizione"},n("blockquote",null,'"la partizione e composta da e uno, e due, e tre..."'),n("p",null,"Un insieme di esiti e eventi:"),n("ul",null,n("li",null,n("b",null,"Finito"),"."),n("li",null,"In cui tutti gli eventi hanno ",n("b",null,"probabilità diversa da 0"),"."),n("li",null,"In cui tutti gli eventi sono ",n("b",null,"mutualmente esclusivi"),"."),n("li",null,"In cui l'unione di tutti i suoi elementi ",n("b",null,"copre lo spazio campionario"),".")),n("p",null,"La partizione ",n(Je.b,null,ta(ye()))," è composta dagli eventi ",n(Je.b,null,ta(Fe())),", ",n(Je.b,null,ta(Le())),", ",n(Je.b,null,ta(ke())),", fino a ",n(Je.b,null,ta(xe())),"."),n(na.a,null,"Se lo spazio campionario fosse una torta, una sua partizione sarebbe l'insieme delle fette di uno dei modi in cui si potrebbe tagliare."))),n($e.a,{title:"Assiomi della probabilità"},n(Ze.a,{title:"Primo assioma della probabilità"},n("p",null,"La probabilità di un evento è un numero tra 0 e 1."),n("p",null,n(Je.b,null,ta(Pe())))),n(Ze.a,{title:"Secondo assioma della probabilità"},n("p",null,"La probabilità dello spazio campionario è sempre 1."),n("p",null,n(Je.b,null,ta(Ee())))),n(Ze.a,{title:"Terzo assioma della probabilità"},n("p",null,"La probabilità dell'unione di eventi indipendenti è uguale alla somma delle loro probabilità."),n("p",null,n(Je.b,null,ta(ze()))))),n($e.a,{title:"Conseguenze degli assiomi"},n(Ze.a,{title:"Probabilità di un evento negato"},n("p",null,"La probabilità di un evento negato è uguale a 1 meno la probabilità dell'evento non negato."),n("p",null,n(Je.b,null,ta(qe())))),n(Ze.a,{title:"Probabilità di un evento incluso"},n("p",null,"La probabilità di un evento incluso in un altro è sempre minore o uguale alla probabilità dell'evento in cui è incluso."),n("p",null,n(Je.b,null,ta(ge())))),n(Ze.a,{title:"Unione"},n("p",null,"La probabilità di un evento unito a un altro è uguale alla somma delle probabilità dei due eventi meno la probabilità della loro intersezione."),n("p",null,n(Je.b,null,ta(Xe()))),n(na.a,null,"Sommando le probabilità dei due eventi, l'intersezione viene contata due volte, e va 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Ripeto per ",n(Je.b,null,"k")," volte."),n("p",null,n("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),n("p",null,n(Je.b,null,ta(fe())))),n(Ze.a,{title:"Permutazioni"},n("p",null,"Estraggo ",n(Je.b,null,"n")," numeri e guardo in quanti ordini diversi li posso mettere."),n("p",null,n(Je.b,null,ta(me()))))),n($e.a,{title:"Probabilità condizionata"},n(Ze.a,{title:"Eventi condizionati"},n("blockquote",null,'"E dato F"'),n("p",null,"La probabilità che si verifichi ",n(Je.b,null,"E")," sapendo che ",n("b",null,"si è già verificato")," ",n(Je.b,null,"F"),"."),n("p",null,n(Je.b,null,ta(de()))),n(na.a,null,"Ricorda vagamente le pipe di ",n("code",null,"bash"),", però al contrario...")),n(Ze.a,{title:"Eventi mutualmente esclusivi"},n("p",null,"Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0."),n("p",null,n(Je.b,null,ta(pe()))))),n($e.a,null,n(Ze.a,{title:"Regola della catena"},n("p",null,"Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:"),n("p",null,n(Je.b,null,ta(se()))))),n($e.a,{title:"Le alternative"},n(Ze.a,{title:"Legge delle alternative"},n("p",null,"La probabilità che si verifichi un evento è pari alla somma delle probabilità dell'evento stesso dati tutti gli eventi di una partizione."),n("p",null,n(Je.b,null,ta(ce())))),n(Ze.a,{title:"Legge condizionata delle alternative"},n("p",null,"La legge delle alternative funziona anche quando ad essere partizionato è un ",n("b",null,"evento"),":"),n("p",null,n(Je.b,null,ta(ue())))),n(Ze.a,{title:"Formula di Bayes"},n("p",null,"Tramite la ",n("i",null,"formula di Bayes")," possiamo risalire alla probabilità di un evento condizionato a un altro partendo dalla probabilità di quest'ultimo condizionato al primo:"),n("p",null,n(Je.b,null,ta(oe()))),n(na.a,null,"In pratica, invertiamo gli eventi."))),n($e.a,{title:"Eventi indipendenti"},n(Ze.a,{title:"Due eventi indipendenti"},n("blockquote",null,'"eventi indipendenti a due a due"'),n("p",null,"Se due eventi sono indipendenti, sapere che uno dei due si è verificato non influisce sulle probabilità che si sia verificato l'altro."),n("p",null,n(Je.b,null,ta(re())))),n(Ze.a,{title:"Più eventi indipendenti"},n("blockquote",null,'"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque..."'),n("p",null,"Si può verificare l'indipendenza di più eventi alla volta:"),n("p",null,n(Je.b,null,ta(te()))),n("p",null,"Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.")),n(Ze.a,{title:"Famiglia di eventi indipendenti"},n("p",null,"Un insieme di ",n(Je.b,null,"n")," eventi è una ",n("i",null,"famiglia di eventi indipendenti")," se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti."),n(na.a,null,"Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e così via!"))),n($e.a,{title:"Variabili aleatorie"},n(Ze.a,{title:"Variabile aleatoria"},n("p",null,"Una funzione che fa corrispondere un numero reale a ogni possibile esito dello spazio campionario. ",n(Je.b,null,ta(ae())),".")),n(Ze.a,{title:n("abbr",{title:"Nome artigianale dato da Steffo."},"Insieme di ripartizione")},n("p",null,"Ad ogni variabile aleatoria sono associati gli eventi ",n(Je.b,null,ta(ee())),", che contengono tutti gli esiti a cui la variabile aleatoria associa un valore minore o uguale a ",n(Je.b,null,"t"),"."),n("p",null,"Per definizione, tutte le variabili aleatorie devono rispettare questa condizione:"),n("p",null,n(Je.b,null,ta(ie()))),n(na.a,null,"All'aumentare di t, l'insieme conterrà sempre più elementi.")),n(Ze.a,{title:"Supporto"},n("blockquote",null,'"supporto di X"'),n("p",null,"Il ",n("b",null,"codominio")," della variabile aleatoria è il suo ",n("i",null,"supporto"),"."),n("p",null,"Per indicare che un valore ",n(Je.b,null,"x_0")," appartiene al supporto di ",n(Je.b,null,"X"),", si usa la notazione ",n(Je.b,null,"X \\mapsto x_0"),"."))),n($e.a,{title:"Densità"},n(Ze.a,{title:"Funzione probabilità"},n("p",null,"La ",n("i",null,"funzione 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uguale a ",n(Je.b,null,"t"),":"),n("p",null,"Si può dire che essa rappresenti la probabilità dell'evento ",n(Je.b,null,ta(Wi())),":"),n("p",null,n(Je.b,null,ta(Qi())))),n(Ze.a,{title:"Proprietà della funzione"},n("ul",null,n("li",null,"È sempre ",n("b",null,"monotona crescente")," (non strettamente)."),n("br",null),n("li",null,"Vale ",n("b",null,"0")," a ",n(Je.b,null,"-\\infty")," e ",n("b",null,"1")," a ",n(Je.b,null,"+\\infty"),"."),n("br",null),n("li",null,"È ",n("b",null,"continua da destra"),": ",n(Je.b,null,ta(Ki()))))),n(Ze.a,{title:"Probabilità di un valore"},n("p",null,"Possiamo usare la funzione di ripartizione per calcolare la probabilità di un certo valore reale:"),n("p",null,n(Je.b,null,ta(ji()))))),n($e.a,{title:"Trasformazioni di variabili aleatorie"},n(Ze.a,{title:"Nel discreto"},n("p",null,"Nel discreto basta abbinare un nuovo valore a ogni valore della variabile originale.")),n(Ze.a,{title:"Nel continuo (invertibile)"},n("p",null,"Nel continuo applichiamo la formula 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",n("b",null,"funzione probabilità")," o ",n("b",null,"funzione densità")," è ",n("b",null,"massima"),".")),n(Ze.a,{title:"Quantili"},n("p",null,"Il ",n("i",null,"quantile")," ",n(Je.b,null,ta(Bi()))," di ordine ",n(Je.b,null,ta(Ui()))," della variabile aleatoria ",n(Je.b,null,"X")," è il più piccolo numero tale che:"),n("p",null,n(Je.b,null,ta(Ti()))),n("p",null),n("p",null,"Il quantile di ordine 0.5 ",n(Je.b,null,ta(Ai()))," è detto ",n("i",null,"mediana"),"."),n("p",null,"I quantili di ordine 0.25 ",n(Je.b,null,ta(Mi()))," e 0.75 ",n(Je.b,null,ta(Di()))," sono detti ",n("i",null,"quartili"),"."),n("p",null,"I quantili di ordine ",n(Je.b,null,ta(Ii()))," sono detti ",n("i",null,n(Je.b,null,"n"),"-esima percentile"),".")),n(Ze.a,{title:"Varianza"},n("p",null,"È un valore che indica quanto la variabile aleatoria si discosta generalmente dalla media:"),n("p",null,n(Je.b,null,ta(wi()))))),n($e.a,{title:"Disuguaglianze notevoli"},n(Ze.a,{title:"Disuguaglianza di Markov"},n("p",null,"Data una variabile aleatoria non-negativa:"),n("p",null,n(Je.b,null,ta(Si()))),n("p",null,"Divide in due parti (",n(Je.b,null,ta(Ci()))," e ",n(Je.b,null,ta(Yi())),") la funzione X, la cui media risulterà uguale a:"),n("p",null,n(Je.b,null,ta(Vi())))),n(Ze.a,{title:"Disuguaglianza di Čebyšëv"},n("blockquote",null,'"disuguaglianza di cebicev"'),n("p",null,"Se la variabile aleatoria ",n(Je.b,null,"X")," ha media e varianza, allora la probabilità che essa abbia un valore a più di ",n(Je.b,null,ta(Ni()))," di distanza dal valore medio è minore o uguale a ",n(Je.b,null,ta(yi())),"."),n("p",null,n(Je.b,null,ta(Fi()))),n("p",null,"E anche:"),n("p",null,n(Je.b,null,ta(Li()))),n(na.a,null,"Serve per semplificare i calcoli quando la funzione di ripartizione è difficile da calcolare!"))),n($e.a,{title:"Un momento...!"},n(Ze.a,{title:"Momento"},n("p",null,"Il ",n("i",null,"momento")," ",n(Je.b,null,"k"),"-esimo di una variabile aleatoria è:"),n("p",null,n(Je.b,null,ta(ki()))),n(na.a,null,"La media di una variabile aleatoria è anche il suo primo momento.")),n(Ze.a,{title:"Funzione generatrice dei momenti"},n("p",null,"La ",n("i",null,"funzione generatrice dei momenti")," è:"),n("p",null,n(Je.b,null,ta(xi()))),n("p",null,"Se due variabile aleatorie hanno la stessa funzione generatrice dei momenti, allora esse hanno la ",n("b",null,"stessa distribuzione"),"."),n("p",null,"E' la ",n("b",null,"trasformata di Laplace")," della variabile aleatoria di X.")),n(Ze.a,{title:"Funzione caratteristica"},n("p",null,"La ",n("i",null,"funzione caratteristica")," è:"),n("p",null,n(Je.b,null,ta(Pi()))),n("p",null,"Se due variabile aleatorie hanno la stessa funzione caratteristica, allora esse hanno la ",n("b",null,"stessa distribuzione"),"."),n("p",null,"E' la ",n("b",null,"trasformata di Fourier")," della variabile aleatoria di X."))),n($e.a,{title:"Prove e schemi"},n(Ze.a,{title:"Variabile con distribuzione"},n("p",null,"Per dire che una variabile ha una certa distribuzione, si usa la notazione:"),n("p",null,n(Je.b,null,ta(Ei())))),n(Ze.a,{title:"Prova di Bernoulli"},n("p",null,"Una prova con solo due possibili esiti: ",n(la.a,null,"successo")," e ",n(ia.a,null,"insuccesso"),".")),n(Ze.a,{title:"Schema di Bernoulli"},n("p",null,"Una sequenza di prove di Bernoulli per le quali le probabilità di successo e fallimento rimangono invariate."))),n($e.a,{title:"Bernoulliana"},n(Ze.a,{title:"Distribuzione bernoulliana"},n("p",null,"Una variabile aleatoria che rappresenta una prova di Bernoulli:"),n("ul",null,n("li",null,"vale ",n(la.a,null,"1")," in caso di ",n(la.a,null,"successo"),"."),n("li",null,"vale ",n(ia.a,null,"0")," in caso di ",n(ia.a,null,"insuccesso"),".")),n("p",null,"Il suo simbolo è ",n(Je.b,null,ta(zi())))),n(Ze.a,{title:"Densità della bernoulliana"},n("p",null,"La distribuzione bernoulliana ha come densità:"),n("p",null,n(Je.b,null,ta(qi()))))),n($e.a,{title:"Binomiale"},n(Ze.a,{title:"Distribuzione binomiale"},n("p",null,"Una variabile aleatoria che conta il numero di successi di ",n(Je.b,null,"n")," prove di uno schema di Bernoulli."),n("p",null,"Il suo simbolo è ",n(Je.b,null,ta(gi())),".")),n(Ze.a,{title:"Densità della binomiale"},n("p",null,"La binomiale ha come densità:"),n("p",null,n(Je.b,null,ta(Xi())))),n(Ze.a,{title:"Momenti della binomiale"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della binomiale è:"),n("p",null,n(Je.b,null,ta(hi()))),n("p",null,"La ",n("b",null,"media")," di una binomiale è:"),n("p",null,n(Je.b,null,ta(_i()))),n("p",null,"La ",n("b",null,"varianza")," di una binomiale è:"),n("p",null,n(Je.b,null,ta(vi()))))),n($e.a,{title:"Geometrica"},n(Ze.a,{title:"Distribuzione geometrica"},n("p",null,"Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli fino alla comparsa del primo successo."),n("p",null,"Il suo simbolo è ",n(Je.b,null,"Geo(p)"),".")),n(Ze.a,{title:"Densità della geometrica"},n("p",null,"La geometrica ha come densità:"),n("p",null,n(Je.b,null,ta(bi())))),n(Ze.a,{title:"Momenti della geometrica"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della geometrica è:"),n("p",null,n(Je.b,null,ta(fi()))),n("p",null,"La ",n("b",null,"media")," della geometrica è:"),n("p",null,n(Je.b,null,ta(mi()))),n("p",null,"La ",n("b",null,"varianza")," della geometrica è:"),n("p",null,n(Je.b,null,ta(di())))),n(Ze.a,{title:"Assenza di memoria della geometrica"},n("p",null,"La geometrica non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),n("p",null,n(Je.b,null,ta(pi()))),n(na.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),n($e.a,{title:"Binomiale negativa"},n(Ze.a,{title:"Distribuzione binomiale negativa"},n("p",null,"Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli necessarie perchè si verifichi l'",n(Je.b,null,"n"),"-esimo successo."),n("p",null,"Il suo simbolo è ",n(Je.b,null,ta(si())),".")),n(Ze.a,{title:"Densità della binomiale negativa"},n("p",null,"La binomiale negativa ha come densità:"),n("p",null,n(Je.b,null,ta(ci())))),n(Ze.a,{title:"Momenti della binomiale negativa"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della binomiale negativa è:"),n("p",null,n(Je.b,null,ta(ui()))),n("p",null,"La ",n("b",null,"media")," della binomiale negativa è:"),n("p",null,n(Je.b,null,ta(oi()))),n("p",null,"La ",n("b",null,"varianza")," della binomiale negativa è:"),n("p",null,n(Je.b,null,ta(ri())))))),n($e.a,{title:"Geometrica traslata"},n(Ze.a,{title:"Distribuzione geometrica traslata"},n("p",null,"Una variabile aleatoria che conta il numero ",n(Je.b,null,"k")," di insuccessi consecutivi in uno schema di Bernoulli:"),n("p",null,"Il suo simbolo rimane ",n(Je.b,null,ta(ti())),".")),n(Ze.a,{title:"Densità della geometrica tralsata"},n("p",null,"La geometrica traslata ha come densità:"),n("p",null,n(Je.b,null,ta(ai())))),n(Ze.a,{title:"Momenti della geometrica traslata"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della geometrica traslata è:"),n("p",null,n(Je.b,null,ta(ei()))),n("p",null,"La ",n("b",null,"media")," della geometrica traslata è:"),n("p",null,n(Je.b,null,ta(ii()))),n("p",null,"La ",n("b",null,"varianza")," della geometrica è:"),n("p",null,n(Je.b,null,ta(li())))),n(Ze.a,{title:"Assenza di memoria della geometrica traslata"},n("p",null,"La geometrica traslata non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),n("p",null,n(Je.b,null,ta(ni()))),n(na.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),n($e.a,{title:"Binomiale negativa traslata"},n(Ze.a,{title:"Distribuzione binomiale negativa traslata"},n("p",null,"Una variabile aleatoria che conta il numero di insuccessi in uno schema di Bernoulli prima che si verifichi l'",n(Je.b,null,"n"),"-esimo successo."),n("p",null,"Il suo simbolo rimane ",n(Je.b,null,ta($l())),".")),n(Ze.a,{title:"Densità della binomiale negativa traslata"},n("p",null,"La binomiale negativa traslata ha come densità:"),n("p",null,n(Je.b,null,ta(Zl())))),n(Ze.a,{title:"Momenti della binomiale negativa traslata"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della binomiale negativa traslata è:"),n("p",null,n(Je.b,null,ta(Jl()))),n("p",null,"La ",n("b",null,"media")," della binomiale negativa traslata è:"),n("p",null,n(Je.b,null,ta(Wl()))),n("p",null,"La ",n("b",null,"varianza")," della binomiale negativa traslata è:"),n("p",null,n(Je.b,null,ta(Ql())))))),n($e.a,{title:"Ipergeometrica"},n(Ze.a,{title:"Distribuzione ipergeometrica"},n("p",null,"Una variabile aleatoria che, sapendo il numero di successi ",n(Je.b,null,"K")," e di insuccessi ",n(Je.b,null,"N-K"),", conta quanti successi si otterrebbero se se ne estraessero ",n(Je.b,null,"n")," in blocco."),n("p",null,"Il suo simbolo è ",n(Je.b,null,"Ipe(N, K, n)"),".")),n(Ze.a,{title:"Densità della ipergeometrica"},n("p",null,"La ipergeometrica ha come densità:"),n("p",null,n(Je.b,null,ta(Kl())))),n(Ze.a,{title:"Momenti della ipergeometrica"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della ipergeometrica è trascurabile."),n("p",null,"La ",n("b",null,"media")," della ipergeometrica è:"),n("p",null,n(Je.b,null,ta(jl()))),n("p",null,"La ",n("b",null,"varianza")," della ipergeometrica è:"),n("p",null,n(Je.b,null,ta(Hl())))))),n($e.a,{title:"Poissoniana"},n(Ze.a,{title:"Distribuzione poissoniana"},n("p",null,"Una variabile aleatoria che soddisfa tutte le seguenti caratteristiche:"),n("ul",null,n("li",null,"Binomiale: ",n(Je.b,null,ta(Rl()))),n("li",null,"Il numero di prove tende a infinito: ",n(Je.b,null,ta(Gl()))),n("li",null,"La probabilità di successo tende a 0: ",n(Je.b,null,ta(Ol()))),n("li",null,"La media è finita: ",n(Je.b,null,ta(Bl())))),n("p",null,"Il suo simbolo è ",n(Je.b,null,ta(Ul())))),n(Ze.a,{title:"Densità della poissoniana"},n("p",null,"La poissoniana ha come densità:"),n("p",null,n(Je.b,null,ta(Tl())))),n(Ze.a,{title:"Momenti della poissoniana"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della poissoniana è:"),n("p",null,n(Je.b,null,ta(Al()))),n("p",null,"La ",n("b",null,"media")," della poissoniana è:"),n("p",null,n(Je.b,null,ta(Ml()))),n("p",null,"La ",n("b",null,"varianza")," della poissoniana è:"),n("p",null,n(Je.b,null,ta(Dl()))),n("p",null,"Gli altri momenti della poissoniana sono:"),n("ol",{start:2},n("li",null,n(Je.b,null,ta(Il()))))))),n($e.a,{title:"Un altro schema"},n(Ze.a,{title:"Schema di Poisson"},n("p",null,"Una successione di ",n("b",null,"arrivi")," avvenuti in un certo arco temporale che:"),n("ul",null,n("li",null,"non sono sovrapposti."),n("li",null,"hanno intensità ",n(Je.b,null,ta(wl()))," costante."),n("li",null,"avvengono indipendentemente gli uni dagli altri."))),n(Ze.a,{title:"Processo di Poisson"},n("p",null,"Una variabile aleatoria ",n(Je.b,null,"N_t")," che conta il numero di arrivi di uno schema di Poisson di intensità ",n(Je.b,null,ta(Sl()))," in un intervallo di tempo di durata ",n(Je.b,null,"t"),"."),n("p",null,"E' una distribuzione poissoniana con ",n(Je.b,null,ta(Cl())),": ",n(Je.b,null,ta(Yl()))),n(na.a,null,"E' paragonabile a una bernoulliana: ogni successo corrisponde a un arrivo, mentre il tempo è il numero di prove effettuate (ma nel continuo)."))),n($e.a,{title:"Esponenziale"},n(Ze.a,{title:"Distribuzione esponenziale"},n("p",null,"Una variabile aleatoria che conta il tempo diwidehattesa prima del primo arrivo di un processo di Poisson di intensità ",n(Je.b,null,ta(Vl())),"."),n("p",null,"Il suo simbolo è ",n(Je.b,null,ta(Nl())),".")),n(Ze.a,{title:"Densità dell'esponenziale"},n("p",null,"L'esponenziale ha come ",n("b",null,"densità"),":"),n("p",null,n(Je.b,null,ta(yl()))),n("p",null,"L'esponenziale ha come ",n("b",null,"funzione di ripartizione"),":"),n("p",null,n(Je.b,null,ta(Fl())))),n(Ze.a,{title:"Momenti dell'esponenziale"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," dell'esponenziale è:"),n("p",null,n(Je.b,null,ta(Ll()))),n("p",null,"La ",n("b",null,"media")," dell'esponenziale è:"),n("p",null,n(Je.b,null,ta(kl()))),n("p",null,"La ",n("b",null,"varianza")," dell'esponenziale è:"),n("p",null,n(Je.b,null,ta(xl())))),n(Ze.a,{title:"Assenza di memoria della esponenziale"},n("p",null,"L'esponenziale non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),n("p",null,n(Je.b,null,ta(Pl()))),n(na.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),n($e.a,{title:"Legge gamma"},n(Ze.a,{title:"Distribuzione gamma"},n("p",null,"Una variabile aleatoria che conta il tempo diwidehattesa prima dell'",n(Je.b,null,"n"),"-esimo arrivo di un processo di Poisson di intensità ",n(Je.b,null,ta(El())),"."),n("p",null,"Il suo simbolo è ",n(Je.b,null,ta(zl())),".")),n(Ze.a,{title:"Densità della legge gamma"},n("p",null,"La legge gamma ha come densità:"),n("p",null,n(Je.b,null,ta(ql())))),n(Ze.a,{title:"Momenti della legge gamma"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della legge gamma è:"),n("p",null,n(Je.b,null,ta(gl()))),n("p",null,"La ",n("b",null,"media")," della legge gamma è:"),n("p",null,n(Je.b,null,ta(Xl()))),n("p",null,"La ",n("b",null,"varianza")," della legge gamma è:"),n("p",null,n(Je.b,null,ta(hl())))))),n($e.a,{title:"Uniforme"},n(Ze.a,{title:"Distribuzione uniforme"},n("p",null,"Una variabile aleatoria che può assumere qualsiasi valore in un intervallo ",n(Je.b,null,ta(_l()))," in modo equiprobabile."),n("p",null,"Il suo simbolo è ",n(Je.b,null,ta(vl()))),n("p",null,"Su di essa vale la seguente proprietà:"),n("p",null,n(Je.b,null,ta(bl())))),n(Ze.a,{title:"Densità della distribuzione uniforme"},n("p",null,"La distribuzione uniforme ha come ",n("b",null,"densità"),":"),n("p",null,n(Je.b,null,ta(fl()))),n("p",null,"La distribuzione uniforme ha come ",n("b",null,"funzione di ripartizione"),":"),n("p",null,n(Je.b,null,ta(ml())))),n(Ze.a,{title:"Momenti della distribuzione uniforme"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della distribuzione uniforme è:"),n("p",null,n(Je.b,null,ta(dl()))),n("p",null,"La ",n("b",null,"media")," della distribuzione uniforme è:"),n("p",null,n(Je.b,null,ta(pl()))),n("p",null,"La ",n("b",null,"varianza")," della distribuzione uniforme è:"),n("p",null,n(Je.b,null,ta(sl())))))),n($e.a,{title:"Normale o Gaussiana"},n(Ze.a,{title:"Distribuzione normale"},n("p",null,"Una variabile aleatoria con una specifica distribuzione."),n("p",null,"Il suo simbolo è ",n(Je.b,null,ta(cl())),"."),n(na.a,null,n(Je.b,null,"\\mu")," e ",n(Je.b,null,"\\sigma^2")," sono rispettivamente la media e la varianza della distribuzione!")),n(Ze.a,{title:"Densità della distribuzione normale"},n("p",null,"La distribuzione normale ha come densità:"),n("p",null,n(Je.b,null,ta(ul())))),n(Ze.a,{title:"Momenti della distribuzione normale"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della distribuzione normale è:"),n("p",null,n(Je.b,null,ta(ol()))),n("p",null,"La ",n("b",null,"media")," della distribuzione normale è:"),n("p",null,n(Je.b,null,ta(rl()))),n("p",null,"La ",n("b",null,"varianza")," della distribuzione normale è:"),n("p",null,n(Je.b,null,ta(tl())))))),n($e.a,null,n(Ze.a,{title:"Trasformazione della normale"},n("p",null,"Qualsiasi normale può essere trasformata in qualsiasi altra normale:"),n("p",null,n(Je.b,null,ta(al())))),n(Ze.a,{title:"Normale standard"},n("p",null,"La distribuzione normale standard ",n(Je.b,null,"Z")," è:"),n("p",null,n(Je.b,null,"Z \\sim Nor(0, 1)")),n("p",null,"La sua funzione di ripartizione è detta ",n(Je.b,null,ta(el()))," e vale:"),n("p",null,n(Je.b,null,ta(il())))),n(Ze.a,{title:"Quantili normali"},n("p",null,"Da un quantile ",n(Je.b,null,ta(ll()))," della normale standard è possibile risalire allo stesso quantile di qualsiasi altra normale:"),n("p",null,n(Je.b,null,ta(nl()))))),n($e.a,null,n(Ze.a,{title:"Gamma e normale"},n("p",null,"La distribuzione normale ha una particolare relazione con la distribuzione Gamma:"),n("p",null,n(Je.b,null,ta($n())))),n(Ze.a,{title:"La funzione Chi"},n("blockquote",null,'"chi-quadro a un grado di libertà"'),n("p",null,"Esiste una distribuzione Gamma particolare:"),n("p",null,n(Je.b,null,ta(Zn()))),n("p",null,"Più chi-quadro possono essere sommate per aumentare i loro gradi di libertà:"),n("p",null,n(Je.b,null,ta(Jn())))),n(Ze.a,{title:"T di Student"},n("p",null,"Un'altra funzione particolare è la funzione T di Student:"),n("p",null,n(Je.b,null,ta(Wn()))))),n($e.a,{title:"Approssimazioni notevoli"},n(Ze.a,{title:"Ipergeometrica e binomiale"},n("p",null,"La binomiale è come una ipergeometrica ma con ripetizioni, quindi per valori molto grandi di ",n(Je.b,null,"N")," rispetto a ",n(Je.b,null,"n"),", si può dire che:"),n("p",null,n(Je.b,null,ta(Qn())))),n(Ze.a,{title:"Binomiale e poissoniana"},n("p",null,"La binomiale non è altro che una poissoniana a tempo discreto, quindi, se ",n(Je.b,null,"n")," è grande e ",n(Je.b,null,"n \\cdot p")," è nell'ordine di grandezza delle unità, allora:"),n("p",null,n(Je.b,null,ta(Kn())))),n(Ze.a,{title:"Binomiale e normale"},n("p",null,"Per il Teorema di De Moivre-Laplace, se una binomiale ha una ",n(Je.b,null,"n")," grande e ",n(Je.b,null,"p")," non vicina a 0 o 1, si può approssimare con:"),n("p",null,n(Je.b,null,ta(jn())))),n(Ze.a,{title:"Correzione di Yates"},n("p",null,"Passando da una variabile discreta ",n(Je.b,null,"X")," a una continua ",n(Je.b,null,"Y"),", per ogni valore discreto ",n(Je.b,null,"k"),' la probabilità viene "spalmata" su tutto l\'intervallo ',n(Je.b,null,ta(Hn())),":"),n("ul",null,n("li",null,n(Je.b,null,ta(Rn()))),n("li",null,n(Je.b,null,ta(Gn()))),n("li",null,n(Je.b,null,ta(On()))),n("li",null,n(Je.b,null,ta(Bn())))))),n($e.a,{title:"Vettori aleatori"},n(Ze.a,{title:"Vettore aleatorio"},n("p",null,"Un vettore ",n("b",null,"composto da variabili aleatorie"),"."),n("p",null,"Il suo simbolo generalmente è ",n(Je.b,null,ta(Un()))," oppure ",n(Je.b,null,ta(Tn())),".")),n(Ze.a,{title:"Funzioni di ripartizione"},n("p",null,"I vettori aleatori hanno più funzioni di ripartizione che si differenziano in base al numero di parametri."),n("p",null,"Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"funzione di ripartizione congiunta"),":"),n("p",null,n(Je.b,null,ta(An()))),n("p",null,"Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"funzione di ripartizione marginale"),":"),n("p",null,n(Je.b,null,ta(Mn())))),n(Ze.a,{title:"Densità discreta"},n("p",null,"I vettori aleatori ",n("b",null,"discreti")," hanno più densità che si differenziano in base al numero di parametri."),n("p",null,"Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"densità congiunta"),":"),n("p",null,n(Je.b,null,ta(Dn()))),n("p",null,"Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"densità marginale"),":"),n("p",null,n(Je.b,null,ta(In()))))),n($e.a,{title:"Più variabili aleatorie"},n(Ze.a,{title:"Indipendenza delle variabili aleatorie"},n("p",null,"Più variabili aleatorie sono indipendenti se, per qualsiasi scelta di intervalli ",n(Je.b,null,"A_i"),":"),n("p",null,n(Je.b,null,ta(wn())))),n(Ze.a,{title:"Media dei vettori aleatori"},n("p",null,"E' possibile calcolare la media di qualsiasi funzione ",n(Je.b,null,"g(X, Y)")," avente elementi del vettore come variabili:"),n("p",null,n(Je.b,null,ta(Sn()))),n(na.a,null,"Solitamente si calcola la media di ",n(Je.b,null,"x \\cdot y"),"."),n("p",null,"Le medie di più variabili aleatorie si possono sommare:"),n("p",null,n(Je.b,null,ta(Cn()))))),n($e.a,null,n(Ze.a,{title:"Covarianza"},n("p",null,"Un ",n("b",null,"operatore")," che misura la correlazione di due variabili aleatorie."),n("p",null,"Si calcola con il valore atteso dei prodotti delle distanze dalla media:"),n("p",null,n(Je.b,null,ta(Yn()))),n("p",null,"Ha diverse proprietà:"),n("ul",null,n("li",null,"Il suo ",n("b",null,"valore nullo")," è 0: ",n(Je.b,null,ta(Vn()))),n("li",null,"E' ",n("b",null,"commutativa"),": ",n(Je.b,null,ta(Nn()))),n("li",null,"E' ",n("b",null,"semplificabile"),": ",n(Je.b,null,ta(yn()))),n("li",null,"E' ",n("b",null,"lineare"),": ",n(Je.b,null,ta(Fn()))),n("li",null,"E' ",n("b",null,"distributiva"),": ",n(Je.b,null,ta(Ln()))))),n(Ze.a,{title:"Variabili incorrelate"},n("p",null,"Due variabili sono ",n("i",null,"variabili incorrelate")," se:"),n("p",null,n(Je.b,null,ta(kn()))),n("p",null,"Variabili indipendenti sono sempre incorrelate.")),n(Ze.a,{title:"Matrice di covarianza"},n("p",null,"Una matrice ",n(Je.b,null,ta(xn()))," che contiene la covarianza tra tutte le variabili di un vettore aleatorio ",n(Je.b,null,ta(Pn())),":"),n("p",null,n(Je.b,null,ta(En()))),n("p",null,"E' sempre simmetrica e semidefinita positiva (tutti gli autovalori sono ",n(Je.b,null,"\\geq 0"),".")),n(Ze.a,{title:"Coefficiente di correlazione"},n("p",null,"Un valore che misura come due variabili aleatorie sono correlate:"),n("p",null,n(Je.b,null,ta(zn()))),n("p",null,"E' sempre compreso tra -1 e 1:"),n("p",null,n(Je.b,null,ta(qn()))),n("p",null,"Vale esattamente -1 o 1 solo se esiste un legame lineare tra le due variaibli:"),n("p",null,n(Je.b,null,ta(gn())))),n(Ze.a,{title:"Varianza di variabili aleatorie sommate"},n("p",null,"La varianza di due variabili aleatorie sommate è:"),n("p",null,n(Je.b,null,ta(Xn()))),n(na.a,null,"Si dimostra applicando le proprietà della covarianza!"),n("p",null,"Se più variabili aleatorie ",n(Je.b,null,"X_i")," sono ",n("b",null,"indipendenti")," (",n(Je.b,null,ta(hn())),"), allora:"),n("p",null,n(Je.b,null,ta(_n()))))),n($e.a,{title:"Campioni"},n(Ze.a,{title:"Campione casuale"},n("p",null,"Una ",n("b",null,"n-pla")," di variabili aleatorie con la stessa distribuzione della variabile aleatoria ",n(Je.b,null,"X"),' ("popolazione") ma ',n("b",null,"indipendenti")," tra loro."),n(na.a,null,"Le variabili aleatorie sono come un lazy-load in programmazione; quando ci sarà bisogno del loro valore numerico, esse si ",n("b",null,"realizzeranno")," nel loro valore.")),n(Ze.a,{title:"Momento campionario"},n("p",null,"Il valore dato dalla media aritmetica degli ",n(Je.b,null,"n")," elementi del campione elevati alla potenza ",n(Je.b,null,"k"),":"),n("p",null,n(Je.b,null,ta(vn()))),n("p",null,"Il momento campionario di primo ordine è la ",n("i",null,"media campionaria")," ",n(Je.b,null,ta(bn())),".")),n(Ze.a,{title:"Varianza campionaria"},n("p",null,"La media aritmetica dello scarto quadratico medio degli elementi del campione."),n("p",null,"Se è noto il valore medio ",n(Je.b,null,ta(fn()))," di X:"),n("p",null,n(Je.b,null,ta(mn()))),n("p",null,"Altrimenti:"),n("p",null,n(Je.b,null,ta(dn()))))),n($e.a,{title:"Media-ception"},n(Ze.a,{title:"Media campionaria"},n("p",null,"Se calcoliamo la media della media campionaria, risulterà vero che:"),n("p",null,n(Je.b,null,ta(pn()))),n(na.a,null,"Quindi, è possibile usare i campioni per trovare la media di una variabile aleatoria!")),n(Ze.a,{title:"Varianza campionaria"},n("p",null,"Se calcoliamo la varianza della media campionaria, risulterà vero che:"),n("p",null,n(Je.b,null,ta(sn()))),n(na.a,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!")),n(Ze.a,{title:"Correzione campionaria"},n("p",null,"Se calcoliamo la media della varianza campionaria, risulterà vero che:"),n("p",null,n(Je.b,null,ta(cn()))),n(na.a,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!"))),n($e.a,{title:"Campionamento di una distribuzione normale"},n(Ze.a,{title:"Campionamento di una distribuzione normale"},n("p",null,"Se la popolazione ",n(Je.b,null,"X")," ha una distribuzione normale (",n(Je.b,null,ta(un())),")...")),n(Ze.a,{title:"Distribuzione della media campionaria"},n("p",null,"...allora sappiamo anche la distribuzione della media campionaria!"),n("p",null,n(Je.b,null,ta(on())))),n(Ze.a,{title:"Distribuzione della varianza campionaria"},n("p",null,"...e anche della varianza campionaria!"),n("p",null,n(Je.b,null,ta(rn()))),n("p",null,n(Je.b,null,ta(tn())))),n(Ze.a,{title:"Indipendenza"},n("p",null,"...e che media campionaria e varianza campionaria sono indipendenti tra loro!"))),n($e.a,{title:"Quando i campioni hanno dimensioni infinite"},n(Ze.a,{title:"Convergenza in distribuzione"},n("p",null,"Se la successione di variabili aleatorie ",n(Je.b,null,"X_n")," all'infinito ha la ",n("b",null,"stessa funzione di ripartizione")," della popolazione ",n(Je.b,null,"X"),", allora essa ",n("i",null,"converge in distribuzione"),"."),n("p",null,n(Je.b,null,"\\lim_{n \\to +\\infty} F_{X_n} (x) = F_X (x) \\implies X_n \\xrightarrow{d} X"))),n(Ze.a,{title:"Convergenza in probabilità"},n("p",null,"Se la successione di variabili aleatorie ",n(Je.b,null,"X_n")," all'infinito ha la ",n("b",null,"stessa probabilità")," della popolazione ",n(Je.b,null,"X"),", allora essa ",n("i",null,"converge in probabilità"),"."),n("p",null,n(Je.b,null,"\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | X_n - X | < \\epsilon) = 1 \\implies X_n \\xrightarrow{p} X"))),n(Ze.a,{title:"Convergenza quasi certa"},n("p",null,"Se la successione di variabili aleatorie ",n(Je.b,null,"X_n")," all'infinito ha la ",n("b",null,"stessa probabilità a ")," della popolazione ",n(Je.b,null,"X"),", allora essa ",n("i",null,"converge quasi certamente"),"."),n("p",null,n(Je.b,null,"\\forall \\epsilon > 0, P left( \\lim_{n \\to +\\infty} | X_n - X | < \\epsilon) \right) = 1 \\implies X_n \\xrightarrow{qc} X"))),n(Ze.a,{title:"Convergenza in media quadratica"},n("p",null,"Se la successione di variabili aleatorie ",n(Je.b,null,"X_n")," all'infinito ha la ",n("b",null,"media del quadrato della distanza")," tra la successione e la popolazione ",n(Je.b,null,"X")," ",n("b",null,"uguale a 0"),", allora essa ",n("i",null,"converge in media quadratica"),"."),n("p",null,n(Je.b,null,"\\lim_{n \\to +\\infty} E( | X_n - X |^2 = 0 \\implies X_n \\xrightarrow{mq} X"))),n(Ze.a,{title:"Gerarchia delle convergenze"},n("p",null,n(Je.b,null,"\n                                \\begin{matrix}\n                                X_n \\xrightarrow{mq} X\\\\\n                                X_n \\xrightarrow{qc} X\n                                \\end{matrix} \\implies X_n \\xrightarrow{p} X \\implies X_n \\xrightarrow{d} X")),n("p",null,"In più:"),n("p",null,n(Je.b,null,"X_n \\xrightarrow{p} x \\Longleftrightarrow X_n \\xrightarrow{d} x")))),n($e.a,{title:"I grandi numeri"},n(Ze.a,{title:"Legge debole dei grandi numeri"},n("p",null,"La successione delle medie campionarie ",n(Je.b,null,ta(an()))," ",n("b",null,"converge in probabilità")," alla media della popolazione ",n(Je.b,null,ta(en())),", se essa esiste."),n("p",null,n(Je.b,null,"\\overline{X}_n \\xrightarrow{p} X")),n("p",null,"Ovvero:"),n("p",null,n(Je.b,null,ta(ln()))),n("p",null,n(Je.b,null,ta(nn())))),n(Ze.a,{title:"Legge forte dei grandi numeri"},n("p",null,"La successione delle medie campionarie ",n(Je.b,null,ta($()))," ",n("b",null,"converge quasi certamente")," alla media della popolazione ",n(Je.b,null,ta(Z())),", se essa esiste."),n("p",null,n(Je.b,null,"\\overline{X}_n \\xrightarrow{qc} X")),n("p",null,"Ovvero:"),n("p",null,n(Je.b,null,ta(J()))),n(na.a,null,"Dimostra che l'interpretazione frequentista della probabilità è valida!"))),n($e.a,{title:"Al limite"},n(Ze.a,{title:"Teorema centrale del limite"},n("p",null,"La successione delle medie campionarie ",n(Je.b,null,ta(W()))," ",n("b",null,"converge in distribuzione")," a ",n(Je.b,null,ta(Q())),"."),n("p",null,n(Je.b,null,ta(K()))),n("p",null,"Ovvero:"),n("p",null,n(Je.b,null,ta(j()))))),n($e.a,{title:"Altre approsimazioni"},n(Ze.a,{title:"Binomiale e normale"},n("p",null,"E' una somma di ",n("b",null,"bernoulliane"),", e quindi si approssima a una normale:"),n("p",null,n(Je.b,null,ta(H())))),n(Ze.a,{title:"Binomiale negativa e normale"},n("p",null,"E' una somma di ",n("b",null,"geometriche"),", e quindi si approssima a una normale:"),n("p",null,n(Je.b,null,ta(R())))),n(Ze.a,{title:"Poissoniana e normale"},n("p",null,"E' una somma di altre ",n("b",null,"poissoniane"),", e quindi si approssima a una normale:"),n("p",null,n(Je.b,null,ta(G())))),n(Ze.a,{title:"Gamma e normale"},n("p",null,"E' una somma di ",n("b",null,"esponenziali"),", e quindi si approssima a una normale:"),n("p",null,n(Je.b,null,ta(O())))),n(Ze.a,{title:"In generale"},n("p",null,"Se ",n(Je.b,null,"n")," è grande, allora:"),n("p",null,n(Je.b,null,ta(B()))))),n($e.a,{title:"Actually statistica"},n(Ze.a,{title:"Parametri sconosciuti"},n("p",null,"Per indicare parametri sconosciuti di una legge si usa ",n(Je.b,null,"\\theta"),".")),n(Ze.a,{title:"Statistica"},n("p",null,"Una variabile aleatoria funzione di un campione:"),n("p",null,n(Je.b,null,ta(U()))),n(na.a,null,"Ad esempio, sono statistiche media e varianza campionaria, così come il campione stesso ",n(Je.b,null,ta(T())),"."))),n($e.a,{title:"Stimatori"},n(Ze.a,{title:"Stimatore"},n("p",null,"Una statistica ",n(Je.b,null,"T_n")," ottenuta da ",n(Je.b,null,"n")," osservazioni, che stimi i parametri di una legge e sia indipendente da essi.")),n(Ze.a,{title:"Corretto"},n("p",null,"Uno stimatore è ",n("i",null,"corretto")," se il suo valore atteso coincide con quello dei parametri che stima:"),n("p",null,n(Je.b,null,ta(A())))),n(Ze.a,{title:"Asintoticamente corretto"},n("p",null,"Uno stimatore è ",n("i",null,"asintoticamente corretto")," se, per infinite osservazioni, il suo valore atteso coincide con quello dei parametri che stima:"),n("p",null,n(Je.b,null,ta(M())))),n(Ze.a,{title:"Consistente in media quadratica"},n("p",null,"Uno stimatore è ",n("i",null,"consistente in media quadratica")," se:"),n("p",null,n(Je.b,null,ta(D())))),n(Ze.a,{title:"Consistente in probabilità"},n("p",null,"Uno stimatore è ",n("i",null,"consistente in probabilità")," se:"),n("p",null,n(Je.b,null,ta(I())))),n(Ze.a,{title:"Asintoticamente normale"},n("p",null,"Uno stimatore è ",n("i",null,"asintoticamente normale")," se:"),n("p",null,n(Je.b,null,ta(w()))))),n($e.a,{title:"Metodo dei momenti"},n(Ze.a,{title:"Metodo dei momenti"},n("p",null,"Si può usare il ",n("i",null,"metodo dei momenti")," per ottenere uno stimatore di una popolazione ",n(Je.b,null,"X"),"."),n("p",null,"Lo stimatore di ",n(Je.b,null,ta(S()))," così ottenuto sarà indicato aggiungendo un cappellino e una ",n(Je.b,null,"M")," a ",n(Je.b,null,"\\theta"),": ",n(Je.b,null,ta(C()))),n("p",null,"Visto che:"),n("ul",null,n("li",null,n(Je.b,null,ta(Y()))),n("li",null,n(Je.b,null,ta(V())))),n("p",null,"Allora:"),n("p",null,n(Je.b,null,ta(N()))),n("p",null,"Se ",n(Je.b,null,ta(y()))," non è esprimibile in termini di ",n(Je.b,null,ta(F())),", si possono usare i momenti successivi ",n(Je.b,null,ta(L())),", ",n(Je.b,null,ta(k())),", ",n(Je.b,null,ta(x())),"..."))),n($e.a,{title:"Metodo della massima verosomiglianza"},n(Ze.a,{title:"Metodo della massima verosomiglianza"},n("p",null,"Si può usare il ",n("i",null,"metodo della massima verosomiglianza")," per ottenere uno stimatore di una popolazione ",n(Je.b,null,"X"),"."),n("p",null,"Lo stimatore di ",n(Je.b,null,ta(P()))," così ottenuto sarà indicato aggiungendo un cappellino e una ",n(Je.b,null,"L")," a ",n(Je.b,null,"\\theta"),": ",n(Je.b,null,ta(E()))),n("p",null,"Consiste nel trovare il massimo assoluto ",n(Je.b,null,ta(z()))," della la funzione di verosomiglianza ",n(Je.b,null,ta(q())),":"),n("p",null,n(Je.b,null,ta(g()))),n("p",null,"Gli stimatori di massima verosomiglianza sono ",n("b",null,"asintoticamente corretti"),", ",n("b",null,"consistenti in probabilità")," e ",n("b",null,"asintoticamente normali"),".")),n(Ze.a,{title:"Proprietà degli stimatori di massima verosomiglianza"},n("p",null,"Gli stimatori di massima verosomiglianza godono delle seguenti proprietà:"),n("ul",null,n("li",null,"Sono ",n("b",null,"asintoticamente corretti"),"."),n("li",null,"Sono ",n("b",null,"consistenti in probabilità"),"."),n("li",null,"Sono ",n("b",null,"asintoticamente normali"),"."),n("li",null,"Sono ",n("b",null,"invarianti"),": ",n(Je.b,null,ta(X())))))),n($e.a,{title:"Nuove stime notevoli"},n(Ze.a,{title:"Stima di una bernoulliana"},n("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),n("p",null,n(Je.b,null,ta(h())))),n(Ze.a,{title:"Stima di una poissoniana"},n("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),n("p",null,n(Je.b,null,ta(_())))),n(Ze.a,{title:"Stima di una esponenziale"},n("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),n("p",null,n(Je.b,null,ta(v())))),n(Ze.a,{title:"Stima di una normale"},n("p",null,"Per il metodo della massima verosomiglianza:"),n("ul",null,n("li",null,n(Je.b,null,ta(b()))),n("br",null),n("li",null,n(Je.b,null,ta(f())))))),n($e.a,{title:"Intervalli di confidenza"},n(Ze.a,{title:"Confidenza"},n("blockquote",null,'"intervallo di confidenza al 95%"'),n("p",null,"L'intervallo di valori di ",n(Je.b,null,"\\theta"),' all\'interno del quale siamo "più o meno sicuri" si trovi il valore effettivo:'),n("p",null,"L'intervallo di confidenza a N della stima ",n(Je.b,null,ta(m()))," è l'intervallo ",n(Je.b,null,"]a, b[")," tale che:"),n("p",null,n(Je.b,null,ta(d()))),n("p",null,"Può anche essere ",n("b",null,"unilatero")," nel caso limiti la stima in una sola direzione, positiva o negativa."))),n($e.a,{title:"Confidenza nella media di una normale"},n(Ze.a,{title:"Varianza nota"},n("p",null,"Se conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'",n(Je.b,null,"\\alpha"),"% con queste formule:"),n("ul",null,n("li",null,"Intervalli bilateri: ",n(Je.b,null,ta(p()))),n("li",null,"Intervallo unilatero da sinistra: ",n(Je.b,null,ta(s()))),n("li",null,"Intervallo unilatero da destra: ",n(Je.b,null,ta(c()))))),n(Ze.a,{title:"Varianza incognita"},n("p",null,"Se non conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'",n(Je.b,null,"\\alpha"),"% con queste formule:"),n("ul",null,n("li",null,"Intervalli bilateri: ",n(Je.b,null,ta(u()))),n("li",null,"Intervallo unilatero da sinistra: 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n=We(["\boldsymbol{C_X}"],["\\boldsymbol{C_X}"]);return xn=function(){return n},n}function kn(){var n=We(["Cov(X, Y) = 0"]);return kn=function(){return n},n}function Ln(){var n=We(["Cov(X + Y, V + W) = Cov(X, Y) + Cov(X, W) + Cov(Y, V) + Cov(Y, W)"]);return Ln=function(){return n},n}function Fn(){var n=We(["Cov(alpha X, \beta Y) = alpha cdot \beta cdot Cov(X, Y)"],["Cov(\\alpha X, \\beta Y) = \\alpha \\cdot \\beta \\cdot Cov(X, Y)"]);return Fn=function(){return n},n}function yn(){var n=We(["Cov(X, X) = Var(X)"]);return yn=function(){return n},n}function Nn(){var n=We(["Cov(X, Y) = Cov(Y, X)"]);return Nn=function(){return n},n}function Vn(){var n=We(["Cov(X, alpha) = 0"],["Cov(X, \\alpha) = 0"]);return Vn=function(){return n},n}function Yn(){var n=We(["Cov(X, Y) = E((X - E(X) cdot (Y - E(Y)) = E(XY) - E(X) cdot E(Y)"],["Cov(X, Y) = E((X - E(X) \\cdot (Y - E(Y)) = E(XY) - E(X) \\cdot E(Y)"]);return Yn=function(){return n},n}function Cn(){var n=We(["E(X + Y) = E(X) + E(Y)"]);return Cn=function(){return n},n}function Sn(){var n=We(["E(g(X, Y)) = sum_{i, j} g(x_i, y_i) cdot p_{X, Y} (x_i, y_i)"],["E(g(X, Y)) = \\sum_{i, j} g(x_i, y_i) \\cdot p_{X, Y} (x_i, y_i)"]);return Sn=function(){return n},n}function wn(){var n=We(["P(X_1 in A_1, dots, X_n in A_n) = P(X_1 in A_1) \times dots \times P(X_n in A_n)"],["P(X_1 \\in A_1, \\dots, X_n \\in A_n) = P(X_1 \\in A_1) \\times \\dots \\times P(X_n \\in A_n)"]);return wn=function(){return n},n}function In(){var n=We(["p_X (x) = sum_j p_{X, Y} (x_i, y_j)"],["p_X (x) = \\sum_j p_{X, Y} (x_i, y_j)"]);return In=function(){return n},n}function Dn(){var n=We(["p_{X, Y} (x, y) = P(X = x, Y = y)"]);return Dn=function(){return n},n}function Mn(){var n=We(["F_X (x) = P(X leq x) = lim_{y \to +infty} F_{X, Y} (x, y)"],["F_X (x) = P(X \\leq x) = \\lim_{y \\to +\\infty} F_{X, Y} (x, y)"]);return Mn=function(){return n},n}function An(){var n=We(["F_{X, Y} (x, y) = P(X leq x, Y leq y)"],["F_{X, Y} (x, y) = P(X \\leq x, Y \\leq y)"]);return An=function(){return n},n}function Tn(){var n=We(["X, Y"]);return Tn=function(){return n},n}function Un(){var n=We(["\boldsymbol{X}"],["\\boldsymbol{X}"]);return Un=function(){return n},n}function Bn(){var n=We(["P(X > k) simeq P(Y geq k + \frac{1}{2})"],["P(X > k) \\simeq P(Y \\geq k + \\frac{1}{2})"]);return Bn=function(){return n},n}function On(){var n=We(["P(X geq k) simeq P(Y geq k - \frac{1}{2})"],["P(X \\geq k) \\simeq P(Y \\geq k - \\frac{1}{2})"]);return On=function(){return n},n}function Gn(){var n=We(["P(X leq k) simeq P(Y leq k + \frac{1}{2})"],["P(X \\leq k) \\simeq P(Y \\leq k + \\frac{1}{2})"]);return Gn=function(){return n},n}function Rn(){var n=We(["P(X < k) simeq P(Y leq k - \frac{1}{2})"],["P(X < k) \\simeq P(Y \\leq k - \\frac{1}{2})"]);return Rn=function(){return n},n}function Hn(){var n=We(["(k - \frac{1}{2}, k + \frac{1}{2})"],["(k - \\frac{1}{2}, k + \\frac{1}{2})"]);return Hn=function(){return n},n}function jn(){var n=We(["Bin(n, p) approx Nor(n cdot p, n cdot p cdot q)"],["Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)"]);return jn=function(){return n},n}function Kn(){var n=We(["Bin(n, p) approx Poi(n cdot p)"],["Bin(n, p) \\approx Poi(n \\cdot p)"]);return Kn=function(){return n},n}function Qn(){var n=We(["Ipe(N, K, n) approx Bin(n, \frac{K}{N})"],["Ipe(N, K, n) \\approx Bin(n, \\frac{K}{N})"]);return Qn=function(){return n},n}function Wn(){var n=We(["T(v) = \frac{Nor(0, 1)}{sqrt{\frac{chi^2(v)}{v}}}"],["T(v) = \\frac{Nor(0, 1)}{\\sqrt{\\frac{\\chi^2(v)}{v}}}"]);return Wn=function(){return n},n}function Jn(){var n=We(["chi^2 (n) + chi^2 (m) = chi^2 (n + m)"],["\\chi^2 (n) + \\chi^2 (m) = \\chi^2 (n + m)"]);return Jn=function(){return n},n}function Zn(){var n=We(["Gamma left( \frac{1}{2}, \frac{1}{2} \right) = chi^2 (v = 1)"],["\\Gamma \\left( \\frac{1}{2}, \\frac{1}{2} \\right) = \\chi^2 (v = 1)"]);return Zn=function(){return n},n}function $n(){var n=We(["Z^2 sim chi^2 (v = 1)"],["Z^2 \\sim \\chi^2 (v = 1)"]);return $n=function(){return n},n}function nl(){var n=We(["x_alpha = mu + z_alpha cdot sqrt{sigma^2}"],["x_\\alpha = \\mu + z_\\alpha \\cdot \\sqrt{\\sigma^2}"]);return nl=function(){return n},n}function ll(){var n=We(["z_alpha"],["z_\\alpha"]);return ll=function(){return n},n}function il(){var n=We(["F_Z(z) = phi(z) = \frac{1}{sqrt{2 pi}} int_{-infty}^{z} e^{-\frac{x^2}{2}} dx"],["F_Z(z) = \\phi(z) = \\frac{1}{\\sqrt{2 \\pi}} \\int_{-\\infty}^{z} e^{-\\frac{x^2}{2}} dx"]);return il=function(){return n},n}function el(){var n=We(["phi(z)"],["\\phi(z)"]);return el=function(){return n},n}function al(){var n=We(["X sim Nor(m, v^2) implies alpha X + \beta sim Nor(alpha m + \beta, (alpha v)^2)"],["X \\sim Nor(m, v^2) \\implies \\alpha X + \\beta \\sim Nor(\\alpha m + \\beta, (\\alpha v)^2)"]);return al=function(){return n},n}function tl(){var n=We(["Var(X) = sigma^2"],["Var(X) = \\sigma^2"]);return tl=function(){return n},n}function rl(){var n=We(["E(X) = mu"],["E(X) = \\mu"]);return rl=function(){return n},n}function ol(){var n=We(["m_X (t) = e^{mu cdot t + \frac{sigma^2 cdot t^2}{2}}"],["m_X (t) = e^{\\mu \\cdot t + \\frac{\\sigma^2 \\cdot t^2}{2}}"]);return ol=function(){return n},n}function ul(){var n=We(["f_X (x) = \frac{e^{-\frac{(x - mu)^2}{2 sigma^2}}}{sqrt{2 pi cdot sigma^2}}"],["f_X (x) = \\frac{e^{-\\frac{(x - \\mu)^2}{2 \\sigma^2}}}{\\sqrt{2 \\pi \\cdot \\sigma^2}}"]);return ul=function(){return n},n}function cl(){var n=We(["Nor(mu, sigma^2)"],["Nor(\\mu, \\sigma^2)"]);return cl=function(){return n},n}function sl(){var n=We(["Var(X) = \frac{(b - a)^2}{12}"],["Var(X) = \\frac{(b - a)^2}{12}"]);return sl=function(){return n},n}function pl(){var n=We(["E(X) = \frac{a + b}{2}"],["E(X) = \\frac{a + b}{2}"]);return pl=function(){return n},n}function dl(){var n=We(["m_X (t) = \frac{e^{b cdot t} - e^{a cdot t}}{(b - a) cdot t}"],["m_X (t) = \\frac{e^{b \\cdot t} - e^{a \\cdot t}}{(b - a) \\cdot t}"]);return dl=function(){return n},n}function ml(){var n=We(["f_X (x) = \begin{cases}\n                                0 qquad quad x < a  \n                                \frac{1}{b - a} qquad a leq x leq b\\\n                                1 qquad quad x > b\n                            end{cases}"],["f_X (x) = \\begin{cases}\n                                0 \\qquad \\quad x < a  \n                                \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n                                1 \\qquad \\quad x > b\n                            \\end{cases}"]);return ml=function(){return n},n}function fl(){var n=We(["f_X (x) = \begin{cases}\n                                \frac{1}{b - a} qquad a leq x leq b\\\n                                0 qquad quad altrimenti    \n                            end{cases}"],["f_X (x) = \\begin{cases}\n                                \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n                                0 \\qquad \\quad altrimenti    \n                            \\end{cases}"]);return fl=function(){return n},n}function bl(){var n=We(["P(X in (c, d)) = \frac{d - c}{b - a}"],["P(X \\in (c, d)) = \\frac{d - c}{b - a}"]);return bl=function(){return n},n}function vl(){var n=We(["Uni(a, b)"]);return vl=function(){return n},n}function _l(){var n=We(["[a, b]"]);return _l=function(){return n},n}function hl(){var n=We(["Var(X) = \frac{alpha}{lambda^2}"],["Var(X) = \\frac{\\alpha}{\\lambda^2}"]);return hl=function(){return n},n}function Xl(){var n=We(["E(X) = \frac{alpha}{lambda}"],["E(X) = \\frac{\\alpha}{\\lambda}"]);return Xl=function(){return n},n}function gl(){var n=We(["m_X (t) : ( t < lambda ) in mathbb{R} = left( \frac{lambda}{lambda - t} \right) ^alpha"],["m_X (t) : ( t < \\lambda ) \\in \\mathbb{R} = \\left( \\frac{\\lambda}{\\lambda - t} \\right) ^\\alpha"]);return gl=function(){return n},n}function ql(){var n=We(["f_X (x) = \begin{cases}\n                            0 qquad qquad qquad qquad qquad x < 0\\\n                            \frac{1}{(n-1)!} cdot lambda^n cdot x^{n-1} cdot e^{-lambda cdot x} quad k > 0\n                            end{cases}"],["f_X (x) = \\begin{cases}\n                            0 \\qquad \\qquad \\qquad \\qquad \\qquad x < 0\\\\\n                            \\frac{1}{(n-1)!} \\cdot \\lambda^n \\cdot x^{n-1} \\cdot e^{-\\lambda \\cdot x} \\quad k > 0\n                            \\end{cases}"]);return ql=function(){return n},n}function zl(){var n=We(["Gamma(n, lambda)"],["\\Gamma(n, \\lambda)"]);return zl=function(){return n},n}function El(){var n=We(["lambda"],["\\lambda"]);return El=function(){return n},n}function Pl(){var n=We(["P([X > s + t | X > s]) = P([X > t])"]);return Pl=function(){return n},n}function xl(){var n=We(["Var(X) = \frac{1}{lambda^2}"],["Var(X) = \\frac{1}{\\lambda^2}"]);return xl=function(){return n},n}function kl(){var n=We(["E(X) = \frac{1}{lambda}"],["E(X) = \\frac{1}{\\lambda}"]);return kl=function(){return n},n}function Ll(){var n=We(["m_X (t) : { t | t < lambda } in mathbb{R} = \frac{lambda}{lambda - t}"],["m_X (t) : \\{ t | t < \\lambda \\} \\in \\mathbb{R} = \\frac{\\lambda}{\\lambda - t}"]);return Ll=function(){return n},n}function Fl(){var n=We(["F_X (t) = \begin{cases}\n                            0 qquad qquad t < 0\\\n                            1 - e^{-lambda cdot t} quad t geq 0\n                            end{cases}"],["F_X (t) = \\begin{cases}\n                            0 \\qquad \\qquad t < 0\\\\\n                            1 - e^{-\\lambda \\cdot t} \\quad t \\geq 0\n                            \\end{cases}"]);return Fl=function(){return n},n}function yl(){var n=We(["f_X (x) = \begin{cases}\n                            0 qquad qquad x < 0\\\n                            lambda cdot e^{-lambda cdot x} quad x > 0\n                            end{cases}"],["f_X (x) = \\begin{cases}\n                            0 \\qquad \\qquad x < 0\\\\\n                            \\lambda \\cdot e^{-\\lambda \\cdot x} \\quad x > 0\n                            \\end{cases}"]);return yl=function(){return n},n}function Nl(){var n=We(["Esp(lambda)"],["Esp(\\lambda)"]);return Nl=function(){return n},n}function Vl(){var n=We(["lambda"],["\\lambda"]);return Vl=function(){return n},n}function Yl(){var n=We(["Poi(t cdot lambda)"],["Poi(t \\cdot \\lambda)"]);return Yl=function(){return n},n}function Cl(){var n=We(["mu = t cdot lambda"],["\\mu = t \\cdot \\lambda"]);return Cl=function(){return n},n}function Sl(){var n=We(["lambda"],["\\lambda"]);return Sl=function(){return n},n}function wl(){var n=We(["lambda"],["\\lambda"]);return wl=function(){return n},n}function Il(){var n=We(["E(X^2) = mu^2 + mu"],["E(X^2) = \\mu^2 + \\mu"]);return Il=function(){return n},n}function Dl(){var n=We(["Var(X) = mu"],["Var(X) = \\mu"]);return Dl=function(){return n},n}function Ml(){var n=We(["E(X) = mu"],["E(X) = \\mu"]);return Ml=function(){return n},n}function Al(){var n=We(["m_X (t) = e^{mu cdot (e^t - 1)}"],["m_X (t) = e^{\\mu \\cdot (e^t - 1)}"]);return Al=function(){return n},n}function Tl(){var n=We(["f_X (k) : mathbb{N} = \frac{e^{-mu} cdot mu^k}{k!}"],["f_X (k) : \\mathbb{N} = \\frac{e^{-\\mu} \\cdot \\mu^k}{k!}"]);return Tl=function(){return n},n}function Ul(){var n=We(["Poi(mu)"],["Poi(\\mu)"]);return Ul=function(){return n},n}function Bl(){var n=We(["E(X) = n cdot p \to mu \neq 0"],["E(X) = n \\cdot p \\to \\mu \\neq 0"]);return Bl=function(){return n},n}function Ol(){var n=We(["p \to 0"],["p \\to 0"]);return Ol=function(){return n},n}function Gl(){var n=We(["n \to +infty"],["n \\to +\\infty"]);return Gl=function(){return n},n}function Rl(){var n=We(["X sim Bin(n, p)"],["X \\sim Bin(n, p)"]);return Rl=function(){return n},n}function Hl(){var n=We(["Var(X) = n cdot \frac{K}{N} cdot \frac{N - K}{N} cdot \frac{N - n}{N - 1}"],["Var(X) = n \\cdot \\frac{K}{N} \\cdot \\frac{N - K}{N} \\cdot \\frac{N - n}{N - 1}"]);return Hl=function(){return n},n}function jl(){var n=We(["E(X) = n cdot \frac{K}{N}"],["E(X) = n \\cdot \\frac{K}{N}"]);return jl=function(){return n},n}function Kl(){var n=We(["f_X (k) : {0..n} in mathbb{N} = \frac{\binom{K}{k} cdot \binom{N - K}{n - k}}{\binom{N}{n}}"],["f_X (k) : \\{0..n\\} \\in \\mathbb{N} = \\frac{\\binom{K}{k} \\cdot \\binom{N - K}{n - k}}{\\binom{N}{n}}"]);return Kl=function(){return n},n}function Ql(){var n=We(["Var(X) = \frac{n cdot q}{p^2}"],["Var(X) = \\frac{n \\cdot q}{p^2}"]);return Ql=function(){return n},n}function Wl(){var n=We(["E(X) = \frac{n cdot q}{p}"],["E(X) = \\frac{n \\cdot q}{p}"]);return Wl=function(){return n},n}function Jl(){var n=We(["m_X (t) : left{ t < ln left( \frac{1}{q} \right) \right} = left( \frac{p cdot e^t}{1 - q cdot e^t} \right) ^n"],["m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n"]);return Jl=function(){return n},n}function Zl(){var n=We(["f_X (k) : mathbb{N} = \binom{k + n - 1}{n - 1} cdot p^n cdot q^k "],["f_X (k) : \\mathbb{N} = \\binom{k + n - 1}{n - 1} \\cdot p^n \\cdot q^k "]);return Zl=function(){return n},n}function $l(){var n=We(["overline{Bin}(n, p)"],["\\overline{Bin}(n, p)"]);return $l=function(){return n},n}function ni(){var n=We(["P([X = i + j | X > i ]) = P([X = j])"]);return ni=function(){return n},n}function li(){var n=We(["Var(X) = \frac{q}{p^2}"],["Var(X) = \\frac{q}{p^2}"]);return li=function(){return n},n}function ii(){var n=We(["E(X) = \frac{q}{p}"],["E(X) = \\frac{q}{p}"]);return ii=function(){return n},n}function ei(){var n=We(["m_X (t) : left{ t < ln left( \frac{1}{q} \right) \right} = \frac{p}{1 - q cdot e^t}"],["m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\frac{p}{1 - q \\cdot e^t}"]);return ei=function(){return n},n}function ai(){var n=We(["f_X (k) : mathbb{N} = p cdot q^k "],["f_X (k) : \\mathbb{N} = p \\cdot q^k "]);return ai=function(){return n},n}function ti(){var n=We(["Geo(p)"]);return ti=function(){return n},n}function ri(){var n=We(["Var(X) = \frac{n cdot q}{p^2}"],["Var(X) = \\frac{n \\cdot q}{p^2}"]);return ri=function(){return n},n}function oi(){var n=We(["E(X) = \frac{n}{p}"],["E(X) = \\frac{n}{p}"]);return oi=function(){return n},n}function ui(){var n=We(["m_X (t) : { t < ln(\frac{1}{q}) } = left( \frac{p cdot e^t}{1 - q cdot e^t} \right) ^n"],["m_X (t) : \\{ t < ln(\\frac{1}{q}) \\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n"]);return ui=function(){return n},n}function ci(){var n=We(["f_X (k) : { n .. +infty } in mathbb{N} = \binom{k - 1}{n - 1} cdot p^n cdot q^{k - n} "],["f_X (k) : \\{ n .. +\\infty \\} \\in \\mathbb{N} = \\binom{k - 1}{n - 1} \\cdot p^n \\cdot q^{k - n} "]);return ci=function(){return n},n}function si(){var n=We(["overline{Bin}(n, p)"],["\\overline{Bin}(n, p)"]);return si=function(){return n},n}function pi(){var n=We(["P([X = i + j | X > i ]) = P([X = j])"]);return pi=function(){return n},n}function di(){var n=We(["Var(X) = \frac{q}{p^2}"],["Var(X) = \\frac{q}{p^2}"]);return di=function(){return n},n}function mi(){var n=We(["E(X) = \frac{1}{p}"],["E(X) = \\frac{1}{p}"]);return mi=function(){return n},n}function fi(){var n=We(["m_X (t) = \frac{p cdot e^t}{1 - q cdot e^t}"],["m_X (t) = \\frac{p \\cdot e^t}{1 - q \\cdot e^t}"]);return fi=function(){return n},n}function bi(){var n=We(["f_X (k) : mathbb{N} = q^{k - 1} p"],["f_X (k) : \\mathbb{N} = q^{k - 1} p"]);return bi=function(){return n},n}function vi(){var n=We(["Var(X) = n cdot p cdot q"],["Var(X) = n \\cdot p \\cdot q"]);return vi=function(){return n},n}function _i(){var n=We(["E(X) = n cdot p"],["E(X) = n \\cdot p"]);return _i=function(){return n},n}function hi(){var n=We(["m_X (t) = (q + p cdot e^t) ^ n"],["m_X (t) = (q + p \\cdot e^t) ^ n"]);return hi=function(){return n},n}function Xi(){var n=We(["f_X (k) : {0..n} = \binom{n}{k} cdot p^k cdot q^{n - k}"],["f_X (k) : \\{0..n\\} = \\binom{n}{k} \\cdot p^k \\cdot q^{n - k}"]);return Xi=function(){return n},n}function gi(){var n=We(["Bin(n, p)"]);return gi=function(){return n},n}function qi(){var n=We(["f_X (k) : {0, 1} = \begin{cases}\n                            p quad se k = 1\\\n                            q quad se k = 0\\\n                            0 quad altrimenti\n                            end{cases} = p^x cdot q^{1 - k}"],["f_X (k) : \\{0, 1\\} = \\begin{cases}\n                            p \\quad se\\ k = 1\\\\\n                            q \\quad se\\ k = 0\\\\\n                            0 \\quad altrimenti\n                            \\end{cases} = p^x \\cdot q^{1 - k}"]);return qi=function(){return n},n}function zi(){var n=We(["Ber(p)"]);return zi=function(){return n},n}function Ei(){var n=We(["X sim Distribuzione()"],["X \\sim Distribuzione()"]);return Ei=function(){return n},n}function Pi(){var n=We(["H_X (t) = E ( e^{i cdot t cdot X} )"],["H_X (t) = E ( e^{i \\cdot t \\cdot X} )"]);return Pi=function(){return n},n}function xi(){var n=We(["m_X (t) = E( e^{t cdot X} )"],["m_X (t) = E( e^{t \\cdot X} )"]);return xi=function(){return n},n}function ki(){var n=We(["mu_k = E ( X^k ) = \begin{cases}\n                                sum_i x_i^k p_X (x_i) qquad nel discreto\\\n                                \\\n                                int_{-infty}^{+infty} x^k f_X (x) dx qquad nel continuo\n                                end{cases}"],["\\mu_k = E ( X^k ) = \\begin{cases}\n                                \\sum_i x_i^k p_X (x_i) \\qquad nel\\ discreto\\\\\n                                \\\\\n                                \\int_{-\\infty}^{+\\infty} x^k f_X (x) dx \\qquad nel\\ continuo\n                                \\end{cases}"]);return ki=function(){return n},n}function Li(){var n=We(["\forall epsilon > 0, P([ left| X - E(X) \right| < epsilon]) geq 1 - \frac{Var(X)}{epsilon^2}"],["\\forall \\epsilon > 0, P([ \\left| X - E(X) \\right| < \\epsilon]) \\geq 1 - \\frac{Var(X)}{\\epsilon^2}"]);return Li=function(){return n},n}function Fi(){var n=We(["\forall epsilon > 0, P([ left| X - E(X) 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quindi rimossa!"))),n($e.a,{title:"Spazi equiprobabili"},n(Ze.a,{title:"Cosa sono?"},n("p",null,"Spazi campionari in cui ci sono un numero finito di esiti e ogni esito ha la stessa probabilità di verificarsi."),n("p",null,n(Je.b,null,ta(he())))),n(Ze.a,{title:"Spazi equiprobabili geometrici"},n("p",null,"Gli spazi campionari possono avere un numero infinito di esiti: sono ",n("i",null,"equiprobabili geometrici")," se nessun esito è privilegiato rispetto agli altri."))),n($e.a,{title:"Calcolo combinatorio"},n(Ze.a,{title:"Disposizioni"},n("p",null,"Estraggo un numero, da un sacchetto con ",n(Je.b,null,"n")," numeri, mi segno che numero ho estratto e lo ",n("b",null,"tengo fuori dal sacchetto"),". Ripeto per ",n(Je.b,null,"k")," volte."),n("p",null,n("b",null,"Tengo conto")," dell'ordine in cui ho estratto i numeri."),n("p",null,n(Je.b,null,ta(_e())))),n(Ze.a,{title:"Disposizioni con ripetizione"},n("p",null,"Estraggo un numero, da un sacchetto con ",n(Je.b,null,"n")," numeri, mi segno che numero ho estratto e lo ",n("b",null,"rimetto nel sacchetto"),". Ripeto per ",n(Je.b,null,"k")," volte."),n("p",null,n("b",null,"Tengo conto")," dell'ordine in cui ho estratto i numeri."),n("p",null,n(Je.b,null,ta(ve())))),n(Ze.a,{title:"Combinazioni"},n("p",null,"Estraggo un numero, da un sacchetto con ",n(Je.b,null,"n")," numeri, mi segno che numero ho estratto e lo ",n("b",null,"tengo fuori dal sacchetto"),". Ripeto per ",n(Je.b,null,"k")," volte."),n("p",null,n("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),n("p",null,n(Je.b,null,ta(be())))),n(Ze.a,{title:"Combinazioni con ripetizione"},n("p",null,"Estraggo un numero, da un sacchetto con ",n(Je.b,null,"n")," numeri, mi segno che numero ho estratto e lo ",n("b",null,"rimetto nel sacchetto"),". Ripeto per ",n(Je.b,null,"k")," volte."),n("p",null,n("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),n("p",null,n(Je.b,null,ta(fe())))),n(Ze.a,{title:"Permutazioni"},n("p",null,"Estraggo ",n(Je.b,null,"n")," numeri e guardo in quanti ordini diversi li posso mettere."),n("p",null,n(Je.b,null,ta(me()))))),n($e.a,{title:"Probabilità condizionata"},n(Ze.a,{title:"Eventi condizionati"},n("blockquote",null,'"E dato F"'),n("p",null,"La probabilità che si verifichi ",n(Je.b,null,"E")," sapendo che ",n("b",null,"si è già verificato")," ",n(Je.b,null,"F"),"."),n("p",null,n(Je.b,null,ta(de()))),n(na.a,null,"Ricorda vagamente le pipe di ",n("code",null,"bash"),", però al contrario...")),n(Ze.a,{title:"Eventi mutualmente esclusivi"},n("p",null,"Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0."),n("p",null,n(Je.b,null,ta(pe()))))),n($e.a,null,n(Ze.a,{title:"Regola della catena"},n("p",null,"Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:"),n("p",null,n(Je.b,null,ta(se()))))),n($e.a,{title:"Le alternative"},n(Ze.a,{title:"Legge delle alternative"},n("p",null,"La probabilità che si verifichi un evento è pari alla somma delle probabilità dell'evento stesso dati tutti gli eventi di una partizione."),n("p",null,n(Je.b,null,ta(ce())))),n(Ze.a,{title:"Legge condizionata delle alternative"},n("p",null,"La legge delle alternative funziona anche quando ad essere partizionato è un ",n("b",null,"evento"),":"),n("p",null,n(Je.b,null,ta(ue())))),n(Ze.a,{title:"Formula di Bayes"},n("p",null,"Tramite la ",n("i",null,"formula di Bayes")," possiamo risalire alla probabilità di un evento condizionato a un altro partendo dalla probabilità di quest'ultimo condizionato al primo:"),n("p",null,n(Je.b,null,ta(oe()))),n(na.a,null,"In pratica, invertiamo gli eventi."))),n($e.a,{title:"Eventi indipendenti"},n(Ze.a,{title:"Due eventi indipendenti"},n("blockquote",null,'"eventi indipendenti a due a due"'),n("p",null,"Se due eventi sono indipendenti, sapere che uno dei due si è verificato non influisce sulle probabilità che si sia verificato l'altro."),n("p",null,n(Je.b,null,ta(re())))),n(Ze.a,{title:"Più eventi indipendenti"},n("blockquote",null,'"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque..."'),n("p",null,"Si può verificare l'indipendenza di più eventi alla volta:"),n("p",null,n(Je.b,null,ta(te()))),n("p",null,"Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.")),n(Ze.a,{title:"Famiglia di eventi indipendenti"},n("p",null,"Un insieme di ",n(Je.b,null,"n")," eventi è una ",n("i",null,"famiglia di eventi indipendenti")," se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti."),n(na.a,null,"Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e così via!"))),n($e.a,{title:"Variabili aleatorie"},n(Ze.a,{title:"Variabile aleatoria"},n("p",null,"Una funzione che fa corrispondere un numero reale a ogni possibile esito dello spazio campionario. ",n(Je.b,null,ta(ae())),".")),n(Ze.a,{title:n("abbr",{title:"Nome artigianale dato da Steffo."},"Insieme di ripartizione")},n("p",null,"Ad ogni variabile aleatoria sono associati gli eventi ",n(Je.b,null,ta(ee())),", che contengono tutti gli esiti a cui la variabile aleatoria associa un valore minore o uguale a ",n(Je.b,null,"t"),"."),n("p",null,"Per definizione, tutte le variabili aleatorie devono rispettare questa condizione:"),n("p",null,n(Je.b,null,ta(ie()))),n(na.a,null,"All'aumentare di t, l'insieme conterrà sempre più elementi.")),n(Ze.a,{title:"Supporto"},n("blockquote",null,'"supporto di X"'),n("p",null,"Il ",n("b",null,"codominio")," della variabile aleatoria è il suo ",n("i",null,"supporto"),"."),n("p",null,"Per indicare che un valore ",n(Je.b,null,"x_0")," appartiene al supporto di ",n(Je.b,null,"X"),", si usa la notazione ",n(Je.b,null,"X \\mapsto x_0"),"."))),n($e.a,{title:"Densità"},n(Ze.a,{title:"Funzione probabilità"},n("p",null,"La ",n("i",null,"funzione probabilità")," ",n(Je.b,null,ta(le()))," di una variabile aleatoria ",n("b",null,"discreta")," ",n(Je.b,null,"X")," è la funzione che associa ad ogni esito la sua probabilità:"),n("p",null,n(Je.b,null,ta(ne())))),n(Ze.a,{title:"Funzione densità"},n("p",null,"La ",n("i",null,"funzione densità")," ",n(Je.b,null,ta($i()))," di una variabile aleatoria ",n("b",null,"continua")," ",n(Je.b,null,"X")," è l'equivalente continuo della funzione probabilità:"),n("p",null,n(Je.b,null,ta(Zi()))),n("p",null,"A differenza della funzione probabilità, è possibile che la funzione densità ",n("b",null,"non esista")," per una certa variabile aleatoria."),n(na.a,null,"Rappresenta \"quanta\" probabilità c'è in un'unità di x!"))),n($e.a,{title:"Funzione di ripartizione"},n(Ze.a,{title:"Definizione"},n("p",null,"Ogni variabile aleatoria ha una ",n("i",null,"funzione di ripartizione")," ",n(Je.b,null,ta(Ji()))," associata, che rappresenta la probabilità che la variabile aleatoria assuma un valore minore o uguale a ",n(Je.b,null,"t"),":"),n("p",null,"Si può dire che essa rappresenti la probabilità dell'evento ",n(Je.b,null,ta(Wi())),":"),n("p",null,n(Je.b,null,ta(Qi())))),n(Ze.a,{title:"Proprietà della funzione"},n("ul",null,n("li",null,"È sempre ",n("b",null,"monotona crescente")," (non strettamente)."),n("br",null),n("li",null,"Vale ",n("b",null,"0")," a ",n(Je.b,null,"-\\infty")," e ",n("b",null,"1")," a ",n(Je.b,null,"+\\infty"),"."),n("br",null),n("li",null,"È ",n("b",null,"continua da destra"),": ",n(Je.b,null,ta(Ki()))))),n(Ze.a,{title:"Probabilità di un valore"},n("p",null,"Possiamo usare la funzione di ripartizione per calcolare la probabilità di un certo valore reale:"),n("p",null,n(Je.b,null,ta(ji()))))),n($e.a,{title:"Trasformazioni di variabili aleatorie"},n(Ze.a,{title:"Nel discreto"},n("p",null,"Nel discreto basta abbinare un nuovo valore a ogni valore della variabile originale.")),n(Ze.a,{title:"Nel continuo (invertibile)"},n("p",null,"Nel continuo applichiamo la formula dell'integrazione per sostituzione:"),n("p",null,n(Je.b,null,ta(Hi())))),n(Ze.a,{title:"Nel... digitale"},n("p",null,"Trasformare variabili aleatorie è molto utile nell'informatica per creare distribuzioni partendo da una funzione ",n("a",{href:"https://docs.python.org/3/library/random.html#random.random"},n("code",null,"random()"))," che restituisce numeri da 0 a 1 con una distribuzione lineare."))),n($e.a,{title:"Informazioni delle variabili aleatorie"},n(Ze.a,{title:"Media"},n("p",null,"Ogni variabile aleatoria che ha una ",n("b",null,"funzione di ripartizione")," e un ",n("b",null,"supporto finito")," ha anche una ",n("i",null,"media")," (o ",n("i",null,"valore medio")," o ",n("i",null,"atteso"),"):"),n("p",null,n(Je.b,null,ta(Ri()))),n("p",null,"Nel discreto, si può calcolare con:"),n("p",null,n(Je.b,null,ta(Gi()))),n("p",null,"Nel continuo, si può calcolare con:"),n("p",null,n(Je.b,null,ta(Oi()))))),n($e.a,null,n(Ze.a,{title:"Moda"},n("p",null,"Valore per cui la ",n("b",null,"funzione probabilità")," o ",n("b",null,"funzione densità")," è ",n("b",null,"massima"),".")),n(Ze.a,{title:"Quantili"},n("p",null,"Il ",n("i",null,"quantile")," ",n(Je.b,null,ta(Bi()))," di ordine ",n(Je.b,null,ta(Ui()))," della variabile aleatoria ",n(Je.b,null,"X")," è il più piccolo numero tale che:"),n("p",null,n(Je.b,null,ta(Ti()))),n("p",null),n("p",null,"Il quantile di ordine 0.5 ",n(Je.b,null,ta(Ai()))," è detto ",n("i",null,"mediana"),"."),n("p",null,"I quantili di ordine 0.25 ",n(Je.b,null,ta(Mi()))," e 0.75 ",n(Je.b,null,ta(Di()))," sono detti ",n("i",null,"quartili"),"."),n("p",null,"I quantili di ordine ",n(Je.b,null,ta(Ii()))," sono detti ",n("i",null,n(Je.b,null,"n"),"-esima percentile"),".")),n(Ze.a,{title:"Varianza"},n("p",null,"È un valore che indica quanto la variabile aleatoria si discosta generalmente dalla media:"),n("p",null,n(Je.b,null,ta(wi()))))),n($e.a,{title:"Disuguaglianze notevoli"},n(Ze.a,{title:"Disuguaglianza di Markov"},n("p",null,"Data una variabile aleatoria non-negativa:"),n("p",null,n(Je.b,null,ta(Si()))),n("p",null,"Divide in due parti (",n(Je.b,null,ta(Ci()))," e ",n(Je.b,null,ta(Yi())),") la funzione X, la cui media risulterà uguale a:"),n("p",null,n(Je.b,null,ta(Vi())))),n(Ze.a,{title:"Disuguaglianza di Čebyšëv"},n("blockquote",null,'"disuguaglianza di cebicev"'),n("p",null,"Se la variabile aleatoria ",n(Je.b,null,"X")," ha media e varianza, allora la probabilità che essa abbia un valore a più di ",n(Je.b,null,ta(Ni()))," di distanza dal valore medio è minore o uguale a ",n(Je.b,null,ta(yi())),"."),n("p",null,n(Je.b,null,ta(Fi()))),n("p",null,"E anche:"),n("p",null,n(Je.b,null,ta(Li()))),n(na.a,null,"Serve per semplificare i calcoli quando la funzione di ripartizione è difficile da calcolare!"))),n($e.a,{title:"Un momento...!"},n(Ze.a,{title:"Momento"},n("p",null,"Il ",n("i",null,"momento")," ",n(Je.b,null,"k"),"-esimo di una variabile aleatoria è:"),n("p",null,n(Je.b,null,ta(ki()))),n(na.a,null,"La media di una variabile aleatoria è anche il suo primo momento.")),n(Ze.a,{title:"Funzione generatrice dei momenti"},n("p",null,"La ",n("i",null,"funzione generatrice dei momenti")," è:"),n("p",null,n(Je.b,null,ta(xi()))),n("p",null,"Se due variabile aleatorie hanno la stessa funzione generatrice dei momenti, allora esse hanno la ",n("b",null,"stessa distribuzione"),"."),n("p",null,"E' la ",n("b",null,"trasformata di Laplace")," della variabile aleatoria di X.")),n(Ze.a,{title:"Funzione caratteristica"},n("p",null,"La ",n("i",null,"funzione caratteristica")," è:"),n("p",null,n(Je.b,null,ta(Pi()))),n("p",null,"Se due variabile aleatorie hanno la stessa funzione caratteristica, allora esse hanno la ",n("b",null,"stessa distribuzione"),"."),n("p",null,"E' la ",n("b",null,"trasformata di Fourier")," della variabile aleatoria di X."))),n($e.a,{title:"Prove e schemi"},n(Ze.a,{title:"Variabile con distribuzione"},n("p",null,"Per dire che una variabile ha una certa distribuzione, si usa la notazione:"),n("p",null,n(Je.b,null,ta(Ei())))),n(Ze.a,{title:"Prova di Bernoulli"},n("p",null,"Una prova con solo due possibili esiti: ",n(la.a,null,"successo")," e ",n(ia.a,null,"insuccesso"),".")),n(Ze.a,{title:"Schema di Bernoulli"},n("p",null,"Una sequenza di prove di Bernoulli per le quali le probabilità di successo e fallimento rimangono invariate."))),n($e.a,{title:"Bernoulliana"},n(Ze.a,{title:"Distribuzione bernoulliana"},n("p",null,"Una variabile aleatoria che rappresenta una prova di Bernoulli:"),n("ul",null,n("li",null,"vale ",n(la.a,null,"1")," in caso di ",n(la.a,null,"successo"),"."),n("li",null,"vale ",n(ia.a,null,"0")," in caso di ",n(ia.a,null,"insuccesso"),".")),n("p",null,"Il suo simbolo è ",n(Je.b,null,ta(zi())))),n(Ze.a,{title:"Densità della bernoulliana"},n("p",null,"La distribuzione bernoulliana ha come densità:"),n("p",null,n(Je.b,null,ta(qi()))))),n($e.a,{title:"Binomiale"},n(Ze.a,{title:"Distribuzione binomiale"},n("p",null,"Una variabile aleatoria che conta il numero di successi di ",n(Je.b,null,"n")," prove di uno schema di Bernoulli."),n("p",null,"Il suo simbolo è ",n(Je.b,null,ta(gi())),".")),n(Ze.a,{title:"Densità della binomiale"},n("p",null,"La binomiale ha come densità:"),n("p",null,n(Je.b,null,ta(Xi())))),n(Ze.a,{title:"Momenti della binomiale"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della binomiale è:"),n("p",null,n(Je.b,null,ta(hi()))),n("p",null,"La ",n("b",null,"media")," di una binomiale è:"),n("p",null,n(Je.b,null,ta(_i()))),n("p",null,"La ",n("b",null,"varianza")," di una binomiale è:"),n("p",null,n(Je.b,null,ta(vi()))))),n($e.a,{title:"Geometrica"},n(Ze.a,{title:"Distribuzione geometrica"},n("p",null,"Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli fino alla comparsa del primo successo."),n("p",null,"Il suo simbolo è ",n(Je.b,null,"Geo(p)"),".")),n(Ze.a,{title:"Densità della geometrica"},n("p",null,"La geometrica ha come densità:"),n("p",null,n(Je.b,null,ta(bi())))),n(Ze.a,{title:"Momenti della geometrica"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della geometrica è:"),n("p",null,n(Je.b,null,ta(fi()))),n("p",null,"La ",n("b",null,"media")," della geometrica è:"),n("p",null,n(Je.b,null,ta(mi()))),n("p",null,"La ",n("b",null,"varianza")," della geometrica è:"),n("p",null,n(Je.b,null,ta(di())))),n(Ze.a,{title:"Assenza di memoria della geometrica"},n("p",null,"La geometrica non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),n("p",null,n(Je.b,null,ta(pi()))),n(na.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),n($e.a,{title:"Binomiale negativa"},n(Ze.a,{title:"Distribuzione binomiale negativa"},n("p",null,"Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli necessarie perchè si verifichi l'",n(Je.b,null,"n"),"-esimo successo."),n("p",null,"Il suo simbolo è ",n(Je.b,null,ta(si())),".")),n(Ze.a,{title:"Densità della binomiale negativa"},n("p",null,"La binomiale negativa ha come densità:"),n("p",null,n(Je.b,null,ta(ci())))),n(Ze.a,{title:"Momenti della binomiale negativa"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della binomiale negativa è:"),n("p",null,n(Je.b,null,ta(ui()))),n("p",null,"La ",n("b",null,"media")," della binomiale negativa è:"),n("p",null,n(Je.b,null,ta(oi()))),n("p",null,"La ",n("b",null,"varianza")," della binomiale negativa è:"),n("p",null,n(Je.b,null,ta(ri())))))),n($e.a,{title:"Geometrica traslata"},n(Ze.a,{title:"Distribuzione geometrica traslata"},n("p",null,"Una variabile aleatoria che conta il numero ",n(Je.b,null,"k")," di insuccessi consecutivi in uno schema di Bernoulli:"),n("p",null,"Il suo simbolo rimane ",n(Je.b,null,ta(ti())),".")),n(Ze.a,{title:"Densità della geometrica tralsata"},n("p",null,"La geometrica traslata ha come densità:"),n("p",null,n(Je.b,null,ta(ai())))),n(Ze.a,{title:"Momenti della geometrica traslata"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della geometrica traslata è:"),n("p",null,n(Je.b,null,ta(ei()))),n("p",null,"La ",n("b",null,"media")," della geometrica traslata è:"),n("p",null,n(Je.b,null,ta(ii()))),n("p",null,"La ",n("b",null,"varianza")," della geometrica è:"),n("p",null,n(Je.b,null,ta(li())))),n(Ze.a,{title:"Assenza di memoria della geometrica traslata"},n("p",null,"La geometrica traslata non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),n("p",null,n(Je.b,null,ta(ni()))),n(na.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),n($e.a,{title:"Binomiale negativa traslata"},n(Ze.a,{title:"Distribuzione binomiale negativa traslata"},n("p",null,"Una variabile aleatoria che conta il numero di insuccessi in uno schema di Bernoulli prima che si verifichi l'",n(Je.b,null,"n"),"-esimo successo."),n("p",null,"Il suo simbolo rimane ",n(Je.b,null,ta($l())),".")),n(Ze.a,{title:"Densità della binomiale negativa traslata"},n("p",null,"La binomiale negativa traslata ha come densità:"),n("p",null,n(Je.b,null,ta(Zl())))),n(Ze.a,{title:"Momenti della binomiale negativa traslata"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della binomiale negativa traslata è:"),n("p",null,n(Je.b,null,ta(Jl()))),n("p",null,"La ",n("b",null,"media")," della binomiale negativa traslata è:"),n("p",null,n(Je.b,null,ta(Wl()))),n("p",null,"La ",n("b",null,"varianza")," della binomiale negativa traslata è:"),n("p",null,n(Je.b,null,ta(Ql())))))),n($e.a,{title:"Ipergeometrica"},n(Ze.a,{title:"Distribuzione ipergeometrica"},n("p",null,"Una variabile aleatoria che, sapendo il numero di successi ",n(Je.b,null,"K")," e di insuccessi ",n(Je.b,null,"N-K"),", conta quanti successi si otterrebbero se se ne estraessero ",n(Je.b,null,"n")," in blocco."),n("p",null,"Il suo simbolo è ",n(Je.b,null,"Ipe(N, K, n)"),".")),n(Ze.a,{title:"Densità della ipergeometrica"},n("p",null,"La ipergeometrica ha come densità:"),n("p",null,n(Je.b,null,ta(Kl())))),n(Ze.a,{title:"Momenti della ipergeometrica"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della ipergeometrica è trascurabile."),n("p",null,"La ",n("b",null,"media")," della ipergeometrica è:"),n("p",null,n(Je.b,null,ta(jl()))),n("p",null,"La ",n("b",null,"varianza")," della ipergeometrica è:"),n("p",null,n(Je.b,null,ta(Hl())))))),n($e.a,{title:"Poissoniana"},n(Ze.a,{title:"Distribuzione poissoniana"},n("p",null,"Una variabile aleatoria che soddisfa tutte le seguenti caratteristiche:"),n("ul",null,n("li",null,"Binomiale: ",n(Je.b,null,ta(Rl()))),n("li",null,"Il numero di prove tende a infinito: ",n(Je.b,null,ta(Gl()))),n("li",null,"La probabilità di successo tende a 0: ",n(Je.b,null,ta(Ol()))),n("li",null,"La media è finita: ",n(Je.b,null,ta(Bl())))),n("p",null,"Il suo simbolo è ",n(Je.b,null,ta(Ul())))),n(Ze.a,{title:"Densità della poissoniana"},n("p",null,"La poissoniana ha come densità:"),n("p",null,n(Je.b,null,ta(Tl())))),n(Ze.a,{title:"Momenti della poissoniana"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della poissoniana è:"),n("p",null,n(Je.b,null,ta(Al()))),n("p",null,"La ",n("b",null,"media")," della poissoniana è:"),n("p",null,n(Je.b,null,ta(Ml()))),n("p",null,"La ",n("b",null,"varianza")," della poissoniana è:"),n("p",null,n(Je.b,null,ta(Dl()))),n("p",null,"Gli altri momenti della poissoniana sono:"),n("ol",{start:2},n("li",null,n(Je.b,null,ta(Il()))))))),n($e.a,{title:"Un altro schema"},n(Ze.a,{title:"Schema di Poisson"},n("p",null,"Una successione di ",n("b",null,"arrivi")," avvenuti in un certo arco temporale che:"),n("ul",null,n("li",null,"non sono sovrapposti."),n("li",null,"hanno intensità ",n(Je.b,null,ta(wl()))," costante."),n("li",null,"avvengono indipendentemente gli uni dagli altri."))),n(Ze.a,{title:"Processo di Poisson"},n("p",null,"Una variabile aleatoria ",n(Je.b,null,"N_t")," che conta il numero di arrivi di uno schema di Poisson di intensità ",n(Je.b,null,ta(Sl()))," in un intervallo di tempo di durata ",n(Je.b,null,"t"),"."),n("p",null,"E' una distribuzione poissoniana con ",n(Je.b,null,ta(Cl())),": ",n(Je.b,null,ta(Yl()))),n(na.a,null,"E' paragonabile a una bernoulliana: ogni successo corrisponde a un arrivo, mentre il tempo è il numero di prove effettuate (ma nel continuo)."))),n($e.a,{title:"Esponenziale"},n(Ze.a,{title:"Distribuzione esponenziale"},n("p",null,"Una variabile aleatoria che conta il tempo diwidehattesa prima del primo arrivo di un processo di Poisson di intensità ",n(Je.b,null,ta(Vl())),"."),n("p",null,"Il suo simbolo è ",n(Je.b,null,ta(Nl())),".")),n(Ze.a,{title:"Densità dell'esponenziale"},n("p",null,"L'esponenziale ha come ",n("b",null,"densità"),":"),n("p",null,n(Je.b,null,ta(yl()))),n("p",null,"L'esponenziale ha come ",n("b",null,"funzione di ripartizione"),":"),n("p",null,n(Je.b,null,ta(Fl())))),n(Ze.a,{title:"Momenti dell'esponenziale"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," dell'esponenziale è:"),n("p",null,n(Je.b,null,ta(Ll()))),n("p",null,"La ",n("b",null,"media")," dell'esponenziale è:"),n("p",null,n(Je.b,null,ta(kl()))),n("p",null,"La ",n("b",null,"varianza")," dell'esponenziale è:"),n("p",null,n(Je.b,null,ta(xl())))),n(Ze.a,{title:"Assenza di memoria della esponenziale"},n("p",null,"L'esponenziale non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),n("p",null,n(Je.b,null,ta(Pl()))),n(na.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),n($e.a,{title:"Legge gamma"},n(Ze.a,{title:"Distribuzione gamma"},n("p",null,"Una variabile aleatoria che conta il tempo diwidehattesa prima dell'",n(Je.b,null,"n"),"-esimo arrivo di un processo di Poisson di intensità ",n(Je.b,null,ta(El())),"."),n("p",null,"Il suo simbolo è ",n(Je.b,null,ta(zl())),".")),n(Ze.a,{title:"Densità della legge gamma"},n("p",null,"La legge gamma ha come densità:"),n("p",null,n(Je.b,null,ta(ql())))),n(Ze.a,{title:"Momenti della legge gamma"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della legge gamma è:"),n("p",null,n(Je.b,null,ta(gl()))),n("p",null,"La ",n("b",null,"media")," della legge gamma è:"),n("p",null,n(Je.b,null,ta(Xl()))),n("p",null,"La ",n("b",null,"varianza")," della legge gamma è:"),n("p",null,n(Je.b,null,ta(hl())))))),n($e.a,{title:"Uniforme"},n(Ze.a,{title:"Distribuzione uniforme"},n("p",null,"Una variabile aleatoria che può assumere qualsiasi valore in un intervallo ",n(Je.b,null,ta(_l()))," in modo equiprobabile."),n("p",null,"Il suo simbolo è ",n(Je.b,null,ta(vl()))),n("p",null,"Su di essa vale la seguente proprietà:"),n("p",null,n(Je.b,null,ta(bl())))),n(Ze.a,{title:"Densità della distribuzione uniforme"},n("p",null,"La distribuzione uniforme ha come ",n("b",null,"densità"),":"),n("p",null,n(Je.b,null,ta(fl()))),n("p",null,"La distribuzione uniforme ha come ",n("b",null,"funzione di ripartizione"),":"),n("p",null,n(Je.b,null,ta(ml())))),n(Ze.a,{title:"Momenti della distribuzione uniforme"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della distribuzione uniforme è:"),n("p",null,n(Je.b,null,ta(dl()))),n("p",null,"La ",n("b",null,"media")," della distribuzione uniforme è:"),n("p",null,n(Je.b,null,ta(pl()))),n("p",null,"La ",n("b",null,"varianza")," della distribuzione uniforme è:"),n("p",null,n(Je.b,null,ta(sl())))))),n($e.a,{title:"Normale o Gaussiana"},n(Ze.a,{title:"Distribuzione normale"},n("p",null,"Una variabile aleatoria con una specifica distribuzione."),n("p",null,"Il suo simbolo è ",n(Je.b,null,ta(cl())),"."),n(na.a,null,n(Je.b,null,"\\mu")," e ",n(Je.b,null,"\\sigma^2")," sono rispettivamente la media e la varianza della distribuzione!")),n(Ze.a,{title:"Densità della distribuzione normale"},n("p",null,"La distribuzione normale ha come densità:"),n("p",null,n(Je.b,null,ta(ul())))),n(Ze.a,{title:"Momenti della distribuzione normale"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della distribuzione normale è:"),n("p",null,n(Je.b,null,ta(ol()))),n("p",null,"La ",n("b",null,"media")," della distribuzione normale è:"),n("p",null,n(Je.b,null,ta(rl()))),n("p",null,"La ",n("b",null,"varianza")," della distribuzione normale è:"),n("p",null,n(Je.b,null,ta(tl())))))),n($e.a,null,n(Ze.a,{title:"Trasformazione della normale"},n("p",null,"Qualsiasi normale può essere trasformata in qualsiasi altra normale:"),n("p",null,n(Je.b,null,ta(al())))),n(Ze.a,{title:"Normale standard"},n("p",null,"La distribuzione normale standard ",n(Je.b,null,"Z")," è:"),n("p",null,n(Je.b,null,"Z \\sim Nor(0, 1)")),n("p",null,"La sua funzione di ripartizione è detta ",n(Je.b,null,ta(el()))," e vale:"),n("p",null,n(Je.b,null,ta(il())))),n(Ze.a,{title:"Quantili normali"},n("p",null,"Da un quantile ",n(Je.b,null,ta(ll()))," della normale standard è possibile risalire allo stesso quantile di qualsiasi altra normale:"),n("p",null,n(Je.b,null,ta(nl()))))),n($e.a,null,n(Ze.a,{title:"Gamma e normale"},n("p",null,"La distribuzione normale ha una particolare relazione con la distribuzione Gamma:"),n("p",null,n(Je.b,null,ta($n())))),n(Ze.a,{title:"La funzione Chi"},n("blockquote",null,'"chi-quadro a un grado di libertà"'),n("p",null,"Esiste una distribuzione Gamma particolare:"),n("p",null,n(Je.b,null,ta(Zn()))),n("p",null,"Più chi-quadro possono essere sommate per aumentare i loro gradi di libertà:"),n("p",null,n(Je.b,null,ta(Jn())))),n(Ze.a,{title:"T di Student"},n("p",null,"Un'altra funzione particolare è la funzione T di Student:"),n("p",null,n(Je.b,null,ta(Wn()))))),n($e.a,{title:"Approssimazioni notevoli"},n(Ze.a,{title:"Ipergeometrica e binomiale"},n("p",null,"La binomiale è come una ipergeometrica ma con ripetizioni, quindi per valori molto grandi di ",n(Je.b,null,"N")," rispetto a ",n(Je.b,null,"n"),", si può dire che:"),n("p",null,n(Je.b,null,ta(Qn())))),n(Ze.a,{title:"Binomiale e poissoniana"},n("p",null,"La binomiale non è altro che una poissoniana a tempo discreto, quindi, se ",n(Je.b,null,"n")," è grande e ",n(Je.b,null,"n \\cdot p")," è nell'ordine di grandezza delle unità, allora:"),n("p",null,n(Je.b,null,ta(Kn())))),n(Ze.a,{title:"Binomiale e normale"},n("p",null,"Per il Teorema di De Moivre-Laplace, se una binomiale ha una ",n(Je.b,null,"n")," grande e ",n(Je.b,null,"p")," non vicina a 0 o 1, si può approssimare con:"),n("p",null,n(Je.b,null,ta(jn())))),n(Ze.a,{title:"Correzione di Yates"},n("p",null,"Passando da una variabile discreta ",n(Je.b,null,"X")," a una continua ",n(Je.b,null,"Y"),", per ogni valore discreto ",n(Je.b,null,"k"),' la probabilità viene "spalmata" su tutto l\'intervallo ',n(Je.b,null,ta(Hn())),":"),n("ul",null,n("li",null,n(Je.b,null,ta(Rn()))),n("li",null,n(Je.b,null,ta(Gn()))),n("li",null,n(Je.b,null,ta(On()))),n("li",null,n(Je.b,null,ta(Bn())))))),n($e.a,{title:"Vettori aleatori"},n(Ze.a,{title:"Vettore aleatorio"},n("p",null,"Un vettore ",n("b",null,"composto da variabili aleatorie"),"."),n("p",null,"Il suo simbolo generalmente è ",n(Je.b,null,ta(Un()))," oppure ",n(Je.b,null,ta(Tn())),".")),n(Ze.a,{title:"Funzioni di ripartizione"},n("p",null,"I vettori aleatori hanno più funzioni di ripartizione che si differenziano in base al numero di parametri."),n("p",null,"Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"funzione di ripartizione congiunta"),":"),n("p",null,n(Je.b,null,ta(An()))),n("p",null,"Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"funzione di ripartizione marginale"),":"),n("p",null,n(Je.b,null,ta(Mn())))),n(Ze.a,{title:"Densità discreta"},n("p",null,"I vettori aleatori ",n("b",null,"discreti")," hanno più densità che si differenziano in base al numero di parametri."),n("p",null,"Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"densità congiunta"),":"),n("p",null,n(Je.b,null,ta(Dn()))),n("p",null,"Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"densità marginale"),":"),n("p",null,n(Je.b,null,ta(In()))))),n($e.a,{title:"Più variabili aleatorie"},n(Ze.a,{title:"Indipendenza delle variabili aleatorie"},n("p",null,"Più variabili aleatorie sono indipendenti se, per qualsiasi scelta di intervalli ",n(Je.b,null,"A_i"),":"),n("p",null,n(Je.b,null,ta(wn())))),n(Ze.a,{title:"Media dei vettori aleatori"},n("p",null,"E' possibile calcolare la media di qualsiasi funzione ",n(Je.b,null,"g(X, Y)")," avente elementi del vettore come variabili:"),n("p",null,n(Je.b,null,ta(Sn()))),n(na.a,null,"Solitamente si calcola la media di ",n(Je.b,null,"x \\cdot y"),"."),n("p",null,"Le medie di più variabili aleatorie si possono sommare:"),n("p",null,n(Je.b,null,ta(Cn()))))),n($e.a,null,n(Ze.a,{title:"Covarianza"},n("p",null,"Un ",n("b",null,"operatore")," che misura la correlazione di due variabili aleatorie."),n("p",null,"Si calcola con il valore atteso dei prodotti delle distanze dalla media:"),n("p",null,n(Je.b,null,ta(Yn()))),n("p",null,"Ha diverse proprietà:"),n("ul",null,n("li",null,"Il suo ",n("b",null,"valore nullo")," è 0: ",n(Je.b,null,ta(Vn()))),n("li",null,"E' ",n("b",null,"commutativa"),": ",n(Je.b,null,ta(Nn()))),n("li",null,"E' ",n("b",null,"semplificabile"),": ",n(Je.b,null,ta(yn()))),n("li",null,"E' ",n("b",null,"lineare"),": ",n(Je.b,null,ta(Fn()))),n("li",null,"E' ",n("b",null,"distributiva"),": ",n(Je.b,null,ta(Ln()))))),n(Ze.a,{title:"Variabili incorrelate"},n("p",null,"Due variabili sono ",n("i",null,"variabili incorrelate")," se:"),n("p",null,n(Je.b,null,ta(kn()))),n("p",null,"Variabili indipendenti sono sempre incorrelate.")),n(Ze.a,{title:"Matrice di covarianza"},n("p",null,"Una matrice ",n(Je.b,null,ta(xn()))," che contiene la covarianza tra tutte le variabili di un vettore aleatorio ",n(Je.b,null,ta(Pn())),":"),n("p",null,n(Je.b,null,ta(En()))),n("p",null,"E' sempre simmetrica e semidefinita positiva (tutti gli autovalori sono ",n(Je.b,null,"\\geq 0"),".")),n(Ze.a,{title:"Coefficiente di correlazione"},n("p",null,"Un valore che misura come due variabili aleatorie sono correlate:"),n("p",null,n(Je.b,null,ta(zn()))),n("p",null,"E' sempre compreso tra -1 e 1:"),n("p",null,n(Je.b,null,ta(qn()))),n("p",null,"Vale esattamente -1 o 1 solo se esiste un legame lineare tra le due variaibli:"),n("p",null,n(Je.b,null,ta(gn())))),n(Ze.a,{title:"Varianza di variabili aleatorie sommate"},n("p",null,"La varianza di due variabili aleatorie sommate è:"),n("p",null,n(Je.b,null,ta(Xn()))),n(na.a,null,"Si dimostra applicando le proprietà della covarianza!"),n("p",null,"Se più variabili aleatorie ",n(Je.b,null,"X_i")," sono ",n("b",null,"indipendenti")," (",n(Je.b,null,ta(hn())),"), allora:"),n("p",null,n(Je.b,null,ta(_n()))))),n($e.a,{title:"Campioni"},n(Ze.a,{title:"Campione casuale"},n("p",null,"Una ",n("b",null,"n-pla")," di variabili aleatorie con la stessa distribuzione della variabile aleatoria ",n(Je.b,null,"X"),' ("popolazione") ma ',n("b",null,"indipendenti")," tra loro."),n(na.a,null,"Le variabili aleatorie sono come un lazy-load in programmazione; quando ci sarà bisogno del loro valore numerico, esse si ",n("b",null,"realizzeranno")," nel loro valore.")),n(Ze.a,{title:"Momento campionario"},n("p",null,"Il valore dato dalla media aritmetica degli ",n(Je.b,null,"n")," elementi del campione elevati alla potenza ",n(Je.b,null,"k"),":"),n("p",null,n(Je.b,null,ta(vn()))),n("p",null,"Il momento campionario di primo ordine è la ",n("i",null,"media campionaria")," ",n(Je.b,null,ta(bn())),".")),n(Ze.a,{title:"Varianza campionaria"},n("p",null,"La media aritmetica dello scarto quadratico medio degli elementi del campione."),n("p",null,"Se è noto il valore medio ",n(Je.b,null,ta(fn()))," di X:"),n("p",null,n(Je.b,null,ta(mn()))),n("p",null,"Altrimenti:"),n("p",null,n(Je.b,null,ta(dn()))))),n($e.a,{title:"Media-ception"},n(Ze.a,{title:"Media campionaria"},n("p",null,"Se calcoliamo la media della media campionaria, risulterà vero che:"),n("p",null,n(Je.b,null,ta(pn()))),n(na.a,null,"Quindi, è possibile usare i campioni per trovare la media di una variabile aleatoria!")),n(Ze.a,{title:"Varianza campionaria"},n("p",null,"Se calcoliamo la varianza della media campionaria, risulterà vero che:"),n("p",null,n(Je.b,null,ta(sn()))),n(na.a,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!")),n(Ze.a,{title:"Correzione campionaria"},n("p",null,"Se calcoliamo la media della varianza campionaria, risulterà vero che:"),n("p",null,n(Je.b,null,ta(cn()))),n(na.a,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!"))),n($e.a,{title:"Campionamento di una distribuzione normale"},n(Ze.a,{title:"Campionamento di una distribuzione normale"},n("p",null,"Se la popolazione ",n(Je.b,null,"X")," ha una distribuzione normale (",n(Je.b,null,ta(un())),")...")),n(Ze.a,{title:"Distribuzione della media campionaria"},n("p",null,"...allora sappiamo anche la distribuzione della media campionaria!"),n("p",null,n(Je.b,null,ta(on())))),n(Ze.a,{title:"Distribuzione della varianza campionaria"},n("p",null,"...e anche della varianza campionaria!"),n("p",null,n(Je.b,null,ta(rn()))),n("p",null,n(Je.b,null,ta(tn())))),n(Ze.a,{title:"Indipendenza"},n("p",null,"...e che media campionaria e varianza campionaria sono indipendenti tra loro!"))),n($e.a,{title:"Quando i campioni hanno dimensioni infinite"},n(Ze.a,{title:"Convergenza in distribuzione"},n("p",null,"Se la successione di variabili aleatorie ",n(Je.b,null,"X_n")," all'infinito ha la ",n("b",null,"stessa funzione di ripartizione")," della popolazione ",n(Je.b,null,"X"),", allora essa ",n("i",null,"converge in distribuzione"),"."),n("p",null,n(Je.b,null,"\\lim_{n \\to +\\infty} F_{X_n} (x) = F_X (x) \\implies X_n \\xrightarrow{d} X"))),n(Ze.a,{title:"Convergenza in probabilità"},n("p",null,"Se la successione di variabili aleatorie ",n(Je.b,null,"X_n")," all'infinito ha la ",n("b",null,"stessa probabilità")," della popolazione ",n(Je.b,null,"X"),", allora essa ",n("i",null,"converge in probabilità"),"."),n("p",null,n(Je.b,null,"\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | X_n - X | < \\epsilon) = 1 \\implies X_n \\xrightarrow{p} X"))),n(Ze.a,{title:"Convergenza quasi certa"},n("p",null,"Se la successione di variabili aleatorie ",n(Je.b,null,"X_n")," all'infinito ha la ",n("b",null,"stessa probabilità a ")," della popolazione ",n(Je.b,null,"X"),", allora essa ",n("i",null,"converge quasi certamente"),"."),n("p",null,n(Je.b,null,"\\forall \\epsilon > 0, P left( \\lim_{n \\to +\\infty} | X_n - X | < \\epsilon) \right) = 1 \\implies X_n \\xrightarrow{qc} X"))),n(Ze.a,{title:"Convergenza in media quadratica"},n("p",null,"Se la successione di variabili aleatorie ",n(Je.b,null,"X_n")," all'infinito ha la ",n("b",null,"media del quadrato della distanza")," tra la successione e la popolazione ",n(Je.b,null,"X")," ",n("b",null,"uguale a 0"),", allora essa ",n("i",null,"converge in media quadratica"),"."),n("p",null,n(Je.b,null,"\\lim_{n \\to +\\infty} E( | X_n - X |^2 = 0 \\implies X_n \\xrightarrow{mq} X"))),n(Ze.a,{title:"Gerarchia delle convergenze"},n("p",null,n(Je.b,null,"\n                                \\begin{matrix}\n                                X_n \\xrightarrow{mq} X\\\\\n                                X_n \\xrightarrow{qc} X\n                                \\end{matrix} \\implies X_n \\xrightarrow{p} X \\implies X_n \\xrightarrow{d} X")),n("p",null,"In più:"),n("p",null,n(Je.b,null,"X_n \\xrightarrow{p} x \\Longleftrightarrow X_n \\xrightarrow{d} x")))),n($e.a,{title:"I grandi numeri"},n(Ze.a,{title:"Legge debole dei grandi numeri"},n("p",null,"La successione delle medie campionarie ",n(Je.b,null,ta(an()))," ",n("b",null,"converge in probabilità")," alla media della popolazione ",n(Je.b,null,ta(en())),", se essa esiste."),n("p",null,n(Je.b,null,"\\overline{X}_n \\xrightarrow{p} X")),n("p",null,"Ovvero:"),n("p",null,n(Je.b,null,ta(ln()))),n("p",null,n(Je.b,null,ta(nn())))),n(Ze.a,{title:"Legge forte dei grandi numeri"},n("p",null,"La successione delle medie campionarie ",n(Je.b,null,ta($()))," ",n("b",null,"converge quasi certamente")," alla media della popolazione ",n(Je.b,null,ta(Z())),", se essa esiste."),n("p",null,n(Je.b,null,"\\overline{X}_n \\xrightarrow{qc} X")),n("p",null,"Ovvero:"),n("p",null,n(Je.b,null,ta(J()))),n(na.a,null,"Dimostra che l'interpretazione frequentista della probabilità è valida!"))),n($e.a,{title:"Al limite"},n(Ze.a,{title:"Teorema centrale del limite"},n("p",null,"La successione delle medie campionarie ",n(Je.b,null,ta(W()))," ",n("b",null,"converge in distribuzione")," a ",n(Je.b,null,ta(Q())),"."),n("p",null,n(Je.b,null,ta(K()))),n("p",null,"Ovvero:"),n("p",null,n(Je.b,null,ta(j()))))),n($e.a,{title:"Altre approsimazioni"},n(Ze.a,{title:"Binomiale e normale"},n("p",null,"E' una somma di ",n("b",null,"bernoulliane"),", e quindi si approssima a una normale:"),n("p",null,n(Je.b,null,ta(H())))),n(Ze.a,{title:"Binomiale negativa e normale"},n("p",null,"E' una somma di ",n("b",null,"geometriche"),", e quindi si approssima a una normale:"),n("p",null,n(Je.b,null,ta(R())))),n(Ze.a,{title:"Poissoniana e normale"},n("p",null,"E' una somma di altre ",n("b",null,"poissoniane"),", e quindi si approssima a una normale:"),n("p",null,n(Je.b,null,ta(G())))),n(Ze.a,{title:"Gamma e normale"},n("p",null,"E' una somma di ",n("b",null,"esponenziali"),", e quindi si approssima a una normale:"),n("p",null,n(Je.b,null,ta(O())))),n(Ze.a,{title:"In generale"},n("p",null,"Se ",n(Je.b,null,"n")," è grande, allora:"),n("p",null,n(Je.b,null,ta(B()))))),n($e.a,{title:"Actually statistica"},n(Ze.a,{title:"Parametri sconosciuti"},n("p",null,"Per indicare parametri sconosciuti di una legge si usa ",n(Je.b,null,"\\theta"),".")),n(Ze.a,{title:"Statistica"},n("p",null,"Una variabile aleatoria funzione di un campione:"),n("p",null,n(Je.b,null,ta(U()))),n(na.a,null,"Ad esempio, sono statistiche media e varianza campionaria, così come il campione stesso ",n(Je.b,null,ta(T())),"."))),n($e.a,{title:"Stimatori"},n(Ze.a,{title:"Stimatore"},n("p",null,"Una statistica ",n(Je.b,null,"T_n")," ottenuta da ",n(Je.b,null,"n")," osservazioni, che stimi i parametri di una legge e sia indipendente da essi.")),n(Ze.a,{title:"Corretto"},n("p",null,"Uno stimatore è ",n("i",null,"corretto")," se il suo valore atteso coincide con quello dei parametri che stima:"),n("p",null,n(Je.b,null,ta(A())))),n(Ze.a,{title:"Asintoticamente corretto"},n("p",null,"Uno stimatore è ",n("i",null,"asintoticamente corretto")," se, per infinite osservazioni, il suo valore atteso coincide con quello dei parametri che stima:"),n("p",null,n(Je.b,null,ta(M())))),n(Ze.a,{title:"Consistente in media quadratica"},n("p",null,"Uno stimatore è ",n("i",null,"consistente in media quadratica")," se:"),n("p",null,n(Je.b,null,ta(D())))),n(Ze.a,{title:"Consistente in probabilità"},n("p",null,"Uno stimatore è ",n("i",null,"consistente in probabilità")," se:"),n("p",null,n(Je.b,null,ta(I())))),n(Ze.a,{title:"Asintoticamente normale"},n("p",null,"Uno stimatore è ",n("i",null,"asintoticamente normale")," se:"),n("p",null,n(Je.b,null,ta(w()))))),n($e.a,{title:"Metodo dei momenti"},n(Ze.a,{title:"Metodo dei momenti"},n("p",null,"Si può usare il ",n("i",null,"metodo dei momenti")," per ottenere uno stimatore di una popolazione ",n(Je.b,null,"X"),"."),n("p",null,"Lo stimatore di ",n(Je.b,null,ta(S()))," così ottenuto sarà indicato aggiungendo un cappellino e una ",n(Je.b,null,"M")," a ",n(Je.b,null,"\\theta"),": ",n(Je.b,null,ta(C()))),n("p",null,"Visto che:"),n("ul",null,n("li",null,n(Je.b,null,ta(Y()))),n("li",null,n(Je.b,null,ta(V())))),n("p",null,"Allora:"),n("p",null,n(Je.b,null,ta(N()))),n("p",null,"Se ",n(Je.b,null,ta(y()))," non è esprimibile in termini di ",n(Je.b,null,ta(F())),", si possono usare i momenti successivi ",n(Je.b,null,ta(L())),", ",n(Je.b,null,ta(k())),", ",n(Je.b,null,ta(x())),"..."))),n($e.a,{title:"Metodo della massima verosomiglianza"},n(Ze.a,{title:"Metodo della massima verosomiglianza"},n("p",null,"Si può usare il ",n("i",null,"metodo della massima verosomiglianza")," per ottenere uno stimatore di una popolazione ",n(Je.b,null,"X"),"."),n("p",null,"Lo stimatore di ",n(Je.b,null,ta(P()))," così ottenuto sarà indicato aggiungendo un cappellino e una ",n(Je.b,null,"L")," a ",n(Je.b,null,"\\theta"),": 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verosomiglianza:"),n("p",null,n(Je.b,null,ta(h())))),n(Ze.a,{title:"Stima di una poissoniana"},n("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),n("p",null,n(Je.b,null,ta(_())))),n(Ze.a,{title:"Stima di una esponenziale"},n("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),n("p",null,n(Je.b,null,ta(v())))),n(Ze.a,{title:"Stima di una normale"},n("p",null,"Per il metodo della massima verosomiglianza:"),n("ul",null,n("li",null,n(Je.b,null,ta(b()))),n("br",null),n("li",null,n(Je.b,null,ta(f())))))),n($e.a,{title:"Intervalli di confidenza"},n(Ze.a,{title:"Confidenza"},n("blockquote",null,'"intervallo di confidenza al 95%"'),n("p",null,"L'intervallo di valori di ",n(Je.b,null,"\\theta"),' all\'interno del quale siamo "più o meno sicuri" si trovi il valore effettivo:'),n("p",null,"L'intervallo di confidenza a N della stima ",n(Je.b,null,ta(m()))," è l'intervallo ",n(Je.b,null,"]a, b[")," tale che:"),n("p",null,n(Je.b,null,ta(d()))),n("p",null,"Può anche essere ",n("b",null,"unilatero")," nel caso limiti la stima in una sola direzione, positiva o negativa."))),n($e.a,{title:"Confidenza nella media di una normale"},n(Ze.a,{title:"Varianza nota"},n("p",null,"Se conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'",n(Je.b,null,"\\alpha"),"% con queste formule:"),n("ul",null,n("li",null,"Intervalli bilateri: ",n(Je.b,null,ta(p()))),n("li",null,"Intervallo unilatero da sinistra: ",n(Je.b,null,ta(s()))),n("li",null,"Intervallo unilatero da destra: ",n(Je.b,null,ta(c()))))),n(Ze.a,{title:"Varianza incognita"},n("p",null,"Se non conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'",n(Je.b,null,"\\alpha"),"% con queste formule:"),n("ul",null,n("li",null,"Intervalli bilateri: ",n(Je.b,null,ta(u()))),n("li",null,"Intervallo unilatero da sinistra: ",n(Je.b,null,ta(o()))),n("li",null,"Intervallo unilatero da destra: ",n(Je.b,null,ta(r())))),n("p",null,n(Je.b,null,ta(t()))," è un quantile della distribuzione di Student di parametro ",n(Je.b,null,"v"),"."))),n($e.a,{title:"Confidenza per la proporzione di una bernoulliana"},n(Ze.a,{title:"Terzo metodo corretto"},n("p",null,"L'intervallo di confidenza per la proprorzione di una bernoulliana qualsiasi si ottiene da questa formula:"),n("p",null,n(Je.b,null,ta(a()))))),n($e.a,{title:"Confidenza per la media di qualsiasi popolazione"},n(Ze.a,{title:"Approssimando con la normale"},n("p",null,"L'intervallo di confidenza per la media di una qualsiasi popolazione si ottiene da questa formula:"),n("p",null,n(Je.b,null,ta(e()))))))))}}.call(this,i("hosL").h)},htlC:function(n){n.exports={splitparent:"splitparent__3-wBs",splitchild:"splitchild__begkX"}},imVn:function(n,l,i){"use strict";(function(n){var e=i("OmdA"),a=i.n(e),t=i("Y9Ml");l.a=function(l){return 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extracted by mini-css-extract-plugin\nmodule.exports = {\"example\":\"example__9acWs\"};","import style from \"./Minus.less\";\n\nexport default function(props) {\n\treturn {props.children};\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"box\":\"box__3cKyY\",\"default\":\"default__v-emJ\",\"red\":\"red__339Cz\",\"orange\":\"orange__24_8v\",\"yellow\":\"yellow__1Jo9W\",\"lime\":\"lime__34yV5\",\"cyan\":\"cyan__3RqLr\",\"blue\":\"blue__13Wnj\",\"magenta\":\"magenta__2tkzq\"};","import style from \"./Plus.less\";\nimport { Component } from 'preact';\n\nexport default function(props) {\n\treturn {props.children};\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"inline\":\"inline__1yl8V\",\"block\":\"block__fPiiB\"};","import Split from \"../Layout/Split\";\nimport {Fragment} from \"preact\";\n\nexport default function (props) {\n    return (\n        \n            
    \n                {props.title}\n            
    \n            \n                {props.children}\n            \n            \n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"title\":\"title__3ZVpg\",\"contents\":\"contents__20_NI\"};","import {createContext} from \"preact\";\n\nexport default createContext(null);\n","import style from './Latex.less';\nimport {useContext} from \"preact/hooks\";\nimport LatexRenderColor from \"../../contexts/LatexRenderColor\";\nimport LatexDefaultInline from \"../../contexts/LatexDefaultInline\";\nimport LatexDefaultDisplay from \"../../contexts/LatexDefaultDisplay\";\n\nexport const LatexDisplay = Object.freeze({\n    INLINE: style.inline,\n    BLOCK: style.block,\n})\n\nexport default function(props) {\n    // black, blue, brown, cyan, darkgray, gray, green, lightgray, lime, magenta, olive, orange, pink, purple, red, teal, violet, white, yellow\n    let renderColor = useContext(LatexRenderColor);\n    let defaultInline = useContext(LatexDefaultInline);\n    let defaultDisplay = useContext(LatexDefaultDisplay);\n\n    let inline;\n    if(props.inline === undefined) {\n        inline = defaultInline;\n    }\n    else {\n        inline = props.inline;\n    }\n\n    let display;\n    if(props.display === undefined) {\n        if(defaultDisplay === null) {\n            display = LatexDisplay.INLINE;\n        }\n        else {\n            display = defaultDisplay;\n        }\n    }\n    else {\n        display = props.display;\n    }\n\n    if(inline) {\n        let equation = `\\\\inline {\\\\color{${renderColor}} ${props.children} }`;\n        return (\n            {props.children}\n\n        );\n    }\n    else {\n        let equation = `{\\\\color{${renderColor}} ${props.children} }`;\n        return (\n            {props.children}\n\n        );\n    }\n}\n","import { options } from 'preact';\n\n/** @type {number} */\nlet currentIndex;\n\n/** @type {import('./internal').Component} */\nlet currentComponent;\n\n/** @type {number} */\nlet currentHook = 0;\n\n/** @type {Array} */\nlet afterPaintEffects = [];\n\nlet oldBeforeRender = options._render;\nlet oldAfterDiff = options.diffed;\nlet oldCommit = options._commit;\nlet oldBeforeUnmount = options.unmount;\n\nconst RAF_TIMEOUT = 100;\nlet prevRaf;\n\noptions._render = vnode => {\n\tif (oldBeforeRender) oldBeforeRender(vnode);\n\n\tcurrentComponent = vnode._component;\n\tcurrentIndex = 0;\n\n\tconst hooks = currentComponent.__hooks;\n\tif (hooks) {\n\t\thooks._pendingEffects.forEach(invokeCleanup);\n\t\thooks._pendingEffects.forEach(invokeEffect);\n\t\thooks._pendingEffects = [];\n\t}\n};\n\noptions.diffed = vnode => {\n\tif (oldAfterDiff) oldAfterDiff(vnode);\n\n\tconst c = vnode._component;\n\tif (c && c.__hooks && c.__hooks._pendingEffects.length) {\n\t\tafterPaint(afterPaintEffects.push(c));\n\t}\n};\n\noptions._commit = (vnode, commitQueue) => {\n\tcommitQueue.some(component => {\n\t\ttry {\n\t\t\tcomponent._renderCallbacks.forEach(invokeCleanup);\n\t\t\tcomponent._renderCallbacks = component._renderCallbacks.filter(cb =>\n\t\t\t\tcb._value ? invokeEffect(cb) : true\n\t\t\t);\n\t\t} catch (e) {\n\t\t\tcommitQueue.some(c => {\n\t\t\t\tif (c._renderCallbacks) c._renderCallbacks = [];\n\t\t\t});\n\t\t\tcommitQueue = [];\n\t\t\toptions._catchError(e, component._vnode);\n\t\t}\n\t});\n\n\tif (oldCommit) oldCommit(vnode, commitQueue);\n};\n\noptions.unmount = vnode => {\n\tif (oldBeforeUnmount) oldBeforeUnmount(vnode);\n\n\tconst c = vnode._component;\n\tif (c && c.__hooks) {\n\t\ttry {\n\t\t\tc.__hooks._list.forEach(invokeCleanup);\n\t\t} catch (e) {\n\t\t\toptions._catchError(e, c._vnode);\n\t\t}\n\t}\n};\n\n/**\n * Get a hook's state from the currentComponent\n * @param {number} index The index of the hook to get\n * @param {number} type The index of the hook to get\n * @returns {import('./internal').HookState}\n */\nfunction getHookState(index, type) {\n\tif (options._hook) {\n\t\toptions._hook(currentComponent, index, currentHook || type);\n\t}\n\tcurrentHook = 0;\n\n\t// Largely inspired by:\n\t// * https://github.com/michael-klein/funcy.js/blob/f6be73468e6ec46b0ff5aa3cc4c9baf72a29025a/src/hooks/core_hooks.mjs\n\t// * https://github.com/michael-klein/funcy.js/blob/650beaa58c43c33a74820a3c98b3c7079cf2e333/src/renderer.mjs\n\t// Other implementations to look at:\n\t// * https://codesandbox.io/s/mnox05qp8\n\tconst hooks =\n\t\tcurrentComponent.__hooks ||\n\t\t(currentComponent.__hooks = {\n\t\t\t_list: [],\n\t\t\t_pendingEffects: []\n\t\t});\n\n\tif (index >= hooks._list.length) {\n\t\thooks._list.push({});\n\t}\n\treturn hooks._list[index];\n}\n\n/**\n * @param {import('./index').StateUpdater} initialState\n */\nexport function useState(initialState) {\n\tcurrentHook = 1;\n\treturn useReducer(invokeOrReturn, initialState);\n}\n\n/**\n * @param {import('./index').Reducer} reducer\n * @param {import('./index').StateUpdater} initialState\n * @param {(initialState: any) => void} [init]\n * @returns {[ any, (state: any) => void ]}\n */\nexport function useReducer(reducer, initialState, init) {\n\t/** @type {import('./internal').ReducerHookState} */\n\tconst hookState = getHookState(currentIndex++, 2);\n\thookState._reducer = reducer;\n\tif (!hookState._component) {\n\t\thookState._component = currentComponent;\n\n\t\thookState._value = [\n\t\t\t!init ? invokeOrReturn(undefined, initialState) : init(initialState),\n\n\t\t\taction => {\n\t\t\t\tconst nextValue = hookState._reducer(hookState._value[0], action);\n\t\t\t\tif (hookState._value[0] !== nextValue) {\n\t\t\t\t\thookState._value[0] = nextValue;\n\t\t\t\t\thookState._component.setState({});\n\t\t\t\t}\n\t\t\t}\n\t\t];\n\t}\n\n\treturn hookState._value;\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++, 3);\n\tif (!options._skipEffects && argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent.__hooks._pendingEffects.push(state);\n\t}\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useLayoutEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++, 4);\n\tif (!options._skipEffects && argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent._renderCallbacks.push(state);\n\t}\n}\n\nexport function useRef(initialValue) {\n\tcurrentHook = 5;\n\treturn useMemo(() => ({ current: initialValue }), []);\n}\n\n/**\n * @param {object} ref\n * @param {() => object} createHandle\n * @param {any[]} args\n */\nexport function useImperativeHandle(ref, createHandle, args) {\n\tcurrentHook = 6;\n\tuseLayoutEffect(\n\t\t() => {\n\t\t\tif (typeof ref == 'function') ref(createHandle());\n\t\t\telse if (ref) ref.current = createHandle();\n\t\t},\n\t\targs == null ? args : args.concat(ref)\n\t);\n}\n\n/**\n * @param {() => any} factory\n * @param {any[]} args\n */\nexport function useMemo(factory, args) {\n\t/** @type {import('./internal').MemoHookState} */\n\tconst state = getHookState(currentIndex++, 7);\n\tif (argsChanged(state._args, args)) {\n\t\tstate._args = args;\n\t\tstate._factory = factory;\n\t\treturn (state._value = factory());\n\t}\n\n\treturn state._value;\n}\n\n/**\n * @param {() => void} callback\n * @param {any[]} args\n */\nexport function useCallback(callback, args) {\n\tcurrentHook = 8;\n\treturn useMemo(() => callback, args);\n}\n\n/**\n * @param {import('./internal').PreactContext} context\n */\nexport function useContext(context) {\n\tconst provider = currentComponent.context[context._id];\n\t// We could skip this call here, but than we'd not call\n\t// `options._hook`. We need to do that in order to make\n\t// the devtools aware of this hook.\n\tconst state = getHookState(currentIndex++, 9);\n\t// The devtools needs access to the context object to\n\t// be able to pull of the default value when no provider\n\t// is present in the tree.\n\tstate._context = context;\n\tif (!provider) return context._defaultValue;\n\t// This is probably not safe to convert to \"!\"\n\tif (state._value == null) {\n\t\tstate._value = true;\n\t\tprovider.sub(currentComponent);\n\t}\n\treturn provider.props.value;\n}\n\n/**\n * Display a custom label for a custom hook for the devtools panel\n * @type {(value: T, cb?: (value: T) => string | number) => void}\n */\nexport function useDebugValue(value, formatter) {\n\tif (options.useDebugValue) {\n\t\toptions.useDebugValue(formatter ? formatter(value) : value);\n\t}\n}\n\nexport function useErrorBoundary(cb) {\n\tconst state = getHookState(currentIndex++, 10);\n\tconst errState = useState();\n\tstate._value = cb;\n\tif (!currentComponent.componentDidCatch) {\n\t\tcurrentComponent.componentDidCatch = err => {\n\t\t\tif (state._value) state._value(err);\n\t\t\terrState[1](err);\n\t\t};\n\t}\n\treturn [\n\t\terrState[0],\n\t\t() => {\n\t\t\terrState[1](undefined);\n\t\t}\n\t];\n}\n\n/**\n * After paint effects consumer.\n */\nfunction flushAfterPaintEffects() {\n\tafterPaintEffects.some(component => {\n\t\tif (component._parentDom) {\n\t\t\ttry {\n\t\t\t\tcomponent.__hooks._pendingEffects.forEach(invokeCleanup);\n\t\t\t\tcomponent.__hooks._pendingEffects.forEach(invokeEffect);\n\t\t\t\tcomponent.__hooks._pendingEffects = [];\n\t\t\t} catch (e) {\n\t\t\t\tcomponent.__hooks._pendingEffects = [];\n\t\t\t\toptions._catchError(e, component._vnode);\n\t\t\t\treturn true;\n\t\t\t}\n\t\t}\n\t});\n\tafterPaintEffects = [];\n}\n\n/**\n * Schedule a callback to be invoked after the browser has a chance to paint a new frame.\n * Do this by combining requestAnimationFrame (rAF) + setTimeout to invoke a callback after\n * the next browser frame.\n *\n * Also, schedule a timeout in parallel to the the rAF to ensure the callback is invoked\n * even if RAF doesn't fire (for example if the browser tab is not visible)\n *\n * @param {() => void} callback\n */\nfunction afterNextFrame(callback) {\n\tconst done = () => {\n\t\tclearTimeout(timeout);\n\t\tcancelAnimationFrame(raf);\n\t\tsetTimeout(callback);\n\t};\n\tconst timeout = setTimeout(done, RAF_TIMEOUT);\n\n\tlet raf;\n\tif (typeof window != 'undefined') {\n\t\traf = requestAnimationFrame(done);\n\t}\n}\n\n// Note: if someone used options.debounceRendering = requestAnimationFrame,\n// then effects will ALWAYS run on the NEXT frame instead of the current one, incurring a ~16ms delay.\n// Perhaps this is not such a big deal.\n/**\n * Schedule afterPaintEffects flush after the browser paints\n * @param {number} newQueueLength\n */\nfunction afterPaint(newQueueLength) {\n\tif (newQueueLength === 1 || prevRaf !== options.requestAnimationFrame) {\n\t\tprevRaf = options.requestAnimationFrame;\n\t\t(prevRaf || afterNextFrame)(flushAfterPaintEffects);\n\t}\n}\n\n/**\n * @param {import('./internal').EffectHookState} hook\n */\nfunction invokeCleanup(hook) {\n\tif (typeof hook._cleanup == 'function') hook._cleanup();\n}\n\n/**\n * Invoke a Hook's effect\n * @param {import('./internal').EffectHookState} hook\n */\nfunction invokeEffect(hook) {\n\thook._cleanup = hook._value();\n}\n\n/**\n * @param {any[]} oldArgs\n * @param {any[]} newArgs\n */\nfunction argsChanged(oldArgs, newArgs) {\n\treturn !oldArgs || newArgs.some((arg, index) => arg !== oldArgs[index]);\n}\n\nfunction invokeOrReturn(arg, f) {\n\treturn typeof f == 'function' ? f(arg) : f;\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"minus\":\"minus__VM3UF\"};","import style from \"./Split.less\";\n\nexport default function (props) {\n    let children;\n\n    if(Array.isArray(props.children)) {\n        children = props.children.map(element => {\n            return (\n                
    \n                    {element}\n                
    \n            );\n        });\n    }\n\n    else {\n        children = (\n            
    \n                {props.children}\n            
    \n        );\n    }\n    return (\n        
    \n            
    {children}
    \n        
    \n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"plus\":\"plus__5AywL\"};","import style from \"./Example.less\";\nimport {Component} from \"preact\";\n\nexport default function(props) {\n    return (\n        
    \n            {props.children}\n        
    \n    );\n}\n","import style from \"./Box.less\";\n\nexport const BoxColors = Object.freeze({\n    RED: style.red,\n    ORANGE: style.orange,\n    YELLOW: style.yellow,\n    LIME: style.lime,\n    CYAN: style.cyan,\n    BLUE: style.blue,\n    MAGENTA: style.magenta,\n    DEFAULT: style.default\n})\n\nexport default function (props) {\n    let color = BoxColors.DEFAULT;\n    if(props.color) {\n        color = props.color;\n    }\n\n    return (\n        
    \n            {props.children}\n        
    \n    );\n}\n","import Latex, {LatexDisplay} from '../components/Rendering/Latex';\nimport Panel from '../components/Elements/Panel';\nimport Section from \"../components/Elements/Section\";\nimport Example from \"../components/Elements/Example\";\nimport Plus from \"../components/PageSpecific/Fisica/Plus\";\nimport Minus from \"../components/PageSpecific/Fisica/Minus\";\nimport LatexDefaultInline from \"../contexts/LatexDefaultInline\";\nimport LatexDefaultDisplay from \"../contexts/LatexDefaultDisplay\";\n\nconst r = String.raw;\n\nexport default function(props) {\n    return (\n        \n        \n            
    \n                
    Statistica ed Elementi di Probabilità
    \n                
    \n                    \n                        
    \n                            {r`P(E) = \\frac{casi\\ favorevoli}{casi\\ possibili}`}\n                        
    \n                        \n                    \n                        
    \n                            {r`P(E) = \\frac{successi}{prove\\ totali}`}\n                        
    \n                        \n                    \n                        
    \n                            Il prezzo che un individuo coerente riterrebbe equo per ricevere 1 nel caso l'evento si verificasse e 0 nel caso l'evento non si verificasse.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            \"omegone\"\n                        
    \n                        
    \n                            L'insieme di tutti gli esiti possibili di un esperimento.\n                        
    \n                        
    \n                            {r`\\Omega = \\left \\{ 1, 2, 3, 4, 5, 6 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"omeghino\"\n                        
    \n                        
    \n                            Un elemento dello spazio campionario.\n                        
    \n                        
    \n                            {r`\\omega = 1`}\n                        
    \n                        \n                    \n                        
    \n                            \"e\"\n                        
    \n                        
    \n                            Un sottoinsieme dello spazio campionario.\n                        
    \n                        
    \n                            {r`E = \\left \\{ 1, 2 \\right \\}`}\n                        
    \n                        
    \n                            Lo spazio campionario stesso è un evento certo.\n                        
    \n                        \n                    \n                        
    \n                            \"not e\"\n                        
    \n                        
    \n                            Il complementare di un sottoinsieme.\n                        
    \n                        
    \n                            {r`\\bar{E} = \\left \\{ 3, 4, 5, 6 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e intersecato effe\"\n                        
    \n                        
    \n                            L'intersezione di più sottoinsiemi.\n                        
    \n                        
    \n                            {r`E \\cap F = \\left \\{ 1 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e unito a effe\"\n                        
    \n                        
    \n                            L'unione di più sottoinsiemi.\n                        
    \n                        
    \n                            {r`E \\cup F = \\left \\{ 1, 2, 3, 4 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e meno effe\"\n                        
    \n                        
    \n                            {r`E \\setminus F = E \\cap \\bar{F}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e contenuto in effe\"\n                        
    \n                        
    \n                            L'inclusione del primo insieme in un altro.\n                        
    \n                        
    \n                            {r`E \\subseteq F`}\n                        
    \n                        
    \n                            Se si verifica E, allora si verifica anche F.\n                        
    \n                        \n                    \n                        
    \n                            \"e è impossibile\"\n                        
    \n                        
    \n                            Un sottoinsieme vuoto.\n                        
    \n                        
    \n                            {r`E = \\emptyset`}\n                        
    \n                        \n                    \n                        
    \n                            \"e ed effe si escludono mutualmente\"\n                        
    \n                        
    \n                            La disgiunzione di due insiemi.\n                        
    \n                        
    \n                            {r`E \\cap F = \\emptyset`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            \"famiglia effe\"\n                        
    \n                        
    \n                            I sottoinsiemi dello spazio campionario formano una famiglia di sottoinsiemi detta famiglia degli eventi.\n                        
    \n                        
    \n                            {r`\\mathcal{F}`}\n                        
    \n                        
    \n                            Qualsiasi sottoinsieme appartenente a {r`\\mathcal{F}`} è considerato un evento.\n                        
    \n                        \n                    {r`\\sigma`}-algebra}>\n                        
    \n                            \"sigma algebra\"\n                        
    \n                        
    \n                            Se la famiglia degli eventi soddisfa questi tre requisiti, allora viene detta {r`\\sigma`}-algebra:\n                        
    \n                        
      \n                            
    1. \n                                Lo spazio campionario è un evento: {r`\\Omega \\in \\mathcal{F}`}\n                            
      2. \n                            
    2. \n                                Se un sottoinsieme è un evento, allora anche il suo complementare lo è: {r`E \\in \\mathcal{F} \\implies \\bar{E} \\in \\mathcal{F}`}\n                            
      3. \n                            
    3. \n                                Se due sottoinsiemi sono eventi, allora lo sono anche la loro unione e intersezione: {r`(E, F) \\in \\mathcal{F} \\implies (E \\cup F, E \\cap F) \\in \\mathcal{F}`}\n                            
      4. \n                        
    \n                        
    \n                            Un esempio: {r`E \\in \\mathcal{F} \\implies \\mathcal{F} = \\{ \\emptyset, E, \\bar{E}, \\Omega \\}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            \"la partizione e composta da e uno, e due, e tre...\"\n                        
    \n                        
    \n                            Un insieme di esiti e eventi:\n                        
    \n                        
      \n                            
    • Finito.
      • \n                            
    • In cui tutti gli eventi hanno probabilità diversa da 0.
      • \n                            
    • In cui tutti gli eventi sono mutualmente esclusivi.
      • \n                            
    • In cui l'unione di tutti i suoi elementi copre lo spazio campionario.
      • \n                        
    \n                        
    \n                            La partizione {r`E_i`} è composta dagli eventi {r`E_1`}, {r`E_2`}, {r`E_3`}, fino a {r`E_n`}.\n                        
    \n                        \n                            Se lo spazio campionario fosse una torta, una sua partizione sarebbe l'insieme delle fette di uno dei modi in cui si potrebbe tagliare.\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            La probabilità di un evento è un numero tra 0 e 1.\n                        
    \n                        
    \n                            {r`\\forall E \\in \\mathcal{F}, 0 \\leq P(E) \\leq 1`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità dello spazio campionario è sempre 1.\n                        
    \n                        
    \n                            {r`P(\\Omega) = 1`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità dell'unione di eventi indipendenti è uguale alla somma delle loro probabilità.\n                        
    \n                        
    \n                            {r`P \\left ( \\bigcup_i E_i \\right ) = \\sum_i P ( E_i )`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            La probabilità di un evento negato è uguale a 1 meno la probabilità dell'evento non negato.\n                        
    \n                        
    \n                            {r`P(\\bar{E}) = 1 - P({E})`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità di un evento incluso in un altro è sempre minore o uguale alla probabilità dell'evento in cui è incluso.\n                        
    \n                        
    \n                            {r`F \\subseteq E \\implies P(F) \\leq P(E)`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità di un evento unito a un altro è uguale alla somma delle probabilità dei due eventi meno la probabilità della loro intersezione.\n                        
    \n                        
    \n                            {r`P(E \\cup F) = P(E) + P(F) - P(E \\cap F)`}\n                        
    \n                        \n                            Sommando le probabilità dei due eventi, l'intersezione viene contata due volte, e va quindi rimossa!\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Spazi campionari in cui ci sono un numero finito di esiti e ogni esito ha la stessa probabilità di verificarsi.\n                        
    \n                        
    \n                            {r`P(E) = \\frac{len(E)}{len(\\Omega)}`}\n                        
    \n                        \n                    \n                        
    \n                            Gli spazi campionari possono avere un numero infinito di esiti: sono equiprobabili geometrici se nessun esito è privilegiato rispetto agli altri.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo tengo fuori dal sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Tengo conto dell'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{D}_{n, k} = \\frac{n!}{(n - k)!}`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo rimetto nel sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Tengo conto dell'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{D}^{r}_{n, k} = n^k`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo tengo fuori dal sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Non mi interessa l'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{C}_{n, k} = \\binom{n}{k} = \\frac{n!}{(k)! \\cdot (n - k)!}`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo rimetto nel sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Non mi interessa l'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{C}^{r}_{n, k} = \\binom{n + k - 1}{k} = \\frac{(n + k - 1)!}{(k)! \\cdot (n - 1)!}`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo n numeri e guardo in quanti ordini diversi li posso mettere.\n                        
    \n                        
    \n                            {r`\\boldsymbol{P}_n = n!`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            \"E dato F\"\n                        
    \n                        
    \n                            La probabilità che si verifichi E sapendo che si è già verificato F.\n                        
    \n                        
    \n                            {r`P(E|F) = \\frac{P(E \\cap F)}{P(F)}`}\n                        
    \n                        \n                            Ricorda vagamente le pipe di bash, però al contrario...\n                        \n                        \n                    \n                        
    \n                            Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0.\n                        
    \n                        
    \n                            {r`E \\cap F = \\emptyset \\Longleftrightarrow P(E|F) = P(F|E) = 0`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:\n                        
    \n                        
    \n                            {r`P(E_1 \\cap \\times \\cap E_n) = P(E_1) \\times P(E_2 | E_1) \\times \\dots \\times P(E_n | E_1 \\cap E_2 \\cap \\dots \\cap E_{n-1})`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            La probabilità che si verifichi un evento è pari alla somma delle probabilità dell'evento stesso dati tutti gli eventi di una partizione.\n                        
    \n                        
    \n                            {r`P(F) = \\sum_{i} P(F|E_i) \\cdot P(E_i)`}\n                        
    \n                        \n                    \n                        
    \n                            La legge delle alternative funziona anche quando ad essere partizionato è un evento:\n                        
    \n                        
    \n                            {r`P(F|G) = \\sum_i P(F|E_i \\cap G) \\cdot P(E_i | G)`}\n                        
    \n                        \n                    \n                        
    \n                            Tramite la formula di Bayes possiamo risalire alla probabilità di un evento condizionato a un altro partendo dalla probabilità di quest'ultimo condizionato al primo:\n                        
    \n                        
    \n                            {r`P(E_h | F) = \\frac{P(F | E_h) \\cdot P(E_h)}{P(F)}`}\n                        
    \n                        \n                            In pratica, invertiamo gli eventi.\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            \"eventi indipendenti a due a due\"\n                        
    \n                        
    \n                            Se due eventi sono indipendenti, sapere che uno dei due si è verificato non influisce sulle probabilità che si sia verificato l'altro.\n                        
    \n                        
    \n                            {r`P(E \\cap F) = P(E) \\cdot P(F) \\Longleftrightarrow P(E|F) = P(E) \\Longleftrightarrow P(F|E) = P(F)`}\n                        
    \n                        \n                    \n                        
    \n                            \"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque...\"\n                        
    \n                        
    \n                            Si può verificare l'indipendenza di più eventi alla volta:\n                        
    \n                        
    \n                            {r`P(E \\cap F \\cap G) = P(E) \\cdot P(F) \\cdot P(G)`}\n                        
    \n                        
    \n                            Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.\n                        
    \n                        \n                    \n                        
    \n                            Un insieme di n eventi è una famiglia di eventi indipendenti se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti.\n                        
    \n                        \n                            Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e così via!\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una funzione che fa corrispondere un numero reale a ogni possibile esito dello spazio campionario. {r`X(\\omega) : \\Omega \\to \\mathbb{R}`}.\n                        
    \n                        \n                    Insieme di ripartizione}>\n                        
    \n                            Ad ogni variabile aleatoria sono associati gli eventi {r`A_t = \\{ \\omega | X(\\omega) \\leq t \\}`}, che contengono tutti gli esiti a cui la variabile aleatoria associa un valore minore o uguale a t.\n                        
    \n                        
    \n                            Per definizione, tutte le variabili aleatorie devono rispettare questa condizione:\n                        
    \n                        
    \n                            {r`\\forall t \\in \\mathbb{R}, A_t \\in \\mathcal{F}`}\n                        
    \n                        \n                            All'aumentare di t, l'insieme conterrà sempre più elementi.\n                        \n                        \n                    \n                        
    \n                            \"supporto di X\"\n                        
    \n                        
    \n                            Il codominio della variabile aleatoria è il suo supporto.\n                        
    \n                        
    \n                            Per indicare che un valore x_0 appartiene al supporto di X, si usa la notazione X \\mapsto x_0.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            La funzione probabilità {r`p_X : X \\to [0, 1]`} di una variabile aleatoria discreta X è la funzione che associa ad ogni esito la sua probabilità:\n                        
    \n                        
    \n                            {r`p_X (x) = \\begin{cases}\n                            P([X = x]) \\quad se\\ X \\mapsto x \\\\\n                            0 \\qquad \\qquad \\quad se\\ X \\not\\mapsto x\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione densità {r`f_X : X \\to [0, 1]`} di una variabile aleatoria continua X è l'equivalente continuo della funzione probabilità:\n                        
    \n                        
    \n                            {r`P([a < X \\leq b]) = \\int_a^b f_X (x) dx`}\n                        
    \n                        
    \n                            A differenza della funzione probabilità, è possibile che la funzione densità non esista per una certa variabile aleatoria.\n                        
    \n                        \n                            Rappresenta \"quanta\" probabilità c'è in un'unità di x!\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Ogni variabile aleatoria ha una funzione di ripartizione {r`F_X : \\mathbb{R} \\to [0, 1]`} associata, che rappresenta la probabilità che la variabile aleatoria assuma un valore minore o uguale a t:\n                        
    \n                        
    \n                            Si può dire che essa rappresenti la probabilità dell'evento {r`A_t`}:\n                        
    \n                        
    \n                            {r`F_X (t) = P(A_t) = \\begin{cases}\n                            \\sum_{i = 0}^{t} p_X (x_i) \\quad nel\\ discreto\\\\\n                            \\\\\n                            \\int_{-\\infty}^t f_X (x) dx \\quad nel\\ continuo\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
      \n                            
    • È sempre monotona crescente (non strettamente).

      • \n                            
    • Vale 0 a -\\infty e 1 a +\\infty.

      • \n                            
    • È continua da destra: {r`\\forall x_0 \\in \\mathbb{R}, F_X (x_0) = \\lim_{t \\to x^+_0} F_X (t)`}
      • \n                        
    \n                        \n                    \n                        
    \n                            Possiamo usare la funzione di ripartizione per calcolare la probabilità di un certo valore reale:\n                        
    \n                        
    \n                            {r`P([X = x_0]) = \\lim_{t \\to x^+_0} F_X (t) - \\lim_{t \\to x^-_0} F_X (t)`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Nel discreto basta abbinare un nuovo valore a ogni valore della variabile originale.\n                        
    \n                        \n                    \n                        
    \n                            Nel continuo applichiamo la formula dell'integrazione per sostituzione:\n                        
    \n                        
    \n                            {r`f_Y (y) = \\int_{g(a)}^{g(b)} f_X ( g^{-1} (x) ) g^{-2} (x)`}\n                        
    \n                        \n                    \n                        
    \n                            Trasformare variabili aleatorie è molto utile nell'informatica per creare distribuzioni partendo da una funzione random() che restituisce numeri da 0 a 1 con una distribuzione lineare.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Ogni variabile aleatoria che ha una funzione di ripartizione e un supporto finito ha anche una media (o valore medio o atteso):\n                        
    \n                        
    \n                            {r`E(X) = \\int_0^{+infty} (1 - F_X (t)) dt - \\int_{-\\infty}^{0} F_X (t) dt`}\n                        
    \n                        
    \n                            Nel discreto, si può calcolare con:\n                        
    \n                        
    \n                            {r`E(X) = \\sum_i P(X = x_i) \\cdot x_i`}\n                        
    \n                        
    \n                            Nel continuo, si può calcolare con:\n                        
    \n                        
    \n                            {r`E(X) = \\int_{-\\infty}^{+\\infty} f_X (x) \\cdot x \\cdot dx`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Valore per cui la funzione probabilità o funzione densità è massima.\n                        
    \n                        \n                    \n                        
    \n                            Il quantile {r`x_{\\alpha}`} di ordine {r`0 \\leq \\alpha \\leq 1`} della variabile aleatoria X è il più piccolo numero tale che:\n                        
    \n                        
    \n                            \n                                {r`P([X < x_{\\alpha}]) \\leq \\alpha \\leq P([X \\leq x_{\\alpha}])`}\n                            \n                        
    \n                        
    \n\n                        
    \n                        
    \n                            Il quantile di ordine 0.5 {r`x_{0.5}`} è detto mediana.\n                        
    \n                        
    \n                            I quantili di ordine 0.25 {r`x_{0.25}`} e 0.75 {r`x_{0.75}`} sono detti quartili.\n                        
    \n                        
    \n                            I quantili di ordine {r`\\frac{n}{100}`} sono detti n-esima percentile.\n                        
    \n                        \n                    \n                        
    \n                            È un valore che indica quanto la variabile aleatoria si discosta generalmente dalla media:\n                        
    \n                        
    \n                            {r`Var(X) = E( (X - E(X) )^2 ) = E ( X^2 ) - (E(X))^2`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Data una variabile aleatoria non-negativa:\n                        
    \n                        
    \n                            {r`\\forall k > 0, P([X \\geq k]) \\leq \\frac{E(X)}{k}`}\n                        
    \n                        
    \n                            Divide in due parti ({r`P(X < k)`} e {r`P(X \\geq k)`}) la funzione X, la cui media risulterà uguale a:\n                        
    \n                        
    \n                            {r`E(X) = \\overline{k} \\cdot P(X < k) + k \\cdot P(X \\geq k)`}\n                        
    \n                        \n                    \n                        
    \n                            \"disuguaglianza di cebicev\"\n                        
    \n                        
    \n                            Se la variabile aleatoria X ha media e varianza, allora la probabilità che essa abbia un valore a più di {r`\\epsilon`} di distanza dal valore medio è minore o uguale a {r`\\frac{Var(X)}{\\epsilon^2}`}.\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, P([ \\left| X - E(X) \\right| \\geq \\epsilon]) \\leq \\frac{Var(X)}{\\epsilon^2}`}\n                        
    \n                        
    \n                            E anche:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, P([ \\left| X - E(X) \\right| < \\epsilon]) \\geq 1 - \\frac{Var(X)}{\\epsilon^2}`}\n                        
    \n                        \n                            Serve per semplificare i calcoli quando la funzione di ripartizione è difficile da calcolare!\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Il momento k-esimo di una variabile aleatoria è:\n                        
    \n                        
    \n                            \n                                {r`\\mu_k = E ( X^k ) = \\begin{cases}\n                                \\sum_i x_i^k p_X (x_i) \\qquad nel\\ discreto\\\\\n                                \\\\\n                                \\int_{-\\infty}^{+\\infty} x^k f_X (x) dx \\qquad nel\\ continuo\n                                \\end{cases}`}\n                            \n                        
    \n                        \n                            La media di una variabile aleatoria è anche il suo primo momento.\n                        \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti è:\n                        
    \n                        
    \n                            {r`m_X (t) = E( e^{t \\cdot X} )`}\n                        
    \n                        
    \n                            Se due variabile aleatorie hanno la stessa funzione generatrice dei momenti, allora esse hanno la stessa distribuzione.\n                        
    \n                        
    \n                            E' la trasformata di Laplace della variabile aleatoria di X.\n                        
    \n                        \n                    \n                        
    \n                            La funzione caratteristica è:\n                        
    \n                        
    \n                            {r`H_X (t) = E ( e^{i \\cdot t \\cdot X} )`}\n                        
    \n                        
    \n                            Se due variabile aleatorie hanno la stessa funzione caratteristica, allora esse hanno la stessa distribuzione.\n                        
    \n                        
    \n                            E' la trasformata di Fourier della variabile aleatoria di X.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Per dire che una variabile ha una certa distribuzione, si usa la notazione:\n                        
    \n                        
    \n                            {r`X \\sim Distribuzione()`}\n                        
    \n                        \n                    \n                        
    \n                            Una prova con solo due possibili esiti: successo e insuccesso.\n                        
    \n                        \n                    \n                        
    \n                            Una sequenza di prove di Bernoulli per le quali le probabilità di successo e fallimento rimangono invariate.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che rappresenta una prova di Bernoulli:\n                        
    \n                        
      \n                            
    • vale 1 in caso di successo.
      • \n                            
    • vale 0 in caso di insuccesso.
      • \n                        
    \n                        
    \n                            Il suo simbolo è {r`Ber(p)`}\n                        
    \n                        \n                    \n                        
    \n                            La distribuzione bernoulliana ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{0, 1\\} = \\begin{cases}\n                            p \\quad se\\ k = 1\\\\\n                            q \\quad se\\ k = 0\\\\\n                            0 \\quad altrimenti\n                            \\end{cases} = p^x \\cdot q^{1 - k}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di successi di n prove di uno schema di Bernoulli.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Bin(n, p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La binomiale ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{0..n\\} = \\binom{n}{k} \\cdot p^k \\cdot q^{n - k}`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti della binomiale è:\n                        
    \n                        
    \n                            {r`m_X (t) = (q + p \\cdot e^t) ^ n`}\n                        
    \n                        
    \n                            La media di una binomiale è:\n                        
    \n                        
    \n                            {r`E(X) = n \\cdot p`}\n                        
    \n                        
    \n                            La varianza di una binomiale è:\n                        
    \n                        
    \n                            {r`Var(X) = n \\cdot p \\cdot q`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli fino alla comparsa del primo successo.\n                        
    \n                        
    \n                            Il suo simbolo è Geo(p).\n                        
    \n                        \n                    \n                        
    \n                            La geometrica ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = q^{k - 1} p`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti della geometrica è:\n                        
    \n                        
    \n                            {r`m_X (t) = \\frac{p \\cdot e^t}{1 - q \\cdot e^t}`}\n                        
    \n                        
    \n                            La media della geometrica è:\n                        
    \n                        
    \n                            {r`E(X) = \\frac{1}{p}`}\n                        
    \n                        
    \n                            La varianza della geometrica è:\n                        
    \n                        
    \n                            {r`Var(X) = \\frac{q}{p^2}`}\n                        
    \n                        \n                    \n                        
    \n                            La geometrica non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n                        
    \n                        
    \n                            {r`P([X = i + j | X > i ]) = P([X = j])`}\n                        
    \n                        \n                            Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli necessarie perchè si verifichi l'n-esimo successo.\n                        
    \n                        
    \n                            Il suo simbolo è {r`\\overline{Bin}(n, p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La binomiale negativa ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{ n .. +\\infty \\} \\in \\mathbb{N} = \\binom{k - 1}{n - 1} \\cdot p^n \\cdot q^{k - n} `}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della binomiale negativa è:\n                            
    \n                            
    \n                                {r`m_X (t) : \\{ t < ln(\\frac{1}{q}) \\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n`}\n                            
    \n                            
    \n                                La media della binomiale negativa è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{n}{p}`}\n                            
    \n                            
    \n                                La varianza della binomiale negativa è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{n \\cdot q}{p^2}`}\n                            
    \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero k di insuccessi consecutivi in uno schema di Bernoulli:\n                        
    \n                        
    \n                            Il suo simbolo rimane {r`Geo(p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La geometrica traslata ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = p \\cdot q^k `}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti della geometrica traslata è:\n                        
    \n                        
    \n                            {r`m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\frac{p}{1 - q \\cdot e^t}`}\n                        
    \n                        
    \n                            La media della geometrica traslata è:\n                        
    \n                        
    \n                            {r`E(X) = \\frac{q}{p}`}\n                        
    \n                        
    \n                            La varianza della geometrica è:\n                        
    \n                        
    \n                            {r`Var(X) = \\frac{q}{p^2}`}\n                        
    \n                        \n                    \n                        
    \n                            La geometrica traslata non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n                        
    \n                        
    \n                            {r`P([X = i + j | X > i ]) = P([X = j])`}\n                        
    \n                        \n                            Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di insuccessi in uno schema di Bernoulli prima che si verifichi l'n-esimo successo.\n                        
    \n                        
    \n                            Il suo simbolo rimane {r`\\overline{Bin}(n, p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La binomiale negativa traslata ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = \\binom{k + n - 1}{n - 1} \\cdot p^n \\cdot q^k `}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della binomiale negativa traslata è:\n                            
    \n                            
    \n                                {r`m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n`}\n                            
    \n                            
    \n                                La media della binomiale negativa traslata è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{n \\cdot q}{p}`}\n                            
    \n                            
    \n                                La varianza della binomiale negativa traslata è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{n \\cdot q}{p^2}`}\n                            
    \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che, sapendo il numero di successi K e di insuccessi N-K, conta quanti successi si otterrebbero se se ne estraessero n in blocco.\n                        
    \n                        
    \n                            Il suo simbolo è Ipe(N, K, n).\n                        
    \n                        \n                    \n                        
    \n                            La ipergeometrica ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{0..n\\} \\in \\mathbb{N} = \\frac{\\binom{K}{k} \\cdot \\binom{N - K}{n - k}}{\\binom{N}{n}}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della ipergeometrica è trascurabile.\n                            
    \n                            
    \n                                La media della ipergeometrica è:\n                            
    \n                            
    \n                                {r`E(X) = n \\cdot \\frac{K}{N}`}\n                            
    \n                            
    \n                                La varianza della ipergeometrica è:\n                            
    \n                            
    \n                                {r`Var(X) = n \\cdot \\frac{K}{N} \\cdot \\frac{N - K}{N} \\cdot \\frac{N - n}{N - 1}`}\n                            
    \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che soddisfa tutte le seguenti caratteristiche:\n                        
    \n                        
      \n                            
    • Binomiale: {r`X \\sim Bin(n, p)`}
      • \n                            
    • Il numero di prove tende a infinito: {r`n \\to +\\infty`}
      • \n                            
    • La probabilità di successo tende a 0: {r`p \\to 0`}
      • \n                            
    • La media è finita: {r`E(X) = n \\cdot p \\to \\mu \\neq 0`}
      • \n                        
    \n                        
    \n                            Il suo simbolo è {r`Poi(\\mu)`}\n                        
    \n                        \n                    \n                        
    \n                            La poissoniana ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = \\frac{e^{-\\mu} \\cdot \\mu^k}{k!}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della poissoniana è:\n                            
    \n                            
    \n                                {r`m_X (t) = e^{\\mu \\cdot (e^t - 1)}`}\n                            
    \n                            
    \n                                La media della poissoniana è:\n                            
    \n                            
    \n                                {r`E(X) = \\mu`}\n                            
    \n                            
    \n                                La varianza della poissoniana è:\n                            
    \n                            
    \n                                {r`Var(X) = \\mu`}\n                            
    \n                            
    \n                                Gli altri momenti della poissoniana sono:\n                            
    \n                            
      \n                                
    1. {r`E(X^2) = \\mu^2 + \\mu`}
      2. \n                            
    \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una successione di arrivi avvenuti in un certo arco temporale che:\n                        
    \n                        
      \n                            
    • non sono sovrapposti.
      • \n                            
    • hanno intensità {r`\\lambda`} costante.
      • \n                            
    • avvengono indipendentemente gli uni dagli altri.
      • \n                        
    \n                        \n                    \n                        
    \n                            Una variabile aleatoria N_t che conta il numero di arrivi di uno schema di Poisson di intensità {r`\\lambda`} in un intervallo di tempo di durata t.\n                        
    \n                        
    \n                            E' una distribuzione poissoniana con {r`\\mu = t \\cdot \\lambda`}: {r`Poi(t \\cdot \\lambda)`}\n                        
    \n                        \n                            E' paragonabile a una bernoulliana: ogni successo corrisponde a un arrivo, mentre il tempo è il numero di prove effettuate (ma nel continuo).\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che conta il tempo diwidehattesa prima del primo arrivo di un processo di Poisson di intensità {r`\\lambda`}.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Esp(\\lambda)`}.\n                        
    \n                        \n                    \n                        
    \n                            L'esponenziale ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                            0 \\qquad \\qquad x < 0\\\\\n                            \\lambda \\cdot e^{-\\lambda \\cdot x} \\quad x > 0\n                            \\end{cases}`}\n                        
    \n                        
    \n                            L'esponenziale ha come funzione di ripartizione:\n                        
    \n                        
    \n                            {r`F_X (t) = \\begin{cases}\n                            0 \\qquad \\qquad t < 0\\\\\n                            1 - e^{-\\lambda \\cdot t} \\quad t \\geq 0\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti dell'esponenziale è:\n                        
    \n                        
    \n                            {r`m_X (t) : \\{ t | t < \\lambda \\} \\in \\mathbb{R} = \\frac{\\lambda}{\\lambda - t}`}\n                        
    \n                        
    \n                            La media dell'esponenziale è:\n                        
    \n                        
    \n                            {r`E(X) = \\frac{1}{\\lambda}`}\n                        
    \n                        
    \n                            La varianza dell'esponenziale è:\n                        
    \n                        
    \n                            {r`Var(X) = \\frac{1}{\\lambda^2}`}\n                        
    \n                        \n                    \n                        
    \n                            L'esponenziale non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n                        
    \n                        
    \n                            {r`P([X > s + t | X > s]) = P([X > t])`}\n                        
    \n                        \n                            Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che conta il tempo diwidehattesa prima dell'n-esimo arrivo di un processo di Poisson di intensità {r`\\lambda`}.\n                        
    \n                        
    \n                            Il suo simbolo è {r`\\Gamma(n, \\lambda)`}.\n                        
    \n                        \n                    \n                        
    \n                            La legge gamma ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                            0 \\qquad \\qquad \\qquad \\qquad \\qquad x < 0\\\\\n                            \\frac{1}{(n-1)!} \\cdot \\lambda^n \\cdot x^{n-1} \\cdot e^{-\\lambda \\cdot x} \\quad k > 0\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della legge gamma è:\n                            
    \n                            
    \n                                {r`m_X (t) : ( t < \\lambda ) \\in \\mathbb{R} = \\left( \\frac{\\lambda}{\\lambda - t} \\right) ^\\alpha`}\n                            
    \n                            
    \n                                La media della legge gamma è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{\\alpha}{\\lambda}`}\n                            
    \n                            
    \n                                La varianza della legge gamma è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{\\alpha}{\\lambda^2}`}\n                            
    \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che può assumere qualsiasi valore in un intervallo {r`[a, b]`} in modo equiprobabile.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Uni(a, b)`}\n                        
    \n                        
    \n                            Su di essa vale la seguente proprietà:\n                        
    \n                        
    \n                            {r`P(X \\in (c, d)) = \\frac{d - c}{b - a}`}\n                        
    \n                        \n                    \n                        
    \n                            La distribuzione uniforme ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                                \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n                                0 \\qquad \\quad altrimenti    \n                            \\end{cases}`}\n                        
    \n                        
    \n                            La distribuzione uniforme ha come funzione di ripartizione:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                                0 \\qquad \\quad x < a  \n                                \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n                                1 \\qquad \\quad x > b\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della distribuzione uniforme è:\n                            
    \n                            
    \n                                {r`m_X (t) = \\frac{e^{b \\cdot t} - e^{a \\cdot t}}{(b - a) \\cdot t}`}\n                            
    \n                            
    \n                                La media della distribuzione uniforme è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{a + b}{2}`}\n                            
    \n                            
    \n                                La varianza della distribuzione uniforme è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{(b - a)^2}{12}`}\n                            
    \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria con una specifica distribuzione.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Nor(\\mu, \\sigma^2)`}.\n                        
    \n                        \n                            \\mu e \\sigma^2 sono rispettivamente la media e la varianza della distribuzione!\n                        \n                        \n                    \n                        
    \n                            La distribuzione normale ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\frac{e^{-\\frac{(x - \\mu)^2}{2 \\sigma^2}}}{\\sqrt{2 \\pi \\cdot \\sigma^2}}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della distribuzione normale è:\n                            
    \n                            
    \n                                {r`m_X (t) = e^{\\mu \\cdot t + \\frac{\\sigma^2 \\cdot t^2}{2}}`}\n                            
    \n                            
    \n                                La media della distribuzione normale è:\n                            
    \n                            
    \n                                {r`E(X) = \\mu`}\n                            
    \n                            
    \n                                La varianza della distribuzione normale è:\n                            
    \n                            
    \n                                {r`Var(X) = \\sigma^2`}\n                            
    \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Qualsiasi normale può essere trasformata in qualsiasi altra normale:\n                        
    \n                        
    \n                            {r`X \\sim Nor(m, v^2) \\implies \\alpha X + \\beta \\sim Nor(\\alpha m + \\beta, (\\alpha v)^2)`}\n                        
    \n                        \n                    \n                        
    \n                            La distribuzione normale standard Z è:\n                        
    \n                        
    \n                            Z \\sim Nor(0, 1)\n                        
    \n                        
    \n                            La sua funzione di ripartizione è detta {r`\\phi(z)`} e vale:\n                        
    \n                        
    \n                            {r`F_Z(z) = \\phi(z) = \\frac{1}{\\sqrt{2 \\pi}} \\int_{-\\infty}^{z} e^{-\\frac{x^2}{2}} dx`}\n                        
    \n                        \n                    \n                        
    \n                            Da un quantile {r`z_\\alpha`} della normale standard è possibile risalire allo stesso quantile di qualsiasi altra normale:\n                        
    \n                        
    \n                            {r`x_\\alpha = \\mu + z_\\alpha \\cdot \\sqrt{\\sigma^2}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            La distribuzione normale ha una particolare relazione con la distribuzione Gamma:\n                        
    \n                        
    \n                            {r`Z^2 \\sim \\chi^2 (v = 1)`}\n                        
    \n                        \n                    \n                        
    \n                            \"chi-quadro a un grado di libertà\"\n                        
    \n                        
    \n                            Esiste una distribuzione Gamma particolare:\n                        
    \n                        
    \n                            {r`\\Gamma \\left( \\frac{1}{2}, \\frac{1}{2} \\right) = \\chi^2 (v = 1)`}\n                        
    \n                        
    \n                            Più chi-quadro possono essere sommate per aumentare i loro gradi di libertà:\n                        
    \n                        
    \n                            {r`\\chi^2 (n) + \\chi^2 (m) = \\chi^2 (n + m)`}\n                        
    \n                        \n                    \n                        
    \n                            Un'altra funzione particolare è la funzione T di Student:\n                        
    \n                        
    \n                            {r`T(v) = \\frac{Nor(0, 1)}{\\sqrt{\\frac{\\chi^2(v)}{v}}}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            La binomiale è come una ipergeometrica ma con ripetizioni, quindi per valori molto grandi di N rispetto a n, si può dire che:\n                        
    \n                        
    \n                            {r`Ipe(N, K, n) \\approx Bin(n, \\frac{K}{N})`}\n                        
    \n                        \n                    \n                        
    \n                            La binomiale non è altro che una poissoniana a tempo discreto, quindi, se n è grande e n \\cdot p è nell'ordine di grandezza delle unità, allora:\n                        
    \n                        
    \n                            {r`Bin(n, p) \\approx Poi(n \\cdot p)`}\n                        
    \n                        \n                    \n                        
    \n                            Per il Teorema di De Moivre-Laplace, se una binomiale ha una n grande e p non vicina a 0 o 1, si può approssimare con:\n                        
    \n                        
    \n                            {r`Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)`}\n                        
    \n                        \n                    \n                        
    \n                            Passando da una variabile discreta X a una continua Y, per ogni valore discreto k la probabilità viene \"spalmata\" su tutto l'intervallo {r`(k - \\frac{1}{2}, k + \\frac{1}{2})`}:\n                        
    \n                        
      \n                            
    • {r`P(X < k) \\simeq P(Y \\leq k - \\frac{1}{2})`}
      • \n                            
    • {r`P(X \\leq k) \\simeq P(Y \\leq k + \\frac{1}{2})`}
      • \n                            
    • {r`P(X \\geq k) \\simeq P(Y \\geq k - \\frac{1}{2})`}
      • \n                            
    • {r`P(X > k) \\simeq P(Y \\geq k + \\frac{1}{2})`}
      • \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Un vettore composto da variabili aleatorie.\n                        
    \n                        
    \n                            Il suo simbolo generalmente è {r`\\boldsymbol{X}`} oppure {r`X, Y`}.\n                        
    \n                        \n                    \n                        
    \n                            I vettori aleatori hanno più funzioni di ripartizione che si differenziano in base al numero di parametri.\n                        
    \n                        
    \n                            Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una funzione di ripartizione congiunta:\n                        
    \n                        
    \n                            {r`F_{X, Y} (x, y) = P(X \\leq x, Y \\leq y)`}\n                        
    \n                        
    \n                            Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una funzione di ripartizione marginale:\n                        
    \n                        
    \n                            {r`F_X (x) = P(X \\leq x) = \\lim_{y \\to +\\infty} F_{X, Y} (x, y)`}\n                        
    \n                        \n                    \n                        
    \n                            I vettori aleatori discreti hanno più densità che si differenziano in base al numero di parametri.\n                        
    \n                        
    \n                            Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una densità congiunta:\n                        
    \n                        
    \n                            {r`p_{X, Y} (x, y) = P(X = x, Y = y)`}\n                        
    \n                        
    \n                            Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una densità marginale:\n                        
    \n                        
    \n                            {r`p_X (x) = \\sum_j p_{X, Y} (x_i, y_j)`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Più variabili aleatorie sono indipendenti se, per qualsiasi scelta di intervalli A_i:\n                        
    \n                        
    \n                            {r`P(X_1 \\in A_1, \\dots, X_n \\in A_n) = P(X_1 \\in A_1) \\times \\dots \\times P(X_n \\in A_n)`}\n                        
    \n                        \n                    \n                        
    \n                            E' possibile calcolare la media di qualsiasi funzione g(X, Y) avente elementi del vettore come variabili:\n                        
    \n                        
    \n                            {r`E(g(X, Y)) = \\sum_{i, j} g(x_i, y_i) \\cdot p_{X, Y} (x_i, y_i)`}\n                        
    \n                        \n                            Solitamente si calcola la media di x \\cdot y.\n                        \n                        
    \n                            Le medie di più variabili aleatorie si possono sommare:\n                        
    \n                        
    \n                            {r`E(X + Y) = E(X) + E(Y)`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Un operatore che misura la correlazione di due variabili aleatorie.\n                        
    \n                        
    \n                            Si calcola con il valore atteso dei prodotti delle distanze dalla media:\n                        
    \n                        
    \n                            {r`Cov(X, Y) = E((X - E(X) \\cdot (Y - E(Y)) = E(XY) - E(X) \\cdot E(Y)`}\n                        
    \n                        
    \n                            Ha diverse proprietà:\n                        
    \n                        
      \n                            
    • Il suo valore nullo è 0: {r`Cov(X, \\alpha) = 0`}
      • \n                            
    • E' commutativa: {r`Cov(X, Y) = Cov(Y, X)`}
      • \n                            
    • E' semplificabile: {r`Cov(X, X) = Var(X)`}
      • \n                            
    • E' lineare: {r`Cov(\\alpha X, \\beta Y) = \\alpha \\cdot \\beta \\cdot Cov(X, Y)`}
      • \n                            
    • E' distributiva: {r`Cov(X + Y, V + W) = Cov(X, Y) + Cov(X, W) + Cov(Y, V) + Cov(Y, W)`}
      • \n                        
    \n                        \n                    \n                        
    \n                            Due variabili sono variabili incorrelate se:\n                        
    \n                        
    \n                            {r`Cov(X, Y) = 0`}\n                        
    \n                        
    \n                            Variabili indipendenti sono sempre incorrelate.\n                        
    \n                        \n                    \n                        
    \n                            Una matrice {r`\\boldsymbol{C_X}`} che contiene la covarianza tra tutte le variabili di un vettore aleatorio {r`\\boldsymbol{X}`}:\n                        
    \n                        
    \n                            {r`\n                                \\boldsymbol{C_X} = \n                                \\begin{bmatrix}\n                                    Var(X_1) & Cov(X_1, X_2) & Cov(X_1, X_3)\\\\\n                                    Cov(X_2, X_1) & Var(X_2) & Cov(X_2, X_3)\\\\\n                                    Cov(X_3, X_1) & Cov(X_3, X_2) & Var(X_3)\n                                \\end{bmatrix}\n                            `}\n                        
    \n                        
    \n                            E' sempre simmetrica e semidefinita positiva (tutti gli autovalori sono \\geq 0.\n                        
    \n                        \n                    \n                        
    \n                            Un valore che misura come due variabili aleatorie sono correlate:\n                        
    \n                        
    \n                            {r`\\rho_{X, Y} = \\frac{Cov(X, Y)}{\\sqrt{Var(X)} \\cdot \\sqrt{Var(Y)}}`}\n                        
    \n                        
    \n                            E' sempre compreso tra -1 e 1:\n                        
    \n                        
    \n                            {r`-1 \\leq \\rho_{X, Y} \\leq 1`}\n                        
    \n                        
    \n                            Vale esattamente -1 o 1 solo se esiste un legame lineare tra le due variaibli:\n                        
    \n                        
    \n                            {r`Y = a X + b \\Longleftrightarrow | \\rho_{X, Y} | = 1`}\n                        
    \n                        \n                    \n                        
    \n                            La varianza di due variabili aleatorie sommate è:\n                        
    \n                        
    \n                            {r`Var(X + Y) = Var(X) + Var(Y) + 2 \\cdot Cov(X, Y)`}\n                        
    \n                        \n                            Si dimostra applicando le proprietà della covarianza!\n                        \n                        
    \n                            Se più variabili aleatorie X_i sono indipendenti ({r`Cov(X, Y) = 0`}), allora:\n                        
    \n                        
    \n                            {r`Var \\left( \\sum_i X_i \\right) = \\sum_i Var(X_i)`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una n-pla di variabili aleatorie con la stessa distribuzione della variabile aleatoria X (\"popolazione\") ma indipendenti tra loro.\n                        
    \n                        \n                            Le variabili aleatorie sono come un lazy-load in programmazione; quando ci sarà bisogno del loro valore numerico, esse si realizzeranno nel loro valore.\n                        \n                        \n                    \n                        
    \n                            Il valore dato dalla media aritmetica degli n elementi del campione elevati alla potenza k:\n                        
    \n                        
    \n                            {r`M^{(k)}_n = \\frac{1}{n} \\cdot \\sum_{i = 1}^n X_i^k `}\n                        
    \n                        
    \n                            Il momento campionario di primo ordine è la media campionaria {r`\\overline{X}_n`}.\n                        
    \n                        \n                    \n                        
    \n                            La media aritmetica dello scarto quadratico medio degli elementi del campione.\n                        
    \n                        
    \n                            Se è noto il valore medio {r`m = E(X)`} di X:\n                        
    \n                        
    \n                            {r`S_0^2 = \\frac{1}{n} \\cdot \\sum_{i = 1}^n (X_i - m)^2 = M_n^(2) - 2 \\cdot m \\cdot \\overline{X}_n + m^2`}\n                        
    \n                        
    \n                            Altrimenti:\n                        
    \n                        
    \n                            {r`S_n^2 = \\frac{1}{n - 1} \\cdot \\sum_{i = 1}^n (X_i - \\overline{X}_n)^2 = \\frac{1}{n - 1} \\cdot ( n \\cdot M_2^{(2)} - n \\cdot \\overline{X}_n^2)`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Se calcoliamo la media della media campionaria, risulterà vero che:\n                        
    \n                        
    \n                            {r`E(\\overline{X}_n) = E(X)`}\n                        
    \n                        \n                            Quindi, è possibile usare i campioni per trovare la media di una variabile aleatoria!\n                        \n                        \n                    \n                        
    \n                            Se calcoliamo la varianza della media campionaria, risulterà vero che:\n                        
    \n                        
    \n                            {r`Var(\\overline{X}_n) = \\frac{Var(X)}{n}`}\n                        
    \n                        \n                            Quindi, possiamo stimare l'errore della media calcolata tramite campioni!\n                        \n                        \n                    \n                        
    \n                            Se calcoliamo la media della varianza campionaria, risulterà vero che:\n                        
    \n                        
    \n                            {r`E(S_0^2) = E(S_n^2) = Var(X)`}\n                        
    \n                        \n                            Quindi, possiamo stimare l'errore della media calcolata tramite campioni!\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Se la popolazione X ha una distribuzione normale ({r`X \\sim Nor(\\mu, \\sigma^2)`})...\n                        
    \n                        \n                    \n                        
    \n                            ...allora sappiamo anche la distribuzione della media campionaria!\n                        
    \n                        
    \n                            {r`\\overline{X}_n \\sim Nor \\left( \\mu, \\frac{\\sigma^2}{n} \\right)`}\n                        
    \n                        \n                    \n                        
    \n                            ...e anche della varianza campionaria!\n                        
    \n                        
    \n                            {r`S_0^2 \\sim \\frac{\\sigma^2}{n} \\cdot \\chi^2 (n)`}\n                        
    \n                        
    \n                            {r`S_n^2 \\sim \\frac{\\sigma^2}{n - 1} \\cdot \\chi^2 (n-1)`}\n                        
    \n                        \n                    \n                        
    \n                            ...e che media campionaria e varianza campionaria sono indipendenti tra loro!\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la stessa funzione di ripartizione della popolazione X, allora essa converge in distribuzione.\n                        
    \n                        
    \n                            {`\\\\lim_{n \\\\to +\\\\infty} F_{X_n} (x) = F_X (x) \\\\implies X_n \\\\xrightarrow{d} X`}\n                        
    \n                        \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la stessa probabilità della popolazione X, allora essa converge in probabilità.\n                        
    \n                        
    \n                            {`\\\\forall \\\\epsilon > 0, \\\\lim_{n \\\\to +\\\\infty} P( | X_n - X | < \\\\epsilon) = 1 \\\\implies X_n \\\\xrightarrow{p} X`}\n                        
    \n                        \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la stessa probabilità a  della popolazione X, allora essa converge quasi certamente.\n                        
    \n                        
    \n                            {`\\\\forall \\\\epsilon > 0, P \\left( \\\\lim_{n \\\\to +\\\\infty} | X_n - X | < \\\\epsilon) \\right) = 1 \\\\implies X_n \\\\xrightarrow{qc} X`}\n                        
    \n                        \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la media del quadrato della distanza tra la successione e la popolazione X uguale a 0, allora essa converge in media quadratica.\n                        
    \n                        
    \n                            {`\\\\lim_{n \\\\to +\\\\infty} E( | X_n - X |^2 = 0 \\\\implies X_n \\\\xrightarrow{mq} X`}\n                        
    \n                        \n                    \n                        
    \n                            {`\n                                \\\\begin{matrix}\n                                X_n \\\\xrightarrow{mq} X\\\\\\\\\n                                X_n \\\\xrightarrow{qc} X\n                                \\\\end{matrix} \\\\implies X_n \\\\xrightarrow{p} X \\\\implies X_n \\\\xrightarrow{d} X`\n                            }\n                        
    \n                        
    \n                            In più:\n                        
    \n                        
    \n                            {`X_n \\\\xrightarrow{p} x \\\\Longleftrightarrow X_n \\\\xrightarrow{d} x`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            La successione delle medie campionarie {r`\\overline{X}_n`} converge in probabilità alla media della popolazione {r`E(X)`}, se essa esiste.\n                        
    \n                        
    \n                            {`\\\\overline{X}_n \\\\xrightarrow{p} X`}\n                        
    \n                        
    \n                            Ovvero:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | \\overline{X}_n - E(X) | < \\epsilon) = 1`}\n                        
    \n                        
    \n                            {r`P( | \\overline{X}_n - E(X) | < \\epsilon) \\to 1`}\n                        
    \n                        \n                    \n                        
    \n                            La successione delle medie campionarie {r`\\overline{X}_n`} converge quasi certamente alla media della popolazione {r`E(X)`}, se essa esiste.\n                        
    \n                        
    \n                            {`\\\\overline{X}_n \\\\xrightarrow{qc} X`}\n                        
    \n                        
    \n                            Ovvero:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, P \\left( \\lim_{n \\to +\\infty} | \\overline{X}_n - E(X) | < \\epsilon \\right) = 1`}\n                        
    \n                        \n                            Dimostra che l'interpretazione frequentista della probabilità è valida!\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            La successione delle medie campionarie {r`\\overline{X}_n`} converge in distribuzione a {r`Nor(0, 1) = \\Phi()`}.\n                        
    \n                        
    \n                            {r`\\overline{X}_n \\approx Nor \\left(E(X), \\frac{Var(X)}{n} \\right)`}\n                        
    \n                        
    \n                            Ovvero:\n                        
    \n                        
    \n                            {r`\\forall x \\in \\mathbb{R}, \\lim_{n \\to +\\infty} P \\left( \\frac{\\overline{X}_n - E(X)}{\\sqrt{\\frac{Var(X)}{n}}} \\leq x \\right) = \\Phi(x)`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            E' una somma di bernoulliane, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)`}\n                        
    \n                        \n                    \n                        
    \n                            E' una somma di geometriche, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`\\overline{Bin} (n, p) \\approx Nor \\left( \\frac{n}{p}, \\frac{n \\cdot (1 - p)}{p^2} \\right)`}\n                        
    \n                        \n                    \n                        
    \n                            E' una somma di altre poissoniane, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`Poi(\\lambda) \\approx Nor(\\lambda, \\lambda)`}\n                        
    \n                        \n                    \n                        
    \n                            E' una somma di esponenziali, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`\\Gamma (\\alpha, \\lambda) \\approx Nor \\left( \\frac{\\alpha}{\\lambda}, \\frac{\\alpha}{\\lambda^2} \\right)`}\n                        
    \n                        \n                    \n                        
    \n                            Se n è grande, allora:\n                        
    \n                        
    \n                            {r`Y = \\sum_{i=1}^{n} X_i`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Per indicare parametri sconosciuti di una legge si usa \\theta.\n                        
    \n                        \n                    \n                        
    \n                            Una variabile aleatoria funzione di un campione:\n                        
    \n                        
    \n                            {r`T(\\boldsymbol{X})`}\n                        
    \n                        \n                            Ad esempio, sono statistiche media e varianza campionaria, così come il campione stesso {r`T(\\boldsymbol{X}) = \\boldsymbol{X}`}.\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una statistica T_n ottenuta da n osservazioni, che stimi i parametri di una legge e sia indipendente da essi.\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è corretto se il suo valore atteso coincide con quello dei parametri che stima:\n                        
    \n                        
    \n                            {r`E(T_n) = \\theta`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è asintoticamente corretto se, per infinite osservazioni, il suo valore atteso coincide con quello dei parametri che stima:\n                        
    \n                        
    \n                            {r`\\lim_{n \\to +\\infty} E(T_n) = \\theta`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è consistente in media quadratica se:\n                        
    \n                        
    \n                            {r`\\lim_{n \\to +\\infty} E((T_n - \\theta)^2) = 0`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è consistente in probabilità se:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( |T_n - \\theta| < \\epsilon) = 1`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è asintoticamente normale se:\n                        
    \n                        
    \n                            {r`\\lim_{n \\to +\\infty} \\frac{T_n - E(T_n)}{\\sqrt{Var(T_n)}} \\sim Nor(0, 1)`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Si può usare il metodo dei momenti per ottenere uno stimatore di una popolazione X.\n                        
    \n                        
    \n                            Lo stimatore di {r`\\theta`} così ottenuto sarà indicato aggiungendo un cappellino e una M a \\theta: {r`\\widehat{\\theta}_M`}\n                        
    \n                        
    \n                            Visto che:\n                        
    \n                        
      \n                            
    • {r`\\theta = g(E(X))`}
      • \n                            
    • {r`\\widehat{E(X)} = \\overline{X}_n`}
      • \n                        
    \n                        
    \n                            Allora:\n                        
    \n                        
    \n                            {r`\\widehat{\\theta}_M = g( \\overline{X}_n )`}\n                        
    \n                        
    \n                            Se {r`\\theta`} non è esprimibile in termini di {r`E(X)`}, si possono usare i momenti successivi {r`M_n^2`}, {r`M_n^3`}, {r`M_n^3`}...\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Si può usare il metodo della massima verosomiglianza per ottenere uno stimatore di una popolazione X.\n                        
    \n                        
    \n                            Lo stimatore di {r`\\theta`} così ottenuto sarà indicato aggiungendo un cappellino e una L a \\theta: {r`\\widehat{\\theta}_L`}\n                        
    \n                        
    \n                            Consiste nel trovare il massimo assoluto {r`\\widehat{\\theta}_L`} della la funzione di verosomiglianza {r`L`}:\n                        
    \n                        
    \n                            {r`L(x_1, ..., x_n; \\theta) = \\prod_{i=1}^n f_X(x_i; \\theta)`}\n                        
    \n                        
    \n                            Gli stimatori di massima verosomiglianza sono asintoticamente corretti, consistenti in probabilità e asintoticamente normali.\n                        
    \n                        \n                    \n                        
    \n                            Gli stimatori di massima verosomiglianza godono delle seguenti proprietà:\n                        
    \n                        
      \n                            
    • Sono asintoticamente corretti.
      • \n                            
    • Sono consistenti in probabilità.
      • \n                            
    • Sono asintoticamente normali.
      • \n                            
    • Sono invarianti: {r`\\widehat{g(\\theta)}_L = g(\\widehat{\\theta}_L)`}
      • \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n                        
    \n                        
    \n                            {r`\\widehat{p}_M = \\widehat{p}_L = \\overline{X}_n`}\n                        
    \n                        \n                    \n                        
    \n                            Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n                        
    \n                        
    \n                            {r`\\widehat{\\mu}_M = \\widehat{\\mu}_L = \\overline{X}_n`}\n                        
    \n                        \n                    \n                        
    \n                            Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n                        
    \n                        
    \n                            {r`\\widehat{\\lambda}_M = \\widehat{\\lambda}_L = \\frac{1}{\\overline{X}_n}`}\n                        
    \n                        \n                    \n                        
    \n                            Per il metodo della massima verosomiglianza:\n                        
    \n                        
      \n                            
    • {r`\\widehat{\\mu}_L = \\overline{X}_n`}

      • \n                            
    • {r`\\widehat{\\sigma^2}_L = \\frac{\\sum (X_i - \\overline{X}_n)^2 }{n}`}
      • \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            \"intervallo di confidenza al 95%\"\n                        
    \n                        
    \n                            L'intervallo di valori di \\theta all'interno del quale siamo \"più o meno sicuri\" si trovi il valore effettivo:\n                        
    \n                        
    \n                            L'intervallo di confidenza a N della stima {r`\\widehat{W}`} è l'intervallo ]a, b[ tale che:\n                        
    \n                        
    \n                            {r`P( a < W < b ) = N`}\n                        
    \n                        
    \n                            Può anche essere unilatero nel caso limiti la stima in una sola direzione, positiva o negativa.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Se conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'\\alpha% con queste formule:\n                        
    \n                        
      \n                            
    • Intervalli bilateri: {r`\\mu \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}}, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da sinistra: {r`\\mu \\in \\left( -\\infty, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da destra: {r`\\mu \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}}, +\\infty \\right)`}
      • \n                        
    \n                        \n                    \n                        
    \n                            Se non conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'\\alpha% con queste formule:\n                        
    \n                        
      \n                            
    • Intervalli bilateri: {r`\\mu \\in \\left[ \\overline{x}_n - t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}}, \\overline{x}_n + t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da sinistra: {r`\\mu \\in \\left( -\\infty, \\overline{x}_n + t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da destra: {r`\\mu \\in \\left[ \\overline{x}_n - t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}}, +\\infty \\right)`}
      • \n                        
    \n                        
    \n                            {r`t_{\\alpha, v}`} è un quantile della distribuzione di Student di parametro v.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            L'intervallo di confidenza per la proprorzione di una bernoulliana qualsiasi si ottiene da questa formula:\n                        
    \n                        
    \n                            {r`p \\in \\left[ \\overline{p} - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\overline{p} \\cdot (1 - \\overline{p})}{n+4}}, \\overline{p} + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\overline{p} \\cdot (1 - \\overline{p})}{n+4}} \\right]`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            L'intervallo di confidenza per la media di una qualsiasi popolazione si ottiene da questa formula:\n                        
    \n                        
    \n                            {r`m \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{s^2_n}{n}}, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{s^2_n}{n}} \\right]`}\n                        
    \n                        \n                
    \n            
    \n            \n            \n    )\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"splitparent\":\"splitparent__3-wBs\",\"splitchild\":\"splitchild__begkX\"};","import style from \"./Panel.less\";\nimport Box from \"./Box\";\n\nexport default function(props) {\n\treturn (\n\t\t\n\t\t\t
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extracted by mini-css-extract-plugin\nmodule.exports = {\"example\":\"example__9acWs\"};","import style from \"./Minus.less\";\n\nexport default function(props) {\n\treturn {props.children};\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"box\":\"box__3cKyY\",\"default\":\"default__v-emJ\",\"red\":\"red__339Cz\",\"orange\":\"orange__24_8v\",\"yellow\":\"yellow__1Jo9W\",\"lime\":\"lime__34yV5\",\"cyan\":\"cyan__3RqLr\",\"blue\":\"blue__13Wnj\",\"magenta\":\"magenta__2tkzq\"};","import style from \"./Plus.less\";\nimport { Component } from 'preact';\n\nexport default function(props) {\n\treturn {props.children};\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"inline\":\"inline__1yl8V\",\"block\":\"block__fPiiB\"};","import Split from \"../Layout/Split\";\nimport {Fragment} from \"preact\";\n\nexport default function (props) {\n    return (\n        \n            
    \n                {props.title}\n            
    \n            \n                {props.children}\n            \n            \n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"title\":\"title__3ZVpg\",\"contents\":\"contents__20_NI\"};","import {createContext} from \"preact\";\n\nexport default createContext(null);\n","import style from './Latex.less';\nimport {useContext} from \"preact/hooks\";\nimport LatexRenderColor from \"../../contexts/LatexRenderColor\";\nimport LatexDefaultInline from \"../../contexts/LatexDefaultInline\";\nimport LatexDefaultDisplay from \"../../contexts/LatexDefaultDisplay\";\n\nexport const LatexDisplay = Object.freeze({\n    INLINE: style.inline,\n    BLOCK: style.block,\n})\n\nexport default function(props) {\n    // black, blue, brown, cyan, darkgray, gray, green, lightgray, lime, magenta, olive, orange, pink, purple, red, teal, violet, white, yellow\n    let renderColor = useContext(LatexRenderColor);\n    let defaultInline = useContext(LatexDefaultInline);\n    let defaultDisplay = useContext(LatexDefaultDisplay);\n\n    let inline;\n    if(props.inline === undefined) {\n        inline = defaultInline;\n    }\n    else {\n        inline = props.inline;\n    }\n\n    let display;\n    if(props.display === undefined) {\n        if(defaultDisplay === null) {\n            display = LatexDisplay.INLINE;\n        }\n        else {\n            display = defaultDisplay;\n        }\n    }\n    else {\n        display = props.display;\n    }\n\n    if(inline) {\n        let equation = `\\\\inline {\\\\color{${renderColor}} ${props.children} }`;\n        return (\n            {props.children}\n\n        );\n    }\n    else {\n        let equation = `{\\\\color{${renderColor}} ${props.children} }`;\n        return (\n            {props.children}\n\n        );\n    }\n}\n","import { options } from 'preact';\n\n/** @type {number} */\nlet currentIndex;\n\n/** @type {import('./internal').Component} */\nlet currentComponent;\n\n/** @type {number} */\nlet currentHook = 0;\n\n/** @type {Array} */\nlet afterPaintEffects = [];\n\nlet oldBeforeRender = options._render;\nlet oldAfterDiff = options.diffed;\nlet oldCommit = options._commit;\nlet oldBeforeUnmount = options.unmount;\n\nconst RAF_TIMEOUT = 100;\nlet prevRaf;\n\noptions._render = vnode => {\n\tif (oldBeforeRender) oldBeforeRender(vnode);\n\n\tcurrentComponent = vnode._component;\n\tcurrentIndex = 0;\n\n\tconst hooks = currentComponent.__hooks;\n\tif (hooks) {\n\t\thooks._pendingEffects.forEach(invokeCleanup);\n\t\thooks._pendingEffects.forEach(invokeEffect);\n\t\thooks._pendingEffects = [];\n\t}\n};\n\noptions.diffed = vnode => {\n\tif (oldAfterDiff) oldAfterDiff(vnode);\n\n\tconst c = vnode._component;\n\tif (c && c.__hooks && c.__hooks._pendingEffects.length) {\n\t\tafterPaint(afterPaintEffects.push(c));\n\t}\n};\n\noptions._commit = (vnode, commitQueue) => {\n\tcommitQueue.some(component => {\n\t\ttry {\n\t\t\tcomponent._renderCallbacks.forEach(invokeCleanup);\n\t\t\tcomponent._renderCallbacks = component._renderCallbacks.filter(cb =>\n\t\t\t\tcb._value ? invokeEffect(cb) : true\n\t\t\t);\n\t\t} catch (e) {\n\t\t\tcommitQueue.some(c => {\n\t\t\t\tif (c._renderCallbacks) c._renderCallbacks = [];\n\t\t\t});\n\t\t\tcommitQueue = [];\n\t\t\toptions._catchError(e, component._vnode);\n\t\t}\n\t});\n\n\tif (oldCommit) oldCommit(vnode, commitQueue);\n};\n\noptions.unmount = vnode => {\n\tif (oldBeforeUnmount) oldBeforeUnmount(vnode);\n\n\tconst c = vnode._component;\n\tif (c && c.__hooks) {\n\t\ttry {\n\t\t\tc.__hooks._list.forEach(invokeCleanup);\n\t\t} catch (e) {\n\t\t\toptions._catchError(e, c._vnode);\n\t\t}\n\t}\n};\n\n/**\n * Get a hook's state from the currentComponent\n * @param {number} index The index of the hook to get\n * @param {number} type The index of the hook to get\n * @returns {import('./internal').HookState}\n */\nfunction getHookState(index, type) {\n\tif (options._hook) {\n\t\toptions._hook(currentComponent, index, currentHook || type);\n\t}\n\tcurrentHook = 0;\n\n\t// Largely inspired by:\n\t// * https://github.com/michael-klein/funcy.js/blob/f6be73468e6ec46b0ff5aa3cc4c9baf72a29025a/src/hooks/core_hooks.mjs\n\t// * https://github.com/michael-klein/funcy.js/blob/650beaa58c43c33a74820a3c98b3c7079cf2e333/src/renderer.mjs\n\t// Other implementations to look at:\n\t// * https://codesandbox.io/s/mnox05qp8\n\tconst hooks =\n\t\tcurrentComponent.__hooks ||\n\t\t(currentComponent.__hooks = {\n\t\t\t_list: [],\n\t\t\t_pendingEffects: []\n\t\t});\n\n\tif (index >= hooks._list.length) {\n\t\thooks._list.push({});\n\t}\n\treturn hooks._list[index];\n}\n\n/**\n * @param {import('./index').StateUpdater} initialState\n */\nexport function useState(initialState) {\n\tcurrentHook = 1;\n\treturn useReducer(invokeOrReturn, initialState);\n}\n\n/**\n * @param {import('./index').Reducer} reducer\n * @param {import('./index').StateUpdater} initialState\n * @param {(initialState: any) => void} [init]\n * @returns {[ any, (state: any) => void ]}\n */\nexport function useReducer(reducer, initialState, init) {\n\t/** @type {import('./internal').ReducerHookState} */\n\tconst hookState = getHookState(currentIndex++, 2);\n\thookState._reducer = reducer;\n\tif (!hookState._component) {\n\t\thookState._component = currentComponent;\n\n\t\thookState._value = [\n\t\t\t!init ? invokeOrReturn(undefined, initialState) : init(initialState),\n\n\t\t\taction => {\n\t\t\t\tconst nextValue = hookState._reducer(hookState._value[0], action);\n\t\t\t\tif (hookState._value[0] !== nextValue) {\n\t\t\t\t\thookState._value[0] = nextValue;\n\t\t\t\t\thookState._component.setState({});\n\t\t\t\t}\n\t\t\t}\n\t\t];\n\t}\n\n\treturn hookState._value;\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++, 3);\n\tif (!options._skipEffects && argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent.__hooks._pendingEffects.push(state);\n\t}\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useLayoutEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++, 4);\n\tif (!options._skipEffects && argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent._renderCallbacks.push(state);\n\t}\n}\n\nexport function useRef(initialValue) {\n\tcurrentHook = 5;\n\treturn useMemo(() => ({ current: initialValue }), []);\n}\n\n/**\n * @param {object} ref\n * @param {() => object} createHandle\n * @param {any[]} args\n */\nexport function useImperativeHandle(ref, createHandle, args) {\n\tcurrentHook = 6;\n\tuseLayoutEffect(\n\t\t() => {\n\t\t\tif (typeof ref == 'function') ref(createHandle());\n\t\t\telse if (ref) ref.current = createHandle();\n\t\t},\n\t\targs == null ? args : args.concat(ref)\n\t);\n}\n\n/**\n * @param {() => any} factory\n * @param {any[]} args\n */\nexport function useMemo(factory, args) {\n\t/** @type {import('./internal').MemoHookState} */\n\tconst state = getHookState(currentIndex++, 7);\n\tif (argsChanged(state._args, args)) {\n\t\tstate._args = args;\n\t\tstate._factory = factory;\n\t\treturn (state._value = factory());\n\t}\n\n\treturn state._value;\n}\n\n/**\n * @param {() => void} callback\n * @param {any[]} args\n */\nexport function useCallback(callback, args) {\n\tcurrentHook = 8;\n\treturn useMemo(() => callback, args);\n}\n\n/**\n * @param {import('./internal').PreactContext} context\n */\nexport function useContext(context) {\n\tconst provider = currentComponent.context[context._id];\n\t// We could skip this call here, but than we'd not call\n\t// `options._hook`. We need to do that in order to make\n\t// the devtools aware of this hook.\n\tconst state = getHookState(currentIndex++, 9);\n\t// The devtools needs access to the context object to\n\t// be able to pull of the default value when no provider\n\t// is present in the tree.\n\tstate._context = context;\n\tif (!provider) return context._defaultValue;\n\t// This is probably not safe to convert to \"!\"\n\tif (state._value == null) {\n\t\tstate._value = true;\n\t\tprovider.sub(currentComponent);\n\t}\n\treturn provider.props.value;\n}\n\n/**\n * Display a custom label for a custom hook for the devtools panel\n * @type {(value: T, cb?: (value: T) => string | number) => void}\n */\nexport function useDebugValue(value, formatter) {\n\tif (options.useDebugValue) {\n\t\toptions.useDebugValue(formatter ? formatter(value) : value);\n\t}\n}\n\nexport function useErrorBoundary(cb) {\n\tconst state = getHookState(currentIndex++, 10);\n\tconst errState = useState();\n\tstate._value = cb;\n\tif (!currentComponent.componentDidCatch) {\n\t\tcurrentComponent.componentDidCatch = err => {\n\t\t\tif (state._value) state._value(err);\n\t\t\terrState[1](err);\n\t\t};\n\t}\n\treturn [\n\t\terrState[0],\n\t\t() => {\n\t\t\terrState[1](undefined);\n\t\t}\n\t];\n}\n\n/**\n * After paint effects consumer.\n */\nfunction flushAfterPaintEffects() {\n\tafterPaintEffects.some(component => {\n\t\tif (component._parentDom) {\n\t\t\ttry {\n\t\t\t\tcomponent.__hooks._pendingEffects.forEach(invokeCleanup);\n\t\t\t\tcomponent.__hooks._pendingEffects.forEach(invokeEffect);\n\t\t\t\tcomponent.__hooks._pendingEffects = [];\n\t\t\t} catch (e) {\n\t\t\t\tcomponent.__hooks._pendingEffects = [];\n\t\t\t\toptions._catchError(e, component._vnode);\n\t\t\t\treturn true;\n\t\t\t}\n\t\t}\n\t});\n\tafterPaintEffects = [];\n}\n\n/**\n * Schedule a callback to be invoked after the browser has a chance to paint a new frame.\n * Do this by combining requestAnimationFrame (rAF) + setTimeout to invoke a callback after\n * the next browser frame.\n *\n * Also, schedule a timeout in parallel to the the rAF to ensure the callback is invoked\n * even if RAF doesn't fire (for example if the browser tab is not visible)\n *\n * @param {() => void} callback\n */\nfunction afterNextFrame(callback) {\n\tconst done = () => {\n\t\tclearTimeout(timeout);\n\t\tcancelAnimationFrame(raf);\n\t\tsetTimeout(callback);\n\t};\n\tconst timeout = setTimeout(done, RAF_TIMEOUT);\n\n\tlet raf;\n\tif (typeof window != 'undefined') {\n\t\traf = requestAnimationFrame(done);\n\t}\n}\n\n// Note: if someone used options.debounceRendering = requestAnimationFrame,\n// then effects will ALWAYS run on the NEXT frame instead of the current one, incurring a ~16ms delay.\n// Perhaps this is not such a big deal.\n/**\n * Schedule afterPaintEffects flush after the browser paints\n * @param {number} newQueueLength\n */\nfunction afterPaint(newQueueLength) {\n\tif (newQueueLength === 1 || prevRaf !== options.requestAnimationFrame) {\n\t\tprevRaf = options.requestAnimationFrame;\n\t\t(prevRaf || afterNextFrame)(flushAfterPaintEffects);\n\t}\n}\n\n/**\n * @param {import('./internal').EffectHookState} hook\n */\nfunction invokeCleanup(hook) {\n\tif (typeof hook._cleanup == 'function') hook._cleanup();\n}\n\n/**\n * Invoke a Hook's effect\n * @param {import('./internal').EffectHookState} hook\n */\nfunction invokeEffect(hook) {\n\thook._cleanup = hook._value();\n}\n\n/**\n * @param {any[]} oldArgs\n * @param {any[]} newArgs\n */\nfunction argsChanged(oldArgs, newArgs) {\n\treturn !oldArgs || newArgs.some((arg, index) => arg !== oldArgs[index]);\n}\n\nfunction invokeOrReturn(arg, f) {\n\treturn typeof f == 'function' ? f(arg) : f;\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"minus\":\"minus__VM3UF\"};","import style from \"./Split.less\";\n\nexport default function (props) {\n    let children;\n\n    if(Array.isArray(props.children)) {\n        children = props.children.map(element => {\n            return (\n                
    \n                    {element}\n                
    \n            );\n        });\n    }\n\n    else {\n        children = (\n            
    \n                {props.children}\n            
    \n        );\n    }\n    return (\n        
    \n            
    {children}
    \n        
    \n    );\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"plus\":\"plus__5AywL\"};","import style from \"./Example.less\";\nimport {Component} from \"preact\";\n\nexport default function(props) {\n    return (\n        
    \n            {props.children}\n        
    \n    );\n}\n","import style from \"./Box.less\";\n\nexport const BoxColors = Object.freeze({\n    RED: style.red,\n    ORANGE: style.orange,\n    YELLOW: style.yellow,\n    LIME: style.lime,\n    CYAN: style.cyan,\n    BLUE: style.blue,\n    MAGENTA: style.magenta,\n    DEFAULT: style.default\n})\n\nexport default function (props) {\n    let color = BoxColors.DEFAULT;\n    if(props.color) {\n        color = props.color;\n    }\n\n    return (\n        
    \n            {props.children}\n        
    \n    );\n}\n","import Latex, {LatexDisplay} from '../components/Rendering/Latex';\nimport Panel from '../components/Elements/Panel';\nimport Section from \"../components/Elements/Section\";\nimport Example from \"../components/Elements/Example\";\nimport Plus from \"../components/PageSpecific/Fisica/Plus\";\nimport Minus from \"../components/PageSpecific/Fisica/Minus\";\nimport LatexDefaultInline from \"../contexts/LatexDefaultInline\";\nimport LatexDefaultDisplay from \"../contexts/LatexDefaultDisplay\";\n\nconst r = String.raw;\n\nexport default function(props) {\n    return (\n        \n        \n            
    \n                
    Statistica ed Elementi di Probabilità
    \n                
    \n                    \n                        
    \n                            {r`P(E) = \\frac{casi\\ favorevoli}{casi\\ possibili}`}\n                        
    \n                        \n                    \n                        
    \n                            {r`P(E) = \\frac{successi}{prove\\ totali}`}\n                        
    \n                        \n                    \n                        
    \n                            Il prezzo che un individuo coerente riterrebbe equo per ricevere 1 nel caso l'evento si verificasse e 0 nel caso l'evento non si verificasse.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            \"omegone\"\n                        
    \n                        
    \n                            L'insieme di tutti gli esiti possibili di un esperimento.\n                        
    \n                        
    \n                            {r`\\Omega = \\left \\{ 1, 2, 3, 4, 5, 6 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"omeghino\"\n                        
    \n                        
    \n                            Un elemento dello spazio campionario.\n                        
    \n                        
    \n                            {r`\\omega = 1`}\n                        
    \n                        \n                    \n                        
    \n                            \"e\"\n                        
    \n                        
    \n                            Un sottoinsieme dello spazio campionario.\n                        
    \n                        
    \n                            {r`E = \\left \\{ 1, 2 \\right \\}`}\n                        
    \n                        
    \n                            Lo spazio campionario stesso è un evento certo.\n                        
    \n                        \n                    \n                        
    \n                            \"not e\"\n                        
    \n                        
    \n                            Il complementare di un sottoinsieme.\n                        
    \n                        
    \n                            {r`\\bar{E} = \\left \\{ 3, 4, 5, 6 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e intersecato effe\"\n                        
    \n                        
    \n                            L'intersezione di più sottoinsiemi.\n                        
    \n                        
    \n                            {r`E \\cap F = \\left \\{ 1 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e unito a effe\"\n                        
    \n                        
    \n                            L'unione di più sottoinsiemi.\n                        
    \n                        
    \n                            {r`E \\cup F = \\left \\{ 1, 2, 3, 4 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e meno effe\"\n                        
    \n                        
    \n                            {r`E \\setminus F = E \\cap \\bar{F}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e contenuto in effe\"\n                        
    \n                        
    \n                            L'inclusione del primo insieme in un altro.\n                        
    \n                        
    \n                            {r`E \\subseteq F`}\n                        
    \n                        
    \n                            Se si verifica E, allora si verifica anche F.\n                        
    \n                        \n                    \n                        
    \n                            \"e è impossibile\"\n                        
    \n                        
    \n                            Un sottoinsieme vuoto.\n                        
    \n                        
    \n                            {r`E = \\emptyset`}\n                        
    \n                        \n                    \n                        
    \n                            \"e ed effe si escludono mutualmente\"\n                        
    \n                        
    \n                            La disgiunzione di due insiemi.\n                        
    \n                        
    \n                            {r`E \\cap F = \\emptyset`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            \"famiglia effe\"\n                        
    \n                        
    \n                            I sottoinsiemi dello spazio campionario formano una famiglia di sottoinsiemi detta famiglia degli eventi.\n                        
    \n                        
    \n                            {r`\\mathcal{F}`}\n                        
    \n                        
    \n                            Qualsiasi sottoinsieme appartenente a {r`\\mathcal{F}`} è considerato un evento.\n                        
    \n                        \n                    {r`\\sigma`}-algebra}>\n                        
    \n                            \"sigma algebra\"\n                        
    \n                        
    \n                            Se la famiglia degli eventi soddisfa questi tre requisiti, allora viene detta {r`\\sigma`}-algebra:\n                        
    \n                        
      \n                            
    1. \n                                Lo spazio campionario è un evento: {r`\\Omega \\in \\mathcal{F}`}\n                            
      2. \n                            
    2. \n                                Se un sottoinsieme è un evento, allora anche il suo complementare lo è: {r`E \\in \\mathcal{F} \\implies \\bar{E} \\in \\mathcal{F}`}\n                            
      3. \n                            
    3. \n                                Se due sottoinsiemi sono eventi, allora lo sono anche la loro unione e intersezione: {r`(E, F) \\in \\mathcal{F} \\implies (E \\cup F, E \\cap F) \\in \\mathcal{F}`}\n                            
      4. \n                        
    \n                        
    \n                            Un esempio: {r`E \\in \\mathcal{F} \\implies \\mathcal{F} = \\{ \\emptyset, E, \\bar{E}, \\Omega \\}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            \"la partizione e composta da e uno, e due, e tre...\"\n                        
    \n                        
    \n                            Un insieme di esiti e eventi:\n                        
    \n                        
      \n                            
    • Finito.
      • \n                            
    • In cui tutti gli eventi hanno probabilità diversa da 0.
      • \n                            
    • In cui tutti gli eventi sono mutualmente esclusivi.
      • \n                            
    • In cui l'unione di tutti i suoi elementi copre lo spazio campionario.
      • \n                        
    \n                        
    \n                            La partizione {r`E_i`} è composta dagli eventi {r`E_1`}, {r`E_2`}, {r`E_3`}, fino a {r`E_n`}.\n                        
    \n                        \n                            Se lo spazio campionario fosse una torta, una sua partizione sarebbe l'insieme delle fette di uno dei modi in cui si potrebbe tagliare.\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            La probabilità di un evento è un numero tra 0 e 1.\n                        
    \n                        
    \n                            {r`\\forall E \\in \\mathcal{F}, 0 \\leq P(E) \\leq 1`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità dello spazio campionario è sempre 1.\n                        
    \n                        
    \n                            {r`P(\\Omega) = 1`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità dell'unione di eventi indipendenti è uguale alla somma delle loro probabilità.\n                        
    \n                        
    \n                            {r`P \\left ( \\bigcup_i E_i \\right ) = \\sum_i P ( E_i )`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            La probabilità di un evento negato è uguale a 1 meno la probabilità dell'evento non negato.\n                        
    \n                        
    \n                            {r`P(\\bar{E}) = 1 - P({E})`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità di un evento incluso in un altro è sempre minore o uguale alla probabilità dell'evento in cui è incluso.\n                        
    \n                        
    \n                            {r`F \\subseteq E \\implies P(F) \\leq P(E)`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità di un evento unito a un altro è uguale alla somma delle probabilità dei due eventi meno la probabilità della loro intersezione.\n                        
    \n                        
    \n                            {r`P(E \\cup F) = P(E) + P(F) - P(E \\cap F)`}\n                        
    \n                        \n                            Sommando le probabilità dei due eventi, l'intersezione viene contata due volte, e va quindi rimossa!\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Spazi campionari in cui ci sono un numero finito di esiti e ogni esito ha la stessa probabilità di verificarsi.\n                        
    \n                        
    \n                            {r`P(E) = \\frac{len(E)}{len(\\Omega)}`}\n                        
    \n                        \n                    \n                        
    \n                            Gli spazi campionari possono avere un numero infinito di esiti: sono equiprobabili geometrici se nessun esito è privilegiato rispetto agli altri.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo tengo fuori dal sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Tengo conto dell'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{D}_{n, k} = \\frac{n!}{(n - k)!}`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo rimetto nel sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Tengo conto dell'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{D}^{r}_{n, k} = n^k`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo tengo fuori dal sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Non mi interessa l'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{C}_{n, k} = \\binom{n}{k} = \\frac{n!}{(k)! \\cdot (n - k)!}`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo rimetto nel sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Non mi interessa l'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{C}^{r}_{n, k} = \\binom{n + k - 1}{k} = \\frac{(n + k - 1)!}{(k)! \\cdot (n - 1)!}`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo n numeri e guardo in quanti ordini diversi li posso mettere.\n                        
    \n                        
    \n                            {r`\\boldsymbol{P}_n = n!`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            \"E dato F\"\n                        
    \n                        
    \n                            La probabilità che si verifichi E sapendo che si è già verificato F.\n                        
    \n                        
    \n                            {r`P(E|F) = \\frac{P(E \\cap F)}{P(F)}`}\n                        
    \n                        \n                            Ricorda vagamente le pipe di bash, però al contrario...\n                        \n                        \n                    \n                        
    \n                            Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0.\n                        
    \n                        
    \n                            {r`E \\cap F = \\emptyset \\Longleftrightarrow P(E|F) = P(F|E) = 0`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:\n                        
    \n                        
    \n                            {r`P(E_1 \\cap \\times \\cap E_n) = P(E_1) \\times P(E_2 | E_1) \\times \\dots \\times P(E_n | E_1 \\cap E_2 \\cap \\dots \\cap E_{n-1})`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            La probabilità che si verifichi un evento è pari alla somma delle probabilità dell'evento stesso dati tutti gli eventi di una partizione.\n                        
    \n                        
    \n                            {r`P(F) = \\sum_{i} P(F|E_i) \\cdot P(E_i)`}\n                        
    \n                        \n                    \n                        
    \n                            La legge delle alternative funziona anche quando ad essere partizionato è un evento:\n                        
    \n                        
    \n                            {r`P(F|G) = \\sum_i P(F|E_i \\cap G) \\cdot P(E_i | G)`}\n                        
    \n                        \n                    \n                        
    \n                            Tramite la formula di Bayes possiamo risalire alla probabilità di un evento condizionato a un altro partendo dalla probabilità di quest'ultimo condizionato al primo:\n                        
    \n                        
    \n                            {r`P(E_h | F) = \\frac{P(F | E_h) \\cdot P(E_h)}{P(F)}`}\n                        
    \n                        \n                            In pratica, invertiamo gli eventi.\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            \"eventi indipendenti a due a due\"\n                        
    \n                        
    \n                            Se due eventi sono indipendenti, sapere che uno dei due si è verificato non influisce sulle probabilità che si sia verificato l'altro.\n                        
    \n                        
    \n                            {r`P(E \\cap F) = P(E) \\cdot P(F) \\Longleftrightarrow P(E|F) = P(E) \\Longleftrightarrow P(F|E) = P(F)`}\n                        
    \n                        \n                    \n                        
    \n                            \"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque...\"\n                        
    \n                        
    \n                            Si può verificare l'indipendenza di più eventi alla volta:\n                        
    \n                        
    \n                            {r`P(E \\cap F \\cap G) = P(E) \\cdot P(F) \\cdot P(G)`}\n                        
    \n                        
    \n                            Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.\n                        
    \n                        \n                    \n                        
    \n                            Un insieme di n eventi è una famiglia di eventi indipendenti se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti.\n                        
    \n                        \n                            Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e così via!\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una funzione che fa corrispondere un numero reale a ogni possibile esito dello spazio campionario. {r`X(\\omega) : \\Omega \\to \\mathbb{R}`}.\n                        
    \n                        \n                    Insieme di ripartizione}>\n                        
    \n                            Ad ogni variabile aleatoria sono associati gli eventi {r`A_t = \\{ \\omega | X(\\omega) \\leq t \\}`}, che contengono tutti gli esiti a cui la variabile aleatoria associa un valore minore o uguale a t.\n                        
    \n                        
    \n                            Per definizione, tutte le variabili aleatorie devono rispettare questa condizione:\n                        
    \n                        
    \n                            {r`\\forall t \\in \\mathbb{R}, A_t \\in \\mathcal{F}`}\n                        
    \n                        \n                            All'aumentare di t, l'insieme conterrà sempre più elementi.\n                        \n                        \n                    \n                        
    \n                            \"supporto di X\"\n                        
    \n                        
    \n                            Il codominio della variabile aleatoria è il suo supporto.\n                        
    \n                        
    \n                            Per indicare che un valore x_0 appartiene al supporto di X, si usa la notazione X \\mapsto x_0.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            La funzione probabilità {r`p_X : X \\to [0, 1]`} di una variabile aleatoria discreta X è la funzione che associa ad ogni esito la sua probabilità:\n                        
    \n                        
    \n                            {r`p_X (x) = \\begin{cases}\n                            P([X = x]) \\quad se\\ X \\mapsto x \\\\\n                            0 \\qquad \\qquad \\quad se\\ X \\not\\mapsto x\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione densità {r`f_X : X \\to [0, 1]`} di una variabile aleatoria continua X è l'equivalente continuo della funzione probabilità:\n                        
    \n                        
    \n                            {r`P([a < X \\leq b]) = \\int_a^b f_X (x) dx`}\n                        
    \n                        
    \n                            A differenza della funzione probabilità, è possibile che la funzione densità non esista per una certa variabile aleatoria.\n                        
    \n                        \n                            Rappresenta \"quanta\" probabilità c'è in un'unità di x!\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Ogni variabile aleatoria ha una funzione di ripartizione {r`F_X : \\mathbb{R} \\to [0, 1]`} associata, che rappresenta la probabilità che la variabile aleatoria assuma un valore minore o uguale a t:\n                        
    \n                        
    \n                            Si può dire che essa rappresenti la probabilità dell'evento {r`A_t`}:\n                        
    \n                        
    \n                            {r`F_X (t) = P(A_t) = \\begin{cases}\n                            \\sum_{i = 0}^{t} p_X (x_i) \\quad nel\\ discreto\\\\\n                            \\\\\n                            \\int_{-\\infty}^t f_X (x) dx \\quad nel\\ continuo\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
      \n                            
    • È sempre monotona crescente (non strettamente).

      • \n                            
    • Vale 0 a -\\infty e 1 a +\\infty.

      • \n                            
    • È continua da destra: {r`\\forall x_0 \\in \\mathbb{R}, F_X (x_0) = \\lim_{t \\to x^+_0} F_X (t)`}
      • \n                        
    \n                        \n                    \n                        
    \n                            Possiamo usare la funzione di ripartizione per calcolare la probabilità di un certo valore reale:\n                        
    \n                        
    \n                            {r`P([X = x_0]) = \\lim_{t \\to x^+_0} F_X (t) - \\lim_{t \\to x^-_0} F_X (t)`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Nel discreto basta abbinare un nuovo valore a ogni valore della variabile originale.\n                        
    \n                        \n                    \n                        
    \n                            Nel continuo applichiamo la formula dell'integrazione per sostituzione:\n                        
    \n                        
    \n                            {r`f_Y (y) = \\int_{g(a)}^{g(b)} f_X ( g^{-1} (x) ) g^{-2} (x)`}\n                        
    \n                        \n                    \n                        
    \n                            Trasformare variabili aleatorie è molto utile nell'informatica per creare distribuzioni partendo da una funzione random() che restituisce numeri da 0 a 1 con una distribuzione lineare.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Ogni variabile aleatoria che ha una funzione di ripartizione e un supporto finito ha anche una media (o valore medio o atteso):\n                        
    \n                        
    \n                            {r`E(X) = \\int_0^{+infty} (1 - F_X (t)) dt - \\int_{-\\infty}^{0} F_X (t) dt`}\n                        
    \n                        
    \n                            Nel discreto, si può calcolare con:\n                        
    \n                        
    \n                            {r`E(X) = \\sum_i P(X = x_i) \\cdot x_i`}\n                        
    \n                        
    \n                            Nel continuo, si può calcolare con:\n                        
    \n                        
    \n                            {r`E(X) = \\int_{-\\infty}^{+\\infty} f_X (x) \\cdot x \\cdot dx`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Valore per cui la funzione probabilità o funzione densità è massima.\n                        
    \n                        \n                    \n                        
    \n                            Il quantile {r`x_{\\alpha}`} di ordine {r`0 \\leq \\alpha \\leq 1`} della variabile aleatoria X è il più piccolo numero tale che:\n                        
    \n                        
    \n                            \n                                {r`P([X < x_{\\alpha}]) \\leq \\alpha \\leq P([X \\leq x_{\\alpha}])`}\n                            \n                        
    \n                        
    \n\n                        
    \n                        
    \n                            Il quantile di ordine 0.5 {r`x_{0.5}`} è detto mediana.\n                        
    \n                        
    \n                            I quantili di ordine 0.25 {r`x_{0.25}`} e 0.75 {r`x_{0.75}`} sono detti quartili.\n                        
    \n                        
    \n                            I quantili di ordine {r`\\frac{n}{100}`} sono detti n-esima percentile.\n                        
    \n                        \n                    \n                        
    \n                            È un valore che indica quanto la variabile aleatoria si discosta generalmente dalla media:\n                        
    \n                        
    \n                            {r`Var(X) = E( (X - E(X) )^2 ) = E ( X^2 ) - (E(X))^2`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Data una variabile aleatoria non-negativa:\n                        
    \n                        
    \n                            {r`\\forall k > 0, P([X \\geq k]) \\leq \\frac{E(X)}{k}`}\n                        
    \n                        
    \n                            Divide in due parti ({r`P(X < k)`} e {r`P(X \\geq k)`}) la funzione X, la cui media risulterà uguale a:\n                        
    \n                        
    \n                            {r`E(X) = \\overline{k} \\cdot P(X < k) + k \\cdot P(X \\geq k)`}\n                        
    \n                        \n                    \n                        
    \n                            \"disuguaglianza di cebicev\"\n                        
    \n                        
    \n                            Se la variabile aleatoria X ha media e varianza, allora la probabilità che essa abbia un valore a più di {r`\\epsilon`} di distanza dal valore medio è minore o uguale a {r`\\frac{Var(X)}{\\epsilon^2}`}.\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, P([ \\left| X - E(X) \\right| \\geq \\epsilon]) \\leq \\frac{Var(X)}{\\epsilon^2}`}\n                        
    \n                        
    \n                            E anche:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, P([ \\left| X - E(X) \\right| < \\epsilon]) \\geq 1 - \\frac{Var(X)}{\\epsilon^2}`}\n                        
    \n                        \n                            Serve per semplificare i calcoli quando la funzione di ripartizione è difficile da calcolare!\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Il momento k-esimo di una variabile aleatoria è:\n                        
    \n                        
    \n                            \n                                {r`\\mu_k = E ( X^k ) = \\begin{cases}\n                                \\sum_i x_i^k p_X (x_i) \\qquad nel\\ discreto\\\\\n                                \\\\\n                                \\int_{-\\infty}^{+\\infty} x^k f_X (x) dx \\qquad nel\\ continuo\n                                \\end{cases}`}\n                            \n                        
    \n                        \n                            La media di una variabile aleatoria è anche il suo primo momento.\n                        \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti è:\n                        
    \n                        
    \n                            {r`m_X (t) = E( e^{t \\cdot X} )`}\n                        
    \n                        
    \n                            Se due variabile aleatorie hanno la stessa funzione generatrice dei momenti, allora esse hanno la stessa distribuzione.\n                        
    \n                        
    \n                            E' la trasformata di Laplace della variabile aleatoria di X.\n                        
    \n                        \n                    \n                        
    \n                            La funzione caratteristica è:\n                        
    \n                        
    \n                            {r`H_X (t) = E ( e^{i \\cdot t \\cdot X} )`}\n                        
    \n                        
    \n                            Se due variabile aleatorie hanno la stessa funzione caratteristica, allora esse hanno la stessa distribuzione.\n                        
    \n                        
    \n                            E' la trasformata di Fourier della variabile aleatoria di X.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Per dire che una variabile ha una certa distribuzione, si usa la notazione:\n                        
    \n                        
    \n                            {r`X \\sim Distribuzione()`}\n                        
    \n                        \n                    \n                        
    \n                            Una prova con solo due possibili esiti: successo e insuccesso.\n                        
    \n                        \n                    \n                        
    \n                            Una sequenza di prove di Bernoulli per le quali le probabilità di successo e fallimento rimangono invariate.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che rappresenta una prova di Bernoulli:\n                        
    \n                        
      \n                            
    • vale 1 in caso di successo.
      • \n                            
    • vale 0 in caso di insuccesso.
      • \n                        
    \n                        
    \n                            Il suo simbolo è {r`Ber(p)`}\n                        
    \n                        \n                    \n                        
    \n                            La distribuzione bernoulliana ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{0, 1\\} = \\begin{cases}\n                            p \\quad se\\ k = 1\\\\\n                            q \\quad se\\ k = 0\\\\\n                            0 \\quad altrimenti\n                            \\end{cases} = p^x \\cdot q^{1 - k}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di successi di n prove di uno schema di Bernoulli.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Bin(n, p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La binomiale ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{0..n\\} = \\binom{n}{k} \\cdot p^k \\cdot q^{n - k}`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti della binomiale è:\n                        
    \n                        
    \n                            {r`m_X (t) = (q + p \\cdot e^t) ^ n`}\n                        
    \n                        
    \n                            La media di una binomiale è:\n                        
    \n                        
    \n                            {r`E(X) = n \\cdot p`}\n                        
    \n                        
    \n                            La varianza di una binomiale è:\n                        
    \n                        
    \n                            {r`Var(X) = n \\cdot p \\cdot q`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli fino alla comparsa del primo successo.\n                        
    \n                        
    \n                            Il suo simbolo è Geo(p).\n                        
    \n                        \n                    \n                        
    \n                            La geometrica ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = q^{k - 1} p`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti della geometrica è:\n                        
    \n                        
    \n                            {r`m_X (t) = \\frac{p \\cdot e^t}{1 - q \\cdot e^t}`}\n                        
    \n                        
    \n                            La media della geometrica è:\n                        
    \n                        
    \n                            {r`E(X) = \\frac{1}{p}`}\n                        
    \n                        
    \n                            La varianza della geometrica è:\n                        
    \n                        
    \n                            {r`Var(X) = \\frac{q}{p^2}`}\n                        
    \n                        \n                    \n                        
    \n                            La geometrica non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n                        
    \n                        
    \n                            {r`P([X = i + j | X > i ]) = P([X = j])`}\n                        
    \n                        \n                            Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli necessarie perchè si verifichi l'n-esimo successo.\n                        
    \n                        
    \n                            Il suo simbolo è {r`\\overline{Bin}(n, p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La binomiale negativa ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{ n .. +\\infty \\} \\in \\mathbb{N} = \\binom{k - 1}{n - 1} \\cdot p^n \\cdot q^{k - n} `}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della binomiale negativa è:\n                            
    \n                            
    \n                                {r`m_X (t) : \\{ t < ln(\\frac{1}{q}) \\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n`}\n                            
    \n                            
    \n                                La media della binomiale negativa è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{n}{p}`}\n                            
    \n                            
    \n                                La varianza della binomiale negativa è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{n \\cdot q}{p^2}`}\n                            
    \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero k di insuccessi consecutivi in uno schema di Bernoulli:\n                        
    \n                        
    \n                            Il suo simbolo rimane {r`Geo(p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La geometrica traslata ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = p \\cdot q^k `}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti della geometrica traslata è:\n                        
    \n                        
    \n                            {r`m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\frac{p}{1 - q \\cdot e^t}`}\n                        
    \n                        
    \n                            La media della geometrica traslata è:\n                        
    \n                        
    \n                            {r`E(X) = \\frac{q}{p}`}\n                        
    \n                        
    \n                            La varianza della geometrica è:\n                        
    \n                        
    \n                            {r`Var(X) = \\frac{q}{p^2}`}\n                        
    \n                        \n                    \n                        
    \n                            La geometrica traslata non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n                        
    \n                        
    \n                            {r`P([X = i + j | X > i ]) = P([X = j])`}\n                        
    \n                        \n                            Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di insuccessi in uno schema di Bernoulli prima che si verifichi l'n-esimo successo.\n                        
    \n                        
    \n                            Il suo simbolo rimane {r`\\overline{Bin}(n, p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La binomiale negativa traslata ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = \\binom{k + n - 1}{n - 1} \\cdot p^n \\cdot q^k `}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della binomiale negativa traslata è:\n                            
    \n                            
    \n                                {r`m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n`}\n                            
    \n                            
    \n                                La media della binomiale negativa traslata è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{n \\cdot q}{p}`}\n                            
    \n                            
    \n                                La varianza della binomiale negativa traslata è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{n \\cdot q}{p^2}`}\n                            
    \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che, sapendo il numero di successi K e di insuccessi N-K, conta quanti successi si otterrebbero se se ne estraessero n in blocco.\n                        
    \n                        
    \n                            Il suo simbolo è Ipe(N, K, n).\n                        
    \n                        \n                    \n                        
    \n                            La ipergeometrica ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{0..n\\} \\in \\mathbb{N} = \\frac{\\binom{K}{k} \\cdot \\binom{N - K}{n - k}}{\\binom{N}{n}}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della ipergeometrica è trascurabile.\n                            
    \n                            
    \n                                La media della ipergeometrica è:\n                            
    \n                            
    \n                                {r`E(X) = n \\cdot \\frac{K}{N}`}\n                            
    \n                            
    \n                                La varianza della ipergeometrica è:\n                            
    \n                            
    \n                                {r`Var(X) = n \\cdot \\frac{K}{N} \\cdot \\frac{N - K}{N} \\cdot \\frac{N - n}{N - 1}`}\n                            
    \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che soddisfa tutte le seguenti caratteristiche:\n                        
    \n                        
      \n                            
    • Binomiale: {r`X \\sim Bin(n, p)`}
      • \n                            
    • Il numero di prove tende a infinito: {r`n \\to +\\infty`}
      • \n                            
    • La probabilità di successo tende a 0: {r`p \\to 0`}
      • \n                            
    • La media è finita: {r`E(X) = n \\cdot p \\to \\mu \\neq 0`}
      • \n                        
    \n                        
    \n                            Il suo simbolo è {r`Poi(\\mu)`}\n                        
    \n                        \n                    \n                        
    \n                            La poissoniana ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = \\frac{e^{-\\mu} \\cdot \\mu^k}{k!}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della poissoniana è:\n                            
    \n                            
    \n                                {r`m_X (t) = e^{\\mu \\cdot (e^t - 1)}`}\n                            
    \n                            
    \n                                La media della poissoniana è:\n                            
    \n                            
    \n                                {r`E(X) = \\mu`}\n                            
    \n                            
    \n                                La varianza della poissoniana è:\n                            
    \n                            
    \n                                {r`Var(X) = \\mu`}\n                            
    \n                            
    \n                                Gli altri momenti della poissoniana sono:\n                            
    \n                            
      \n                                
    1. {r`E(X^2) = \\mu^2 + \\mu`}
      2. \n                            
    \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una successione di arrivi avvenuti in un certo arco temporale che:\n                        
    \n                        
      \n                            
    • non sono sovrapposti.
      • \n                            
    • hanno intensità {r`\\lambda`} costante.
      • \n                            
    • avvengono indipendentemente gli uni dagli altri.
      • \n                        
    \n                        \n                    \n                        
    \n                            Una variabile aleatoria N_t che conta il numero di arrivi di uno schema di Poisson di intensità {r`\\lambda`} in un intervallo di tempo di durata t.\n                        
    \n                        
    \n                            E' una distribuzione poissoniana con {r`\\mu = t \\cdot \\lambda`}: {r`Poi(t \\cdot \\lambda)`}\n                        
    \n                        \n                            E' paragonabile a una bernoulliana: ogni successo corrisponde a un arrivo, mentre il tempo è il numero di prove effettuate (ma nel continuo).\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che conta il tempo diwidehattesa prima del primo arrivo di un processo di Poisson di intensità {r`\\lambda`}.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Esp(\\lambda)`}.\n                        
    \n                        \n                    \n                        
    \n                            L'esponenziale ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                            0 \\qquad \\qquad x < 0\\\\\n                            \\lambda \\cdot e^{-\\lambda \\cdot x} \\quad x > 0\n                            \\end{cases}`}\n                        
    \n                        
    \n                            L'esponenziale ha come funzione di ripartizione:\n                        
    \n                        
    \n                            {r`F_X (t) = \\begin{cases}\n                            0 \\qquad \\qquad t < 0\\\\\n                            1 - e^{-\\lambda \\cdot t} \\quad t \\geq 0\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti dell'esponenziale è:\n                        
    \n                        
    \n                            {r`m_X (t) : \\{ t | t < \\lambda \\} \\in \\mathbb{R} = \\frac{\\lambda}{\\lambda - t}`}\n                        
    \n                        
    \n                            La media dell'esponenziale è:\n                        
    \n                        
    \n                            {r`E(X) = \\frac{1}{\\lambda}`}\n                        
    \n                        
    \n                            La varianza dell'esponenziale è:\n                        
    \n                        
    \n                            {r`Var(X) = \\frac{1}{\\lambda^2}`}\n                        
    \n                        \n                    \n                        
    \n                            L'esponenziale non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n                        
    \n                        
    \n                            {r`P([X > s + t | X > s]) = P([X > t])`}\n                        
    \n                        \n                            Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che conta il tempo diwidehattesa prima dell'n-esimo arrivo di un processo di Poisson di intensità {r`\\lambda`}.\n                        
    \n                        
    \n                            Il suo simbolo è {r`\\Gamma(n, \\lambda)`}.\n                        
    \n                        \n                    \n                        
    \n                            La legge gamma ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                            0 \\qquad \\qquad \\qquad \\qquad \\qquad x < 0\\\\\n                            \\frac{1}{(n-1)!} \\cdot \\lambda^n \\cdot x^{n-1} \\cdot e^{-\\lambda \\cdot x} \\quad k > 0\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della legge gamma è:\n                            
    \n                            
    \n                                {r`m_X (t) : ( t < \\lambda ) \\in \\mathbb{R} = \\left( \\frac{\\lambda}{\\lambda - t} \\right) ^\\alpha`}\n                            
    \n                            
    \n                                La media della legge gamma è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{\\alpha}{\\lambda}`}\n                            
    \n                            
    \n                                La varianza della legge gamma è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{\\alpha}{\\lambda^2}`}\n                            
    \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria che può assumere qualsiasi valore in un intervallo {r`[a, b]`} in modo equiprobabile.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Uni(a, b)`}\n                        
    \n                        
    \n                            Su di essa vale la seguente proprietà:\n                        
    \n                        
    \n                            {r`P(X \\in (c, d)) = \\frac{d - c}{b - a}`}\n                        
    \n                        \n                    \n                        
    \n                            La distribuzione uniforme ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                                \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n                                0 \\qquad \\quad altrimenti    \n                            \\end{cases}`}\n                        
    \n                        
    \n                            La distribuzione uniforme ha come funzione di ripartizione:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                                0 \\qquad \\quad x < a  \n                                \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n                                1 \\qquad \\quad x > b\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della distribuzione uniforme è:\n                            
    \n                            
    \n                                {r`m_X (t) = \\frac{e^{b \\cdot t} - e^{a \\cdot t}}{(b - a) \\cdot t}`}\n                            
    \n                            
    \n                                La media della distribuzione uniforme è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{a + b}{2}`}\n                            
    \n                            
    \n                                La varianza della distribuzione uniforme è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{(b - a)^2}{12}`}\n                            
    \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una variabile aleatoria con una specifica distribuzione.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Nor(\\mu, \\sigma^2)`}.\n                        
    \n                        \n                            \\mu e \\sigma^2 sono rispettivamente la media e la varianza della distribuzione!\n                        \n                        \n                    \n                        
    \n                            La distribuzione normale ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\frac{e^{-\\frac{(x - \\mu)^2}{2 \\sigma^2}}}{\\sqrt{2 \\pi \\cdot \\sigma^2}}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della distribuzione normale è:\n                            
    \n                            
    \n                                {r`m_X (t) = e^{\\mu \\cdot t + \\frac{\\sigma^2 \\cdot t^2}{2}}`}\n                            
    \n                            
    \n                                La media della distribuzione normale è:\n                            
    \n                            
    \n                                {r`E(X) = \\mu`}\n                            
    \n                            
    \n                                La varianza della distribuzione normale è:\n                            
    \n                            
    \n                                {r`Var(X) = \\sigma^2`}\n                            
    \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Qualsiasi normale può essere trasformata in qualsiasi altra normale:\n                        
    \n                        
    \n                            {r`X \\sim Nor(m, v^2) \\implies \\alpha X + \\beta \\sim Nor(\\alpha m + \\beta, (\\alpha v)^2)`}\n                        
    \n                        \n                    \n                        
    \n                            La distribuzione normale standard Z è:\n                        
    \n                        
    \n                            Z \\sim Nor(0, 1)\n                        
    \n                        
    \n                            La sua funzione di ripartizione è detta {r`\\phi(z)`} e vale:\n                        
    \n                        
    \n                            {r`F_Z(z) = \\phi(z) = \\frac{1}{\\sqrt{2 \\pi}} \\int_{-\\infty}^{z} e^{-\\frac{x^2}{2}} dx`}\n                        
    \n                        \n                    \n                        
    \n                            Da un quantile {r`z_\\alpha`} della normale standard è possibile risalire allo stesso quantile di qualsiasi altra normale:\n                        
    \n                        
    \n                            {r`x_\\alpha = \\mu + z_\\alpha \\cdot \\sqrt{\\sigma^2}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            La distribuzione normale ha una particolare relazione con la distribuzione Gamma:\n                        
    \n                        
    \n                            {r`Z^2 \\sim \\chi^2 (v = 1)`}\n                        
    \n                        \n                    \n                        
    \n                            \"chi-quadro a un grado di libertà\"\n                        
    \n                        
    \n                            Esiste una distribuzione Gamma particolare:\n                        
    \n                        
    \n                            {r`\\Gamma \\left( \\frac{1}{2}, \\frac{1}{2} \\right) = \\chi^2 (v = 1)`}\n                        
    \n                        
    \n                            Più chi-quadro possono essere sommate per aumentare i loro gradi di libertà:\n                        
    \n                        
    \n                            {r`\\chi^2 (n) + \\chi^2 (m) = \\chi^2 (n + m)`}\n                        
    \n                        \n                    \n                        
    \n                            Un'altra funzione particolare è la funzione T di Student:\n                        
    \n                        
    \n                            {r`T(v) = \\frac{Nor(0, 1)}{\\sqrt{\\frac{\\chi^2(v)}{v}}}`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            La binomiale è come una ipergeometrica ma con ripetizioni, quindi per valori molto grandi di N rispetto a n, si può dire che:\n                        
    \n                        
    \n                            {r`Ipe(N, K, n) \\approx Bin(n, \\frac{K}{N})`}\n                        
    \n                        \n                    \n                        
    \n                            La binomiale non è altro che una poissoniana a tempo discreto, quindi, se n è grande e n \\cdot p è nell'ordine di grandezza delle unità, allora:\n                        
    \n                        
    \n                            {r`Bin(n, p) \\approx Poi(n \\cdot p)`}\n                        
    \n                        \n                    \n                        
    \n                            Per il Teorema di De Moivre-Laplace, se una binomiale ha una n grande e p non vicina a 0 o 1, si può approssimare con:\n                        
    \n                        
    \n                            {r`Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)`}\n                        
    \n                        \n                    \n                        
    \n                            Passando da una variabile discreta X a una continua Y, per ogni valore discreto k la probabilità viene \"spalmata\" su tutto l'intervallo {r`(k - \\frac{1}{2}, k + \\frac{1}{2})`}:\n                        
    \n                        
      \n                            
    • {r`P(X < k) \\simeq P(Y \\leq k - \\frac{1}{2})`}
      • \n                            
    • {r`P(X \\leq k) \\simeq P(Y \\leq k + \\frac{1}{2})`}
      • \n                            
    • {r`P(X \\geq k) \\simeq P(Y \\geq k - \\frac{1}{2})`}
      • \n                            
    • {r`P(X > k) \\simeq P(Y \\geq k + \\frac{1}{2})`}
      • \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Un vettore composto da variabili aleatorie.\n                        
    \n                        
    \n                            Il suo simbolo generalmente è {r`\\boldsymbol{X}`} oppure {r`X, Y`}.\n                        
    \n                        \n                    \n                        
    \n                            I vettori aleatori hanno più funzioni di ripartizione che si differenziano in base al numero di parametri.\n                        
    \n                        
    \n                            Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una funzione di ripartizione congiunta:\n                        
    \n                        
    \n                            {r`F_{X, Y} (x, y) = P(X \\leq x, Y \\leq y)`}\n                        
    \n                        
    \n                            Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una funzione di ripartizione marginale:\n                        
    \n                        
    \n                            {r`F_X (x) = P(X \\leq x) = \\lim_{y \\to +\\infty} F_{X, Y} (x, y)`}\n                        
    \n                        \n                    \n                        
    \n                            I vettori aleatori discreti hanno più densità che si differenziano in base al numero di parametri.\n                        
    \n                        
    \n                            Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una densità congiunta:\n                        
    \n                        
    \n                            {r`p_{X, Y} (x, y) = P(X = x, Y = y)`}\n                        
    \n                        
    \n                            Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una densità marginale:\n                        
    \n                        
    \n                            {r`p_X (x) = \\sum_j p_{X, Y} (x_i, y_j)`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Più variabili aleatorie sono indipendenti se, per qualsiasi scelta di intervalli A_i:\n                        
    \n                        
    \n                            {r`P(X_1 \\in A_1, \\dots, X_n \\in A_n) = P(X_1 \\in A_1) \\times \\dots \\times P(X_n \\in A_n)`}\n                        
    \n                        \n                    \n                        
    \n                            E' possibile calcolare la media di qualsiasi funzione g(X, Y) avente elementi del vettore come variabili:\n                        
    \n                        
    \n                            {r`E(g(X, Y)) = \\sum_{i, j} g(x_i, y_i) \\cdot p_{X, Y} (x_i, y_i)`}\n                        
    \n                        \n                            Solitamente si calcola la media di x \\cdot y.\n                        \n                        
    \n                            Le medie di più variabili aleatorie si possono sommare:\n                        
    \n                        
    \n                            {r`E(X + Y) = E(X) + E(Y)`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Un operatore che misura la correlazione di due variabili aleatorie.\n                        
    \n                        
    \n                            Si calcola con il valore atteso dei prodotti delle distanze dalla media:\n                        
    \n                        
    \n                            {r`Cov(X, Y) = E((X - E(X) \\cdot (Y - E(Y)) = E(XY) - E(X) \\cdot E(Y)`}\n                        
    \n                        
    \n                            Ha diverse proprietà:\n                        
    \n                        
      \n                            
    • Il suo valore nullo è 0: {r`Cov(X, \\alpha) = 0`}
      • \n                            
    • E' commutativa: {r`Cov(X, Y) = Cov(Y, X)`}
      • \n                            
    • E' semplificabile: {r`Cov(X, X) = Var(X)`}
      • \n                            
    • E' lineare: {r`Cov(\\alpha X, \\beta Y) = \\alpha \\cdot \\beta \\cdot Cov(X, Y)`}
      • \n                            
    • E' distributiva: {r`Cov(X + Y, V + W) = Cov(X, Y) + Cov(X, W) + Cov(Y, V) + Cov(Y, W)`}
      • \n                        
    \n                        \n                    \n                        
    \n                            Due variabili sono variabili incorrelate se:\n                        
    \n                        
    \n                            {r`Cov(X, Y) = 0`}\n                        
    \n                        
    \n                            Variabili indipendenti sono sempre incorrelate.\n                        
    \n                        \n                    \n                        
    \n                            Una matrice {r`\\boldsymbol{C_X}`} che contiene la covarianza tra tutte le variabili di un vettore aleatorio {r`\\boldsymbol{X}`}:\n                        
    \n                        
    \n                            {r`\n                                \\boldsymbol{C_X} = \n                                \\begin{bmatrix}\n                                    Var(X_1) & Cov(X_1, X_2) & Cov(X_1, X_3)\\\\\n                                    Cov(X_2, X_1) & Var(X_2) & Cov(X_2, X_3)\\\\\n                                    Cov(X_3, X_1) & Cov(X_3, X_2) & Var(X_3)\n                                \\end{bmatrix}\n                            `}\n                        
    \n                        
    \n                            E' sempre simmetrica e semidefinita positiva (tutti gli autovalori sono \\geq 0.\n                        
    \n                        \n                    \n                        
    \n                            Un valore che misura come due variabili aleatorie sono correlate:\n                        
    \n                        
    \n                            {r`\\rho_{X, Y} = \\frac{Cov(X, Y)}{\\sqrt{Var(X)} \\cdot \\sqrt{Var(Y)}}`}\n                        
    \n                        
    \n                            E' sempre compreso tra -1 e 1:\n                        
    \n                        
    \n                            {r`-1 \\leq \\rho_{X, Y} \\leq 1`}\n                        
    \n                        
    \n                            Vale esattamente -1 o 1 solo se esiste un legame lineare tra le due variaibli:\n                        
    \n                        
    \n                            {r`Y = a X + b \\Longleftrightarrow | \\rho_{X, Y} | = 1`}\n                        
    \n                        \n                    \n                        
    \n                            La varianza di due variabili aleatorie sommate è:\n                        
    \n                        
    \n                            {r`Var(X + Y) = Var(X) + Var(Y) + 2 \\cdot Cov(X, Y)`}\n                        
    \n                        \n                            Si dimostra applicando le proprietà della covarianza!\n                        \n                        
    \n                            Se più variabili aleatorie X_i sono indipendenti ({r`Cov(X, Y) = 0`}), allora:\n                        
    \n                        
    \n                            {r`Var \\left( \\sum_i X_i \\right) = \\sum_i Var(X_i)`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una n-pla di variabili aleatorie con la stessa distribuzione della variabile aleatoria X (\"popolazione\") ma indipendenti tra loro.\n                        
    \n                        \n                            Le variabili aleatorie sono come un lazy-load in programmazione; quando ci sarà bisogno del loro valore numerico, esse si realizzeranno nel loro valore.\n                        \n                        \n                    \n                        
    \n                            Il valore dato dalla media aritmetica degli n elementi del campione elevati alla potenza k:\n                        
    \n                        
    \n                            {r`M^{(k)}_n = \\frac{1}{n} \\cdot \\sum_{i = 1}^n X_i^k `}\n                        
    \n                        
    \n                            Il momento campionario di primo ordine è la media campionaria {r`\\overline{X}_n`}.\n                        
    \n                        \n                    \n                        
    \n                            La media aritmetica dello scarto quadratico medio degli elementi del campione.\n                        
    \n                        
    \n                            Se è noto il valore medio {r`m = E(X)`} di X:\n                        
    \n                        
    \n                            {r`S_0^2 = \\frac{1}{n} \\cdot \\sum_{i = 1}^n (X_i - m)^2 = M_n^(2) - 2 \\cdot m \\cdot \\overline{X}_n + m^2`}\n                        
    \n                        
    \n                            Altrimenti:\n                        
    \n                        
    \n                            {r`S_n^2 = \\frac{1}{n - 1} \\cdot \\sum_{i = 1}^n (X_i - \\overline{X}_n)^2 = \\frac{1}{n - 1} \\cdot ( n \\cdot M_2^{(2)} - n \\cdot \\overline{X}_n^2)`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Se calcoliamo la media della media campionaria, risulterà vero che:\n                        
    \n                        
    \n                            {r`E(\\overline{X}_n) = E(X)`}\n                        
    \n                        \n                            Quindi, è possibile usare i campioni per trovare la media di una variabile aleatoria!\n                        \n                        \n                    \n                        
    \n                            Se calcoliamo la varianza della media campionaria, risulterà vero che:\n                        
    \n                        
    \n                            {r`Var(\\overline{X}_n) = \\frac{Var(X)}{n}`}\n                        
    \n                        \n                            Quindi, possiamo stimare l'errore della media calcolata tramite campioni!\n                        \n                        \n                    \n                        
    \n                            Se calcoliamo la media della varianza campionaria, risulterà vero che:\n                        
    \n                        
    \n                            {r`E(S_0^2) = E(S_n^2) = Var(X)`}\n                        
    \n                        \n                            Quindi, possiamo stimare l'errore della media calcolata tramite campioni!\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Se la popolazione X ha una distribuzione normale ({r`X \\sim Nor(\\mu, \\sigma^2)`})...\n                        
    \n                        \n                    \n                        
    \n                            ...allora sappiamo anche la distribuzione della media campionaria!\n                        
    \n                        
    \n                            {r`\\overline{X}_n \\sim Nor \\left( \\mu, \\frac{\\sigma^2}{n} \\right)`}\n                        
    \n                        \n                    \n                        
    \n                            ...e anche della varianza campionaria!\n                        
    \n                        
    \n                            {r`S_0^2 \\sim \\frac{\\sigma^2}{n} \\cdot \\chi^2 (n)`}\n                        
    \n                        
    \n                            {r`S_n^2 \\sim \\frac{\\sigma^2}{n - 1} \\cdot \\chi^2 (n-1)`}\n                        
    \n                        \n                    \n                        
    \n                            ...e che media campionaria e varianza campionaria sono indipendenti tra loro!\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la stessa funzione di ripartizione della popolazione X, allora essa converge in distribuzione.\n                        
    \n                        
    \n                            {`\\\\lim_{n \\\\to +\\\\infty} F_{X_n} (x) = F_X (x) \\\\implies X_n \\\\xrightarrow{d} X`}\n                        
    \n                        \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la stessa probabilità della popolazione X, allora essa converge in probabilità.\n                        
    \n                        
    \n                            {`\\\\forall \\\\epsilon > 0, \\\\lim_{n \\\\to +\\\\infty} P( | X_n - X | < \\\\epsilon) = 1 \\\\implies X_n \\\\xrightarrow{p} X`}\n                        
    \n                        \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la stessa probabilità a  della popolazione X, allora essa converge quasi certamente.\n                        
    \n                        
    \n                            {`\\\\forall \\\\epsilon > 0, P \\left( \\\\lim_{n \\\\to +\\\\infty} | X_n - X | < \\\\epsilon) \\right) = 1 \\\\implies X_n \\\\xrightarrow{qc} X`}\n                        
    \n                        \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la media del quadrato della distanza tra la successione e la popolazione X uguale a 0, allora essa converge in media quadratica.\n                        
    \n                        
    \n                            {`\\\\lim_{n \\\\to +\\\\infty} E( | X_n - X |^2 = 0 \\\\implies X_n \\\\xrightarrow{mq} X`}\n                        
    \n                        \n                    \n                        
    \n                            {`\n                                \\\\begin{matrix}\n                                X_n \\\\xrightarrow{mq} X\\\\\\\\\n                                X_n \\\\xrightarrow{qc} X\n                                \\\\end{matrix} \\\\implies X_n \\\\xrightarrow{p} X \\\\implies X_n \\\\xrightarrow{d} X`\n                            }\n                        
    \n                        
    \n                            In più:\n                        
    \n                        
    \n                            {`X_n \\\\xrightarrow{p} x \\\\Longleftrightarrow X_n \\\\xrightarrow{d} x`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            La successione delle medie campionarie {r`\\overline{X}_n`} converge in probabilità alla media della popolazione {r`E(X)`}, se essa esiste.\n                        
    \n                        
    \n                            {`\\\\overline{X}_n \\\\xrightarrow{p} X`}\n                        
    \n                        
    \n                            Ovvero:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | \\overline{X}_n - E(X) | < \\epsilon) = 1`}\n                        
    \n                        
    \n                            {r`P( | \\overline{X}_n - E(X) | < \\epsilon) \\to 1`}\n                        
    \n                        \n                    \n                        
    \n                            La successione delle medie campionarie {r`\\overline{X}_n`} converge quasi certamente alla media della popolazione {r`E(X)`}, se essa esiste.\n                        
    \n                        
    \n                            {`\\\\overline{X}_n \\\\xrightarrow{qc} X`}\n                        
    \n                        
    \n                            Ovvero:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, P \\left( \\lim_{n \\to +\\infty} | \\overline{X}_n - E(X) | < \\epsilon \\right) = 1`}\n                        
    \n                        \n                            Dimostra che l'interpretazione frequentista della probabilità è valida!\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            La successione delle medie campionarie {r`\\overline{X}_n`} converge in distribuzione a {r`Nor(0, 1) = \\Phi()`}.\n                        
    \n                        
    \n                            {r`\\overline{X}_n \\approx Nor \\left(E(X), \\frac{Var(X)}{n} \\right)`}\n                        
    \n                        
    \n                            Ovvero:\n                        
    \n                        
    \n                            {r`\\forall x \\in \\mathbb{R}, \\lim_{n \\to +\\infty} P \\left( \\frac{\\overline{X}_n - E(X)}{\\sqrt{\\frac{Var(X)}{n}}} \\leq x \\right) = \\Phi(x)`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            E' una somma di bernoulliane, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)`}\n                        
    \n                        \n                    \n                        
    \n                            E' una somma di geometriche, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`\\overline{Bin} (n, p) \\approx Nor \\left( \\frac{n}{p}, \\frac{n \\cdot (1 - p)}{p^2} \\right)`}\n                        
    \n                        \n                    \n                        
    \n                            E' una somma di altre poissoniane, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`Poi(\\lambda) \\approx Nor(\\lambda, \\lambda)`}\n                        
    \n                        \n                    \n                        
    \n                            E' una somma di esponenziali, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`\\Gamma (\\alpha, \\lambda) \\approx Nor \\left( \\frac{\\alpha}{\\lambda}, \\frac{\\alpha}{\\lambda^2} \\right)`}\n                        
    \n                        \n                    \n                        
    \n                            Se n è grande, allora:\n                        
    \n                        
    \n                            {r`Y = \\sum_{i=1}^{n} X_i`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Per indicare parametri sconosciuti di una legge si usa \\theta.\n                        
    \n                        \n                    \n                        
    \n                            Una variabile aleatoria funzione di un campione:\n                        
    \n                        
    \n                            {r`T(\\boldsymbol{X})`}\n                        
    \n                        \n                            Ad esempio, sono statistiche media e varianza campionaria, così come il campione stesso {r`T(\\boldsymbol{X}) = \\boldsymbol{X}`}.\n                        \n                        \n                
    \n                
    \n                    \n                        
    \n                            Una statistica T_n ottenuta da n osservazioni, che stimi i parametri di una legge e sia indipendente da essi.\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è corretto se il suo valore atteso coincide con quello dei parametri che stima:\n                        
    \n                        
    \n                            {r`E(T_n) = \\theta`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è asintoticamente corretto se, per infinite osservazioni, il suo valore atteso coincide con quello dei parametri che stima:\n                        
    \n                        
    \n                            {r`\\lim_{n \\to +\\infty} E(T_n) = \\theta`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è consistente in media quadratica se:\n                        
    \n                        
    \n                            {r`\\lim_{n \\to +\\infty} E((T_n - \\theta)^2) = 0`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è consistente in probabilità se:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( |T_n - \\theta| < \\epsilon) = 1`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è asintoticamente normale se:\n                        
    \n                        
    \n                            {r`\\lim_{n \\to +\\infty} \\frac{T_n - E(T_n)}{\\sqrt{Var(T_n)}} \\sim Nor(0, 1)`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Si può usare il metodo dei momenti per ottenere uno stimatore di una popolazione X.\n                        
    \n                        
    \n                            Lo stimatore di {r`\\theta`} così ottenuto sarà indicato aggiungendo un cappellino e una M a \\theta: {r`\\widehat{\\theta}_M`}\n                        
    \n                        
    \n                            Visto che:\n                        
    \n                        
      \n                            
    • {r`\\theta = g(E(X))`}
      • \n                            
    • {r`\\widehat{E(X)} = \\overline{X}_n`}
      • \n                        
    \n                        
    \n                            Allora:\n                        
    \n                        
    \n                            {r`\\widehat{\\theta}_M = g( \\overline{X}_n )`}\n                        
    \n                        
    \n                            Se {r`\\theta`} non è esprimibile in termini di {r`E(X)`}, si possono usare i momenti successivi {r`M_n^2`}, {r`M_n^3`}, {r`M_n^3`}...\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Si può usare il metodo della massima verosomiglianza per ottenere uno stimatore di una popolazione X.\n                        
    \n                        
    \n                            Lo stimatore di {r`\\theta`} così ottenuto sarà indicato aggiungendo un cappellino e una L a \\theta: {r`\\widehat{\\theta}_L`}\n                        
    \n                        
    \n                            Consiste nel trovare il massimo assoluto {r`\\widehat{\\theta}_L`} della la funzione di verosomiglianza {r`L`}:\n                        
    \n                        
    \n                            {r`L(x_1, ..., x_n; \\theta) = \\prod_{i=1}^n f_X(x_i; \\theta)`}\n                        
    \n                        
    \n                            Gli stimatori di massima verosomiglianza sono asintoticamente corretti, consistenti in probabilità e asintoticamente normali.\n                        
    \n                        \n                    \n                        
    \n                            Gli stimatori di massima verosomiglianza godono delle seguenti proprietà:\n                        
    \n                        
      \n                            
    • Sono asintoticamente corretti.
      • \n                            
    • Sono consistenti in probabilità.
      • \n                            
    • Sono asintoticamente normali.
      • \n                            
    • Sono invarianti: {r`\\widehat{g(\\theta)}_L = g(\\widehat{\\theta}_L)`}
      • \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n                        
    \n                        
    \n                            {r`\\widehat{p}_M = \\widehat{p}_L = \\overline{X}_n`}\n                        
    \n                        \n                    \n                        
    \n                            Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n                        
    \n                        
    \n                            {r`\\widehat{\\mu}_M = \\widehat{\\mu}_L = \\overline{X}_n`}\n                        
    \n                        \n                    \n                        
    \n                            Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n                        
    \n                        
    \n                            {r`\\widehat{\\lambda}_M = \\widehat{\\lambda}_L = \\frac{1}{\\overline{X}_n}`}\n                        
    \n                        \n                    \n                        
    \n                            Per il metodo della massima verosomiglianza:\n                        
    \n                        
      \n                            
    • {r`\\widehat{\\mu}_L = \\overline{X}_n`}

      • \n                            
    • {r`\\widehat{\\sigma^2}_L = \\frac{\\sum (X_i - \\overline{X}_n)^2 }{n}`}
      • \n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            \"intervallo di confidenza al 95%\"\n                        
    \n                        
    \n                            L'intervallo di valori di \\theta all'interno del quale siamo \"più o meno sicuri\" si trovi il valore effettivo:\n                        
    \n                        
    \n                            L'intervallo di confidenza a N della stima {r`\\widehat{W}`} è l'intervallo ]a, b[ tale che:\n                        
    \n                        
    \n                            {r`P( a < W < b ) = N`}\n                        
    \n                        
    \n                            Può anche essere unilatero nel caso limiti la stima in una sola direzione, positiva o negativa.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            Se conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'\\alpha% con queste formule:\n                        
    \n                        
      \n                            
    • Intervalli bilateri: {r`\\mu \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}}, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da sinistra: {r`\\mu \\in \\left( -\\infty, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da destra: {r`\\mu \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}}, +\\infty \\right)`}
      • \n                        
    \n                        \n                    \n                        
    \n                            Se non conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'\\alpha% con queste formule:\n                        
    \n                        
      \n                            
    • Intervalli bilateri: {r`\\mu \\in \\left[ \\overline{x}_n - t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}}, \\overline{x}_n + t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da sinistra: {r`\\mu \\in \\left( -\\infty, \\overline{x}_n + t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da destra: {r`\\mu \\in \\left[ \\overline{x}_n - t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}}, +\\infty \\right)`}
      • \n                        
    \n                        
    \n                            {r`t_{\\alpha, v}`} è un quantile della distribuzione di Student di parametro v.\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            L'intervallo di confidenza per la proprorzione di una bernoulliana qualsiasi si ottiene da questa formula:\n                        
    \n                        
    \n                            {r`p \\in \\left[ \\overline{p} - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\overline{p} \\cdot (1 - \\overline{p})}{n+4}}, \\overline{p} + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\overline{p} \\cdot (1 - \\overline{p})}{n+4}} \\right]`}\n                        
    \n                        \n                
    \n                
    \n                    \n                        
    \n                            L'intervallo di confidenza per la media di una qualsiasi popolazione si ottiene da questa formula:\n                        
    \n                        
    \n                            {r`m \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{s^2_n}{n}}, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{s^2_n}{n}} \\right]`}\n                        
    \n                        \n                
    \n            
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diff --git a/docs/route-Statistica.chunk.04c26.esm.js b/docs/route-Statistica.chunk.86883.esm.js
similarity index 99%
rename from docs/route-Statistica.chunk.04c26.esm.js
rename to docs/route-Statistica.chunk.86883.esm.js
index 23af883..1cfd9be 100644
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contenuto in effe"'),l("p",null,"L'",l("b",null,"inclusione")," del primo insieme in un altro."),l("p",null,l(a.b,null,te(z||(z=ee`E \subseteq F`)))),l("p",null,"Se si verifica ",l(a.b,null,"E"),", allora si verifica anche ",l(a.b,null,"F"),".")),l(e.a,{title:"Evento impossibile"},l("blockquote",null,'"e è impossibile"'),l("p",null,"Un sottoinsieme ",l("b",null,"vuoto"),"."),l("p",null,l(a.b,null,te(X||(X=ee`E = \emptyset`))))),l(e.a,{title:"Mutua esclusione"},l("blockquote",null,'"e ed effe si escludono mutualmente"'),l("p",null,"La ",l("b",null,"disgiunzione")," di due insiemi."),l("p",null,l(a.b,null,te(q||(q=ee`E \cap F = \emptyset`)))))),l(t.a,null,l(e.a,{title:"Famiglia degli eventi"},l("blockquote",null,'"famiglia effe"'),l("p",null,"I sottoinsiemi dello spazio campionario formano una ",l("b",null,"famiglia")," di sottoinsiemi detta ",l("i",null,"famiglia degli eventi"),"."),l("p",null,l(a.b,null,te(E||(E=ee`\mathcal{F}`)))),l("p",null,"Qualsiasi sottoinsieme appartenente a ",l(a.b,null,te(L||(L=ee`\mathcal{F}`)))," è considerato un evento.")),l(e.a,{title:l("span",null,l(a.b,null,te(P||(P=ee`\sigma`))),"-algebra")},l("blockquote",null,'"sigma algebra"'),l("p",null,"Se la famiglia degli eventi soddisfa questi tre requisiti, allora viene detta ",l("i",null,l(a.b,null,te(x||(x=ee`\sigma`))),"-algebra"),":"),l("ol",null,l("li",null,"Lo spazio campionario è un evento: ",l(a.b,null,te(k||(k=ee`\Omega \in \mathcal{F}`)))),l("li",null,"Se un sottoinsieme è un evento, allora anche il suo complementare lo è: ",l(a.b,null,te(F||(F=ee`E \in \mathcal{F} \implies \bar{E} \in \mathcal{F}`)))),l("li",null,"Se due sottoinsiemi sono eventi, allora lo sono anche la loro unione e intersezione: ",l(a.b,null,te(y||(y=ee`(E, F) \in \mathcal{F} \implies (E \cup F, E \cap F) \in \mathcal{F}`))))),l("p",null,"Un esempio: ",l(a.b,null,te(S||(S=ee`E \in \mathcal{F} \implies \mathcal{F} = \{ \emptyset, E, \bar{E}, \Omega \}`)))))),l(t.a,null,l(e.a,{title:"Partizione"},l("blockquote",null,'"la partizione e composta da e uno, e due, e tre..."'),l("p",null,"Un insieme di esiti e eventi:"),l("ul",null,l("li",null,l("b",null,"Finito"),"."),l("li",null,"In cui tutti gli eventi hanno ",l("b",null,"probabilità diversa da 0"),"."),l("li",null,"In cui tutti gli eventi sono ",l("b",null,"mutualmente esclusivi"),"."),l("li",null,"In cui l'unione di tutti i suoi elementi ",l("b",null,"copre lo spazio campionario"),".")),l("p",null,"La partizione ",l(a.b,null,te(N||(N=ee`E_i`)))," è composta dagli eventi ",l(a.b,null,te(C||(C=ee`E_1`))),", ",l(a.b,null,te(V||(V=ee`E_2`))),", ",l(a.b,null,te(I||(I=ee`E_3`))),", fino a ",l(a.b,null,te(Y||(Y=ee`E_n`))),"."),l(o.a,null,"Se lo spazio campionario fosse una torta, una sua partizione sarebbe l'insieme delle fette di uno dei modi in cui si potrebbe tagliare."))),l(t.a,{title:"Assiomi della probabilità"},l(e.a,{title:"Primo assioma della probabilità"},l("p",null,"La probabilità di un evento è un numero tra 0 e 1."),l("p",null,l(a.b,null,te(w||(w=ee`\forall E \in \mathcal{F}, 0 \leq P(E) \leq 1`))))),l(e.a,{title:"Secondo assioma della probabilità"},l("p",null,"La probabilità dello spazio campionario è sempre 1."),l("p",null,l(a.b,null,te(D||(D=ee`P(\Omega) = 1`))))),l(e.a,{title:"Terzo assioma della probabilità"},l("p",null,"La probabilità dell'unione di eventi indipendenti è uguale alla somma delle loro probabilità."),l("p",null,l(a.b,null,te(U||(U=ee`P \left ( \bigcup_i E_i \right ) = \sum_i P ( E_i )`)))))),l(t.a,{title:"Conseguenze degli assiomi"},l(e.a,{title:"Probabilità di un evento negato"},l("p",null,"La probabilità di un evento negato è uguale a 1 meno la probabilità dell'evento non negato."),l("p",null,l(a.b,null,te(M||(M=ee`P(\bar{E}) = 1 - P({E})`))))),l(e.a,{title:"Probabilità di un evento incluso"},l("p",null,"La probabilità di un evento incluso in un altro è sempre minore o uguale alla probabilità dell'evento in cui è incluso."),l("p",null,l(a.b,null,te(A||(A=ee`F \subseteq E \implies P(F) \leq P(E)`))))),l(e.a,{title:"Unione"},l("p",null,"La probabilità di un evento unito a un altro è uguale alla somma delle probabilità dei due eventi meno la probabilità della loro intersezione."),l("p",null,l(a.b,null,te(T||(T=ee`P(E \cup F) = P(E) + P(F) - P(E \cap F)`)))),l(o.a,null,"Sommando le probabilità dei due eventi, l'intersezione viene contata due volte, e va quindi rimossa!"))),l(t.a,{title:"Spazi equiprobabili"},l(e.a,{title:"Cosa sono?"},l("p",null,"Spazi campionari in cui ci sono un numero finito di esiti e ogni esito ha la stessa probabilità di verificarsi."),l("p",null,l(a.b,null,te(B||(B=ee`P(E) = \frac{len(E)}{len(\Omega)}`))))),l(e.a,{title:"Spazi equiprobabili geometrici"},l("p",null,"Gli spazi campionari possono avere un numero infinito di esiti: sono ",l("i",null,"equiprobabili geometrici")," se nessun esito è privilegiato rispetto agli altri."))),l(t.a,{title:"Calcolo combinatorio"},l(e.a,{title:"Disposizioni"},l("p",null,"Estraggo un numero, da un sacchetto con ",l(a.b,null,"n")," numeri, mi segno che numero ho estratto e lo ",l("b",null,"tengo fuori dal sacchetto"),". Ripeto per ",l(a.b,null,"k")," volte."),l("p",null,l("b",null,"Tengo conto")," dell'ordine in cui ho estratto i numeri."),l("p",null,l(a.b,null,te(O||(O=ee`\boldsymbol{D}_{n, k} = \frac{n!}{(n - k)!}`))))),l(e.a,{title:"Disposizioni con ripetizione"},l("p",null,"Estraggo un numero, da un sacchetto con ",l(a.b,null,"n")," numeri, mi segno che numero ho estratto e lo ",l("b",null,"rimetto nel sacchetto"),". Ripeto per ",l(a.b,null,"k")," volte."),l("p",null,l("b",null,"Tengo conto")," dell'ordine in cui ho estratto i numeri."),l("p",null,l(a.b,null,te(G||(G=ee`\boldsymbol{D}^{r}_{n, k} = n^k`))))),l(e.a,{title:"Combinazioni"},l("p",null,"Estraggo un numero, da un sacchetto con ",l(a.b,null,"n")," numeri, mi segno che numero ho estratto e lo ",l("b",null,"tengo fuori dal sacchetto"),". Ripeto per ",l(a.b,null,"k")," volte."),l("p",null,l("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),l("p",null,l(a.b,null,te(H||(H=ee`\boldsymbol{C}_{n, k} = \binom{n}{k} = \frac{n!}{(k)! \cdot (n - k)!}`))))),l(e.a,{title:"Combinazioni con ripetizione"},l("p",null,"Estraggo un numero, da un sacchetto con ",l(a.b,null,"n")," numeri, mi segno che numero ho estratto e lo ",l("b",null,"rimetto nel sacchetto"),". Ripeto per ",l(a.b,null,"k")," volte."),l("p",null,l("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),l("p",null,l(a.b,null,te(R||(R=ee`\boldsymbol{C}^{r}_{n, k} = \binom{n + k - 1}{k} = \frac{(n + k - 1)!}{(k)! \cdot (n - 1)!}`))))),l(e.a,{title:"Permutazioni"},l("p",null,"Estraggo ",l(a.b,null,"n")," numeri e guardo in quanti ordini diversi li posso mettere."),l("p",null,l(a.b,null,te(j||(j=ee`\boldsymbol{P}_n = n!`)))))),l(t.a,{title:"Probabilità condizionata"},l(e.a,{title:"Eventi condizionati"},l("blockquote",null,'"E dato F"'),l("p",null,"La probabilità che si verifichi ",l(a.b,null,"E")," sapendo che ",l("b",null,"si è già verificato")," ",l(a.b,null,"F"),"."),l("p",null,l(a.b,null,te(Q||(Q=ee`P(E|F) = \frac{P(E \cap F)}{P(F)}`)))),l(o.a,null,"Ricorda vagamente le pipe di ",l("code",null,"bash"),", però al contrario...")),l(e.a,{title:"Eventi mutualmente esclusivi"},l("p",null,"Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0."),l("p",null,l(a.b,null,te(W||(W=ee`E \cap F = \emptyset \Longleftrightarrow P(E|F) = P(F|E) = 0`)))))),l(t.a,null,l(e.a,{title:"Regola della catena"},l("p",null,"Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:"),l("p",null,l(a.b,null,te(K||(K=ee`P(E_1 \cap \times \cap E_n) = P(E_1) \times P(E_2 | E_1) \times \dots \times P(E_n | E_1 \cap E_2 \cap \dots \cap E_{n-1})`)))))),l(t.a,{title:"Le alternative"},l(e.a,{title:"Legge delle alternative"},l("p",null,"La probabilità che si verifichi un evento è pari alla somma delle probabilità dell'evento stesso dati tutti gli eventi di una partizione."),l("p",null,l(a.b,null,te(J||(J=ee`P(F) = \sum_{i} P(F|E_i) \cdot P(E_i)`))))),l(e.a,{title:"Legge condizionata delle alternative"},l("p",null,"La legge delle alternative funziona anche quando ad essere partizionato è un ",l("b",null,"evento"),":"),l("p",null,l(a.b,null,te(Z||(Z=ee`P(F|G) = \sum_i P(F|E_i \cap G) \cdot P(E_i | G)`))))),l(e.a,{title:"Formula di Bayes"},l("p",null,"Tramite la ",l("i",null,"formula di Bayes")," possiamo risalire alla probabilità di un evento condizionato a un altro partendo dalla probabilità di quest'ultimo condizionato al primo:"),l("p",null,l(a.b,null,te($||($=ee`P(E_h | F) = \frac{P(F | E_h) \cdot P(E_h)}{P(F)}`)))),l(o.a,null,"In pratica, invertiamo gli eventi."))),l(t.a,{title:"Eventi indipendenti"},l(e.a,{title:"Due eventi indipendenti"},l("blockquote",null,'"eventi indipendenti a due a due"'),l("p",null,"Se due eventi sono indipendenti, sapere che uno dei due si è verificato non influisce sulle probabilità che si sia verificato l'altro."),l("p",null,l(a.b,null,te(ll||(ll=ee`P(E \cap F) = P(E) \cdot P(F) \Longleftrightarrow P(E|F) = P(E) \Longleftrightarrow P(F|E) = P(F)`))))),l(e.a,{title:"Più eventi indipendenti"},l("blockquote",null,'"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque..."'),l("p",null,"Si può verificare l'indipendenza di più eventi alla volta:"),l("p",null,l(a.b,null,te(il||(il=ee`P(E \cap F \cap G) = P(E) \cdot P(F) \cdot P(G)`)))),l("p",null,"Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.")),l(e.a,{title:"Famiglia di eventi indipendenti"},l("p",null,"Un insieme di ",l(a.b,null,"n")," eventi è una ",l("i",null,"famiglia di eventi indipendenti")," se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti."),l(o.a,null,"Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e così via!"))),l(t.a,{title:"Variabili aleatorie"},l(e.a,{title:"Variabile aleatoria"},l("p",null,"Una funzione che fa corrispondere un numero reale a ogni possibile esito dello spazio campionario. 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Ripeto per ",l(a.b,null,"k")," volte."),l("p",null,l("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),l("p",null,l(a.b,null,te(H||(H=ee`\boldsymbol{C}_{n, k} = \binom{n}{k} = \frac{n!}{(k)! \cdot (n - k)!}`))))),l(e.a,{title:"Combinazioni con ripetizione"},l("p",null,"Estraggo un numero, da un sacchetto con ",l(a.b,null,"n")," numeri, mi segno che numero ho estratto e lo ",l("b",null,"rimetto nel sacchetto"),". Ripeto per ",l(a.b,null,"k")," volte."),l("p",null,l("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),l("p",null,l(a.b,null,te(R||(R=ee`\boldsymbol{C}^{r}_{n, k} = \binom{n + k - 1}{k} = \frac{(n + k - 1)!}{(k)! \cdot (n - 1)!}`))))),l(e.a,{title:"Permutazioni"},l("p",null,"Estraggo ",l(a.b,null,"n")," numeri e guardo in quanti ordini diversi li posso mettere."),l("p",null,l(a.b,null,te(j||(j=ee`\boldsymbol{P}_n = n!`)))))),l(t.a,{title:"Probabilità condizionata"},l(e.a,{title:"Eventi condizionati"},l("blockquote",null,'"E dato F"'),l("p",null,"La probabilità che si verifichi ",l(a.b,null,"E")," sapendo che ",l("b",null,"si è già verificato")," ",l(a.b,null,"F"),"."),l("p",null,l(a.b,null,te(Q||(Q=ee`P(E|F) = \frac{P(E \cap F)}{P(F)}`)))),l(o.a,null,"Ricorda vagamente le pipe di ",l("code",null,"bash"),", però al contrario...")),l(e.a,{title:"Eventi mutualmente esclusivi"},l("p",null,"Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0."),l("p",null,l(a.b,null,te(W||(W=ee`E \cap F = \emptyset \Longleftrightarrow P(E|F) = P(F|E) = 0`)))))),l(t.a,null,l(e.a,{title:"Regola della catena"},l("p",null,"Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:"),l("p",null,l(a.b,null,te(K||(K=ee`P(E_1 \cap \times \cap E_n) = P(E_1) \times P(E_2 | E_1) \times \dots \times P(E_n | E_1 \cap E_2 \cap \dots \cap E_{n-1})`)))))),l(t.a,{title:"Le alternative"},l(e.a,{title:"Legge delle alternative"},l("p",null,"La probabilità che si verifichi un evento è pari alla somma delle probabilità dell'evento stesso dati tutti gli eventi di una partizione."),l("p",null,l(a.b,null,te(J||(J=ee`P(F) = \sum_{i} P(F|E_i) \cdot P(E_i)`))))),l(e.a,{title:"Legge condizionata delle alternative"},l("p",null,"La legge delle alternative funziona anche quando ad essere partizionato è un ",l("b",null,"evento"),":"),l("p",null,l(a.b,null,te(Z||(Z=ee`P(F|G) = \sum_i P(F|E_i \cap G) \cdot P(E_i | G)`))))),l(e.a,{title:"Formula di Bayes"},l("p",null,"Tramite la ",l("i",null,"formula di Bayes")," possiamo risalire alla probabilità di un evento condizionato a un altro partendo dalla probabilità di quest'ultimo condizionato al primo:"),l("p",null,l(a.b,null,te($||($=ee`P(E_h | F) = \frac{P(F | E_h) \cdot P(E_h)}{P(F)}`)))),l(o.a,null,"In pratica, invertiamo gli eventi."))),l(t.a,{title:"Eventi indipendenti"},l(e.a,{title:"Due eventi indipendenti"},l("blockquote",null,'"eventi indipendenti a due a due"'),l("p",null,"Se due eventi sono indipendenti, sapere che uno dei due si è verificato non influisce sulle probabilità che si sia verificato l'altro."),l("p",null,l(a.b,null,te(ll||(ll=ee`P(E \cap F) = P(E) \cdot P(F) \Longleftrightarrow P(E|F) = P(E) \Longleftrightarrow P(F|E) = P(F)`))))),l(e.a,{title:"Più eventi indipendenti"},l("blockquote",null,'"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque..."'),l("p",null,"Si può verificare l'indipendenza di più eventi alla volta:"),l("p",null,l(a.b,null,te(il||(il=ee`P(E \cap F \cap G) = P(E) \cdot P(F) \cdot P(G)`)))),l("p",null,"Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.")),l(e.a,{title:"Famiglia di eventi indipendenti"},l("p",null,"Un insieme di ",l(a.b,null,"n")," eventi è una ",l("i",null,"famiglia di eventi indipendenti")," se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti."),l(o.a,null,"Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e così via!"))),l(t.a,{title:"Variabili aleatorie"},l(e.a,{title:"Variabile aleatoria"},l("p",null,"Una funzione che fa corrispondere un numero reale a ogni possibile esito dello spazio campionario. ",l(a.b,null,te(nl||(nl=ee`X(\omega) : \Omega \to \mathbb{R}`))),".")),l(e.a,{title:l("abbr",{title:"Nome artigianale dato da Steffo."},"Insieme di ripartizione")},l("p",null,"Ad ogni variabile aleatoria sono associati gli eventi ",l(a.b,null,te(al||(al=ee`A_t = \{ \omega | X(\omega) \leq t \}`))),", che contengono tutti gli esiti a cui la variabile aleatoria associa un valore minore o uguale a ",l(a.b,null,"t"),"."),l("p",null,"Per definizione, tutte le variabili aleatorie devono rispettare questa condizione:"),l("p",null,l(a.b,null,te(el||(el=ee`\forall t \in \mathbb{R}, A_t \in \mathcal{F}`)))),l(o.a,null,"All'aumentare di t, l'insieme conterrà sempre più elementi.")),l(e.a,{title:"Supporto"},l("blockquote",null,'"supporto di X"'),l("p",null,"Il ",l("b",null,"codominio")," della variabile aleatoria è il suo ",l("i",null,"supporto"),"."),l("p",null,"Per indicare che un valore ",l(a.b,null,"x_0")," appartiene al supporto di ",l(a.b,null,"X"),", si usa la notazione ",l(a.b,null,"X \\mapsto x_0"),"."))),l(t.a,{title:"Densità"},l(e.a,{title:"Funzione probabilità"},l("p",null,"La ",l("i",null,"funzione probabilità")," ",l(a.b,null,te(tl||(tl=ee`p_X : X \to [0, 1]`)))," di una variabile aleatoria ",l("b",null,"discreta")," ",l(a.b,null,"X")," è la funzione che associa ad ogni esito la sua probabilità:"),l("p",null,l(a.b,null,te(ol||(ol=ee`p_X (x) = \begin{cases}
                             P([X = x]) \quad se\ X \mapsto x \\
                             0 \qquad \qquad \quad se\ X \not\mapsto x
                             \end{cases}`))))),l(e.a,{title:"Funzione densità"},l("p",null,"La ",l("i",null,"funzione densità")," ",l(a.b,null,te(ul||(ul=ee`f_X : X \to [0, 1]`)))," di una variabile aleatoria ",l("b",null,"continua")," ",l(a.b,null,"X")," è l'equivalente continuo della funzione probabilità:"),l("p",null,l(a.b,null,te(rl||(rl=ee`P([a < X \leq b]) = \int_a^b f_X (x) dx`)))),l("p",null,"A differenza della funzione probabilità, è possibile che la funzione densità ",l("b",null,"non esista")," per una certa variabile aleatoria."),l(o.a,null,"Rappresenta \"quanta\" probabilità c'è in un'unità di x!"))),l(t.a,{title:"Funzione di ripartizione"},l(e.a,{title:"Definizione"},l("p",null,"Ogni variabile aleatoria ha una ",l("i",null,"funzione di ripartizione")," ",l(a.b,null,te(sl||(sl=ee`F_X : \mathbb{R} \to [0, 1]`)))," associata, che rappresenta la probabilità che la variabile aleatoria assuma un valore minore o uguale a ",l(a.b,null,"t"),":"),l("p",null,"Si può dire che essa rappresenti la probabilità dell'evento ",l(a.b,null,te(pl||(pl=ee`A_t`))),":"),l("p",null,l(a.b,null,te(dl||(dl=ee`F_X (t) = P(A_t) = \begin{cases}
@@ -37,4 +37,4 @@
                                     Cov(X_3, X_1) & Cov(X_3, X_2) & Var(X_3)
                                 \end{bmatrix}
                             `)))),l("p",null,"E' sempre simmetrica e semidefinita positiva (tutti gli autovalori sono ",l(a.b,null,"\\geq 0"),".")),l(e.a,{title:"Coefficiente di correlazione"},l("p",null,"Un valore che misura come due variabili aleatorie sono correlate:"),l("p",null,l(a.b,null,te(Mn||(Mn=ee`\rho_{X, Y} = \frac{Cov(X, Y)}{\sqrt{Var(X)} \cdot \sqrt{Var(Y)}}`)))),l("p",null,"E' sempre compreso tra -1 e 1:"),l("p",null,l(a.b,null,te(An||(An=ee`-1 \leq \rho_{X, Y} \leq 1`)))),l("p",null,"Vale esattamente -1 o 1 solo se esiste un legame lineare tra le due variaibli:"),l("p",null,l(a.b,null,te(Tn||(Tn=ee`Y = a X + b \Longleftrightarrow | \rho_{X, Y} | = 1`))))),l(e.a,{title:"Varianza di variabili aleatorie sommate"},l("p",null,"La varianza di due variabili aleatorie sommate è:"),l("p",null,l(a.b,null,te(Bn||(Bn=ee`Var(X + Y) = Var(X) + Var(Y) + 2 \cdot Cov(X, Y)`)))),l(o.a,null,"Si dimostra applicando le proprietà della covarianza!"),l("p",null,"Se più variabili aleatorie ",l(a.b,null,"X_i")," sono ",l("b",null,"indipendenti")," (",l(a.b,null,te(On||(On=ee`Cov(X, Y) = 0`))),"), allora:"),l("p",null,l(a.b,null,te(Gn||(Gn=ee`Var \left( \sum_i X_i \right) = \sum_i Var(X_i)`)))))),l(t.a,{title:"Campioni"},l(e.a,{title:"Campione casuale"},l("p",null,"Una ",l("b",null,"n-pla")," di variabili aleatorie con la stessa distribuzione della variabile aleatoria ",l(a.b,null,"X"),' ("popolazione") ma ',l("b",null,"indipendenti")," tra loro."),l(o.a,null,"Le variabili aleatorie sono come un lazy-load in programmazione; quando ci sarà bisogno del loro valore numerico, esse si ",l("b",null,"realizzeranno")," nel loro valore.")),l(e.a,{title:"Momento campionario"},l("p",null,"Il valore dato dalla media aritmetica degli ",l(a.b,null,"n")," elementi del campione elevati alla potenza ",l(a.b,null,"k"),":"),l("p",null,l(a.b,null,te(Hn||(Hn=ee`M^{(k)}_n = \frac{1}{n} \cdot \sum_{i = 1}^n X_i^k `)))),l("p",null,"Il momento campionario di primo ordine è la ",l("i",null,"media campionaria")," ",l(a.b,null,te(Rn||(Rn=ee`\overline{X}_n`))),".")),l(e.a,{title:"Varianza campionaria"},l("p",null,"La media aritmetica dello scarto quadratico medio degli elementi del campione."),l("p",null,"Se è noto il valore medio ",l(a.b,null,te(jn||(jn=ee`m = E(X)`)))," di X:"),l("p",null,l(a.b,null,te(Qn||(Qn=ee`S_0^2 = \frac{1}{n} \cdot \sum_{i = 1}^n (X_i - m)^2 = M_n^(2) - 2 \cdot m \cdot \overline{X}_n + m^2`)))),l("p",null,"Altrimenti:"),l("p",null,l(a.b,null,te(Wn||(Wn=ee`S_n^2 = \frac{1}{n - 1} \cdot \sum_{i = 1}^n (X_i - \overline{X}_n)^2 = \frac{1}{n - 1} \cdot ( n \cdot M_2^{(2)} - n \cdot \overline{X}_n^2)`)))))),l(t.a,{title:"Media-ception"},l(e.a,{title:"Media campionaria"},l("p",null,"Se calcoliamo la media della media campionaria, risulterà vero che:"),l("p",null,l(a.b,null,te(Kn||(Kn=ee`E(\overline{X}_n) = E(X)`)))),l(o.a,null,"Quindi, è possibile usare i campioni per trovare la media di una variabile aleatoria!")),l(e.a,{title:"Varianza campionaria"},l("p",null,"Se calcoliamo la varianza della media campionaria, risulterà vero che:"),l("p",null,l(a.b,null,te(Jn||(Jn=ee`Var(\overline{X}_n) = \frac{Var(X)}{n}`)))),l(o.a,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!")),l(e.a,{title:"Correzione campionaria"},l("p",null,"Se calcoliamo la media della varianza campionaria, risulterà vero che:"),l("p",null,l(a.b,null,te(Zn||(Zn=ee`E(S_0^2) = E(S_n^2) = Var(X)`)))),l(o.a,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!"))),l(t.a,{title:"Campionamento di una distribuzione normale"},l(e.a,{title:"Campionamento di una distribuzione normale"},l("p",null,"Se la popolazione ",l(a.b,null,"X")," ha una distribuzione normale (",l(a.b,null,te($n||($n=ee`X \sim Nor(\mu, \sigma^2)`))),")...")),l(e.a,{title:"Distribuzione della media campionaria"},l("p",null,"...allora sappiamo anche la distribuzione della media campionaria!"),l("p",null,l(a.b,null,te(la||(la=ee`\overline{X}_n \sim Nor \left( \mu, \frac{\sigma^2}{n} \right)`))))),l(e.a,{title:"Distribuzione della varianza campionaria"},l("p",null,"...e anche della varianza campionaria!"),l("p",null,l(a.b,null,te(ia||(ia=ee`S_0^2 \sim \frac{\sigma^2}{n} \cdot \chi^2 (n)`)))),l("p",null,l(a.b,null,te(na||(na=ee`S_n^2 \sim \frac{\sigma^2}{n - 1} \cdot \chi^2 (n-1)`))))),l(e.a,{title:"Indipendenza"},l("p",null,"...e che media campionaria e varianza campionaria sono indipendenti tra loro!"))),l(t.a,{title:"Quando i campioni hanno dimensioni infinite"},l(e.a,{title:"Convergenza in distribuzione"},l("p",null,"Se la successione di variabili aleatorie ",l(a.b,null,"X_n")," all'infinito ha la ",l("b",null,"stessa funzione di ripartizione")," della popolazione ",l(a.b,null,"X"),", allora essa ",l("i",null,"converge in distribuzione"),"."),l("p",null,l(a.b,null,"\\lim_{n \\to +\\infty} F_{X_n} (x) = F_X (x) \\implies X_n \\xrightarrow{d} X"))),l(e.a,{title:"Convergenza in probabilità"},l("p",null,"Se la successione di variabili aleatorie ",l(a.b,null,"X_n")," all'infinito ha la ",l("b",null,"stessa probabilità")," della popolazione ",l(a.b,null,"X"),", allora essa ",l("i",null,"converge in probabilità"),"."),l("p",null,l(a.b,null,"\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | X_n - X | < \\epsilon) = 1 \\implies X_n \\xrightarrow{p} X"))),l(e.a,{title:"Convergenza quasi certa"},l("p",null,"Se la successione di variabili aleatorie ",l(a.b,null,"X_n")," all'infinito ha la ",l("b",null,"stessa probabilità a ")," della popolazione ",l(a.b,null,"X"),", allora essa ",l("i",null,"converge quasi certamente"),"."),l("p",null,l(a.b,null,"\\forall \\epsilon > 0, P left( \\lim_{n \\to +\\infty} | X_n - X | < \\epsilon) \right) = 1 \\implies X_n \\xrightarrow{qc} X"))),l(e.a,{title:"Convergenza in media quadratica"},l("p",null,"Se la successione di variabili aleatorie ",l(a.b,null,"X_n")," all'infinito ha la ",l("b",null,"media del quadrato della distanza")," tra la successione e la popolazione ",l(a.b,null,"X")," ",l("b",null,"uguale a 0"),", allora essa ",l("i",null,"converge in media quadratica"),"."),l("p",null,l(a.b,null,"\\lim_{n \\to +\\infty} E( | X_n - X |^2 = 0 \\implies X_n \\xrightarrow{mq} X"))),l(e.a,{title:"Gerarchia delle convergenze"},l("p",null,l(a.b,null,"\n                                \\begin{matrix}\n                                X_n \\xrightarrow{mq} X\\\\\n                                X_n \\xrightarrow{qc} X\n                                \\end{matrix} \\implies X_n \\xrightarrow{p} X \\implies X_n \\xrightarrow{d} X")),l("p",null,"In più:"),l("p",null,l(a.b,null,"X_n \\xrightarrow{p} x \\Longleftrightarrow X_n \\xrightarrow{d} x")))),l(t.a,{title:"I grandi numeri"},l(e.a,{title:"Legge debole dei grandi numeri"},l("p",null,"La successione delle medie campionarie ",l(a.b,null,te(aa||(aa=ee`\overline{X}_n`)))," ",l("b",null,"converge in probabilità")," alla media della popolazione ",l(a.b,null,te(ea||(ea=ee`E(X)`))),", se essa esiste."),l("p",null,l(a.b,null,"\\overline{X}_n \\xrightarrow{p} X")),l("p",null,"Ovvero:"),l("p",null,l(a.b,null,te(ta||(ta=ee`\forall \epsilon > 0, \lim_{n \to +\infty} P( | \overline{X}_n - E(X) | < \epsilon) = 1`)))),l("p",null,l(a.b,null,te(oa||(oa=ee`P( | \overline{X}_n - E(X) | < \epsilon) \to 1`))))),l(e.a,{title:"Legge forte dei grandi numeri"},l("p",null,"La successione delle medie campionarie ",l(a.b,null,te(ua||(ua=ee`\overline{X}_n`)))," ",l("b",null,"converge quasi certamente")," alla media della popolazione ",l(a.b,null,te(ra||(ra=ee`E(X)`))),", se essa esiste."),l("p",null,l(a.b,null,"\\overline{X}_n \\xrightarrow{qc} X")),l("p",null,"Ovvero:"),l("p",null,l(a.b,null,te(sa||(sa=ee`\forall \epsilon > 0, P \left( \lim_{n \to +\infty} | \overline{X}_n - E(X) | < \epsilon \right) = 1`)))),l(o.a,null,"Dimostra che l'interpretazione frequentista della probabilità è valida!"))),l(t.a,{title:"Al limite"},l(e.a,{title:"Teorema centrale del limite"},l("p",null,"La successione delle medie campionarie ",l(a.b,null,te(pa||(pa=ee`\overline{X}_n`)))," ",l("b",null,"converge in distribuzione")," a ",l(a.b,null,te(da||(da=ee`Nor(0, 1) = \Phi()`))),"."),l("p",null,l(a.b,null,te(ca||(ca=ee`\overline{X}_n \approx Nor \left(E(X), \frac{Var(X)}{n} \right)`)))),l("p",null,"Ovvero:"),l("p",null,l(a.b,null,te(ma||(ma=ee`\forall x \in \mathbb{R}, \lim_{n \to +\infty} P \left( \frac{\overline{X}_n - E(X)}{\sqrt{\frac{Var(X)}{n}}} \leq x \right) = \Phi(x)`)))))),l(t.a,{title:"Altre approsimazioni"},l(e.a,{title:"Binomiale e normale"},l("p",null,"E' una somma di ",l("b",null,"bernoulliane"),", e quindi si approssima a una normale:"),l("p",null,l(a.b,null,te(ba||(ba=ee`Bin(n, p) \approx Nor(n \cdot p, n \cdot p \cdot q)`))))),l(e.a,{title:"Binomiale negativa e normale"},l("p",null,"E' una somma di ",l("b",null,"geometriche"),", e quindi si approssima a una normale:"),l("p",null,l(a.b,null,te(va||(va=ee`\overline{Bin} (n, p) \approx Nor \left( \frac{n}{p}, \frac{n \cdot (1 - p)}{p^2} \right)`))))),l(e.a,{title:"Poissoniana e normale"},l("p",null,"E' una somma di altre ",l("b",null,"poissoniane"),", e quindi si approssima a una normale:"),l("p",null,l(a.b,null,te(_a||(_a=ee`Poi(\lambda) \approx Nor(\lambda, \lambda)`))))),l(e.a,{title:"Gamma e normale"},l("p",null,"E' una somma di ",l("b",null,"esponenziali"),", e quindi si approssima a una normale:"),l("p",null,l(a.b,null,te(fa||(fa=ee`\Gamma (\alpha, \lambda) \approx Nor \left( \frac{\alpha}{\lambda}, \frac{\alpha}{\lambda^2} \right)`))))),l(e.a,{title:"In generale"},l("p",null,"Se ",l(a.b,null,"n")," è grande, allora:"),l("p",null,l(a.b,null,te(ha||(ha=ee`Y = \sum_{i=1}^{n} X_i`)))))),l(t.a,{title:"Actually statistica"},l(e.a,{title:"Parametri sconosciuti"},l("p",null,"Per indicare parametri sconosciuti di una legge si usa ",l(a.b,null,"\\theta"),".")),l(e.a,{title:"Statistica"},l("p",null,"Una variabile aleatoria funzione di un campione:"),l("p",null,l(a.b,null,te(ga||(ga=ee`T(\boldsymbol{X})`)))),l(o.a,null,"Ad esempio, sono statistiche media e varianza campionaria, così come il campione stesso ",l(a.b,null,te(za||(za=ee`T(\boldsymbol{X}) = \boldsymbol{X}`))),"."))),l(t.a,{title:"Stimatori"},l(e.a,{title:"Stimatore"},l("p",null,"Una statistica ",l(a.b,null,"T_n")," ottenuta da ",l(a.b,null,"n")," osservazioni, che stimi i parametri di una legge e sia indipendente da essi.")),l(e.a,{title:"Corretto"},l("p",null,"Uno stimatore è ",l("i",null,"corretto")," se il suo valore atteso coincide con quello dei parametri che stima:"),l("p",null,l(a.b,null,te(Xa||(Xa=ee`E(T_n) = \theta`))))),l(e.a,{title:"Asintoticamente corretto"},l("p",null,"Uno stimatore è ",l("i",null,"asintoticamente corretto")," se, per infinite osservazioni, il suo valore atteso coincide con quello dei parametri che stima:"),l("p",null,l(a.b,null,te(qa||(qa=ee`\lim_{n \to +\infty} E(T_n) = \theta`))))),l(e.a,{title:"Consistente in media quadratica"},l("p",null,"Uno stimatore è ",l("i",null,"consistente in media quadratica")," se:"),l("p",null,l(a.b,null,te(Ea||(Ea=ee`\lim_{n \to +\infty} E((T_n - \theta)^2) = 0`))))),l(e.a,{title:"Consistente in probabilità"},l("p",null,"Uno stimatore è ",l("i",null,"consistente in probabilità")," se:"),l("p",null,l(a.b,null,te(La||(La=ee`\forall \epsilon > 0, \lim_{n \to +\infty} P( |T_n - \theta| < \epsilon) = 1`))))),l(e.a,{title:"Asintoticamente normale"},l("p",null,"Uno stimatore è ",l("i",null,"asintoticamente normale")," se:"),l("p",null,l(a.b,null,te(Pa||(Pa=ee`\lim_{n \to +\infty} \frac{T_n - E(T_n)}{\sqrt{Var(T_n)}} \sim Nor(0, 1)`)))))),l(t.a,{title:"Metodo dei momenti"},l(e.a,{title:"Metodo dei momenti"},l("p",null,"Si può usare il ",l("i",null,"metodo dei momenti")," per ottenere uno stimatore di una popolazione ",l(a.b,null,"X"),"."),l("p",null,"Lo stimatore di ",l(a.b,null,te(xa||(xa=ee`\theta`)))," così ottenuto sarà indicato aggiungendo un cappellino e una ",l(a.b,null,"M")," a ",l(a.b,null,"\\theta"),": ",l(a.b,null,te(ka||(ka=ee`\widehat{\theta}_M`)))),l("p",null,"Visto che:"),l("ul",null,l("li",null,l(a.b,null,te(Fa||(Fa=ee`\theta = g(E(X))`)))),l("li",null,l(a.b,null,te(ya||(ya=ee`\widehat{E(X)} = \overline{X}_n`))))),l("p",null,"Allora:"),l("p",null,l(a.b,null,te(Sa||(Sa=ee`\widehat{\theta}_M = g( \overline{X}_n )`)))),l("p",null,"Se ",l(a.b,null,te(Na||(Na=ee`\theta`)))," non è esprimibile in termini di ",l(a.b,null,te(Ca||(Ca=ee`E(X)`))),", si possono usare i momenti successivi ",l(a.b,null,te(Va||(Va=ee`M_n^2`))),", ",l(a.b,null,te(Ia||(Ia=ee`M_n^3`))),", ",l(a.b,null,te(Ya||(Ya=ee`M_n^3`))),"..."))),l(t.a,{title:"Metodo della massima verosomiglianza"},l(e.a,{title:"Metodo della massima verosomiglianza"},l("p",null,"Si può usare il ",l("i",null,"metodo della massima verosomiglianza")," per ottenere uno stimatore di una popolazione ",l(a.b,null,"X"),"."),l("p",null,"Lo stimatore di ",l(a.b,null,te(wa||(wa=ee`\theta`)))," così ottenuto sarà indicato aggiungendo un cappellino e una ",l(a.b,null,"L")," a ",l(a.b,null,"\\theta"),": ",l(a.b,null,te(Da||(Da=ee`\widehat{\theta}_L`)))),l("p",null,"Consiste nel trovare il massimo assoluto ",l(a.b,null,te(Ua||(Ua=ee`\widehat{\theta}_L`)))," della la funzione di verosomiglianza ",l(a.b,null,te(Ma||(Ma=ee`L`))),":"),l("p",null,l(a.b,null,te(Aa||(Aa=ee`L(x_1, ..., x_n; \theta) = \prod_{i=1}^n f_X(x_i; \theta)`)))),l("p",null,"Gli stimatori di massima verosomiglianza sono ",l("b",null,"asintoticamente corretti"),", ",l("b",null,"consistenti in probabilità")," e ",l("b",null,"asintoticamente normali"),".")),l(e.a,{title:"Proprietà degli stimatori di massima verosomiglianza"},l("p",null,"Gli stimatori di massima verosomiglianza godono delle seguenti proprietà:"),l("ul",null,l("li",null,"Sono ",l("b",null,"asintoticamente corretti"),"."),l("li",null,"Sono ",l("b",null,"consistenti in probabilità"),"."),l("li",null,"Sono ",l("b",null,"asintoticamente normali"),"."),l("li",null,"Sono ",l("b",null,"invarianti"),": ",l(a.b,null,te(Ta||(Ta=ee`\widehat{g(\theta)}_L = g(\widehat{\theta}_L)`))))))),l(t.a,{title:"Nuove stime notevoli"},l(e.a,{title:"Stima di una bernoulliana"},l("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),l("p",null,l(a.b,null,te(Ba||(Ba=ee`\widehat{p}_M = \widehat{p}_L = \overline{X}_n`))))),l(e.a,{title:"Stima di una poissoniana"},l("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),l("p",null,l(a.b,null,te(Oa||(Oa=ee`\widehat{\mu}_M = \widehat{\mu}_L = \overline{X}_n`))))),l(e.a,{title:"Stima di una esponenziale"},l("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),l("p",null,l(a.b,null,te(Ga||(Ga=ee`\widehat{\lambda}_M = \widehat{\lambda}_L = \frac{1}{\overline{X}_n}`))))),l(e.a,{title:"Stima di una normale"},l("p",null,"Per il metodo della massima verosomiglianza:"),l("ul",null,l("li",null,l(a.b,null,te(Ha||(Ha=ee`\widehat{\mu}_L = \overline{X}_n`)))),l("br",null),l("li",null,l(a.b,null,te(Ra||(Ra=ee`\widehat{\sigma^2}_L = \frac{\sum (X_i - \overline{X}_n)^2 }{n}`))))))),l(t.a,{title:"Intervalli di confidenza"},l(e.a,{title:"Confidenza"},l("blockquote",null,'"intervallo di confidenza al 95%"'),l("p",null,"L'intervallo di valori di ",l(a.b,null,"\\theta"),' all\'interno del quale siamo "più o meno sicuri" si trovi il valore effettivo:'),l("p",null,"L'intervallo di confidenza a N della stima ",l(a.b,null,te(ja||(ja=ee`\widehat{W}`)))," è l'intervallo ",l(a.b,null,"]a, b[")," tale che:"),l("p",null,l(a.b,null,te(Qa||(Qa=ee`P( a < W < b ) = N`)))),l("p",null,"Può anche essere ",l("b",null,"unilatero")," nel caso limiti la stima in una sola direzione, positiva o negativa."))),l(t.a,{title:"Confidenza nella media di una normale"},l(e.a,{title:"Varianza nota"},l("p",null,"Se conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'",l(a.b,null,"\\alpha"),"% con queste formule:"),l("ul",null,l("li",null,"Intervalli bilateri: ",l(a.b,null,te(Wa||(Wa=ee`\mu \in \left[ \overline{x}_n - z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{\sigma^2}{n}}, \overline{x}_n + z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{\sigma^2}{n}} \right]`)))),l("li",null,"Intervallo unilatero da sinistra: ",l(a.b,null,te(Ka||(Ka=ee`\mu \in \left( -\infty, \overline{x}_n + z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{\sigma^2}{n}} \right]`)))),l("li",null,"Intervallo unilatero da destra: ",l(a.b,null,te(Ja||(Ja=ee`\mu \in \left[ \overline{x}_n - z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{\sigma^2}{n}}, +\infty \right)`)))))),l(e.a,{title:"Varianza incognita"},l("p",null,"Se non conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'",l(a.b,null,"\\alpha"),"% con queste formule:"),l("ul",null,l("li",null,"Intervalli bilateri: ",l(a.b,null,te(Za||(Za=ee`\mu \in \left[ \overline{x}_n - t_{1 - \frac{\alpha}{2}; n-1} \cdot \sqrt{\frac{s_n^2}{n}}, \overline{x}_n + t_{1 - \frac{\alpha}{2}; n-1} \cdot \sqrt{\frac{s_n^2}{n}} \right]`)))),l("li",null,"Intervallo unilatero da sinistra: ",l(a.b,null,te($a||($a=ee`\mu \in \left( -\infty, \overline{x}_n + t_{1 - \frac{\alpha}{2}; n-1} \cdot \sqrt{\frac{s_n^2}{n}} \right]`)))),l("li",null,"Intervallo unilatero da destra: ",l(a.b,null,te(le||(le=ee`\mu \in \left[ \overline{x}_n - t_{1 - \frac{\alpha}{2}; n-1} \cdot \sqrt{\frac{s_n^2}{n}}, +\infty \right)`))))),l("p",null,l(a.b,null,te(ie||(ie=ee`t_{\alpha, v}`)))," è un quantile della distribuzione di Student di parametro ",l(a.b,null,"v"),"."))),l(t.a,{title:"Confidenza per la proporzione di una bernoulliana"},l(e.a,{title:"Terzo metodo corretto"},l("p",null,"L'intervallo di confidenza per la proprorzione di una bernoulliana qualsiasi si ottiene da questa formula:"),l("p",null,l(a.b,null,te(ne||(ne=ee`p \in \left[ \overline{p} - z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{\overline{p} \cdot (1 - \overline{p})}{n+4}}, \overline{p} + z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{\overline{p} \cdot (1 - \overline{p})}{n+4}} \right]`)))))),l(t.a,{title:"Confidenza per la media di qualsiasi popolazione"},l(e.a,{title:"Approssimando con la normale"},l("p",null,"L'intervallo di confidenza per la media di una qualsiasi popolazione si ottiene da questa formula:"),l("p",null,l(a.b,null,te(ae||(ae=ee`m \in \left[ \overline{x}_n - z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{s^2_n}{n}}, \overline{x}_n + z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{s^2_n}{n}} \right]`)))))))))}}.call(this,n("hosL").h)},htlC:function(l){l.exports={splitparent:"splitparent__3-wBs",splitchild:"splitchild__begkX"}},imVn:function(l,i,n){"use strict";(function(l){var a=n("OmdA"),e=n.n(a),t=n("Y9Ml");i.a=function(i){return l(t.a,{color:i.color},l("h3",{class:e.a.title},i.title),l("div",{class:e.a.contents},i.children))}}).call(this,n("hosL").h)},wQ73:function(l,i,n){"use strict";var a=n("hosL");i.a=Object(a.createContext)(!0)}}]);
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    Videolezioni di Geometria
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o&&o.integrity){if(this._cacheKeysToIntegrities.has(u)&&this._cacheKeysToIntegrities.get(u)!==o.integrity)throw new E("add-to-cache-list-conflicting-integrities",{url:c});this._cacheKeysToIntegrities.set(u,o.integrity)}if(this._urlsToCacheKeys.set(c,u),this._urlsToCacheModes.set(c,s),r.length>0){var a="Workbox is precaching URLs without revision info: "+r.join(", ")+"\nThis is generally NOT safe. Learn more at https://bit.ly/wb-precache";console.warn(a)}}},t.install=function(e){return new Promise(function(t,r){var n,o,i,u,c,s,a,l,h,f,d,p,y,v;return n=this,i=(o=void 0===e?{}:e).event,u=o.plugins,c=[],s=[],Promise.resolve(self.caches.open(this._cacheName)).then(function(e){try{return Promise.resolve(e.keys()).then(function(e){try{for(a=new Set(e.map((function(e){return e.url}))),l=P(this._urlsToCacheKeys);!(h=l()).done;)d=(f=h.value)[0],a.has(p=f[1])?s.push(d):c.push({cacheKey:p,url:d});return y=c.map((function(e){var t=e.cacheKey,r=e.url,o=n._cacheKeysToIntegrities.get(t),c=n._urlsToCacheModes.get(r);return n._addURLToCache({cacheKey:t,cacheMode:c,event:i,integrity:o,plugins:u,url:r})})),Promise.resolve(Promise.all(y)).then((function(){try{return v=c.map((function(e){return e.url})),t({updatedURLs:v,notUpdatedURLs:s})}catch(e){return r(e)}}),r)}catch(e){return r(e)}}.bind(this),r)}catch(e){return r(e)}}.bind(this),r)}.bind(this))},t.activate=function(){return new 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Request(o,{integrity:e.integrity,cache:e.cacheMode,credentials:"same-origin"}),Promise.resolve(ie({event:i,plugins:u,request:c})).then(function(e){try{for(s=e,l=P(u||[]);!(h=l()).done;)"cacheWillUpdate"in(f=h.value)&&(a=f);return Promise.resolve(new Promise((function(e,t){return a?Promise.resolve(a.cacheWillUpdate({event:i,request:c,response:s})).then(e,t):e(s.status<400)}))).then(function(e){try{if(!e)return r(new E("bad-precaching-response",{url:o,status:s.status}));if(s.redirected)return Promise.resolve(w(s)).then(function(e){try{return s=e,a.call(this)}catch(e){return r(e)}}.bind(this),r);function a(){return Promise.resolve(ne({event:i,plugins:u,response:s,request:n===o?c:new Request(n),cacheName:this._cacheName,matchOptions:{ignoreSearch:!0}})).then((function(){try{return t()}catch(e){return r(e)}}),r)}return a.call(this)}catch(e){return r(e)}}.bind(this),r)}catch(e){return r(e)}}.bind(this),r)}.bind(this))},t.getURLsToCacheKeys=function(){return this._urlsToCacheKeys},t.getCachedURLs=function(){return[].concat(this._urlsToCacheKeys.keys())},t.getCacheKeyForURL=function(e){var t=new URL(e,location.href);return this._urlsToCacheKeys.get(t.href)},t.matchPrecache=function(e){return new Promise(function(t,r){var n,o;return n=e instanceof Request?e.url:e,(o=this.getCacheKeyForURL(n))?Promise.resolve(self.caches.open(this._cacheName)).then((function(e){try{return t(e.match(o))}catch(e){return r(e)}}),r):t(void 0)}.bind(this))},t.createHandler=function(e){var t=this;return void 0===e&&(e=!0),function(r){return new Promise((function(n,o){var i,u;i=r.request;var c=function(t){try{if(e)return n(fetch(i));throw t}catch(e){return o(e)}};try{return Promise.resolve(t.matchPrecache(i)).then((function(e){try{if(u=e)return n(u);throw new E("missing-precache-entry",{cacheName:t._cacheName,url:i instanceof Request?i.url:i})}catch(e){return c(e)}}),c)}catch(e){c(e)}}))}},t.createHandlerBoundToURL=function(e,t){if(void 0===t&&(t=!0),!this.getCacheKeyForURL(e))throw new E("non-precached-url",{url:e});var r=this.createHandler(t),n=new Request(e);return function(){return r({request:n})}},e}(),ce=function(){return K||(K=new ue),K},se=!1,ae=function(e){var t=ce(),r=$();e.waitUntil(t.install({event:e,plugins:r}).catch((function(e){throw e})))},le=function(e){var t=ce();e.waitUntil(t.activate())},he=function(e){return"navigate"===e.request.mode},fe=(r("myed"),{cacheWillUpdate:function(e){return new Promise((function(t){var r=e.response;return t(200===r.status||0===r.status?r:null)}))}}),de=function(){function e(e){if(void 0===e&&(e={}),this._cacheName=V(e.cacheName),e.plugins){var t=e.plugins.some((function(e){return!!e.cacheWillUpdate}));this._plugins=t?e.plugins:[fe].concat(e.plugins)}else this._plugins=[fe];this._networkTimeoutSeconds=e.networkTimeoutSeconds||0,this._fetchOptions=e.fetchOptions,this._matchOptions=e.matchOptions}var t=e.prototype;return t.handle=function(e){return new Promise(function(t,r){var n,o,i,u,c,s,a,l;return n=e.event,i=[],"string"==typeof(o=e.request)&&(o=new Request(o)),u=[],this._networkTimeoutSeconds&&(c=(s=this._getTimeoutPromise({request:o,event:n,logs:i})).id,u.push(s.promise)),a=this._getNetworkPromise({timeoutId:c,request:o,event:n,logs:i}),u.push(a),Promise.resolve(Promise.race(u)).then(function(e){try{if(!(l=e))return Promise.resolve(a).then(function(e){try{return l=e,n.call(this)}catch(e){return r(e)}}.bind(this),r);function n(){return l?t(l):r(new E("no-response",{url:o.url}))}return n.call(this)}catch(e){return r(e)}}.bind(this),r)}.bind(this))},t._getTimeoutPromise=function(e){var t,r=this,n=e.request,o=e.event;return{promise:new Promise((function(e){t=setTimeout((function(){return new Promise((function(t,i){return Promise.resolve(r._respondFromCache({request:n,event:o})).then((function(r){try{return e(r),t()}catch(e){return i(e)}}),i)}))}),1e3*r._networkTimeoutSeconds)})),id:t}},t._getNetworkPromise=function(e){return new Promise(function(t,r){var n,o,i,u,c,s,a;n=e.timeoutId,o=e.request,i=e.event;var l=function(){try{if(n&&clearTimeout(n),u||!c)return Promise.resolve(this._respondFromCache({request:o,event:i})).then(function(t){try{return c=t,e.call(this)}catch(e){return r(e)}}.bind(this),r);if(s=c.clone(),a=ne({cacheName:this._cacheName,request:o,response:s,event:i,plugins:this._plugins}),i)try{i.waitUntil(a)}catch(e){0}return e.call(this);function e(){return t(c)}}catch(e){return r(e)}}.bind(this),h=function(e){try{return u=e,l()}catch(e){return r(e)}};try{return Promise.resolve(ie({request:o,event:i,fetchOptions:this._fetchOptions,plugins:this._plugins})).then((function(e){try{return c=e,l()}catch(e){return h(e)}}),h)}catch(e){h(e)}}.bind(this))},t._respondFromCache=function(e){return oe({cacheName:this._cacheName,request:e.request,event:e.event,matchOptions:this._matchOptions,plugins:this._plugins})},e}(),pe=function(){function e(e,t,r){var n=this,o=void 0===r?{}:r,i=o.onupgradeneeded,u=o.onversionchange;this._db=null,this._name=e,this._version=t,this._onupgradeneeded=i,this._onversionchange=u||function(){return n.close()}}var t,r,n,o=e.prototype;return o.open=function(){return new Promise(function(e,t){var r;return r=this,this._db?e():Promise.resolve(new Promise((function(e,t){var n=!1;setTimeout((function(){n=!0,t(new Error("The open request was blocked and timed out"))}),r.OPEN_TIMEOUT);var o=indexedDB.open(r._name,r._version);o.onerror=function(){return t(o.error)},o.onupgradeneeded=function(e){n?(o.transaction.abort(),o.result.close()):"function"==typeof r._onupgradeneeded&&r._onupgradeneeded(e)},o.onsuccess=function(){var t=o.result;n?t.close():(t.onversionchange=r._onversionchange.bind(r),e(t))}}))).then(function(r){try{return this._db=r,e(this)}catch(e){return t(e)}}.bind(this),t)}.bind(this))},o.getKey=function(e,t){return new Promise(function(r,n){return Promise.resolve(this.getAllKeys(e,t,1)).then((function(e){try{return r(e[0])}catch(e){return n(e)}}),n)}.bind(this))},o.getAll=function(e,t,r){return new Promise(function(n,o){return Promise.resolve(this.getAllMatching(e,{query:t,count:r})).then(n,o)}.bind(this))},o.getAllKeys=function(e,t,r){return new Promise(function(n,o){return Promise.resolve(this.getAllMatching(e,{query:t,count:r,includeKeys:!0})).then((function(e){try{return n(e.map((function(e){return e.key})))}catch(e){return o(e)}}),o)}.bind(this))},o.getAllMatching=function(e,t){return new Promise(function(r,n){var o,i,u,c,s,a,l,h,f;return i=(o=void 0===t?{}:t).index,c=void 0===(u=o.query)?null:u,a=void 0===(s=o.direction)?"next":s,l=o.count,f=void 0!==(h=o.includeKeys)&&h,Promise.resolve(this.transaction([e],"readonly",(function(t,r){var n=t.objectStore(e),o=i?n.index(i):n,u=[],s=o.openCursor(c,a);s.onsuccess=function(){var e=s.result;e?(u.push(f?e:e.value),l&&u.length>=l?r(u):e.continue()):r(u)}}))).then(r,n)}.bind(this))},o.transaction=function(e,t,r){return new Promise(function(n,o){var i;return i=this,Promise.resolve(this.open()).then((function(){try{return Promise.resolve(new Promise((function(n,o){var u=i._db.transaction(e,t);u.onabort=function(){return o(u.error)},u.oncomplete=function(){return n()},r(u,(function(e){return n(e)}))}))).then(n,o)}catch(e){return o(e)}}),o)}.bind(this))},o._call=function(e,t,r){var n=arguments;return new Promise(function(o,i){var u,c,s;for(u=n.length,c=new Array(u>3?u-3:0),s=3;s1?u-1:0),s=1;s} [options.ignoreURLParametersMatching=[/^utm_/]] An\n * array of regex's to remove search params when looking for a cache match.\n * @param {boolean} [options.cleanURLs=true] The `cleanURLs` option will\n * check the cache for the URL with a `.html` added to the end of the end.\n * @param {module:workbox-precaching~urlManipulation} [options.urlManipulation]\n * This is a function that should take a URL and return an array of\n * alternative URLs that should be checked for precache matches.\n *\n * @memberof module:workbox-precaching\n */\nfunction addRoute(options) {\n    if (!listenerAdded) {\n        addFetchListener(options);\n        listenerAdded = true;\n    }\n}\nexport { addRoute };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { cacheNames } from 'workbox-core/_private/cacheNames.js';\nimport { getFriendlyURL } from 'workbox-core/_private/getFriendlyURL.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { getCacheKeyForURL } from './getCacheKeyForURL.js';\nimport '../_version.js';\n/**\n * Adds a `fetch` listener to the service worker that will\n * respond to\n * [network requests]{@link https://developer.mozilla.org/en-US/docs/Web/API/Service_Worker_API/Using_Service_Workers#Custom_responses_to_requests}\n * with precached assets.\n *\n * Requests for assets that aren't precached, the `FetchEvent` will not be\n * responded to, allowing the event to fall through to other `fetch` event\n * listeners.\n *\n * NOTE: when called more than once this method will replace the previously set\n * configuration options. Calling it more than once is not recommended outside\n * of tests.\n *\n * @private\n * @param {Object} [options]\n * @param {string} [options.directoryIndex=index.html] The `directoryIndex` will\n * check cache entries for a URLs ending with '/' to see if there is a hit when\n * appending the `directoryIndex` value.\n * @param {Array} [options.ignoreURLParametersMatching=[/^utm_/]] An\n * array of regex's to remove search params when looking for a cache match.\n * @param {boolean} [options.cleanURLs=true] The `cleanURLs` option will\n * check the cache for the URL with a `.html` added to the end of the end.\n * @param {workbox.precaching~urlManipulation} [options.urlManipulation]\n * This is a function that should take a URL and return an array of\n * alternative URLs that should be checked for precache matches.\n */\nexport const addFetchListener = ({ ignoreURLParametersMatching = [/^utm_/], directoryIndex = 'index.html', cleanURLs = true, urlManipulation, } = {}) => {\n    const cacheName = cacheNames.getPrecacheName();\n    // See https://github.com/Microsoft/TypeScript/issues/28357#issuecomment-436484705\n    self.addEventListener('fetch', ((event) => {\n        const precachedURL = getCacheKeyForURL(event.request.url, {\n            cleanURLs,\n            directoryIndex,\n            ignoreURLParametersMatching,\n            urlManipulation,\n        });\n        if (!precachedURL) {\n            if (process.env.NODE_ENV !== 'production') {\n                logger.debug(`Precaching did not find a match for ` +\n                    getFriendlyURL(event.request.url));\n            }\n            return;\n        }\n        let responsePromise = self.caches.open(cacheName).then((cache) => {\n            return cache.match(precachedURL);\n        }).then((cachedResponse) => {\n            if (cachedResponse) {\n                return cachedResponse;\n            }\n            // Fall back to the network if we don't have a cached response\n            // (perhaps due to manual cache cleanup).\n            if (process.env.NODE_ENV !== 'production') {\n                logger.warn(`The precached response for ` +\n                    `${getFriendlyURL(precachedURL)} in ${cacheName} was not found. ` +\n                    `Falling back to the network instead.`);\n            }\n            return fetch(precachedURL);\n        });\n        if (process.env.NODE_ENV !== 'production') {\n            responsePromise = responsePromise.then((response) => {\n                // Workbox is going to handle the route.\n                // print the routing details to the console.\n                logger.groupCollapsed(`Precaching is responding to: ` +\n                    getFriendlyURL(event.request.url));\n                logger.log(`Serving the precached url: ${precachedURL}`);\n                logger.groupCollapsed(`View request details here.`);\n                logger.log(event.request);\n                logger.groupEnd();\n                logger.groupCollapsed(`View response details here.`);\n                logger.log(response);\n                logger.groupEnd();\n                logger.groupEnd();\n                return response;\n            });\n        }\n        event.respondWith(responsePromise);\n    }));\n};\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { getOrCreatePrecacheController } from './getOrCreatePrecacheController.js';\nimport { generateURLVariations } from './generateURLVariations.js';\nimport '../_version.js';\n/**\n * This function will take the request URL and manipulate it based on the\n * configuration options.\n *\n * @param {string} url\n * @param {Object} options\n * @return {string} Returns the URL in the cache that matches the request,\n * if possible.\n *\n * @private\n */\nexport const getCacheKeyForURL = (url, options) => {\n    const precacheController = getOrCreatePrecacheController();\n    const urlsToCacheKeys = precacheController.getURLsToCacheKeys();\n    for (const possibleURL of generateURLVariations(url, options)) {\n        const possibleCacheKey = urlsToCacheKeys.get(possibleURL);\n        if (possibleCacheKey) {\n            return possibleCacheKey;\n        }\n    }\n};\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { removeIgnoredSearchParams } from './removeIgnoredSearchParams.js';\nimport '../_version.js';\n/**\n * Generator function that yields possible variations on the original URL to\n * check, one at a time.\n *\n * @param {string} url\n * @param {Object} options\n *\n * @private\n * @memberof module:workbox-precaching\n */\nexport function* generateURLVariations(url, { ignoreURLParametersMatching, directoryIndex, cleanURLs, urlManipulation, } = {}) {\n    const urlObject = new URL(url, location.href);\n    urlObject.hash = '';\n    yield urlObject.href;\n    const urlWithoutIgnoredParams = removeIgnoredSearchParams(urlObject, ignoreURLParametersMatching);\n    yield urlWithoutIgnoredParams.href;\n    if (directoryIndex && urlWithoutIgnoredParams.pathname.endsWith('/')) {\n        const directoryURL = new URL(urlWithoutIgnoredParams.href);\n        directoryURL.pathname += directoryIndex;\n        yield directoryURL.href;\n    }\n    if (cleanURLs) {\n        const cleanURL = new URL(urlWithoutIgnoredParams.href);\n        cleanURL.pathname += '.html';\n        yield cleanURL.href;\n    }\n    if (urlManipulation) {\n        const additionalURLs = urlManipulation({ url: urlObject });\n        for (const urlToAttempt of additionalURLs) {\n            yield urlToAttempt.href;\n        }\n    }\n}\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\n/**\n * Removes any URL search parameters that should be ignored.\n *\n * @param {URL} urlObject The original URL.\n * @param {Array} ignoreURLParametersMatching RegExps to test against\n * each search parameter name. Matches mean that the search parameter should be\n * ignored.\n * @return {URL} The URL with any ignored search parameters removed.\n *\n * @private\n * @memberof module:workbox-precaching\n */\nexport function removeIgnoredSearchParams(urlObject, ignoreURLParametersMatching = []) {\n    // Convert the iterable into an array at the start of the loop to make sure\n    // deletion doesn't mess up iteration.\n    for (const paramName of [...urlObject.searchParams.keys()]) {\n        if (ignoreURLParametersMatching.some((regExp) => regExp.test(paramName))) {\n            urlObject.searchParams.delete(paramName);\n        }\n    }\n    return urlObject;\n}\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { addRoute } from './addRoute.js';\nimport { precache } from './precache.js';\nimport './_version.js';\n/**\n * This method will add entries to the precache list and add a route to\n * respond to fetch events.\n *\n * This is a convenience method that will call\n * [precache()]{@link module:workbox-precaching.precache} and\n * [addRoute()]{@link module:workbox-precaching.addRoute} in a single call.\n *\n * @param {Array} entries Array of entries to precache.\n * @param {Object} [options] See\n * [addRoute() options]{@link module:workbox-precaching.addRoute}.\n *\n * @memberof module:workbox-precaching\n */\nfunction precacheAndRoute(entries, options) {\n    precache(entries);\n    addRoute(options);\n}\nexport { precacheAndRoute };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { getOrCreatePrecacheController } from './utils/getOrCreatePrecacheController.js';\nimport { precachePlugins } from './utils/precachePlugins.js';\nimport './_version.js';\nconst installListener = (event) => {\n    const precacheController = getOrCreatePrecacheController();\n    const plugins = precachePlugins.get();\n    event.waitUntil(precacheController.install({ event, plugins })\n        .catch((error) => {\n        if (process.env.NODE_ENV !== 'production') {\n            logger.error(`Service worker installation failed. It will ` +\n                `be retried automatically during the next navigation.`);\n        }\n        // Re-throw the error to ensure installation fails.\n        throw error;\n    }));\n};\nconst activateListener = (event) => {\n    const precacheController = getOrCreatePrecacheController();\n    event.waitUntil(precacheController.activate());\n};\n/**\n * Adds items to the precache list, removing any duplicates and\n * stores the files in the\n * [\"precache cache\"]{@link module:workbox-core.cacheNames} when the service\n * worker installs.\n *\n * This method can be called multiple times.\n *\n * Please note: This method **will not** serve any of the cached files for you.\n * It only precaches files. To respond to a network request you call\n * [addRoute()]{@link module:workbox-precaching.addRoute}.\n *\n * If you have a single array of files to precache, you can just call\n * [precacheAndRoute()]{@link module:workbox-precaching.precacheAndRoute}.\n *\n * @param {Array} [entries=[]] Array of entries to precache.\n *\n * @memberof module:workbox-precaching\n */\nfunction precache(entries) {\n    const precacheController = getOrCreatePrecacheController();\n    precacheController.addToCacheList(entries);\n    if (entries.length > 0) {\n        // NOTE: these listeners will only be added once (even if the `precache()`\n        // method is called multiple times) because event listeners are implemented\n        // as a set, where each listener must be unique.\n        // See https://github.com/Microsoft/TypeScript/issues/28357#issuecomment-436484705\n        self.addEventListener('install', installListener);\n        self.addEventListener('activate', activateListener);\n    }\n}\nexport { precache };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { Router } from '../Router.js';\nimport '../_version.js';\nlet defaultRouter;\n/**\n * Creates a new, singleton Router instance if one does not exist. If one\n * does already exist, that instance is returned.\n *\n * @private\n * @return {Router}\n */\nexport const getOrCreateDefaultRouter = () => {\n    if (!defaultRouter) {\n        defaultRouter = new Router();\n        // The helpers that use the default Router assume these listeners exist.\n        defaultRouter.addFetchListener();\n        defaultRouter.addCacheListener();\n    }\n    return defaultRouter;\n};\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { PrecacheController } from '../PrecacheController.js';\nimport '../_version.js';\nlet precacheController;\n/**\n * @return {PrecacheController}\n * @private\n */\nexport const getOrCreatePrecacheController = () => {\n    if (!precacheController) {\n        precacheController = new PrecacheController();\n    }\n    return precacheController;\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { messages } from './messages.js';\nimport '../../_version.js';\nconst fallback = (code, ...args) => {\n    let msg = code;\n    if (args.length > 0) {\n        msg += ` :: ${JSON.stringify(args)}`;\n    }\n    return msg;\n};\nconst generatorFunction = (code, details = {}) => {\n    const message = messages[code];\n    if (!message) {\n        throw new Error(`Unable to find message for code '${code}'.`);\n    }\n    return message(details);\n};\nexport const messageGenerator = (process.env.NODE_ENV === 'production') ?\n    fallback : generatorFunction;\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { messageGenerator } from '../models/messages/messageGenerator.js';\nimport '../_version.js';\n/**\n * Workbox errors should be thrown with this class.\n * This allows use to ensure the type easily in tests,\n * helps developers identify errors from workbox\n * easily and allows use to optimise error\n * messages correctly.\n *\n * @private\n */\nclass WorkboxError extends Error {\n    /**\n     *\n     * @param {string} errorCode The error code that\n     * identifies this particular error.\n     * @param {Object=} details Any relevant arguments\n     * that will help developers identify issues should\n     * be added as a key on the context object.\n     */\n    constructor(errorCode, details) {\n        const message = messageGenerator(errorCode, details);\n        super(message);\n        this.name = errorCode;\n        this.details = details;\n    }\n}\nexport { WorkboxError };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport '../_version.js';\n/**\n * @param {function()|Object} handler Either a function, or an object with a\n * 'handle' method.\n * @return {Object} An object with a handle method.\n *\n * @private\n */\nexport const normalizeHandler = (handler) => {\n    if (handler && typeof handler === 'object') {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.hasMethod(handler, 'handle', {\n                moduleName: 'workbox-routing',\n                className: 'Route',\n                funcName: 'constructor',\n                paramName: 'handler',\n            });\n        }\n        return handler;\n    }\n    else {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isType(handler, 'function', {\n                moduleName: 'workbox-routing',\n                className: 'Route',\n                funcName: 'constructor',\n                paramName: 'handler',\n            });\n        }\n        return { handle: handler };\n    }\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { defaultMethod, validMethods } from './utils/constants.js';\nimport { normalizeHandler } from './utils/normalizeHandler.js';\nimport './_version.js';\n/**\n * A `Route` consists of a pair of callback functions, \"match\" and \"handler\".\n * The \"match\" callback determine if a route should be used to \"handle\" a\n * request by returning a non-falsy value if it can. The \"handler\" callback\n * is called when there is a match and should return a Promise that resolves\n * to a `Response`.\n *\n * @memberof module:workbox-routing\n */\nclass Route {\n    /**\n     * Constructor for Route class.\n     *\n     * @param {module:workbox-routing~matchCallback} match\n     * A callback function that determines whether the route matches a given\n     * `fetch` event by returning a non-falsy value.\n     * @param {module:workbox-routing~handlerCallback} handler A callback\n     * function that returns a Promise resolving to a Response.\n     * @param {string} [method='GET'] The HTTP method to match the Route\n     * against.\n     */\n    constructor(match, handler, method = defaultMethod) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isType(match, 'function', {\n                moduleName: 'workbox-routing',\n                className: 'Route',\n                funcName: 'constructor',\n                paramName: 'match',\n            });\n            if (method) {\n                assert.isOneOf(method, validMethods, { paramName: 'method' });\n            }\n        }\n        // These values are referenced directly by Router so cannot be\n        // altered by minificaton.\n        this.handler = normalizeHandler(handler);\n        this.match = match;\n        this.method = method;\n    }\n}\nexport { Route };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\n/**\n * The default HTTP method, 'GET', used when there's no specific method\n * configured for a route.\n *\n * @type {string}\n *\n * @private\n */\nexport const defaultMethod = 'GET';\n/**\n * The list of valid HTTP methods associated with requests that could be routed.\n *\n * @type {Array}\n *\n * @private\n */\nexport const validMethods = [\n    'DELETE',\n    'GET',\n    'HEAD',\n    'PATCH',\n    'POST',\n    'PUT',\n];\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { Route } from './Route.js';\nimport './_version.js';\n/**\n * RegExpRoute makes it easy to create a regular expression based\n * [Route]{@link module:workbox-routing.Route}.\n *\n * For same-origin requests the RegExp only needs to match part of the URL. For\n * requests against third-party servers, you must define a RegExp that matches\n * the start of the URL.\n *\n * [See the module docs for info.]{@link https://developers.google.com/web/tools/workbox/modules/workbox-routing}\n *\n * @memberof module:workbox-routing\n * @extends module:workbox-routing.Route\n */\nclass RegExpRoute extends Route {\n    /**\n     * If the regular expression contains\n     * [capture groups]{@link https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/RegExp#grouping-back-references},\n     * the captured values will be passed to the\n     * [handler's]{@link module:workbox-routing~handlerCallback} `params`\n     * argument.\n     *\n     * @param {RegExp} regExp The regular expression to match against URLs.\n     * @param {module:workbox-routing~handlerCallback} handler A callback\n     * function that returns a Promise resulting in a Response.\n     * @param {string} [method='GET'] The HTTP method to match the Route\n     * against.\n     */\n    constructor(regExp, handler, method) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(regExp, RegExp, {\n                moduleName: 'workbox-routing',\n                className: 'RegExpRoute',\n                funcName: 'constructor',\n                paramName: 'pattern',\n            });\n        }\n        const match = ({ url }) => {\n            const result = regExp.exec(url.href);\n            // Return immediately if there's no match.\n            if (!result) {\n                return;\n            }\n            // Require that the match start at the first character in the URL string\n            // if it's a cross-origin request.\n            // See https://github.com/GoogleChrome/workbox/issues/281 for the context\n            // behind this behavior.\n            if ((url.origin !== location.origin) && (result.index !== 0)) {\n                if (process.env.NODE_ENV !== 'production') {\n                    logger.debug(`The regular expression '${regExp}' only partially matched ` +\n                        `against the cross-origin URL '${url}'. RegExpRoute's will only ` +\n                        `handle cross-origin requests if they match the entire URL.`);\n                }\n                return;\n            }\n            // If the route matches, but there aren't any capture groups defined, then\n            // this will return [], which is truthy and therefore sufficient to\n            // indicate a match.\n            // If there are capture groups, then it will return their values.\n            return result.slice(1);\n        };\n        super(match, handler, method);\n    }\n}\nexport { RegExpRoute };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nconst getFriendlyURL = (url) => {\n    const urlObj = new URL(String(url), location.href);\n    // See https://github.com/GoogleChrome/workbox/issues/2323\n    // We want to include everything, except for the origin if it's same-origin.\n    return urlObj.href.replace(new RegExp(`^${location.origin}`), '');\n};\nexport { getFriendlyURL };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { getFriendlyURL } from 'workbox-core/_private/getFriendlyURL.js';\nimport { normalizeHandler } from './utils/normalizeHandler.js';\nimport './_version.js';\n/**\n * The Router can be used to process a FetchEvent through one or more\n * [Routes]{@link module:workbox-routing.Route} responding  with a Request if\n * a matching route exists.\n *\n * If no route matches a given a request, the Router will use a \"default\"\n * handler if one is defined.\n *\n * Should the matching Route throw an error, the Router will use a \"catch\"\n * handler if one is defined to gracefully deal with issues and respond with a\n * Request.\n *\n * If a request matches multiple routes, the **earliest** registered route will\n * be used to respond to the request.\n *\n * @memberof module:workbox-routing\n */\nclass Router {\n    /**\n     * Initializes a new Router.\n     */\n    constructor() {\n        this._routes = new Map();\n    }\n    /**\n     * @return {Map>} routes A `Map` of HTTP\n     * method name ('GET', etc.) to an array of all the corresponding `Route`\n     * instances that are registered.\n     */\n    get routes() {\n        return this._routes;\n    }\n    /**\n     * Adds a fetch event listener to respond to events when a route matches\n     * the event's request.\n     */\n    addFetchListener() {\n        // See https://github.com/Microsoft/TypeScript/issues/28357#issuecomment-436484705\n        self.addEventListener('fetch', ((event) => {\n            const { request } = event;\n            const responsePromise = this.handleRequest({ request, event });\n            if (responsePromise) {\n                event.respondWith(responsePromise);\n            }\n        }));\n    }\n    /**\n     * Adds a message event listener for URLs to cache from the window.\n     * This is useful to cache resources loaded on the page prior to when the\n     * service worker started controlling it.\n     *\n     * The format of the message data sent from the window should be as follows.\n     * Where the `urlsToCache` array may consist of URL strings or an array of\n     * URL string + `requestInit` object (the same as you'd pass to `fetch()`).\n     *\n     * ```\n     * {\n     *   type: 'CACHE_URLS',\n     *   payload: {\n     *     urlsToCache: [\n     *       './script1.js',\n     *       './script2.js',\n     *       ['./script3.js', {mode: 'no-cors'}],\n     *     ],\n     *   },\n     * }\n     * ```\n     */\n    addCacheListener() {\n        // See https://github.com/Microsoft/TypeScript/issues/28357#issuecomment-436484705\n        self.addEventListener('message', ((event) => {\n            if (event.data && event.data.type === 'CACHE_URLS') {\n                const { payload } = event.data;\n                if (process.env.NODE_ENV !== 'production') {\n                    logger.debug(`Caching URLs from the window`, payload.urlsToCache);\n                }\n                const requestPromises = Promise.all(payload.urlsToCache.map((entry) => {\n                    if (typeof entry === 'string') {\n                        entry = [entry];\n                    }\n                    const request = new Request(...entry);\n                    return this.handleRequest({ request });\n                    // TODO(philipwalton): TypeScript errors without this typecast for\n                    // some reason (probably a bug). The real type here should work but\n                    // doesn't: `Array | undefined>`.\n                })); // TypeScript\n                event.waitUntil(requestPromises);\n                // If a MessageChannel was used, reply to the message on success.\n                if (event.ports && event.ports[0]) {\n                    requestPromises.then(() => event.ports[0].postMessage(true));\n                }\n            }\n        }));\n    }\n    /**\n     * Apply the routing rules to a FetchEvent object to get a Response from an\n     * appropriate Route's handler.\n     *\n     * @param {Object} options\n     * @param {Request} options.request The request to handle (this is usually\n     *     from a fetch event, but it does not have to be).\n     * @param {FetchEvent} [options.event] The event that triggered the request,\n     *     if applicable.\n     * @return {Promise|undefined} A promise is returned if a\n     *     registered route can handle the request. If there is no matching\n     *     route and there's no `defaultHandler`, `undefined` is returned.\n     */\n    handleRequest({ request, event }) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(request, Request, {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'handleRequest',\n                paramName: 'options.request',\n            });\n        }\n        const url = new URL(request.url, location.href);\n        if (!url.protocol.startsWith('http')) {\n            if (process.env.NODE_ENV !== 'production') {\n                logger.debug(`Workbox Router only supports URLs that start with 'http'.`);\n            }\n            return;\n        }\n        const { params, route } = this.findMatchingRoute({ url, request, event });\n        let handler = route && route.handler;\n        const debugMessages = [];\n        if (process.env.NODE_ENV !== 'production') {\n            if (handler) {\n                debugMessages.push([\n                    `Found a route to handle this request:`, route,\n                ]);\n                if (params) {\n                    debugMessages.push([\n                        `Passing the following params to the route's handler:`, params,\n                    ]);\n                }\n            }\n        }\n        // If we don't have a handler because there was no matching route, then\n        // fall back to defaultHandler if that's defined.\n        if (!handler && this._defaultHandler) {\n            if (process.env.NODE_ENV !== 'production') {\n                debugMessages.push(`Failed to find a matching route. Falling ` +\n                    `back to the default handler.`);\n            }\n            handler = this._defaultHandler;\n        }\n        if (!handler) {\n            if (process.env.NODE_ENV !== 'production') {\n                // No handler so Workbox will do nothing. If logs is set of debug\n                // i.e. verbose, we should print out this information.\n                logger.debug(`No route found for: ${getFriendlyURL(url)}`);\n            }\n            return;\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            // We have a handler, meaning Workbox is going to handle the route.\n            // print the routing details to the console.\n            logger.groupCollapsed(`Router is responding to: ${getFriendlyURL(url)}`);\n            debugMessages.forEach((msg) => {\n                if (Array.isArray(msg)) {\n                    logger.log(...msg);\n                }\n                else {\n                    logger.log(msg);\n                }\n            });\n            logger.groupEnd();\n        }\n        // Wrap in try and catch in case the handle method throws a synchronous\n        // error. It should still callback to the catch handler.\n        let responsePromise;\n        try {\n            responsePromise = handler.handle({ url, request, event, params });\n        }\n        catch (err) {\n            responsePromise = Promise.reject(err);\n        }\n        if (responsePromise instanceof Promise && this._catchHandler) {\n            responsePromise = responsePromise.catch((err) => {\n                if (process.env.NODE_ENV !== 'production') {\n                    // Still include URL here as it will be async from the console group\n                    // and may not make sense without the URL\n                    logger.groupCollapsed(`Error thrown when responding to: ` +\n                        ` ${getFriendlyURL(url)}. Falling back to Catch Handler.`);\n                    logger.error(`Error thrown by:`, route);\n                    logger.error(err);\n                    logger.groupEnd();\n                }\n                return this._catchHandler.handle({ url, request, event });\n            });\n        }\n        return responsePromise;\n    }\n    /**\n     * Checks a request and URL (and optionally an event) against the list of\n     * registered routes, and if there's a match, returns the corresponding\n     * route along with any params generated by the match.\n     *\n     * @param {Object} options\n     * @param {URL} options.url\n     * @param {Request} options.request The request to match.\n     * @param {Event} [options.event] The corresponding event (unless N/A).\n     * @return {Object} An object with `route` and `params` properties.\n     *     They are populated if a matching route was found or `undefined`\n     *     otherwise.\n     */\n    findMatchingRoute({ url, request, event }) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(url, URL, {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'findMatchingRoute',\n                paramName: 'options.url',\n            });\n            assert.isInstance(request, Request, {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'findMatchingRoute',\n                paramName: 'options.request',\n            });\n        }\n        const routes = this._routes.get(request.method) || [];\n        for (const route of routes) {\n            let params;\n            const matchResult = route.match({ url, request, event });\n            if (matchResult) {\n                // See https://github.com/GoogleChrome/workbox/issues/2079\n                params = matchResult;\n                if (Array.isArray(matchResult) && matchResult.length === 0) {\n                    // Instead of passing an empty array in as params, use undefined.\n                    params = undefined;\n                }\n                else if ((matchResult.constructor === Object &&\n                    Object.keys(matchResult).length === 0)) {\n                    // Instead of passing an empty object in as params, use undefined.\n                    params = undefined;\n                }\n                else if (typeof matchResult === 'boolean') {\n                    // For the boolean value true (rather than just something truth-y),\n                    // don't set params.\n                    // See https://github.com/GoogleChrome/workbox/pull/2134#issuecomment-513924353\n                    params = undefined;\n                }\n                // Return early if have a match.\n                return { route, params };\n            }\n        }\n        // If no match was found above, return and empty object.\n        return {};\n    }\n    /**\n     * Define a default `handler` that's called when no routes explicitly\n     * match the incoming request.\n     *\n     * Without a default handler, unmatched requests will go against the\n     * network as if there were no service worker present.\n     *\n     * @param {module:workbox-routing~handlerCallback} handler A callback\n     * function that returns a Promise resulting in a Response.\n     */\n    setDefaultHandler(handler) {\n        this._defaultHandler = normalizeHandler(handler);\n    }\n    /**\n     * If a Route throws an error while handling a request, this `handler`\n     * will be called and given a chance to provide a response.\n     *\n     * @param {module:workbox-routing~handlerCallback} handler A callback\n     * function that returns a Promise resulting in a Response.\n     */\n    setCatchHandler(handler) {\n        this._catchHandler = normalizeHandler(handler);\n    }\n    /**\n     * Registers a route with the router.\n     *\n     * @param {module:workbox-routing.Route} route The route to register.\n     */\n    registerRoute(route) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isType(route, 'object', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route',\n            });\n            assert.hasMethod(route, 'match', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route',\n            });\n            assert.isType(route.handler, 'object', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route',\n            });\n            assert.hasMethod(route.handler, 'handle', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route.handler',\n            });\n            assert.isType(route.method, 'string', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route.method',\n            });\n        }\n        if (!this._routes.has(route.method)) {\n            this._routes.set(route.method, []);\n        }\n        // Give precedence to all of the earlier routes by adding this additional\n        // route to the end of the array.\n        this._routes.get(route.method).push(route);\n    }\n    /**\n     * Unregisters a route with the router.\n     *\n     * @param {module:workbox-routing.Route} route The route to unregister.\n     */\n    unregisterRoute(route) {\n        if (!this._routes.has(route.method)) {\n            throw new WorkboxError('unregister-route-but-not-found-with-method', {\n                method: route.method,\n            });\n        }\n        const routeIndex = this._routes.get(route.method).indexOf(route);\n        if (routeIndex > -1) {\n            this._routes.get(route.method).splice(routeIndex, 1);\n        }\n        else {\n            throw new WorkboxError('unregister-route-route-not-registered');\n        }\n    }\n}\nexport { Router };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nconst plugins = [];\nexport const precachePlugins = {\n    /*\n     * @return {Array}\n     * @private\n     */\n    get() {\n        return plugins;\n    },\n    /*\n     * @param {Array} newPlugins\n     * @private\n     */\n    add(newPlugins) {\n        plugins.push(...newPlugins);\n    },\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nconst _cacheNameDetails = {\n    googleAnalytics: 'googleAnalytics',\n    precache: 'precache-v2',\n    prefix: 'workbox',\n    runtime: 'runtime',\n    suffix: typeof registration !== 'undefined' ? registration.scope : '',\n};\nconst _createCacheName = (cacheName) => {\n    return [_cacheNameDetails.prefix, cacheName, _cacheNameDetails.suffix]\n        .filter((value) => value && value.length > 0)\n        .join('-');\n};\nconst eachCacheNameDetail = (fn) => {\n    for (const key of Object.keys(_cacheNameDetails)) {\n        fn(key);\n    }\n};\nexport const cacheNames = {\n    updateDetails: (details) => {\n        eachCacheNameDetail((key) => {\n            if (typeof details[key] === 'string') {\n                _cacheNameDetails[key] = details[key];\n            }\n        });\n    },\n    getGoogleAnalyticsName: (userCacheName) => {\n        return userCacheName || _createCacheName(_cacheNameDetails.googleAnalytics);\n    },\n    getPrecacheName: (userCacheName) => {\n        return userCacheName || _createCacheName(_cacheNameDetails.precache);\n    },\n    getPrefix: () => {\n        return _cacheNameDetails.prefix;\n    },\n    getRuntimeName: (userCacheName) => {\n        return userCacheName || _createCacheName(_cacheNameDetails.runtime);\n    },\n    getSuffix: () => {\n        return _cacheNameDetails.suffix;\n    },\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\n// Callbacks to be executed whenever there's a quota error.\nconst quotaErrorCallbacks = new Set();\nexport { quotaErrorCallbacks };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nexport const pluginUtils = {\n    filter: (plugins, callbackName) => {\n        return plugins.filter((plugin) => callbackName in plugin);\n    },\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from './assert.js';\nimport { executeQuotaErrorCallbacks } from './executeQuotaErrorCallbacks.js';\nimport { getFriendlyURL } from './getFriendlyURL.js';\nimport { logger } from './logger.js';\nimport { pluginUtils } from '../utils/pluginUtils.js';\nimport { WorkboxError } from './WorkboxError.js';\nimport '../_version.js';\n/**\n * Checks the list of plugins for the cacheKeyWillBeUsed callback, and\n * executes any of those callbacks found in sequence. The final `Request` object\n * returned by the last plugin is treated as the cache key for cache reads\n * and/or writes.\n *\n * @param {Object} options\n * @param {Request} options.request\n * @param {string} options.mode\n * @param {Array} [options.plugins=[]]\n * @return {Promise}\n *\n * @private\n * @memberof module:workbox-core\n */\nconst _getEffectiveRequest = async ({ request, mode, plugins = [], }) => {\n    const cacheKeyWillBeUsedPlugins = pluginUtils.filter(plugins, \"cacheKeyWillBeUsed\" /* CACHE_KEY_WILL_BE_USED */);\n    let effectiveRequest = request;\n    for (const plugin of cacheKeyWillBeUsedPlugins) {\n        effectiveRequest = await plugin[\"cacheKeyWillBeUsed\" /* CACHE_KEY_WILL_BE_USED */].call(plugin, { mode, request: effectiveRequest });\n        if (typeof effectiveRequest === 'string') {\n            effectiveRequest = new Request(effectiveRequest);\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(effectiveRequest, Request, {\n                moduleName: 'Plugin',\n                funcName: \"cacheKeyWillBeUsed\" /* CACHE_KEY_WILL_BE_USED */,\n                isReturnValueProblem: true,\n            });\n        }\n    }\n    return effectiveRequest;\n};\n/**\n * This method will call cacheWillUpdate on the available plugins (or use\n * status === 200) to determine if the Response is safe and valid to cache.\n *\n * @param {Object} options\n * @param {Request} options.request\n * @param {Response} options.response\n * @param {Event} [options.event]\n * @param {Array} [options.plugins=[]]\n * @return {Promise}\n *\n * @private\n * @memberof module:workbox-core\n */\nconst _isResponseSafeToCache = async ({ request, response, event, plugins = [], }) => {\n    let responseToCache = response;\n    let pluginsUsed = false;\n    for (const plugin of plugins) {\n        if (\"cacheWillUpdate\" /* CACHE_WILL_UPDATE */ in plugin) {\n            pluginsUsed = true;\n            const pluginMethod = plugin[\"cacheWillUpdate\" /* CACHE_WILL_UPDATE */];\n            responseToCache = await pluginMethod.call(plugin, {\n                request,\n                response: responseToCache,\n                event,\n            });\n            if (process.env.NODE_ENV !== 'production') {\n                if (responseToCache) {\n                    assert.isInstance(responseToCache, Response, {\n                        moduleName: 'Plugin',\n                        funcName: \"cacheWillUpdate\" /* CACHE_WILL_UPDATE */,\n                        isReturnValueProblem: true,\n                    });\n                }\n            }\n            if (!responseToCache) {\n                break;\n            }\n        }\n    }\n    if (!pluginsUsed) {\n        if (process.env.NODE_ENV !== 'production') {\n            if (responseToCache) {\n                if (responseToCache.status !== 200) {\n                    if (responseToCache.status === 0) {\n                        logger.warn(`The response for '${request.url}' is an opaque ` +\n                            `response. The caching strategy that you're using will not ` +\n                            `cache opaque responses by default.`);\n                    }\n                    else {\n                        logger.debug(`The response for '${request.url}' returned ` +\n                            `a status code of '${response.status}' and won't be cached as a ` +\n                            `result.`);\n                    }\n                }\n            }\n        }\n        responseToCache = responseToCache && responseToCache.status === 200 ?\n            responseToCache : undefined;\n    }\n    return responseToCache ? responseToCache : null;\n};\n/**\n * This is a wrapper around cache.match().\n *\n * @param {Object} options\n * @param {string} options.cacheName Name of the cache to match against.\n * @param {Request} options.request The Request that will be used to look up\n *     cache entries.\n * @param {Event} [options.event] The event that prompted the action.\n * @param {Object} [options.matchOptions] Options passed to cache.match().\n * @param {Array} [options.plugins=[]] Array of plugins.\n * @return {Response} A cached response if available.\n *\n * @private\n * @memberof module:workbox-core\n */\nconst matchWrapper = async ({ cacheName, request, event, matchOptions, plugins = [], }) => {\n    const cache = await self.caches.open(cacheName);\n    const effectiveRequest = await _getEffectiveRequest({\n        plugins, request, mode: 'read'\n    });\n    let cachedResponse = await cache.match(effectiveRequest, matchOptions);\n    if (process.env.NODE_ENV !== 'production') {\n        if (cachedResponse) {\n            logger.debug(`Found a cached response in '${cacheName}'.`);\n        }\n        else {\n            logger.debug(`No cached response found in '${cacheName}'.`);\n        }\n    }\n    for (const plugin of plugins) {\n        if (\"cachedResponseWillBeUsed\" /* CACHED_RESPONSE_WILL_BE_USED */ in plugin) {\n            const pluginMethod = plugin[\"cachedResponseWillBeUsed\" /* CACHED_RESPONSE_WILL_BE_USED */];\n            cachedResponse = await pluginMethod.call(plugin, {\n                cacheName,\n                event,\n                matchOptions,\n                cachedResponse,\n                request: effectiveRequest,\n            });\n            if (process.env.NODE_ENV !== 'production') {\n                if (cachedResponse) {\n                    assert.isInstance(cachedResponse, Response, {\n                        moduleName: 'Plugin',\n                        funcName: \"cachedResponseWillBeUsed\" /* CACHED_RESPONSE_WILL_BE_USED */,\n                        isReturnValueProblem: true,\n                    });\n                }\n            }\n        }\n    }\n    return cachedResponse;\n};\n/**\n * Wrapper around cache.put().\n *\n * Will call `cacheDidUpdate` on plugins if the cache was updated, using\n * `matchOptions` when determining what the old entry is.\n *\n * @param {Object} options\n * @param {string} options.cacheName\n * @param {Request} options.request\n * @param {Response} options.response\n * @param {Event} [options.event]\n * @param {Array} [options.plugins=[]]\n * @param {Object} [options.matchOptions]\n *\n * @private\n * @memberof module:workbox-core\n */\nconst putWrapper = async ({ cacheName, request, response, event, plugins = [], matchOptions, }) => {\n    if (process.env.NODE_ENV !== 'production') {\n        if (request.method && request.method !== 'GET') {\n            throw new WorkboxError('attempt-to-cache-non-get-request', {\n                url: getFriendlyURL(request.url),\n                method: request.method,\n            });\n        }\n    }\n    const effectiveRequest = await _getEffectiveRequest({\n        plugins, request, mode: 'write'\n    });\n    if (!response) {\n        if (process.env.NODE_ENV !== 'production') {\n            logger.error(`Cannot cache non-existent response for ` +\n                `'${getFriendlyURL(effectiveRequest.url)}'.`);\n        }\n        throw new WorkboxError('cache-put-with-no-response', {\n            url: getFriendlyURL(effectiveRequest.url),\n        });\n    }\n    const responseToCache = await _isResponseSafeToCache({\n        event,\n        plugins,\n        response,\n        request: effectiveRequest,\n    });\n    if (!responseToCache) {\n        if (process.env.NODE_ENV !== 'production') {\n            logger.debug(`Response '${getFriendlyURL(effectiveRequest.url)}' will ` +\n                `not be cached.`, responseToCache);\n        }\n        return;\n    }\n    const cache = await self.caches.open(cacheName);\n    const updatePlugins = pluginUtils.filter(plugins, \"cacheDidUpdate\" /* CACHE_DID_UPDATE */);\n    const oldResponse = updatePlugins.length > 0 ?\n        await matchWrapper({ cacheName, matchOptions, request: effectiveRequest }) :\n        null;\n    if (process.env.NODE_ENV !== 'production') {\n        logger.debug(`Updating the '${cacheName}' cache with a new Response for ` +\n            `${getFriendlyURL(effectiveRequest.url)}.`);\n    }\n    try {\n        await cache.put(effectiveRequest, responseToCache);\n    }\n    catch (error) {\n        // See https://developer.mozilla.org/en-US/docs/Web/API/DOMException#exception-QuotaExceededError\n        if (error.name === 'QuotaExceededError') {\n            await executeQuotaErrorCallbacks();\n        }\n        throw error;\n    }\n    for (const plugin of updatePlugins) {\n        await plugin[\"cacheDidUpdate\" /* CACHE_DID_UPDATE */].call(plugin, {\n            cacheName,\n            event,\n            oldResponse,\n            newResponse: responseToCache,\n            request: effectiveRequest,\n        });\n    }\n};\nexport const cacheWrapper = {\n    put: putWrapper,\n    match: matchWrapper,\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { logger } from '../_private/logger.js';\nimport { quotaErrorCallbacks } from '../models/quotaErrorCallbacks.js';\nimport '../_version.js';\n/**\n * Runs all of the callback functions, one at a time sequentially, in the order\n * in which they were registered.\n *\n * @memberof module:workbox-core\n * @private\n */\nasync function executeQuotaErrorCallbacks() {\n    if (process.env.NODE_ENV !== 'production') {\n        logger.log(`About to run ${quotaErrorCallbacks.size} ` +\n            `callbacks to clean up caches.`);\n    }\n    for (const callback of quotaErrorCallbacks) {\n        await callback();\n        if (process.env.NODE_ENV !== 'production') {\n            logger.log(callback, 'is complete.');\n        }\n    }\n    if (process.env.NODE_ENV !== 'production') {\n        logger.log('Finished running callbacks.');\n    }\n}\nexport { executeQuotaErrorCallbacks };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { WorkboxError } from './WorkboxError.js';\nimport { logger } from './logger.js';\nimport { assert } from './assert.js';\nimport { getFriendlyURL } from '../_private/getFriendlyURL.js';\nimport { pluginUtils } from '../utils/pluginUtils.js';\nimport '../_version.js';\n/**\n * Wrapper around the fetch API.\n *\n * Will call requestWillFetch on available plugins.\n *\n * @param {Object} options\n * @param {Request|string} options.request\n * @param {Object} [options.fetchOptions]\n * @param {ExtendableEvent} [options.event]\n * @param {Array} [options.plugins=[]]\n * @return {Promise}\n *\n * @private\n * @memberof module:workbox-core\n */\nconst wrappedFetch = async ({ request, fetchOptions, event, plugins = [], }) => {\n    if (typeof request === 'string') {\n        request = new Request(request);\n    }\n    // We *should* be able to call `await event.preloadResponse` even if it's\n    // undefined, but for some reason, doing so leads to errors in our Node unit\n    // tests. To work around that, explicitly check preloadResponse's value first.\n    if (event instanceof FetchEvent && event.preloadResponse) {\n        const possiblePreloadResponse = await event.preloadResponse;\n        if (possiblePreloadResponse) {\n            if (process.env.NODE_ENV !== 'production') {\n                logger.log(`Using a preloaded navigation response for ` +\n                    `'${getFriendlyURL(request.url)}'`);\n            }\n            return possiblePreloadResponse;\n        }\n    }\n    if (process.env.NODE_ENV !== 'production') {\n        assert.isInstance(request, Request, {\n            paramName: 'request',\n            expectedClass: Request,\n            moduleName: 'workbox-core',\n            className: 'fetchWrapper',\n            funcName: 'wrappedFetch',\n        });\n    }\n    const failedFetchPlugins = pluginUtils.filter(plugins, \"fetchDidFail\" /* FETCH_DID_FAIL */);\n    // If there is a fetchDidFail plugin, we need to save a clone of the\n    // original request before it's either modified by a requestWillFetch\n    // plugin or before the original request's body is consumed via fetch().\n    const originalRequest = failedFetchPlugins.length > 0 ?\n        request.clone() : null;\n    try {\n        for (const plugin of plugins) {\n            if (\"requestWillFetch\" /* REQUEST_WILL_FETCH */ in plugin) {\n                const pluginMethod = plugin[\"requestWillFetch\" /* REQUEST_WILL_FETCH */];\n                const requestClone = request.clone();\n                request = await pluginMethod.call(plugin, {\n                    request: requestClone,\n                    event,\n                });\n                if (process.env.NODE_ENV !== 'production') {\n                    if (request) {\n                        assert.isInstance(request, Request, {\n                            moduleName: 'Plugin',\n                            funcName: \"cachedResponseWillBeUsed\" /* CACHED_RESPONSE_WILL_BE_USED */,\n                            isReturnValueProblem: true,\n                        });\n                    }\n                }\n            }\n        }\n    }\n    catch (err) {\n        throw new WorkboxError('plugin-error-request-will-fetch', {\n            thrownError: err,\n        });\n    }\n    // The request can be altered by plugins with `requestWillFetch` making\n    // the original request (Most likely from a `fetch` event) to be different\n    // to the Request we make. Pass both to `fetchDidFail` to aid debugging.\n    const pluginFilteredRequest = request.clone();\n    try {\n        let fetchResponse;\n        // See https://github.com/GoogleChrome/workbox/issues/1796\n        if (request.mode === 'navigate') {\n            fetchResponse = await fetch(request);\n        }\n        else {\n            fetchResponse = await fetch(request, fetchOptions);\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            logger.debug(`Network request for ` +\n                `'${getFriendlyURL(request.url)}' returned a response with ` +\n                `status '${fetchResponse.status}'.`);\n        }\n        for (const plugin of plugins) {\n            if (\"fetchDidSucceed\" /* FETCH_DID_SUCCEED */ in plugin) {\n                fetchResponse = await plugin[\"fetchDidSucceed\" /* FETCH_DID_SUCCEED */]\n                    .call(plugin, {\n                    event,\n                    request: pluginFilteredRequest,\n                    response: fetchResponse,\n                });\n                if (process.env.NODE_ENV !== 'production') {\n                    if (fetchResponse) {\n                        assert.isInstance(fetchResponse, Response, {\n                            moduleName: 'Plugin',\n                            funcName: \"fetchDidSucceed\" /* FETCH_DID_SUCCEED */,\n                            isReturnValueProblem: true,\n                        });\n                    }\n                }\n            }\n        }\n        return fetchResponse;\n    }\n    catch (error) {\n        if (process.env.NODE_ENV !== 'production') {\n            logger.error(`Network request for ` +\n                `'${getFriendlyURL(request.url)}' threw an error.`, error);\n        }\n        for (const plugin of failedFetchPlugins) {\n            await plugin[\"fetchDidFail\" /* FETCH_DID_FAIL */].call(plugin, {\n                error,\n                event,\n                originalRequest: originalRequest.clone(),\n                request: pluginFilteredRequest.clone(),\n            });\n        }\n        throw error;\n    }\n};\nconst fetchWrapper = {\n    fetch: wrappedFetch,\n};\nexport { fetchWrapper };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { cacheNames } from 'workbox-core/_private/cacheNames.js';\nimport { cacheWrapper } from 'workbox-core/_private/cacheWrapper.js';\nimport { fetchWrapper } from 'workbox-core/_private/fetchWrapper.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { copyResponse } from 'workbox-core/copyResponse.js';\nimport { createCacheKey } from './utils/createCacheKey.js';\nimport { printCleanupDetails } from './utils/printCleanupDetails.js';\nimport { printInstallDetails } from './utils/printInstallDetails.js';\nimport './_version.js';\n/**\n * Performs efficient precaching of assets.\n *\n * @memberof module:workbox-precaching\n */\nclass PrecacheController {\n    /**\n     * Create a new PrecacheController.\n     *\n     * @param {string} [cacheName] An optional name for the cache, to override\n     * the default precache name.\n     */\n    constructor(cacheName) {\n        this._cacheName = cacheNames.getPrecacheName(cacheName);\n        this._urlsToCacheKeys = new Map();\n        this._urlsToCacheModes = new Map();\n        this._cacheKeysToIntegrities = new Map();\n    }\n    /**\n     * This method will add items to the precache list, removing duplicates\n     * and ensuring the information is valid.\n     *\n     * @param {\n     * Array\n     * } entries Array of entries to precache.\n     */\n    addToCacheList(entries) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isArray(entries, {\n                moduleName: 'workbox-precaching',\n                className: 'PrecacheController',\n                funcName: 'addToCacheList',\n                paramName: 'entries',\n            });\n        }\n        const urlsToWarnAbout = [];\n        for (const entry of entries) {\n            // See https://github.com/GoogleChrome/workbox/issues/2259\n            if (typeof entry === 'string') {\n                urlsToWarnAbout.push(entry);\n            }\n            else if (entry && entry.revision === undefined) {\n                urlsToWarnAbout.push(entry.url);\n            }\n            const { cacheKey, url } = createCacheKey(entry);\n            const cacheMode = (typeof entry !== 'string' && entry.revision) ?\n                'reload' : 'default';\n            if (this._urlsToCacheKeys.has(url) &&\n                this._urlsToCacheKeys.get(url) !== cacheKey) {\n                throw new WorkboxError('add-to-cache-list-conflicting-entries', {\n                    firstEntry: this._urlsToCacheKeys.get(url),\n                    secondEntry: cacheKey,\n                });\n            }\n            if (typeof entry !== 'string' && entry.integrity) {\n                if (this._cacheKeysToIntegrities.has(cacheKey) &&\n                    this._cacheKeysToIntegrities.get(cacheKey) !== entry.integrity) {\n                    throw new WorkboxError('add-to-cache-list-conflicting-integrities', {\n                        url,\n                    });\n                }\n                this._cacheKeysToIntegrities.set(cacheKey, entry.integrity);\n            }\n            this._urlsToCacheKeys.set(url, cacheKey);\n            this._urlsToCacheModes.set(url, cacheMode);\n            if (urlsToWarnAbout.length > 0) {\n                const warningMessage = `Workbox is precaching URLs without revision ` +\n                    `info: ${urlsToWarnAbout.join(', ')}\\nThis is generally NOT safe. ` +\n                    `Learn more at https://bit.ly/wb-precache`;\n                if (process.env.NODE_ENV === 'production') {\n                    // Use console directly to display this warning without bloating\n                    // bundle sizes by pulling in all of the logger codebase in prod.\n                    console.warn(warningMessage);\n                }\n                else {\n                    logger.warn(warningMessage);\n                }\n            }\n        }\n    }\n    /**\n     * Precaches new and updated assets. Call this method from the service worker\n     * install event.\n     *\n     * @param {Object} options\n     * @param {Event} [options.event] The install event (if needed).\n     * @param {Array} [options.plugins] Plugins to be used for fetching\n     * and caching during install.\n     * @return {Promise}\n     */\n    async install({ event, plugins } = {}) {\n        if (process.env.NODE_ENV !== 'production') {\n            if (plugins) {\n                assert.isArray(plugins, {\n                    moduleName: 'workbox-precaching',\n                    className: 'PrecacheController',\n                    funcName: 'install',\n                    paramName: 'plugins',\n                });\n            }\n        }\n        const toBePrecached = [];\n        const alreadyPrecached = [];\n        const cache = await self.caches.open(this._cacheName);\n        const alreadyCachedRequests = await cache.keys();\n        const existingCacheKeys = new Set(alreadyCachedRequests.map((request) => request.url));\n        for (const [url, cacheKey] of this._urlsToCacheKeys) {\n            if (existingCacheKeys.has(cacheKey)) {\n                alreadyPrecached.push(url);\n            }\n            else {\n                toBePrecached.push({ cacheKey, url });\n            }\n        }\n        const precacheRequests = toBePrecached.map(({ cacheKey, url }) => {\n            const integrity = this._cacheKeysToIntegrities.get(cacheKey);\n            const cacheMode = this._urlsToCacheModes.get(url);\n            return this._addURLToCache({\n                cacheKey,\n                cacheMode,\n                event,\n                integrity,\n                plugins,\n                url,\n            });\n        });\n        await Promise.all(precacheRequests);\n        const updatedURLs = toBePrecached.map((item) => item.url);\n        if (process.env.NODE_ENV !== 'production') {\n            printInstallDetails(updatedURLs, alreadyPrecached);\n        }\n        return {\n            updatedURLs,\n            notUpdatedURLs: alreadyPrecached,\n        };\n    }\n    /**\n     * Deletes assets that are no longer present in the current precache manifest.\n     * Call this method from the service worker activate event.\n     *\n     * @return {Promise}\n     */\n    async activate() {\n        const cache = await self.caches.open(this._cacheName);\n        const currentlyCachedRequests = await cache.keys();\n        const expectedCacheKeys = new Set(this._urlsToCacheKeys.values());\n        const deletedURLs = [];\n        for (const request of currentlyCachedRequests) {\n            if (!expectedCacheKeys.has(request.url)) {\n                await cache.delete(request);\n                deletedURLs.push(request.url);\n            }\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            printCleanupDetails(deletedURLs);\n        }\n        return { deletedURLs };\n    }\n    /**\n     * Requests the entry and saves it to the cache if the response is valid.\n     * By default, any response with a status code of less than 400 (including\n     * opaque responses) is considered valid.\n     *\n     * If you need to use custom criteria to determine what's valid and what\n     * isn't, then pass in an item in `options.plugins` that implements the\n     * `cacheWillUpdate()` lifecycle event.\n     *\n     * @private\n     * @param {Object} options\n     * @param {string} options.cacheKey The string to use a cache key.\n     * @param {string} options.url The URL to fetch and cache.\n     * @param {string} [options.cacheMode] The cache mode for the network request.\n     * @param {Event} [options.event] The install event (if passed).\n     * @param {Array} [options.plugins] An array of plugins to apply to\n     * fetch and caching.\n     * @param {string} [options.integrity] The value to use for the `integrity`\n     * field when making the request.\n     */\n    async _addURLToCache({ cacheKey, url, cacheMode, event, plugins, integrity }) {\n        const request = new Request(url, {\n            integrity,\n            cache: cacheMode,\n            credentials: 'same-origin',\n        });\n        let response = await fetchWrapper.fetch({\n            event,\n            plugins,\n            request,\n        });\n        // Allow developers to override the default logic about what is and isn't\n        // valid by passing in a plugin implementing cacheWillUpdate(), e.g.\n        // a `CacheableResponsePlugin` instance.\n        let cacheWillUpdatePlugin;\n        for (const plugin of (plugins || [])) {\n            if ('cacheWillUpdate' in plugin) {\n                cacheWillUpdatePlugin = plugin;\n            }\n        }\n        const isValidResponse = cacheWillUpdatePlugin ?\n            // Use a callback if provided. It returns a truthy value if valid.\n            // NOTE: invoke the method on the plugin instance so the `this` context\n            // is correct.\n            await cacheWillUpdatePlugin.cacheWillUpdate({ event, request, response }) :\n            // Otherwise, default to considering any response status under 400 valid.\n            // This includes, by default, considering opaque responses valid.\n            response.status < 400;\n        // Consider this a failure, leading to the `install` handler failing, if\n        // we get back an invalid response.\n        if (!isValidResponse) {\n            throw new WorkboxError('bad-precaching-response', {\n                url,\n                status: response.status,\n            });\n        }\n        // Redirected responses cannot be used to satisfy a navigation request, so\n        // any redirected response must be \"copied\" rather than cloned, so the new\n        // response doesn't contain the `redirected` flag. See:\n        // https://bugs.chromium.org/p/chromium/issues/detail?id=669363&desc=2#c1\n        if (response.redirected) {\n            response = await copyResponse(response);\n        }\n        await cacheWrapper.put({\n            event,\n            plugins,\n            response,\n            // `request` already uses `url`. We may be able to reuse it.\n            request: cacheKey === url ? request : new Request(cacheKey),\n            cacheName: this._cacheName,\n            matchOptions: {\n                ignoreSearch: true,\n            },\n        });\n    }\n    /**\n     * Returns a mapping of a precached URL to the corresponding cache key, taking\n     * into account the revision information for the URL.\n     *\n     * @return {Map} A URL to cache key mapping.\n     */\n    getURLsToCacheKeys() {\n        return this._urlsToCacheKeys;\n    }\n    /**\n     * Returns a list of all the URLs that have been precached by the current\n     * service worker.\n     *\n     * @return {Array} The precached URLs.\n     */\n    getCachedURLs() {\n        return [...this._urlsToCacheKeys.keys()];\n    }\n    /**\n     * Returns the cache key used for storing a given URL. If that URL is\n     * unversioned, like `/index.html', then the cache key will be the original\n     * URL with a search parameter appended to it.\n     *\n     * @param {string} url A URL whose cache key you want to look up.\n     * @return {string} The versioned URL that corresponds to a cache key\n     * for the original URL, or undefined if that URL isn't precached.\n     */\n    getCacheKeyForURL(url) {\n        const urlObject = new URL(url, location.href);\n        return this._urlsToCacheKeys.get(urlObject.href);\n    }\n    /**\n     * This acts as a drop-in replacement for [`cache.match()`](https://developer.mozilla.org/en-US/docs/Web/API/Cache/match)\n     * with the following differences:\n     *\n     * - It knows what the name of the precache is, and only checks in that cache.\n     * - It allows you to pass in an \"original\" URL without versioning parameters,\n     * and it will automatically look up the correct cache key for the currently\n     * active revision of that URL.\n     *\n     * E.g., `matchPrecache('index.html')` will find the correct precached\n     * response for the currently active service worker, even if the actual cache\n     * key is `'/index.html?__WB_REVISION__=1234abcd'`.\n     *\n     * @param {string|Request} request The key (without revisioning parameters)\n     * to look up in the precache.\n     * @return {Promise}\n     */\n    async matchPrecache(request) {\n        const url = request instanceof Request ? request.url : request;\n        const cacheKey = this.getCacheKeyForURL(url);\n        if (cacheKey) {\n            const cache = await self.caches.open(this._cacheName);\n            return cache.match(cacheKey);\n        }\n        return undefined;\n    }\n    /**\n     * Returns a function that can be used within a\n     * {@link module:workbox-routing.Route} that will find a response for the\n     * incoming request against the precache.\n     *\n     * If for an unexpected reason there is a cache miss for the request,\n     * this will fall back to retrieving the `Response` via `fetch()` when\n     * `fallbackToNetwork` is `true`.\n     *\n     * @param {boolean} [fallbackToNetwork=true] Whether to attempt to get the\n     * response from the network if there's a precache miss.\n     * @return {module:workbox-routing~handlerCallback}\n     */\n    createHandler(fallbackToNetwork = true) {\n        return async ({ request }) => {\n            try {\n                const response = await this.matchPrecache(request);\n                if (response) {\n                    return response;\n                }\n                // This shouldn't normally happen, but there are edge cases:\n                // https://github.com/GoogleChrome/workbox/issues/1441\n                throw new WorkboxError('missing-precache-entry', {\n                    cacheName: this._cacheName,\n                    url: request instanceof Request ? request.url : request,\n                });\n            }\n            catch (error) {\n                if (fallbackToNetwork) {\n                    if (process.env.NODE_ENV !== 'production') {\n                        logger.debug(`Unable to respond with precached response. ` +\n                            `Falling back to network.`, error);\n                    }\n                    return fetch(request);\n                }\n                throw error;\n            }\n        };\n    }\n    /**\n     * Returns a function that looks up `url` in the precache (taking into\n     * account revision information), and returns the corresponding `Response`.\n     *\n     * If for an unexpected reason there is a cache miss when looking up `url`,\n     * this will fall back to retrieving the `Response` via `fetch()` when\n     * `fallbackToNetwork` is `true`.\n     *\n     * @param {string} url The precached URL which will be used to lookup the\n     * `Response`.\n     * @param {boolean} [fallbackToNetwork=true] Whether to attempt to get the\n     * response from the network if there's a precache miss.\n     * @return {module:workbox-routing~handlerCallback}\n     */\n    createHandlerBoundToURL(url, fallbackToNetwork = true) {\n        const cacheKey = this.getCacheKeyForURL(url);\n        if (!cacheKey) {\n            throw new WorkboxError('non-precached-url', { url });\n        }\n        const handler = this.createHandler(fallbackToNetwork);\n        const request = new Request(url);\n        return () => handler({ request });\n    }\n}\nexport { PrecacheController };\n","export const isNav = event => event.request.mode === 'navigate';\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nexport const cacheOkAndOpaquePlugin = {\n    /**\n     * Returns a valid response (to allow caching) if the status is 200 (OK) or\n     * 0 (opaque).\n     *\n     * @param {Object} options\n     * @param {Response} options.response\n     * @return {Response|null}\n     *\n     * @private\n     */\n    cacheWillUpdate: async ({ response }) => {\n        if (response.status === 200 || response.status === 0) {\n            return response;\n        }\n        return null;\n    },\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { cacheNames } from 'workbox-core/_private/cacheNames.js';\nimport { cacheWrapper } from 'workbox-core/_private/cacheWrapper.js';\nimport { fetchWrapper } from 'workbox-core/_private/fetchWrapper.js';\nimport { getFriendlyURL } from 'workbox-core/_private/getFriendlyURL.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { messages } from './utils/messages.js';\nimport { cacheOkAndOpaquePlugin } from './plugins/cacheOkAndOpaquePlugin.js';\nimport './_version.js';\n/**\n * An implementation of a\n * [network first]{@link https://developers.google.com/web/fundamentals/instant-and-offline/offline-cookbook/#network-falling-back-to-cache}\n * request strategy.\n *\n * By default, this strategy will cache responses with a 200 status code as\n * well as [opaque responses]{@link https://developers.google.com/web/tools/workbox/guides/handle-third-party-requests}.\n * Opaque responses are are cross-origin requests where the response doesn't\n * support [CORS]{@link https://enable-cors.org/}.\n *\n * If the network request fails, and there is no cache match, this will throw\n * a `WorkboxError` exception.\n *\n * @memberof module:workbox-strategies\n */\nclass NetworkFirst {\n    /**\n     * @param {Object} options\n     * @param {string} options.cacheName Cache name to store and retrieve\n     * requests. Defaults to cache names provided by\n     * [workbox-core]{@link module:workbox-core.cacheNames}.\n     * @param {Array} options.plugins [Plugins]{@link https://developers.google.com/web/tools/workbox/guides/using-plugins}\n     * to use in conjunction with this caching strategy.\n     * @param {Object} options.fetchOptions Values passed along to the\n     * [`init`](https://developer.mozilla.org/en-US/docs/Web/API/WindowOrWorkerGlobalScope/fetch#Parameters)\n     * of all fetch() requests made by this strategy.\n     * @param {Object} options.matchOptions [`CacheQueryOptions`](https://w3c.github.io/ServiceWorker/#dictdef-cachequeryoptions)\n     * @param {number} options.networkTimeoutSeconds If set, any network requests\n     * that fail to respond within the timeout will fallback to the cache.\n     *\n     * This option can be used to combat\n     * \"[lie-fi]{@link https://developers.google.com/web/fundamentals/performance/poor-connectivity/#lie-fi}\"\n     * scenarios.\n     */\n    constructor(options = {}) {\n        this._cacheName = cacheNames.getRuntimeName(options.cacheName);\n        if (options.plugins) {\n            const isUsingCacheWillUpdate = options.plugins.some((plugin) => !!plugin.cacheWillUpdate);\n            this._plugins = isUsingCacheWillUpdate ?\n                options.plugins : [cacheOkAndOpaquePlugin, ...options.plugins];\n        }\n        else {\n            // No plugins passed in, use the default plugin.\n            this._plugins = [cacheOkAndOpaquePlugin];\n        }\n        this._networkTimeoutSeconds = options.networkTimeoutSeconds || 0;\n        if (process.env.NODE_ENV !== 'production') {\n            if (this._networkTimeoutSeconds) {\n                assert.isType(this._networkTimeoutSeconds, 'number', {\n                    moduleName: 'workbox-strategies',\n                    className: 'NetworkFirst',\n                    funcName: 'constructor',\n                    paramName: 'networkTimeoutSeconds',\n                });\n            }\n        }\n        this._fetchOptions = options.fetchOptions;\n        this._matchOptions = options.matchOptions;\n    }\n    /**\n     * This method will perform a request strategy and follows an API that\n     * will work with the\n     * [Workbox Router]{@link module:workbox-routing.Router}.\n     *\n     * @param {Object} options\n     * @param {Request|string} options.request A request to run this strategy for.\n     * @param {Event} [options.event] The event that triggered the request.\n     * @return {Promise}\n     */\n    async handle({ event, request }) {\n        const logs = [];\n        if (typeof request === 'string') {\n            request = new Request(request);\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(request, Request, {\n                moduleName: 'workbox-strategies',\n                className: 'NetworkFirst',\n                funcName: 'handle',\n                paramName: 'makeRequest',\n            });\n        }\n        const promises = [];\n        let timeoutId;\n        if (this._networkTimeoutSeconds) {\n            const { id, promise } = this._getTimeoutPromise({ request, event, logs });\n            timeoutId = id;\n            promises.push(promise);\n        }\n        const networkPromise = this._getNetworkPromise({ timeoutId, request, event, logs });\n        promises.push(networkPromise);\n        // Promise.race() will resolve as soon as the first promise resolves.\n        let response = await Promise.race(promises);\n        // If Promise.race() resolved with null, it might be due to a network\n        // timeout + a cache miss. If that were to happen, we'd rather wait until\n        // the networkPromise resolves instead of returning null.\n        // Note that it's fine to await an already-resolved promise, so we don't\n        // have to check to see if it's still \"in flight\".\n        if (!response) {\n            response = await networkPromise;\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            logger.groupCollapsed(messages.strategyStart('NetworkFirst', request));\n            for (const log of logs) {\n                logger.log(log);\n            }\n            messages.printFinalResponse(response);\n            logger.groupEnd();\n        }\n        if (!response) {\n            throw new WorkboxError('no-response', { url: request.url });\n        }\n        return response;\n    }\n    /**\n     * @param {Object} options\n     * @param {Request} options.request\n     * @param {Array} options.logs A reference to the logs array\n     * @param {Event} [options.event]\n     * @return {Promise}\n     *\n     * @private\n     */\n    _getTimeoutPromise({ request, logs, event }) {\n        let timeoutId;\n        const timeoutPromise = new Promise((resolve) => {\n            const onNetworkTimeout = async () => {\n                if (process.env.NODE_ENV !== 'production') {\n                    logs.push(`Timing out the network response at ` +\n                        `${this._networkTimeoutSeconds} seconds.`);\n                }\n                resolve(await this._respondFromCache({ request, event }));\n            };\n            timeoutId = setTimeout(onNetworkTimeout, this._networkTimeoutSeconds * 1000);\n        });\n        return {\n            promise: timeoutPromise,\n            id: timeoutId,\n        };\n    }\n    /**\n     * @param {Object} options\n     * @param {number|undefined} options.timeoutId\n     * @param {Request} options.request\n     * @param {Array} options.logs A reference to the logs Array.\n     * @param {Event} [options.event]\n     * @return {Promise}\n     *\n     * @private\n     */\n    async _getNetworkPromise({ timeoutId, request, logs, event }) {\n        let error;\n        let response;\n        try {\n            response = await fetchWrapper.fetch({\n                request,\n                event,\n                fetchOptions: this._fetchOptions,\n                plugins: this._plugins,\n            });\n        }\n        catch (err) {\n            error = err;\n        }\n        if (timeoutId) {\n            clearTimeout(timeoutId);\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            if (response) {\n                logs.push(`Got response from network.`);\n            }\n            else {\n                logs.push(`Unable to get a response from the network. Will respond ` +\n                    `with a cached response.`);\n            }\n        }\n        if (error || !response) {\n            response = await this._respondFromCache({ request, event });\n            if (process.env.NODE_ENV !== 'production') {\n                if (response) {\n                    logs.push(`Found a cached response in the '${this._cacheName}'` +\n                        ` cache.`);\n                }\n                else {\n                    logs.push(`No response found in the '${this._cacheName}' cache.`);\n                }\n            }\n        }\n        else {\n            // Keep the service worker alive while we put the request in the cache\n            const responseClone = response.clone();\n            const cachePut = cacheWrapper.put({\n                cacheName: this._cacheName,\n                request,\n                response: responseClone,\n                event,\n                plugins: this._plugins,\n            });\n            if (event) {\n                try {\n                    // The event has been responded to so we can keep the SW alive to\n                    // respond to the request\n                    event.waitUntil(cachePut);\n                }\n                catch (err) {\n                    if (process.env.NODE_ENV !== 'production') {\n                        logger.warn(`Unable to ensure service worker stays alive when ` +\n                            `updating cache for '${getFriendlyURL(request.url)}'.`);\n                    }\n                }\n            }\n        }\n        return response;\n    }\n    /**\n     * Used if the network timeouts or fails to make the request.\n     *\n     * @param {Object} options\n     * @param {Request} request The request to match in the cache\n     * @param {Event} [options.event]\n     * @return {Promise}\n     *\n     * @private\n     */\n    _respondFromCache({ event, request }) {\n        return cacheWrapper.match({\n            cacheName: this._cacheName,\n            request,\n            event,\n            matchOptions: this._matchOptions,\n            plugins: this._plugins,\n        });\n    }\n}\nexport { NetworkFirst };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\n/**\n * A class that wraps common IndexedDB functionality in a promise-based API.\n * It exposes all the underlying power and functionality of IndexedDB, but\n * wraps the most commonly used features in a way that's much simpler to use.\n *\n * @private\n */\nexport class DBWrapper {\n    /**\n     * @param {string} name\n     * @param {number} version\n     * @param {Object=} [callback]\n     * @param {!Function} [callbacks.onupgradeneeded]\n     * @param {!Function} [callbacks.onversionchange] Defaults to\n     *     DBWrapper.prototype._onversionchange when not specified.\n     * @private\n     */\n    constructor(name, version, { onupgradeneeded, onversionchange, } = {}) {\n        this._db = null;\n        this._name = name;\n        this._version = version;\n        this._onupgradeneeded = onupgradeneeded;\n        this._onversionchange = onversionchange || (() => this.close());\n    }\n    /**\n     * Returns the IDBDatabase instance (not normally needed).\n     * @return {IDBDatabase|undefined}\n     *\n     * @private\n     */\n    get db() {\n        return this._db;\n    }\n    /**\n     * Opens a connected to an IDBDatabase, invokes any onupgradedneeded\n     * callback, and added an onversionchange callback to the database.\n     *\n     * @return {IDBDatabase}\n     * @private\n     */\n    async open() {\n        if (this._db)\n            return;\n        this._db = await new Promise((resolve, reject) => {\n            // This flag is flipped to true if the timeout callback runs prior\n            // to the request failing or succeeding. Note: we use a timeout instead\n            // of an onblocked handler since there are cases where onblocked will\n            // never never run. A timeout better handles all possible scenarios:\n            // https://github.com/w3c/IndexedDB/issues/223\n            let openRequestTimedOut = false;\n            setTimeout(() => {\n                openRequestTimedOut = true;\n                reject(new Error('The open request was blocked and timed out'));\n            }, this.OPEN_TIMEOUT);\n            const openRequest = indexedDB.open(this._name, this._version);\n            openRequest.onerror = () => reject(openRequest.error);\n            openRequest.onupgradeneeded = (evt) => {\n                if (openRequestTimedOut) {\n                    openRequest.transaction.abort();\n                    openRequest.result.close();\n                }\n                else if (typeof this._onupgradeneeded === 'function') {\n                    this._onupgradeneeded(evt);\n                }\n            };\n            openRequest.onsuccess = () => {\n                const db = openRequest.result;\n                if (openRequestTimedOut) {\n                    db.close();\n                }\n                else {\n                    db.onversionchange = this._onversionchange.bind(this);\n                    resolve(db);\n                }\n            };\n        });\n        return this;\n    }\n    /**\n     * Polyfills the native `getKey()` method. Note, this is overridden at\n     * runtime if the browser supports the native method.\n     *\n     * @param {string} storeName\n     * @param {*} query\n     * @return {Array}\n     * @private\n     */\n    async getKey(storeName, query) {\n        return (await this.getAllKeys(storeName, query, 1))[0];\n    }\n    /**\n     * Polyfills the native `getAll()` method. Note, this is overridden at\n     * runtime if the browser supports the native method.\n     *\n     * @param {string} storeName\n     * @param {*} query\n     * @param {number} count\n     * @return {Array}\n     * @private\n     */\n    async getAll(storeName, query, count) {\n        return await this.getAllMatching(storeName, { query, count });\n    }\n    /**\n     * Polyfills the native `getAllKeys()` method. Note, this is overridden at\n     * runtime if the browser supports the native method.\n     *\n     * @param {string} storeName\n     * @param {*} query\n     * @param {number} count\n     * @return {Array}\n     * @private\n     */\n    async getAllKeys(storeName, query, count) {\n        const entries = await this.getAllMatching(storeName, { query, count, includeKeys: true });\n        return entries.map((entry) => entry.key);\n    }\n    /**\n     * Supports flexible lookup in an object store by specifying an index,\n     * query, direction, and count. This method returns an array of objects\n     * with the signature .\n     *\n     * @param {string} storeName\n     * @param {Object} [opts]\n     * @param {string} [opts.index] The index to use (if specified).\n     * @param {*} [opts.query]\n     * @param {IDBCursorDirection} [opts.direction]\n     * @param {number} [opts.count] The max number of results to return.\n     * @param {boolean} [opts.includeKeys] When true, the structure of the\n     *     returned objects is changed from an array of values to an array of\n     *     objects in the form {key, primaryKey, value}.\n     * @return {Array}\n     * @private\n     */\n    async getAllMatching(storeName, { index, query = null, // IE/Edge errors if query === `undefined`.\n    direction = 'next', count, includeKeys = false, } = {}) {\n        return await this.transaction([storeName], 'readonly', (txn, done) => {\n            const store = txn.objectStore(storeName);\n            const target = index ? store.index(index) : store;\n            const results = [];\n            const request = target.openCursor(query, direction);\n            request.onsuccess = () => {\n                const cursor = request.result;\n                if (cursor) {\n                    results.push(includeKeys ? cursor : cursor.value);\n                    if (count && results.length >= count) {\n                        done(results);\n                    }\n                    else {\n                        cursor.continue();\n                    }\n                }\n                else {\n                    done(results);\n                }\n            };\n        });\n    }\n    /**\n     * Accepts a list of stores, a transaction type, and a callback and\n     * performs a transaction. A promise is returned that resolves to whatever\n     * value the callback chooses. The callback holds all the transaction logic\n     * and is invoked with two arguments:\n     *   1. The IDBTransaction object\n     *   2. A `done` function, that's used to resolve the promise when\n     *      when the transaction is done, if passed a value, the promise is\n     *      resolved to that value.\n     *\n     * @param {Array} storeNames An array of object store names\n     *     involved in the transaction.\n     * @param {string} type Can be `readonly` or `readwrite`.\n     * @param {!Function} callback\n     * @return {*} The result of the transaction ran by the callback.\n     * @private\n     */\n    async transaction(storeNames, type, callback) {\n        await this.open();\n        return await new Promise((resolve, reject) => {\n            const txn = this._db.transaction(storeNames, type);\n            txn.onabort = () => reject(txn.error);\n            txn.oncomplete = () => resolve();\n            callback(txn, (value) => resolve(value));\n        });\n    }\n    /**\n     * Delegates async to a native IDBObjectStore method.\n     *\n     * @param {string} method The method name.\n     * @param {string} storeName The object store name.\n     * @param {string} type Can be `readonly` or `readwrite`.\n     * @param {...*} args The list of args to pass to the native method.\n     * @return {*} The result of the transaction.\n     * @private\n     */\n    async _call(method, storeName, type, ...args) {\n        const callback = (txn, done) => {\n            const objStore = txn.objectStore(storeName);\n            // TODO(philipwalton): Fix this underlying TS2684 error.\n            // @ts-ignore\n            const request = objStore[method].apply(objStore, args);\n            request.onsuccess = () => done(request.result);\n        };\n        return await this.transaction([storeName], type, callback);\n    }\n    /**\n     * Closes the connection opened by `DBWrapper.open()`. Generally this method\n     * doesn't need to be called since:\n     *   1. It's usually better to keep a connection open since opening\n     *      a new connection is somewhat slow.\n     *   2. Connections are automatically closed when the reference is\n     *      garbage collected.\n     * The primary use case for needing to close a connection is when another\n     * reference (typically in another tab) needs to upgrade it and would be\n     * blocked by the current, open connection.\n     *\n     * @private\n     */\n    close() {\n        if (this._db) {\n            this._db.close();\n            this._db = null;\n        }\n    }\n}\n// Exposed on the prototype to let users modify the default timeout on a\n// per-instance or global basis.\nDBWrapper.prototype.OPEN_TIMEOUT = 2000;\n// Wrap native IDBObjectStore methods according to their mode.\nconst methodsToWrap = {\n    readonly: ['get', 'count', 'getKey', 'getAll', 'getAllKeys'],\n    readwrite: ['add', 'put', 'clear', 'delete'],\n};\nfor (const [mode, methods] of Object.entries(methodsToWrap)) {\n    for (const method of methods) {\n        if (method in IDBObjectStore.prototype) {\n            // Don't use arrow functions here since we're outside of the class.\n            DBWrapper.prototype[method] =\n                async function (storeName, ...args) {\n                    return await this._call(method, storeName, mode, ...args);\n                };\n        }\n    }\n}\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { getOrCreateDefaultRouter } from './utils/getOrCreateDefaultRouter.js';\nimport './_version.js';\n/**\n * If a Route throws an error while handling a request, this `handler`\n * will be called and given a chance to provide a response.\n *\n * @param {module:workbox-routing~handlerCallback} handler A callback\n * function that returns a Promise resulting in a Response.\n *\n * @memberof module:workbox-routing\n */\nfunction setCatchHandler(handler) {\n    const defaultRouter = getOrCreateDefaultRouter();\n    defaultRouter.setCatchHandler(handler);\n}\nexport { setCatchHandler };\n","import { registerRoute, setCatchHandler } from 'workbox-routing';\nimport { precacheAndRoute, getCacheKeyForURL } from 'workbox-precaching';\nimport { isNav } from './utils';\nimport { NETWORK_HANDLER, PRECACHING_OPTIONS } from './contants';\n\nexport function getFiles() {\n\treturn self.__WB_MANIFEST;\n}\n\nexport function setupPrecaching(precacheFiles, precachingOptions) {\n\tprecacheAndRoute(precacheFiles, precachingOptions || PRECACHING_OPTIONS);\n}\n\nexport function setupRouting() {\n\t/**\n\t * Adding this before `precacheAndRoute` lets us handle all\n\t * the navigation requests even if they are in precache.\n\t */\n\tregisterRoute(({ event }) => isNav(event), NETWORK_HANDLER);\n\n\tsetCatchHandler(({ event }) => {\n\t\tif (isNav(event)) {\n\t\t\treturn caches.match(getCacheKeyForURL('/index.html'));\n\t\t}\n\t\treturn Response.error();\n\t});\n}\n\nexport { PRECACHING_OPTIONS };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { cacheNames as _cacheNames } from './_private/cacheNames.js';\nimport './_version.js';\n/**\n * Get the current cache names and prefix/suffix used by Workbox.\n *\n * `cacheNames.precache` is used for precached assets,\n * `cacheNames.googleAnalytics` is used by `workbox-google-analytics` to\n * store `analytics.js`, and `cacheNames.runtime` is used for everything else.\n *\n * `cacheNames.prefix` can be used to retrieve just the current prefix value.\n * `cacheNames.suffix` can be used to retrieve just the current suffix value.\n *\n * @return {Object} An object with `precache`, `runtime`, `prefix`, and\n *     `googleAnalytics` properties.\n *\n * @memberof module:workbox-core\n */\nconst cacheNames = {\n    get googleAnalytics() {\n        return _cacheNames.getGoogleAnalyticsName();\n    },\n    get precache() {\n        return _cacheNames.getPrecacheName();\n    },\n    get prefix() {\n        return _cacheNames.getPrefix();\n    },\n    get runtime() {\n        return _cacheNames.getRuntimeName();\n    },\n    get suffix() {\n        return _cacheNames.getSuffix();\n    },\n};\nexport { cacheNames };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { getFriendlyURL } from 'workbox-core/_private/getFriendlyURL.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport './_version.js';\n/**\n * This class allows you to set up rules determining what\n * status codes and/or headers need to be present in order for a\n * [`Response`](https://developer.mozilla.org/en-US/docs/Web/API/Response)\n * to be considered cacheable.\n *\n * @memberof module:workbox-cacheable-response\n */\nclass CacheableResponse {\n    /**\n     * To construct a new CacheableResponse instance you must provide at least\n     * one of the `config` properties.\n     *\n     * If both `statuses` and `headers` are specified, then both conditions must\n     * be met for the `Response` to be considered cacheable.\n     *\n     * @param {Object} config\n     * @param {Array} [config.statuses] One or more status codes that a\n     * `Response` can have and be considered cacheable.\n     * @param {Object} [config.headers] A mapping of header names\n     * and expected values that a `Response` can have and be considered cacheable.\n     * If multiple headers are provided, only one needs to be present.\n     */\n    constructor(config = {}) {\n        if (process.env.NODE_ENV !== 'production') {\n            if (!(config.statuses || config.headers)) {\n                throw new WorkboxError('statuses-or-headers-required', {\n                    moduleName: 'workbox-cacheable-response',\n                    className: 'CacheableResponse',\n                    funcName: 'constructor',\n                });\n            }\n            if (config.statuses) {\n                assert.isArray(config.statuses, {\n                    moduleName: 'workbox-cacheable-response',\n                    className: 'CacheableResponse',\n                    funcName: 'constructor',\n                    paramName: 'config.statuses',\n                });\n            }\n            if (config.headers) {\n                assert.isType(config.headers, 'object', {\n                    moduleName: 'workbox-cacheable-response',\n                    className: 'CacheableResponse',\n                    funcName: 'constructor',\n                    paramName: 'config.headers',\n                });\n            }\n        }\n        this._statuses = config.statuses;\n        this._headers = config.headers;\n    }\n    /**\n     * Checks a response to see whether it's cacheable or not, based on this\n     * object's configuration.\n     *\n     * @param {Response} response The response whose cacheability is being\n     * checked.\n     * @return {boolean} `true` if the `Response` is cacheable, and `false`\n     * otherwise.\n     */\n    isResponseCacheable(response) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(response, Response, {\n                moduleName: 'workbox-cacheable-response',\n                className: 'CacheableResponse',\n                funcName: 'isResponseCacheable',\n                paramName: 'response',\n            });\n        }\n        let cacheable = true;\n        if (this._statuses) {\n            cacheable = this._statuses.includes(response.status);\n        }\n        if (this._headers && cacheable) {\n            cacheable = Object.keys(this._headers).some((headerName) => {\n                return response.headers.get(headerName) === this._headers[headerName];\n            });\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            if (!cacheable) {\n                logger.groupCollapsed(`The request for ` +\n                    `'${getFriendlyURL(response.url)}' returned a response that does ` +\n                    `not meet the criteria for being cached.`);\n                logger.groupCollapsed(`View cacheability criteria here.`);\n                logger.log(`Cacheable statuses: ` +\n                    JSON.stringify(this._statuses));\n                logger.log(`Cacheable headers: ` +\n                    JSON.stringify(this._headers, null, 2));\n                logger.groupEnd();\n                const logFriendlyHeaders = {};\n                response.headers.forEach((value, key) => {\n                    logFriendlyHeaders[key] = value;\n                });\n                logger.groupCollapsed(`View response status and headers here.`);\n                logger.log(`Response status: ` + response.status);\n                logger.log(`Response headers: ` +\n                    JSON.stringify(logFriendlyHeaders, null, 2));\n                logger.groupEnd();\n                logger.groupCollapsed(`View full response details here.`);\n                logger.log(response.headers);\n                logger.log(response);\n                logger.groupEnd();\n                logger.groupEnd();\n            }\n        }\n        return cacheable;\n    }\n}\nexport { CacheableResponse };\n","import { NetworkFirst } from 'workbox-strategies';\nimport { cacheNames } from 'workbox-core';\nimport { CacheableResponsePlugin } from 'workbox-cacheable-response';\n\nexport const PRECACHING_OPTIONS = {};\n\nexport const NETWORK_HANDLER = new NetworkFirst({\n\t// this cache is plunged with every new service worker deploy so we dont need to care about purging the cache.\n\tcacheName: cacheNames.precache,\n\tnetworkTimeoutSeconds: 5, // if u dont start getting headers within 5 sec fallback to cache.\n\tplugins: [\n\t\tnew CacheableResponsePlugin({\n\t\t\tstatuses: [200], // only cache valid responses, not opaque responses e.g. wifi portal.\n\t\t}),\n\t],\n});\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { Route } from './Route.js';\nimport { RegExpRoute } from './RegExpRoute.js';\nimport { getOrCreateDefaultRouter } from './utils/getOrCreateDefaultRouter.js';\nimport './_version.js';\n/**\n * Easily register a RegExp, string, or function with a caching\n * strategy to a singleton Router instance.\n *\n * This method will generate a Route for you if needed and\n * call [registerRoute()]{@link module:workbox-routing.Router#registerRoute}.\n *\n * @param {RegExp|string|module:workbox-routing.Route~matchCallback|module:workbox-routing.Route} capture\n * If the capture param is a `Route`, all other arguments will be ignored.\n * @param {module:workbox-routing~handlerCallback} [handler] A callback\n * function that returns a Promise resulting in a Response. This parameter\n * is required if `capture` is not a `Route` object.\n * @param {string} [method='GET'] The HTTP method to match the Route\n * against.\n * @return {module:workbox-routing.Route} The generated `Route`(Useful for\n * unregistering).\n *\n * @memberof module:workbox-routing\n */\nfunction registerRoute(capture, handler, method) {\n    let route;\n    if (typeof capture === 'string') {\n        const captureUrl = new URL(capture, location.href);\n        if (process.env.NODE_ENV !== 'production') {\n            if (!(capture.startsWith('/') || capture.startsWith('http'))) {\n                throw new WorkboxError('invalid-string', {\n                    moduleName: 'workbox-routing',\n                    funcName: 'registerRoute',\n                    paramName: 'capture',\n                });\n            }\n            // We want to check if Express-style wildcards are in the pathname only.\n            // TODO: Remove this log message in v4.\n            const valueToCheck = capture.startsWith('http') ?\n                captureUrl.pathname : capture;\n            // See https://github.com/pillarjs/path-to-regexp#parameters\n            const wildcards = '[*:?+]';\n            if ((new RegExp(`${wildcards}`)).exec(valueToCheck)) {\n                logger.debug(`The '$capture' parameter contains an Express-style wildcard ` +\n                    `character (${wildcards}). Strings are now always interpreted as ` +\n                    `exact matches; use a RegExp for partial or wildcard matches.`);\n            }\n        }\n        const matchCallback = ({ url }) => {\n            if (process.env.NODE_ENV !== 'production') {\n                if ((url.pathname === captureUrl.pathname) &&\n                    (url.origin !== captureUrl.origin)) {\n                    logger.debug(`${capture} only partially matches the cross-origin URL ` +\n                        `${url}. This route will only handle cross-origin requests ` +\n                        `if they match the entire URL.`);\n                }\n            }\n            return url.href === captureUrl.href;\n        };\n        // If `capture` is a string then `handler` and `method` must be present.\n        route = new Route(matchCallback, handler, method);\n    }\n    else if (capture instanceof RegExp) {\n        // If `capture` is a `RegExp` then `handler` and `method` must be present.\n        route = new RegExpRoute(capture, handler, method);\n    }\n    else if (typeof capture === 'function') {\n        // If `capture` is a function then `handler` and `method` must be present.\n        route = new Route(capture, handler, method);\n    }\n    else if (capture instanceof Route) {\n        route = capture;\n    }\n    else {\n        throw new WorkboxError('unsupported-route-type', {\n            moduleName: 'workbox-routing',\n            funcName: 'registerRoute',\n            paramName: 'capture',\n        });\n    }\n    const defaultRouter = getOrCreateDefaultRouter();\n    defaultRouter.registerRoute(route);\n    return route;\n}\nexport { registerRoute };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { CacheableResponse } from './CacheableResponse.js';\nimport './_version.js';\n/**\n * A class implementing the `cacheWillUpdate` lifecycle callback. This makes it\n * easier to add in cacheability checks to requests made via Workbox's built-in\n * strategies.\n *\n * @memberof module:workbox-cacheable-response\n */\nclass CacheableResponsePlugin {\n    /**\n     * To construct a new CacheableResponsePlugin instance you must provide at\n     * least one of the `config` properties.\n     *\n     * If both `statuses` and `headers` are specified, then both conditions must\n     * be met for the `Response` to be considered cacheable.\n     *\n     * @param {Object} config\n     * @param {Array} [config.statuses] One or more status codes that a\n     * `Response` can have and be considered cacheable.\n     * @param {Object} [config.headers] A mapping of header names\n     * and expected values that a `Response` can have and be considered cacheable.\n     * If multiple headers are provided, only one needs to be present.\n     */\n    constructor(config) {\n        /**\n         * @param {Object} options\n         * @param {Response} options.response\n         * @return {Response|null}\n         * @private\n         */\n        this.cacheWillUpdate = async ({ response }) => {\n            if (this._cacheableResponse.isResponseCacheable(response)) {\n                return response;\n            }\n            return null;\n        };\n        this._cacheableResponse = new CacheableResponse(config);\n    }\n}\nexport { CacheableResponsePlugin };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { getOrCreatePrecacheController } from './utils/getOrCreatePrecacheController.js';\nimport './_version.js';\n/**\n * Takes in a URL, and returns the corresponding URL that could be used to\n * lookup the entry in the precache.\n *\n * If a relative URL is provided, the location of the service worker file will\n * be used as the base.\n *\n * For precached entries without revision information, the cache key will be the\n * same as the original URL.\n *\n * For precached entries with revision information, the cache key will be the\n * original URL with the addition of a query parameter used for keeping track of\n * the revision info.\n *\n * @param {string} url The URL whose cache key to look up.\n * @return {string} The cache key that corresponds to that URL.\n *\n * @memberof module:workbox-precaching\n */\nfunction getCacheKeyForURL(url) {\n    const precacheController = getOrCreatePrecacheController();\n    return precacheController.getCacheKeyForURL(url);\n}\nexport { getCacheKeyForURL };\n","\"use strict\";\n// @ts-ignore\ntry {\n    self['workbox:core:5.1.3'] && _();\n}\ncatch (e) { }\n"]}
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\"p5Qz\");\n","\"use strict\";\n// @ts-ignore\ntry {\n    self['workbox:cacheable-response:5.1.3'] && _();\n}\ncatch (e) { }\n","\"use strict\";\n// @ts-ignore\ntry {\n    self['workbox:precaching:5.1.3'] && _();\n}\ncatch (e) { }\n","\"use strict\";\n// @ts-ignore\ntry {\n    self['workbox:routing:5.1.3'] && _();\n}\ncatch (e) { }\n","\"use strict\";\n// @ts-ignore\ntry {\n    self['workbox:strategies:5.1.3'] && _();\n}\ncatch (e) { }\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { canConstructResponseFromBodyStream } from './_private/canConstructResponseFromBodyStream.js';\nimport './_version.js';\n/**\n * Allows developers to copy a response and modify its `headers`, `status`,\n * or `statusText` values (the values settable via a\n * [`ResponseInit`]{@link https://developer.mozilla.org/en-US/docs/Web/API/Response/Response#Syntax}\n 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That\n * function will be invoked with a single object with the response properties\n * `{headers, status, statusText}`. The return value of this function will\n * be used as the `ResponseInit` for the new `Response`. To change the values\n * either modify the passed parameter(s) and return it, or return a totally\n * new object.\n *\n * @param {Response} response\n * @param {Function} modifier\n * @memberof module:workbox-core\n */\nasync function copyResponse(response, modifier) {\n    const clonedResponse = response.clone();\n    // Create a fresh `ResponseInit` object by cloning the headers.\n    const responseInit = {\n        headers: new Headers(clonedResponse.headers),\n        status: clonedResponse.status,\n        statusText: clonedResponse.statusText,\n    };\n    // Apply any user modifications.\n    const modifiedResponseInit = modifier ? modifier(responseInit) : responseInit;\n    // Create the new response from the body stream and `ResponseInit`\n    // modifications. 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Return as-is.\n    if (typeof entry === 'string') {\n        const urlObject = new URL(entry, location.href);\n        return {\n            cacheKey: urlObject.href,\n            url: urlObject.href,\n        };\n    }\n    const { revision, url } = entry;\n    if (!url) {\n        throw new WorkboxError('add-to-cache-list-unexpected-type', { entry });\n    }\n    // If there's just a URL and no revision, then it's also assumed to be a\n    // versioned URL.\n    if (!revision) {\n        const urlObject = new URL(url, location.href);\n        return {\n            cacheKey: urlObject.href,\n            url: urlObject.href,\n        };\n    }\n    // Otherwise, construct a properly versioned URL using the custom Workbox\n    // search parameter along with the revision info.\n    const cacheKeyURL = new URL(url, location.href);\n    const originalURL = new URL(url, location.href);\n    cacheKeyURL.searchParams.set(REVISION_SEARCH_PARAM, revision);\n    return {\n        cacheKey: cacheKeyURL.href,\n        url: originalURL.href,\n    };\n}\n","/*\n  Copyright 2019 Google LLC\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { addFetchListener } from './utils/addFetchListener.js';\nimport './_version.js';\nlet listenerAdded = false;\n/**\n * Add a `fetch` listener to the service worker that will\n * respond to\n * [network requests]{@link https://developer.mozilla.org/en-US/docs/Web/API/Service_Worker_API/Using_Service_Workers#Custom_responses_to_requests}\n * with precached assets.\n *\n * Requests for assets that aren't precached, the `FetchEvent` will not be\n * responded to, allowing the event to fall through to other `fetch` event\n * listeners.\n *\n * @param {Object} [options]\n * @param {string} [options.directoryIndex=index.html] The `directoryIndex` will\n * check cache entries for a URLs ending with '/' to see if there is a hit when\n * appending the `directoryIndex` value.\n * @param {Array} [options.ignoreURLParametersMatching=[/^utm_/]] An\n * array of regex's to remove search params when looking for a cache match.\n * @param {boolean} [options.cleanURLs=true] The `cleanURLs` option will\n * check the cache for the URL with a `.html` added to the end of the end.\n * @param {module:workbox-precaching~urlManipulation} [options.urlManipulation]\n * This is a function that should take a URL and return an array of\n * alternative URLs that should be checked for precache matches.\n *\n * @memberof module:workbox-precaching\n */\nfunction addRoute(options) {\n    if (!listenerAdded) {\n        addFetchListener(options);\n        listenerAdded = true;\n    }\n}\nexport { addRoute };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { cacheNames } from 'workbox-core/_private/cacheNames.js';\nimport { getFriendlyURL } from 'workbox-core/_private/getFriendlyURL.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { getCacheKeyForURL } from './getCacheKeyForURL.js';\nimport '../_version.js';\n/**\n * Adds a `fetch` listener to the service worker that will\n * respond to\n * [network requests]{@link https://developer.mozilla.org/en-US/docs/Web/API/Service_Worker_API/Using_Service_Workers#Custom_responses_to_requests}\n * with precached assets.\n *\n * Requests for assets that aren't precached, the `FetchEvent` will not be\n * responded to, allowing the event to fall through to other `fetch` event\n * listeners.\n *\n * NOTE: when called more than once this method will replace the previously set\n * configuration options. Calling it more than once is not recommended outside\n * of tests.\n *\n * @private\n * @param {Object} [options]\n * @param {string} [options.directoryIndex=index.html] The `directoryIndex` will\n * check cache entries for a URLs ending with '/' to see if there is a hit when\n * appending the `directoryIndex` value.\n * @param {Array} [options.ignoreURLParametersMatching=[/^utm_/]] An\n * array of regex's to remove search params when looking for a cache match.\n * @param {boolean} [options.cleanURLs=true] The `cleanURLs` option will\n * check the cache for the URL with a `.html` added to the end of the end.\n * @param {workbox.precaching~urlManipulation} [options.urlManipulation]\n * This is a function that should take a URL and return an array of\n * alternative URLs that should be checked for precache matches.\n */\nexport const addFetchListener = ({ ignoreURLParametersMatching = [/^utm_/], directoryIndex = 'index.html', cleanURLs = true, urlManipulation, } = {}) => {\n    const cacheName = cacheNames.getPrecacheName();\n    // See https://github.com/Microsoft/TypeScript/issues/28357#issuecomment-436484705\n    self.addEventListener('fetch', ((event) => {\n        const precachedURL = getCacheKeyForURL(event.request.url, {\n            cleanURLs,\n            directoryIndex,\n            ignoreURLParametersMatching,\n            urlManipulation,\n        });\n        if (!precachedURL) {\n            if (process.env.NODE_ENV !== 'production') {\n                logger.debug(`Precaching did not find a match for ` +\n                    getFriendlyURL(event.request.url));\n            }\n            return;\n        }\n        let responsePromise = self.caches.open(cacheName).then((cache) => {\n            return cache.match(precachedURL);\n        }).then((cachedResponse) => {\n            if (cachedResponse) {\n                return cachedResponse;\n            }\n            // Fall back to the network if we don't have a cached response\n            // (perhaps due to manual cache cleanup).\n            if (process.env.NODE_ENV !== 'production') {\n                logger.warn(`The precached response for ` +\n                    `${getFriendlyURL(precachedURL)} in ${cacheName} was not found. ` +\n                    `Falling back to the network instead.`);\n            }\n            return fetch(precachedURL);\n        });\n        if (process.env.NODE_ENV !== 'production') {\n            responsePromise = responsePromise.then((response) => {\n                // Workbox is going to handle the route.\n                // print the routing details to the console.\n                logger.groupCollapsed(`Precaching is responding to: ` +\n                    getFriendlyURL(event.request.url));\n                logger.log(`Serving the precached url: ${precachedURL}`);\n                logger.groupCollapsed(`View request details here.`);\n                logger.log(event.request);\n                logger.groupEnd();\n                logger.groupCollapsed(`View response details here.`);\n                logger.log(response);\n                logger.groupEnd();\n                logger.groupEnd();\n                return response;\n            });\n        }\n        event.respondWith(responsePromise);\n    }));\n};\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { getOrCreatePrecacheController } from './getOrCreatePrecacheController.js';\nimport { generateURLVariations } from './generateURLVariations.js';\nimport '../_version.js';\n/**\n * This function will take the request URL and manipulate it based on the\n * configuration options.\n *\n * @param {string} url\n * @param {Object} options\n * @return {string} Returns the URL in the cache that matches the request,\n * if possible.\n *\n * @private\n */\nexport const getCacheKeyForURL = (url, options) => {\n    const precacheController = getOrCreatePrecacheController();\n    const urlsToCacheKeys = precacheController.getURLsToCacheKeys();\n    for (const possibleURL of generateURLVariations(url, options)) {\n        const possibleCacheKey = urlsToCacheKeys.get(possibleURL);\n        if (possibleCacheKey) {\n            return possibleCacheKey;\n        }\n    }\n};\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { removeIgnoredSearchParams } from './removeIgnoredSearchParams.js';\nimport '../_version.js';\n/**\n * Generator function that yields possible variations on the original URL to\n * check, one at a time.\n *\n * @param {string} url\n * @param {Object} options\n *\n * @private\n * @memberof module:workbox-precaching\n */\nexport function* generateURLVariations(url, { ignoreURLParametersMatching, directoryIndex, cleanURLs, urlManipulation, } = {}) {\n    const urlObject = new URL(url, location.href);\n    urlObject.hash = '';\n    yield urlObject.href;\n    const urlWithoutIgnoredParams = removeIgnoredSearchParams(urlObject, ignoreURLParametersMatching);\n    yield urlWithoutIgnoredParams.href;\n    if (directoryIndex && urlWithoutIgnoredParams.pathname.endsWith('/')) {\n        const directoryURL = new URL(urlWithoutIgnoredParams.href);\n        directoryURL.pathname += directoryIndex;\n        yield directoryURL.href;\n    }\n    if (cleanURLs) {\n        const cleanURL = new URL(urlWithoutIgnoredParams.href);\n        cleanURL.pathname += '.html';\n        yield cleanURL.href;\n    }\n    if (urlManipulation) {\n        const additionalURLs = urlManipulation({ url: urlObject });\n        for (const urlToAttempt of additionalURLs) {\n            yield urlToAttempt.href;\n        }\n    }\n}\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\n/**\n * Removes any URL search parameters that should be ignored.\n *\n * @param {URL} urlObject The original URL.\n * @param {Array} ignoreURLParametersMatching RegExps to test against\n * each search parameter name. Matches mean that the search parameter should be\n * ignored.\n * @return {URL} The URL with any ignored search parameters removed.\n *\n * @private\n * @memberof module:workbox-precaching\n */\nexport function removeIgnoredSearchParams(urlObject, ignoreURLParametersMatching = []) {\n    // Convert the iterable into an array at the start of the loop to make sure\n    // deletion doesn't mess up iteration.\n    for (const paramName of [...urlObject.searchParams.keys()]) {\n        if (ignoreURLParametersMatching.some((regExp) => regExp.test(paramName))) {\n            urlObject.searchParams.delete(paramName);\n        }\n    }\n    return urlObject;\n}\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { addRoute } from './addRoute.js';\nimport { precache } from './precache.js';\nimport './_version.js';\n/**\n * This method will add entries to the precache list and add a route to\n * respond to fetch events.\n *\n * This is a convenience method that will call\n * [precache()]{@link module:workbox-precaching.precache} and\n * [addRoute()]{@link module:workbox-precaching.addRoute} in a single call.\n *\n * @param {Array} entries Array of entries to precache.\n * @param {Object} [options] See\n * [addRoute() options]{@link module:workbox-precaching.addRoute}.\n *\n * @memberof module:workbox-precaching\n */\nfunction precacheAndRoute(entries, options) {\n    precache(entries);\n    addRoute(options);\n}\nexport { precacheAndRoute };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { getOrCreatePrecacheController } from './utils/getOrCreatePrecacheController.js';\nimport { precachePlugins } from './utils/precachePlugins.js';\nimport './_version.js';\nconst installListener = (event) => {\n    const precacheController = getOrCreatePrecacheController();\n    const plugins = precachePlugins.get();\n    event.waitUntil(precacheController.install({ event, plugins })\n        .catch((error) => {\n        if (process.env.NODE_ENV !== 'production') {\n            logger.error(`Service worker installation failed. It will ` +\n                `be retried automatically during the next navigation.`);\n        }\n        // Re-throw the error to ensure installation fails.\n        throw error;\n    }));\n};\nconst activateListener = (event) => {\n    const precacheController = getOrCreatePrecacheController();\n    event.waitUntil(precacheController.activate());\n};\n/**\n * Adds items to the precache list, removing any duplicates and\n * stores the files in the\n * [\"precache cache\"]{@link module:workbox-core.cacheNames} when the service\n * worker installs.\n *\n * This method can be called multiple times.\n *\n * Please note: This method **will not** serve any of the cached files for you.\n * It only precaches files. To respond to a network request you call\n * [addRoute()]{@link module:workbox-precaching.addRoute}.\n *\n * If you have a single array of files to precache, you can just call\n * [precacheAndRoute()]{@link module:workbox-precaching.precacheAndRoute}.\n *\n * @param {Array} [entries=[]] Array of entries to precache.\n *\n * @memberof module:workbox-precaching\n */\nfunction precache(entries) {\n    const precacheController = getOrCreatePrecacheController();\n    precacheController.addToCacheList(entries);\n    if (entries.length > 0) {\n        // NOTE: these listeners will only be added once (even if the `precache()`\n        // method is called multiple times) because event listeners are implemented\n        // as a set, where each listener must be unique.\n        // See https://github.com/Microsoft/TypeScript/issues/28357#issuecomment-436484705\n        self.addEventListener('install', installListener);\n        self.addEventListener('activate', activateListener);\n    }\n}\nexport { precache };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { Router } from '../Router.js';\nimport '../_version.js';\nlet defaultRouter;\n/**\n * Creates a new, singleton Router instance if one does not exist. If one\n * does already exist, that instance is returned.\n *\n * @private\n * @return {Router}\n */\nexport const getOrCreateDefaultRouter = () => {\n    if (!defaultRouter) {\n        defaultRouter = new Router();\n        // The helpers that use the default Router assume these listeners exist.\n        defaultRouter.addFetchListener();\n        defaultRouter.addCacheListener();\n    }\n    return defaultRouter;\n};\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { PrecacheController } from '../PrecacheController.js';\nimport '../_version.js';\nlet precacheController;\n/**\n * @return {PrecacheController}\n * @private\n */\nexport const getOrCreatePrecacheController = () => {\n    if (!precacheController) {\n        precacheController = new PrecacheController();\n    }\n    return precacheController;\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { messages } from './messages.js';\nimport '../../_version.js';\nconst fallback = (code, ...args) => {\n    let msg = code;\n    if (args.length > 0) {\n        msg += ` :: ${JSON.stringify(args)}`;\n    }\n    return msg;\n};\nconst generatorFunction = (code, details = {}) => {\n    const message = messages[code];\n    if (!message) {\n        throw new Error(`Unable to find message for code '${code}'.`);\n    }\n    return message(details);\n};\nexport const messageGenerator = (process.env.NODE_ENV === 'production') ?\n    fallback : generatorFunction;\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { messageGenerator } from '../models/messages/messageGenerator.js';\nimport '../_version.js';\n/**\n * Workbox errors should be thrown with this class.\n * This allows use to ensure the type easily in tests,\n * helps developers identify errors from workbox\n * easily and allows use to optimise error\n * messages correctly.\n *\n * @private\n */\nclass WorkboxError extends Error {\n    /**\n     *\n     * @param {string} errorCode The error code that\n     * identifies this particular error.\n     * @param {Object=} details Any relevant arguments\n     * that will help developers identify issues should\n     * be added as a key on the context object.\n     */\n    constructor(errorCode, details) {\n        const message = messageGenerator(errorCode, details);\n        super(message);\n        this.name = errorCode;\n        this.details = details;\n    }\n}\nexport { WorkboxError };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport '../_version.js';\n/**\n * @param {function()|Object} handler Either a function, or an object with a\n * 'handle' method.\n * @return {Object} An object with a handle method.\n *\n * @private\n */\nexport const normalizeHandler = (handler) => {\n    if (handler && typeof handler === 'object') {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.hasMethod(handler, 'handle', {\n                moduleName: 'workbox-routing',\n                className: 'Route',\n                funcName: 'constructor',\n                paramName: 'handler',\n            });\n        }\n        return handler;\n    }\n    else {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isType(handler, 'function', {\n                moduleName: 'workbox-routing',\n                className: 'Route',\n                funcName: 'constructor',\n                paramName: 'handler',\n            });\n        }\n        return { handle: handler };\n    }\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { defaultMethod, validMethods } from './utils/constants.js';\nimport { normalizeHandler } from './utils/normalizeHandler.js';\nimport './_version.js';\n/**\n * A `Route` consists of a pair of callback functions, \"match\" and \"handler\".\n * The \"match\" callback determine if a route should be used to \"handle\" a\n * request by returning a non-falsy value if it can. The \"handler\" callback\n * is called when there is a match and should return a Promise that resolves\n * to a `Response`.\n *\n * @memberof module:workbox-routing\n */\nclass Route {\n    /**\n     * Constructor for Route class.\n     *\n     * @param {module:workbox-routing~matchCallback} match\n     * A callback function that determines whether the route matches a given\n     * `fetch` event by returning a non-falsy value.\n     * @param {module:workbox-routing~handlerCallback} handler A callback\n     * function that returns a Promise resolving to a Response.\n     * @param {string} [method='GET'] The HTTP method to match the Route\n     * against.\n     */\n    constructor(match, handler, method = defaultMethod) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isType(match, 'function', {\n                moduleName: 'workbox-routing',\n                className: 'Route',\n                funcName: 'constructor',\n                paramName: 'match',\n            });\n            if (method) {\n                assert.isOneOf(method, validMethods, { paramName: 'method' });\n            }\n        }\n        // These values are referenced directly by Router so cannot be\n        // altered by minificaton.\n        this.handler = normalizeHandler(handler);\n        this.match = match;\n        this.method = method;\n    }\n}\nexport { Route };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\n/**\n * The default HTTP method, 'GET', used when there's no specific method\n * configured for a route.\n *\n * @type {string}\n *\n * @private\n */\nexport const defaultMethod = 'GET';\n/**\n * The list of valid HTTP methods associated with requests that could be routed.\n *\n * @type {Array}\n *\n * @private\n */\nexport const validMethods = [\n    'DELETE',\n    'GET',\n    'HEAD',\n    'PATCH',\n    'POST',\n    'PUT',\n];\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { Route } from './Route.js';\nimport './_version.js';\n/**\n * RegExpRoute makes it easy to create a regular expression based\n * [Route]{@link module:workbox-routing.Route}.\n *\n * For same-origin requests the RegExp only needs to match part of the URL. For\n * requests against third-party servers, you must define a RegExp that matches\n * the start of the URL.\n *\n * [See the module docs for info.]{@link https://developers.google.com/web/tools/workbox/modules/workbox-routing}\n *\n * @memberof module:workbox-routing\n * @extends module:workbox-routing.Route\n */\nclass RegExpRoute extends Route {\n    /**\n     * If the regular expression contains\n     * [capture groups]{@link https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/RegExp#grouping-back-references},\n     * the captured values will be passed to the\n     * [handler's]{@link module:workbox-routing~handlerCallback} `params`\n     * argument.\n     *\n     * @param {RegExp} regExp The regular expression to match against URLs.\n     * @param {module:workbox-routing~handlerCallback} handler A callback\n     * function that returns a Promise resulting in a Response.\n     * @param {string} [method='GET'] The HTTP method to match the Route\n     * against.\n     */\n    constructor(regExp, handler, method) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(regExp, RegExp, {\n                moduleName: 'workbox-routing',\n                className: 'RegExpRoute',\n                funcName: 'constructor',\n                paramName: 'pattern',\n            });\n        }\n        const match = ({ url }) => {\n            const result = regExp.exec(url.href);\n            // Return immediately if there's no match.\n            if (!result) {\n                return;\n            }\n            // Require that the match start at the first character in the URL string\n            // if it's a cross-origin request.\n            // See https://github.com/GoogleChrome/workbox/issues/281 for the context\n            // behind this behavior.\n            if ((url.origin !== location.origin) && (result.index !== 0)) {\n                if (process.env.NODE_ENV !== 'production') {\n                    logger.debug(`The regular expression '${regExp}' only partially matched ` +\n                        `against the cross-origin URL '${url}'. RegExpRoute's will only ` +\n                        `handle cross-origin requests if they match the entire URL.`);\n                }\n                return;\n            }\n            // If the route matches, but there aren't any capture groups defined, then\n            // this will return [], which is truthy and therefore sufficient to\n            // indicate a match.\n            // If there are capture groups, then it will return their values.\n            return result.slice(1);\n        };\n        super(match, handler, method);\n    }\n}\nexport { RegExpRoute };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nconst getFriendlyURL = (url) => {\n    const urlObj = new URL(String(url), location.href);\n    // See https://github.com/GoogleChrome/workbox/issues/2323\n    // We want to include everything, except for the origin if it's same-origin.\n    return urlObj.href.replace(new RegExp(`^${location.origin}`), '');\n};\nexport { getFriendlyURL };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { getFriendlyURL } from 'workbox-core/_private/getFriendlyURL.js';\nimport { normalizeHandler } from './utils/normalizeHandler.js';\nimport './_version.js';\n/**\n * The Router can be used to process a FetchEvent through one or more\n * [Routes]{@link module:workbox-routing.Route} responding  with a Request if\n * a matching route exists.\n *\n * If no route matches a given a request, the Router will use a \"default\"\n * handler if one is defined.\n *\n * Should the matching Route throw an error, the Router will use a \"catch\"\n * handler if one is defined to gracefully deal with issues and respond with a\n * Request.\n *\n * If a request matches multiple routes, the **earliest** registered route will\n * be used to respond to the request.\n *\n * @memberof module:workbox-routing\n */\nclass Router {\n    /**\n     * Initializes a new Router.\n     */\n    constructor() {\n        this._routes = new Map();\n    }\n    /**\n     * @return {Map>} routes A `Map` of HTTP\n     * method name ('GET', etc.) to an array of all the corresponding `Route`\n     * instances that are registered.\n     */\n    get routes() {\n        return this._routes;\n    }\n    /**\n     * Adds a fetch event listener to respond to events when a route matches\n     * the event's request.\n     */\n    addFetchListener() {\n        // See https://github.com/Microsoft/TypeScript/issues/28357#issuecomment-436484705\n        self.addEventListener('fetch', ((event) => {\n            const { request } = event;\n            const responsePromise = this.handleRequest({ request, event });\n            if (responsePromise) {\n                event.respondWith(responsePromise);\n            }\n        }));\n    }\n    /**\n     * Adds a message event listener for URLs to cache from the window.\n     * This is useful to cache resources loaded on the page prior to when the\n     * service worker started controlling it.\n     *\n     * The format of the message data sent from the window should be as follows.\n     * Where the `urlsToCache` array may consist of URL strings or an array of\n     * URL string + `requestInit` object (the same as you'd pass to `fetch()`).\n     *\n     * ```\n     * {\n     *   type: 'CACHE_URLS',\n     *   payload: {\n     *     urlsToCache: [\n     *       './script1.js',\n     *       './script2.js',\n     *       ['./script3.js', {mode: 'no-cors'}],\n     *     ],\n     *   },\n     * }\n     * ```\n     */\n    addCacheListener() {\n        // See https://github.com/Microsoft/TypeScript/issues/28357#issuecomment-436484705\n        self.addEventListener('message', ((event) => {\n            if (event.data && event.data.type === 'CACHE_URLS') {\n                const { payload } = event.data;\n                if (process.env.NODE_ENV !== 'production') {\n                    logger.debug(`Caching URLs from the window`, payload.urlsToCache);\n                }\n                const requestPromises = Promise.all(payload.urlsToCache.map((entry) => {\n                    if (typeof entry === 'string') {\n                        entry = [entry];\n                    }\n                    const request = new Request(...entry);\n                    return this.handleRequest({ request });\n                    // TODO(philipwalton): TypeScript errors without this typecast for\n                    // some reason (probably a bug). The real type here should work but\n                    // doesn't: `Array | undefined>`.\n                })); // TypeScript\n                event.waitUntil(requestPromises);\n                // If a MessageChannel was used, reply to the message on success.\n                if (event.ports && event.ports[0]) {\n                    requestPromises.then(() => event.ports[0].postMessage(true));\n                }\n            }\n        }));\n    }\n    /**\n     * Apply the routing rules to a FetchEvent object to get a Response from an\n     * appropriate Route's handler.\n     *\n     * @param {Object} options\n     * @param {Request} options.request The request to handle (this is usually\n     *     from a fetch event, but it does not have to be).\n     * @param {FetchEvent} [options.event] The event that triggered the request,\n     *     if applicable.\n     * @return {Promise|undefined} A promise is returned if a\n     *     registered route can handle the request. If there is no matching\n     *     route and there's no `defaultHandler`, `undefined` is returned.\n     */\n    handleRequest({ request, event }) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(request, Request, {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'handleRequest',\n                paramName: 'options.request',\n            });\n        }\n        const url = new URL(request.url, location.href);\n        if (!url.protocol.startsWith('http')) {\n            if (process.env.NODE_ENV !== 'production') {\n                logger.debug(`Workbox Router only supports URLs that start with 'http'.`);\n            }\n            return;\n        }\n        const { params, route } = this.findMatchingRoute({ url, request, event });\n        let handler = route && route.handler;\n        const debugMessages = [];\n        if (process.env.NODE_ENV !== 'production') {\n            if (handler) {\n                debugMessages.push([\n                    `Found a route to handle this request:`, route,\n                ]);\n                if (params) {\n                    debugMessages.push([\n                        `Passing the following params to the route's handler:`, params,\n                    ]);\n                }\n            }\n        }\n        // If we don't have a handler because there was no matching route, then\n        // fall back to defaultHandler if that's defined.\n        if (!handler && this._defaultHandler) {\n            if (process.env.NODE_ENV !== 'production') {\n                debugMessages.push(`Failed to find a matching route. Falling ` +\n                    `back to the default handler.`);\n            }\n            handler = this._defaultHandler;\n        }\n        if (!handler) {\n            if (process.env.NODE_ENV !== 'production') {\n                // No handler so Workbox will do nothing. If logs is set of debug\n                // i.e. verbose, we should print out this information.\n                logger.debug(`No route found for: ${getFriendlyURL(url)}`);\n            }\n            return;\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            // We have a handler, meaning Workbox is going to handle the route.\n            // print the routing details to the console.\n            logger.groupCollapsed(`Router is responding to: ${getFriendlyURL(url)}`);\n            debugMessages.forEach((msg) => {\n                if (Array.isArray(msg)) {\n                    logger.log(...msg);\n                }\n                else {\n                    logger.log(msg);\n                }\n            });\n            logger.groupEnd();\n        }\n        // Wrap in try and catch in case the handle method throws a synchronous\n        // error. It should still callback to the catch handler.\n        let responsePromise;\n        try {\n            responsePromise = handler.handle({ url, request, event, params });\n        }\n        catch (err) {\n            responsePromise = Promise.reject(err);\n        }\n        if (responsePromise instanceof Promise && this._catchHandler) {\n            responsePromise = responsePromise.catch((err) => {\n                if (process.env.NODE_ENV !== 'production') {\n                    // Still include URL here as it will be async from the console group\n                    // and may not make sense without the URL\n                    logger.groupCollapsed(`Error thrown when responding to: ` +\n                        ` ${getFriendlyURL(url)}. Falling back to Catch Handler.`);\n                    logger.error(`Error thrown by:`, route);\n                    logger.error(err);\n                    logger.groupEnd();\n                }\n                return this._catchHandler.handle({ url, request, event });\n            });\n        }\n        return responsePromise;\n    }\n    /**\n     * Checks a request and URL (and optionally an event) against the list of\n     * registered routes, and if there's a match, returns the corresponding\n     * route along with any params generated by the match.\n     *\n     * @param {Object} options\n     * @param {URL} options.url\n     * @param {Request} options.request The request to match.\n     * @param {Event} [options.event] The corresponding event (unless N/A).\n     * @return {Object} An object with `route` and `params` properties.\n     *     They are populated if a matching route was found or `undefined`\n     *     otherwise.\n     */\n    findMatchingRoute({ url, request, event }) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(url, URL, {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'findMatchingRoute',\n                paramName: 'options.url',\n            });\n            assert.isInstance(request, Request, {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'findMatchingRoute',\n                paramName: 'options.request',\n            });\n        }\n        const routes = this._routes.get(request.method) || [];\n        for (const route of routes) {\n            let params;\n            const matchResult = route.match({ url, request, event });\n            if (matchResult) {\n                // See https://github.com/GoogleChrome/workbox/issues/2079\n                params = matchResult;\n                if (Array.isArray(matchResult) && matchResult.length === 0) {\n                    // Instead of passing an empty array in as params, use undefined.\n                    params = undefined;\n                }\n                else if ((matchResult.constructor === Object &&\n                    Object.keys(matchResult).length === 0)) {\n                    // Instead of passing an empty object in as params, use undefined.\n                    params = undefined;\n                }\n                else if (typeof matchResult === 'boolean') {\n                    // For the boolean value true (rather than just something truth-y),\n                    // don't set params.\n                    // See https://github.com/GoogleChrome/workbox/pull/2134#issuecomment-513924353\n                    params = undefined;\n                }\n                // Return early if have a match.\n                return { route, params };\n            }\n        }\n        // If no match was found above, return and empty object.\n        return {};\n    }\n    /**\n     * Define a default `handler` that's called when no routes explicitly\n     * match the incoming request.\n     *\n     * Without a default handler, unmatched requests will go against the\n     * network as if there were no service worker present.\n     *\n     * @param {module:workbox-routing~handlerCallback} handler A callback\n     * function that returns a Promise resulting in a Response.\n     */\n    setDefaultHandler(handler) {\n        this._defaultHandler = normalizeHandler(handler);\n    }\n    /**\n     * If a Route throws an error while handling a request, this `handler`\n     * will be called and given a chance to provide a response.\n     *\n     * @param {module:workbox-routing~handlerCallback} handler A callback\n     * function that returns a Promise resulting in a Response.\n     */\n    setCatchHandler(handler) {\n        this._catchHandler = normalizeHandler(handler);\n    }\n    /**\n     * Registers a route with the router.\n     *\n     * @param {module:workbox-routing.Route} route The route to register.\n     */\n    registerRoute(route) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isType(route, 'object', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route',\n            });\n            assert.hasMethod(route, 'match', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route',\n            });\n            assert.isType(route.handler, 'object', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route',\n            });\n            assert.hasMethod(route.handler, 'handle', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route.handler',\n            });\n            assert.isType(route.method, 'string', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route.method',\n            });\n        }\n        if (!this._routes.has(route.method)) {\n            this._routes.set(route.method, []);\n        }\n        // Give precedence to all of the earlier routes by adding this additional\n        // route to the end of the array.\n        this._routes.get(route.method).push(route);\n    }\n    /**\n     * Unregisters a route with the router.\n     *\n     * @param {module:workbox-routing.Route} route The route to unregister.\n     */\n    unregisterRoute(route) {\n        if (!this._routes.has(route.method)) {\n            throw new WorkboxError('unregister-route-but-not-found-with-method', {\n                method: route.method,\n            });\n        }\n        const routeIndex = this._routes.get(route.method).indexOf(route);\n        if (routeIndex > -1) {\n            this._routes.get(route.method).splice(routeIndex, 1);\n        }\n        else {\n            throw new WorkboxError('unregister-route-route-not-registered');\n        }\n    }\n}\nexport { Router };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nconst plugins = [];\nexport const precachePlugins = {\n    /*\n     * @return {Array}\n     * @private\n     */\n    get() {\n        return plugins;\n    },\n    /*\n     * @param {Array} newPlugins\n     * @private\n     */\n    add(newPlugins) {\n        plugins.push(...newPlugins);\n    },\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nconst _cacheNameDetails = {\n    googleAnalytics: 'googleAnalytics',\n    precache: 'precache-v2',\n    prefix: 'workbox',\n    runtime: 'runtime',\n    suffix: typeof registration !== 'undefined' ? registration.scope : '',\n};\nconst _createCacheName = (cacheName) => {\n    return [_cacheNameDetails.prefix, cacheName, _cacheNameDetails.suffix]\n        .filter((value) => value && value.length > 0)\n        .join('-');\n};\nconst eachCacheNameDetail = (fn) => {\n    for (const key of Object.keys(_cacheNameDetails)) {\n        fn(key);\n    }\n};\nexport const cacheNames = {\n    updateDetails: (details) => {\n        eachCacheNameDetail((key) => {\n            if (typeof details[key] === 'string') {\n                _cacheNameDetails[key] = details[key];\n            }\n        });\n    },\n    getGoogleAnalyticsName: (userCacheName) => {\n        return userCacheName || _createCacheName(_cacheNameDetails.googleAnalytics);\n    },\n    getPrecacheName: (userCacheName) => {\n        return userCacheName || _createCacheName(_cacheNameDetails.precache);\n    },\n    getPrefix: () => {\n        return _cacheNameDetails.prefix;\n    },\n    getRuntimeName: (userCacheName) => {\n        return userCacheName || _createCacheName(_cacheNameDetails.runtime);\n    },\n    getSuffix: () => {\n        return _cacheNameDetails.suffix;\n    },\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\n// Callbacks to be executed whenever there's a quota error.\nconst quotaErrorCallbacks = new Set();\nexport { quotaErrorCallbacks };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nexport const pluginUtils = {\n    filter: (plugins, callbackName) => {\n        return plugins.filter((plugin) => callbackName in plugin);\n    },\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from './assert.js';\nimport { executeQuotaErrorCallbacks } from './executeQuotaErrorCallbacks.js';\nimport { getFriendlyURL } from './getFriendlyURL.js';\nimport { logger } from './logger.js';\nimport { pluginUtils } from '../utils/pluginUtils.js';\nimport { WorkboxError } from './WorkboxError.js';\nimport '../_version.js';\n/**\n * Checks the list of plugins for the cacheKeyWillBeUsed callback, and\n * executes any of those callbacks found in sequence. The final `Request` object\n * returned by the last plugin is treated as the cache key for cache reads\n * and/or writes.\n *\n * @param {Object} options\n * @param {Request} options.request\n * @param {string} options.mode\n * @param {Array} [options.plugins=[]]\n * @return {Promise}\n *\n * @private\n * @memberof module:workbox-core\n */\nconst _getEffectiveRequest = async ({ request, mode, plugins = [], }) => {\n    const cacheKeyWillBeUsedPlugins = pluginUtils.filter(plugins, \"cacheKeyWillBeUsed\" /* CACHE_KEY_WILL_BE_USED */);\n    let effectiveRequest = request;\n    for (const plugin of cacheKeyWillBeUsedPlugins) {\n        effectiveRequest = await plugin[\"cacheKeyWillBeUsed\" /* CACHE_KEY_WILL_BE_USED */].call(plugin, { mode, request: effectiveRequest });\n        if (typeof effectiveRequest === 'string') {\n            effectiveRequest = new Request(effectiveRequest);\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(effectiveRequest, Request, {\n                moduleName: 'Plugin',\n                funcName: \"cacheKeyWillBeUsed\" /* CACHE_KEY_WILL_BE_USED */,\n                isReturnValueProblem: true,\n            });\n        }\n    }\n    return effectiveRequest;\n};\n/**\n * This method will call cacheWillUpdate on the available plugins (or use\n * status === 200) to determine if the Response is safe and valid to cache.\n *\n * @param {Object} options\n * @param {Request} options.request\n * @param {Response} options.response\n * @param {Event} [options.event]\n * @param {Array} [options.plugins=[]]\n * @return {Promise}\n *\n * @private\n * @memberof module:workbox-core\n */\nconst _isResponseSafeToCache = async ({ request, response, event, plugins = [], }) => {\n    let responseToCache = response;\n    let pluginsUsed = false;\n    for (const plugin of plugins) {\n        if (\"cacheWillUpdate\" /* CACHE_WILL_UPDATE */ in plugin) {\n            pluginsUsed = true;\n            const pluginMethod = plugin[\"cacheWillUpdate\" /* CACHE_WILL_UPDATE */];\n            responseToCache = await pluginMethod.call(plugin, {\n                request,\n                response: responseToCache,\n                event,\n            });\n            if (process.env.NODE_ENV !== 'production') {\n                if (responseToCache) {\n                    assert.isInstance(responseToCache, Response, {\n                        moduleName: 'Plugin',\n                        funcName: \"cacheWillUpdate\" /* CACHE_WILL_UPDATE */,\n                        isReturnValueProblem: true,\n                    });\n                }\n            }\n            if (!responseToCache) {\n                break;\n            }\n        }\n    }\n    if (!pluginsUsed) {\n        if (process.env.NODE_ENV !== 'production') {\n            if (responseToCache) {\n                if (responseToCache.status !== 200) {\n                    if (responseToCache.status === 0) {\n                        logger.warn(`The response for '${request.url}' is an opaque ` +\n                            `response. The caching strategy that you're using will not ` +\n                            `cache opaque responses by default.`);\n                    }\n                    else {\n                        logger.debug(`The response for '${request.url}' returned ` +\n                            `a status code of '${response.status}' and won't be cached as a ` +\n                            `result.`);\n                    }\n                }\n            }\n        }\n        responseToCache = responseToCache && responseToCache.status === 200 ?\n            responseToCache : undefined;\n    }\n    return responseToCache ? responseToCache : null;\n};\n/**\n * This is a wrapper around cache.match().\n *\n * @param {Object} options\n * @param {string} options.cacheName Name of the cache to match against.\n * @param {Request} options.request The Request that will be used to look up\n *     cache entries.\n * @param {Event} [options.event] The event that prompted the action.\n * @param {Object} [options.matchOptions] Options passed to cache.match().\n * @param {Array} [options.plugins=[]] Array of plugins.\n * @return {Response} A cached response if available.\n *\n * @private\n * @memberof module:workbox-core\n */\nconst matchWrapper = async ({ cacheName, request, event, matchOptions, plugins = [], }) => {\n    const cache = await self.caches.open(cacheName);\n    const effectiveRequest = await _getEffectiveRequest({\n        plugins, request, mode: 'read'\n    });\n    let cachedResponse = await cache.match(effectiveRequest, matchOptions);\n    if (process.env.NODE_ENV !== 'production') {\n        if (cachedResponse) {\n            logger.debug(`Found a cached response in '${cacheName}'.`);\n        }\n        else {\n            logger.debug(`No cached response found in '${cacheName}'.`);\n        }\n    }\n    for (const plugin of plugins) {\n        if (\"cachedResponseWillBeUsed\" /* CACHED_RESPONSE_WILL_BE_USED */ in plugin) {\n            const pluginMethod = plugin[\"cachedResponseWillBeUsed\" /* CACHED_RESPONSE_WILL_BE_USED */];\n            cachedResponse = await pluginMethod.call(plugin, {\n                cacheName,\n                event,\n                matchOptions,\n                cachedResponse,\n                request: effectiveRequest,\n            });\n            if (process.env.NODE_ENV !== 'production') {\n                if (cachedResponse) {\n                    assert.isInstance(cachedResponse, Response, {\n                        moduleName: 'Plugin',\n                        funcName: \"cachedResponseWillBeUsed\" /* CACHED_RESPONSE_WILL_BE_USED */,\n                        isReturnValueProblem: true,\n                    });\n                }\n            }\n        }\n    }\n    return cachedResponse;\n};\n/**\n * Wrapper around cache.put().\n *\n * Will call `cacheDidUpdate` on plugins if the cache was updated, using\n * `matchOptions` when determining what the old entry is.\n *\n * @param {Object} options\n * @param {string} options.cacheName\n * @param {Request} options.request\n * @param {Response} options.response\n * @param {Event} [options.event]\n * @param {Array} [options.plugins=[]]\n * @param {Object} [options.matchOptions]\n *\n * @private\n * @memberof module:workbox-core\n */\nconst putWrapper = async ({ cacheName, request, response, event, plugins = [], matchOptions, }) => {\n    if (process.env.NODE_ENV !== 'production') {\n        if (request.method && request.method !== 'GET') {\n            throw new WorkboxError('attempt-to-cache-non-get-request', {\n                url: getFriendlyURL(request.url),\n                method: request.method,\n            });\n        }\n    }\n    const effectiveRequest = await _getEffectiveRequest({\n        plugins, request, mode: 'write'\n    });\n    if (!response) {\n        if (process.env.NODE_ENV !== 'production') {\n            logger.error(`Cannot cache non-existent response for ` +\n                `'${getFriendlyURL(effectiveRequest.url)}'.`);\n        }\n        throw new WorkboxError('cache-put-with-no-response', {\n            url: getFriendlyURL(effectiveRequest.url),\n        });\n    }\n    const responseToCache = await _isResponseSafeToCache({\n        event,\n        plugins,\n        response,\n        request: effectiveRequest,\n    });\n    if (!responseToCache) {\n        if (process.env.NODE_ENV !== 'production') {\n            logger.debug(`Response '${getFriendlyURL(effectiveRequest.url)}' will ` +\n                `not be cached.`, responseToCache);\n        }\n        return;\n    }\n    const cache = await self.caches.open(cacheName);\n    const updatePlugins = pluginUtils.filter(plugins, \"cacheDidUpdate\" /* CACHE_DID_UPDATE */);\n    const oldResponse = updatePlugins.length > 0 ?\n        await matchWrapper({ cacheName, matchOptions, request: effectiveRequest }) :\n        null;\n    if (process.env.NODE_ENV !== 'production') {\n        logger.debug(`Updating the '${cacheName}' cache with a new Response for ` +\n            `${getFriendlyURL(effectiveRequest.url)}.`);\n    }\n    try {\n        await cache.put(effectiveRequest, responseToCache);\n    }\n    catch (error) {\n        // See https://developer.mozilla.org/en-US/docs/Web/API/DOMException#exception-QuotaExceededError\n        if (error.name === 'QuotaExceededError') {\n            await executeQuotaErrorCallbacks();\n        }\n        throw error;\n    }\n    for (const plugin of updatePlugins) {\n        await plugin[\"cacheDidUpdate\" /* CACHE_DID_UPDATE */].call(plugin, {\n            cacheName,\n            event,\n            oldResponse,\n            newResponse: responseToCache,\n            request: effectiveRequest,\n        });\n    }\n};\nexport const cacheWrapper = {\n    put: putWrapper,\n    match: matchWrapper,\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { logger } from '../_private/logger.js';\nimport { quotaErrorCallbacks } from '../models/quotaErrorCallbacks.js';\nimport '../_version.js';\n/**\n * Runs all of the callback functions, one at a time sequentially, in the order\n * in which they were registered.\n *\n * @memberof module:workbox-core\n * @private\n */\nasync function executeQuotaErrorCallbacks() {\n    if (process.env.NODE_ENV !== 'production') {\n        logger.log(`About to run ${quotaErrorCallbacks.size} ` +\n            `callbacks to clean up caches.`);\n    }\n    for (const callback of quotaErrorCallbacks) {\n        await callback();\n        if (process.env.NODE_ENV !== 'production') {\n            logger.log(callback, 'is complete.');\n        }\n    }\n    if (process.env.NODE_ENV !== 'production') {\n        logger.log('Finished running callbacks.');\n    }\n}\nexport { executeQuotaErrorCallbacks };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { WorkboxError } from './WorkboxError.js';\nimport { logger } from './logger.js';\nimport { assert } from './assert.js';\nimport { getFriendlyURL } from '../_private/getFriendlyURL.js';\nimport { pluginUtils } from '../utils/pluginUtils.js';\nimport '../_version.js';\n/**\n * Wrapper around the fetch API.\n *\n * Will call requestWillFetch on available plugins.\n *\n * @param {Object} options\n * @param {Request|string} options.request\n * @param {Object} [options.fetchOptions]\n * @param {ExtendableEvent} [options.event]\n * @param {Array} [options.plugins=[]]\n * @return {Promise}\n *\n * @private\n * @memberof module:workbox-core\n */\nconst wrappedFetch = async ({ request, fetchOptions, event, plugins = [], }) => {\n    if (typeof request === 'string') {\n        request = new Request(request);\n    }\n    // We *should* be able to call `await event.preloadResponse` even if it's\n    // undefined, but for some reason, doing so leads to errors in our Node unit\n    // tests. To work around that, explicitly check preloadResponse's value first.\n    if (event instanceof FetchEvent && event.preloadResponse) {\n        const possiblePreloadResponse = await event.preloadResponse;\n        if (possiblePreloadResponse) {\n            if (process.env.NODE_ENV !== 'production') {\n                logger.log(`Using a preloaded navigation response for ` +\n                    `'${getFriendlyURL(request.url)}'`);\n            }\n            return possiblePreloadResponse;\n        }\n    }\n    if (process.env.NODE_ENV !== 'production') {\n        assert.isInstance(request, Request, {\n            paramName: 'request',\n            expectedClass: Request,\n            moduleName: 'workbox-core',\n            className: 'fetchWrapper',\n            funcName: 'wrappedFetch',\n        });\n    }\n    const failedFetchPlugins = pluginUtils.filter(plugins, \"fetchDidFail\" /* FETCH_DID_FAIL */);\n    // If there is a fetchDidFail plugin, we need to save a clone of the\n    // original request before it's either modified by a requestWillFetch\n    // plugin or before the original request's body is consumed via fetch().\n    const originalRequest = failedFetchPlugins.length > 0 ?\n        request.clone() : null;\n    try {\n        for (const plugin of plugins) {\n            if (\"requestWillFetch\" /* REQUEST_WILL_FETCH */ in plugin) {\n                const pluginMethod = plugin[\"requestWillFetch\" /* REQUEST_WILL_FETCH */];\n                const requestClone = request.clone();\n                request = await pluginMethod.call(plugin, {\n                    request: requestClone,\n                    event,\n                });\n                if (process.env.NODE_ENV !== 'production') {\n                    if (request) {\n                        assert.isInstance(request, Request, {\n                            moduleName: 'Plugin',\n                            funcName: \"cachedResponseWillBeUsed\" /* CACHED_RESPONSE_WILL_BE_USED */,\n                            isReturnValueProblem: true,\n                        });\n                    }\n                }\n            }\n        }\n    }\n    catch (err) {\n        throw new WorkboxError('plugin-error-request-will-fetch', {\n            thrownError: err,\n        });\n    }\n    // The request can be altered by plugins with `requestWillFetch` making\n    // the original request (Most likely from a `fetch` event) to be different\n    // to the Request we make. Pass both to `fetchDidFail` to aid debugging.\n    const pluginFilteredRequest = request.clone();\n    try {\n        let fetchResponse;\n        // See https://github.com/GoogleChrome/workbox/issues/1796\n        if (request.mode === 'navigate') {\n            fetchResponse = await fetch(request);\n        }\n        else {\n            fetchResponse = await fetch(request, fetchOptions);\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            logger.debug(`Network request for ` +\n                `'${getFriendlyURL(request.url)}' returned a response with ` +\n                `status '${fetchResponse.status}'.`);\n        }\n        for (const plugin of plugins) {\n            if (\"fetchDidSucceed\" /* FETCH_DID_SUCCEED */ in plugin) {\n                fetchResponse = await plugin[\"fetchDidSucceed\" /* FETCH_DID_SUCCEED */]\n                    .call(plugin, {\n                    event,\n                    request: pluginFilteredRequest,\n                    response: fetchResponse,\n                });\n                if (process.env.NODE_ENV !== 'production') {\n                    if (fetchResponse) {\n                        assert.isInstance(fetchResponse, Response, {\n                            moduleName: 'Plugin',\n                            funcName: \"fetchDidSucceed\" /* FETCH_DID_SUCCEED */,\n                            isReturnValueProblem: true,\n                        });\n                    }\n                }\n            }\n        }\n        return fetchResponse;\n    }\n    catch (error) {\n        if (process.env.NODE_ENV !== 'production') {\n            logger.error(`Network request for ` +\n                `'${getFriendlyURL(request.url)}' threw an error.`, error);\n        }\n        for (const plugin of failedFetchPlugins) {\n            await plugin[\"fetchDidFail\" /* FETCH_DID_FAIL */].call(plugin, {\n                error,\n                event,\n                originalRequest: originalRequest.clone(),\n                request: pluginFilteredRequest.clone(),\n            });\n        }\n        throw error;\n    }\n};\nconst fetchWrapper = {\n    fetch: wrappedFetch,\n};\nexport { fetchWrapper };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { cacheNames } from 'workbox-core/_private/cacheNames.js';\nimport { cacheWrapper } from 'workbox-core/_private/cacheWrapper.js';\nimport { fetchWrapper } from 'workbox-core/_private/fetchWrapper.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { copyResponse } from 'workbox-core/copyResponse.js';\nimport { createCacheKey } from './utils/createCacheKey.js';\nimport { printCleanupDetails } from './utils/printCleanupDetails.js';\nimport { printInstallDetails } from './utils/printInstallDetails.js';\nimport './_version.js';\n/**\n * Performs efficient precaching of assets.\n *\n * @memberof module:workbox-precaching\n */\nclass PrecacheController {\n    /**\n     * Create a new PrecacheController.\n     *\n     * @param {string} [cacheName] An optional name for the cache, to override\n     * the default precache name.\n     */\n    constructor(cacheName) {\n        this._cacheName = cacheNames.getPrecacheName(cacheName);\n        this._urlsToCacheKeys = new Map();\n        this._urlsToCacheModes = new Map();\n        this._cacheKeysToIntegrities = new Map();\n    }\n    /**\n     * This method will add items to the precache list, removing duplicates\n     * and ensuring the information is valid.\n     *\n     * @param {\n     * Array\n     * } entries Array of entries to precache.\n     */\n    addToCacheList(entries) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isArray(entries, {\n                moduleName: 'workbox-precaching',\n                className: 'PrecacheController',\n                funcName: 'addToCacheList',\n                paramName: 'entries',\n            });\n        }\n        const urlsToWarnAbout = [];\n        for (const entry of entries) {\n            // See https://github.com/GoogleChrome/workbox/issues/2259\n            if (typeof entry === 'string') {\n                urlsToWarnAbout.push(entry);\n            }\n            else if (entry && entry.revision === undefined) {\n                urlsToWarnAbout.push(entry.url);\n            }\n            const { cacheKey, url } = createCacheKey(entry);\n            const cacheMode = (typeof entry !== 'string' && entry.revision) ?\n                'reload' : 'default';\n            if (this._urlsToCacheKeys.has(url) &&\n                this._urlsToCacheKeys.get(url) !== cacheKey) {\n                throw new WorkboxError('add-to-cache-list-conflicting-entries', {\n                    firstEntry: this._urlsToCacheKeys.get(url),\n                    secondEntry: cacheKey,\n                });\n            }\n            if (typeof entry !== 'string' && entry.integrity) {\n                if (this._cacheKeysToIntegrities.has(cacheKey) &&\n                    this._cacheKeysToIntegrities.get(cacheKey) !== entry.integrity) {\n                    throw new WorkboxError('add-to-cache-list-conflicting-integrities', {\n                        url,\n                    });\n                }\n                this._cacheKeysToIntegrities.set(cacheKey, entry.integrity);\n            }\n            this._urlsToCacheKeys.set(url, cacheKey);\n            this._urlsToCacheModes.set(url, cacheMode);\n            if (urlsToWarnAbout.length > 0) {\n                const warningMessage = `Workbox is precaching URLs without revision ` +\n                    `info: ${urlsToWarnAbout.join(', ')}\\nThis is generally NOT safe. ` +\n                    `Learn more at https://bit.ly/wb-precache`;\n                if (process.env.NODE_ENV === 'production') {\n                    // Use console directly to display this warning without bloating\n                    // bundle sizes by pulling in all of the logger codebase in prod.\n                    console.warn(warningMessage);\n                }\n                else {\n                    logger.warn(warningMessage);\n                }\n            }\n        }\n    }\n    /**\n     * Precaches new and updated assets. Call this method from the service worker\n     * install event.\n     *\n     * @param {Object} options\n     * @param {Event} [options.event] The install event (if needed).\n     * @param {Array} [options.plugins] Plugins to be used for fetching\n     * and caching during install.\n     * @return {Promise}\n     */\n    async install({ event, plugins } = {}) {\n        if (process.env.NODE_ENV !== 'production') {\n            if (plugins) {\n                assert.isArray(plugins, {\n                    moduleName: 'workbox-precaching',\n                    className: 'PrecacheController',\n                    funcName: 'install',\n                    paramName: 'plugins',\n                });\n            }\n        }\n        const toBePrecached = [];\n        const alreadyPrecached = [];\n        const cache = await self.caches.open(this._cacheName);\n        const alreadyCachedRequests = await cache.keys();\n        const existingCacheKeys = new Set(alreadyCachedRequests.map((request) => request.url));\n        for (const [url, cacheKey] of this._urlsToCacheKeys) {\n            if (existingCacheKeys.has(cacheKey)) {\n                alreadyPrecached.push(url);\n            }\n            else {\n                toBePrecached.push({ cacheKey, url });\n            }\n        }\n        const precacheRequests = toBePrecached.map(({ cacheKey, url }) => {\n            const integrity = this._cacheKeysToIntegrities.get(cacheKey);\n            const cacheMode = this._urlsToCacheModes.get(url);\n            return this._addURLToCache({\n                cacheKey,\n                cacheMode,\n                event,\n                integrity,\n                plugins,\n                url,\n            });\n        });\n        await Promise.all(precacheRequests);\n        const updatedURLs = toBePrecached.map((item) => item.url);\n        if (process.env.NODE_ENV !== 'production') {\n            printInstallDetails(updatedURLs, alreadyPrecached);\n        }\n        return {\n            updatedURLs,\n            notUpdatedURLs: alreadyPrecached,\n        };\n    }\n    /**\n     * Deletes assets that are no longer present in the current precache manifest.\n     * Call this method from the service worker activate event.\n     *\n     * @return {Promise}\n     */\n    async activate() {\n        const cache = await self.caches.open(this._cacheName);\n        const currentlyCachedRequests = await cache.keys();\n        const expectedCacheKeys = new Set(this._urlsToCacheKeys.values());\n        const deletedURLs = [];\n        for (const request of currentlyCachedRequests) {\n            if (!expectedCacheKeys.has(request.url)) {\n                await cache.delete(request);\n                deletedURLs.push(request.url);\n            }\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            printCleanupDetails(deletedURLs);\n        }\n        return { deletedURLs };\n    }\n    /**\n     * Requests the entry and saves it to the cache if the response is valid.\n     * By default, any response with a status code of less than 400 (including\n     * opaque responses) is considered valid.\n     *\n     * If you need to use custom criteria to determine what's valid and what\n     * isn't, then pass in an item in `options.plugins` that implements the\n     * `cacheWillUpdate()` lifecycle event.\n     *\n     * @private\n     * @param {Object} options\n     * @param {string} options.cacheKey The string to use a cache key.\n     * @param {string} options.url The URL to fetch and cache.\n     * @param {string} [options.cacheMode] The cache mode for the network request.\n     * @param {Event} [options.event] The install event (if passed).\n     * @param {Array} [options.plugins] An array of plugins to apply to\n     * fetch and caching.\n     * @param {string} [options.integrity] The value to use for the `integrity`\n     * field when making the request.\n     */\n    async _addURLToCache({ cacheKey, url, cacheMode, event, plugins, integrity }) {\n        const request = new Request(url, {\n            integrity,\n            cache: cacheMode,\n            credentials: 'same-origin',\n        });\n        let response = await fetchWrapper.fetch({\n            event,\n            plugins,\n            request,\n        });\n        // Allow developers to override the default logic about what is and isn't\n        // valid by passing in a plugin implementing cacheWillUpdate(), e.g.\n        // a `CacheableResponsePlugin` instance.\n        let cacheWillUpdatePlugin;\n        for (const plugin of (plugins || [])) {\n            if ('cacheWillUpdate' in plugin) {\n                cacheWillUpdatePlugin = plugin;\n            }\n        }\n        const isValidResponse = cacheWillUpdatePlugin ?\n            // Use a callback if provided. It returns a truthy value if valid.\n            // NOTE: invoke the method on the plugin instance so the `this` context\n            // is correct.\n            await cacheWillUpdatePlugin.cacheWillUpdate({ event, request, response }) :\n            // Otherwise, default to considering any response status under 400 valid.\n            // This includes, by default, considering opaque responses valid.\n            response.status < 400;\n        // Consider this a failure, leading to the `install` handler failing, if\n        // we get back an invalid response.\n        if (!isValidResponse) {\n            throw new WorkboxError('bad-precaching-response', {\n                url,\n                status: response.status,\n            });\n        }\n        // Redirected responses cannot be used to satisfy a navigation request, so\n        // any redirected response must be \"copied\" rather than cloned, so the new\n        // response doesn't contain the `redirected` flag. See:\n        // https://bugs.chromium.org/p/chromium/issues/detail?id=669363&desc=2#c1\n        if (response.redirected) {\n            response = await copyResponse(response);\n        }\n        await cacheWrapper.put({\n            event,\n            plugins,\n            response,\n            // `request` already uses `url`. We may be able to reuse it.\n            request: cacheKey === url ? request : new Request(cacheKey),\n            cacheName: this._cacheName,\n            matchOptions: {\n                ignoreSearch: true,\n            },\n        });\n    }\n    /**\n     * Returns a mapping of a precached URL to the corresponding cache key, taking\n     * into account the revision information for the URL.\n     *\n     * @return {Map} A URL to cache key mapping.\n     */\n    getURLsToCacheKeys() {\n        return this._urlsToCacheKeys;\n    }\n    /**\n     * Returns a list of all the URLs that have been precached by the current\n     * service worker.\n     *\n     * @return {Array} The precached URLs.\n     */\n    getCachedURLs() {\n        return [...this._urlsToCacheKeys.keys()];\n    }\n    /**\n     * Returns the cache key used for storing a given URL. If that URL is\n     * unversioned, like `/index.html', then the cache key will be the original\n     * URL with a search parameter appended to it.\n     *\n     * @param {string} url A URL whose cache key you want to look up.\n     * @return {string} The versioned URL that corresponds to a cache key\n     * for the original URL, or undefined if that URL isn't precached.\n     */\n    getCacheKeyForURL(url) {\n        const urlObject = new URL(url, location.href);\n        return this._urlsToCacheKeys.get(urlObject.href);\n    }\n    /**\n     * This acts as a drop-in replacement for [`cache.match()`](https://developer.mozilla.org/en-US/docs/Web/API/Cache/match)\n     * with the following differences:\n     *\n     * - It knows what the name of the precache is, and only checks in that cache.\n     * - It allows you to pass in an \"original\" URL without versioning parameters,\n     * and it will automatically look up the correct cache key for the currently\n     * active revision of that URL.\n     *\n     * E.g., `matchPrecache('index.html')` will find the correct precached\n     * response for the currently active service worker, even if the actual cache\n     * key is `'/index.html?__WB_REVISION__=1234abcd'`.\n     *\n     * @param {string|Request} request The key (without revisioning parameters)\n     * to look up in the precache.\n     * @return {Promise}\n     */\n    async matchPrecache(request) {\n        const url = request instanceof Request ? request.url : request;\n        const cacheKey = this.getCacheKeyForURL(url);\n        if (cacheKey) {\n            const cache = await self.caches.open(this._cacheName);\n            return cache.match(cacheKey);\n        }\n        return undefined;\n    }\n    /**\n     * Returns a function that can be used within a\n     * {@link module:workbox-routing.Route} that will find a response for the\n     * incoming request against the precache.\n     *\n     * If for an unexpected reason there is a cache miss for the request,\n     * this will fall back to retrieving the `Response` via `fetch()` when\n     * `fallbackToNetwork` is `true`.\n     *\n     * @param {boolean} [fallbackToNetwork=true] Whether to attempt to get the\n     * response from the network if there's a precache miss.\n     * @return {module:workbox-routing~handlerCallback}\n     */\n    createHandler(fallbackToNetwork = true) {\n        return async ({ request }) => {\n            try {\n                const response = await this.matchPrecache(request);\n                if (response) {\n                    return response;\n                }\n                // This shouldn't normally happen, but there are edge cases:\n                // https://github.com/GoogleChrome/workbox/issues/1441\n                throw new WorkboxError('missing-precache-entry', {\n                    cacheName: this._cacheName,\n                    url: request instanceof Request ? request.url : request,\n                });\n            }\n            catch (error) {\n                if (fallbackToNetwork) {\n                    if (process.env.NODE_ENV !== 'production') {\n                        logger.debug(`Unable to respond with precached response. ` +\n                            `Falling back to network.`, error);\n                    }\n                    return fetch(request);\n                }\n                throw error;\n            }\n        };\n    }\n    /**\n     * Returns a function that looks up `url` in the precache (taking into\n     * account revision information), and returns the corresponding `Response`.\n     *\n     * If for an unexpected reason there is a cache miss when looking up `url`,\n     * this will fall back to retrieving the `Response` via `fetch()` when\n     * `fallbackToNetwork` is `true`.\n     *\n     * @param {string} url The precached URL which will be used to lookup the\n     * `Response`.\n     * @param {boolean} [fallbackToNetwork=true] Whether to attempt to get the\n     * response from the network if there's a precache miss.\n     * @return {module:workbox-routing~handlerCallback}\n     */\n    createHandlerBoundToURL(url, fallbackToNetwork = true) {\n        const cacheKey = this.getCacheKeyForURL(url);\n        if (!cacheKey) {\n            throw new WorkboxError('non-precached-url', { url });\n        }\n        const handler = this.createHandler(fallbackToNetwork);\n        const request = new Request(url);\n        return () => handler({ request });\n    }\n}\nexport { PrecacheController };\n","export const isNav = event => event.request.mode === 'navigate';\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nexport const cacheOkAndOpaquePlugin = {\n    /**\n     * Returns a valid response (to allow caching) if the status is 200 (OK) or\n     * 0 (opaque).\n     *\n     * @param {Object} options\n     * @param {Response} options.response\n     * @return {Response|null}\n     *\n     * @private\n     */\n    cacheWillUpdate: async ({ response }) => {\n        if (response.status === 200 || response.status === 0) {\n            return response;\n        }\n        return null;\n    },\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { cacheNames } from 'workbox-core/_private/cacheNames.js';\nimport { cacheWrapper } from 'workbox-core/_private/cacheWrapper.js';\nimport { fetchWrapper } from 'workbox-core/_private/fetchWrapper.js';\nimport { getFriendlyURL } from 'workbox-core/_private/getFriendlyURL.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { messages } from './utils/messages.js';\nimport { cacheOkAndOpaquePlugin } from './plugins/cacheOkAndOpaquePlugin.js';\nimport './_version.js';\n/**\n * An implementation of a\n * [network first]{@link https://developers.google.com/web/fundamentals/instant-and-offline/offline-cookbook/#network-falling-back-to-cache}\n * request strategy.\n *\n * By default, this strategy will cache responses with a 200 status code as\n * well as [opaque responses]{@link https://developers.google.com/web/tools/workbox/guides/handle-third-party-requests}.\n * Opaque responses are are cross-origin requests where the response doesn't\n * support [CORS]{@link https://enable-cors.org/}.\n *\n * If the network request fails, and there is no cache match, this will throw\n * a `WorkboxError` exception.\n *\n * @memberof module:workbox-strategies\n */\nclass NetworkFirst {\n    /**\n     * @param {Object} options\n     * @param {string} options.cacheName Cache name to store and retrieve\n     * requests. Defaults to cache names provided by\n     * [workbox-core]{@link module:workbox-core.cacheNames}.\n     * @param {Array} options.plugins [Plugins]{@link https://developers.google.com/web/tools/workbox/guides/using-plugins}\n     * to use in conjunction with this caching strategy.\n     * @param {Object} options.fetchOptions Values passed along to the\n     * [`init`](https://developer.mozilla.org/en-US/docs/Web/API/WindowOrWorkerGlobalScope/fetch#Parameters)\n     * of all fetch() requests made by this strategy.\n     * @param {Object} options.matchOptions [`CacheQueryOptions`](https://w3c.github.io/ServiceWorker/#dictdef-cachequeryoptions)\n     * @param {number} options.networkTimeoutSeconds If set, any network requests\n     * that fail to respond within the timeout will fallback to the cache.\n     *\n     * This option can be used to combat\n     * \"[lie-fi]{@link https://developers.google.com/web/fundamentals/performance/poor-connectivity/#lie-fi}\"\n     * scenarios.\n     */\n    constructor(options = {}) {\n        this._cacheName = cacheNames.getRuntimeName(options.cacheName);\n        if (options.plugins) {\n            const isUsingCacheWillUpdate = options.plugins.some((plugin) => !!plugin.cacheWillUpdate);\n            this._plugins = isUsingCacheWillUpdate ?\n                options.plugins : [cacheOkAndOpaquePlugin, ...options.plugins];\n        }\n        else {\n            // No plugins passed in, use the default plugin.\n            this._plugins = [cacheOkAndOpaquePlugin];\n        }\n        this._networkTimeoutSeconds = options.networkTimeoutSeconds || 0;\n        if (process.env.NODE_ENV !== 'production') {\n            if (this._networkTimeoutSeconds) {\n                assert.isType(this._networkTimeoutSeconds, 'number', {\n                    moduleName: 'workbox-strategies',\n                    className: 'NetworkFirst',\n                    funcName: 'constructor',\n                    paramName: 'networkTimeoutSeconds',\n                });\n            }\n        }\n        this._fetchOptions = options.fetchOptions;\n        this._matchOptions = options.matchOptions;\n    }\n    /**\n     * This method will perform a request strategy and follows an API that\n     * will work with the\n     * [Workbox Router]{@link module:workbox-routing.Router}.\n     *\n     * @param {Object} options\n     * @param {Request|string} options.request A request to run this strategy for.\n     * @param {Event} [options.event] The event that triggered the request.\n     * @return {Promise}\n     */\n    async handle({ event, request }) {\n        const logs = [];\n        if (typeof request === 'string') {\n            request = new Request(request);\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(request, Request, {\n                moduleName: 'workbox-strategies',\n                className: 'NetworkFirst',\n                funcName: 'handle',\n                paramName: 'makeRequest',\n            });\n        }\n        const promises = [];\n        let timeoutId;\n        if (this._networkTimeoutSeconds) {\n            const { id, promise } = this._getTimeoutPromise({ request, event, logs });\n            timeoutId = id;\n            promises.push(promise);\n        }\n        const networkPromise = this._getNetworkPromise({ timeoutId, request, event, logs });\n        promises.push(networkPromise);\n        // Promise.race() will resolve as soon as the first promise resolves.\n        let response = await Promise.race(promises);\n        // If Promise.race() resolved with null, it might be due to a network\n        // timeout + a cache miss. If that were to happen, we'd rather wait until\n        // the networkPromise resolves instead of returning null.\n        // Note that it's fine to await an already-resolved promise, so we don't\n        // have to check to see if it's still \"in flight\".\n        if (!response) {\n            response = await networkPromise;\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            logger.groupCollapsed(messages.strategyStart('NetworkFirst', request));\n            for (const log of logs) {\n                logger.log(log);\n            }\n            messages.printFinalResponse(response);\n            logger.groupEnd();\n        }\n        if (!response) {\n            throw new WorkboxError('no-response', { url: request.url });\n        }\n        return response;\n    }\n    /**\n     * @param {Object} options\n     * @param {Request} options.request\n     * @param {Array} options.logs A reference to the logs array\n     * @param {Event} [options.event]\n     * @return {Promise}\n     *\n     * @private\n     */\n    _getTimeoutPromise({ request, logs, event }) {\n        let timeoutId;\n        const timeoutPromise = new Promise((resolve) => {\n            const onNetworkTimeout = async () => {\n                if (process.env.NODE_ENV !== 'production') {\n                    logs.push(`Timing out the network response at ` +\n                        `${this._networkTimeoutSeconds} seconds.`);\n                }\n                resolve(await this._respondFromCache({ request, event }));\n            };\n            timeoutId = setTimeout(onNetworkTimeout, this._networkTimeoutSeconds * 1000);\n        });\n        return {\n            promise: timeoutPromise,\n            id: timeoutId,\n        };\n    }\n    /**\n     * @param {Object} options\n     * @param {number|undefined} options.timeoutId\n     * @param {Request} options.request\n     * @param {Array} options.logs A reference to the logs Array.\n     * @param {Event} [options.event]\n     * @return {Promise}\n     *\n     * @private\n     */\n    async _getNetworkPromise({ timeoutId, request, logs, event }) {\n        let error;\n        let response;\n        try {\n            response = await fetchWrapper.fetch({\n                request,\n                event,\n                fetchOptions: this._fetchOptions,\n                plugins: this._plugins,\n            });\n        }\n        catch (err) {\n            error = err;\n        }\n        if (timeoutId) {\n            clearTimeout(timeoutId);\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            if (response) {\n                logs.push(`Got response from network.`);\n            }\n            else {\n                logs.push(`Unable to get a response from the network. Will respond ` +\n                    `with a cached response.`);\n            }\n        }\n        if (error || !response) {\n            response = await this._respondFromCache({ request, event });\n            if (process.env.NODE_ENV !== 'production') {\n                if (response) {\n                    logs.push(`Found a cached response in the '${this._cacheName}'` +\n                        ` cache.`);\n                }\n                else {\n                    logs.push(`No response found in the '${this._cacheName}' cache.`);\n                }\n            }\n        }\n        else {\n            // Keep the service worker alive while we put the request in the cache\n            const responseClone = response.clone();\n            const cachePut = cacheWrapper.put({\n                cacheName: this._cacheName,\n                request,\n                response: responseClone,\n                event,\n                plugins: this._plugins,\n            });\n            if (event) {\n                try {\n                    // The event has been responded to so we can keep the SW alive to\n                    // respond to the request\n                    event.waitUntil(cachePut);\n                }\n                catch (err) {\n                    if (process.env.NODE_ENV !== 'production') {\n                        logger.warn(`Unable to ensure service worker stays alive when ` +\n                            `updating cache for '${getFriendlyURL(request.url)}'.`);\n                    }\n                }\n            }\n        }\n        return response;\n    }\n    /**\n     * Used if the network timeouts or fails to make the request.\n     *\n     * @param {Object} options\n     * @param {Request} request The request to match in the cache\n     * @param {Event} [options.event]\n     * @return {Promise}\n     *\n     * @private\n     */\n    _respondFromCache({ event, request }) {\n        return cacheWrapper.match({\n            cacheName: this._cacheName,\n            request,\n            event,\n            matchOptions: this._matchOptions,\n            plugins: this._plugins,\n        });\n    }\n}\nexport { NetworkFirst };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\n/**\n * A class that wraps common IndexedDB functionality in a promise-based API.\n * It exposes all the underlying power and functionality of IndexedDB, but\n * wraps the most commonly used features in a way that's much simpler to use.\n *\n * @private\n */\nexport class DBWrapper {\n    /**\n     * @param {string} name\n     * @param {number} version\n     * @param {Object=} [callback]\n     * @param {!Function} [callbacks.onupgradeneeded]\n     * @param {!Function} [callbacks.onversionchange] Defaults to\n     *     DBWrapper.prototype._onversionchange when not specified.\n     * @private\n     */\n    constructor(name, version, { onupgradeneeded, onversionchange, } = {}) {\n        this._db = null;\n        this._name = name;\n        this._version = version;\n        this._onupgradeneeded = onupgradeneeded;\n        this._onversionchange = onversionchange || (() => this.close());\n    }\n    /**\n     * Returns the IDBDatabase instance (not normally needed).\n     * @return {IDBDatabase|undefined}\n     *\n     * @private\n     */\n    get db() {\n        return this._db;\n    }\n    /**\n     * Opens a connected to an IDBDatabase, invokes any onupgradedneeded\n     * callback, and added an onversionchange callback to the database.\n     *\n     * @return {IDBDatabase}\n     * @private\n     */\n    async open() {\n        if (this._db)\n            return;\n        this._db = await new Promise((resolve, reject) => {\n            // This flag is flipped to true if the timeout callback runs prior\n            // to the request failing or succeeding. Note: we use a timeout instead\n            // of an onblocked handler since there are cases where onblocked will\n            // never never run. A timeout better handles all possible scenarios:\n            // https://github.com/w3c/IndexedDB/issues/223\n            let openRequestTimedOut = false;\n            setTimeout(() => {\n                openRequestTimedOut = true;\n                reject(new Error('The open request was blocked and timed out'));\n            }, this.OPEN_TIMEOUT);\n            const openRequest = indexedDB.open(this._name, this._version);\n            openRequest.onerror = () => reject(openRequest.error);\n            openRequest.onupgradeneeded = (evt) => {\n                if (openRequestTimedOut) {\n                    openRequest.transaction.abort();\n                    openRequest.result.close();\n                }\n                else if (typeof this._onupgradeneeded === 'function') {\n                    this._onupgradeneeded(evt);\n                }\n            };\n            openRequest.onsuccess = () => {\n                const db = openRequest.result;\n                if (openRequestTimedOut) {\n                    db.close();\n                }\n                else {\n                    db.onversionchange = this._onversionchange.bind(this);\n                    resolve(db);\n                }\n            };\n        });\n        return this;\n    }\n    /**\n     * Polyfills the native `getKey()` method. Note, this is overridden at\n     * runtime if the browser supports the native method.\n     *\n     * @param {string} storeName\n     * @param {*} query\n     * @return {Array}\n     * @private\n     */\n    async getKey(storeName, query) {\n        return (await this.getAllKeys(storeName, query, 1))[0];\n    }\n    /**\n     * Polyfills the native `getAll()` method. Note, this is overridden at\n     * runtime if the browser supports the native method.\n     *\n     * @param {string} storeName\n     * @param {*} query\n     * @param {number} count\n     * @return {Array}\n     * @private\n     */\n    async getAll(storeName, query, count) {\n        return await this.getAllMatching(storeName, { query, count });\n    }\n    /**\n     * Polyfills the native `getAllKeys()` method. Note, this is overridden at\n     * runtime if the browser supports the native method.\n     *\n     * @param {string} storeName\n     * @param {*} query\n     * @param {number} count\n     * @return {Array}\n     * @private\n     */\n    async getAllKeys(storeName, query, count) {\n        const entries = await this.getAllMatching(storeName, { query, count, includeKeys: true });\n        return entries.map((entry) => entry.key);\n    }\n    /**\n     * Supports flexible lookup in an object store by specifying an index,\n     * query, direction, and count. This method returns an array of objects\n     * with the signature .\n     *\n     * @param {string} storeName\n     * @param {Object} [opts]\n     * @param {string} [opts.index] The index to use (if specified).\n     * @param {*} [opts.query]\n     * @param {IDBCursorDirection} [opts.direction]\n     * @param {number} [opts.count] The max number of results to return.\n     * @param {boolean} [opts.includeKeys] When true, the structure of the\n     *     returned objects is changed from an array of values to an array of\n     *     objects in the form {key, primaryKey, value}.\n     * @return {Array}\n     * @private\n     */\n    async getAllMatching(storeName, { index, query = null, // IE/Edge errors if query === `undefined`.\n    direction = 'next', count, includeKeys = false, } = {}) {\n        return await this.transaction([storeName], 'readonly', (txn, done) => {\n            const store = txn.objectStore(storeName);\n            const target = index ? store.index(index) : store;\n            const results = [];\n            const request = target.openCursor(query, direction);\n            request.onsuccess = () => {\n                const cursor = request.result;\n                if (cursor) {\n                    results.push(includeKeys ? cursor : cursor.value);\n                    if (count && results.length >= count) {\n                        done(results);\n                    }\n                    else {\n                        cursor.continue();\n                    }\n                }\n                else {\n                    done(results);\n                }\n            };\n        });\n    }\n    /**\n     * Accepts a list of stores, a transaction type, and a callback and\n     * performs a transaction. A promise is returned that resolves to whatever\n     * value the callback chooses. The callback holds all the transaction logic\n     * and is invoked with two arguments:\n     *   1. The IDBTransaction object\n     *   2. A `done` function, that's used to resolve the promise when\n     *      when the transaction is done, if passed a value, the promise is\n     *      resolved to that value.\n     *\n     * @param {Array} storeNames An array of object store names\n     *     involved in the transaction.\n     * @param {string} type Can be `readonly` or `readwrite`.\n     * @param {!Function} callback\n     * @return {*} The result of the transaction ran by the callback.\n     * @private\n     */\n    async transaction(storeNames, type, callback) {\n        await this.open();\n        return await new Promise((resolve, reject) => {\n            const txn = this._db.transaction(storeNames, type);\n            txn.onabort = () => reject(txn.error);\n            txn.oncomplete = () => resolve();\n            callback(txn, (value) => resolve(value));\n        });\n    }\n    /**\n     * Delegates async to a native IDBObjectStore method.\n     *\n     * @param {string} method The method name.\n     * @param {string} storeName The object store name.\n     * @param {string} type Can be `readonly` or `readwrite`.\n     * @param {...*} args The list of args to pass to the native method.\n     * @return {*} The result of the transaction.\n     * @private\n     */\n    async _call(method, storeName, type, ...args) {\n        const callback = (txn, done) => {\n            const objStore = txn.objectStore(storeName);\n            // TODO(philipwalton): Fix this underlying TS2684 error.\n            // @ts-ignore\n            const request = objStore[method].apply(objStore, args);\n            request.onsuccess = () => done(request.result);\n        };\n        return await this.transaction([storeName], type, callback);\n    }\n    /**\n     * Closes the connection opened by `DBWrapper.open()`. Generally this method\n     * doesn't need to be called since:\n     *   1. It's usually better to keep a connection open since opening\n     *      a new connection is somewhat slow.\n     *   2. Connections are automatically closed when the reference is\n     *      garbage collected.\n     * The primary use case for needing to close a connection is when another\n     * reference (typically in another tab) needs to upgrade it and would be\n     * blocked by the current, open connection.\n     *\n     * @private\n     */\n    close() {\n        if (this._db) {\n            this._db.close();\n            this._db = null;\n        }\n    }\n}\n// Exposed on the prototype to let users modify the default timeout on a\n// per-instance or global basis.\nDBWrapper.prototype.OPEN_TIMEOUT = 2000;\n// Wrap native IDBObjectStore methods according to their mode.\nconst methodsToWrap = {\n    readonly: ['get', 'count', 'getKey', 'getAll', 'getAllKeys'],\n    readwrite: ['add', 'put', 'clear', 'delete'],\n};\nfor (const [mode, methods] of Object.entries(methodsToWrap)) {\n    for (const method of methods) {\n        if (method in IDBObjectStore.prototype) {\n            // Don't use arrow functions here since we're outside of the class.\n            DBWrapper.prototype[method] =\n                async function (storeName, ...args) {\n                    return await this._call(method, storeName, mode, ...args);\n                };\n        }\n    }\n}\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { getOrCreateDefaultRouter } from './utils/getOrCreateDefaultRouter.js';\nimport './_version.js';\n/**\n * If a Route throws an error while handling a request, this `handler`\n * will be called and given a chance to provide a response.\n *\n * @param {module:workbox-routing~handlerCallback} handler A callback\n * function that returns a Promise resulting in a Response.\n *\n * @memberof module:workbox-routing\n */\nfunction setCatchHandler(handler) {\n    const defaultRouter = getOrCreateDefaultRouter();\n    defaultRouter.setCatchHandler(handler);\n}\nexport { setCatchHandler };\n","import { registerRoute, setCatchHandler } from 'workbox-routing';\nimport { precacheAndRoute, getCacheKeyForURL } from 'workbox-precaching';\nimport { isNav } from './utils';\nimport { NETWORK_HANDLER, PRECACHING_OPTIONS } from './contants';\n\nexport function getFiles() {\n\treturn self.__WB_MANIFEST;\n}\n\nexport function setupPrecaching(precacheFiles, precachingOptions) {\n\tprecacheAndRoute(precacheFiles, precachingOptions || PRECACHING_OPTIONS);\n}\n\nexport function setupRouting() {\n\t/**\n\t * Adding this before `precacheAndRoute` lets us handle all\n\t * the navigation requests even if they are in precache.\n\t */\n\tregisterRoute(({ event }) => isNav(event), NETWORK_HANDLER);\n\n\tsetCatchHandler(({ event }) => {\n\t\tif (isNav(event)) {\n\t\t\treturn caches.match(getCacheKeyForURL('/index.html'));\n\t\t}\n\t\treturn Response.error();\n\t});\n}\n\nexport { PRECACHING_OPTIONS };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { cacheNames as _cacheNames } from './_private/cacheNames.js';\nimport './_version.js';\n/**\n * Get the current cache names and prefix/suffix used by Workbox.\n *\n * `cacheNames.precache` is used for precached assets,\n * `cacheNames.googleAnalytics` is used by `workbox-google-analytics` to\n * store `analytics.js`, and `cacheNames.runtime` is used for everything else.\n *\n * `cacheNames.prefix` can be used to retrieve just the current prefix value.\n * `cacheNames.suffix` can be used to retrieve just the current suffix value.\n *\n * @return {Object} An object with `precache`, `runtime`, `prefix`, and\n *     `googleAnalytics` properties.\n *\n * @memberof module:workbox-core\n */\nconst cacheNames = {\n    get googleAnalytics() {\n        return _cacheNames.getGoogleAnalyticsName();\n    },\n    get precache() {\n        return _cacheNames.getPrecacheName();\n    },\n    get prefix() {\n        return _cacheNames.getPrefix();\n    },\n    get runtime() {\n        return _cacheNames.getRuntimeName();\n    },\n    get suffix() {\n        return _cacheNames.getSuffix();\n    },\n};\nexport { cacheNames };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { getFriendlyURL } from 'workbox-core/_private/getFriendlyURL.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport './_version.js';\n/**\n * This class allows you to set up rules determining what\n * status codes and/or headers need to be present in order for a\n * [`Response`](https://developer.mozilla.org/en-US/docs/Web/API/Response)\n * to be considered cacheable.\n *\n * @memberof module:workbox-cacheable-response\n */\nclass CacheableResponse {\n    /**\n     * To construct a new CacheableResponse instance you must provide at least\n     * one of the `config` properties.\n     *\n     * If both `statuses` and `headers` are specified, then both conditions must\n     * be met for the `Response` to be considered cacheable.\n     *\n     * @param {Object} config\n     * @param {Array} [config.statuses] One or more status codes that a\n     * `Response` can have and be considered cacheable.\n     * @param {Object} [config.headers] A mapping of header names\n     * and expected values that a `Response` can have and be considered cacheable.\n     * If multiple headers are provided, only one needs to be present.\n     */\n    constructor(config = {}) {\n        if (process.env.NODE_ENV !== 'production') {\n            if (!(config.statuses || config.headers)) {\n                throw new WorkboxError('statuses-or-headers-required', {\n                    moduleName: 'workbox-cacheable-response',\n                    className: 'CacheableResponse',\n                    funcName: 'constructor',\n                });\n            }\n            if (config.statuses) {\n                assert.isArray(config.statuses, {\n                    moduleName: 'workbox-cacheable-response',\n                    className: 'CacheableResponse',\n                    funcName: 'constructor',\n                    paramName: 'config.statuses',\n                });\n            }\n            if (config.headers) {\n                assert.isType(config.headers, 'object', {\n                    moduleName: 'workbox-cacheable-response',\n                    className: 'CacheableResponse',\n                    funcName: 'constructor',\n                    paramName: 'config.headers',\n                });\n            }\n        }\n        this._statuses = config.statuses;\n        this._headers = config.headers;\n    }\n    /**\n     * Checks a response to see whether it's cacheable or not, based on this\n     * object's configuration.\n     *\n     * @param {Response} response The response whose cacheability is being\n     * checked.\n     * @return {boolean} `true` if the `Response` is cacheable, and `false`\n     * otherwise.\n     */\n    isResponseCacheable(response) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(response, Response, {\n                moduleName: 'workbox-cacheable-response',\n                className: 'CacheableResponse',\n                funcName: 'isResponseCacheable',\n                paramName: 'response',\n            });\n        }\n        let cacheable = true;\n        if (this._statuses) {\n            cacheable = this._statuses.includes(response.status);\n        }\n        if (this._headers && cacheable) {\n            cacheable = Object.keys(this._headers).some((headerName) => {\n                return response.headers.get(headerName) === this._headers[headerName];\n            });\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            if (!cacheable) {\n                logger.groupCollapsed(`The request for ` +\n                    `'${getFriendlyURL(response.url)}' returned a response that does ` +\n                    `not meet the criteria for being cached.`);\n                logger.groupCollapsed(`View cacheability criteria here.`);\n                logger.log(`Cacheable statuses: ` +\n                    JSON.stringify(this._statuses));\n                logger.log(`Cacheable headers: ` +\n                    JSON.stringify(this._headers, null, 2));\n                logger.groupEnd();\n                const logFriendlyHeaders = {};\n                response.headers.forEach((value, key) => {\n                    logFriendlyHeaders[key] = value;\n                });\n                logger.groupCollapsed(`View response status and headers here.`);\n                logger.log(`Response status: ` + response.status);\n                logger.log(`Response headers: ` +\n                    JSON.stringify(logFriendlyHeaders, null, 2));\n                logger.groupEnd();\n                logger.groupCollapsed(`View full response details here.`);\n                logger.log(response.headers);\n                logger.log(response);\n                logger.groupEnd();\n                logger.groupEnd();\n            }\n        }\n        return cacheable;\n    }\n}\nexport { CacheableResponse };\n","import { NetworkFirst } from 'workbox-strategies';\nimport { cacheNames } from 'workbox-core';\nimport { CacheableResponsePlugin } from 'workbox-cacheable-response';\n\nexport const PRECACHING_OPTIONS = {};\n\nexport const NETWORK_HANDLER = new NetworkFirst({\n\t// this cache is plunged with every new service worker deploy so we dont need to care about purging the cache.\n\tcacheName: cacheNames.precache,\n\tnetworkTimeoutSeconds: 5, // if u dont start getting headers within 5 sec fallback to cache.\n\tplugins: [\n\t\tnew CacheableResponsePlugin({\n\t\t\tstatuses: [200], // only cache valid responses, not opaque responses e.g. wifi portal.\n\t\t}),\n\t],\n});\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { Route } from './Route.js';\nimport { RegExpRoute } from './RegExpRoute.js';\nimport { getOrCreateDefaultRouter } from './utils/getOrCreateDefaultRouter.js';\nimport './_version.js';\n/**\n * Easily register a RegExp, string, or function with a caching\n * strategy to a singleton Router instance.\n *\n * This method will generate a Route for you if needed and\n * call [registerRoute()]{@link module:workbox-routing.Router#registerRoute}.\n *\n * @param {RegExp|string|module:workbox-routing.Route~matchCallback|module:workbox-routing.Route} capture\n * If the capture param is a `Route`, all other arguments will be ignored.\n * @param {module:workbox-routing~handlerCallback} [handler] A callback\n * function that returns a Promise resulting in a Response. This parameter\n * is required if `capture` is not a `Route` object.\n * @param {string} [method='GET'] The HTTP method to match the Route\n * against.\n * @return {module:workbox-routing.Route} The generated `Route`(Useful for\n * unregistering).\n *\n * @memberof module:workbox-routing\n */\nfunction registerRoute(capture, handler, method) {\n    let route;\n    if (typeof capture === 'string') {\n        const captureUrl = new URL(capture, location.href);\n        if (process.env.NODE_ENV !== 'production') {\n            if (!(capture.startsWith('/') || capture.startsWith('http'))) {\n                throw new WorkboxError('invalid-string', {\n                    moduleName: 'workbox-routing',\n                    funcName: 'registerRoute',\n                    paramName: 'capture',\n                });\n            }\n            // We want to check if Express-style wildcards are in the pathname only.\n            // TODO: Remove this log message in v4.\n            const valueToCheck = capture.startsWith('http') ?\n                captureUrl.pathname : capture;\n            // See https://github.com/pillarjs/path-to-regexp#parameters\n            const wildcards = '[*:?+]';\n            if ((new RegExp(`${wildcards}`)).exec(valueToCheck)) {\n                logger.debug(`The '$capture' parameter contains an Express-style wildcard ` +\n                    `character (${wildcards}). Strings are now always interpreted as ` +\n                    `exact matches; use a RegExp for partial or wildcard matches.`);\n            }\n        }\n        const matchCallback = ({ url }) => {\n            if (process.env.NODE_ENV !== 'production') {\n                if ((url.pathname === captureUrl.pathname) &&\n                    (url.origin !== captureUrl.origin)) {\n                    logger.debug(`${capture} only partially matches the cross-origin URL ` +\n                        `${url}. This route will only handle cross-origin requests ` +\n                        `if they match the entire URL.`);\n                }\n            }\n            return url.href === captureUrl.href;\n        };\n        // If `capture` is a string then `handler` and `method` must be present.\n        route = new Route(matchCallback, handler, method);\n    }\n    else if (capture instanceof RegExp) {\n        // If `capture` is a `RegExp` then `handler` and `method` must be present.\n        route = new RegExpRoute(capture, handler, method);\n    }\n    else if (typeof capture === 'function') {\n        // If `capture` is a function then `handler` and `method` must be present.\n        route = new Route(capture, handler, method);\n    }\n    else if (capture instanceof Route) {\n        route = capture;\n    }\n    else {\n        throw new WorkboxError('unsupported-route-type', {\n            moduleName: 'workbox-routing',\n            funcName: 'registerRoute',\n            paramName: 'capture',\n        });\n    }\n    const defaultRouter = getOrCreateDefaultRouter();\n    defaultRouter.registerRoute(route);\n    return route;\n}\nexport { registerRoute };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { CacheableResponse } from './CacheableResponse.js';\nimport './_version.js';\n/**\n * A class implementing the `cacheWillUpdate` lifecycle callback. This makes it\n * easier to add in cacheability checks to requests made via Workbox's built-in\n * strategies.\n *\n * @memberof module:workbox-cacheable-response\n */\nclass CacheableResponsePlugin {\n    /**\n     * To construct a new CacheableResponsePlugin instance you must provide at\n     * least one of the `config` properties.\n     *\n     * If both `statuses` and `headers` are specified, then both conditions must\n     * be met for the `Response` to be considered cacheable.\n     *\n     * @param {Object} config\n     * @param {Array} [config.statuses] One or more status codes that a\n     * `Response` can have and be considered cacheable.\n     * @param {Object} [config.headers] A mapping of header names\n     * and expected values that a `Response` can have and be considered cacheable.\n     * If multiple headers are provided, only one needs to be present.\n     */\n    constructor(config) {\n        /**\n         * @param {Object} options\n         * @param {Response} options.response\n         * @return {Response|null}\n         * @private\n         */\n        this.cacheWillUpdate = async ({ response }) => {\n            if (this._cacheableResponse.isResponseCacheable(response)) {\n                return response;\n            }\n            return null;\n        };\n        this._cacheableResponse = new CacheableResponse(config);\n    }\n}\nexport { CacheableResponsePlugin };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { getOrCreatePrecacheController } from './utils/getOrCreatePrecacheController.js';\nimport './_version.js';\n/**\n * Takes in a URL, and returns the corresponding URL that could be used to\n * lookup the entry in the precache.\n *\n * If a relative URL is provided, the location of the service worker file will\n * be used as the base.\n *\n * For precached entries without revision information, the cache key will be the\n * same as the original URL.\n *\n * For precached entries with revision information, the cache key will be the\n * original URL with the addition of a query parameter used for keeping track of\n * the revision info.\n *\n * @param {string} url The URL whose cache key to look up.\n * @return {string} The cache key that corresponds to that URL.\n *\n * @memberof module:workbox-precaching\n */\nfunction getCacheKeyForURL(url) {\n    const precacheController = getOrCreatePrecacheController();\n    return precacheController.getCacheKeyForURL(url);\n}\nexport { getCacheKeyForURL };\n","\"use strict\";\n// @ts-ignore\ntry {\n    self['workbox:core:5.1.3'] && _();\n}\ncatch (e) { }\n"]}
\ No newline at end of file
diff --git a/docs/sw.js b/docs/sw.js
index 0e54779..86a5840 100644
--- a/docs/sw.js
+++ b/docs/sw.js
@@ -1,2 +1,2 @@
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Promise(function(t,r){var n,o,i,u,c,s,a;n=e.timeoutId,o=e.request,i=e.event;var l=function(){try{if(n&&clearTimeout(n),u||!c)return Promise.resolve(this._respondFromCache({request:o,event:i})).then(function(t){try{return c=t,e.call(this)}catch(e){return r(e)}}.bind(this),r);if(s=c.clone(),a=ne({cacheName:this._cacheName,request:o,response:s,event:i,plugins:this._plugins}),i)try{i.waitUntil(a)}catch(e){0}return e.call(this);function e(){return t(c)}}catch(e){return r(e)}}.bind(this),h=function(e){try{return u=e,l()}catch(e){return r(e)}};try{return Promise.resolve(ie({request:o,event:i,fetchOptions:this._fetchOptions,plugins:this._plugins})).then((function(e){try{return c=e,l()}catch(e){return h(e)}}),h)}catch(e){h(e)}}.bind(this))},t._respondFromCache=function(e){return oe({cacheName:this._cacheName,request:e.request,event:e.event,matchOptions:this._matchOptions,plugins:this._plugins})},e}(),pe=function(){function e(e,t,r){var n=this,o=void 0===r?{}:r,i=o.onupgradeneeded,u=o.onversionchange;this._db=null,this._name=e,this._version=t,this._onupgradeneeded=i,this._onversionchange=u||function(){return n.close()}}var t,r,n,o=e.prototype;return o.open=function(){return new Promise(function(e,t){var r;return r=this,this._db?e():Promise.resolve(new Promise((function(e,t){var n=!1;setTimeout((function(){n=!0,t(new Error("The open request was blocked and timed out"))}),r.OPEN_TIMEOUT);var o=indexedDB.open(r._name,r._version);o.onerror=function(){return t(o.error)},o.onupgradeneeded=function(e){n?(o.transaction.abort(),o.result.close()):"function"==typeof r._onupgradeneeded&&r._onupgradeneeded(e)},o.onsuccess=function(){var t=o.result;n?t.close():(t.onversionchange=r._onversionchange.bind(r),e(t))}}))).then(function(r){try{return this._db=r,e(this)}catch(e){return t(e)}}.bind(this),t)}.bind(this))},o.getKey=function(e,t){return new Promise(function(r,n){return Promise.resolve(this.getAllKeys(e,t,1)).then((function(e){try{return r(e[0])}catch(e){return n(e)}}),n)}.bind(this))},o.getAll=function(e,t,r){return new Promise(function(n,o){return Promise.resolve(this.getAllMatching(e,{query:t,count:r})).then(n,o)}.bind(this))},o.getAllKeys=function(e,t,r){return new Promise(function(n,o){return Promise.resolve(this.getAllMatching(e,{query:t,count:r,includeKeys:!0})).then((function(e){try{return n(e.map((function(e){return e.key})))}catch(e){return o(e)}}),o)}.bind(this))},o.getAllMatching=function(e,t){return new Promise(function(r,n){var o,i,u,c,s,a,l,h,f;return i=(o=void 0===t?{}:t).index,c=void 0===(u=o.query)?null:u,a=void 0===(s=o.direction)?"next":s,l=o.count,f=void 0!==(h=o.includeKeys)&&h,Promise.resolve(this.transaction([e],"readonly",(function(t,r){var n=t.objectStore(e),o=i?n.index(i):n,u=[],s=o.openCursor(c,a);s.onsuccess=function(){var e=s.result;e?(u.push(f?e:e.value),l&&u.length>=l?r(u):e.continue()):r(u)}}))).then(r,n)}.bind(this))},o.transaction=function(e,t,r){return new Promise(function(n,o){var i;return i=this,Promise.resolve(this.open()).then((function(){try{return Promise.resolve(new Promise((function(n,o){var u=i._db.transaction(e,t);u.onabort=function(){return o(u.error)},u.oncomplete=function(){return n()},r(u,(function(e){return n(e)}))}))).then(n,o)}catch(e){return o(e)}}),o)}.bind(this))},o._call=function(e,t,r){var n=arguments;return new Promise(function(o,i){var u,c,s;for(u=n.length,c=new Array(u>3?u-3:0),s=3;s1?u-1:0),s=1;s} [options.ignoreURLParametersMatching=[/^utm_/]] An\n * array of regex's to remove search params when looking for a cache match.\n * @param {boolean} [options.cleanURLs=true] The `cleanURLs` option will\n * check the cache for the URL with a `.html` added to the end of the end.\n * @param {module:workbox-precaching~urlManipulation} [options.urlManipulation]\n * This is a function that should take a URL and return an array of\n * alternative URLs that should be checked for precache matches.\n *\n * @memberof module:workbox-precaching\n */\nfunction addRoute(options) {\n    if (!listenerAdded) {\n        addFetchListener(options);\n        listenerAdded = true;\n    }\n}\nexport { addRoute };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { cacheNames } from 'workbox-core/_private/cacheNames.js';\nimport { getFriendlyURL } from 'workbox-core/_private/getFriendlyURL.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { getCacheKeyForURL } from './getCacheKeyForURL.js';\nimport '../_version.js';\n/**\n * Adds a `fetch` listener to the service worker that will\n * respond to\n * [network requests]{@link https://developer.mozilla.org/en-US/docs/Web/API/Service_Worker_API/Using_Service_Workers#Custom_responses_to_requests}\n * with precached assets.\n *\n * Requests for assets that aren't precached, the `FetchEvent` will not be\n * responded to, allowing the event to fall through to other `fetch` event\n * listeners.\n *\n * NOTE: when called more than once this method will replace the previously set\n * configuration options. Calling it more than once is not recommended outside\n * of tests.\n *\n * @private\n * @param {Object} [options]\n * @param {string} [options.directoryIndex=index.html] The `directoryIndex` will\n * check cache entries for a URLs ending with '/' to see if there is a hit when\n * appending the `directoryIndex` value.\n * @param {Array} [options.ignoreURLParametersMatching=[/^utm_/]] An\n * array of regex's to remove search params when looking for a cache match.\n * @param {boolean} [options.cleanURLs=true] The `cleanURLs` option will\n * check the cache for the URL with a `.html` added to the end of the end.\n * @param {workbox.precaching~urlManipulation} [options.urlManipulation]\n * This is a function that should take a URL and return an array of\n * alternative URLs that should be checked for precache matches.\n */\nexport const addFetchListener = ({ ignoreURLParametersMatching = [/^utm_/], directoryIndex = 'index.html', cleanURLs = true, urlManipulation, } = {}) => {\n    const cacheName = cacheNames.getPrecacheName();\n    // See https://github.com/Microsoft/TypeScript/issues/28357#issuecomment-436484705\n    self.addEventListener('fetch', ((event) => {\n        const precachedURL = getCacheKeyForURL(event.request.url, {\n            cleanURLs,\n            directoryIndex,\n            ignoreURLParametersMatching,\n            urlManipulation,\n        });\n        if (!precachedURL) {\n            if (process.env.NODE_ENV !== 'production') {\n                logger.debug(`Precaching did not find a match for ` +\n                    getFriendlyURL(event.request.url));\n            }\n            return;\n        }\n        let responsePromise = self.caches.open(cacheName).then((cache) => {\n            return cache.match(precachedURL);\n        }).then((cachedResponse) => {\n            if (cachedResponse) {\n                return cachedResponse;\n            }\n            // Fall back to the network if we don't have a cached response\n            // (perhaps due to manual cache cleanup).\n            if (process.env.NODE_ENV !== 'production') {\n                logger.warn(`The precached response for ` +\n                    `${getFriendlyURL(precachedURL)} in ${cacheName} was not found. ` +\n                    `Falling back to the network instead.`);\n            }\n            return fetch(precachedURL);\n        });\n        if (process.env.NODE_ENV !== 'production') {\n            responsePromise = responsePromise.then((response) => {\n                // Workbox is going to handle the route.\n                // print the routing details to the console.\n                logger.groupCollapsed(`Precaching is responding to: ` +\n                    getFriendlyURL(event.request.url));\n                logger.log(`Serving the precached url: ${precachedURL}`);\n                logger.groupCollapsed(`View request details here.`);\n                logger.log(event.request);\n                logger.groupEnd();\n                logger.groupCollapsed(`View response details here.`);\n                logger.log(response);\n                logger.groupEnd();\n                logger.groupEnd();\n                return response;\n            });\n        }\n        event.respondWith(responsePromise);\n    }));\n};\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { getOrCreatePrecacheController } from './getOrCreatePrecacheController.js';\nimport { generateURLVariations } from './generateURLVariations.js';\nimport '../_version.js';\n/**\n * This function will take the request URL and manipulate it based on the\n * configuration options.\n *\n * @param {string} url\n * @param {Object} options\n * @return {string} Returns the URL in the cache that matches the request,\n * if possible.\n *\n * @private\n */\nexport const getCacheKeyForURL = (url, options) => {\n    const precacheController = getOrCreatePrecacheController();\n    const urlsToCacheKeys = precacheController.getURLsToCacheKeys();\n    for (const possibleURL of generateURLVariations(url, options)) {\n        const possibleCacheKey = urlsToCacheKeys.get(possibleURL);\n        if (possibleCacheKey) {\n            return possibleCacheKey;\n        }\n    }\n};\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { removeIgnoredSearchParams } from './removeIgnoredSearchParams.js';\nimport '../_version.js';\n/**\n * Generator function that yields possible variations on the original URL to\n * check, one at a time.\n *\n * @param {string} url\n * @param {Object} options\n *\n * @private\n * @memberof module:workbox-precaching\n */\nexport function* generateURLVariations(url, { ignoreURLParametersMatching, directoryIndex, cleanURLs, urlManipulation, } = {}) {\n    const urlObject = new URL(url, location.href);\n    urlObject.hash = '';\n    yield urlObject.href;\n    const urlWithoutIgnoredParams = removeIgnoredSearchParams(urlObject, ignoreURLParametersMatching);\n    yield urlWithoutIgnoredParams.href;\n    if (directoryIndex && urlWithoutIgnoredParams.pathname.endsWith('/')) {\n        const directoryURL = new URL(urlWithoutIgnoredParams.href);\n        directoryURL.pathname += directoryIndex;\n        yield directoryURL.href;\n    }\n    if (cleanURLs) {\n        const cleanURL = new URL(urlWithoutIgnoredParams.href);\n        cleanURL.pathname += '.html';\n        yield cleanURL.href;\n    }\n    if (urlManipulation) {\n        const additionalURLs = urlManipulation({ url: urlObject });\n        for (const urlToAttempt of additionalURLs) {\n            yield urlToAttempt.href;\n        }\n    }\n}\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\n/**\n * Removes any URL search parameters that should be ignored.\n *\n * @param {URL} urlObject The original URL.\n * @param {Array} ignoreURLParametersMatching RegExps to test against\n * each search parameter name. Matches mean that the search parameter should be\n * ignored.\n * @return {URL} The URL with any ignored search parameters removed.\n *\n * @private\n * @memberof module:workbox-precaching\n */\nexport function removeIgnoredSearchParams(urlObject, ignoreURLParametersMatching = []) {\n    // Convert the iterable into an array at the start of the loop to make sure\n    // deletion doesn't mess up iteration.\n    for (const paramName of [...urlObject.searchParams.keys()]) {\n        if (ignoreURLParametersMatching.some((regExp) => regExp.test(paramName))) {\n            urlObject.searchParams.delete(paramName);\n        }\n    }\n    return urlObject;\n}\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { addRoute } from './addRoute.js';\nimport { precache } from './precache.js';\nimport './_version.js';\n/**\n * This method will add entries to the precache list and add a route to\n * respond to fetch events.\n *\n * This is a convenience method that will call\n * [precache()]{@link module:workbox-precaching.precache} and\n * [addRoute()]{@link module:workbox-precaching.addRoute} in a single call.\n *\n * @param {Array} entries Array of entries to precache.\n * @param {Object} [options] See\n * [addRoute() options]{@link module:workbox-precaching.addRoute}.\n *\n * @memberof module:workbox-precaching\n */\nfunction precacheAndRoute(entries, options) {\n    precache(entries);\n    addRoute(options);\n}\nexport { precacheAndRoute };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { getOrCreatePrecacheController } from './utils/getOrCreatePrecacheController.js';\nimport { precachePlugins } from './utils/precachePlugins.js';\nimport './_version.js';\nconst installListener = (event) => {\n    const precacheController = getOrCreatePrecacheController();\n    const plugins = precachePlugins.get();\n    event.waitUntil(precacheController.install({ event, plugins })\n        .catch((error) => {\n        if (process.env.NODE_ENV !== 'production') {\n            logger.error(`Service worker installation failed. It will ` +\n                `be retried automatically during the next navigation.`);\n        }\n        // Re-throw the error to ensure installation fails.\n        throw error;\n    }));\n};\nconst activateListener = (event) => {\n    const precacheController = getOrCreatePrecacheController();\n    event.waitUntil(precacheController.activate());\n};\n/**\n * Adds items to the precache list, removing any duplicates and\n * stores the files in the\n * [\"precache cache\"]{@link module:workbox-core.cacheNames} when the service\n * worker installs.\n *\n * This method can be called multiple times.\n *\n * Please note: This method **will not** serve any of the cached files for you.\n * It only precaches files. To respond to a network request you call\n * [addRoute()]{@link module:workbox-precaching.addRoute}.\n *\n * If you have a single array of files to precache, you can just call\n * [precacheAndRoute()]{@link module:workbox-precaching.precacheAndRoute}.\n *\n * @param {Array} [entries=[]] Array of entries to precache.\n *\n * @memberof module:workbox-precaching\n */\nfunction precache(entries) {\n    const precacheController = getOrCreatePrecacheController();\n    precacheController.addToCacheList(entries);\n    if (entries.length > 0) {\n        // NOTE: these listeners will only be added once (even if the `precache()`\n        // method is called multiple times) because event listeners are implemented\n        // as a set, where each listener must be unique.\n        // See https://github.com/Microsoft/TypeScript/issues/28357#issuecomment-436484705\n        self.addEventListener('install', installListener);\n        self.addEventListener('activate', activateListener);\n    }\n}\nexport { precache };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { Router } from '../Router.js';\nimport '../_version.js';\nlet defaultRouter;\n/**\n * Creates a new, singleton Router instance if one does not exist. If one\n * does already exist, that instance is returned.\n *\n * @private\n * @return {Router}\n */\nexport const getOrCreateDefaultRouter = () => {\n    if (!defaultRouter) {\n        defaultRouter = new Router();\n        // The helpers that use the default Router assume these listeners exist.\n        defaultRouter.addFetchListener();\n        defaultRouter.addCacheListener();\n    }\n    return defaultRouter;\n};\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { PrecacheController } from '../PrecacheController.js';\nimport '../_version.js';\nlet precacheController;\n/**\n * @return {PrecacheController}\n * @private\n */\nexport const getOrCreatePrecacheController = () => {\n    if (!precacheController) {\n        precacheController = new PrecacheController();\n    }\n    return precacheController;\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { messages } from './messages.js';\nimport '../../_version.js';\nconst fallback = (code, ...args) => {\n    let msg = code;\n    if (args.length > 0) {\n        msg += ` :: ${JSON.stringify(args)}`;\n    }\n    return msg;\n};\nconst generatorFunction = (code, details = {}) => {\n    const message = messages[code];\n    if (!message) {\n        throw new Error(`Unable to find message for code '${code}'.`);\n    }\n    return message(details);\n};\nexport const messageGenerator = (process.env.NODE_ENV === 'production') ?\n    fallback : generatorFunction;\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { messageGenerator } from '../models/messages/messageGenerator.js';\nimport '../_version.js';\n/**\n * Workbox errors should be thrown with this class.\n * This allows use to ensure the type easily in tests,\n * helps developers identify errors from workbox\n * easily and allows use to optimise error\n * messages correctly.\n *\n * @private\n */\nclass WorkboxError extends Error {\n    /**\n     *\n     * @param {string} errorCode The error code that\n     * identifies this particular error.\n     * @param {Object=} details Any relevant arguments\n     * that will help developers identify issues should\n     * be added as a key on the context object.\n     */\n    constructor(errorCode, details) {\n        const message = messageGenerator(errorCode, details);\n        super(message);\n        this.name = errorCode;\n        this.details = details;\n    }\n}\nexport { WorkboxError };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport '../_version.js';\n/**\n * @param {function()|Object} handler Either a function, or an object with a\n * 'handle' method.\n * @return {Object} An object with a handle method.\n *\n * @private\n */\nexport const normalizeHandler = (handler) => {\n    if (handler && typeof handler === 'object') {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.hasMethod(handler, 'handle', {\n                moduleName: 'workbox-routing',\n                className: 'Route',\n                funcName: 'constructor',\n                paramName: 'handler',\n            });\n        }\n        return handler;\n    }\n    else {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isType(handler, 'function', {\n                moduleName: 'workbox-routing',\n                className: 'Route',\n                funcName: 'constructor',\n                paramName: 'handler',\n            });\n        }\n        return { handle: handler };\n    }\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { defaultMethod, validMethods } from './utils/constants.js';\nimport { normalizeHandler } from './utils/normalizeHandler.js';\nimport './_version.js';\n/**\n * A `Route` consists of a pair of callback functions, \"match\" and \"handler\".\n * The \"match\" callback determine if a route should be used to \"handle\" a\n * request by returning a non-falsy value if it can. The \"handler\" callback\n * is called when there is a match and should return a Promise that resolves\n * to a `Response`.\n *\n * @memberof module:workbox-routing\n */\nclass Route {\n    /**\n     * Constructor for Route class.\n     *\n     * @param {module:workbox-routing~matchCallback} match\n     * A callback function that determines whether the route matches a given\n     * `fetch` event by returning a non-falsy value.\n     * @param {module:workbox-routing~handlerCallback} handler A callback\n     * function that returns a Promise resolving to a Response.\n     * @param {string} [method='GET'] The HTTP method to match the Route\n     * against.\n     */\n    constructor(match, handler, method = defaultMethod) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isType(match, 'function', {\n                moduleName: 'workbox-routing',\n                className: 'Route',\n                funcName: 'constructor',\n                paramName: 'match',\n            });\n            if (method) {\n                assert.isOneOf(method, validMethods, { paramName: 'method' });\n            }\n        }\n        // These values are referenced directly by Router so cannot be\n        // altered by minificaton.\n        this.handler = normalizeHandler(handler);\n        this.match = match;\n        this.method = method;\n    }\n}\nexport { Route };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\n/**\n * The default HTTP method, 'GET', used when there's no specific method\n * configured for a route.\n *\n * @type {string}\n *\n * @private\n */\nexport const defaultMethod = 'GET';\n/**\n * The list of valid HTTP methods associated with requests that could be routed.\n *\n * @type {Array}\n *\n * @private\n */\nexport const validMethods = [\n    'DELETE',\n    'GET',\n    'HEAD',\n    'PATCH',\n    'POST',\n    'PUT',\n];\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { Route } from './Route.js';\nimport './_version.js';\n/**\n * RegExpRoute makes it easy to create a regular expression based\n * [Route]{@link module:workbox-routing.Route}.\n *\n * For same-origin requests the RegExp only needs to match part of the URL. For\n * requests against third-party servers, you must define a RegExp that matches\n * the start of the URL.\n *\n * [See the module docs for info.]{@link https://developers.google.com/web/tools/workbox/modules/workbox-routing}\n *\n * @memberof module:workbox-routing\n * @extends module:workbox-routing.Route\n */\nclass RegExpRoute extends Route {\n    /**\n     * If the regular expression contains\n     * [capture groups]{@link https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/RegExp#grouping-back-references},\n     * the captured values will be passed to the\n     * [handler's]{@link module:workbox-routing~handlerCallback} `params`\n     * argument.\n     *\n     * @param {RegExp} regExp The regular expression to match against URLs.\n     * @param {module:workbox-routing~handlerCallback} handler A callback\n     * function that returns a Promise resulting in a Response.\n     * @param {string} [method='GET'] The HTTP method to match the Route\n     * against.\n     */\n    constructor(regExp, handler, method) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(regExp, RegExp, {\n                moduleName: 'workbox-routing',\n                className: 'RegExpRoute',\n                funcName: 'constructor',\n                paramName: 'pattern',\n            });\n        }\n        const match = ({ url }) => {\n            const result = regExp.exec(url.href);\n            // Return immediately if there's no match.\n            if (!result) {\n                return;\n            }\n            // Require that the match start at the first character in the URL string\n            // if it's a cross-origin request.\n            // See https://github.com/GoogleChrome/workbox/issues/281 for the context\n            // behind this behavior.\n            if ((url.origin !== location.origin) && (result.index !== 0)) {\n                if (process.env.NODE_ENV !== 'production') {\n                    logger.debug(`The regular expression '${regExp}' only partially matched ` +\n                        `against the cross-origin URL '${url}'. RegExpRoute's will only ` +\n                        `handle cross-origin requests if they match the entire URL.`);\n                }\n                return;\n            }\n            // If the route matches, but there aren't any capture groups defined, then\n            // this will return [], which is truthy and therefore sufficient to\n            // indicate a match.\n            // If there are capture groups, then it will return their values.\n            return result.slice(1);\n        };\n        super(match, handler, method);\n    }\n}\nexport { RegExpRoute };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nconst getFriendlyURL = (url) => {\n    const urlObj = new URL(String(url), location.href);\n    // See https://github.com/GoogleChrome/workbox/issues/2323\n    // We want to include everything, except for the origin if it's same-origin.\n    return urlObj.href.replace(new RegExp(`^${location.origin}`), '');\n};\nexport { getFriendlyURL };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { getFriendlyURL } from 'workbox-core/_private/getFriendlyURL.js';\nimport { normalizeHandler } from './utils/normalizeHandler.js';\nimport './_version.js';\n/**\n * The Router can be used to process a FetchEvent through one or more\n * [Routes]{@link module:workbox-routing.Route} responding  with a Request if\n * a matching route exists.\n *\n * If no route matches a given a request, the Router will use a \"default\"\n * handler if one is defined.\n *\n * Should the matching Route throw an error, the Router will use a \"catch\"\n * handler if one is defined to gracefully deal with issues and respond with a\n * Request.\n *\n * If a request matches multiple routes, the **earliest** registered route will\n * be used to respond to the request.\n *\n * @memberof module:workbox-routing\n */\nclass Router {\n    /**\n     * Initializes a new Router.\n     */\n    constructor() {\n        this._routes = new Map();\n    }\n    /**\n     * @return {Map>} routes A `Map` of HTTP\n     * method name ('GET', etc.) to an array of all the corresponding `Route`\n     * instances that are registered.\n     */\n    get routes() {\n        return this._routes;\n    }\n    /**\n     * Adds a fetch event listener to respond to events when a route matches\n     * the event's request.\n     */\n    addFetchListener() {\n        // See https://github.com/Microsoft/TypeScript/issues/28357#issuecomment-436484705\n        self.addEventListener('fetch', ((event) => {\n            const { request } = event;\n            const responsePromise = this.handleRequest({ request, event });\n            if (responsePromise) {\n                event.respondWith(responsePromise);\n            }\n        }));\n    }\n    /**\n     * Adds a message event listener for URLs to cache from the window.\n     * This is useful to cache resources loaded on the page prior to when the\n     * service worker started controlling it.\n     *\n     * The format of the message data sent from the window should be as follows.\n     * Where the `urlsToCache` array may consist of URL strings or an array of\n     * URL string + `requestInit` object (the same as you'd pass to `fetch()`).\n     *\n     * ```\n     * {\n     *   type: 'CACHE_URLS',\n     *   payload: {\n     *     urlsToCache: [\n     *       './script1.js',\n     *       './script2.js',\n     *       ['./script3.js', {mode: 'no-cors'}],\n     *     ],\n     *   },\n     * }\n     * ```\n     */\n    addCacheListener() {\n        // See https://github.com/Microsoft/TypeScript/issues/28357#issuecomment-436484705\n        self.addEventListener('message', ((event) => {\n            if (event.data && event.data.type === 'CACHE_URLS') {\n                const { payload } = event.data;\n                if (process.env.NODE_ENV !== 'production') {\n                    logger.debug(`Caching URLs from the window`, payload.urlsToCache);\n                }\n                const requestPromises = Promise.all(payload.urlsToCache.map((entry) => {\n                    if (typeof entry === 'string') {\n                        entry = [entry];\n                    }\n                    const request = new Request(...entry);\n                    return this.handleRequest({ request });\n                    // TODO(philipwalton): TypeScript errors without this typecast for\n                    // some reason (probably a bug). The real type here should work but\n                    // doesn't: `Array | undefined>`.\n                })); // TypeScript\n                event.waitUntil(requestPromises);\n                // If a MessageChannel was used, reply to the message on success.\n                if (event.ports && event.ports[0]) {\n                    requestPromises.then(() => event.ports[0].postMessage(true));\n                }\n            }\n        }));\n    }\n    /**\n     * Apply the routing rules to a FetchEvent object to get a Response from an\n     * appropriate Route's handler.\n     *\n     * @param {Object} options\n     * @param {Request} options.request The request to handle (this is usually\n     *     from a fetch event, but it does not have to be).\n     * @param {FetchEvent} [options.event] The event that triggered the request,\n     *     if applicable.\n     * @return {Promise|undefined} A promise is returned if a\n     *     registered route can handle the request. If there is no matching\n     *     route and there's no `defaultHandler`, `undefined` is returned.\n     */\n    handleRequest({ request, event }) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(request, Request, {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'handleRequest',\n                paramName: 'options.request',\n            });\n        }\n        const url = new URL(request.url, location.href);\n        if (!url.protocol.startsWith('http')) {\n            if (process.env.NODE_ENV !== 'production') {\n                logger.debug(`Workbox Router only supports URLs that start with 'http'.`);\n            }\n            return;\n        }\n        const { params, route } = this.findMatchingRoute({ url, request, event });\n        let handler = route && route.handler;\n        const debugMessages = [];\n        if (process.env.NODE_ENV !== 'production') {\n            if (handler) {\n                debugMessages.push([\n                    `Found a route to handle this request:`, route,\n                ]);\n                if (params) {\n                    debugMessages.push([\n                        `Passing the following params to the route's handler:`, params,\n                    ]);\n                }\n            }\n        }\n        // If we don't have a handler because there was no matching route, then\n        // fall back to defaultHandler if that's defined.\n        if (!handler && this._defaultHandler) {\n            if (process.env.NODE_ENV !== 'production') {\n                debugMessages.push(`Failed to find a matching route. Falling ` +\n                    `back to the default handler.`);\n            }\n            handler = this._defaultHandler;\n        }\n        if (!handler) {\n            if (process.env.NODE_ENV !== 'production') {\n                // No handler so Workbox will do nothing. If logs is set of debug\n                // i.e. verbose, we should print out this information.\n                logger.debug(`No route found for: ${getFriendlyURL(url)}`);\n            }\n            return;\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            // We have a handler, meaning Workbox is going to handle the route.\n            // print the routing details to the console.\n            logger.groupCollapsed(`Router is responding to: ${getFriendlyURL(url)}`);\n            debugMessages.forEach((msg) => {\n                if (Array.isArray(msg)) {\n                    logger.log(...msg);\n                }\n                else {\n                    logger.log(msg);\n                }\n            });\n            logger.groupEnd();\n        }\n        // Wrap in try and catch in case the handle method throws a synchronous\n        // error. It should still callback to the catch handler.\n        let responsePromise;\n        try {\n            responsePromise = handler.handle({ url, request, event, params });\n        }\n        catch (err) {\n            responsePromise = Promise.reject(err);\n        }\n        if (responsePromise instanceof Promise && this._catchHandler) {\n            responsePromise = responsePromise.catch((err) => {\n                if (process.env.NODE_ENV !== 'production') {\n                    // Still include URL here as it will be async from the console group\n                    // and may not make sense without the URL\n                    logger.groupCollapsed(`Error thrown when responding to: ` +\n                        ` ${getFriendlyURL(url)}. Falling back to Catch Handler.`);\n                    logger.error(`Error thrown by:`, route);\n                    logger.error(err);\n                    logger.groupEnd();\n                }\n                return this._catchHandler.handle({ url, request, event });\n            });\n        }\n        return responsePromise;\n    }\n    /**\n     * Checks a request and URL (and optionally an event) against the list of\n     * registered routes, and if there's a match, returns the corresponding\n     * route along with any params generated by the match.\n     *\n     * @param {Object} options\n     * @param {URL} options.url\n     * @param {Request} options.request The request to match.\n     * @param {Event} [options.event] The corresponding event (unless N/A).\n     * @return {Object} An object with `route` and `params` properties.\n     *     They are populated if a matching route was found or `undefined`\n     *     otherwise.\n     */\n    findMatchingRoute({ url, request, event }) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(url, URL, {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'findMatchingRoute',\n                paramName: 'options.url',\n            });\n            assert.isInstance(request, Request, {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'findMatchingRoute',\n                paramName: 'options.request',\n            });\n        }\n        const routes = this._routes.get(request.method) || [];\n        for (const route of routes) {\n            let params;\n            const matchResult = route.match({ url, request, event });\n            if (matchResult) {\n                // See https://github.com/GoogleChrome/workbox/issues/2079\n                params = matchResult;\n                if (Array.isArray(matchResult) && matchResult.length === 0) {\n                    // Instead of passing an empty array in as params, use undefined.\n                    params = undefined;\n                }\n                else if ((matchResult.constructor === Object &&\n                    Object.keys(matchResult).length === 0)) {\n                    // Instead of passing an empty object in as params, use undefined.\n                    params = undefined;\n                }\n                else if (typeof matchResult === 'boolean') {\n                    // For the boolean value true (rather than just something truth-y),\n                    // don't set params.\n                    // See https://github.com/GoogleChrome/workbox/pull/2134#issuecomment-513924353\n                    params = undefined;\n                }\n                // Return early if have a match.\n                return { route, params };\n            }\n        }\n        // If no match was found above, return and empty object.\n        return {};\n    }\n    /**\n     * Define a default `handler` that's called when no routes explicitly\n     * match the incoming request.\n     *\n     * Without a default handler, unmatched requests will go against the\n     * network as if there were no service worker present.\n     *\n     * @param {module:workbox-routing~handlerCallback} handler A callback\n     * function that returns a Promise resulting in a Response.\n     */\n    setDefaultHandler(handler) {\n        this._defaultHandler = normalizeHandler(handler);\n    }\n    /**\n     * If a Route throws an error while handling a request, this `handler`\n     * will be called and given a chance to provide a response.\n     *\n     * @param {module:workbox-routing~handlerCallback} handler A callback\n     * function that returns a Promise resulting in a Response.\n     */\n    setCatchHandler(handler) {\n        this._catchHandler = normalizeHandler(handler);\n    }\n    /**\n     * Registers a route with the router.\n     *\n     * @param {module:workbox-routing.Route} route The route to register.\n     */\n    registerRoute(route) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isType(route, 'object', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route',\n            });\n            assert.hasMethod(route, 'match', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route',\n            });\n            assert.isType(route.handler, 'object', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route',\n            });\n            assert.hasMethod(route.handler, 'handle', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route.handler',\n            });\n            assert.isType(route.method, 'string', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route.method',\n            });\n        }\n        if (!this._routes.has(route.method)) {\n            this._routes.set(route.method, []);\n        }\n        // Give precedence to all of the earlier routes by adding this additional\n        // route to the end of the array.\n        this._routes.get(route.method).push(route);\n    }\n    /**\n     * Unregisters a route with the router.\n     *\n     * @param {module:workbox-routing.Route} route The route to unregister.\n     */\n    unregisterRoute(route) {\n        if (!this._routes.has(route.method)) {\n            throw new WorkboxError('unregister-route-but-not-found-with-method', {\n                method: route.method,\n            });\n        }\n        const routeIndex = this._routes.get(route.method).indexOf(route);\n        if (routeIndex > -1) {\n            this._routes.get(route.method).splice(routeIndex, 1);\n        }\n        else {\n            throw new WorkboxError('unregister-route-route-not-registered');\n        }\n    }\n}\nexport { Router };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nconst plugins = [];\nexport const precachePlugins = {\n    /*\n     * @return {Array}\n     * @private\n     */\n    get() {\n        return plugins;\n    },\n    /*\n     * @param {Array} newPlugins\n     * @private\n     */\n    add(newPlugins) {\n        plugins.push(...newPlugins);\n    },\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nconst _cacheNameDetails = {\n    googleAnalytics: 'googleAnalytics',\n    precache: 'precache-v2',\n    prefix: 'workbox',\n    runtime: 'runtime',\n    suffix: typeof registration !== 'undefined' ? registration.scope : '',\n};\nconst _createCacheName = (cacheName) => {\n    return [_cacheNameDetails.prefix, cacheName, _cacheNameDetails.suffix]\n        .filter((value) => value && value.length > 0)\n        .join('-');\n};\nconst eachCacheNameDetail = (fn) => {\n    for (const key of Object.keys(_cacheNameDetails)) {\n        fn(key);\n    }\n};\nexport const cacheNames = {\n    updateDetails: (details) => {\n        eachCacheNameDetail((key) => {\n            if (typeof details[key] === 'string') {\n                _cacheNameDetails[key] = details[key];\n            }\n        });\n    },\n    getGoogleAnalyticsName: (userCacheName) => {\n        return userCacheName || _createCacheName(_cacheNameDetails.googleAnalytics);\n    },\n    getPrecacheName: (userCacheName) => {\n        return userCacheName || _createCacheName(_cacheNameDetails.precache);\n    },\n    getPrefix: () => {\n        return _cacheNameDetails.prefix;\n    },\n    getRuntimeName: (userCacheName) => {\n        return userCacheName || _createCacheName(_cacheNameDetails.runtime);\n    },\n    getSuffix: () => {\n        return _cacheNameDetails.suffix;\n    },\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\n// Callbacks to be executed whenever there's a quota error.\nconst quotaErrorCallbacks = new Set();\nexport { quotaErrorCallbacks };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nexport const pluginUtils = {\n    filter: (plugins, callbackName) => {\n        return plugins.filter((plugin) => callbackName in plugin);\n    },\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from './assert.js';\nimport { executeQuotaErrorCallbacks } from './executeQuotaErrorCallbacks.js';\nimport { getFriendlyURL } from './getFriendlyURL.js';\nimport { logger } from './logger.js';\nimport { pluginUtils } from '../utils/pluginUtils.js';\nimport { WorkboxError } from './WorkboxError.js';\nimport '../_version.js';\n/**\n * Checks the list of plugins for the cacheKeyWillBeUsed callback, and\n * executes any of those callbacks found in sequence. The final `Request` object\n * returned by the last plugin is treated as the cache key for cache reads\n * and/or writes.\n *\n * @param {Object} options\n * @param {Request} options.request\n * @param {string} options.mode\n * @param {Array} [options.plugins=[]]\n * @return {Promise}\n *\n * @private\n * @memberof module:workbox-core\n */\nconst _getEffectiveRequest = async ({ request, mode, plugins = [], }) => {\n    const cacheKeyWillBeUsedPlugins = pluginUtils.filter(plugins, \"cacheKeyWillBeUsed\" /* CACHE_KEY_WILL_BE_USED */);\n    let effectiveRequest = request;\n    for (const plugin of cacheKeyWillBeUsedPlugins) {\n        effectiveRequest = await plugin[\"cacheKeyWillBeUsed\" /* CACHE_KEY_WILL_BE_USED */].call(plugin, { mode, request: effectiveRequest });\n        if (typeof effectiveRequest === 'string') {\n            effectiveRequest = new Request(effectiveRequest);\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(effectiveRequest, Request, {\n                moduleName: 'Plugin',\n                funcName: \"cacheKeyWillBeUsed\" /* CACHE_KEY_WILL_BE_USED */,\n                isReturnValueProblem: true,\n            });\n        }\n    }\n    return effectiveRequest;\n};\n/**\n * This method will call cacheWillUpdate on the available plugins (or use\n * status === 200) to determine if the Response is safe and valid to cache.\n *\n * @param {Object} options\n * @param {Request} options.request\n * @param {Response} options.response\n * @param {Event} [options.event]\n * @param {Array} [options.plugins=[]]\n * @return {Promise}\n *\n * @private\n * @memberof module:workbox-core\n */\nconst _isResponseSafeToCache = async ({ request, response, event, plugins = [], }) => {\n    let responseToCache = response;\n    let pluginsUsed = false;\n    for (const plugin of plugins) {\n        if (\"cacheWillUpdate\" /* CACHE_WILL_UPDATE */ in plugin) {\n            pluginsUsed = true;\n            const pluginMethod = plugin[\"cacheWillUpdate\" /* CACHE_WILL_UPDATE */];\n            responseToCache = await pluginMethod.call(plugin, {\n                request,\n                response: responseToCache,\n                event,\n            });\n            if (process.env.NODE_ENV !== 'production') {\n                if (responseToCache) {\n                    assert.isInstance(responseToCache, Response, {\n                        moduleName: 'Plugin',\n                        funcName: \"cacheWillUpdate\" /* CACHE_WILL_UPDATE */,\n                        isReturnValueProblem: true,\n                    });\n                }\n            }\n            if (!responseToCache) {\n                break;\n            }\n        }\n    }\n    if (!pluginsUsed) {\n        if (process.env.NODE_ENV !== 'production') {\n            if (responseToCache) {\n                if (responseToCache.status !== 200) {\n                    if (responseToCache.status === 0) {\n                        logger.warn(`The response for '${request.url}' is an opaque ` +\n                            `response. The caching strategy that you're using will not ` +\n                            `cache opaque responses by default.`);\n                    }\n                    else {\n                        logger.debug(`The response for '${request.url}' returned ` +\n                            `a status code of '${response.status}' and won't be cached as a ` +\n                            `result.`);\n                    }\n                }\n            }\n        }\n        responseToCache = responseToCache && responseToCache.status === 200 ?\n            responseToCache : undefined;\n    }\n    return responseToCache ? responseToCache : null;\n};\n/**\n * This is a wrapper around cache.match().\n *\n * @param {Object} options\n * @param {string} options.cacheName Name of the cache to match against.\n * @param {Request} options.request The Request that will be used to look up\n *     cache entries.\n * @param {Event} [options.event] The event that prompted the action.\n * @param {Object} [options.matchOptions] Options passed to cache.match().\n * @param {Array} [options.plugins=[]] Array of plugins.\n * @return {Response} A cached response if available.\n *\n * @private\n * @memberof module:workbox-core\n */\nconst matchWrapper = async ({ cacheName, request, event, matchOptions, plugins = [], }) => {\n    const cache = await self.caches.open(cacheName);\n    const effectiveRequest = await _getEffectiveRequest({\n        plugins, request, mode: 'read'\n    });\n    let cachedResponse = await cache.match(effectiveRequest, matchOptions);\n    if (process.env.NODE_ENV !== 'production') {\n        if (cachedResponse) {\n            logger.debug(`Found a cached response in '${cacheName}'.`);\n        }\n        else {\n            logger.debug(`No cached response found in '${cacheName}'.`);\n        }\n    }\n    for (const plugin of plugins) {\n        if (\"cachedResponseWillBeUsed\" /* CACHED_RESPONSE_WILL_BE_USED */ in plugin) {\n            const pluginMethod = plugin[\"cachedResponseWillBeUsed\" /* CACHED_RESPONSE_WILL_BE_USED */];\n            cachedResponse = await pluginMethod.call(plugin, {\n                cacheName,\n                event,\n                matchOptions,\n                cachedResponse,\n                request: effectiveRequest,\n            });\n            if (process.env.NODE_ENV !== 'production') {\n                if (cachedResponse) {\n                    assert.isInstance(cachedResponse, Response, {\n                        moduleName: 'Plugin',\n                        funcName: \"cachedResponseWillBeUsed\" /* CACHED_RESPONSE_WILL_BE_USED */,\n                        isReturnValueProblem: true,\n                    });\n                }\n            }\n        }\n    }\n    return cachedResponse;\n};\n/**\n * Wrapper around cache.put().\n *\n * Will call `cacheDidUpdate` on plugins if the cache was updated, using\n * `matchOptions` when determining what the old entry is.\n *\n * @param {Object} options\n * @param {string} options.cacheName\n * @param {Request} options.request\n * @param {Response} options.response\n * @param {Event} [options.event]\n * @param {Array} [options.plugins=[]]\n * @param {Object} [options.matchOptions]\n *\n * @private\n * @memberof module:workbox-core\n */\nconst putWrapper = async ({ cacheName, request, response, event, plugins = [], matchOptions, }) => {\n    if (process.env.NODE_ENV !== 'production') {\n        if (request.method && request.method !== 'GET') {\n            throw new WorkboxError('attempt-to-cache-non-get-request', {\n                url: getFriendlyURL(request.url),\n                method: request.method,\n            });\n        }\n    }\n    const effectiveRequest = await _getEffectiveRequest({\n        plugins, request, mode: 'write'\n    });\n    if (!response) {\n        if (process.env.NODE_ENV !== 'production') {\n            logger.error(`Cannot cache non-existent response for ` +\n                `'${getFriendlyURL(effectiveRequest.url)}'.`);\n        }\n        throw new WorkboxError('cache-put-with-no-response', {\n            url: getFriendlyURL(effectiveRequest.url),\n        });\n    }\n    const responseToCache = await _isResponseSafeToCache({\n        event,\n        plugins,\n        response,\n        request: effectiveRequest,\n    });\n    if (!responseToCache) {\n        if (process.env.NODE_ENV !== 'production') {\n            logger.debug(`Response '${getFriendlyURL(effectiveRequest.url)}' will ` +\n                `not be cached.`, responseToCache);\n        }\n        return;\n    }\n    const cache = await self.caches.open(cacheName);\n    const updatePlugins = pluginUtils.filter(plugins, \"cacheDidUpdate\" /* CACHE_DID_UPDATE */);\n    const oldResponse = updatePlugins.length > 0 ?\n        await matchWrapper({ cacheName, matchOptions, request: effectiveRequest }) :\n        null;\n    if (process.env.NODE_ENV !== 'production') {\n        logger.debug(`Updating the '${cacheName}' cache with a new Response for ` +\n            `${getFriendlyURL(effectiveRequest.url)}.`);\n    }\n    try {\n        await cache.put(effectiveRequest, responseToCache);\n    }\n    catch (error) {\n        // See https://developer.mozilla.org/en-US/docs/Web/API/DOMException#exception-QuotaExceededError\n        if (error.name === 'QuotaExceededError') {\n            await executeQuotaErrorCallbacks();\n        }\n        throw error;\n    }\n    for (const plugin of updatePlugins) {\n        await plugin[\"cacheDidUpdate\" /* CACHE_DID_UPDATE */].call(plugin, {\n            cacheName,\n            event,\n            oldResponse,\n            newResponse: responseToCache,\n            request: effectiveRequest,\n        });\n    }\n};\nexport const cacheWrapper = {\n    put: putWrapper,\n    match: matchWrapper,\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { logger } from '../_private/logger.js';\nimport { quotaErrorCallbacks } from '../models/quotaErrorCallbacks.js';\nimport '../_version.js';\n/**\n * Runs all of the callback functions, one at a time sequentially, in the order\n * in which they were registered.\n *\n * @memberof module:workbox-core\n * @private\n */\nasync function executeQuotaErrorCallbacks() {\n    if (process.env.NODE_ENV !== 'production') {\n        logger.log(`About to run ${quotaErrorCallbacks.size} ` +\n            `callbacks to clean up caches.`);\n    }\n    for (const callback of quotaErrorCallbacks) {\n        await callback();\n        if (process.env.NODE_ENV !== 'production') {\n            logger.log(callback, 'is complete.');\n        }\n    }\n    if (process.env.NODE_ENV !== 'production') {\n        logger.log('Finished running callbacks.');\n    }\n}\nexport { executeQuotaErrorCallbacks };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { WorkboxError } from './WorkboxError.js';\nimport { logger } from './logger.js';\nimport { assert } from './assert.js';\nimport { getFriendlyURL } from '../_private/getFriendlyURL.js';\nimport { pluginUtils } from '../utils/pluginUtils.js';\nimport '../_version.js';\n/**\n * Wrapper around the fetch API.\n *\n * Will call requestWillFetch on available plugins.\n *\n * @param {Object} options\n * @param {Request|string} options.request\n * @param {Object} [options.fetchOptions]\n * @param {ExtendableEvent} [options.event]\n * @param {Array} [options.plugins=[]]\n * @return {Promise}\n *\n * @private\n * @memberof module:workbox-core\n */\nconst wrappedFetch = async ({ request, fetchOptions, event, plugins = [], }) => {\n    if (typeof request === 'string') {\n        request = new Request(request);\n    }\n    // We *should* be able to call `await event.preloadResponse` even if it's\n    // undefined, but for some reason, doing so leads to errors in our Node unit\n    // tests. To work around that, explicitly check preloadResponse's value first.\n    if (event instanceof FetchEvent && event.preloadResponse) {\n        const possiblePreloadResponse = await event.preloadResponse;\n        if (possiblePreloadResponse) {\n            if (process.env.NODE_ENV !== 'production') {\n                logger.log(`Using a preloaded navigation response for ` +\n                    `'${getFriendlyURL(request.url)}'`);\n            }\n            return possiblePreloadResponse;\n        }\n    }\n    if (process.env.NODE_ENV !== 'production') {\n        assert.isInstance(request, Request, {\n            paramName: 'request',\n            expectedClass: Request,\n            moduleName: 'workbox-core',\n            className: 'fetchWrapper',\n            funcName: 'wrappedFetch',\n        });\n    }\n    const failedFetchPlugins = pluginUtils.filter(plugins, \"fetchDidFail\" /* FETCH_DID_FAIL */);\n    // If there is a fetchDidFail plugin, we need to save a clone of the\n    // original request before it's either modified by a requestWillFetch\n    // plugin or before the original request's body is consumed via fetch().\n    const originalRequest = failedFetchPlugins.length > 0 ?\n        request.clone() : null;\n    try {\n        for (const plugin of plugins) {\n            if (\"requestWillFetch\" /* REQUEST_WILL_FETCH */ in plugin) {\n                const pluginMethod = plugin[\"requestWillFetch\" /* REQUEST_WILL_FETCH */];\n                const requestClone = request.clone();\n                request = await pluginMethod.call(plugin, {\n                    request: requestClone,\n                    event,\n                });\n                if (process.env.NODE_ENV !== 'production') {\n                    if (request) {\n                        assert.isInstance(request, Request, {\n                            moduleName: 'Plugin',\n                            funcName: \"cachedResponseWillBeUsed\" /* CACHED_RESPONSE_WILL_BE_USED */,\n                            isReturnValueProblem: true,\n                        });\n                    }\n                }\n            }\n        }\n    }\n    catch (err) {\n        throw new WorkboxError('plugin-error-request-will-fetch', {\n            thrownError: err,\n        });\n    }\n    // The request can be altered by plugins with `requestWillFetch` making\n    // the original request (Most likely from a `fetch` event) to be different\n    // to the Request we make. Pass both to `fetchDidFail` to aid debugging.\n    const pluginFilteredRequest = request.clone();\n    try {\n        let fetchResponse;\n        // See https://github.com/GoogleChrome/workbox/issues/1796\n        if (request.mode === 'navigate') {\n            fetchResponse = await fetch(request);\n        }\n        else {\n            fetchResponse = await fetch(request, fetchOptions);\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            logger.debug(`Network request for ` +\n                `'${getFriendlyURL(request.url)}' returned a response with ` +\n                `status '${fetchResponse.status}'.`);\n        }\n        for (const plugin of plugins) {\n            if (\"fetchDidSucceed\" /* FETCH_DID_SUCCEED */ in plugin) {\n                fetchResponse = await plugin[\"fetchDidSucceed\" /* FETCH_DID_SUCCEED */]\n                    .call(plugin, {\n                    event,\n                    request: pluginFilteredRequest,\n                    response: fetchResponse,\n                });\n                if (process.env.NODE_ENV !== 'production') {\n                    if (fetchResponse) {\n                        assert.isInstance(fetchResponse, Response, {\n                            moduleName: 'Plugin',\n                            funcName: \"fetchDidSucceed\" /* FETCH_DID_SUCCEED */,\n                            isReturnValueProblem: true,\n                        });\n                    }\n                }\n            }\n        }\n        return fetchResponse;\n    }\n    catch (error) {\n        if (process.env.NODE_ENV !== 'production') {\n            logger.error(`Network request for ` +\n                `'${getFriendlyURL(request.url)}' threw an error.`, error);\n        }\n        for (const plugin of failedFetchPlugins) {\n            await plugin[\"fetchDidFail\" /* FETCH_DID_FAIL */].call(plugin, {\n                error,\n                event,\n                originalRequest: originalRequest.clone(),\n                request: pluginFilteredRequest.clone(),\n            });\n        }\n        throw error;\n    }\n};\nconst fetchWrapper = {\n    fetch: wrappedFetch,\n};\nexport { fetchWrapper };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { cacheNames } from 'workbox-core/_private/cacheNames.js';\nimport { cacheWrapper } from 'workbox-core/_private/cacheWrapper.js';\nimport { fetchWrapper } from 'workbox-core/_private/fetchWrapper.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { copyResponse } from 'workbox-core/copyResponse.js';\nimport { createCacheKey } from './utils/createCacheKey.js';\nimport { printCleanupDetails } from './utils/printCleanupDetails.js';\nimport { printInstallDetails } from './utils/printInstallDetails.js';\nimport './_version.js';\n/**\n * Performs efficient precaching of assets.\n *\n * @memberof module:workbox-precaching\n */\nclass PrecacheController {\n    /**\n     * Create a new PrecacheController.\n     *\n     * @param {string} [cacheName] An optional name for the cache, to override\n     * the default precache name.\n     */\n    constructor(cacheName) {\n        this._cacheName = cacheNames.getPrecacheName(cacheName);\n        this._urlsToCacheKeys = new Map();\n        this._urlsToCacheModes = new Map();\n        this._cacheKeysToIntegrities = new Map();\n    }\n    /**\n     * This method will add items to the precache list, removing duplicates\n     * and ensuring the information is valid.\n     *\n     * @param {\n     * Array\n     * } entries Array of entries to precache.\n     */\n    addToCacheList(entries) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isArray(entries, {\n                moduleName: 'workbox-precaching',\n                className: 'PrecacheController',\n                funcName: 'addToCacheList',\n                paramName: 'entries',\n            });\n        }\n        const urlsToWarnAbout = [];\n        for (const entry of entries) {\n            // See https://github.com/GoogleChrome/workbox/issues/2259\n            if (typeof entry === 'string') {\n                urlsToWarnAbout.push(entry);\n            }\n            else if (entry && entry.revision === undefined) {\n                urlsToWarnAbout.push(entry.url);\n            }\n            const { cacheKey, url } = createCacheKey(entry);\n            const cacheMode = (typeof entry !== 'string' && entry.revision) ?\n                'reload' : 'default';\n            if (this._urlsToCacheKeys.has(url) &&\n                this._urlsToCacheKeys.get(url) !== cacheKey) {\n                throw new WorkboxError('add-to-cache-list-conflicting-entries', {\n                    firstEntry: this._urlsToCacheKeys.get(url),\n                    secondEntry: cacheKey,\n                });\n            }\n            if (typeof entry !== 'string' && entry.integrity) {\n                if (this._cacheKeysToIntegrities.has(cacheKey) &&\n                    this._cacheKeysToIntegrities.get(cacheKey) !== entry.integrity) {\n                    throw new WorkboxError('add-to-cache-list-conflicting-integrities', {\n                        url,\n                    });\n                }\n                this._cacheKeysToIntegrities.set(cacheKey, entry.integrity);\n            }\n            this._urlsToCacheKeys.set(url, cacheKey);\n            this._urlsToCacheModes.set(url, cacheMode);\n            if (urlsToWarnAbout.length > 0) {\n                const warningMessage = `Workbox is precaching URLs without revision ` +\n                    `info: ${urlsToWarnAbout.join(', ')}\\nThis is generally NOT safe. ` +\n                    `Learn more at https://bit.ly/wb-precache`;\n                if (process.env.NODE_ENV === 'production') {\n                    // Use console directly to display this warning without bloating\n                    // bundle sizes by pulling in all of the logger codebase in prod.\n                    console.warn(warningMessage);\n                }\n                else {\n                    logger.warn(warningMessage);\n                }\n            }\n        }\n    }\n    /**\n     * Precaches new and updated assets. Call this method from the service worker\n     * install event.\n     *\n     * @param {Object} options\n     * @param {Event} [options.event] The install event (if needed).\n     * @param {Array} [options.plugins] Plugins to be used for fetching\n     * and caching during install.\n     * @return {Promise}\n     */\n    async install({ event, plugins } = {}) {\n        if (process.env.NODE_ENV !== 'production') {\n            if (plugins) {\n                assert.isArray(plugins, {\n                    moduleName: 'workbox-precaching',\n                    className: 'PrecacheController',\n                    funcName: 'install',\n                    paramName: 'plugins',\n                });\n            }\n        }\n        const toBePrecached = [];\n        const alreadyPrecached = [];\n        const cache = await self.caches.open(this._cacheName);\n        const alreadyCachedRequests = await cache.keys();\n        const existingCacheKeys = new Set(alreadyCachedRequests.map((request) => request.url));\n        for (const [url, cacheKey] of this._urlsToCacheKeys) {\n            if (existingCacheKeys.has(cacheKey)) {\n                alreadyPrecached.push(url);\n            }\n            else {\n                toBePrecached.push({ cacheKey, url });\n            }\n        }\n        const precacheRequests = toBePrecached.map(({ cacheKey, url }) => {\n            const integrity = this._cacheKeysToIntegrities.get(cacheKey);\n            const cacheMode = this._urlsToCacheModes.get(url);\n            return this._addURLToCache({\n                cacheKey,\n                cacheMode,\n                event,\n                integrity,\n                plugins,\n                url,\n            });\n        });\n        await Promise.all(precacheRequests);\n        const updatedURLs = toBePrecached.map((item) => item.url);\n        if (process.env.NODE_ENV !== 'production') {\n            printInstallDetails(updatedURLs, alreadyPrecached);\n        }\n        return {\n            updatedURLs,\n            notUpdatedURLs: alreadyPrecached,\n        };\n    }\n    /**\n     * Deletes assets that are no longer present in the current precache manifest.\n     * Call this method from the service worker activate event.\n     *\n     * @return {Promise}\n     */\n    async activate() {\n        const cache = await self.caches.open(this._cacheName);\n        const currentlyCachedRequests = await cache.keys();\n        const expectedCacheKeys = new Set(this._urlsToCacheKeys.values());\n        const deletedURLs = [];\n        for (const request of currentlyCachedRequests) {\n            if (!expectedCacheKeys.has(request.url)) {\n                await cache.delete(request);\n                deletedURLs.push(request.url);\n            }\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            printCleanupDetails(deletedURLs);\n        }\n        return { deletedURLs };\n    }\n    /**\n     * Requests the entry and saves it to the cache if the response is valid.\n     * By default, any response with a status code of less than 400 (including\n     * opaque responses) is considered valid.\n     *\n     * If you need to use custom criteria to determine what's valid and what\n     * isn't, then pass in an item in `options.plugins` that implements the\n     * `cacheWillUpdate()` lifecycle event.\n     *\n     * @private\n     * @param {Object} options\n     * @param {string} options.cacheKey The string to use a cache key.\n     * @param {string} options.url The URL to fetch and cache.\n     * @param {string} [options.cacheMode] The cache mode for the network request.\n     * @param {Event} [options.event] The install event (if passed).\n     * @param {Array} [options.plugins] An array of plugins to apply to\n     * fetch and caching.\n     * @param {string} [options.integrity] The value to use for the `integrity`\n     * field when making the request.\n     */\n    async _addURLToCache({ cacheKey, url, cacheMode, event, plugins, integrity }) {\n        const request = new Request(url, {\n            integrity,\n            cache: cacheMode,\n            credentials: 'same-origin',\n        });\n        let response = await fetchWrapper.fetch({\n            event,\n            plugins,\n            request,\n        });\n        // Allow developers to override the default logic about what is and isn't\n        // valid by passing in a plugin implementing cacheWillUpdate(), e.g.\n        // a `CacheableResponsePlugin` instance.\n        let cacheWillUpdatePlugin;\n        for (const plugin of (plugins || [])) {\n            if ('cacheWillUpdate' in plugin) {\n                cacheWillUpdatePlugin = plugin;\n            }\n        }\n        const isValidResponse = cacheWillUpdatePlugin ?\n            // Use a callback if provided. It returns a truthy value if valid.\n            // NOTE: invoke the method on the plugin instance so the `this` context\n            // is correct.\n            await cacheWillUpdatePlugin.cacheWillUpdate({ event, request, response }) :\n            // Otherwise, default to considering any response status under 400 valid.\n            // This includes, by default, considering opaque responses valid.\n            response.status < 400;\n        // Consider this a failure, leading to the `install` handler failing, if\n        // we get back an invalid response.\n        if (!isValidResponse) {\n            throw new WorkboxError('bad-precaching-response', {\n                url,\n                status: response.status,\n            });\n        }\n        // Redirected responses cannot be used to satisfy a navigation request, so\n        // any redirected response must be \"copied\" rather than cloned, so the new\n        // response doesn't contain the `redirected` flag. See:\n        // https://bugs.chromium.org/p/chromium/issues/detail?id=669363&desc=2#c1\n        if (response.redirected) {\n            response = await copyResponse(response);\n        }\n        await cacheWrapper.put({\n            event,\n            plugins,\n            response,\n            // `request` already uses `url`. We may be able to reuse it.\n            request: cacheKey === url ? request : new Request(cacheKey),\n            cacheName: this._cacheName,\n            matchOptions: {\n                ignoreSearch: true,\n            },\n        });\n    }\n    /**\n     * Returns a mapping of a precached URL to the corresponding cache key, taking\n     * into account the revision information for the URL.\n     *\n     * @return {Map} A URL to cache key mapping.\n     */\n    getURLsToCacheKeys() {\n        return this._urlsToCacheKeys;\n    }\n    /**\n     * Returns a list of all the URLs that have been precached by the current\n     * service worker.\n     *\n     * @return {Array} The precached URLs.\n     */\n    getCachedURLs() {\n        return [...this._urlsToCacheKeys.keys()];\n    }\n    /**\n     * Returns the cache key used for storing a given URL. If that URL is\n     * unversioned, like `/index.html', then the cache key will be the original\n     * URL with a search parameter appended to it.\n     *\n     * @param {string} url A URL whose cache key you want to look up.\n     * @return {string} The versioned URL that corresponds to a cache key\n     * for the original URL, or undefined if that URL isn't precached.\n     */\n    getCacheKeyForURL(url) {\n        const urlObject = new URL(url, location.href);\n        return this._urlsToCacheKeys.get(urlObject.href);\n    }\n    /**\n     * This acts as a drop-in replacement for [`cache.match()`](https://developer.mozilla.org/en-US/docs/Web/API/Cache/match)\n     * with the following differences:\n     *\n     * - It knows what the name of the precache is, and only checks in that cache.\n     * - It allows you to pass in an \"original\" URL without versioning parameters,\n     * and it will automatically look up the correct cache key for the currently\n     * active revision of that URL.\n     *\n     * E.g., `matchPrecache('index.html')` will find the correct precached\n     * response for the currently active service worker, even if the actual cache\n     * key is `'/index.html?__WB_REVISION__=1234abcd'`.\n     *\n     * @param {string|Request} request The key (without revisioning parameters)\n     * to look up in the precache.\n     * @return {Promise}\n     */\n    async matchPrecache(request) {\n        const url = request instanceof Request ? request.url : request;\n        const cacheKey = this.getCacheKeyForURL(url);\n        if (cacheKey) {\n            const cache = await self.caches.open(this._cacheName);\n            return cache.match(cacheKey);\n        }\n        return undefined;\n    }\n    /**\n     * Returns a function that can be used within a\n     * {@link module:workbox-routing.Route} that will find a response for the\n     * incoming request against the precache.\n     *\n     * If for an unexpected reason there is a cache miss for the request,\n     * this will fall back to retrieving the `Response` via `fetch()` when\n     * `fallbackToNetwork` is `true`.\n     *\n     * @param {boolean} [fallbackToNetwork=true] Whether to attempt to get the\n     * response from the network if there's a precache miss.\n     * @return {module:workbox-routing~handlerCallback}\n     */\n    createHandler(fallbackToNetwork = true) {\n        return async ({ request }) => {\n            try {\n                const response = await this.matchPrecache(request);\n                if (response) {\n                    return response;\n                }\n                // This shouldn't normally happen, but there are edge cases:\n                // https://github.com/GoogleChrome/workbox/issues/1441\n                throw new WorkboxError('missing-precache-entry', {\n                    cacheName: this._cacheName,\n                    url: request instanceof Request ? request.url : request,\n                });\n            }\n            catch (error) {\n                if (fallbackToNetwork) {\n                    if (process.env.NODE_ENV !== 'production') {\n                        logger.debug(`Unable to respond with precached response. ` +\n                            `Falling back to network.`, error);\n                    }\n                    return fetch(request);\n                }\n                throw error;\n            }\n        };\n    }\n    /**\n     * Returns a function that looks up `url` in the precache (taking into\n     * account revision information), and returns the corresponding `Response`.\n     *\n     * If for an unexpected reason there is a cache miss when looking up `url`,\n     * this will fall back to retrieving the `Response` via `fetch()` when\n     * `fallbackToNetwork` is `true`.\n     *\n     * @param {string} url The precached URL which will be used to lookup the\n     * `Response`.\n     * @param {boolean} [fallbackToNetwork=true] Whether to attempt to get the\n     * response from the network if there's a precache miss.\n     * @return {module:workbox-routing~handlerCallback}\n     */\n    createHandlerBoundToURL(url, fallbackToNetwork = true) {\n        const cacheKey = this.getCacheKeyForURL(url);\n        if (!cacheKey) {\n            throw new WorkboxError('non-precached-url', { url });\n        }\n        const handler = this.createHandler(fallbackToNetwork);\n        const request = new Request(url);\n        return () => handler({ request });\n    }\n}\nexport { PrecacheController };\n","export const isNav = event => event.request.mode === 'navigate';\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nexport const cacheOkAndOpaquePlugin = {\n    /**\n     * Returns a valid response (to allow caching) if the status is 200 (OK) or\n     * 0 (opaque).\n     *\n     * @param {Object} options\n     * @param {Response} options.response\n     * @return {Response|null}\n     *\n     * @private\n     */\n    cacheWillUpdate: async ({ response }) => {\n        if (response.status === 200 || response.status === 0) {\n            return response;\n        }\n        return null;\n    },\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { cacheNames } from 'workbox-core/_private/cacheNames.js';\nimport { cacheWrapper } from 'workbox-core/_private/cacheWrapper.js';\nimport { fetchWrapper } from 'workbox-core/_private/fetchWrapper.js';\nimport { getFriendlyURL } from 'workbox-core/_private/getFriendlyURL.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { messages } from './utils/messages.js';\nimport { cacheOkAndOpaquePlugin } from './plugins/cacheOkAndOpaquePlugin.js';\nimport './_version.js';\n/**\n * An implementation of a\n * [network first]{@link https://developers.google.com/web/fundamentals/instant-and-offline/offline-cookbook/#network-falling-back-to-cache}\n * request strategy.\n *\n * By default, this strategy will cache responses with a 200 status code as\n * well as [opaque responses]{@link https://developers.google.com/web/tools/workbox/guides/handle-third-party-requests}.\n * Opaque responses are are cross-origin requests where the response doesn't\n * support [CORS]{@link https://enable-cors.org/}.\n *\n * If the network request fails, and there is no cache match, this will throw\n * a `WorkboxError` exception.\n *\n * @memberof module:workbox-strategies\n */\nclass NetworkFirst {\n    /**\n     * @param {Object} options\n     * @param {string} options.cacheName Cache name to store and retrieve\n     * requests. Defaults to cache names provided by\n     * [workbox-core]{@link module:workbox-core.cacheNames}.\n     * @param {Array} options.plugins [Plugins]{@link https://developers.google.com/web/tools/workbox/guides/using-plugins}\n     * to use in conjunction with this caching strategy.\n     * @param {Object} options.fetchOptions Values passed along to the\n     * [`init`](https://developer.mozilla.org/en-US/docs/Web/API/WindowOrWorkerGlobalScope/fetch#Parameters)\n     * of all fetch() requests made by this strategy.\n     * @param {Object} options.matchOptions [`CacheQueryOptions`](https://w3c.github.io/ServiceWorker/#dictdef-cachequeryoptions)\n     * @param {number} options.networkTimeoutSeconds If set, any network requests\n     * that fail to respond within the timeout will fallback to the cache.\n     *\n     * This option can be used to combat\n     * \"[lie-fi]{@link https://developers.google.com/web/fundamentals/performance/poor-connectivity/#lie-fi}\"\n     * scenarios.\n     */\n    constructor(options = {}) {\n        this._cacheName = cacheNames.getRuntimeName(options.cacheName);\n        if (options.plugins) {\n            const isUsingCacheWillUpdate = options.plugins.some((plugin) => !!plugin.cacheWillUpdate);\n            this._plugins = isUsingCacheWillUpdate ?\n                options.plugins : [cacheOkAndOpaquePlugin, ...options.plugins];\n        }\n        else {\n            // No plugins passed in, use the default plugin.\n            this._plugins = [cacheOkAndOpaquePlugin];\n        }\n        this._networkTimeoutSeconds = options.networkTimeoutSeconds || 0;\n        if (process.env.NODE_ENV !== 'production') {\n            if (this._networkTimeoutSeconds) {\n                assert.isType(this._networkTimeoutSeconds, 'number', {\n                    moduleName: 'workbox-strategies',\n                    className: 'NetworkFirst',\n                    funcName: 'constructor',\n                    paramName: 'networkTimeoutSeconds',\n                });\n            }\n        }\n        this._fetchOptions = options.fetchOptions;\n        this._matchOptions = options.matchOptions;\n    }\n    /**\n     * This method will perform a request strategy and follows an API that\n     * will work with the\n     * [Workbox Router]{@link module:workbox-routing.Router}.\n     *\n     * @param {Object} options\n     * @param {Request|string} options.request A request to run this strategy for.\n     * @param {Event} [options.event] The event that triggered the request.\n     * @return {Promise}\n     */\n    async handle({ event, request }) {\n        const logs = [];\n        if (typeof request === 'string') {\n            request = new Request(request);\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(request, Request, {\n                moduleName: 'workbox-strategies',\n                className: 'NetworkFirst',\n                funcName: 'handle',\n                paramName: 'makeRequest',\n            });\n        }\n        const promises = [];\n        let timeoutId;\n        if (this._networkTimeoutSeconds) {\n            const { id, promise } = this._getTimeoutPromise({ request, event, logs });\n            timeoutId = id;\n            promises.push(promise);\n        }\n        const networkPromise = this._getNetworkPromise({ timeoutId, request, event, logs });\n        promises.push(networkPromise);\n        // Promise.race() will resolve as soon as the first promise resolves.\n        let response = await Promise.race(promises);\n        // If Promise.race() resolved with null, it might be due to a network\n        // timeout + a cache miss. If that were to happen, we'd rather wait until\n        // the networkPromise resolves instead of returning null.\n        // Note that it's fine to await an already-resolved promise, so we don't\n        // have to check to see if it's still \"in flight\".\n        if (!response) {\n            response = await networkPromise;\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            logger.groupCollapsed(messages.strategyStart('NetworkFirst', request));\n            for (const log of logs) {\n                logger.log(log);\n            }\n            messages.printFinalResponse(response);\n            logger.groupEnd();\n        }\n        if (!response) {\n            throw new WorkboxError('no-response', { url: request.url });\n        }\n        return response;\n    }\n    /**\n     * @param {Object} options\n     * @param {Request} options.request\n     * @param {Array} options.logs A reference to the logs array\n     * @param {Event} [options.event]\n     * @return {Promise}\n     *\n     * @private\n     */\n    _getTimeoutPromise({ request, logs, event }) {\n        let timeoutId;\n        const timeoutPromise = new Promise((resolve) => {\n            const onNetworkTimeout = async () => {\n                if (process.env.NODE_ENV !== 'production') {\n                    logs.push(`Timing out the network response at ` +\n                        `${this._networkTimeoutSeconds} seconds.`);\n                }\n                resolve(await this._respondFromCache({ request, event }));\n            };\n            timeoutId = setTimeout(onNetworkTimeout, this._networkTimeoutSeconds * 1000);\n        });\n        return {\n            promise: timeoutPromise,\n            id: timeoutId,\n        };\n    }\n    /**\n     * @param {Object} options\n     * @param {number|undefined} options.timeoutId\n     * @param {Request} options.request\n     * @param {Array} options.logs A reference to the logs Array.\n     * @param {Event} [options.event]\n     * @return {Promise}\n     *\n     * @private\n     */\n    async _getNetworkPromise({ timeoutId, request, logs, event }) {\n        let error;\n        let response;\n        try {\n            response = await fetchWrapper.fetch({\n                request,\n                event,\n                fetchOptions: this._fetchOptions,\n                plugins: this._plugins,\n            });\n        }\n        catch (err) {\n            error = err;\n        }\n        if (timeoutId) {\n            clearTimeout(timeoutId);\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            if (response) {\n                logs.push(`Got response from network.`);\n            }\n            else {\n                logs.push(`Unable to get a response from the network. Will respond ` +\n                    `with a cached response.`);\n            }\n        }\n        if (error || !response) {\n            response = await this._respondFromCache({ request, event });\n            if (process.env.NODE_ENV !== 'production') {\n                if (response) {\n                    logs.push(`Found a cached response in the '${this._cacheName}'` +\n                        ` cache.`);\n                }\n                else {\n                    logs.push(`No response found in the '${this._cacheName}' cache.`);\n                }\n            }\n        }\n        else {\n            // Keep the service worker alive while we put the request in the cache\n            const responseClone = response.clone();\n            const cachePut = cacheWrapper.put({\n                cacheName: this._cacheName,\n                request,\n                response: responseClone,\n                event,\n                plugins: this._plugins,\n            });\n            if (event) {\n                try {\n                    // The event has been responded to so we can keep the SW alive to\n                    // respond to the request\n                    event.waitUntil(cachePut);\n                }\n                catch (err) {\n                    if (process.env.NODE_ENV !== 'production') {\n                        logger.warn(`Unable to ensure service worker stays alive when ` +\n                            `updating cache for '${getFriendlyURL(request.url)}'.`);\n                    }\n                }\n            }\n        }\n        return response;\n    }\n    /**\n     * Used if the network timeouts or fails to make the request.\n     *\n     * @param {Object} options\n     * @param {Request} request The request to match in the cache\n     * @param {Event} [options.event]\n     * @return {Promise}\n     *\n     * @private\n     */\n    _respondFromCache({ event, request }) {\n        return cacheWrapper.match({\n            cacheName: this._cacheName,\n            request,\n            event,\n            matchOptions: this._matchOptions,\n            plugins: this._plugins,\n        });\n    }\n}\nexport { NetworkFirst };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\n/**\n * A class that wraps common IndexedDB functionality in a promise-based API.\n * It exposes all the underlying power and functionality of IndexedDB, but\n * wraps the most commonly used features in a way that's much simpler to use.\n *\n * @private\n */\nexport class DBWrapper {\n    /**\n     * @param {string} name\n     * @param {number} version\n     * @param {Object=} [callback]\n     * @param {!Function} [callbacks.onupgradeneeded]\n     * @param {!Function} [callbacks.onversionchange] Defaults to\n     *     DBWrapper.prototype._onversionchange when not specified.\n     * @private\n     */\n    constructor(name, version, { onupgradeneeded, onversionchange, } = {}) {\n        this._db = null;\n        this._name = name;\n        this._version = version;\n        this._onupgradeneeded = onupgradeneeded;\n        this._onversionchange = onversionchange || (() => this.close());\n    }\n    /**\n     * Returns the IDBDatabase instance (not normally needed).\n     * @return {IDBDatabase|undefined}\n     *\n     * @private\n     */\n    get db() {\n        return this._db;\n    }\n    /**\n     * Opens a connected to an IDBDatabase, invokes any onupgradedneeded\n     * callback, and added an onversionchange callback to the database.\n     *\n     * @return {IDBDatabase}\n     * @private\n     */\n    async open() {\n        if (this._db)\n            return;\n        this._db = await new Promise((resolve, reject) => {\n            // This flag is flipped to true if the timeout callback runs prior\n            // to the request failing or succeeding. Note: we use a timeout instead\n            // of an onblocked handler since there are cases where onblocked will\n            // never never run. A timeout better handles all possible scenarios:\n            // https://github.com/w3c/IndexedDB/issues/223\n            let openRequestTimedOut = false;\n            setTimeout(() => {\n                openRequestTimedOut = true;\n                reject(new Error('The open request was blocked and timed out'));\n            }, this.OPEN_TIMEOUT);\n            const openRequest = indexedDB.open(this._name, this._version);\n            openRequest.onerror = () => reject(openRequest.error);\n            openRequest.onupgradeneeded = (evt) => {\n                if (openRequestTimedOut) {\n                    openRequest.transaction.abort();\n                    openRequest.result.close();\n                }\n                else if (typeof this._onupgradeneeded === 'function') {\n                    this._onupgradeneeded(evt);\n                }\n            };\n            openRequest.onsuccess = () => {\n                const db = openRequest.result;\n                if (openRequestTimedOut) {\n                    db.close();\n                }\n                else {\n                    db.onversionchange = this._onversionchange.bind(this);\n                    resolve(db);\n                }\n            };\n        });\n        return this;\n    }\n    /**\n     * Polyfills the native `getKey()` method. Note, this is overridden at\n     * runtime if the browser supports the native method.\n     *\n     * @param {string} storeName\n     * @param {*} query\n     * @return {Array}\n     * @private\n     */\n    async getKey(storeName, query) {\n        return (await this.getAllKeys(storeName, query, 1))[0];\n    }\n    /**\n     * Polyfills the native `getAll()` method. Note, this is overridden at\n     * runtime if the browser supports the native method.\n     *\n     * @param {string} storeName\n     * @param {*} query\n     * @param {number} count\n     * @return {Array}\n     * @private\n     */\n    async getAll(storeName, query, count) {\n        return await this.getAllMatching(storeName, { query, count });\n    }\n    /**\n     * Polyfills the native `getAllKeys()` method. Note, this is overridden at\n     * runtime if the browser supports the native method.\n     *\n     * @param {string} storeName\n     * @param {*} query\n     * @param {number} count\n     * @return {Array}\n     * @private\n     */\n    async getAllKeys(storeName, query, count) {\n        const entries = await this.getAllMatching(storeName, { query, count, includeKeys: true });\n        return entries.map((entry) => entry.key);\n    }\n    /**\n     * Supports flexible lookup in an object store by specifying an index,\n     * query, direction, and count. This method returns an array of objects\n     * with the signature .\n     *\n     * @param {string} storeName\n     * @param {Object} [opts]\n     * @param {string} [opts.index] The index to use (if specified).\n     * @param {*} [opts.query]\n     * @param {IDBCursorDirection} [opts.direction]\n     * @param {number} [opts.count] The max number of results to return.\n     * @param {boolean} [opts.includeKeys] When true, the structure of the\n     *     returned objects is changed from an array of values to an array of\n     *     objects in the form {key, primaryKey, value}.\n     * @return {Array}\n     * @private\n     */\n    async getAllMatching(storeName, { index, query = null, // IE/Edge errors if query === `undefined`.\n    direction = 'next', count, includeKeys = false, } = {}) {\n        return await this.transaction([storeName], 'readonly', (txn, done) => {\n            const store = txn.objectStore(storeName);\n            const target = index ? store.index(index) : store;\n            const results = [];\n            const request = target.openCursor(query, direction);\n            request.onsuccess = () => {\n                const cursor = request.result;\n                if (cursor) {\n                    results.push(includeKeys ? cursor : cursor.value);\n                    if (count && results.length >= count) {\n                        done(results);\n                    }\n                    else {\n                        cursor.continue();\n                    }\n                }\n                else {\n                    done(results);\n                }\n            };\n        });\n    }\n    /**\n     * Accepts a list of stores, a transaction type, and a callback and\n     * performs a transaction. A promise is returned that resolves to whatever\n     * value the callback chooses. The callback holds all the transaction logic\n     * and is invoked with two arguments:\n     *   1. The IDBTransaction object\n     *   2. A `done` function, that's used to resolve the promise when\n     *      when the transaction is done, if passed a value, the promise is\n     *      resolved to that value.\n     *\n     * @param {Array} storeNames An array of object store names\n     *     involved in the transaction.\n     * @param {string} type Can be `readonly` or `readwrite`.\n     * @param {!Function} callback\n     * @return {*} The result of the transaction ran by the callback.\n     * @private\n     */\n    async transaction(storeNames, type, callback) {\n        await this.open();\n        return await new Promise((resolve, reject) => {\n            const txn = this._db.transaction(storeNames, type);\n            txn.onabort = () => reject(txn.error);\n            txn.oncomplete = () => resolve();\n            callback(txn, (value) => resolve(value));\n        });\n    }\n    /**\n     * Delegates async to a native IDBObjectStore method.\n     *\n     * @param {string} method The method name.\n     * @param {string} storeName The object store name.\n     * @param {string} type Can be `readonly` or `readwrite`.\n     * @param {...*} args The list of args to pass to the native method.\n     * @return {*} The result of the transaction.\n     * @private\n     */\n    async _call(method, storeName, type, ...args) {\n        const callback = (txn, done) => {\n            const objStore = txn.objectStore(storeName);\n            // TODO(philipwalton): Fix this underlying TS2684 error.\n            // @ts-ignore\n            const request = objStore[method].apply(objStore, args);\n            request.onsuccess = () => done(request.result);\n        };\n        return await this.transaction([storeName], type, callback);\n    }\n    /**\n     * Closes the connection opened by `DBWrapper.open()`. Generally this method\n     * doesn't need to be called since:\n     *   1. It's usually better to keep a connection open since opening\n     *      a new connection is somewhat slow.\n     *   2. Connections are automatically closed when the reference is\n     *      garbage collected.\n     * The primary use case for needing to close a connection is when another\n     * reference (typically in another tab) needs to upgrade it and would be\n     * blocked by the current, open connection.\n     *\n     * @private\n     */\n    close() {\n        if (this._db) {\n            this._db.close();\n            this._db = null;\n        }\n    }\n}\n// Exposed on the prototype to let users modify the default timeout on a\n// per-instance or global basis.\nDBWrapper.prototype.OPEN_TIMEOUT = 2000;\n// Wrap native IDBObjectStore methods according to their mode.\nconst methodsToWrap = {\n    readonly: ['get', 'count', 'getKey', 'getAll', 'getAllKeys'],\n    readwrite: ['add', 'put', 'clear', 'delete'],\n};\nfor (const [mode, methods] of Object.entries(methodsToWrap)) {\n    for (const method of methods) {\n        if (method in IDBObjectStore.prototype) {\n            // Don't use arrow functions here since we're outside of the class.\n            DBWrapper.prototype[method] =\n                async function (storeName, ...args) {\n                    return await this._call(method, storeName, mode, ...args);\n                };\n        }\n    }\n}\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { getOrCreateDefaultRouter } from './utils/getOrCreateDefaultRouter.js';\nimport './_version.js';\n/**\n * If a Route throws an error while handling a request, this `handler`\n * will be called and given a chance to provide a response.\n *\n * @param {module:workbox-routing~handlerCallback} handler A callback\n * function that returns a Promise resulting in a Response.\n *\n * @memberof module:workbox-routing\n */\nfunction setCatchHandler(handler) {\n    const defaultRouter = getOrCreateDefaultRouter();\n    defaultRouter.setCatchHandler(handler);\n}\nexport { setCatchHandler };\n","import { registerRoute, setCatchHandler } from 'workbox-routing';\nimport { precacheAndRoute, getCacheKeyForURL } from 'workbox-precaching';\nimport { isNav } from './utils';\nimport { NETWORK_HANDLER, PRECACHING_OPTIONS } from './contants';\n\nexport function getFiles() {\n\treturn self.__WB_MANIFEST;\n}\n\nexport function setupPrecaching(precacheFiles, precachingOptions) {\n\tprecacheAndRoute(precacheFiles, precachingOptions || PRECACHING_OPTIONS);\n}\n\nexport function setupRouting() {\n\t/**\n\t * Adding this before `precacheAndRoute` lets us handle all\n\t * the navigation requests even if they are in precache.\n\t */\n\tregisterRoute(({ event }) => isNav(event), NETWORK_HANDLER);\n\n\tsetCatchHandler(({ event }) => {\n\t\tif (isNav(event)) {\n\t\t\treturn caches.match(getCacheKeyForURL('/index.html'));\n\t\t}\n\t\treturn Response.error();\n\t});\n}\n\nexport { PRECACHING_OPTIONS };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { cacheNames as _cacheNames } from './_private/cacheNames.js';\nimport './_version.js';\n/**\n * Get the current cache names and prefix/suffix used by Workbox.\n *\n * `cacheNames.precache` is used for precached assets,\n * `cacheNames.googleAnalytics` is used by `workbox-google-analytics` to\n * store `analytics.js`, and `cacheNames.runtime` is used for everything else.\n *\n * `cacheNames.prefix` can be used to retrieve just the current prefix value.\n * `cacheNames.suffix` can be used to retrieve just the current suffix value.\n *\n * @return {Object} An object with `precache`, `runtime`, `prefix`, and\n *     `googleAnalytics` properties.\n *\n * @memberof module:workbox-core\n */\nconst cacheNames = {\n    get googleAnalytics() {\n        return _cacheNames.getGoogleAnalyticsName();\n    },\n    get precache() {\n        return _cacheNames.getPrecacheName();\n    },\n    get prefix() {\n        return _cacheNames.getPrefix();\n    },\n    get runtime() {\n        return _cacheNames.getRuntimeName();\n    },\n    get suffix() {\n        return _cacheNames.getSuffix();\n    },\n};\nexport { cacheNames };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { getFriendlyURL } from 'workbox-core/_private/getFriendlyURL.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport './_version.js';\n/**\n * This class allows you to set up rules determining what\n * status codes and/or headers need to be present in order for a\n * [`Response`](https://developer.mozilla.org/en-US/docs/Web/API/Response)\n * to be considered cacheable.\n *\n * @memberof module:workbox-cacheable-response\n */\nclass CacheableResponse {\n    /**\n     * To construct a new CacheableResponse instance you must provide at least\n     * one of the `config` properties.\n     *\n     * If both `statuses` and `headers` are specified, then both conditions must\n     * be met for the `Response` to be considered cacheable.\n     *\n     * @param {Object} config\n     * @param {Array} [config.statuses] One or more status codes that a\n     * `Response` can have and be considered cacheable.\n     * @param {Object} [config.headers] A mapping of header names\n     * and expected values that a `Response` can have and be considered cacheable.\n     * If multiple headers are provided, only one needs to be present.\n     */\n    constructor(config = {}) {\n        if (process.env.NODE_ENV !== 'production') {\n            if (!(config.statuses || config.headers)) {\n                throw new WorkboxError('statuses-or-headers-required', {\n                    moduleName: 'workbox-cacheable-response',\n                    className: 'CacheableResponse',\n                    funcName: 'constructor',\n                });\n            }\n            if (config.statuses) {\n                assert.isArray(config.statuses, {\n                    moduleName: 'workbox-cacheable-response',\n                    className: 'CacheableResponse',\n                    funcName: 'constructor',\n                    paramName: 'config.statuses',\n                });\n            }\n            if (config.headers) {\n                assert.isType(config.headers, 'object', {\n                    moduleName: 'workbox-cacheable-response',\n                    className: 'CacheableResponse',\n                    funcName: 'constructor',\n                    paramName: 'config.headers',\n                });\n            }\n        }\n        this._statuses = config.statuses;\n        this._headers = config.headers;\n    }\n    /**\n     * Checks a response to see whether it's cacheable or not, based on this\n     * object's configuration.\n     *\n     * @param {Response} response The response whose cacheability is being\n     * checked.\n     * @return {boolean} `true` if the `Response` is cacheable, and `false`\n     * otherwise.\n     */\n    isResponseCacheable(response) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(response, Response, {\n                moduleName: 'workbox-cacheable-response',\n                className: 'CacheableResponse',\n                funcName: 'isResponseCacheable',\n                paramName: 'response',\n            });\n        }\n        let cacheable = true;\n        if (this._statuses) {\n            cacheable = this._statuses.includes(response.status);\n        }\n        if (this._headers && cacheable) {\n            cacheable = Object.keys(this._headers).some((headerName) => {\n                return response.headers.get(headerName) === this._headers[headerName];\n            });\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            if (!cacheable) {\n                logger.groupCollapsed(`The request for ` +\n                    `'${getFriendlyURL(response.url)}' returned a response that does ` +\n                    `not meet the criteria for being cached.`);\n                logger.groupCollapsed(`View cacheability criteria here.`);\n                logger.log(`Cacheable statuses: ` +\n                    JSON.stringify(this._statuses));\n                logger.log(`Cacheable headers: ` +\n                    JSON.stringify(this._headers, null, 2));\n                logger.groupEnd();\n                const logFriendlyHeaders = {};\n                response.headers.forEach((value, key) => {\n                    logFriendlyHeaders[key] = value;\n                });\n                logger.groupCollapsed(`View response status and headers here.`);\n                logger.log(`Response status: ` + response.status);\n                logger.log(`Response headers: ` +\n                    JSON.stringify(logFriendlyHeaders, null, 2));\n                logger.groupEnd();\n                logger.groupCollapsed(`View full response details here.`);\n                logger.log(response.headers);\n                logger.log(response);\n                logger.groupEnd();\n                logger.groupEnd();\n            }\n        }\n        return cacheable;\n    }\n}\nexport { CacheableResponse };\n","import { NetworkFirst } from 'workbox-strategies';\nimport { cacheNames } from 'workbox-core';\nimport { CacheableResponsePlugin } from 'workbox-cacheable-response';\n\nexport const PRECACHING_OPTIONS = {};\n\nexport const NETWORK_HANDLER = new NetworkFirst({\n\t// this cache is plunged with every new service worker deploy so we dont need to care about purging the cache.\n\tcacheName: cacheNames.precache,\n\tnetworkTimeoutSeconds: 5, // if u dont start getting headers within 5 sec fallback to cache.\n\tplugins: [\n\t\tnew CacheableResponsePlugin({\n\t\t\tstatuses: [200], // only cache valid responses, not opaque responses e.g. wifi portal.\n\t\t}),\n\t],\n});\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { Route } from './Route.js';\nimport { RegExpRoute } from './RegExpRoute.js';\nimport { getOrCreateDefaultRouter } from './utils/getOrCreateDefaultRouter.js';\nimport './_version.js';\n/**\n * Easily register a RegExp, string, or function with a caching\n * strategy to a singleton Router instance.\n *\n * This method will generate a Route for you if needed and\n * call [registerRoute()]{@link module:workbox-routing.Router#registerRoute}.\n *\n * @param {RegExp|string|module:workbox-routing.Route~matchCallback|module:workbox-routing.Route} capture\n * If the capture param is a `Route`, all other arguments will be ignored.\n * @param {module:workbox-routing~handlerCallback} [handler] A callback\n * function that returns a Promise resulting in a Response. This parameter\n * is required if `capture` is not a `Route` object.\n * @param {string} [method='GET'] The HTTP method to match the Route\n * against.\n * @return {module:workbox-routing.Route} The generated `Route`(Useful for\n * unregistering).\n *\n * @memberof module:workbox-routing\n */\nfunction registerRoute(capture, handler, method) {\n    let route;\n    if (typeof capture === 'string') {\n        const captureUrl = new URL(capture, location.href);\n        if (process.env.NODE_ENV !== 'production') {\n            if (!(capture.startsWith('/') || capture.startsWith('http'))) {\n                throw new WorkboxError('invalid-string', {\n                    moduleName: 'workbox-routing',\n                    funcName: 'registerRoute',\n                    paramName: 'capture',\n                });\n            }\n            // We want to check if Express-style wildcards are in the pathname only.\n            // TODO: Remove this log message in v4.\n            const valueToCheck = capture.startsWith('http') ?\n                captureUrl.pathname : capture;\n            // See https://github.com/pillarjs/path-to-regexp#parameters\n            const wildcards = '[*:?+]';\n            if ((new RegExp(`${wildcards}`)).exec(valueToCheck)) {\n                logger.debug(`The '$capture' parameter contains an Express-style wildcard ` +\n                    `character (${wildcards}). Strings are now always interpreted as ` +\n                    `exact matches; use a RegExp for partial or wildcard matches.`);\n            }\n        }\n        const matchCallback = ({ url }) => {\n            if (process.env.NODE_ENV !== 'production') {\n                if ((url.pathname === captureUrl.pathname) &&\n                    (url.origin !== captureUrl.origin)) {\n                    logger.debug(`${capture} only partially matches the cross-origin URL ` +\n                        `${url}. This route will only handle cross-origin requests ` +\n                        `if they match the entire URL.`);\n                }\n            }\n            return url.href === captureUrl.href;\n        };\n        // If `capture` is a string then `handler` and `method` must be present.\n        route = new Route(matchCallback, handler, method);\n    }\n    else if (capture instanceof RegExp) {\n        // If `capture` is a `RegExp` then `handler` and `method` must be present.\n        route = new RegExpRoute(capture, handler, method);\n    }\n    else if (typeof capture === 'function') {\n        // If `capture` is a function then `handler` and `method` must be present.\n        route = new Route(capture, handler, method);\n    }\n    else if (capture instanceof Route) {\n        route = capture;\n    }\n    else {\n        throw new WorkboxError('unsupported-route-type', {\n            moduleName: 'workbox-routing',\n            funcName: 'registerRoute',\n            paramName: 'capture',\n        });\n    }\n    const defaultRouter = getOrCreateDefaultRouter();\n    defaultRouter.registerRoute(route);\n    return route;\n}\nexport { registerRoute };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { CacheableResponse } from './CacheableResponse.js';\nimport './_version.js';\n/**\n * A class implementing the `cacheWillUpdate` lifecycle callback. This makes it\n * easier to add in cacheability checks to requests made via Workbox's built-in\n * strategies.\n *\n * @memberof module:workbox-cacheable-response\n */\nclass CacheableResponsePlugin {\n    /**\n     * To construct a new CacheableResponsePlugin instance you must provide at\n     * least one of the `config` properties.\n     *\n     * If both `statuses` and `headers` are specified, then both conditions must\n     * be met for the `Response` to be considered cacheable.\n     *\n     * @param {Object} config\n     * @param {Array} [config.statuses] One or more status codes that a\n     * `Response` can have and be considered cacheable.\n     * @param {Object} [config.headers] A mapping of header names\n     * and expected values that a `Response` can have and be considered cacheable.\n     * If multiple headers are provided, only one needs to be present.\n     */\n    constructor(config) {\n        /**\n         * @param {Object} options\n         * @param {Response} options.response\n         * @return {Response|null}\n         * @private\n         */\n        this.cacheWillUpdate = async ({ response }) => {\n            if (this._cacheableResponse.isResponseCacheable(response)) {\n                return response;\n            }\n            return null;\n        };\n        this._cacheableResponse = new CacheableResponse(config);\n    }\n}\nexport { CacheableResponsePlugin };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { getOrCreatePrecacheController } from './utils/getOrCreatePrecacheController.js';\nimport './_version.js';\n/**\n * Takes in a URL, and returns the corresponding URL that could be used to\n * lookup the entry in the precache.\n *\n * If a relative URL is provided, the location of the service worker file will\n * be used as the base.\n *\n * For precached entries without revision information, the cache key will be the\n * same as the original URL.\n *\n * For precached entries with revision information, the cache key will be the\n * original URL with the addition of a query parameter used for keeping track of\n * the revision info.\n *\n * @param {string} url The URL whose cache key to look up.\n * @return {string} The cache key that corresponds to that URL.\n *\n * @memberof module:workbox-precaching\n */\nfunction getCacheKeyForURL(url) {\n    const precacheController = getOrCreatePrecacheController();\n    return precacheController.getCacheKeyForURL(url);\n}\nexport { getCacheKeyForURL };\n","\"use strict\";\n// @ts-ignore\ntry {\n    self['workbox:core:5.1.3'] && _();\n}\ncatch (e) { }\n"]}
\ No newline at end of file
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\"p5Qz\");\n","\"use strict\";\n// @ts-ignore\ntry {\n    self['workbox:cacheable-response:5.1.3'] && _();\n}\ncatch (e) { }\n","\"use strict\";\n// @ts-ignore\ntry {\n    self['workbox:precaching:5.1.3'] && _();\n}\ncatch (e) { }\n","\"use strict\";\n// @ts-ignore\ntry {\n    self['workbox:routing:5.1.3'] && _();\n}\ncatch (e) { }\n","\"use strict\";\n// @ts-ignore\ntry {\n    self['workbox:strategies:5.1.3'] && _();\n}\ncatch (e) { }\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { canConstructResponseFromBodyStream } from './_private/canConstructResponseFromBodyStream.js';\nimport './_version.js';\n/**\n * Allows developers to copy a response and modify its `headers`, `status`,\n * or `statusText` values (the values settable via a\n * [`ResponseInit`]{@link https://developer.mozilla.org/en-US/docs/Web/API/Response/Response#Syntax}\n 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That\n * function will be invoked with a single object with the response properties\n * `{headers, status, statusText}`. The return value of this function will\n * be used as the `ResponseInit` for the new `Response`. To change the values\n * either modify the passed parameter(s) and return it, or return a totally\n * new object.\n *\n * @param {Response} response\n * @param {Function} modifier\n * @memberof module:workbox-core\n */\nasync function copyResponse(response, modifier) {\n    const clonedResponse = response.clone();\n    // Create a fresh `ResponseInit` object by cloning the headers.\n    const responseInit = {\n        headers: new Headers(clonedResponse.headers),\n        status: clonedResponse.status,\n        statusText: clonedResponse.statusText,\n    };\n    // Apply any user modifications.\n    const modifiedResponseInit = modifier ? modifier(responseInit) : responseInit;\n    // Create the new response from the body stream and `ResponseInit`\n    // modifications. 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Return as-is.\n    if (typeof entry === 'string') {\n        const urlObject = new URL(entry, location.href);\n        return {\n            cacheKey: urlObject.href,\n            url: urlObject.href,\n        };\n    }\n    const { revision, url } = entry;\n    if (!url) {\n        throw new WorkboxError('add-to-cache-list-unexpected-type', { entry });\n    }\n    // If there's just a URL and no revision, then it's also assumed to be a\n    // versioned URL.\n    if (!revision) {\n        const urlObject = new URL(url, location.href);\n        return {\n            cacheKey: urlObject.href,\n            url: urlObject.href,\n        };\n    }\n    // Otherwise, construct a properly versioned URL using the custom Workbox\n    // search parameter along with the revision info.\n    const cacheKeyURL = new URL(url, location.href);\n    const originalURL = new URL(url, location.href);\n    cacheKeyURL.searchParams.set(REVISION_SEARCH_PARAM, revision);\n    return {\n        cacheKey: cacheKeyURL.href,\n        url: originalURL.href,\n    };\n}\n","/*\n  Copyright 2019 Google LLC\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { addFetchListener } from './utils/addFetchListener.js';\nimport './_version.js';\nlet listenerAdded = false;\n/**\n * Add a `fetch` listener to the service worker that will\n * respond to\n * [network requests]{@link https://developer.mozilla.org/en-US/docs/Web/API/Service_Worker_API/Using_Service_Workers#Custom_responses_to_requests}\n * with precached assets.\n *\n * Requests for assets that aren't precached, the `FetchEvent` will not be\n * responded to, allowing the event to fall through to other `fetch` event\n * listeners.\n *\n * @param {Object} [options]\n * @param {string} [options.directoryIndex=index.html] The `directoryIndex` will\n * check cache entries for a URLs ending with '/' to see if there is a hit when\n * appending the `directoryIndex` value.\n * @param {Array} [options.ignoreURLParametersMatching=[/^utm_/]] An\n * array of regex's to remove search params when looking for a cache match.\n * @param {boolean} [options.cleanURLs=true] The `cleanURLs` option will\n * check the cache for the URL with a `.html` added to the end of the end.\n * @param {module:workbox-precaching~urlManipulation} [options.urlManipulation]\n * This is a function that should take a URL and return an array of\n * alternative URLs that should be checked for precache matches.\n *\n * @memberof module:workbox-precaching\n */\nfunction addRoute(options) {\n    if (!listenerAdded) {\n        addFetchListener(options);\n        listenerAdded = true;\n    }\n}\nexport { addRoute };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { cacheNames } from 'workbox-core/_private/cacheNames.js';\nimport { getFriendlyURL } from 'workbox-core/_private/getFriendlyURL.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { getCacheKeyForURL } from './getCacheKeyForURL.js';\nimport '../_version.js';\n/**\n * Adds a `fetch` listener to the service worker that will\n * respond to\n * [network requests]{@link https://developer.mozilla.org/en-US/docs/Web/API/Service_Worker_API/Using_Service_Workers#Custom_responses_to_requests}\n * with precached assets.\n *\n * Requests for assets that aren't precached, the `FetchEvent` will not be\n * responded to, allowing the event to fall through to other `fetch` event\n * listeners.\n *\n * NOTE: when called more than once this method will replace the previously set\n * configuration options. Calling it more than once is not recommended outside\n * of tests.\n *\n * @private\n * @param {Object} [options]\n * @param {string} [options.directoryIndex=index.html] The `directoryIndex` will\n * check cache entries for a URLs ending with '/' to see if there is a hit when\n * appending the `directoryIndex` value.\n * @param {Array} [options.ignoreURLParametersMatching=[/^utm_/]] An\n * array of regex's to remove search params when looking for a cache match.\n * @param {boolean} [options.cleanURLs=true] The `cleanURLs` option will\n * check the cache for the URL with a `.html` added to the end of the end.\n * @param {workbox.precaching~urlManipulation} [options.urlManipulation]\n * This is a function that should take a URL and return an array of\n * alternative URLs that should be checked for precache matches.\n */\nexport const addFetchListener = ({ ignoreURLParametersMatching = [/^utm_/], directoryIndex = 'index.html', cleanURLs = true, urlManipulation, } = {}) => {\n    const cacheName = cacheNames.getPrecacheName();\n    // See https://github.com/Microsoft/TypeScript/issues/28357#issuecomment-436484705\n    self.addEventListener('fetch', ((event) => {\n        const precachedURL = getCacheKeyForURL(event.request.url, {\n            cleanURLs,\n            directoryIndex,\n            ignoreURLParametersMatching,\n            urlManipulation,\n        });\n        if (!precachedURL) {\n            if (process.env.NODE_ENV !== 'production') {\n                logger.debug(`Precaching did not find a match for ` +\n                    getFriendlyURL(event.request.url));\n            }\n            return;\n        }\n        let responsePromise = self.caches.open(cacheName).then((cache) => {\n            return cache.match(precachedURL);\n        }).then((cachedResponse) => {\n            if (cachedResponse) {\n                return cachedResponse;\n            }\n            // Fall back to the network if we don't have a cached response\n            // (perhaps due to manual cache cleanup).\n            if (process.env.NODE_ENV !== 'production') {\n                logger.warn(`The precached response for ` +\n                    `${getFriendlyURL(precachedURL)} in ${cacheName} was not found. ` +\n                    `Falling back to the network instead.`);\n            }\n            return fetch(precachedURL);\n        });\n        if (process.env.NODE_ENV !== 'production') {\n            responsePromise = responsePromise.then((response) => {\n                // Workbox is going to handle the route.\n                // print the routing details to the console.\n                logger.groupCollapsed(`Precaching is responding to: ` +\n                    getFriendlyURL(event.request.url));\n                logger.log(`Serving the precached url: ${precachedURL}`);\n                logger.groupCollapsed(`View request details here.`);\n                logger.log(event.request);\n                logger.groupEnd();\n                logger.groupCollapsed(`View response details here.`);\n                logger.log(response);\n                logger.groupEnd();\n                logger.groupEnd();\n                return response;\n            });\n        }\n        event.respondWith(responsePromise);\n    }));\n};\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { getOrCreatePrecacheController } from './getOrCreatePrecacheController.js';\nimport { generateURLVariations } from './generateURLVariations.js';\nimport '../_version.js';\n/**\n * This function will take the request URL and manipulate it based on the\n * configuration options.\n *\n * @param {string} url\n * @param {Object} options\n * @return {string} Returns the URL in the cache that matches the request,\n * if possible.\n *\n * @private\n */\nexport const getCacheKeyForURL = (url, options) => {\n    const precacheController = getOrCreatePrecacheController();\n    const urlsToCacheKeys = precacheController.getURLsToCacheKeys();\n    for (const possibleURL of generateURLVariations(url, options)) {\n        const possibleCacheKey = urlsToCacheKeys.get(possibleURL);\n        if (possibleCacheKey) {\n            return possibleCacheKey;\n        }\n    }\n};\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { removeIgnoredSearchParams } from './removeIgnoredSearchParams.js';\nimport '../_version.js';\n/**\n * Generator function that yields possible variations on the original URL to\n * check, one at a time.\n *\n * @param {string} url\n * @param {Object} options\n *\n * @private\n * @memberof module:workbox-precaching\n */\nexport function* generateURLVariations(url, { ignoreURLParametersMatching, directoryIndex, cleanURLs, urlManipulation, } = {}) {\n    const urlObject = new URL(url, location.href);\n    urlObject.hash = '';\n    yield urlObject.href;\n    const urlWithoutIgnoredParams = removeIgnoredSearchParams(urlObject, ignoreURLParametersMatching);\n    yield urlWithoutIgnoredParams.href;\n    if (directoryIndex && urlWithoutIgnoredParams.pathname.endsWith('/')) {\n        const directoryURL = new URL(urlWithoutIgnoredParams.href);\n        directoryURL.pathname += directoryIndex;\n        yield directoryURL.href;\n    }\n    if (cleanURLs) {\n        const cleanURL = new URL(urlWithoutIgnoredParams.href);\n        cleanURL.pathname += '.html';\n        yield cleanURL.href;\n    }\n    if (urlManipulation) {\n        const additionalURLs = urlManipulation({ url: urlObject });\n        for (const urlToAttempt of additionalURLs) {\n            yield urlToAttempt.href;\n        }\n    }\n}\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\n/**\n * Removes any URL search parameters that should be ignored.\n *\n * @param {URL} urlObject The original URL.\n * @param {Array} ignoreURLParametersMatching RegExps to test against\n * each search parameter name. Matches mean that the search parameter should be\n * ignored.\n * @return {URL} The URL with any ignored search parameters removed.\n *\n * @private\n * @memberof module:workbox-precaching\n */\nexport function removeIgnoredSearchParams(urlObject, ignoreURLParametersMatching = []) {\n    // Convert the iterable into an array at the start of the loop to make sure\n    // deletion doesn't mess up iteration.\n    for (const paramName of [...urlObject.searchParams.keys()]) {\n        if (ignoreURLParametersMatching.some((regExp) => regExp.test(paramName))) {\n            urlObject.searchParams.delete(paramName);\n        }\n    }\n    return urlObject;\n}\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { addRoute } from './addRoute.js';\nimport { precache } from './precache.js';\nimport './_version.js';\n/**\n * This method will add entries to the precache list and add a route to\n * respond to fetch events.\n *\n * This is a convenience method that will call\n * [precache()]{@link module:workbox-precaching.precache} and\n * [addRoute()]{@link module:workbox-precaching.addRoute} in a single call.\n *\n * @param {Array} entries Array of entries to precache.\n * @param {Object} [options] See\n * [addRoute() options]{@link module:workbox-precaching.addRoute}.\n *\n * @memberof module:workbox-precaching\n */\nfunction precacheAndRoute(entries, options) {\n    precache(entries);\n    addRoute(options);\n}\nexport { precacheAndRoute };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { getOrCreatePrecacheController } from './utils/getOrCreatePrecacheController.js';\nimport { precachePlugins } from './utils/precachePlugins.js';\nimport './_version.js';\nconst installListener = (event) => {\n    const precacheController = getOrCreatePrecacheController();\n    const plugins = precachePlugins.get();\n    event.waitUntil(precacheController.install({ event, plugins })\n        .catch((error) => {\n        if (process.env.NODE_ENV !== 'production') {\n            logger.error(`Service worker installation failed. It will ` +\n                `be retried automatically during the next navigation.`);\n        }\n        // Re-throw the error to ensure installation fails.\n        throw error;\n    }));\n};\nconst activateListener = (event) => {\n    const precacheController = getOrCreatePrecacheController();\n    event.waitUntil(precacheController.activate());\n};\n/**\n * Adds items to the precache list, removing any duplicates and\n * stores the files in the\n * [\"precache cache\"]{@link module:workbox-core.cacheNames} when the service\n * worker installs.\n *\n * This method can be called multiple times.\n *\n * Please note: This method **will not** serve any of the cached files for you.\n * It only precaches files. To respond to a network request you call\n * [addRoute()]{@link module:workbox-precaching.addRoute}.\n *\n * If you have a single array of files to precache, you can just call\n * [precacheAndRoute()]{@link module:workbox-precaching.precacheAndRoute}.\n *\n * @param {Array} [entries=[]] Array of entries to precache.\n *\n * @memberof module:workbox-precaching\n */\nfunction precache(entries) {\n    const precacheController = getOrCreatePrecacheController();\n    precacheController.addToCacheList(entries);\n    if (entries.length > 0) {\n        // NOTE: these listeners will only be added once (even if the `precache()`\n        // method is called multiple times) because event listeners are implemented\n        // as a set, where each listener must be unique.\n        // See https://github.com/Microsoft/TypeScript/issues/28357#issuecomment-436484705\n        self.addEventListener('install', installListener);\n        self.addEventListener('activate', activateListener);\n    }\n}\nexport { precache };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { Router } from '../Router.js';\nimport '../_version.js';\nlet defaultRouter;\n/**\n * Creates a new, singleton Router instance if one does not exist. If one\n * does already exist, that instance is returned.\n *\n * @private\n * @return {Router}\n */\nexport const getOrCreateDefaultRouter = () => {\n    if (!defaultRouter) {\n        defaultRouter = new Router();\n        // The helpers that use the default Router assume these listeners exist.\n        defaultRouter.addFetchListener();\n        defaultRouter.addCacheListener();\n    }\n    return defaultRouter;\n};\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { PrecacheController } from '../PrecacheController.js';\nimport '../_version.js';\nlet precacheController;\n/**\n * @return {PrecacheController}\n * @private\n */\nexport const getOrCreatePrecacheController = () => {\n    if (!precacheController) {\n        precacheController = new PrecacheController();\n    }\n    return precacheController;\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { messages } from './messages.js';\nimport '../../_version.js';\nconst fallback = (code, ...args) => {\n    let msg = code;\n    if (args.length > 0) {\n        msg += ` :: ${JSON.stringify(args)}`;\n    }\n    return msg;\n};\nconst generatorFunction = (code, details = {}) => {\n    const message = messages[code];\n    if (!message) {\n        throw new Error(`Unable to find message for code '${code}'.`);\n    }\n    return message(details);\n};\nexport const messageGenerator = (process.env.NODE_ENV === 'production') ?\n    fallback : generatorFunction;\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { messageGenerator } from '../models/messages/messageGenerator.js';\nimport '../_version.js';\n/**\n * Workbox errors should be thrown with this class.\n * This allows use to ensure the type easily in tests,\n * helps developers identify errors from workbox\n * easily and allows use to optimise error\n * messages correctly.\n *\n * @private\n */\nclass WorkboxError extends Error {\n    /**\n     *\n     * @param {string} errorCode The error code that\n     * identifies this particular error.\n     * @param {Object=} details Any relevant arguments\n     * that will help developers identify issues should\n     * be added as a key on the context object.\n     */\n    constructor(errorCode, details) {\n        const message = messageGenerator(errorCode, details);\n        super(message);\n        this.name = errorCode;\n        this.details = details;\n    }\n}\nexport { WorkboxError };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport '../_version.js';\n/**\n * @param {function()|Object} handler Either a function, or an object with a\n * 'handle' method.\n * @return {Object} An object with a handle method.\n *\n * @private\n */\nexport const normalizeHandler = (handler) => {\n    if (handler && typeof handler === 'object') {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.hasMethod(handler, 'handle', {\n                moduleName: 'workbox-routing',\n                className: 'Route',\n                funcName: 'constructor',\n                paramName: 'handler',\n            });\n        }\n        return handler;\n    }\n    else {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isType(handler, 'function', {\n                moduleName: 'workbox-routing',\n                className: 'Route',\n                funcName: 'constructor',\n                paramName: 'handler',\n            });\n        }\n        return { handle: handler };\n    }\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { defaultMethod, validMethods } from './utils/constants.js';\nimport { normalizeHandler } from './utils/normalizeHandler.js';\nimport './_version.js';\n/**\n * A `Route` consists of a pair of callback functions, \"match\" and \"handler\".\n * The \"match\" callback determine if a route should be used to \"handle\" a\n * request by returning a non-falsy value if it can. The \"handler\" callback\n * is called when there is a match and should return a Promise that resolves\n * to a `Response`.\n *\n * @memberof module:workbox-routing\n */\nclass Route {\n    /**\n     * Constructor for Route class.\n     *\n     * @param {module:workbox-routing~matchCallback} match\n     * A callback function that determines whether the route matches a given\n     * `fetch` event by returning a non-falsy value.\n     * @param {module:workbox-routing~handlerCallback} handler A callback\n     * function that returns a Promise resolving to a Response.\n     * @param {string} [method='GET'] The HTTP method to match the Route\n     * against.\n     */\n    constructor(match, handler, method = defaultMethod) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isType(match, 'function', {\n                moduleName: 'workbox-routing',\n                className: 'Route',\n                funcName: 'constructor',\n                paramName: 'match',\n            });\n            if (method) {\n                assert.isOneOf(method, validMethods, { paramName: 'method' });\n            }\n        }\n        // These values are referenced directly by Router so cannot be\n        // altered by minificaton.\n        this.handler = normalizeHandler(handler);\n        this.match = match;\n        this.method = method;\n    }\n}\nexport { Route };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\n/**\n * The default HTTP method, 'GET', used when there's no specific method\n * configured for a route.\n *\n * @type {string}\n *\n * @private\n */\nexport const defaultMethod = 'GET';\n/**\n * The list of valid HTTP methods associated with requests that could be routed.\n *\n * @type {Array}\n *\n * @private\n */\nexport const validMethods = [\n    'DELETE',\n    'GET',\n    'HEAD',\n    'PATCH',\n    'POST',\n    'PUT',\n];\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { Route } from './Route.js';\nimport './_version.js';\n/**\n * RegExpRoute makes it easy to create a regular expression based\n * [Route]{@link module:workbox-routing.Route}.\n *\n * For same-origin requests the RegExp only needs to match part of the URL. For\n * requests against third-party servers, you must define a RegExp that matches\n * the start of the URL.\n *\n * [See the module docs for info.]{@link https://developers.google.com/web/tools/workbox/modules/workbox-routing}\n *\n * @memberof module:workbox-routing\n * @extends module:workbox-routing.Route\n */\nclass RegExpRoute extends Route {\n    /**\n     * If the regular expression contains\n     * [capture groups]{@link https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/RegExp#grouping-back-references},\n     * the captured values will be passed to the\n     * [handler's]{@link module:workbox-routing~handlerCallback} `params`\n     * argument.\n     *\n     * @param {RegExp} regExp The regular expression to match against URLs.\n     * @param {module:workbox-routing~handlerCallback} handler A callback\n     * function that returns a Promise resulting in a Response.\n     * @param {string} [method='GET'] The HTTP method to match the Route\n     * against.\n     */\n    constructor(regExp, handler, method) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(regExp, RegExp, {\n                moduleName: 'workbox-routing',\n                className: 'RegExpRoute',\n                funcName: 'constructor',\n                paramName: 'pattern',\n            });\n        }\n        const match = ({ url }) => {\n            const result = regExp.exec(url.href);\n            // Return immediately if there's no match.\n            if (!result) {\n                return;\n            }\n            // Require that the match start at the first character in the URL string\n            // if it's a cross-origin request.\n            // See https://github.com/GoogleChrome/workbox/issues/281 for the context\n            // behind this behavior.\n            if ((url.origin !== location.origin) && (result.index !== 0)) {\n                if (process.env.NODE_ENV !== 'production') {\n                    logger.debug(`The regular expression '${regExp}' only partially matched ` +\n                        `against the cross-origin URL '${url}'. RegExpRoute's will only ` +\n                        `handle cross-origin requests if they match the entire URL.`);\n                }\n                return;\n            }\n            // If the route matches, but there aren't any capture groups defined, then\n            // this will return [], which is truthy and therefore sufficient to\n            // indicate a match.\n            // If there are capture groups, then it will return their values.\n            return result.slice(1);\n        };\n        super(match, handler, method);\n    }\n}\nexport { RegExpRoute };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nconst getFriendlyURL = (url) => {\n    const urlObj = new URL(String(url), location.href);\n    // See https://github.com/GoogleChrome/workbox/issues/2323\n    // We want to include everything, except for the origin if it's same-origin.\n    return urlObj.href.replace(new RegExp(`^${location.origin}`), '');\n};\nexport { getFriendlyURL };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { getFriendlyURL } from 'workbox-core/_private/getFriendlyURL.js';\nimport { normalizeHandler } from './utils/normalizeHandler.js';\nimport './_version.js';\n/**\n * The Router can be used to process a FetchEvent through one or more\n * [Routes]{@link module:workbox-routing.Route} responding  with a Request if\n * a matching route exists.\n *\n * If no route matches a given a request, the Router will use a \"default\"\n * handler if one is defined.\n *\n * Should the matching Route throw an error, the Router will use a \"catch\"\n * handler if one is defined to gracefully deal with issues and respond with a\n * Request.\n *\n * If a request matches multiple routes, the **earliest** registered route will\n * be used to respond to the request.\n *\n * @memberof module:workbox-routing\n */\nclass Router {\n    /**\n     * Initializes a new Router.\n     */\n    constructor() {\n        this._routes = new Map();\n    }\n    /**\n     * @return {Map>} routes A `Map` of HTTP\n     * method name ('GET', etc.) to an array of all the corresponding `Route`\n     * instances that are registered.\n     */\n    get routes() {\n        return this._routes;\n    }\n    /**\n     * Adds a fetch event listener to respond to events when a route matches\n     * the event's request.\n     */\n    addFetchListener() {\n        // See https://github.com/Microsoft/TypeScript/issues/28357#issuecomment-436484705\n        self.addEventListener('fetch', ((event) => {\n            const { request } = event;\n            const responsePromise = this.handleRequest({ request, event });\n            if (responsePromise) {\n                event.respondWith(responsePromise);\n            }\n        }));\n    }\n    /**\n     * Adds a message event listener for URLs to cache from the window.\n     * This is useful to cache resources loaded on the page prior to when the\n     * service worker started controlling it.\n     *\n     * The format of the message data sent from the window should be as follows.\n     * Where the `urlsToCache` array may consist of URL strings or an array of\n     * URL string + `requestInit` object (the same as you'd pass to `fetch()`).\n     *\n     * ```\n     * {\n     *   type: 'CACHE_URLS',\n     *   payload: {\n     *     urlsToCache: [\n     *       './script1.js',\n     *       './script2.js',\n     *       ['./script3.js', {mode: 'no-cors'}],\n     *     ],\n     *   },\n     * }\n     * ```\n     */\n    addCacheListener() {\n        // See https://github.com/Microsoft/TypeScript/issues/28357#issuecomment-436484705\n        self.addEventListener('message', ((event) => {\n            if (event.data && event.data.type === 'CACHE_URLS') {\n                const { payload } = event.data;\n                if (process.env.NODE_ENV !== 'production') {\n                    logger.debug(`Caching URLs from the window`, payload.urlsToCache);\n                }\n                const requestPromises = Promise.all(payload.urlsToCache.map((entry) => {\n                    if (typeof entry === 'string') {\n                        entry = [entry];\n                    }\n                    const request = new Request(...entry);\n                    return this.handleRequest({ request });\n                    // TODO(philipwalton): TypeScript errors without this typecast for\n                    // some reason (probably a bug). The real type here should work but\n                    // doesn't: `Array | undefined>`.\n                })); // TypeScript\n                event.waitUntil(requestPromises);\n                // If a MessageChannel was used, reply to the message on success.\n                if (event.ports && event.ports[0]) {\n                    requestPromises.then(() => event.ports[0].postMessage(true));\n                }\n            }\n        }));\n    }\n    /**\n     * Apply the routing rules to a FetchEvent object to get a Response from an\n     * appropriate Route's handler.\n     *\n     * @param {Object} options\n     * @param {Request} options.request The request to handle (this is usually\n     *     from a fetch event, but it does not have to be).\n     * @param {FetchEvent} [options.event] The event that triggered the request,\n     *     if applicable.\n     * @return {Promise|undefined} A promise is returned if a\n     *     registered route can handle the request. If there is no matching\n     *     route and there's no `defaultHandler`, `undefined` is returned.\n     */\n    handleRequest({ request, event }) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(request, Request, {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'handleRequest',\n                paramName: 'options.request',\n            });\n        }\n        const url = new URL(request.url, location.href);\n        if (!url.protocol.startsWith('http')) {\n            if (process.env.NODE_ENV !== 'production') {\n                logger.debug(`Workbox Router only supports URLs that start with 'http'.`);\n            }\n            return;\n        }\n        const { params, route } = this.findMatchingRoute({ url, request, event });\n        let handler = route && route.handler;\n        const debugMessages = [];\n        if (process.env.NODE_ENV !== 'production') {\n            if (handler) {\n                debugMessages.push([\n                    `Found a route to handle this request:`, route,\n                ]);\n                if (params) {\n                    debugMessages.push([\n                        `Passing the following params to the route's handler:`, params,\n                    ]);\n                }\n            }\n        }\n        // If we don't have a handler because there was no matching route, then\n        // fall back to defaultHandler if that's defined.\n        if (!handler && this._defaultHandler) {\n            if (process.env.NODE_ENV !== 'production') {\n                debugMessages.push(`Failed to find a matching route. Falling ` +\n                    `back to the default handler.`);\n            }\n            handler = this._defaultHandler;\n        }\n        if (!handler) {\n            if (process.env.NODE_ENV !== 'production') {\n                // No handler so Workbox will do nothing. If logs is set of debug\n                // i.e. verbose, we should print out this information.\n                logger.debug(`No route found for: ${getFriendlyURL(url)}`);\n            }\n            return;\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            // We have a handler, meaning Workbox is going to handle the route.\n            // print the routing details to the console.\n            logger.groupCollapsed(`Router is responding to: ${getFriendlyURL(url)}`);\n            debugMessages.forEach((msg) => {\n                if (Array.isArray(msg)) {\n                    logger.log(...msg);\n                }\n                else {\n                    logger.log(msg);\n                }\n            });\n            logger.groupEnd();\n        }\n        // Wrap in try and catch in case the handle method throws a synchronous\n        // error. It should still callback to the catch handler.\n        let responsePromise;\n        try {\n            responsePromise = handler.handle({ url, request, event, params });\n        }\n        catch (err) {\n            responsePromise = Promise.reject(err);\n        }\n        if (responsePromise instanceof Promise && this._catchHandler) {\n            responsePromise = responsePromise.catch((err) => {\n                if (process.env.NODE_ENV !== 'production') {\n                    // Still include URL here as it will be async from the console group\n                    // and may not make sense without the URL\n                    logger.groupCollapsed(`Error thrown when responding to: ` +\n                        ` ${getFriendlyURL(url)}. Falling back to Catch Handler.`);\n                    logger.error(`Error thrown by:`, route);\n                    logger.error(err);\n                    logger.groupEnd();\n                }\n                return this._catchHandler.handle({ url, request, event });\n            });\n        }\n        return responsePromise;\n    }\n    /**\n     * Checks a request and URL (and optionally an event) against the list of\n     * registered routes, and if there's a match, returns the corresponding\n     * route along with any params generated by the match.\n     *\n     * @param {Object} options\n     * @param {URL} options.url\n     * @param {Request} options.request The request to match.\n     * @param {Event} [options.event] The corresponding event (unless N/A).\n     * @return {Object} An object with `route` and `params` properties.\n     *     They are populated if a matching route was found or `undefined`\n     *     otherwise.\n     */\n    findMatchingRoute({ url, request, event }) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(url, URL, {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'findMatchingRoute',\n                paramName: 'options.url',\n            });\n            assert.isInstance(request, Request, {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'findMatchingRoute',\n                paramName: 'options.request',\n            });\n        }\n        const routes = this._routes.get(request.method) || [];\n        for (const route of routes) {\n            let params;\n            const matchResult = route.match({ url, request, event });\n            if (matchResult) {\n                // See https://github.com/GoogleChrome/workbox/issues/2079\n                params = matchResult;\n                if (Array.isArray(matchResult) && matchResult.length === 0) {\n                    // Instead of passing an empty array in as params, use undefined.\n                    params = undefined;\n                }\n                else if ((matchResult.constructor === Object &&\n                    Object.keys(matchResult).length === 0)) {\n                    // Instead of passing an empty object in as params, use undefined.\n                    params = undefined;\n                }\n                else if (typeof matchResult === 'boolean') {\n                    // For the boolean value true (rather than just something truth-y),\n                    // don't set params.\n                    // See https://github.com/GoogleChrome/workbox/pull/2134#issuecomment-513924353\n                    params = undefined;\n                }\n                // Return early if have a match.\n                return { route, params };\n            }\n        }\n        // If no match was found above, return and empty object.\n        return {};\n    }\n    /**\n     * Define a default `handler` that's called when no routes explicitly\n     * match the incoming request.\n     *\n     * Without a default handler, unmatched requests will go against the\n     * network as if there were no service worker present.\n     *\n     * @param {module:workbox-routing~handlerCallback} handler A callback\n     * function that returns a Promise resulting in a Response.\n     */\n    setDefaultHandler(handler) {\n        this._defaultHandler = normalizeHandler(handler);\n    }\n    /**\n     * If a Route throws an error while handling a request, this `handler`\n     * will be called and given a chance to provide a response.\n     *\n     * @param {module:workbox-routing~handlerCallback} handler A callback\n     * function that returns a Promise resulting in a Response.\n     */\n    setCatchHandler(handler) {\n        this._catchHandler = normalizeHandler(handler);\n    }\n    /**\n     * Registers a route with the router.\n     *\n     * @param {module:workbox-routing.Route} route The route to register.\n     */\n    registerRoute(route) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isType(route, 'object', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route',\n            });\n            assert.hasMethod(route, 'match', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route',\n            });\n            assert.isType(route.handler, 'object', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route',\n            });\n            assert.hasMethod(route.handler, 'handle', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route.handler',\n            });\n            assert.isType(route.method, 'string', {\n                moduleName: 'workbox-routing',\n                className: 'Router',\n                funcName: 'registerRoute',\n                paramName: 'route.method',\n            });\n        }\n        if (!this._routes.has(route.method)) {\n            this._routes.set(route.method, []);\n        }\n        // Give precedence to all of the earlier routes by adding this additional\n        // route to the end of the array.\n        this._routes.get(route.method).push(route);\n    }\n    /**\n     * Unregisters a route with the router.\n     *\n     * @param {module:workbox-routing.Route} route The route to unregister.\n     */\n    unregisterRoute(route) {\n        if (!this._routes.has(route.method)) {\n            throw new WorkboxError('unregister-route-but-not-found-with-method', {\n                method: route.method,\n            });\n        }\n        const routeIndex = this._routes.get(route.method).indexOf(route);\n        if (routeIndex > -1) {\n            this._routes.get(route.method).splice(routeIndex, 1);\n        }\n        else {\n            throw new WorkboxError('unregister-route-route-not-registered');\n        }\n    }\n}\nexport { Router };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nconst plugins = [];\nexport const precachePlugins = {\n    /*\n     * @return {Array}\n     * @private\n     */\n    get() {\n        return plugins;\n    },\n    /*\n     * @param {Array} newPlugins\n     * @private\n     */\n    add(newPlugins) {\n        plugins.push(...newPlugins);\n    },\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nconst _cacheNameDetails = {\n    googleAnalytics: 'googleAnalytics',\n    precache: 'precache-v2',\n    prefix: 'workbox',\n    runtime: 'runtime',\n    suffix: typeof registration !== 'undefined' ? registration.scope : '',\n};\nconst _createCacheName = (cacheName) => {\n    return [_cacheNameDetails.prefix, cacheName, _cacheNameDetails.suffix]\n        .filter((value) => value && value.length > 0)\n        .join('-');\n};\nconst eachCacheNameDetail = (fn) => {\n    for (const key of Object.keys(_cacheNameDetails)) {\n        fn(key);\n    }\n};\nexport const cacheNames = {\n    updateDetails: (details) => {\n        eachCacheNameDetail((key) => {\n            if (typeof details[key] === 'string') {\n                _cacheNameDetails[key] = details[key];\n            }\n        });\n    },\n    getGoogleAnalyticsName: (userCacheName) => {\n        return userCacheName || _createCacheName(_cacheNameDetails.googleAnalytics);\n    },\n    getPrecacheName: (userCacheName) => {\n        return userCacheName || _createCacheName(_cacheNameDetails.precache);\n    },\n    getPrefix: () => {\n        return _cacheNameDetails.prefix;\n    },\n    getRuntimeName: (userCacheName) => {\n        return userCacheName || _createCacheName(_cacheNameDetails.runtime);\n    },\n    getSuffix: () => {\n        return _cacheNameDetails.suffix;\n    },\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\n// Callbacks to be executed whenever there's a quota error.\nconst quotaErrorCallbacks = new Set();\nexport { quotaErrorCallbacks };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nexport const pluginUtils = {\n    filter: (plugins, callbackName) => {\n        return plugins.filter((plugin) => callbackName in plugin);\n    },\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from './assert.js';\nimport { executeQuotaErrorCallbacks } from './executeQuotaErrorCallbacks.js';\nimport { getFriendlyURL } from './getFriendlyURL.js';\nimport { logger } from './logger.js';\nimport { pluginUtils } from '../utils/pluginUtils.js';\nimport { WorkboxError } from './WorkboxError.js';\nimport '../_version.js';\n/**\n * Checks the list of plugins for the cacheKeyWillBeUsed callback, and\n * executes any of those callbacks found in sequence. The final `Request` object\n * returned by the last plugin is treated as the cache key for cache reads\n * and/or writes.\n *\n * @param {Object} options\n * @param {Request} options.request\n * @param {string} options.mode\n * @param {Array} [options.plugins=[]]\n * @return {Promise}\n *\n * @private\n * @memberof module:workbox-core\n */\nconst _getEffectiveRequest = async ({ request, mode, plugins = [], }) => {\n    const cacheKeyWillBeUsedPlugins = pluginUtils.filter(plugins, \"cacheKeyWillBeUsed\" /* CACHE_KEY_WILL_BE_USED */);\n    let effectiveRequest = request;\n    for (const plugin of cacheKeyWillBeUsedPlugins) {\n        effectiveRequest = await plugin[\"cacheKeyWillBeUsed\" /* CACHE_KEY_WILL_BE_USED */].call(plugin, { mode, request: effectiveRequest });\n        if (typeof effectiveRequest === 'string') {\n            effectiveRequest = new Request(effectiveRequest);\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(effectiveRequest, Request, {\n                moduleName: 'Plugin',\n                funcName: \"cacheKeyWillBeUsed\" /* CACHE_KEY_WILL_BE_USED */,\n                isReturnValueProblem: true,\n            });\n        }\n    }\n    return effectiveRequest;\n};\n/**\n * This method will call cacheWillUpdate on the available plugins (or use\n * status === 200) to determine if the Response is safe and valid to cache.\n *\n * @param {Object} options\n * @param {Request} options.request\n * @param {Response} options.response\n * @param {Event} [options.event]\n * @param {Array} [options.plugins=[]]\n * @return {Promise}\n *\n * @private\n * @memberof module:workbox-core\n */\nconst _isResponseSafeToCache = async ({ request, response, event, plugins = [], }) => {\n    let responseToCache = response;\n    let pluginsUsed = false;\n    for (const plugin of plugins) {\n        if (\"cacheWillUpdate\" /* CACHE_WILL_UPDATE */ in plugin) {\n            pluginsUsed = true;\n            const pluginMethod = plugin[\"cacheWillUpdate\" /* CACHE_WILL_UPDATE */];\n            responseToCache = await pluginMethod.call(plugin, {\n                request,\n                response: responseToCache,\n                event,\n            });\n            if (process.env.NODE_ENV !== 'production') {\n                if (responseToCache) {\n                    assert.isInstance(responseToCache, Response, {\n                        moduleName: 'Plugin',\n                        funcName: \"cacheWillUpdate\" /* CACHE_WILL_UPDATE */,\n                        isReturnValueProblem: true,\n                    });\n                }\n            }\n            if (!responseToCache) {\n                break;\n            }\n        }\n    }\n    if (!pluginsUsed) {\n        if (process.env.NODE_ENV !== 'production') {\n            if (responseToCache) {\n                if (responseToCache.status !== 200) {\n                    if (responseToCache.status === 0) {\n                        logger.warn(`The response for '${request.url}' is an opaque ` +\n                            `response. The caching strategy that you're using will not ` +\n                            `cache opaque responses by default.`);\n                    }\n                    else {\n                        logger.debug(`The response for '${request.url}' returned ` +\n                            `a status code of '${response.status}' and won't be cached as a ` +\n                            `result.`);\n                    }\n                }\n            }\n        }\n        responseToCache = responseToCache && responseToCache.status === 200 ?\n            responseToCache : undefined;\n    }\n    return responseToCache ? responseToCache : null;\n};\n/**\n * This is a wrapper around cache.match().\n *\n * @param {Object} options\n * @param {string} options.cacheName Name of the cache to match against.\n * @param {Request} options.request The Request that will be used to look up\n *     cache entries.\n * @param {Event} [options.event] The event that prompted the action.\n * @param {Object} [options.matchOptions] Options passed to cache.match().\n * @param {Array} [options.plugins=[]] Array of plugins.\n * @return {Response} A cached response if available.\n *\n * @private\n * @memberof module:workbox-core\n */\nconst matchWrapper = async ({ cacheName, request, event, matchOptions, plugins = [], }) => {\n    const cache = await self.caches.open(cacheName);\n    const effectiveRequest = await _getEffectiveRequest({\n        plugins, request, mode: 'read'\n    });\n    let cachedResponse = await cache.match(effectiveRequest, matchOptions);\n    if (process.env.NODE_ENV !== 'production') {\n        if (cachedResponse) {\n            logger.debug(`Found a cached response in '${cacheName}'.`);\n        }\n        else {\n            logger.debug(`No cached response found in '${cacheName}'.`);\n        }\n    }\n    for (const plugin of plugins) {\n        if (\"cachedResponseWillBeUsed\" /* CACHED_RESPONSE_WILL_BE_USED */ in plugin) {\n            const pluginMethod = plugin[\"cachedResponseWillBeUsed\" /* CACHED_RESPONSE_WILL_BE_USED */];\n            cachedResponse = await pluginMethod.call(plugin, {\n                cacheName,\n                event,\n                matchOptions,\n                cachedResponse,\n                request: effectiveRequest,\n            });\n            if (process.env.NODE_ENV !== 'production') {\n                if (cachedResponse) {\n                    assert.isInstance(cachedResponse, Response, {\n                        moduleName: 'Plugin',\n                        funcName: \"cachedResponseWillBeUsed\" /* CACHED_RESPONSE_WILL_BE_USED */,\n                        isReturnValueProblem: true,\n                    });\n                }\n            }\n        }\n    }\n    return cachedResponse;\n};\n/**\n * Wrapper around cache.put().\n *\n * Will call `cacheDidUpdate` on plugins if the cache was updated, using\n * `matchOptions` when determining what the old entry is.\n *\n * @param {Object} options\n * @param {string} options.cacheName\n * @param {Request} options.request\n * @param {Response} options.response\n * @param {Event} [options.event]\n * @param {Array} [options.plugins=[]]\n * @param {Object} [options.matchOptions]\n *\n * @private\n * @memberof module:workbox-core\n */\nconst putWrapper = async ({ cacheName, request, response, event, plugins = [], matchOptions, }) => {\n    if (process.env.NODE_ENV !== 'production') {\n        if (request.method && request.method !== 'GET') {\n            throw new WorkboxError('attempt-to-cache-non-get-request', {\n                url: getFriendlyURL(request.url),\n                method: request.method,\n            });\n        }\n    }\n    const effectiveRequest = await _getEffectiveRequest({\n        plugins, request, mode: 'write'\n    });\n    if (!response) {\n        if (process.env.NODE_ENV !== 'production') {\n            logger.error(`Cannot cache non-existent response for ` +\n                `'${getFriendlyURL(effectiveRequest.url)}'.`);\n        }\n        throw new WorkboxError('cache-put-with-no-response', {\n            url: getFriendlyURL(effectiveRequest.url),\n        });\n    }\n    const responseToCache = await _isResponseSafeToCache({\n        event,\n        plugins,\n        response,\n        request: effectiveRequest,\n    });\n    if (!responseToCache) {\n        if (process.env.NODE_ENV !== 'production') {\n            logger.debug(`Response '${getFriendlyURL(effectiveRequest.url)}' will ` +\n                `not be cached.`, responseToCache);\n        }\n        return;\n    }\n    const cache = await self.caches.open(cacheName);\n    const updatePlugins = pluginUtils.filter(plugins, \"cacheDidUpdate\" /* CACHE_DID_UPDATE */);\n    const oldResponse = updatePlugins.length > 0 ?\n        await matchWrapper({ cacheName, matchOptions, request: effectiveRequest }) :\n        null;\n    if (process.env.NODE_ENV !== 'production') {\n        logger.debug(`Updating the '${cacheName}' cache with a new Response for ` +\n            `${getFriendlyURL(effectiveRequest.url)}.`);\n    }\n    try {\n        await cache.put(effectiveRequest, responseToCache);\n    }\n    catch (error) {\n        // See https://developer.mozilla.org/en-US/docs/Web/API/DOMException#exception-QuotaExceededError\n        if (error.name === 'QuotaExceededError') {\n            await executeQuotaErrorCallbacks();\n        }\n        throw error;\n    }\n    for (const plugin of updatePlugins) {\n        await plugin[\"cacheDidUpdate\" /* CACHE_DID_UPDATE */].call(plugin, {\n            cacheName,\n            event,\n            oldResponse,\n            newResponse: responseToCache,\n            request: effectiveRequest,\n        });\n    }\n};\nexport const cacheWrapper = {\n    put: putWrapper,\n    match: matchWrapper,\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { logger } from '../_private/logger.js';\nimport { quotaErrorCallbacks } from '../models/quotaErrorCallbacks.js';\nimport '../_version.js';\n/**\n * Runs all of the callback functions, one at a time sequentially, in the order\n * in which they were registered.\n *\n * @memberof module:workbox-core\n * @private\n */\nasync function executeQuotaErrorCallbacks() {\n    if (process.env.NODE_ENV !== 'production') {\n        logger.log(`About to run ${quotaErrorCallbacks.size} ` +\n            `callbacks to clean up caches.`);\n    }\n    for (const callback of quotaErrorCallbacks) {\n        await callback();\n        if (process.env.NODE_ENV !== 'production') {\n            logger.log(callback, 'is complete.');\n        }\n    }\n    if (process.env.NODE_ENV !== 'production') {\n        logger.log('Finished running callbacks.');\n    }\n}\nexport { executeQuotaErrorCallbacks };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { WorkboxError } from './WorkboxError.js';\nimport { logger } from './logger.js';\nimport { assert } from './assert.js';\nimport { getFriendlyURL } from '../_private/getFriendlyURL.js';\nimport { pluginUtils } from '../utils/pluginUtils.js';\nimport '../_version.js';\n/**\n * Wrapper around the fetch API.\n *\n * Will call requestWillFetch on available plugins.\n *\n * @param {Object} options\n * @param {Request|string} options.request\n * @param {Object} [options.fetchOptions]\n * @param {ExtendableEvent} [options.event]\n * @param {Array} [options.plugins=[]]\n * @return {Promise}\n *\n * @private\n * @memberof module:workbox-core\n */\nconst wrappedFetch = async ({ request, fetchOptions, event, plugins = [], }) => {\n    if (typeof request === 'string') {\n        request = new Request(request);\n    }\n    // We *should* be able to call `await event.preloadResponse` even if it's\n    // undefined, but for some reason, doing so leads to errors in our Node unit\n    // tests. To work around that, explicitly check preloadResponse's value first.\n    if (event instanceof FetchEvent && event.preloadResponse) {\n        const possiblePreloadResponse = await event.preloadResponse;\n        if (possiblePreloadResponse) {\n            if (process.env.NODE_ENV !== 'production') {\n                logger.log(`Using a preloaded navigation response for ` +\n                    `'${getFriendlyURL(request.url)}'`);\n            }\n            return possiblePreloadResponse;\n        }\n    }\n    if (process.env.NODE_ENV !== 'production') {\n        assert.isInstance(request, Request, {\n            paramName: 'request',\n            expectedClass: Request,\n            moduleName: 'workbox-core',\n            className: 'fetchWrapper',\n            funcName: 'wrappedFetch',\n        });\n    }\n    const failedFetchPlugins = pluginUtils.filter(plugins, \"fetchDidFail\" /* FETCH_DID_FAIL */);\n    // If there is a fetchDidFail plugin, we need to save a clone of the\n    // original request before it's either modified by a requestWillFetch\n    // plugin or before the original request's body is consumed via fetch().\n    const originalRequest = failedFetchPlugins.length > 0 ?\n        request.clone() : null;\n    try {\n        for (const plugin of plugins) {\n            if (\"requestWillFetch\" /* REQUEST_WILL_FETCH */ in plugin) {\n                const pluginMethod = plugin[\"requestWillFetch\" /* REQUEST_WILL_FETCH */];\n                const requestClone = request.clone();\n                request = await pluginMethod.call(plugin, {\n                    request: requestClone,\n                    event,\n                });\n                if (process.env.NODE_ENV !== 'production') {\n                    if (request) {\n                        assert.isInstance(request, Request, {\n                            moduleName: 'Plugin',\n                            funcName: \"cachedResponseWillBeUsed\" /* CACHED_RESPONSE_WILL_BE_USED */,\n                            isReturnValueProblem: true,\n                        });\n                    }\n                }\n            }\n        }\n    }\n    catch (err) {\n        throw new WorkboxError('plugin-error-request-will-fetch', {\n            thrownError: err,\n        });\n    }\n    // The request can be altered by plugins with `requestWillFetch` making\n    // the original request (Most likely from a `fetch` event) to be different\n    // to the Request we make. Pass both to `fetchDidFail` to aid debugging.\n    const pluginFilteredRequest = request.clone();\n    try {\n        let fetchResponse;\n        // See https://github.com/GoogleChrome/workbox/issues/1796\n        if (request.mode === 'navigate') {\n            fetchResponse = await fetch(request);\n        }\n        else {\n            fetchResponse = await fetch(request, fetchOptions);\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            logger.debug(`Network request for ` +\n                `'${getFriendlyURL(request.url)}' returned a response with ` +\n                `status '${fetchResponse.status}'.`);\n        }\n        for (const plugin of plugins) {\n            if (\"fetchDidSucceed\" /* FETCH_DID_SUCCEED */ in plugin) {\n                fetchResponse = await plugin[\"fetchDidSucceed\" /* FETCH_DID_SUCCEED */]\n                    .call(plugin, {\n                    event,\n                    request: pluginFilteredRequest,\n                    response: fetchResponse,\n                });\n                if (process.env.NODE_ENV !== 'production') {\n                    if (fetchResponse) {\n                        assert.isInstance(fetchResponse, Response, {\n                            moduleName: 'Plugin',\n                            funcName: \"fetchDidSucceed\" /* FETCH_DID_SUCCEED */,\n                            isReturnValueProblem: true,\n                        });\n                    }\n                }\n            }\n        }\n        return fetchResponse;\n    }\n    catch (error) {\n        if (process.env.NODE_ENV !== 'production') {\n            logger.error(`Network request for ` +\n                `'${getFriendlyURL(request.url)}' threw an error.`, error);\n        }\n        for (const plugin of failedFetchPlugins) {\n            await plugin[\"fetchDidFail\" /* FETCH_DID_FAIL */].call(plugin, {\n                error,\n                event,\n                originalRequest: originalRequest.clone(),\n                request: pluginFilteredRequest.clone(),\n            });\n        }\n        throw error;\n    }\n};\nconst fetchWrapper = {\n    fetch: wrappedFetch,\n};\nexport { fetchWrapper };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { cacheNames } from 'workbox-core/_private/cacheNames.js';\nimport { cacheWrapper } from 'workbox-core/_private/cacheWrapper.js';\nimport { fetchWrapper } from 'workbox-core/_private/fetchWrapper.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { copyResponse } from 'workbox-core/copyResponse.js';\nimport { createCacheKey } from './utils/createCacheKey.js';\nimport { printCleanupDetails } from './utils/printCleanupDetails.js';\nimport { printInstallDetails } from './utils/printInstallDetails.js';\nimport './_version.js';\n/**\n * Performs efficient precaching of assets.\n *\n * @memberof module:workbox-precaching\n */\nclass PrecacheController {\n    /**\n     * Create a new PrecacheController.\n     *\n     * @param {string} [cacheName] An optional name for the cache, to override\n     * the default precache name.\n     */\n    constructor(cacheName) {\n        this._cacheName = cacheNames.getPrecacheName(cacheName);\n        this._urlsToCacheKeys = new Map();\n        this._urlsToCacheModes = new Map();\n        this._cacheKeysToIntegrities = new Map();\n    }\n    /**\n     * This method will add items to the precache list, removing duplicates\n     * and ensuring the information is valid.\n     *\n     * @param {\n     * Array\n     * } entries Array of entries to precache.\n     */\n    addToCacheList(entries) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isArray(entries, {\n                moduleName: 'workbox-precaching',\n                className: 'PrecacheController',\n                funcName: 'addToCacheList',\n                paramName: 'entries',\n            });\n        }\n        const urlsToWarnAbout = [];\n        for (const entry of entries) {\n            // See https://github.com/GoogleChrome/workbox/issues/2259\n            if (typeof entry === 'string') {\n                urlsToWarnAbout.push(entry);\n            }\n            else if (entry && entry.revision === undefined) {\n                urlsToWarnAbout.push(entry.url);\n            }\n            const { cacheKey, url } = createCacheKey(entry);\n            const cacheMode = (typeof entry !== 'string' && entry.revision) ?\n                'reload' : 'default';\n            if (this._urlsToCacheKeys.has(url) &&\n                this._urlsToCacheKeys.get(url) !== cacheKey) {\n                throw new WorkboxError('add-to-cache-list-conflicting-entries', {\n                    firstEntry: this._urlsToCacheKeys.get(url),\n                    secondEntry: cacheKey,\n                });\n            }\n            if (typeof entry !== 'string' && entry.integrity) {\n                if (this._cacheKeysToIntegrities.has(cacheKey) &&\n                    this._cacheKeysToIntegrities.get(cacheKey) !== entry.integrity) {\n                    throw new WorkboxError('add-to-cache-list-conflicting-integrities', {\n                        url,\n                    });\n                }\n                this._cacheKeysToIntegrities.set(cacheKey, entry.integrity);\n            }\n            this._urlsToCacheKeys.set(url, cacheKey);\n            this._urlsToCacheModes.set(url, cacheMode);\n            if (urlsToWarnAbout.length > 0) {\n                const warningMessage = `Workbox is precaching URLs without revision ` +\n                    `info: ${urlsToWarnAbout.join(', ')}\\nThis is generally NOT safe. ` +\n                    `Learn more at https://bit.ly/wb-precache`;\n                if (process.env.NODE_ENV === 'production') {\n                    // Use console directly to display this warning without bloating\n                    // bundle sizes by pulling in all of the logger codebase in prod.\n                    console.warn(warningMessage);\n                }\n                else {\n                    logger.warn(warningMessage);\n                }\n            }\n        }\n    }\n    /**\n     * Precaches new and updated assets. Call this method from the service worker\n     * install event.\n     *\n     * @param {Object} options\n     * @param {Event} [options.event] The install event (if needed).\n     * @param {Array} [options.plugins] Plugins to be used for fetching\n     * and caching during install.\n     * @return {Promise}\n     */\n    async install({ event, plugins } = {}) {\n        if (process.env.NODE_ENV !== 'production') {\n            if (plugins) {\n                assert.isArray(plugins, {\n                    moduleName: 'workbox-precaching',\n                    className: 'PrecacheController',\n                    funcName: 'install',\n                    paramName: 'plugins',\n                });\n            }\n        }\n        const toBePrecached = [];\n        const alreadyPrecached = [];\n        const cache = await self.caches.open(this._cacheName);\n        const alreadyCachedRequests = await cache.keys();\n        const existingCacheKeys = new Set(alreadyCachedRequests.map((request) => request.url));\n        for (const [url, cacheKey] of this._urlsToCacheKeys) {\n            if (existingCacheKeys.has(cacheKey)) {\n                alreadyPrecached.push(url);\n            }\n            else {\n                toBePrecached.push({ cacheKey, url });\n            }\n        }\n        const precacheRequests = toBePrecached.map(({ cacheKey, url }) => {\n            const integrity = this._cacheKeysToIntegrities.get(cacheKey);\n            const cacheMode = this._urlsToCacheModes.get(url);\n            return this._addURLToCache({\n                cacheKey,\n                cacheMode,\n                event,\n                integrity,\n                plugins,\n                url,\n            });\n        });\n        await Promise.all(precacheRequests);\n        const updatedURLs = toBePrecached.map((item) => item.url);\n        if (process.env.NODE_ENV !== 'production') {\n            printInstallDetails(updatedURLs, alreadyPrecached);\n        }\n        return {\n            updatedURLs,\n            notUpdatedURLs: alreadyPrecached,\n        };\n    }\n    /**\n     * Deletes assets that are no longer present in the current precache manifest.\n     * Call this method from the service worker activate event.\n     *\n     * @return {Promise}\n     */\n    async activate() {\n        const cache = await self.caches.open(this._cacheName);\n        const currentlyCachedRequests = await cache.keys();\n        const expectedCacheKeys = new Set(this._urlsToCacheKeys.values());\n        const deletedURLs = [];\n        for (const request of currentlyCachedRequests) {\n            if (!expectedCacheKeys.has(request.url)) {\n                await cache.delete(request);\n                deletedURLs.push(request.url);\n            }\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            printCleanupDetails(deletedURLs);\n        }\n        return { deletedURLs };\n    }\n    /**\n     * Requests the entry and saves it to the cache if the response is valid.\n     * By default, any response with a status code of less than 400 (including\n     * opaque responses) is considered valid.\n     *\n     * If you need to use custom criteria to determine what's valid and what\n     * isn't, then pass in an item in `options.plugins` that implements the\n     * `cacheWillUpdate()` lifecycle event.\n     *\n     * @private\n     * @param {Object} options\n     * @param {string} options.cacheKey The string to use a cache key.\n     * @param {string} options.url The URL to fetch and cache.\n     * @param {string} [options.cacheMode] The cache mode for the network request.\n     * @param {Event} [options.event] The install event (if passed).\n     * @param {Array} [options.plugins] An array of plugins to apply to\n     * fetch and caching.\n     * @param {string} [options.integrity] The value to use for the `integrity`\n     * field when making the request.\n     */\n    async _addURLToCache({ cacheKey, url, cacheMode, event, plugins, integrity }) {\n        const request = new Request(url, {\n            integrity,\n            cache: cacheMode,\n            credentials: 'same-origin',\n        });\n        let response = await fetchWrapper.fetch({\n            event,\n            plugins,\n            request,\n        });\n        // Allow developers to override the default logic about what is and isn't\n        // valid by passing in a plugin implementing cacheWillUpdate(), e.g.\n        // a `CacheableResponsePlugin` instance.\n        let cacheWillUpdatePlugin;\n        for (const plugin of (plugins || [])) {\n            if ('cacheWillUpdate' in plugin) {\n                cacheWillUpdatePlugin = plugin;\n            }\n        }\n        const isValidResponse = cacheWillUpdatePlugin ?\n            // Use a callback if provided. It returns a truthy value if valid.\n            // NOTE: invoke the method on the plugin instance so the `this` context\n            // is correct.\n            await cacheWillUpdatePlugin.cacheWillUpdate({ event, request, response }) :\n            // Otherwise, default to considering any response status under 400 valid.\n            // This includes, by default, considering opaque responses valid.\n            response.status < 400;\n        // Consider this a failure, leading to the `install` handler failing, if\n        // we get back an invalid response.\n        if (!isValidResponse) {\n            throw new WorkboxError('bad-precaching-response', {\n                url,\n                status: response.status,\n            });\n        }\n        // Redirected responses cannot be used to satisfy a navigation request, so\n        // any redirected response must be \"copied\" rather than cloned, so the new\n        // response doesn't contain the `redirected` flag. See:\n        // https://bugs.chromium.org/p/chromium/issues/detail?id=669363&desc=2#c1\n        if (response.redirected) {\n            response = await copyResponse(response);\n        }\n        await cacheWrapper.put({\n            event,\n            plugins,\n            response,\n            // `request` already uses `url`. We may be able to reuse it.\n            request: cacheKey === url ? request : new Request(cacheKey),\n            cacheName: this._cacheName,\n            matchOptions: {\n                ignoreSearch: true,\n            },\n        });\n    }\n    /**\n     * Returns a mapping of a precached URL to the corresponding cache key, taking\n     * into account the revision information for the URL.\n     *\n     * @return {Map} A URL to cache key mapping.\n     */\n    getURLsToCacheKeys() {\n        return this._urlsToCacheKeys;\n    }\n    /**\n     * Returns a list of all the URLs that have been precached by the current\n     * service worker.\n     *\n     * @return {Array} The precached URLs.\n     */\n    getCachedURLs() {\n        return [...this._urlsToCacheKeys.keys()];\n    }\n    /**\n     * Returns the cache key used for storing a given URL. If that URL is\n     * unversioned, like `/index.html', then the cache key will be the original\n     * URL with a search parameter appended to it.\n     *\n     * @param {string} url A URL whose cache key you want to look up.\n     * @return {string} The versioned URL that corresponds to a cache key\n     * for the original URL, or undefined if that URL isn't precached.\n     */\n    getCacheKeyForURL(url) {\n        const urlObject = new URL(url, location.href);\n        return this._urlsToCacheKeys.get(urlObject.href);\n    }\n    /**\n     * This acts as a drop-in replacement for [`cache.match()`](https://developer.mozilla.org/en-US/docs/Web/API/Cache/match)\n     * with the following differences:\n     *\n     * - It knows what the name of the precache is, and only checks in that cache.\n     * - It allows you to pass in an \"original\" URL without versioning parameters,\n     * and it will automatically look up the correct cache key for the currently\n     * active revision of that URL.\n     *\n     * E.g., `matchPrecache('index.html')` will find the correct precached\n     * response for the currently active service worker, even if the actual cache\n     * key is `'/index.html?__WB_REVISION__=1234abcd'`.\n     *\n     * @param {string|Request} request The key (without revisioning parameters)\n     * to look up in the precache.\n     * @return {Promise}\n     */\n    async matchPrecache(request) {\n        const url = request instanceof Request ? request.url : request;\n        const cacheKey = this.getCacheKeyForURL(url);\n        if (cacheKey) {\n            const cache = await self.caches.open(this._cacheName);\n            return cache.match(cacheKey);\n        }\n        return undefined;\n    }\n    /**\n     * Returns a function that can be used within a\n     * {@link module:workbox-routing.Route} that will find a response for the\n     * incoming request against the precache.\n     *\n     * If for an unexpected reason there is a cache miss for the request,\n     * this will fall back to retrieving the `Response` via `fetch()` when\n     * `fallbackToNetwork` is `true`.\n     *\n     * @param {boolean} [fallbackToNetwork=true] Whether to attempt to get the\n     * response from the network if there's a precache miss.\n     * @return {module:workbox-routing~handlerCallback}\n     */\n    createHandler(fallbackToNetwork = true) {\n        return async ({ request }) => {\n            try {\n                const response = await this.matchPrecache(request);\n                if (response) {\n                    return response;\n                }\n                // This shouldn't normally happen, but there are edge cases:\n                // https://github.com/GoogleChrome/workbox/issues/1441\n                throw new WorkboxError('missing-precache-entry', {\n                    cacheName: this._cacheName,\n                    url: request instanceof Request ? request.url : request,\n                });\n            }\n            catch (error) {\n                if (fallbackToNetwork) {\n                    if (process.env.NODE_ENV !== 'production') {\n                        logger.debug(`Unable to respond with precached response. ` +\n                            `Falling back to network.`, error);\n                    }\n                    return fetch(request);\n                }\n                throw error;\n            }\n        };\n    }\n    /**\n     * Returns a function that looks up `url` in the precache (taking into\n     * account revision information), and returns the corresponding `Response`.\n     *\n     * If for an unexpected reason there is a cache miss when looking up `url`,\n     * this will fall back to retrieving the `Response` via `fetch()` when\n     * `fallbackToNetwork` is `true`.\n     *\n     * @param {string} url The precached URL which will be used to lookup the\n     * `Response`.\n     * @param {boolean} [fallbackToNetwork=true] Whether to attempt to get the\n     * response from the network if there's a precache miss.\n     * @return {module:workbox-routing~handlerCallback}\n     */\n    createHandlerBoundToURL(url, fallbackToNetwork = true) {\n        const cacheKey = this.getCacheKeyForURL(url);\n        if (!cacheKey) {\n            throw new WorkboxError('non-precached-url', { url });\n        }\n        const handler = this.createHandler(fallbackToNetwork);\n        const request = new Request(url);\n        return () => handler({ request });\n    }\n}\nexport { PrecacheController };\n","export const isNav = event => event.request.mode === 'navigate';\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\nexport const cacheOkAndOpaquePlugin = {\n    /**\n     * Returns a valid response (to allow caching) if the status is 200 (OK) or\n     * 0 (opaque).\n     *\n     * @param {Object} options\n     * @param {Response} options.response\n     * @return {Response|null}\n     *\n     * @private\n     */\n    cacheWillUpdate: async ({ response }) => {\n        if (response.status === 200 || response.status === 0) {\n            return response;\n        }\n        return null;\n    },\n};\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { cacheNames } from 'workbox-core/_private/cacheNames.js';\nimport { cacheWrapper } from 'workbox-core/_private/cacheWrapper.js';\nimport { fetchWrapper } from 'workbox-core/_private/fetchWrapper.js';\nimport { getFriendlyURL } from 'workbox-core/_private/getFriendlyURL.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { messages } from './utils/messages.js';\nimport { cacheOkAndOpaquePlugin } from './plugins/cacheOkAndOpaquePlugin.js';\nimport './_version.js';\n/**\n * An implementation of a\n * [network first]{@link https://developers.google.com/web/fundamentals/instant-and-offline/offline-cookbook/#network-falling-back-to-cache}\n * request strategy.\n *\n * By default, this strategy will cache responses with a 200 status code as\n * well as [opaque responses]{@link https://developers.google.com/web/tools/workbox/guides/handle-third-party-requests}.\n * Opaque responses are are cross-origin requests where the response doesn't\n * support [CORS]{@link https://enable-cors.org/}.\n *\n * If the network request fails, and there is no cache match, this will throw\n * a `WorkboxError` exception.\n *\n * @memberof module:workbox-strategies\n */\nclass NetworkFirst {\n    /**\n     * @param {Object} options\n     * @param {string} options.cacheName Cache name to store and retrieve\n     * requests. Defaults to cache names provided by\n     * [workbox-core]{@link module:workbox-core.cacheNames}.\n     * @param {Array} options.plugins [Plugins]{@link https://developers.google.com/web/tools/workbox/guides/using-plugins}\n     * to use in conjunction with this caching strategy.\n     * @param {Object} options.fetchOptions Values passed along to the\n     * [`init`](https://developer.mozilla.org/en-US/docs/Web/API/WindowOrWorkerGlobalScope/fetch#Parameters)\n     * of all fetch() requests made by this strategy.\n     * @param {Object} options.matchOptions [`CacheQueryOptions`](https://w3c.github.io/ServiceWorker/#dictdef-cachequeryoptions)\n     * @param {number} options.networkTimeoutSeconds If set, any network requests\n     * that fail to respond within the timeout will fallback to the cache.\n     *\n     * This option can be used to combat\n     * \"[lie-fi]{@link https://developers.google.com/web/fundamentals/performance/poor-connectivity/#lie-fi}\"\n     * scenarios.\n     */\n    constructor(options = {}) {\n        this._cacheName = cacheNames.getRuntimeName(options.cacheName);\n        if (options.plugins) {\n            const isUsingCacheWillUpdate = options.plugins.some((plugin) => !!plugin.cacheWillUpdate);\n            this._plugins = isUsingCacheWillUpdate ?\n                options.plugins : [cacheOkAndOpaquePlugin, ...options.plugins];\n        }\n        else {\n            // No plugins passed in, use the default plugin.\n            this._plugins = [cacheOkAndOpaquePlugin];\n        }\n        this._networkTimeoutSeconds = options.networkTimeoutSeconds || 0;\n        if (process.env.NODE_ENV !== 'production') {\n            if (this._networkTimeoutSeconds) {\n                assert.isType(this._networkTimeoutSeconds, 'number', {\n                    moduleName: 'workbox-strategies',\n                    className: 'NetworkFirst',\n                    funcName: 'constructor',\n                    paramName: 'networkTimeoutSeconds',\n                });\n            }\n        }\n        this._fetchOptions = options.fetchOptions;\n        this._matchOptions = options.matchOptions;\n    }\n    /**\n     * This method will perform a request strategy and follows an API that\n     * will work with the\n     * [Workbox Router]{@link module:workbox-routing.Router}.\n     *\n     * @param {Object} options\n     * @param {Request|string} options.request A request to run this strategy for.\n     * @param {Event} [options.event] The event that triggered the request.\n     * @return {Promise}\n     */\n    async handle({ event, request }) {\n        const logs = [];\n        if (typeof request === 'string') {\n            request = new Request(request);\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(request, Request, {\n                moduleName: 'workbox-strategies',\n                className: 'NetworkFirst',\n                funcName: 'handle',\n                paramName: 'makeRequest',\n            });\n        }\n        const promises = [];\n        let timeoutId;\n        if (this._networkTimeoutSeconds) {\n            const { id, promise } = this._getTimeoutPromise({ request, event, logs });\n            timeoutId = id;\n            promises.push(promise);\n        }\n        const networkPromise = this._getNetworkPromise({ timeoutId, request, event, logs });\n        promises.push(networkPromise);\n        // Promise.race() will resolve as soon as the first promise resolves.\n        let response = await Promise.race(promises);\n        // If Promise.race() resolved with null, it might be due to a network\n        // timeout + a cache miss. If that were to happen, we'd rather wait until\n        // the networkPromise resolves instead of returning null.\n        // Note that it's fine to await an already-resolved promise, so we don't\n        // have to check to see if it's still \"in flight\".\n        if (!response) {\n            response = await networkPromise;\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            logger.groupCollapsed(messages.strategyStart('NetworkFirst', request));\n            for (const log of logs) {\n                logger.log(log);\n            }\n            messages.printFinalResponse(response);\n            logger.groupEnd();\n        }\n        if (!response) {\n            throw new WorkboxError('no-response', { url: request.url });\n        }\n        return response;\n    }\n    /**\n     * @param {Object} options\n     * @param {Request} options.request\n     * @param {Array} options.logs A reference to the logs array\n     * @param {Event} [options.event]\n     * @return {Promise}\n     *\n     * @private\n     */\n    _getTimeoutPromise({ request, logs, event }) {\n        let timeoutId;\n        const timeoutPromise = new Promise((resolve) => {\n            const onNetworkTimeout = async () => {\n                if (process.env.NODE_ENV !== 'production') {\n                    logs.push(`Timing out the network response at ` +\n                        `${this._networkTimeoutSeconds} seconds.`);\n                }\n                resolve(await this._respondFromCache({ request, event }));\n            };\n            timeoutId = setTimeout(onNetworkTimeout, this._networkTimeoutSeconds * 1000);\n        });\n        return {\n            promise: timeoutPromise,\n            id: timeoutId,\n        };\n    }\n    /**\n     * @param {Object} options\n     * @param {number|undefined} options.timeoutId\n     * @param {Request} options.request\n     * @param {Array} options.logs A reference to the logs Array.\n     * @param {Event} [options.event]\n     * @return {Promise}\n     *\n     * @private\n     */\n    async _getNetworkPromise({ timeoutId, request, logs, event }) {\n        let error;\n        let response;\n        try {\n            response = await fetchWrapper.fetch({\n                request,\n                event,\n                fetchOptions: this._fetchOptions,\n                plugins: this._plugins,\n            });\n        }\n        catch (err) {\n            error = err;\n        }\n        if (timeoutId) {\n            clearTimeout(timeoutId);\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            if (response) {\n                logs.push(`Got response from network.`);\n            }\n            else {\n                logs.push(`Unable to get a response from the network. Will respond ` +\n                    `with a cached response.`);\n            }\n        }\n        if (error || !response) {\n            response = await this._respondFromCache({ request, event });\n            if (process.env.NODE_ENV !== 'production') {\n                if (response) {\n                    logs.push(`Found a cached response in the '${this._cacheName}'` +\n                        ` cache.`);\n                }\n                else {\n                    logs.push(`No response found in the '${this._cacheName}' cache.`);\n                }\n            }\n        }\n        else {\n            // Keep the service worker alive while we put the request in the cache\n            const responseClone = response.clone();\n            const cachePut = cacheWrapper.put({\n                cacheName: this._cacheName,\n                request,\n                response: responseClone,\n                event,\n                plugins: this._plugins,\n            });\n            if (event) {\n                try {\n                    // The event has been responded to so we can keep the SW alive to\n                    // respond to the request\n                    event.waitUntil(cachePut);\n                }\n                catch (err) {\n                    if (process.env.NODE_ENV !== 'production') {\n                        logger.warn(`Unable to ensure service worker stays alive when ` +\n                            `updating cache for '${getFriendlyURL(request.url)}'.`);\n                    }\n                }\n            }\n        }\n        return response;\n    }\n    /**\n     * Used if the network timeouts or fails to make the request.\n     *\n     * @param {Object} options\n     * @param {Request} request The request to match in the cache\n     * @param {Event} [options.event]\n     * @return {Promise}\n     *\n     * @private\n     */\n    _respondFromCache({ event, request }) {\n        return cacheWrapper.match({\n            cacheName: this._cacheName,\n            request,\n            event,\n            matchOptions: this._matchOptions,\n            plugins: this._plugins,\n        });\n    }\n}\nexport { NetworkFirst };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport '../_version.js';\n/**\n * A class that wraps common IndexedDB functionality in a promise-based API.\n * It exposes all the underlying power and functionality of IndexedDB, but\n * wraps the most commonly used features in a way that's much simpler to use.\n *\n * @private\n */\nexport class DBWrapper {\n    /**\n     * @param {string} name\n     * @param {number} version\n     * @param {Object=} [callback]\n     * @param {!Function} [callbacks.onupgradeneeded]\n     * @param {!Function} [callbacks.onversionchange] Defaults to\n     *     DBWrapper.prototype._onversionchange when not specified.\n     * @private\n     */\n    constructor(name, version, { onupgradeneeded, onversionchange, } = {}) {\n        this._db = null;\n        this._name = name;\n        this._version = version;\n        this._onupgradeneeded = onupgradeneeded;\n        this._onversionchange = onversionchange || (() => this.close());\n    }\n    /**\n     * Returns the IDBDatabase instance (not normally needed).\n     * @return {IDBDatabase|undefined}\n     *\n     * @private\n     */\n    get db() {\n        return this._db;\n    }\n    /**\n     * Opens a connected to an IDBDatabase, invokes any onupgradedneeded\n     * callback, and added an onversionchange callback to the database.\n     *\n     * @return {IDBDatabase}\n     * @private\n     */\n    async open() {\n        if (this._db)\n            return;\n        this._db = await new Promise((resolve, reject) => {\n            // This flag is flipped to true if the timeout callback runs prior\n            // to the request failing or succeeding. Note: we use a timeout instead\n            // of an onblocked handler since there are cases where onblocked will\n            // never never run. A timeout better handles all possible scenarios:\n            // https://github.com/w3c/IndexedDB/issues/223\n            let openRequestTimedOut = false;\n            setTimeout(() => {\n                openRequestTimedOut = true;\n                reject(new Error('The open request was blocked and timed out'));\n            }, this.OPEN_TIMEOUT);\n            const openRequest = indexedDB.open(this._name, this._version);\n            openRequest.onerror = () => reject(openRequest.error);\n            openRequest.onupgradeneeded = (evt) => {\n                if (openRequestTimedOut) {\n                    openRequest.transaction.abort();\n                    openRequest.result.close();\n                }\n                else if (typeof this._onupgradeneeded === 'function') {\n                    this._onupgradeneeded(evt);\n                }\n            };\n            openRequest.onsuccess = () => {\n                const db = openRequest.result;\n                if (openRequestTimedOut) {\n                    db.close();\n                }\n                else {\n                    db.onversionchange = this._onversionchange.bind(this);\n                    resolve(db);\n                }\n            };\n        });\n        return this;\n    }\n    /**\n     * Polyfills the native `getKey()` method. Note, this is overridden at\n     * runtime if the browser supports the native method.\n     *\n     * @param {string} storeName\n     * @param {*} query\n     * @return {Array}\n     * @private\n     */\n    async getKey(storeName, query) {\n        return (await this.getAllKeys(storeName, query, 1))[0];\n    }\n    /**\n     * Polyfills the native `getAll()` method. Note, this is overridden at\n     * runtime if the browser supports the native method.\n     *\n     * @param {string} storeName\n     * @param {*} query\n     * @param {number} count\n     * @return {Array}\n     * @private\n     */\n    async getAll(storeName, query, count) {\n        return await this.getAllMatching(storeName, { query, count });\n    }\n    /**\n     * Polyfills the native `getAllKeys()` method. Note, this is overridden at\n     * runtime if the browser supports the native method.\n     *\n     * @param {string} storeName\n     * @param {*} query\n     * @param {number} count\n     * @return {Array}\n     * @private\n     */\n    async getAllKeys(storeName, query, count) {\n        const entries = await this.getAllMatching(storeName, { query, count, includeKeys: true });\n        return entries.map((entry) => entry.key);\n    }\n    /**\n     * Supports flexible lookup in an object store by specifying an index,\n     * query, direction, and count. This method returns an array of objects\n     * with the signature .\n     *\n     * @param {string} storeName\n     * @param {Object} [opts]\n     * @param {string} [opts.index] The index to use (if specified).\n     * @param {*} [opts.query]\n     * @param {IDBCursorDirection} [opts.direction]\n     * @param {number} [opts.count] The max number of results to return.\n     * @param {boolean} [opts.includeKeys] When true, the structure of the\n     *     returned objects is changed from an array of values to an array of\n     *     objects in the form {key, primaryKey, value}.\n     * @return {Array}\n     * @private\n     */\n    async getAllMatching(storeName, { index, query = null, // IE/Edge errors if query === `undefined`.\n    direction = 'next', count, includeKeys = false, } = {}) {\n        return await this.transaction([storeName], 'readonly', (txn, done) => {\n            const store = txn.objectStore(storeName);\n            const target = index ? store.index(index) : store;\n            const results = [];\n            const request = target.openCursor(query, direction);\n            request.onsuccess = () => {\n                const cursor = request.result;\n                if (cursor) {\n                    results.push(includeKeys ? cursor : cursor.value);\n                    if (count && results.length >= count) {\n                        done(results);\n                    }\n                    else {\n                        cursor.continue();\n                    }\n                }\n                else {\n                    done(results);\n                }\n            };\n        });\n    }\n    /**\n     * Accepts a list of stores, a transaction type, and a callback and\n     * performs a transaction. A promise is returned that resolves to whatever\n     * value the callback chooses. The callback holds all the transaction logic\n     * and is invoked with two arguments:\n     *   1. The IDBTransaction object\n     *   2. A `done` function, that's used to resolve the promise when\n     *      when the transaction is done, if passed a value, the promise is\n     *      resolved to that value.\n     *\n     * @param {Array} storeNames An array of object store names\n     *     involved in the transaction.\n     * @param {string} type Can be `readonly` or `readwrite`.\n     * @param {!Function} callback\n     * @return {*} The result of the transaction ran by the callback.\n     * @private\n     */\n    async transaction(storeNames, type, callback) {\n        await this.open();\n        return await new Promise((resolve, reject) => {\n            const txn = this._db.transaction(storeNames, type);\n            txn.onabort = () => reject(txn.error);\n            txn.oncomplete = () => resolve();\n            callback(txn, (value) => resolve(value));\n        });\n    }\n    /**\n     * Delegates async to a native IDBObjectStore method.\n     *\n     * @param {string} method The method name.\n     * @param {string} storeName The object store name.\n     * @param {string} type Can be `readonly` or `readwrite`.\n     * @param {...*} args The list of args to pass to the native method.\n     * @return {*} The result of the transaction.\n     * @private\n     */\n    async _call(method, storeName, type, ...args) {\n        const callback = (txn, done) => {\n            const objStore = txn.objectStore(storeName);\n            // TODO(philipwalton): Fix this underlying TS2684 error.\n            // @ts-ignore\n            const request = objStore[method].apply(objStore, args);\n            request.onsuccess = () => done(request.result);\n        };\n        return await this.transaction([storeName], type, callback);\n    }\n    /**\n     * Closes the connection opened by `DBWrapper.open()`. Generally this method\n     * doesn't need to be called since:\n     *   1. It's usually better to keep a connection open since opening\n     *      a new connection is somewhat slow.\n     *   2. Connections are automatically closed when the reference is\n     *      garbage collected.\n     * The primary use case for needing to close a connection is when another\n     * reference (typically in another tab) needs to upgrade it and would be\n     * blocked by the current, open connection.\n     *\n     * @private\n     */\n    close() {\n        if (this._db) {\n            this._db.close();\n            this._db = null;\n        }\n    }\n}\n// Exposed on the prototype to let users modify the default timeout on a\n// per-instance or global basis.\nDBWrapper.prototype.OPEN_TIMEOUT = 2000;\n// Wrap native IDBObjectStore methods according to their mode.\nconst methodsToWrap = {\n    readonly: ['get', 'count', 'getKey', 'getAll', 'getAllKeys'],\n    readwrite: ['add', 'put', 'clear', 'delete'],\n};\nfor (const [mode, methods] of Object.entries(methodsToWrap)) {\n    for (const method of methods) {\n        if (method in IDBObjectStore.prototype) {\n            // Don't use arrow functions here since we're outside of the class.\n            DBWrapper.prototype[method] =\n                async function (storeName, ...args) {\n                    return await this._call(method, storeName, mode, ...args);\n                };\n        }\n    }\n}\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { getOrCreateDefaultRouter } from './utils/getOrCreateDefaultRouter.js';\nimport './_version.js';\n/**\n * If a Route throws an error while handling a request, this `handler`\n * will be called and given a chance to provide a response.\n *\n * @param {module:workbox-routing~handlerCallback} handler A callback\n * function that returns a Promise resulting in a Response.\n *\n * @memberof module:workbox-routing\n */\nfunction setCatchHandler(handler) {\n    const defaultRouter = getOrCreateDefaultRouter();\n    defaultRouter.setCatchHandler(handler);\n}\nexport { setCatchHandler };\n","import { registerRoute, setCatchHandler } from 'workbox-routing';\nimport { precacheAndRoute, getCacheKeyForURL } from 'workbox-precaching';\nimport { isNav } from './utils';\nimport { NETWORK_HANDLER, PRECACHING_OPTIONS } from './contants';\n\nexport function getFiles() {\n\treturn self.__WB_MANIFEST;\n}\n\nexport function setupPrecaching(precacheFiles, precachingOptions) {\n\tprecacheAndRoute(precacheFiles, precachingOptions || PRECACHING_OPTIONS);\n}\n\nexport function setupRouting() {\n\t/**\n\t * Adding this before `precacheAndRoute` lets us handle all\n\t * the navigation requests even if they are in precache.\n\t */\n\tregisterRoute(({ event }) => isNav(event), NETWORK_HANDLER);\n\n\tsetCatchHandler(({ event }) => {\n\t\tif (isNav(event)) {\n\t\t\treturn caches.match(getCacheKeyForURL('/index.html'));\n\t\t}\n\t\treturn Response.error();\n\t});\n}\n\nexport { PRECACHING_OPTIONS };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { cacheNames as _cacheNames } from './_private/cacheNames.js';\nimport './_version.js';\n/**\n * Get the current cache names and prefix/suffix used by Workbox.\n *\n * `cacheNames.precache` is used for precached assets,\n * `cacheNames.googleAnalytics` is used by `workbox-google-analytics` to\n * store `analytics.js`, and `cacheNames.runtime` is used for everything else.\n *\n * `cacheNames.prefix` can be used to retrieve just the current prefix value.\n * `cacheNames.suffix` can be used to retrieve just the current suffix value.\n *\n * @return {Object} An object with `precache`, `runtime`, `prefix`, and\n *     `googleAnalytics` properties.\n *\n * @memberof module:workbox-core\n */\nconst cacheNames = {\n    get googleAnalytics() {\n        return _cacheNames.getGoogleAnalyticsName();\n    },\n    get precache() {\n        return _cacheNames.getPrecacheName();\n    },\n    get prefix() {\n        return _cacheNames.getPrefix();\n    },\n    get runtime() {\n        return _cacheNames.getRuntimeName();\n    },\n    get suffix() {\n        return _cacheNames.getSuffix();\n    },\n};\nexport { cacheNames };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { assert } from 'workbox-core/_private/assert.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { getFriendlyURL } from 'workbox-core/_private/getFriendlyURL.js';\nimport { logger } from 'workbox-core/_private/logger.js';\nimport './_version.js';\n/**\n * This class allows you to set up rules determining what\n * status codes and/or headers need to be present in order for a\n * [`Response`](https://developer.mozilla.org/en-US/docs/Web/API/Response)\n * to be considered cacheable.\n *\n * @memberof module:workbox-cacheable-response\n */\nclass CacheableResponse {\n    /**\n     * To construct a new CacheableResponse instance you must provide at least\n     * one of the `config` properties.\n     *\n     * If both `statuses` and `headers` are specified, then both conditions must\n     * be met for the `Response` to be considered cacheable.\n     *\n     * @param {Object} config\n     * @param {Array} [config.statuses] One or more status codes that a\n     * `Response` can have and be considered cacheable.\n     * @param {Object} [config.headers] A mapping of header names\n     * and expected values that a `Response` can have and be considered cacheable.\n     * If multiple headers are provided, only one needs to be present.\n     */\n    constructor(config = {}) {\n        if (process.env.NODE_ENV !== 'production') {\n            if (!(config.statuses || config.headers)) {\n                throw new WorkboxError('statuses-or-headers-required', {\n                    moduleName: 'workbox-cacheable-response',\n                    className: 'CacheableResponse',\n                    funcName: 'constructor',\n                });\n            }\n            if (config.statuses) {\n                assert.isArray(config.statuses, {\n                    moduleName: 'workbox-cacheable-response',\n                    className: 'CacheableResponse',\n                    funcName: 'constructor',\n                    paramName: 'config.statuses',\n                });\n            }\n            if (config.headers) {\n                assert.isType(config.headers, 'object', {\n                    moduleName: 'workbox-cacheable-response',\n                    className: 'CacheableResponse',\n                    funcName: 'constructor',\n                    paramName: 'config.headers',\n                });\n            }\n        }\n        this._statuses = config.statuses;\n        this._headers = config.headers;\n    }\n    /**\n     * Checks a response to see whether it's cacheable or not, based on this\n     * object's configuration.\n     *\n     * @param {Response} response The response whose cacheability is being\n     * checked.\n     * @return {boolean} `true` if the `Response` is cacheable, and `false`\n     * otherwise.\n     */\n    isResponseCacheable(response) {\n        if (process.env.NODE_ENV !== 'production') {\n            assert.isInstance(response, Response, {\n                moduleName: 'workbox-cacheable-response',\n                className: 'CacheableResponse',\n                funcName: 'isResponseCacheable',\n                paramName: 'response',\n            });\n        }\n        let cacheable = true;\n        if (this._statuses) {\n            cacheable = this._statuses.includes(response.status);\n        }\n        if (this._headers && cacheable) {\n            cacheable = Object.keys(this._headers).some((headerName) => {\n                return response.headers.get(headerName) === this._headers[headerName];\n            });\n        }\n        if (process.env.NODE_ENV !== 'production') {\n            if (!cacheable) {\n                logger.groupCollapsed(`The request for ` +\n                    `'${getFriendlyURL(response.url)}' returned a response that does ` +\n                    `not meet the criteria for being cached.`);\n                logger.groupCollapsed(`View cacheability criteria here.`);\n                logger.log(`Cacheable statuses: ` +\n                    JSON.stringify(this._statuses));\n                logger.log(`Cacheable headers: ` +\n                    JSON.stringify(this._headers, null, 2));\n                logger.groupEnd();\n                const logFriendlyHeaders = {};\n                response.headers.forEach((value, key) => {\n                    logFriendlyHeaders[key] = value;\n                });\n                logger.groupCollapsed(`View response status and headers here.`);\n                logger.log(`Response status: ` + response.status);\n                logger.log(`Response headers: ` +\n                    JSON.stringify(logFriendlyHeaders, null, 2));\n                logger.groupEnd();\n                logger.groupCollapsed(`View full response details here.`);\n                logger.log(response.headers);\n                logger.log(response);\n                logger.groupEnd();\n                logger.groupEnd();\n            }\n        }\n        return cacheable;\n    }\n}\nexport { CacheableResponse };\n","import { NetworkFirst } from 'workbox-strategies';\nimport { cacheNames } from 'workbox-core';\nimport { CacheableResponsePlugin } from 'workbox-cacheable-response';\n\nexport const PRECACHING_OPTIONS = {};\n\nexport const NETWORK_HANDLER = new NetworkFirst({\n\t// this cache is plunged with every new service worker deploy so we dont need to care about purging the cache.\n\tcacheName: cacheNames.precache,\n\tnetworkTimeoutSeconds: 5, // if u dont start getting headers within 5 sec fallback to cache.\n\tplugins: [\n\t\tnew CacheableResponsePlugin({\n\t\t\tstatuses: [200], // only cache valid responses, not opaque responses e.g. wifi portal.\n\t\t}),\n\t],\n});\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { logger } from 'workbox-core/_private/logger.js';\nimport { WorkboxError } from 'workbox-core/_private/WorkboxError.js';\nimport { Route } from './Route.js';\nimport { RegExpRoute } from './RegExpRoute.js';\nimport { getOrCreateDefaultRouter } from './utils/getOrCreateDefaultRouter.js';\nimport './_version.js';\n/**\n * Easily register a RegExp, string, or function with a caching\n * strategy to a singleton Router instance.\n *\n * This method will generate a Route for you if needed and\n * call [registerRoute()]{@link module:workbox-routing.Router#registerRoute}.\n *\n * @param {RegExp|string|module:workbox-routing.Route~matchCallback|module:workbox-routing.Route} capture\n * If the capture param is a `Route`, all other arguments will be ignored.\n * @param {module:workbox-routing~handlerCallback} [handler] A callback\n * function that returns a Promise resulting in a Response. This parameter\n * is required if `capture` is not a `Route` object.\n * @param {string} [method='GET'] The HTTP method to match the Route\n * against.\n * @return {module:workbox-routing.Route} The generated `Route`(Useful for\n * unregistering).\n *\n * @memberof module:workbox-routing\n */\nfunction registerRoute(capture, handler, method) {\n    let route;\n    if (typeof capture === 'string') {\n        const captureUrl = new URL(capture, location.href);\n        if (process.env.NODE_ENV !== 'production') {\n            if (!(capture.startsWith('/') || capture.startsWith('http'))) {\n                throw new WorkboxError('invalid-string', {\n                    moduleName: 'workbox-routing',\n                    funcName: 'registerRoute',\n                    paramName: 'capture',\n                });\n            }\n            // We want to check if Express-style wildcards are in the pathname only.\n            // TODO: Remove this log message in v4.\n            const valueToCheck = capture.startsWith('http') ?\n                captureUrl.pathname : capture;\n            // See https://github.com/pillarjs/path-to-regexp#parameters\n            const wildcards = '[*:?+]';\n            if ((new RegExp(`${wildcards}`)).exec(valueToCheck)) {\n                logger.debug(`The '$capture' parameter contains an Express-style wildcard ` +\n                    `character (${wildcards}). Strings are now always interpreted as ` +\n                    `exact matches; use a RegExp for partial or wildcard matches.`);\n            }\n        }\n        const matchCallback = ({ url }) => {\n            if (process.env.NODE_ENV !== 'production') {\n                if ((url.pathname === captureUrl.pathname) &&\n                    (url.origin !== captureUrl.origin)) {\n                    logger.debug(`${capture} only partially matches the cross-origin URL ` +\n                        `${url}. This route will only handle cross-origin requests ` +\n                        `if they match the entire URL.`);\n                }\n            }\n            return url.href === captureUrl.href;\n        };\n        // If `capture` is a string then `handler` and `method` must be present.\n        route = new Route(matchCallback, handler, method);\n    }\n    else if (capture instanceof RegExp) {\n        // If `capture` is a `RegExp` then `handler` and `method` must be present.\n        route = new RegExpRoute(capture, handler, method);\n    }\n    else if (typeof capture === 'function') {\n        // If `capture` is a function then `handler` and `method` must be present.\n        route = new Route(capture, handler, method);\n    }\n    else if (capture instanceof Route) {\n        route = capture;\n    }\n    else {\n        throw new WorkboxError('unsupported-route-type', {\n            moduleName: 'workbox-routing',\n            funcName: 'registerRoute',\n            paramName: 'capture',\n        });\n    }\n    const defaultRouter = getOrCreateDefaultRouter();\n    defaultRouter.registerRoute(route);\n    return route;\n}\nexport { registerRoute };\n","/*\n  Copyright 2018 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { CacheableResponse } from './CacheableResponse.js';\nimport './_version.js';\n/**\n * A class implementing the `cacheWillUpdate` lifecycle callback. This makes it\n * easier to add in cacheability checks to requests made via Workbox's built-in\n * strategies.\n *\n * @memberof module:workbox-cacheable-response\n */\nclass CacheableResponsePlugin {\n    /**\n     * To construct a new CacheableResponsePlugin instance you must provide at\n     * least one of the `config` properties.\n     *\n     * If both `statuses` and `headers` are specified, then both conditions must\n     * be met for the `Response` to be considered cacheable.\n     *\n     * @param {Object} config\n     * @param {Array} [config.statuses] One or more status codes that a\n     * `Response` can have and be considered cacheable.\n     * @param {Object} [config.headers] A mapping of header names\n     * and expected values that a `Response` can have and be considered cacheable.\n     * If multiple headers are provided, only one needs to be present.\n     */\n    constructor(config) {\n        /**\n         * @param {Object} options\n         * @param {Response} options.response\n         * @return {Response|null}\n         * @private\n         */\n        this.cacheWillUpdate = async ({ response }) => {\n            if (this._cacheableResponse.isResponseCacheable(response)) {\n                return response;\n            }\n            return null;\n        };\n        this._cacheableResponse = new CacheableResponse(config);\n    }\n}\nexport { CacheableResponsePlugin };\n","/*\n  Copyright 2019 Google LLC\n\n  Use of this source code is governed by an MIT-style\n  license that can be found in the LICENSE file or at\n  https://opensource.org/licenses/MIT.\n*/\nimport { getOrCreatePrecacheController } from './utils/getOrCreatePrecacheController.js';\nimport './_version.js';\n/**\n * Takes in a URL, and returns the corresponding URL that could be used to\n * lookup the entry in the precache.\n *\n * If a relative URL is provided, the location of the service worker file will\n * be used as the base.\n *\n * For precached entries without revision information, the cache key will be the\n * same as the original URL.\n *\n * For precached entries with revision information, the cache key will be the\n * original URL with the addition of a query parameter used for keeping track of\n * the revision info.\n *\n * @param {string} url The URL whose cache key to look up.\n * @return {string} The cache key that corresponds to that URL.\n *\n * @memberof module:workbox-precaching\n */\nfunction getCacheKeyForURL(url) {\n    const precacheController = getOrCreatePrecacheController();\n    return precacheController.getCacheKeyForURL(url);\n}\nexport { getCacheKeyForURL };\n","\"use strict\";\n// @ts-ignore\ntry {\n    self['workbox:core:5.1.3'] && _();\n}\ncatch (e) { }\n"]}
\ No newline at end of file
diff --git a/size-plugin.json b/size-plugin.json
index 9f1d48e..9607fe5 100644
--- a/size-plugin.json
+++ b/size-plugin.json
@@ -1 +1 @@
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diff --git a/src/routes/ApprendimentoSistemiArtificiali.js b/src/routes/ApprendimentoSistemiArtificiali.js
index 1f1a806..e37f791 100644
--- a/src/routes/ApprendimentoSistemiArtificiali.js
+++ b/src/routes/ApprendimentoSistemiArtificiali.js
@@ -40,7 +40,7 @@ export default function(props) {
             
    
                 
                     
    
-                        NetLogo è un software di modellazione sistemi multiagente, da noi usat
+                        NetLogo è un software di modellazione sistemi multiagente, da noi usato per le lezioni di laboratorio.
                     
    
                     
    
                         Si può scaricare o usare da browser.
@@ -53,6 +53,82 @@ export default function(props) {
                     
    
                     
             
    
+            
    
+                
+                    
    
+                        Sono sistemi con le seguenti caratteristiche:
+                    
    
+                    
      
+                        
    • Autonomia: agiscono gli uni indipendentemente dagli altri
      • 
+                        
    • Reattività: percepiscono ciò che sta nel loro ambiente e reagiscono ai cambiamenti di quest'ultimo
      • 
+                        
    • Proattività: agiscono in maniera tale da portare a termine i loro obiettivi
      • 
+                        
    • Socialità: comunicano con gli altri agenti, scambiando informazioni
      • 
+                    
    
+                    
+                
+                    
    
+                        Hanno anche caratteristiche di livello più alto derivate dalle quattro precedenti:
+                    
    
+                    
      
+                        
    • Conoscenza
      • 
+                        
    • Intenzioni
      • 
+                        
    • Emozioni
      • 
+                        
    • Obblighi
      • 
+                        
    • Obiettivi
      • 
+                        
    • etc...
      • 
+                    
    
+                    
+                
+                    
    
+                        Gli agenti solitamente hanno anche:
+                    
    
+                    
      
+                        
    • Mobilità: possono muoversi nell'ambiente
      • 
+                        
    • Veridicità: producono informazioni corrette
      • 
+                        
    • Benevolenza: agiscono nel modo corretto
      • 
+                        
    • Razionalità: compiono le azioni necessarie per raggiungere i loro obiettivi, e non altre che glielo impedirebbero
      • 
+                    
    
+                    
+            
    
+            
    
+                
+                    
    
+                        Classificazione in base a come prende le decisioni un agente:
+                    
    
+                    
      
+                        
    • Logic-based: prende le decisioni attraverso deduzioni logiche
      • 
+                        
    • Reactive: mappa una reazione a ogni situazione dell'ambiente
      • 
+                        
    • Belief-desire-intention: per decidere, considera le proprie assunzioni sul mondo (belief), i propri desideri (desire) e le sue intenzioni correnti (intention)
      • 
+                        
    • Layered: utilizza diversi strati di capacità cognitive per giungere a una decisione
      • 
+                    
    
+                    
+                
+                    
    
+                        Classificazione in base a come sono definiti gli obiettivi di un agente:
+                    
    
+                    
      
+                        
    • Teleonomico: gli obiettivi sono predefiniti ed espliciti
      • 
+                        
    • Riflessivo: l'agente è libero di scegliere il suo obiettivo in base alle proprie percezioni interne
      • 
+                    
    
+                    
+                
+                    
    
+                        Classificazione in base a quanto conosce dell'ambiente un agente:
+                    
    
+                    
      
+                        
    • Cognitivo: l'agente è immediatamente a conoscenza di tutto l'ambiente
      • 
+                        
    • Reattivo: l'agente deve scoprire l'ambiente con le sue capacità sensoriali
      • 
+                    
    
+                    
+            
    
+            
    
+                
+                    
      
+                        
    • Distribuzione: più agenti possono coprire aree di ambiente più vaste, o elaborare più in fretta zone più dense di informazione
      • 
+                        
    • Rappresentazione: i sistemi multi-agente modellano più accuratamente il mondo reale
      • 
+                    
    
+                    
+            
    
         
     )
 }