MathJax.Hub.Config({delayJaxRegistration:!0}),MathJax.Ajax.Preloading("[MathJax]/jax/input/TeX/config.js","[MathJax]/jax/input/MathML/config.js","[MathJax]/jax/input/AsciiMath/config.js","[MathJax]/jax/output/HTML-CSS/config.js","[MathJax]/jax/output/NativeMML/config.js","[MathJax]/jax/output/PreviewHTML/config.js","[MathJax]/config/MMLorHTML.js","[MathJax]/extensions/tex2jax.js","[MathJax]/extensions/mml2jax.js","[MathJax]/extensions/asciimath2jax.js","[MathJax]/extensions/MathEvents.js","[MathJax]/extensions/MathZoom.js","[MathJax]/extensions/MathMenu.js","[MathJax]/jax/element/mml/jax.js","[MathJax]/extensions/toMathML.js","[MathJax]/extensions/TeX/noErrors.js","[MathJax]/extensions/TeX/noUndefined.js","[MathJax]/jax/input/TeX/jax.js","[MathJax]/extensions/TeX/AMSmath.js","[MathJax]/extensions/TeX/AMSsymbols.js","[MathJax]/jax/input/MathML/jax.js","[MathJax]/jax/input/AsciiMath/jax.js","[MathJax]/jax/output/PreviewHTML/jax.js","[MathJax]/extensions/fast-preview.js","[MathJax]/extensions/AssistiveMML.js","[MathJax]/extensions/a11y/accessibility-menu.js"),MathJax.Hub.Config({extensions:["[a11y]/accessibility-menu.js"]}),MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.9",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(t){return 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e+"#"+encodeURIComponent(t)},useLabelIds:!0}},resetEquationNumbers:function(){}}),MathJax.InputJax.TeX.Register("math/tex"),MathJax.InputJax.TeX.loadComplete("config.js"),MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.9",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:!1}}),MathJax.InputJax.MathML.Register("math/mml"),MathJax.InputJax.MathML.loadComplete("config.js"),MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.7.9",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{fixphi:!0,useMathMLspacing:!0,displaystyle:!0,decimalsign:"."}}),MathJax.InputJax.AsciiMath.Register("math/asciimath"),MathJax.InputJax.AsciiMath.loadComplete("config.js"),MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.7.9",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{noReflows:!0,matchFontHeight:!0,scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial 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MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter,MathJax.Hub.config.delayJaxRegistration||MathJax.OutputJax["HTML-CSS"].Register("jax/mml"),MathJax.Hub.Register.StartupHook("End Config",[function(t,e){var a=t.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:!0,minBrowserTranslate:function(e){var i,n=t.getJaxFor(e),s=["[Math]"],r=document.createElement("span",{className:"MathJax_Preview"});"TeX"===n.inputJax&&(n.root.Get("displaystyle")?(s=[(i=a.displayMathDelimiters)[0]+n.originalText+i[1]],a.multilineDisplay&&(s=s[0].split(/\n/))):s=[(i=a.inlineMathDelimiters)[0]+n.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+i[1]]);for(var 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a=MathJax.Hub.CombineConfig("MMLorHTML",{prefer:{MSIE:"MML",Firefox:"HTML",Opera:"HTML",Chrome:"HTML",Safari:"HTML",other:"HTML"}}),i="0.0"===e.version||e.versionAtLeast({Firefox:3,Opera:9.52,MSIE:6,Chrome:.3,Safari:2,Konqueror:4}[e]||0),n=e.isFirefox&&e.versionAtLeast("1.5")||e.isMSIE&&e.hasMathPlayer||e.isSafari&&e.versionAtLeast("5.0")||e.isOpera&&e.versionAtLeast("9.52");t.Register.StartupHook("End Config",(function(){var e=a.prefer&&"object"==typeof a.prefer?a.prefer[MathJax.Hub.Browser]||a.prefer.other||"HTML":a.prefer;i||n?!n||"MML"!==e&&i?(MathJax.OutputJax["HTML-CSS"]?MathJax.OutputJax["HTML-CSS"].Register("jax/mml"):t.config.jax.unshift("output/HTML-CSS"),t.Startup.signal.Post("HTML-CSS output selected")):(MathJax.OutputJax.NativeMML?MathJax.OutputJax.NativeMML.Register("jax/mml"):t.config.jax.unshift("output/NativeMML"),t.Startup.signal.Post("NativeMML output selected")):(t.PreProcess.disabled=!0,t.prepareScripts.disabled=!0,MathJax.Message.Set(["MathJaxNotSupported","Your 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t&&(t=document.getElementById(t)),t||(t=document.body),this.createPatterns()&&this.scanElement(t,t.nextSibling)},createPatterns:function(){var t,e,a=[],i=[],n=this.config;for(this.match={},t=0,e=n.inlineMath.length;t<e;t++)a.push(this.patternQuote(n.inlineMath[t][0])),this.match[n.inlineMath[t][0]]={mode:"",end:n.inlineMath[t][1],pattern:this.endPattern(n.inlineMath[t][1])};for(t=0,e=n.displayMath.length;t<e;t++)a.push(this.patternQuote(n.displayMath[t][0])),this.match[n.displayMath[t][0]]={mode:"; mode=display",end:n.displayMath[t][1],pattern:this.endPattern(n.displayMath[t][1])};a.length&&i.push(a.sort(this.sortLength).join("|")),n.processEnvironments&&i.push("\\\\begin\\{([^}]*)\\}"),n.processEscapes&&i.push("\\\\*\\\\\\$"),n.processRefs&&i.push("\\\\(eq)?ref\\{[^}]*\\}"),this.start=new RegExp(i.join("|"),"g"),this.skipTags=new RegExp("^("+n.skipTags.join("|")+")$","i");var s=[];return MathJax.Hub.config.preRemoveClass&&s.push(MathJax.Hub.config.preRemoveClass),n.ignoreClass&&s.push(n.ignoreClass),this.ignoreClass=s.length?new RegExp("(^| )("+s.join("|")+")( |$)"):/^$/,this.processClass=new RegExp("(^| )("+n.processClass+")( |$)"),i.length>0},patternQuote:function(t){return t.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(t){return new RegExp(this.patternQuote(t)+"|\\\\.|[{}]","g")},sortLength:function(t,e){return t.length!==e.length?e.length-t.length:t==e?0:t<e?-1:1},scanElement:function(t,e,a){for(var i,n,s,r;t&&t!=e;)"#text"===t.nodeName.toLowerCase()?a||(t=this.scanText(t)):(i=void 0===t.className?"":t.className,n=void 0===t.tagName?"":t.tagName,"string"!=typeof i&&(i=String(i)),r=this.processClass.exec(i),!t.firstChild||i.match(/(^| )MathJax/)||!r&&this.skipTags.exec(n)||(s=(a||this.ignoreClass.exec(i))&&!r,this.scanElement(t.firstChild,e,s))),t&&(t=t.nextSibling)},scanText:function(t){if(""==t.nodeValue.replace(/\s+/,""))return t;var 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t[0]==a.end&&(a.close&&0!==a.pcount||(a.close=e,a.cpos=this.pattern.lastIndex,a.clen=a.isBeginEnd?0:t[0].length),0===a.pcount&&(a.matched=!0,e=this.encloseMath(e),this.switchPattern(this.start))),"{"===t[0]?a.pcount++:"}"===t[0]&&a.pcount&&a.pcount--,e},prevEndMatch:function(){this.search.matched=!0;var t=this.encloseMath(this.search.close);return this.switchPattern(this.start),t},switchPattern:function(t){t.lastIndex=this.pattern.lastIndex,this.pattern=t,this.search.start=t===this.start},encloseMath:function(t){var e,a,i,n=this.search,s=n.close;for((s=n.cpos===s.length?s.nextSibling:s.splitText(n.cpos))||(e=s=MathJax.HTML.addText(n.close.parentNode,"")),n.close=s,a=n.opos?n.open.splitText(n.opos):n.open;(i=a.nextSibling)&&i!==s;){if(null!==i.nodeValue)"#comment"===i.nodeName?a.nodeValue+=i.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1"):a.nodeValue+=i.nodeValue;else{var r=this.ignoreTags[i.nodeName.toLowerCase()];a.nodeValue+=null==r?" 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t}},MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]),MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js"),MathJax.Extension.mml2jax={version:"2.7.9",config:{preview:"mathml"},MMLnamespace:"http://www.w3.org/1998/Math/MathML",PreProcess:function(t){this.configured||(this.config=MathJax.Hub.CombineConfig("mml2jax",this.config),this.config.Augment&&MathJax.Hub.Insert(this,this.config.Augment),this.InitBrowser(),this.configured=!0),"string"==typeof t&&(t=document.getElementById(t)),t||(t=document.body);var e,a,i=[];if(this.PushMathElements(i,t,"math"),this.PushMathElements(i,t,"math",this.MMLnamespace),void 0!==document.namespaces)try{for(e=0,a=document.namespaces.length;e<a;e++){var n=document.namespaces[e];n.urn===this.MMLnamespace&&this.PushMathElements(i,t,n.name+":math")}}catch(t){}else{var s=document.getElementsByTagName("html")[0];if(s)for(e=0,a=s.attributes.length;e<a;e++){var 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i=!1,n=MathJax.Hub.config.preRemoveClass;if((e.previousSibling||{}).className!==n){if("mathml"===a&&(i=!0,a=this.MathTagBug?"alttext":t.cloneNode(!0)),"alttext"===a||"altimg"===a){i=!0;var s=this.filterPreview(t.getAttribute("alttext"));if("alttext"===a)a=null!=s?MathJax.HTML.TextNode(s):null;else{var r=t.getAttribute("altimg");if(null!=r){var o={width:t.getAttribute("altimg-width"),height:t.getAttribute("altimg-height")};a=MathJax.HTML.Element("img",{src:r,alt:s,style:o})}else a=null}}var l;a&&(i?(l=MathJax.HTML.Element("span",{className:n})).appendChild(a):l=MathJax.HTML.Element("span",{className:n},a),e.parentNode.insertBefore(l,e))}}},filterPreview:function(t){return t},InitBrowser:function(){var t=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"<math><mi>x</mi><mspace 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o=document.documentElement||{},l=window.innerHeight||o.clientHeight||o.scrollHeight||0;x.prototype.msieAboutBug?(r.style.width="20em",r.style.position="absolute",r.style.left=Math.floor((document.documentElement.scrollWidth-r.offsetWidth)/2)+"px",r.style.top=Math.floor((l-r.offsetHeight)/3)+document.body.scrollTop+"px"):(r.style.marginLeft=Math.floor(-r.offsetWidth/2)+"px",r.style.top=Math.floor((l-r.offsetHeight)/3)+"px")},x.About.Remove=function(t){x.About.div&&(document.body.removeChild(x.About.div),delete x.About.div)},x.About.Keydown=function(t){t.keyCode!==h.ESCAPE&&("MathJax_AboutClose"!==this.id||t.keyCode!==h.SPACE&&t.keyCode!==h.RETURN)||(x.About.Remove(t),x.CurrentNode().focus(),o(t))},x.About.GetJax=function(t,e,a,i){var n=[];for(var s in e)e.hasOwnProperty(s)&&e[s]&&(i&&e[s].version||e[s].isa&&e[s].isa(e))&&n.push(u(a[0],a[1],e[s].id||s,e[s].version));n.sort();for(var r=0,o=n.length;r<o;r++)t.push(n[r],["br"]);return t},x.About.GetFont=function(){var t=MathJax.Hub.outputJax["jax/mml"][0]||{};return({SVG:"web SVG",CommonHTML:"web TeX","HTML-CSS":t.imgFonts?"image":(t.webFonts?"web":"local")+" "+t.fontInUse}[t.id]||"generic")+" fonts"},x.About.GetFormat=function(){var t=MathJax.Hub.outputJax["jax/mml"][0]||{};if("HTML-CSS"===t.id&&t.webFonts&&!t.imgFonts)return t.allowWebFonts.replace(/otf/,"woff or otf")+" fonts"},x.Help=function(t){a.Require("[MathJax]/extensions/HelpDialog.js",(function(){MathJax.Extension.Help.Dialog({type:t.type})}))},x.ShowSource=function(t){t||(t=window.event);var e={screenX:t.screenX,screenY:t.screenY};if(x.jax)if("MathML"===this.format){var n=MathJax.ElementJax.mml;if(n&&void 0!==n.mbase.prototype.toMathML)try{x.ShowSource.Text(x.jax.root.toMathML("",x.jax),t)}catch(t){if(!t.restart)throw t;i.After([this,x.ShowSource,e],t.restart)}else if(!a.loadingToMathML)return a.loadingToMathML=!0,x.ShowSource.Window(t),void i.Queue(a.Require("[MathJax]/extensions/toMathML.js"),(function(){delete 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t,i,s,r=a.outerHeight-a.innerHeight||30,o=a.outerWidth-a.innerWidth||30;o=Math.max(140,Math.min(Math.floor(.5*screen.width),n.offsetWidth+o+25)),r=Math.max(40,Math.min(Math.floor(.5*screen.height),n.offsetHeight+r+25)),x.prototype.msieHeightBug&&(r+=35),a.resizeTo(o,r);try{s=e.screenX}catch(t){}e&&null!=s&&(t=Math.max(0,Math.min(e.screenX-Math.floor(o/2),screen.width-o-20)),i=Math.max(0,Math.min(e.screenY-Math.floor(r/2),screen.height-r-20)),a.moveTo(t,i))}),50)}},x.Scale=function(){var e,a,i=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],s=i.length,r=100;for(e=0;e<s;e++)if(a=n[i[e]]){r=a.config.scale;break}var o=prompt(u("ScaleMath","Scale all mathematics (compared to surrounding text) by"),r+"%");if(o)if(o.match(/^\s*\d+(\.\d*)?\s*%?\s*$/))if(o=parseFloat(o)){if(o!==r){for(e=0;e<s;e++)(a=n[i[e]])&&(a.config.scale=o);x.cookie.scale=t.config.scale=o,x.saveCookie(),t.Queue(["Rerender",t])}}else alert(u("NonZeroScale","The scale should not be zero"));else alert(u("PercentScale","The scale should be a percentage (e.g., 120%%)"))},x.Zoom=function(){MathJax.Extension.MathZoom||a.Require("[MathJax]/extensions/MathZoom.js")},x.Renderer=function(){var a=t.outputJax["jax/mml"];if(a[0]!==g.settings.renderer){var i,n,s=t.Browser,r=x.Renderer.Messages;switch(g.settings.renderer){case"NativeMML":g.settings.warnedMML||(s.isChrome&&"24."!==s.version.substr(0,3)||s.isSafari&&!s.versionAtLeast("5.0")?i=r.MML.WebKit:s.isMSIE?s.hasMathPlayer||(i=r.MML.MSIE):i=s.isEdge?r.MML.WebKit:r.MML[s],n="warnedMML");break;case"SVG":g.settings.warnedSVG||s.isMSIE&&!d&&(i=r.SVG.MSIE)}if(i){if(i=u(i[0],i[1]),i+="\n\n",i+=u("SwitchAnyway","Switch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)"),x.cookie.renderer=a[0].id,x.saveCookie(),!confirm(i))return x.cookie.renderer=g.settings.renderer=e.Cookie.Get("menu").renderer,void x.saveCookie();n&&(x.cookie.warned=g.settings.warned=!0),x.cookie.renderer=g.settings.renderer,x.saveCookie()}t.Queue(["setRenderer",t,g.settings.renderer,"jax/mml"],["Rerender",t])}},x.Renderer.Messages={MML:{WebKit:["WebkitNativeMMLWarning","Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable."],MSIE:["MSIENativeMMLWarning","Internet Explorer requires the MathPlayer plugin in order to process MathML output."],Opera:["OperaNativeMMLWarning","Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly."],Safari:["SafariNativeMMLWarning","Your browser's native MathML does not implement all the features used by MathJax, so some expressions may not render properly."],Firefox:["FirefoxNativeMMLWarning","Your browser's native MathML does not implement all the features used by MathJax, so some expressions may not render properly."]},SVG:{MSIE:["MSIESVGWarning","SVG is not implemented in Internet Explorer prior to IE9 or when it is emulating IE8 or below. 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n=this.stack.Prev("nopop");(!n||n.Get("texClass")!==i.TEXCLASS.OP&&null==n.movesupsub)&&t.Error(["MisplacedLimits","%1 is allowed only on operators",e]);var s=this.stack.Top();"munderover"!==n.type||a?"msubsup"===n.type&&a&&(n=s.data[s.data.length-1]=i.munderover.apply(i.underover,n.data)):n=s.data[s.data.length-1]=i.msubsup.apply(i.subsup,n.data),n.movesupsub=!!a,n.Core().movablelimits=!1,n.movablelimits&&(n.movablelimits=!1)},Over:function(t,e,a){var i=o.over().With({name:t});e||a?(i.open=e,i.close=a):t.match(/withdelims$/)&&(i.open=this.GetDelimiter(t),i.close=this.GetDelimiter(t)),t.match(/^\\above/)?i.thickness=this.GetDimen(t):(t.match(/^\\atop/)||e||a)&&(i.thickness=0),this.Push(i)},Frac:function(t){var e=this.ParseArg(t),a=this.ParseArg(t);this.Push(i.mfrac(e,a))},Sqrt:function(e){var a=this.GetBrackets(e),n=this.GetArgument(e);"\\frac"===n&&(n+="{"+this.GetArgument(n)+"}{"+this.GetArgument(n)+"}");var 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e=this.ParseUpTo(t,"\\over"),a=this.ParseArg(t);this.Push(i.TeXAtom(i.munderover(a,null,e)).With({texClass:i.TEXCLASS.REL}))},HBox:function(t,e){this.Push.apply(this,this.InternalMath(this.GetArgument(t),e))},FBox:function(t){this.Push(i.menclose.apply(i,this.InternalMath(this.GetArgument(t))).With({notation:"box"}))},Not:function(t){this.Push(o.not())},Dots:function(t){this.Push(o.dots().With({ldots:this.mmlToken(i.mo(i.entity("#x2026")).With({stretchy:!1})),cdots:this.mmlToken(i.mo(i.entity("#x22EF")).With({stretchy:!1}))}))},Require:function(t){var e=this.GetArgument(t).replace(/.*\//,"").replace(/[^a-z0-9_.-]/gi,"");this.Extension(null,e)},Extension:function(i,n,s){(n=t.extensionDir+"/"+n).match(/\.js$/)||(n+=".js"),a.loaded[a.fileURL(n)]||(null!=i&&delete l[s||"macros"][i.replace(/^\\/,"")],e.RestartAfter(a.Require(n)))},Macro:function(e,a,i,n){if(i){var s=[];if(null!=n){var r=this.GetBrackets(e);s.push(null==r?n:r)}for(var o=s.length;o<i;o++)s.push(this.GetArgument(e));a=this.SubstituteArgs(s,a)}this.string=this.AddArgs(a,this.string.slice(this.i)),this.i=0,++this.macroCount>t.config.MAXMACROS&&t.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])},Matrix:function(e,a,i,n,s,r,l,h,u){var c=this.GetNext();""===c&&t.Error(["MissingArgFor","Missing argument for %1",e]),"{"===c?this.i++:(this.string=c+"}"+this.string.slice(this.i+1),this.i=0);var m=o.array().With({requireClose:!0,arraydef:{rowspacing:r||"4pt",columnspacing:s||"1em"}});h&&(m.isCases=!0),u&&(m.isNumbered=!0,m.arraydef.side=u),(a||i)&&(m.open=a,m.close=i),"D"===l&&(m.arraydef.displaystyle=!0),null!=n&&(m.arraydef.columnalign=n),this.Push(m)},Entry:function(e){if(this.Push(o.cell().With({isEntry:!0,name:e})),this.stack.Top().isCases){for(var a=this.string,i=0,n=-1,s=this.i,r=a.length;s<r;){var 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this.string.charAt(this.i).match(/\s/)},GetNext:function(){for(;this.nextIsSpace();)this.i++;return this.string.charAt(this.i)},GetCS:function(){var t=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);return t?(this.i+=t[1].length,t[1]):(this.i++," ")},GetArgument:function(e,a){switch(this.GetNext()){case"":return a||t.Error(["MissingArgFor","Missing argument for %1",e]),null;case"}":return a||t.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"]),null;case"\\":return this.i++,"\\"+this.GetCS();case"{":for(var i=++this.i,n=1;this.i<this.string.length;)switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":n++;break;case"}":if(0==--n)return this.string.slice(i,this.i-1)}t.Error(["MissingCloseBrace","Missing close brace"])}return this.string.charAt(this.i++)},GetBrackets:function(e,a){if("["!=this.GetNext())return a;for(var 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"+i.VARIANT[e.mathvariant])},PHTMLhandleStyle:function(t){this.style&&(t.style.cssText=this.style)},PHTMLhandleColor:function(t){this.mathcolor&&(t.style.color=this.mathcolor),this.mathbackground&&(t.style.backgroundColor=this.mathbackground)},PHTMLhandleScriptlevel:function(t){this.Get("scriptlevel")&&(t.className+=" MJXp-script")},PHTMLhandleText:function(t,e){for(var n,s,r=0,o=0,l=0,h=0,u=e.length;h<u;h++){s=e.charCodeAt(h),n=e.charAt(h),s>=55296&&s<56319&&(h++,s=(s-55296<<10)+(e.charCodeAt(h)-56320)+65536);var c=.7,m=.22,p=.5;s<127&&(n.match(/[A-Za-ehik-or-xz0-9]/)&&(m=0),n.match(/[A-HK-Z]/)?p=.67:n.match(/[IJ]/)&&(p=.36),n.match(/[acegm-su-z]/)?c=.45:n.match(/[ij]/)&&(c=.75),n.match(/[ijlt]/)&&(p=.28)),i.DELIMITERS[n]&&(p=i.DELIMITERS[n].w||.4),c>r&&(r=c),m>o&&(o=m),l+=p}this.CHML||(this.PHTML={}),this.PHTML={h:.9,d:.3,w:l,l:0,r:0,t:r,b:o},a.addText(t,e)},PHTMLbboxFor:function(t){return this.data[t]&&this.data[t].PHTML?this.data[t].PHTML:{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(t,e,a){if(this.isEmbellished()){var i=this.Core();if(i&&i!==this)return i.PHTMLcanStretch(t,e,a)}return!1},PHTMLstretchV:function(t,e){},PHTMLstretchH:function(t){},CoreParent:function(){for(var t=this;t&&t.isEmbellished()&&t.CoreMO()===this&&!t.isa(n.math);)t=t.Parent();return t},CoreText:function(t){if(!t)return"";if(t.isEmbellished())return t.CoreMO().data.join("");for(;(t.isa(n.mrow)||t.isa(n.TeXAtom)||t.isa(n.mstyle)||t.isa(n.mphantom))&&1===t.data.length&&t.data[0];)t=t.data[0];return t.isToken?t.data.join(""):""}}),n.chars.Augment({toPreviewHTML:function(t){var e=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(t,e)}}),n.entity.Augment({toPreviewHTML:function(t){var e=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(t,e)}}),n.math.Augment({toPreviewHTML:function(t){return t=this.PHTMLdefaultSpan(t),"block"===this.Get("display")&&(t.className+=" MJXp-display"),t}}),n.mo.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t),this.PHTMLadjustAccent(t);var e=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(0===e.scriptlevel?(this.PHTML.l=i.length2em(e.lspace),this.PHTML.r=i.length2em(e.rspace),t.style.marginLeft=i.Em(this.PHTML.l),t.style.marginRight=i.Em(this.PHTML.r)):(this.PHTML.l=.15,this.PHTML.r=.1),e.displaystyle&&e.largeop){var n=a.Element("span",{className:"MJXp-largeop"});n.appendChild(t.firstChild),t.appendChild(n),this.PHTML.h*=1.2,this.PHTML.d*=1.2,"∫"===this.data.join("")&&(n.className+=" MJXp-int")}return t},PHTMLadjustAccent:function(t){var e=this.CoreParent();if(e&&e.isa(n.munderover)&&1===this.CoreText(e.data[e.base]).length){var a,s=e.data[e.over],r=e.data[e.under],o=this.data.join("");s&&this===s.CoreMO()&&e.Get("accent")?a=i.REMAPACCENT[o]:r&&this===r.CoreMO()&&e.Get("accentunder")&&(a=i.REMAPACCENTUNDER[o]),a&&(o=t.innerHTML=a),o.match(/[\u02C6-\u02DC\u00A8]/)?this.PHTML.acc=-.52:"→"===o&&(this.PHTML.acc=-.15,this.PHTML.vec=!0)}},PHTMLcanStretch:function(t,e,a){if(!this.Get("stretchy"))return!1;var n=this.data.join("");if(n.length>1)return!1;var s=(n=i.DELIMITERS[n])&&n.dir===t.substr(0,1);return s&&(s=this.PHTML.h!==e||this.PHTML.d!==a||this.Get("minsize",!0)||this.Get("maxsize",!0)),s},PHTMLstretchV:function(t,e){var n=this.PHTMLspanElement(),s=this.PHTML,r=this.getValues("symmetric","maxsize","minsize");m=r.symmetric?2*Math.max(t-.25,e+.25):t+e,r.maxsize=i.length2em(r.maxsize,s.h+s.d),r.minsize=i.length2em(r.minsize,s.h+s.d);var o=(m=Math.max(r.minsize,Math.min(r.maxsize,m)))/(s.h+s.d-.3),l=a.Element("span",{style:{"font-size":i.Em(o)}});if(o>1.25){var h=Math.ceil(1.25/o*10);l.className="MJXp-right MJXp-scale"+h,l.style.marginLeft=i.Em(s.w*(h/10-1)+.07),s.w*=o*h/10}l.appendChild(n.firstChild),n.appendChild(l),r.symmetric&&(n.style.verticalAlign=i.Em(.25*(1-o)))}}),n.mspace.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t);var e=this.getValues("height","depth","width"),a=i.length2em(e.width),n=i.length2em(e.height),s=i.length2em(e.depth),r=this.PHTML;return r.w=a,r.h=n,r.d=s,a<0&&(i.lastIsInt||(t.style.marginLeft=i.Em(a)),a=0),t.style.width=i.Em(a),t.style.height=i.Em(n+s),s&&(t.style.verticalAlign=i.Em(-s)),t}}),n.mpadded.Augment({toPreviewHTML:function(t){var e=(t=this.PHTMLdefaultSpan(t,{childSpans:!0,className:"MJXp-box",forceChild:!0})).firstChild,a=this.getValues("width","height","depth","lspace","voffset"),n=this.PHTMLdimen(a.lspace),s=0,r=0,o=n.len,l=-n.len,h=0;return""!==a.width&&((n=this.PHTMLdimen(a.width,"w",0)).pm?l+=n.len:t.style.width=i.Em(n.len)),""!==a.height&&((n=this.PHTMLdimen(a.height,"h",0)).pm||(s+=-this.PHTMLbboxFor(0).h),s+=n.len),""!==a.depth&&((n=this.PHTMLdimen(a.depth,"d",0)).pm||(r+=-this.PHTMLbboxFor(0).d,h+=-n.len),r+=n.len),""!==a.voffset&&(s-=(n=this.PHTMLdimen(a.voffset)).len,r+=n.len,h+=n.len),s&&(e.style.marginTop=i.Em(s)),r&&(e.style.marginBottom=i.Em(r)),o&&(e.style.marginLeft=i.Em(o)),l&&(e.style.marginRight=i.Em(l)),h&&(t.style.verticalAlign=i.Em(h)),t},PHTMLdimen:function(t,e,a){null==a&&(a=-u);var n=(t=String(t)).match(/width|height|depth/),s=n?this.PHTML[n[0].charAt(0)]:e?this.PHTML[e]:0;return{len:i.length2em(t,s)||0,pm:!!t.match(/^[-+]/)}}}),n.munderover.Augment({toPreviewHTML:function(t){var e=this.getValues("displaystyle","accent","accentunder","align"),s=this.data[this.base];if(!e.displaystyle&&null!=s&&(s.movablelimits||s.CoreMO().Get("movablelimits")))return(t=n.msubsup.prototype.toPreviewHTML.call(this,t)).className=t.className.replace(/munderover/,"msubsup"),t;t=this.PHTMLdefaultSpan(t,{childSpans:!0,className:"",noBBox:!0});var r=this.PHTMLbboxFor(this.over),o=this.PHTMLbboxFor(this.under),l=this.PHTMLbboxFor(this.base),h=this.PHTML,u=r.acc;if(this.data[this.over]){t.lastChild.firstChild&&(t.lastChild.firstChild.style.marginLeft=r.l=t.lastChild.firstChild.style.marginRight=r.r=0);var c=a.Element("span",{},[["span",{className:"MJXp-over"}]]);c.firstChild.appendChild(t.lastChild),t.childNodes.length>(this.data[this.under]?1:0)&&c.firstChild.appendChild(t.firstChild),this.data[this.over].PHTMLhandleScriptlevel(c.firstChild.firstChild),null!=u&&(r.vec&&(c.firstChild.firstChild.firstChild.style.fontSize="60%",r.h*=.6,r.d*=.6,r.w*=.6),u=u-r.d+.1,null!=l.t&&(u+=l.t-l.h),c.firstChild.firstChild.style.marginBottom=i.Em(u)),t.firstChild?t.insertBefore(c,t.firstChild):t.appendChild(c)}return this.data[this.under]&&(t.lastChild.firstChild&&(t.lastChild.firstChild.style.marginLeft=o.l=t.lastChild.firstChild.marginRight=o.r=0),this.data[this.under].PHTMLhandleScriptlevel(t.lastChild)),h.w=Math.max(.8*r.w,.8*o.w,l.w),h.h=.8*(r.h+r.d+(u||0))+l.h,h.d=l.d+.8*(o.h+o.d),t}}),n.msubsup.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t,{noBBox:!0}),this.data[this.base]||(t.firstChild?t.insertBefore(a.Element("span"),t.firstChild):t.appendChild(a.Element("span")));var e=this.data[this.base],n=this.data[this.sub],s=this.data[this.sup];e||(e={bbox:{h:.8,d:.2}}),t.firstChild.style.marginRight=".05em";var r=Math.max(.4,e.PHTML.h-.4),o=Math.max(.2,e.PHTML.d+.1),l=this.PHTML;if(s&&n){var h=a.Element("span",{className:"MJXp-script-box",style:{height:i.Em(r+.8*s.PHTML.h+o+.8*n.PHTML.d),"vertical-align":i.Em(-o-.8*n.PHTML.d)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":i.Em(-(s.PHTML.d-.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":i.Em(-(s.PHTML.h-.05))}}]]]]]]);n.PHTMLhandleScriptlevel(h.firstChild),s.PHTMLhandleScriptlevel(h.lastChild),h.firstChild.firstChild.firstChild.appendChild(t.lastChild),h.lastChild.firstChild.firstChild.appendChild(t.lastChild),t.appendChild(h),l.h=Math.max(e.PHTML.h,.8*s.PHTML.h+r),l.d=Math.max(e.PHTML.d,.8*n.PHTML.d+o),l.w=e.PHTML.w+Math.max(s.PHTML.w,n.PHTML.w)+.07}else s?(t.lastChild.style.verticalAlign=i.Em(r),s.PHTMLhandleScriptlevel(t.lastChild),l.h=Math.max(e.PHTML.h,.8*s.PHTML.h+r),l.d=Math.max(e.PHTML.d,.8*s.PHTML.d-r),l.w=e.PHTML.w+s.PHTML.w+.07):n&&(t.lastChild.style.verticalAlign=i.Em(-o),n.PHTMLhandleScriptlevel(t.lastChild),l.h=Math.max(e.PHTML.h,.8*n.PHTML.h-o),l.d=Math.max(e.PHTML.d,.8*n.PHTML.d+o),l.w=e.PHTML.w+n.PHTML.w+.07);return t}}),n.mfrac.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t,{childSpans:!0,className:"MJXp-box",forceChild:!0,noBBox:!0});var e=this.getValues("linethickness","displaystyle");e.displaystyle||(this.data[0]&&this.data[0].PHTMLhandleScriptlevel(t.firstChild),this.data[1]&&this.data[1].PHTMLhandleScriptlevel(t.lastChild));var n=a.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(t.lastChild),t.appendChild(n);var s=this.PHTMLbboxFor(0),r=this.PHTMLbboxFor(1),o=this.PHTML;if(o.w=.8*Math.max(s.w,r.w),o.h=s.h+s.d+.1+.25,o.d=r.h+r.d-.25,o.l=o.r=.125,e.linethickness=Math.max(0,i.length2em(e.linethickness||"0",0)),e.linethickness){var l=n.firstChild.firstChild.firstChild,h=i.Em(e.linethickness);l.style.borderTop="none",l.style.borderBottom=(e.linethickness<.15?"1px":h)+" solid",l.style.margin=h+" 0",h=e.linethickness,n.style.marginTop=i.Em(3*h-1.2),t.style.verticalAlign=i.Em(1.5*h+.1),o.h+=1.5*h-.1,o.d+=1.5*h}else n.style.marginTop="-.7em";return t}}),n.msqrt.Augment({toPreviewHTML:function(t){return t=this.PHTMLdefaultSpan(t,{childSpans:!0,className:"MJXp-box",forceChild:!0,noBBox:!0}),this.PHTMLlayoutRoot(t,t.firstChild),t},PHTMLlayoutRoot:function(t,e){var n=this.PHTMLbboxFor(0),s=Math.ceil(100*(n.h+n.d+.14)),r=i.Em(14/s),o=a.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":s+"%","margin-top":r}},["√"]]]),l=a.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]),h=1.2/2.2*s/100;if(s>150){var u=Math.ceil(150/s*10);o.firstChild.className="MJXp-right MJXp-scale"+u,o.firstChild.style.marginLeft=i.Em(h*(u/10-1)/s*100),h=h*u/10,l.firstChild.style.borderTopWidth=i.Em(.08/Math.sqrt(u/10))}return l.appendChild(e),t.appendChild(o),t.appendChild(l),this.PHTML.h=n.h+.18,this.PHTML.d=n.d,this.PHTML.w=n.w+h,t}}),n.mroot.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t,{childSpans:!0,className:"MJXp-box",forceChild:!0,noBBox:!0});var e=this.PHTMLbboxFor(1),n=t.removeChild(t.lastChild),s=this.PHTMLlayoutRoot(a.Element("span"),t.firstChild);n.className="MJXp-script";var r=parseInt(s.firstChild.firstChild.style.fontSize),o=r/120*.55+.8*e.d,l=r/120*-.6;return r>150&&(l*=.95*Math.ceil(150/r*10)/10),n.style.marginRight=i.Em(l),n.style.verticalAlign=i.Em(o),-l>.8*e.w&&(n.style.marginLeft=i.Em(-l-.8*e.w)),t.appendChild(n),t.appendChild(s),this.PHTML.w+=Math.max(0,.8*e.w+l),this.PHTML.h=Math.max(this.PHTML.h,.8*e.h+o),t},PHTMLlayoutRoot:n.msqrt.prototype.PHTMLlayoutRoot}),n.mfenced.Augment({toPreviewHTML:function(t){t=this.PHTMLcreateSpan(t),this.PHTMLhandleStyle(t),this.PHTMLhandleColor(t),this.addFakeNodes(),this.PHTMLaddChild(t,"open",{});for(var e=0,a=this.data.length;e<a;e++)this.PHTMLaddChild(t,"sep"+e,{}),this.PHTMLaddChild(t,e,{});this.PHTMLaddChild(t,"close",{});var i=this.PHTML.h,n=this.PHTML.d;for(this.PHTMLstretchChild("open",i,n),e=0,a=this.data.length;e<a;e++)this.PHTMLstretchChild("sep"+e,i,n),this.PHTMLstretchChild(e,i,n);return this.PHTMLstretchChild("close",i,n),t}}),n.mrow.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t);for(var e=this.PHTML.h,a=this.PHTML.d,i=0,n=this.data.length;i<n;i++)this.PHTMLstretchChild(i,e,a);return t}}),n.mstyle.Augment({toPreviewHTML:function(t){return t=this.PHTMLdefaultSpan(t),this.PHTMLhandleScriptlevel(t),t}}),n.TeXAtom.Augment({toPreviewHTML:function(t){return(t=this.PHTMLdefaultSpan(t)).className="MJXp-mrow",t}}),n.mtable.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t,{noBBox:!0});var e,n,s,r,o=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","width"),l=MathJax.Hub.SplitList,h=l(o.columnspacing),u=l(o.rowspacing),c=l(o.columnalign),m=l(o.rowalign);for(e=0,n=h.length;e<n;e++)h[e]=i.length2em(h[e]);for(e=0,n=u.length;e<n;e++)u[e]=i.length2em(u[e]);for(var p=a.Element("span");t.firstChild;)p.appendChild(t.firstChild);t.appendChild(p);var d=0,f=0;for(e=0,n=this.data.length;e<n;e++){var g=this.data[e];if(g){var M=i.arrayEntry(u,e-1),x=i.arrayEntry(m,e),v=g.PHTML;g.PHTMLspanElement().style.verticalAlign=x;var b="mlabeledtr"===g.type?1:0;for(s=0,r=g.data.length;s<r-b;s++){var E=g.data[s+b];if(E){var T=i.arrayEntry(h,s-1),C=i.arrayEntry(c,s),y=E.PHTMLspanElement();s&&(v.w+=T,y.style.paddingLeft=i.Em(T)),e&&(y.style.paddingTop=i.Em(M)),y.style.textAlign=C}}d+=v.h+v.d,e&&(d+=M),v.w>f&&(f=v.w)}}var A=this.PHTML;return A.w=f,A.h=d/2+.25,A.d=d/2-.25,A.l=A.r=.125,t}}),n.mlabeledtr.Augment({PHTMLdefaultSpan:function(t,e){e||(e={}),t=this.PHTMLcreateSpan(t),this.PHTMLhandleStyle(t),this.PHTMLhandleColor(t),this.isToken&&this.PHTMLhandleToken(t);for(var a=1,i=this.data.length;a<i;a++)this.PHTMLaddChild(t,a,e);return t}}),n.semantics.Augment({toPreviewHTML:function(t){return t=this.PHTMLcreateSpan(t),this.data[0]&&(this.data[0].toPreviewHTML(t),MathJax.Hub.Insert(this.data[0].PHTML||{},this.PHTML)),t}}),n.annotation.Augment({toPreviewHTML:function(t){}}),n["annotation-xml"].Augment({toPreviewHTML:function(t){}}),MathJax.Hub.Register.StartupHook("onLoad",(function(){setTimeout(MathJax.Callback(["loadComplete",i,"jax.js"]),0)}))})),MathJax.Hub.Register.StartupHook("End Cookie",(function(){"None"!==e.config.menuSettings.zoom&&t.Require("[MathJax]/extensions/MathZoom.js")}))}(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.PreviewHTML),function(t,e,a){var i=t.config.menuSettings,n=MathJax.OutputJax,s=a.isMSIE&&(document.documentMode||0)<8,r=MathJax.Extension["fast-preview"]={version:"2.7.9",enabled:!0,config:t.CombineConfig("fast-preview",{Chunks:{EqnChunk:1e4,EqnChunkFactor:1,EqnChunkDelay:0},color:"inherit!important",updateTime:30,updateDelay:6,messageStyle:"none",disabled:a.isMSIE&&!a.versionAtLeast("8.0")}),Config:function(){var e,a,n,s,o;t.config["CHTML-preview"]&&MathJax.Hub.Config({"fast-preview":t.config["CHTML-preview"]});var l=this.config;l.disabled||null!=i.FastPreview||t.Config({menuSettings:{FastPreview:!0}}),i.FastPreview&&(MathJax.Ajax.Styles({".MathJax_Preview .MJXf-math":{color:l.color}}),t.Config({"HTML-CSS":l.Chunks,CommonHTML:l.Chunks,SVG:l.Chunks})),t.Register.MessageHook("Begin Math Output",(function(){!s&&r.Active()&&(e=t.processUpdateTime,a=t.processUpdateDelay,n=t.config.messageStyle,t.processUpdateTime=l.updateTime,t.processUpdateDelay=l.updateDelay,t.Config({messageStyle:l.messageStyle}),MathJax.Message.Clear(0,0),o=!0)})),t.Register.MessageHook("End Math Output",(function(){!s&&o&&(t.processUpdateTime=e,t.processUpdateDelay=a,t.Config({messageStyle:n}),s=!0)}))},Disable:function(){this.enabled=!1},Enable:function(){this.enabled=!0},Active:function(){return i.FastPreview&&this.enabled&&!(n[i.renderer]||{}).noFastPreview},Preview:function(t){if(this.Active()&&t.script.parentNode){var a=t.script.MathJax.preview||t.script.previousSibling;return a&&a.className===MathJax.Hub.config.preRemoveClass||(a=e.Element("span",{className:MathJax.Hub.config.preRemoveClass}),t.script.parentNode.insertBefore(a,t.script),t.script.MathJax.preview=a),a.innerHTML="",a.style.color=s?"black":"inherit",this.postFilter(a,t)}},postFilter:function(e,a){if(!a.math.root.toPreviewHTML){var i=MathJax.Callback.Queue();i.Push(["Require",MathJax.Ajax,"[MathJax]/jax/output/PreviewHTML/config.js"],["Require",MathJax.Ajax,"[MathJax]/jax/output/PreviewHTML/jax.js"]),t.RestartAfter(i.Push({}))}a.math.root.toPreviewHTML(e)},Register:function(e){t.Register.StartupHook(e+" Jax Require",(function(){MathJax.InputJax[e].postfilterHooks.Add(["Preview",MathJax.Extension["fast-preview"]],50)}))}};r.Register("TeX"),r.Register("MathML"),r.Register("AsciiMath"),t.Register.StartupHook("End Config",["Config",r]),t.Startup.signal.Post("fast-preview 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