/*
 *  /MathJax/config/TeX-MML-AM_HTMLorMML-full.js
 *  
 *  Copyright (c) 2010-2015 The MathJax Consortium
 *
 *  Part of the MathJax library.
 *  See http://www.mathjax.org for details.
 * 
 *  Licensed under the Apache License, Version 2.0;
 *  you may not use this file except in compliance with the License.
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 */

MathJax.Hub.Config({delayJaxRegistration: true});

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/CommonHTML/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/NativeMML/jax.js",
  "[MathJax]/jax/output/HTML-CSS/jax.js",
  "[MathJax]/jax/output/HTML-CSS/autoload/mtable.js",
  "[MathJax]/jax/output/CommonHTML/jax.js",
  "[MathJax]/extensions/CHTML-preview.js"
);

MathJax.Hub.Config({"v1.0-compatible":false});

MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.5.0",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/[:"'<>&]/g,"")},formatURL:function(a){return"#"+escape(a)},useLabelIds:true}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js");
MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.5.0",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js");
MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.5.0",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{fixphi:true,useMathMLspacing:true,displaystyle:true,decimalsign:"."}});MathJax.InputJax.AsciiMath.Register("math/asciimath");MathJax.InputJax.AsciiMath.loadComplete("config.js");
MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.5.1",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:true,matchFontHeight:true,scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",mtextFontInherit:false,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"},".MathJax .MJX-monospace":{"font-family":"monospace"},".MathJax .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px","z-index":401}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set(["MathJaxNotSupported","Your browser does not support MathJax"],null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js");
MathJax.OutputJax.NativeMML=MathJax.OutputJax({id:"NativeMML",version:"2.5.1",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{matchFontHeight:true,scale:100,minScaleAdjust:50,styles:{"div.MathJax_MathML":{"text-align":"center",margin:".75em 0px"}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.NativeMML.Register("jax/mml")}MathJax.OutputJax.NativeMML.loadComplete("config.js");
MathJax.OutputJax.CommonHTML=MathJax.OutputJax({id:"CommonHTML",version:"2.5.0",directory:MathJax.OutputJax.directory+"/CommonHTML",extensionDir:MathJax.OutputJax.extensionDir+"/CommonHTML",config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.CommonHTML.Register("jax/mml")}MathJax.OutputJax.CommonHTML.loadComplete("config.js");
(function(c,g){var f="2.5.0";var a=MathJax.Hub.CombineConfig("MMLorHTML",{prefer:{MSIE:"MML",Firefox:"HTML",Opera:"HTML",Chrome:"HTML",Safari:"HTML",other:"HTML"}});var e={Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4};var b=(g.version==="0.0"||g.versionAtLeast(e[g]||0));var d=(g.isFirefox&&g.versionAtLeast("1.5"))||(g.isMSIE&&g.hasMathPlayer)||(g.isSafari&&g.versionAtLeast("5.0"))||(g.isOpera&&g.versionAtLeast("9.52"));c.Register.StartupHook("End Config",function(){var h=(a.prefer&&typeof(a.prefer)==="object"?a.prefer[MathJax.Hub.Browser]||a.prefer.other||"HTML":a.prefer);if(b||d){if(d&&(h==="MML"||!b)){if(MathJax.OutputJax.NativeMML){MathJax.OutputJax.NativeMML.Register("jax/mml")}else{c.config.jax.unshift("output/NativeMML")}c.Startup.signal.Post("NativeMML output selected")}else{if(MathJax.OutputJax["HTML-CSS"]){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}else{c.config.jax.unshift("output/HTML-CSS")}c.Startup.signal.Post("HTML-CSS output selected")}}else{c.PreProcess.disabled=true;c.prepareScripts.disabled=true;MathJax.Message.Set(["MathJaxNotSupported","Your browser does not support MathJax"],null,4000);c.Startup.signal.Post("MathJax not supported")}})})(MathJax.Hub,MathJax.Hub.Browser);MathJax.Ajax.loadComplete("[MathJax]/config/MMLorHTML.js");
MathJax.Extension.tex2jax={version:"2.5.0",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],balanceBraces:true,skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c<a;c++){d.push(this.patternQuote(b.inlineMath[c][0]));this.match[b.inlineMath[c][0]]={mode:"",end:b.inlineMath[c][1],pattern:this.endPattern(b.inlineMath[c][1])}}for(c=0,a=b.displayMath.length;c<a;c++){d.push(this.patternQuote(b.displayMath[c][0]));this.match[b.displayMath[c][0]]={mode:"; mode=display",end:b.displayMath[c][1],pattern:this.endPattern(b.displayMath[c][1])}}if(d.length){e.push(d.sort(this.sortLength).join("|"))}if(b.processEnvironments){e.push("\\\\begin\\{([^}]*)\\}")}if(b.processEscapes){e.push("\\\\*\\\\\\$")}if(b.processRefs){e.push("\\\\(eq)?ref\\{[^}]*\\}")}this.start=new RegExp(e.join("|"),"g");this.skipTags=new RegExp("^("+b.skipTags.join("|")+")$","i");var f=[];if(MathJax.Hub.config.preRemoveClass){f.push(MathJax.Hub.config.preRemoveClass)}if(b.ignoreClass){f.push(b.ignoreClass)}this.ignoreClass=(f.length?new RegExp("(^| )("+f.join("|")+")( |$)"):/^$/);this.processClass=new RegExp("(^| )("+b.processClass+")( |$)");return(e.length>0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d<c?-1:1))},scanElement:function(c,b,g){var a,e,d,f;while(c&&c!=b){if(c.nodeName.toLowerCase()==="#text"){if(!g){c=this.scanText(c)}}else{a=(typeof(c.className)==="undefined"?"":c.className);e=(typeof(c.tagName)==="undefined"?"":c.tagName);if(typeof(a)!=="string"){a=String(a)}f=this.processClass.exec(a);if(c.firstChild&&!a.match(/(^| )MathJax/)&&(f||!this.skipTags.exec(e))){d=(g||this.ignoreClass.exec(a))&&!f;this.scanElement(c.firstChild,b,d)}}if(c){c=c.nextSibling}}},scanText:function(b){if(b.nodeValue.replace(/\s+/,"")==""){return b}var a,c;this.search={start:true};this.pattern=this.start;while(b){this.pattern.lastIndex=0;while(b&&b.nodeName.toLowerCase()==="#text"&&(a=this.pattern.exec(b.nodeValue))){if(this.search.start){b=this.startMatch(a,b)}else{b=this.endMatch(a,b)}}if(this.search.matched){b=this.encloseMath(b)}if(b){do{c=b;b=b.nextSibling}while(b&&(b.nodeName.toLowerCase()==="br"||b.nodeName.toLowerCase()==="#comment"));if(!b||b.nodeName!=="#text"){return(this.search.close?this.prevEndMatch():c)}}}return b},startMatch:function(a,b){var f=this.match[a[0]];if(f!=null){this.search={end:f.end,mode:f.mode,pcount:0,open:b,olen:a[0].length,opos:this.pattern.lastIndex-a[0].length};this.switchPattern(f.pattern)}else{if(a[0].substr(0,6)==="\\begin"){this.search={end:"\\end{"+a[1]+"}",mode:"; mode=display",pcount:0,open:b,olen:0,opos:this.pattern.lastIndex-a[0].length,isBeginEnd:true};this.switchPattern(this.endPattern(this.search.end))}else{if(a[0].substr(0,4)==="\\ref"||a[0].substr(0,6)==="\\eqref"){this.search={mode:"",end:"",open:b,pcount:0,olen:0,opos:this.pattern.lastIndex-a[0].length};return this.endMatch([""],b)}else{var d=a[0].substr(0,a[0].length-1),g,c;if(d.length%2===0){c=[d.replace(/\\\\/g,"\\")];g=1}else{c=[d.substr(1).replace(/\\\\/g,"\\"),"$"];g=0}c=MathJax.HTML.Element("span",null,c);var e=MathJax.HTML.TextNode(b.nodeValue.substr(0,a.index));b.nodeValue=b.nodeValue.substr(a.index+a[0].length-g);b.parentNode.insertBefore(c,b);b.parentNode.insertBefore(e,c);this.pattern.lastIndex=g}}}return b},endMatch:function(a,c){var b=this.search;if(a[0]==b.end){if(!b.close||b.pcount===0){b.close=c;b.cpos=this.pattern.lastIndex;b.clen=(b.isBeginEnd?0:a[0].length)}if(b.pcount===0){b.matched=true;c=this.encloseMath(c);this.switchPattern(this.start)}}else{if(a[0]==="{"){b.pcount++}else{if(a[0]==="}"&&b.pcount){b.pcount--}}}return c},prevEndMatch:function(){this.search.matched=true;var a=this.encloseMath(this.search.close);this.switchPattern(this.start);return a},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=(a===this.start)},encloseMath:function(b){var a=this.search,f=a.close,e,c;if(a.cpos===f.length){f=f.nextSibling}else{f=f.splitText(a.cpos)}if(!f){e=f=MathJax.HTML.addText(a.close.parentNode,"")}a.close=f;c=(a.opos?a.open.splitText(a.opos):a.open);while(c.nextSibling&&c.nextSibling!==f){if(c.nextSibling.nodeValue!==null){if(c.nextSibling.nodeName==="#comment"){c.nodeValue+=c.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{c.nodeValue+=c.nextSibling.nodeValue}}else{if(this.msieNewlineBug){c.nodeValue+=(c.nextSibling.nodeName.toLowerCase()==="br"?"\n":" ")}else{c.nodeValue+=" "}}c.parentNode.removeChild(c.nextSibling)}var d=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);if(this.config.preview!=="none"){this.createPreview(a.mode,d)}c=this.createMathTag(a.mode,d);this.search={};this.pattern.lastIndex=0;if(e){e.parentNode.removeChild(e)}return c},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(c,a){var b=this.config.preview;if(b==="none"){return}if(b==="TeX"){b=[this.filterPreview(a)]}if(b){b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b);this.insertNode(b)}},createMathTag:function(c,b){var a=document.createElement("script");a.type="math/tex"+c;MathJax.HTML.setScript(a,b);this.insertNode(a);return a},filterPreview:function(a){return a},msieNewlineBug:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9)};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js");
MathJax.Extension.mml2jax={version:"2.5.0",config:{preview:"mathml"},MMLnamespace:"http://www.w3.org/1998/Math/MathML",PreProcess:function(e){if(!this.configured){this.config=MathJax.Hub.CombineConfig("mml2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.InitBrowser();this.configured=true}if(typeof(e)==="string"){e=document.getElementById(e)}if(!e){e=document.body}var h=[];this.PushMathElements(h,e,"math");this.PushMathElements(h,e,"math",this.MMLnamespace);var d,b;if(typeof(document.namespaces)!=="undefined"){try{for(d=0,b=document.namespaces.length;d<b;d++){var f=document.namespaces[d];if(f.urn===this.MMLnamespace){this.PushMathElements(h,e,f.name+":math")}}}catch(g){}}else{var c=document.getElementsByTagName("html")[0];if(c){for(d=0,b=c.attributes.length;d<b;d++){var a=c.attributes[d];if(a.nodeName.substr(0,6)==="xmlns:"&&a.nodeValue===this.MMLnamespace){this.PushMathElements(h,e,a.nodeName.substr(6)+":math")}}}}this.ProcessMathArray(h)},PushMathElements:function(f,d,a,c){var h,g=MathJax.Hub.config.preRemoveClass;if(c){if(!d.getElementsByTagNameNS){return}h=d.getElementsByTagNameNS(c,a)}else{h=d.getElementsByTagName(a)}for(var e=0,b=h.length;e<b;e++){var j=h[e].parentNode;if(j&&j.className!==g&&!h[e].prefix===!c){f.push(h[e])}}},ProcessMathArray:function(c){var b,a=c.length;if(a){if(this.MathTagBug){for(b=0;b<a;b++){if(c[b].nodeName==="MATH"){this.ProcessMathFlattened(c[b])}else{this.ProcessMath(c[b])}}}else{for(b=0;b<a;b++){this.ProcessMath(c[b])}}}},ProcessMath:function(e){var d=e.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var a=document.createElement("script");a.type="math/mml";d.insertBefore(a,e);if(this.AttributeBug){var b=this.OuterHTML(e);if(this.CleanupHTML){b=b.replace(/<\?import .*?>/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/&nbsp;/g,"&#xA0;")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"</math>";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c="<!--"+e.nodeValue+"-->"}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b<a;b++){var d=e.attributes[b];if(d.specified&&d.nodeName.substr(0,10)!=="_moz-math-"){c+=" "+d.nodeName.toLowerCase().replace(/xmlns:xmlns/,"xmlns")+"=";var f=d.nodeValue;if(f==null&&d.nodeName==="style"&&e.style){f=e.style.cssText}c+='"'+this.quoteHTML(f)+'"'}}c+=">";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b<a;b++){c+=this.OuterHTML(e.childNodes[b])}c+="</"+e.nodeName.toLowerCase()+">"}}}return c},OuterHTML:function(d){if(d.nodeName.charAt(0)==="#"){return this.NodeHTML(d)}if(!this.AttributeBug){return d.outerHTML}var c=this.NodeHTML(d);for(var b=0,a=d.childNodes.length;b<a;b++){c+=this.OuterHTML(d.childNodes[b])}c+="</"+d.nodeName.toLowerCase()+">";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&#x26;").replace(/</g,"&lt;").replace(/>/g,"&gt;").replace(/\"/g,"&quot;")},createPreview:function(f,b){var g=this.config.preview;if(g==="none"){return}var a=false;if(g==="mathml"){a=true;if(this.MathTagBug){g="alttext"}else{g=f.cloneNode(true)}}if(g==="alttext"||g==="altimg"){a=true;var c=this.filterPreview(f.getAttribute("alttext"));if(g==="alttext"){if(c!=null){g=MathJax.HTML.TextNode(c)}else{g=null}}else{var h=f.getAttribute("altimg");if(h!=null){var e={width:f.getAttribute("altimg-width"),height:f.getAttribute("altimg-height")};g=MathJax.HTML.Element("img",{src:h,alt:c,style:e})}else{g=null}}}if(g){var d;if(a){d=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass});d.appendChild(g)}else{d=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},g)}b.parentNode.insertBefore(d,b)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"<math><mi>x</mi><mspace /></math>"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="&lt;"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax],5);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js");
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(function(a,d,f,c,j){var k="2.5.0";var i=a.CombineConfig("MathZoom",{styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"font-weight":"normal","font-style":"normal","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","box-shadow":"5px 5px 15px #AAAAAA","-webkit-box-shadow":"5px 5px 15px #AAAAAA","-moz-box-shadow":"5px 5px 15px #AAAAAA","-khtml-box-shadow":"5px 5px 15px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', 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true}if(!h[l]){return true}return h[l](n,m)},Click:function(m,l){if(this.settings.zoom==="Click"){return this.Zoom(m,l)}},DblClick:function(m,l){if(this.settings.zoom==="Double-Click"||this.settings.zoom==="DoubleClick"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(o,u){this.Remove();b.ClearHoverTimer();g.ClearSelection();var s=MathJax.OutputJax[u.jaxID];var p=s.getJaxFromMath(u);if(p.hover){b.UnHover(p)}var q=this.findContainer(u);var l=Math.floor(0.85*q.clientWidth),t=Math.max(document.body.clientHeight,document.documentElement.clientHeight);if(this.getOverflow(q)!=="visible"){t=Math.min(q.clientHeight,t)}t=Math.floor(0.85*t);var n=d.Element("span",{id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var z=n.lastChild,w=z.firstChild,r=n.firstChild;u.parentNode.insertBefore(n,u);u.parentNode.insertBefore(u,n);if(w.addEventListener){w.addEventListener("mousedown",this.Remove,true)}var m=z.offsetWidth||z.clientWidth;l-=m;t-=m;z.style.maxWidth=l+"px";z.style.maxHeight=t+"px";if(this.msieTrapEventBug){var y=d.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});n.insertBefore(y,z)}if(this.msieZIndexBug){var v=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});n.style.position="relative";n.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];n=v}var x=s.Zoom(p,w,u,l,t);if(this.msiePositionBug){if(this.msieSizeBug){z.style.height=x.zH+"px";z.style.width=x.zW+"px"}if(z.offsetHeight>t){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m<l&&z.offsetHeight-m<t){z.style.overflow="visible"}this.Position(z,x);if(this.msieTrapEventBug){y.style.height=z.clientHeight+"px";y.style.width=z.clientWidth+"px";y.style.left=(parseFloat(z.style.left)+z.clientLeft)+"px";y.style.top=(parseFloat(z.style.top)+z.clientTop)+"px"}z.style.visibility="";if(this.settings.zoom==="Hover"){r.onmouseover=this.Remove}if(window.addEventListener){addEventListener("resize",this.Resize,false)}else{if(window.attachEvent){attachEvent("onresize",this.Resize)}else{this.onresize=window.onresize;window.onresize=this.Resize}}a.signal.Post(["math zoomed",p]);return e(o)},Position:function(p,r){p.style.display="none";var q=this.Resize(),m=q.x,s=q.y,l=r.mW;p.style.display="";var o=-l-Math.floor((p.offsetWidth-l)/2),n=r.Y;p.style.left=Math.max(o,10-m)+"px";p.style.top=Math.max(n,10-s)+"px";if(!h.msiePositionBug){h.SetWH()}},Resize:function(m){if(h.onresize){h.onresize(m)}var q=document.getElementById("MathJax_ZoomFrame"),l=document.getElementById("MathJax_ZoomOverlay");var o=h.getXY(q),n=h.findContainer(q);if(h.getOverflow(n)!=="visible"){l.scroll_parent=n;var p=h.getXY(n);o.x-=p.x;o.y-=p.y;p=h.getBorder(n);o.x-=p.x;o.y-=p.y}l.style.left=(-o.x)+"px";l.style.top=(-o.y)+"px";if(h.msiePositionBug){setTimeout(h.SetWH,0)}else{h.SetWH()}return o},SetWH:function(){var l=document.getElementById("MathJax_ZoomOverlay");if(!l){return}l.style.display="none";var m=l.scroll_parent||document.documentElement||document.body;l.style.width=m.scrollWidth+"px";l.style.height=Math.max(m.clientHeight,m.scrollHeight)+"px";l.style.display=""},findContainer:function(l){l=l.parentNode;while(l.parentNode&&l!==document.body&&h.getOverflow(l)==="visible"){l=l.parentNode}return l},getOverflow:(window.getComputedStyle?function(l){return getComputedStyle(l).overflow}:function(l){return(l.currentStyle||{overflow:"visible"}).overflow}),getBorder:function(o){var m={thin:1,medium:2,thick:3};var n=(window.getComputedStyle?getComputedStyle(o):(o.currentStyle||{borderLeftWidth:0,borderTopWidth:0}));var l=n.borderLeftWidth,p=n.borderTopWidth;if(m[l]){l=m[l]}else{l=parseInt(l)}if(m[p]){p=m[p]}else{p=parseInt(p)}return{x:l,y:p}},getXY:function(o){var l=0,n=0,m;m=o;while(m.offsetParent){l+=m.offsetLeft;m=m.offsetParent}if(h.operaPositionBug){o.style.border="1px 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m=(n>=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML);
(function(c,g,k,f,b){var q="2.5.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:q,signal:j};var o=function(r){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",r]].concat([].slice.call(arguments,1)))};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var p=c.CombineConfig("MathMenu",{delay:150,closeImg:k.urlRev(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 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#808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 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3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:q,items:[],posted:false,title:null,margin:5,Init:function(r){this.items=[].slice.call(arguments,0)},With:function(r){if(r){c.Insert(this,r)}return this},Post:function(s,C,A){if(!s){s=window.event}var r=document.getElementById("MathJax_MenuFrame");if(!r){r=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax]);a.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var t=g.Element("div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"});if(!A){MathJax.Localization.setCSS(t)}for(var v=0,u=this.items.length;v<u;v++){this.items[v].Create(t)}if(a.isMobile){g.addElement(t,"span",{className:"MathJax_Menu_Close",menu:C,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:p.closeImg,style:{width:"100%",height:"100%"}}]])}r.appendChild(t);this.posted=true;t.style.width=(t.offsetWidth+2)+"px";var B=s.pageX,z=s.pageY;if(!B&&!z){B=s.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;z=s.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!C){if(B+t.offsetWidth>document.body.offsetWidth-this.margin){B=document.body.offsetWidth-t.offsetWidth-this.margin}if(a.isMobile){B=Math.max(5,B-Math.floor(t.offsetWidth/2));z-=20}a.skipUp=s.isContextMenu}else{var w="left",D=C.offsetWidth;B=(a.isMobile?30:D-2);z=0;while(C&&C!==r){B+=C.offsetLeft;z+=C.offsetTop;C=C.parentNode}if(!a.isMobile){if((a.isRTL&&B-D-t.offsetWidth>this.margin)||(!a.isRTL&&B+t.offsetWidth>document.body.offsetWidth-this.margin)){w="right";B=Math.max(this.margin,B-D-t.offsetWidth+6)}}if(!n){t.style["borderRadiusTop"+w]=0;t.style["WebkitBorderRadiusTop"+w]=0;t.style["MozBorderRadiusTop"+w]=0;t.style["KhtmlBorderRadiusTop"+w]=0}}t.style.left=B+"px";t.style.top=z+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(s)},Remove:function(r,s){j.Post(["unpost",a.jax]);var t=document.getElementById("MathJax_MenuFrame");if(t){t.parentNode.removeChild(t);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(r)},Find:function(r){return this.FindN(1,r,[].slice.call(arguments,1))},FindId:function(r){return this.FindN(0,r,[].slice.call(arguments,1))},FindN:function(v,s,u){for(var t=0,r=this.items.length;t<r;t++){if(this.items[t].name[v]===s){if(u.length){if(!this.items[t].menu){return null}return this.items[t].menu.FindN(v,u[0],u.slice(1))}return this.items[t]}}return null},IndexOf:function(r){return this.IndexOfN(1,r)},IndexOfId:function(r){return this.IndexOfN(0,r)},IndexOfN:function(u,s){for(var t=0,r=this.items.length;t<r;t++){if(this.items[t].name[u]===s){return t}}return null}},{config:p,div:null,Close:function(r){return a.Event(r,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(r){return a.Event(r,this,"Remove")},Mouseover:function(r){return a.Event(r,this,"Mouseover")},Mouseout:function(r){return a.Event(r,this,"Mouseout")},Mousedown:function(r){return a.Event(r,this,"Mousedown")},Mouseup:function(r){return a.Event(r,this,"Mouseup")},Touchstart:function(r){return a.Event(r,this,"Touchstart")},Touchend:function(r){return 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clarify"])}if(n.type!=="msubsup"){if(m){if(n.type!=="munderover"||n.data[n.under]){if(n.movablelimits&&n.isa(h.mi)){n=this.mi2mo(n)}n=h.munderover(n,null,null).With({movesupsub:true})}l=n.under}else{n=h.msubsup(n,null,null);l=n.sub}}this.Push(b.subsup(n).With({position:l,primes:p,movesupsub:m}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(n){var m=this.stack.Prev();if(!m){m=h.mi()}if(m.type==="msubsup"&&m.data[m.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var l="";this.i--;do{l+=this.PRIME;this.i++,n=this.GetNext()}while(n==="'"||n===this.SMARTQUOTE);l=["","\u2032","\u2033","\u2034","\u2057"][l.length]||l;this.Push(b.prime(m,this.mmlToken(h.mo(l))))},mi2mo:function(l){var m=h.mo();m.Append.apply(m,l.data);var n;for(n in m.defaults){if(m.defaults.hasOwnProperty(n)&&l[n]!=null){m[n]=l[n]}}for(n in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(n)&&l[n]!=null){m[n]=l[n]}}return m},Comment:function(l){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(l){d.Error(["CantUseHash1","You can't use 'macro parameter character #' in math mode"])},Other:function(n){var m,l;if(this.stack.env.font){m={mathvariant:this.stack.env.font}}if(f.remap[n]){n=f.remap[n];if(n instanceof Array){m=n[1];n=n[0]}l=h.mo(h.entity("#x"+n)).With(m)}else{l=h.mo(n).With(m)}if(l.autoDefault("stretchy",true)){l.stretchy=false}if(l.autoDefault("texClass",true)==""){l=h.TeXAtom(l)}this.Push(this.mmlToken(l))},SetFont:function(m,l){this.stack.env.font=l},SetStyle:function(m,l,n,o){this.stack.env.style=l;this.stack.env.level=o;this.Push(b.style().With({styles:{displaystyle:n,scriptlevel:o}}))},SetSize:function(l,m){this.stack.env.size=m;this.Push(b.style().With({styles:{mathsize:m+"em"}}))},Color:function(n){var m=this.GetArgument(n);var l=this.stack.env.color;this.stack.env.color=m;var o=this.ParseArg(n);if(l){this.stack.env.color}else{delete this.stack.env.color}this.Push(h.mstyle(o).With({mathcolor:m}))},Spacer:function(l,m){this.Push(h.mspace().With({width:m,mathsize:h.SIZE.NORMAL,scriptlevel:0}))},LeftRight:function(l){this.Push(b[l.substr(1)]().With({delim:this.GetDelimiter(l)}))},Middle:function(l){var m=this.GetDelimiter(l);if(this.stack.Top().type!=="left"){d.Error(["MisplacedMiddle","%1 must be within \\left and \\right",l])}this.Push(h.mo(m).With({stretchy:true}))},NamedFn:function(m,n){if(!n){n=m.substr(1)}var l=h.mi(n).With({texClass:h.TEXCLASS.OP});this.Push(b.fn(this.mmlToken(l)))},NamedOp:function(m,n){if(!n){n=m.substr(1)}n=n.replace(/&thinsp;/,"\u2006");var l=h.mo(n).With({movablelimits:true,movesupsub:true,form:h.FORM.PREFIX,texClass:h.TEXCLASS.OP});l.useMMLspacing&=~l.SPACE_ATTR.form;this.Push(this.mmlToken(l))},Limits:function(m,l){var o=this.stack.Prev("nopop");if(!o||(o.Get("texClass")!==h.TEXCLASS.OP&&o.movesupsub==null)){d.Error(["MisplacedLimits","%1 is allowed only on operators",m])}var n=this.stack.Top();if(o.type==="munderover"&&!l){o=n.data[n.data.length-1]=h.msubsup.apply(h.subsup,o.data)}else{if(o.type==="msubsup"&&l){o=n.data[n.data.length-1]=h.munderover.apply(h.underover,o.data)}}o.movesupsub=(l?true:false);o.Core().movablelimits=false},Over:function(n,m,o){var l=b.over().With({name:n});if(m||o){l.open=m;l.close=o}else{if(n.match(/withdelims$/)){l.open=this.GetDelimiter(n);l.close=this.GetDelimiter(n)}}if(n.match(/^\\above/)){l.thickness=this.GetDimen(n)}else{if(n.match(/^\\atop/)||m||o){l.thickness=0}}this.Push(l)},Frac:function(m){var l=this.ParseArg(m);var n=this.ParseArg(m);this.Push(h.mfrac(l,n))},Sqrt:function(o){var p=this.GetBrackets(o),l=this.GetArgument(o);if(l==="\\frac"){l+="{"+this.GetArgument(l)+"}{"+this.GetArgument(l)+"}"}var m=d.Parse(l,this.stack.env).mml();if(!p){m=h.msqrt.apply(h,m.array())}else{m=h.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(m){var o=this.GetUpTo(m,"\\of");var l=this.ParseArg(m);this.Push(h.mroot(l,this.parseRoot(o)))},parseRoot:function(q){var m=this.stack.env,l=m.inRoot;m.inRoot=true;var p=d.Parse(q,m);q=p.mml();var o=p.stack.global;if(o.leftRoot||o.upRoot){q=h.mpadded(q);if(o.leftRoot){q.width=o.leftRoot}if(o.upRoot){q.voffset=o.upRoot;q.height=o.upRoot}}m.inRoot=l;return q},MoveRoot:function(l,o){if(!this.stack.env.inRoot){d.Error(["MisplacedMoveRoot","%1 can appear only within a root",l])}if(this.stack.global[o]){d.Error(["MultipleMoveRoot","Multiple use of %1",l])}var m=this.GetArgument(l);if(!m.match(/-?[0-9]+/)){d.Error(["IntegerArg","The argument to %1 must be an integer",l])}m=(m/15)+"em";if(m.substr(0,1)!=="-"){m="+"+m}this.stack.global[o]=m},Accent:function(n,l,q){var p=this.ParseArg(n);var o={accent:true};if(this.stack.env.font){o.mathvariant=this.stack.env.font}var m=this.mmlToken(h.mo(h.entity("#x"+l)).With(o));m.stretchy=(q?true:false);this.Push(h.TeXAtom(h.munderover(p,null,m).With({accent:true})))},UnderOver:function(n,q,l){var p={o:"over",u:"under"}[n.charAt(1)];var o=this.ParseArg(n);if(o.Get("movablelimits")){o.movablelimits=false}if(o.isa(h.munderover)&&o.isEmbellished()){o.Core().With({lspace:0,rspace:0});o=h.mrow(h.mo().With({rspace:0}),o)}var m=h.munderover(o,null,null);m.SetData(m[p],this.mmlToken(h.mo(h.entity("#x"+q)).With({stretchy:true,accent:(p==="under")})));if(l){m=h.TeXAtom(m).With({texClass:h.TEXCLASS.OP,movesupsub:true})}this.Push(m.With({subsupOK:true}))},Overset:function(l){var n=this.ParseArg(l),m=this.ParseArg(l);this.Push(h.mover(m,n))},Underset:function(l){var n=this.ParseArg(l),m=this.ParseArg(l);this.Push(h.munder(m,n))},TeXAtom:function(o,q){var p={texClass:q},n;if(q==h.TEXCLASS.OP){p.movesupsub=p.movablelimits=true;var l=this.GetArgument(o);var m=l.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(m){p.mathvariant=h.VARIANT.NORMAL;n=b.fn(this.mmlToken(h.mi(m[1]).With(p)))}else{n=b.fn(h.TeXAtom(d.Parse(l,this.stack.env).mml()).With(p))}}else{n=h.TeXAtom(this.ParseArg(o)).With(p)}this.Push(n)},MmlToken:function(n){var o=this.GetArgument(n),l=this.GetBrackets(n,"").replace(/^\s+/,""),r=this.GetArgument(n),q={attrNames:[]},m;if(!h[o]||!h[o].prototype.isToken){d.Error(["NotMathMLToken","%1 is not a token element",o])}while(l!==""){m=l.match(/^([a-z]+)\s*=\s*('[^']*'|"[^"]*"|[^ ,]*)\s*,?\s*/i);if(!m){d.Error(["InvalidMathMLAttr","Invalid MathML attribute: %1",l])}if(h[o].prototype.defaults[m[1]]==null&&!this.MmlTokenAllow[m[1]]){d.Error(["UnknownAttrForElement","%1 is not a recognized attribute for %2",m[1],o])}var p=this.MmlFilterAttribute(m[1],m[2].replace(/^(['"])(.*)\1$/,"$2"));if(p){if(p.toLowerCase()==="true"){p=true}else{if(p.toLowerCase()==="false"){p=false}}q[m[1]]=p;q.attrNames.push(m[1])}l=l.substr(m[0].length)}this.Push(this.mmlToken(h[o](r).With(q)))},MmlFilterAttribute:function(l,m){return m},MmlTokenAllow:{fontfamily:1,fontsize:1,fontweight:1,fontstyle:1,color:1,background:1,id:1,"class":1,href:1,style:1},Strut:function(l){this.Push(h.mpadded(h.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(m,l,n){var o=h.mphantom(this.ParseArg(m));if(l||n){o=h.mpadded(o);if(n){o.height=o.depth=0}if(l){o.width=0}}this.Push(h.TeXAtom(o))},Smash:function(n){var m=this.trimSpaces(this.GetBrackets(n,""));var l=h.mpadded(this.ParseArg(n));switch(m){case"b":l.depth=0;break;case"t":l.height=0;break;default:l.height=l.depth=0}this.Push(h.TeXAtom(l))},Lap:function(m){var l=h.mpadded(this.ParseArg(m)).With({width:0});if(m==="\\llap"){l.lspace="-1width"}this.Push(h.TeXAtom(l))},RaiseLower:function(l){var m=this.GetDimen(l);var n=b.position().With({name:l,move:"vertical"});if(m.charAt(0)==="-"){m=m.slice(1);l={raise:"\\lower",lower:"\\raise"}[l.substr(1)]}if(l==="\\lower"){n.dh="-"+m;n.dd="+"+m}else{n.dh="+"+m;n.dd="-"+m}this.Push(n)},MoveLeftRight:function(l){var o=this.GetDimen(l);var n=(o.charAt(0)==="-"?o.slice(1):"-"+o);if(l==="\\moveleft"){var m=o;o=n;n=m}this.Push(b.position().With({name:l,move:"horizontal",left:h.mspace().With({width:o,mathsize:h.SIZE.NORMAL}),right:h.mspace().With({width:n,mathsize:h.SIZE.NORMAL})}))},Hskip:function(l){this.Push(h.mspace().With({width:this.GetDimen(l),mathsize:h.SIZE.NORMAL}))},Rule:function(n,p){var l=this.GetDimen(n),o=this.GetDimen(n),r=this.GetDimen(n);var m,q={width:l,height:o,depth:r};if(p!=="blank"){if(parseFloat(l)&&parseFloat(o)+parseFloat(r)){q.mathbackground=(this.stack.env.color||"black")}m=h.mpadded(h.mrow()).With(q)}else{m=h.mspace().With(q)}this.Push(m)},MakeBig:function(l,o,m){m*=f.p_height;m=String(m).replace(/(\.\d\d\d).+/,"$1")+"em";var n=this.GetDelimiter(l,true);this.Push(h.TeXAtom(h.mo(n).With({minsize:m,maxsize:m,fence:true,stretchy:true,symmetric:true})).With({texClass:o}))},BuildRel:function(l){var m=this.ParseUpTo(l,"\\over");var n=this.ParseArg(l);this.Push(h.TeXAtom(h.munderover(n,null,m)).With({texClass:h.TEXCLASS.REL}))},HBox:function(l,m){this.Push.apply(this,this.InternalMath(this.GetArgument(l),m))},FBox:function(l){this.Push(h.menclose.apply(h,this.InternalMath(this.GetArgument(l))).With({notation:"box"}))},Not:function(l){this.Push(b.not())},Dots:function(l){this.Push(b.dots().With({ldots:this.mmlToken(h.mo(h.entity("#x2026")).With({stretchy:false})),cdots:this.mmlToken(h.mo(h.entity("#x22EF")).With({stretchy:false}))}))},Require:function(l){var m=this.GetArgument(l).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");this.Extension(null,m)},Extension:function(l,m,n){if(l&&!typeof(l)==="string"){l=l.name}m=d.extensionDir+"/"+m;if(!m.match(/\.js$/)){m+=".js"}if(!i.loaded[i.fileURL(m)]){if(l!=null){delete f[n||"macros"][l.replace(/^\\/,"")]}c.RestartAfter(i.Require(m))}},Macro:function(n,q,p,r){if(p){var m=[];if(r!=null){var l=this.GetBrackets(n);m.push(l==null?r:l)}for(var o=m.length;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(m,o,u,q,t,n,l,v,s){var r=this.GetNext();if(r===""){d.Error(["MissingArgFor","Missing argument for %1",m])}if(r==="{"){this.i++}else{this.string=r+"}"+this.string.slice(this.i+1);this.i=0}var p=b.array().With({requireClose:true,arraydef:{rowspacing:(n||"4pt"),columnspacing:(t||"1em")}});if(v){p.isCases=true}if(s){p.isNumbered=true;p.arraydef.side=s}if(o||u){p.open=o;p.close=u}if(l==="D"){p.arraydef.displaystyle=true}if(q!=null){p.arraydef.columnalign=q}this.Push(p)},Entry:function(o){this.Push(b.cell().With({isEntry:true,name:o}));if(this.stack.Top().isCases){var n=this.string;var r=0,p=this.i,l=n.length;while(p<l){var s=n.charAt(p);if(s==="{"){r++;p++}else{if(s==="}"){if(r===0){l=0}else{r--;p++}}else{if(s==="&"&&r===0){d.Error(["ExtraAlignTab","Extra alignment tab in \\cases text"])}else{if(s==="\\"){if(n.substr(p).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){l=0}else{p+=2}}else{p++}}}}}var q=n.substr(this.i,p-this.i);if(!q.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(q));this.i=p}}},Cr:function(l){this.Push(b.cell().With({isCR:true,name:l}))},CrLaTeX:function(l){var p;if(this.string.charAt(this.i)==="["){p=this.GetBrackets(l,"").replace(/ /g,"").replace(/,/,".");if(p&&!this.matchDimen(p)){d.Error(["BracketMustBeDimension","Bracket argument to %1 must be a dimension",l])}}this.Push(b.cell().With({isCR:true,name:l,linebreak:true}));var o=this.stack.Top();if(o.isa(b.array)){if(p&&o.arraydef.rowspacing){var m=o.arraydef.rowspacing.split(/ /);if(!o.rowspacing){o.rowspacing=this.dimen2em(m[0])}while(m.length<o.table.length){m.push(this.Em(o.rowspacing))}m[o.table.length-1]=this.Em(Math.max(0,o.rowspacing+this.dimen2em(p)));o.arraydef.rowspacing=m.join(" ")}}else{if(p){this.Push(h.mspace().With({depth:p}))}this.Push(h.mspace().With({linebreak:h.LINEBREAK.NEWLINE}))}},emPerInch:7.2,pxPerInch:72,matchDimen:function(l){return l.match(/^(-?(?:\.\d+|\d+(?:\.\d*)?))(px|pt|em|ex|mu|pc|in|mm|cm)$/)},dimen2em:function(p){var n=this.matchDimen(p);var l=parseFloat(n[1]||"1"),o=n[2];if(o==="em"){return l}if(o==="ex"){return l*0.43}if(o==="pt"){return l/10}if(o==="pc"){return l*1.2}if(o==="px"){return l*this.emPerInch/this.pxPerInch}if(o==="in"){return l*this.emPerInch}if(o==="cm"){return l*this.emPerInch/2.54}if(o==="mm"){return l*this.emPerInch/25.4}if(o==="mu"){return l/18}return 0},Em:function(l){if(Math.abs(l)<0.0006){return"0em"}return l.toFixed(3).replace(/\.?0+$/,"")+"em"},HLine:function(m,n){if(n==null){n="solid"}var o=this.stack.Top();if(!o.isa(b.array)||o.data.length){d.Error(["Misplaced","Misplaced %1",m])}if(o.table.length==0){o.frame.push("top")}else{var l=(o.arraydef.rowlines?o.arraydef.rowlines.split(/ /):[]);while(l.length<o.table.length){l.push("none")}l[o.table.length-1]=n;o.arraydef.rowlines=l.join(" ")}},HFill:function(l){var m=this.stack.Top();if(m.isa(b.array)){m.hfill.push(m.data.length)}else{d.Error(["UnsupportedHFill","Unsupported use of %1",l])}},BeginEnd:function(n){var o=this.GetArgument(n),q=false;if(o.match(/^\\end\\/)){q=true;o=o.substr(5)}if(o.match(/\\/i)){d.Error(["InvalidEnv","Invalid environment name '%1'",o])}var p=this.envFindName(o);if(!p){d.Error(["UnknownEnv","Unknown environment '%1'",o])}if(!(p instanceof Array)){p=[p]}var l=(p[1] instanceof Array?p[1][0]:p[1]);var m=b.begin().With({name:o,end:l,parse:this});if(n==="\\end"){if(!q&&p[1] instanceof Array&&this[p[1][1]]){m=this[p[1][1]].apply(this,[m].concat(p.slice(2)))}else{m=b.end().With({name:o})}}else{if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}}this.Push(m)},envFindName:function(l){return f.environment[l]},Equation:function(l,m){return m},ExtensionEnv:function(m,l){this.Extension(m.name,l,"environment")},Array:function(m,o,t,r,s,n,l,p){if(!r){r=this.GetArgument("\\begin{"+m.name+"}")}var u=("c"+r).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");r=r.replace(/[^clr]/g,"").split("").join(" ");r=r.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var q=b.array().With({arraydef:{columnalign:r,columnspacing:(s||"1em"),rowspacing:(n||"4pt")}});if(u.match(/[|:]/)){if(u.charAt(0).match(/[|:]/)){q.frame.push("left");q.frame.dashed=u.charAt(0)===":"}if(u.charAt(u.length-1).match(/[|:]/)){q.frame.push("right")}u=u.substr(1,u.length-2);q.arraydef.columnlines=u.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(o){q.open=this.convertDelimiter(o)}if(t){q.close=this.convertDelimiter(t)}if(l==="D"){q.arraydef.displaystyle=true}else{if(l){q.arraydef.displaystyle=false}}if(l==="S"){q.arraydef.scriptlevel=1}if(p){q.arraydef.useHeight=false}this.Push(m);return q},AlignedArray:function(l){var m=this.GetBrackets("\\begin{"+l.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),m)},setArrayAlign:function(m,l){l=this.trimSpaces(l||"");if(l==="t"){m.arraydef.align="baseline 1"}else{if(l==="b"){m.arraydef.align="baseline 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h.getBBox(n.parentNode)},Zoom:function(n,u,s,m,r){n.root.toNativeMML(u);if(this.msieIE8HeightBug){u.style.position="absolute"}if(l.widthBug){u.style.width=u.parentNode.style.width=""}if(u.parentNode.style.width.match(/%$/)){u.parentNode.style.minWidth=Math.ceil(3*r/4)+"px"}var p=s.offsetWidth||s.scrollWidth,v=s.offsetHeight||s.scrollHeight;var t=u.offsetWidth,q=u.offsetHeight;if(l.widthBug||u.style.width.match(/%/)){var o=u.firstChild.firstChild.scrollWidth;if(o>t){t=o;u.parentNode.style.width=u.style.minWidth=t+"px"}}if(this.msieIE8HeightBug){u.style.position=""}return{Y:-h.getBBox(u.parentNode).h,mW:p,mH:v,zW:t,zH:q}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em",veryverythinmathspace:".0556em",verythinmathspace:".1111em",thinmathspace:".1667em",mediummathspace:".2222em",thickmathspace:".2778em",verythickmathspace:".3333em",veryverythickmathspace:".3889em"}});c.Register.StartupHook("mml Jax Ready",function(){f=MathJax.ElementJax.mml;f.mbase.Augment({toNativeMML:function(r){var p=this.NativeMMLelement(this.type);this.NativeMMLattributes(p);for(var q=0,o=this.data.length;q<o;q++){if(this.data[q]){this.data[q].toNativeMML(p)}else{p.appendChild(this.NativeMMLelement("mrow"))}}r.appendChild(p)},NativeMMLattributes:function(w){var r=(this.type==="mstyle"?f.math.prototype.defaults:this.defaults);var t=(this.attrNames||f.copyAttributeNames),v=f.skipAttributes,o=f.copyAttributes;if(!this.attrNames){for(var p in r){if(!v[p]&&!o[p]&&r.hasOwnProperty(p)){if(this[p]!=null&&this[p]!==r[p]){w.setAttribute(p,this.NativeMMLattribute(this[p]))}}}}for(var s=0,q=t.length;s<q;s++){if(o[t[s]]===1&&!r.hasOwnProperty(t[s])){continue}var u=(this.attr||{})[t[s]];if(u==null){u=this[t[s]]}if(u!=null){w.setAttribute(t[s],this.NativeMMLattribute(u))}}this.NativeMMLclass(w)},NativeMMLclass:function(o){var q=[];if(this["class"]){q.push(this["class"])}if(this.isa(f.TeXAtom)){var p=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(p){q.push("MJX-TeXAtom-"+p)}}if(this.mathvariant&&this.NativeMMLvariants[this.mathvariant]){q.push("MJX"+this.mathvariant)}if(this.variantForm){q.push("MJX-variant")}if(q.length){o.setAttribute("class",q.join(" "))}},NativeMMLattribute:function(o){o=String(o);if(l.NAMEDSPACE[o]){o=l.NAMEDSPACE[o]}else{if(o.match(/^\s*(([-+])?(\d+(\.\d*)?|\.\d+))\s*mu\s*$/)){o=(RegExp.$2||"")+((1/18)*RegExp.$3).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.NativeMMLvariants[o]){o=this.NativeMMLvariants[o]}}}return o},NativeMMLvariants:{"-tex-caligraphic":f.VARIANT.SCRIPT,"-tex-caligraphic-bold":f.VARIANT.BOLDSCRIPT,"-tex-oldstyle":f.VARIANT.NORMAL,"-tex-oldstyle-bold":f.VARIANT.BOLD,"-tex-mathit":f.VARIANT.ITALIC},NativeMMLelement:function(o){var p=(document.createElementNS?document.createElementNS(l.MMLnamespace,o):(c.Browser.mpNamespace?document.createElement("m:"+o):document.createElement(o)));p.isMathJax=true;return p}});f.mrow.Augment({toNativeMML:function(s){var r,p;if(this.inferred&&this.parent.inferRow){for(r=0,p=this.data.length;r<p;r++){if(this.data[r]){this.data[r].toNativeMML(s)}else{s.appendChild(this.NativeMMLelement("mrow"))}}}else{if(l.stretchyMoBug&&(this.open||this.close)){var q=this.NativeMMLelement("mfenced");this.NativeMMLattributes(q);r=0,p=this.data.length;if(this.open){q.setAttribute("open",this.open);r++}if(this.close){q.setAttribute("close",this.close);p--}var o=q;if(p-r+1>1){o=this.NativeMMLelement("mrow");s.appendChild(q);s=q}for(;r<p;r++){if(this.data[r]){this.data[r].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}}s.appendChild(o)}else{this.SUPER(arguments).toNativeMML.call(this,s)}}}});f.msubsup.Augment({toNativeMML:function(s){var r=this.type;if(this.data[this.sup]==null){r="msub"}if(this.data[this.sub]==null){r="msup"}var p=this.NativeMMLelement(r);this.NativeMMLattributes(p);if(this.data[0]){delete this.data[0].inferred}for(var q=0,o=this.data.length;q<o;q++){if(this.data[q]){this.data[q].toNativeMML(p)}}s.appendChild(p)}});f.munderover.Augment({toNativeMML:function(s){var r=this.type;if(this.data[this.under]==null){r="mover"}if(this.data[this.over]==null){r="munder"}var p=this.NativeMMLelement(r);this.NativeMMLattributes(p);if(this.data[0]){delete this.data[0].inferred}for(var q=0,o=this.data.length;q<o;q++){if(this.data[q]){this.data[q].toNativeMML(p)}}s.appendChild(p)}});if(!i){var m=c.SplitList;f.mtable.Augment({toNativeMML:function(z){var s,q;if(l.tableSpacingBug){var A=this.getValues("rowspacing","columnspacing");this.nMMLtopPadding=m("0px "+A.rowspacing);this.nMMLleftPadding=m("0px "+A.columnspacing);var y=this.nMMLtopPadding,v=y.length;for(s=0,q=this.data.length;s<q;s++){if(this.data[s]){this.data[s].nMMLtopPadding=y[s<v?s:v-1]}}}if(l.tableLabelBug){for(s=0,q=this.data.length;s<q;s++){if(this.data[s]&&this.data[s].isa(f.mlabeledtr)){var u=c.config.displayAlign.charAt(0),w=this.Get("side").charAt(0);this.nMMLhasLabels=true;this.nMMLlaMatch=(u===w);this.nMMLforceWidth=(u==="c"||!!((this.width||"").match("%")));break}}}if(this.width&&this.ffTableWidthBug){var B=(this.style||"").replace(/;\s*$/,"").split(";");if(B[0]===""){B.shift()}B.push("width:"+this.width);this.style=B.join(";")}this.SUPER(arguments).toNativeMML.call(this,z);if(this.nMMLhasLabels){var r=z.firstChild;if(this.nMMLforceWidth||w!=="r"){var p=(u!=="l"?1:0)+(w==="l"?1:0);if(p){var t={columnalign:"left",columnwidth:"auto",columnspacing:"0px",columnlines:"none"};for(var o in t){if(t.hasOwnProperty(o)&&this[o]){var x=[t[o],t[o]].slice(2-p).join(" ")+" ";r.setAttribute(o,x+r.getAttribute(o))}}}}if(this.nMMLforceWidth||!this.nMMLlaMatch){r.setAttribute("width","100%")}}}});f.mtr.Augment({toNativeMML:function(v){this.SUPER(arguments).toNativeMML.call(this,v);var p=v.lastChild;if(l.tableSpacingBug){var r=this.parent.nMMLleftPadding,t=r.length;for(var w=p.firstChild,q=0;w;w=w.nextSibling,q++){a(w,this.nMMLtopPadding,r[q<t?q:t-1])}}if(l.tableLabelBug){var o=this.parent.nMMLforceWidth,u=this.parent.Get("side").charAt(0),s=c.config.displayAlign.charAt(0);if(this.parent.nMMLhasLabels&&p.firstChild){if(o||u!=="r"){j("Left",p.firstChild);if(s!=="l"){p.insertBefore(this.NativeMMLelement("mtd"),p.firstChild).setAttribute("style","padding:0")}if(u==="l"){p.insertBefore(this.NativeMMLelement("mtd"),p.firstChild).setAttribute("style","padding:0")}}if(o||u!=="l"){j("Right",p.lastChild)}}}}});f.mlabeledtr.Augment({toNativeMML:function(C){var t=this.NativeMMLelement("mtr");this.NativeMMLattributes(t);for(var u=1,s=this.data.length;u<s;u++){if(this.data[u]){this.data[u].toNativeMML(t)}else{t.appendChild(this.NativeMMLelement("mtd"))}}if(l.tableSpacingBug){var v=this.parent.nMMLleftPadding,y=v.length;u=0;for(var D=t.firstChild;D;D=D.nextSibling,u++){a(D,this.nMMLtopPadding,v[u<y?u:y-1])}}if(l.tableLabelBug&&this.data[0]){var z=this.parent.Get("side").charAt(0),x=c.config.displayAlign.charAt(0),q=c.config.displayIndent;this.data[0].toNativeMML(t);var A=t.lastChild,r=A;if(z===x){A.setAttribute("style","width:"+q);A.setAttribute("columnalign",c.config.displayAlign)}else{r=this.NativeMMLelement("mpadded");r.setAttribute("style","width:0");r.setAttribute("width","0px");r.appendChild(A.firstChild);A.appendChild(r)}j("",A);t.removeChild(A);var o=100,p=this.parent.nMMLforceWidth;if((this.parent.width||"").match(/%/)){o-=parseFloat(this.parent.width)}var B=o;if(p||z!=="r"){j("Left",t.firstChild);if(x!=="l"){if(x==="c"){B/=2}o-=B;t.insertBefore(this.NativeMMLelement("mtd"),t.firstChild).setAttribute("style","padding:0;width:"+B+"%")}if(z==="l"){t.insertBefore(A,t.firstChild)}}if(p||z!=="l"){j("Right",t.lastChild);if(x!=="r"){t.appendChild(this.NativeMMLelement("mtd")).setAttribute("style","padding:0;width:"+o+"%")}if(z==="r"){if(z!==x){r.setAttribute("lspace","-1width")}t.appendChild(A)}}}C.appendChild(t)}});f.mtd.Augment({toNativeMML:function(r){var p=r.appendChild(this.NativeMMLelement(this.type));this.NativeMMLattributes(p);if(l.mtdWidthBug){l.adjustWidths.push(p);p=p.appendChild(this.NativeMMLelement("mrow"))}for(var q=0,o=this.data.length;q<o;q++){if(this.data[q]){this.data[q].toNativeMML(p)}else{p.appendChild(this.NativeMMLelement("mrow"))}}}});f.mspace.Augment({toNativeMML:function(q){this.SUPER(arguments).toNativeMML.call(this,q);if(l.spaceWidthBug&&this.width){var r=q.lastChild;var p=r.getAttribute("width");var o=(r.getAttribute("style")||"").replace(/;?\s*/,"; ");r.setAttribute("style",o+"width:"+p)}}});var n=g.fileURL(MathJax.OutputJax.fontDir+"/HTML-CSS/TeX/otf");l.Augment({config:{styles:{'[class="MJX-tex-oldstyle"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB"},'[class="MJX-tex-oldstyle-bold"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB","font-weight":"bold"},'[class="MJX-tex-caligraphic"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB"},'[class="MJX-tex-caligraphic-bold"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB","font-weight":"bold"},"@font-face /*1*/":{"font-family":"MathJax_Caligraphic-WEB",src:"url('"+n+"/MathJax_Caligraphic-Regular.otf')"},"@font-face /*2*/":{"font-family":"MathJax_Caligraphic-WEB","font-weight":"bold",src:"url('"+n+"/MathJax_Caligraphic-Bold.otf')"}}}});if(!this.handlesVariants){l.Augment({config:{styles:{'[mathvariant="double-struck"]':{"font-family":"MathJax_AMS, MathJax_AMS-WEB"},'[mathvariant="script"]':{"font-family":"MathJax_Script, MathJax_Script-WEB"},'[mathvariant="fraktur"]':{"font-family":"MathJax_Fraktur, MathJax_Fraktur-WEB"},'[mathvariant="bold-script"]':{"font-family":"MathJax_Script, MathJax_Caligraphic-WEB","font-weight":"bold"},'[mathvariant="bold-fraktur"]':{"font-family":"MathJax_Fraktur, MathJax_Fraktur-WEB","font-weight":"bold"},'[mathvariant="monospace"]':{"font-family":"monospace"},'[mathvariant="sans-serif"]':{"font-family":"sans-serif"},'[mathvariant="bold-sans-serif"]':{"font-family":"sans-serif","font-weight":"bold"},'[mathvariant="sans-serif-italic"]':{"font-family":"sans-serif","font-style":"italic"},'[mathvariant="sans-serif-bold-italic"]':{"font-family":"sans-serif","font-style":"italic","font-weight":"bold"},"@font-face /*3*/":{"font-family":"MathJax_AMS-WEB",src:"url('"+n+"/MathJax_AMS-Regular.otf')"},"@font-face /*4*/":{"font-family":"MathJax_Script-WEB",src:"url('"+n+"/MathJax_Script-Regular.otf')"},"@font-face /*5*/":{"font-family":"MathJax_Fraktur-WEB",src:"url('"+n+"/MathJax_Fraktur-Regular.otf')"},"@font-face /*6*/":{"font-family":"MathJax_Fraktur-WEB","font-weight":"bold",src:"url('"+n+"/MathJax_Fraktur-Bold.otf')"}}}})}}f.math.Augment({toNativeMML:function(y,p){var A=this.NativeMMLelement(this.type),w=A;var u=(p?MathJax.InputJax[p.inputJax].annotationEncoding:null);var v,r;l.adjustWidths=[];A.setAttribute("xmlns",l.MMLnamespace);this.NativeMMLattributes(A);if(l.widthBug){A=A.appendChild(this.NativeMMLelement("mrow"))}if(u){A=A.appendChild(this.NativeMMLelement("semantics"));A.appendChild(this.NativeMMLelement("mrow"));var s=A.appendChild(this.NativeMMLelement("annotation"));s.appendChild(document.createTextNode(p.originalText));s.setAttribute("encoding",u);A=A.firstChild}for(v=0,r=this.data.length;v<r;v++){if(this.data[v]){this.data[v].toNativeMML(A)}else{A.appendChild(this.NativeMMLelement("mrow"))}}var t=((this.data[0]||{data:[]}).data[0]||{});if(t.nMMLhasLabels){if(t.nMMLforceWidth||!t.nMMLlaMatch){A.setAttribute("style","width:100%");if(u){A.parentNode.setAttribute("style","width:100%")}}if(t.nMMLlaMatch){if(y.parentNode.parentNode.nodeName.toLowerCase()==="div"){y.parentNode.parentNode.style.setProperty("margin-"+c.config.displayAlign,"0px","important")}}}var x=l.isFullWidth(w);if(x){y.style.width=y.parentNode.style.width="100%"}y.appendChild(w);if(l.widthBug&&!x){y.style.width=(w.firstChild.scrollWidth/l.ex/l.scale).toFixed(3)+"ex";if(p){p.NativeMML.scrollWidth=w.firstChild.scrollWidth}}if(l.adjustWidths.length){var z=[];for(v=0,r=l.adjustWidths.length;v<r;v++){A=l.adjustWidths[v];var o=A.getAttribute("style")||"";if(!o.match(/(^|;)\s*min-width:/)){var q=A.firstChild.scrollWidth;z.push(q);q=(q/l.ex).toFixed(3)+"ex";o=o.replace(/;?\s*$/,"; ");A.setAttribute("style",o+"min-width:"+q)}}if(!p){p=c.getJaxFor(y)}if(p){p.NativeMML.mtds=z}w.MathJaxMtds=l.adjustWidths;l.adjustWidths=[]}}});f.mfenced.Augment({toNativeMML:function(w){if(!l.mfencedBug){this.SUPER(arguments).toNativeMML.call(this,w);return}var t=c.Browser.isOpera;var u,p,r;var q=this.getValues("open","close","separators");q.open=q.open.replace(/^\s+/,"").replace(/\s+$/,"");q.close=q.close.replace(/^\s+/,"").replace(/\s+$/,"");q.separators=q.separators.replace(/\s+/g,"").split("");if(q.separators.length==0){q.separators=null}else{if(q.separators.length<this.data.length-1){var v=q.separators[q.separators.length-1];for(u=this.data.length-1-q.separators.length;u>0;u--){q.separators.push(v)}}}var o=this.NativeMMLelement(t?this.type:"mrow");this.NativeMMLattributes(o);o.removeAttribute("separators");if(t){o.setAttribute("open",q.open);o.setAttribute("close",q.close);if(this.data.length>1){w.appendChild(o);w=o;o=this.NativeMMLelement("mrow")}}else{o.removeAttribute("open");o.removeAttribute("close")}if(!t){r=this.NativeMMLelement("mo");r.setAttribute("fence","true");r.textContent=q.open;o.appendChild(r)}for(u=0,p=this.data.length;u<p;u++){if(q.separators&&u>0){r=this.NativeMMLelement("mo");r.setAttribute("separator","true");r.textContent=q.separators[u-1];o.appendChild(r)}if(this.data[u]){this.data[u].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}}if(!t){r=this.NativeMMLelement("mo");r.setAttribute("fence","true");r.textContent=q.close;o.appendChild(r)}w.appendChild(o)}});f.TeXAtom.Augment({toNativeMML:function(p){var o=this.NativeMMLelement("mrow");this.NativeMMLattributes(o);this.data[0].toNativeMML(o);p.appendChild(o)}});f.chars.Augment({toNativeMML:function(o){o.appendChild(document.createTextNode(this.toString()))}});f.entity.Augment({toNativeMML:function(o){o.appendChild(document.createTextNode(this.toString()))}});f.xml.Augment({toNativeMML:function(q){for(var p=0,o=this.data.length;p<o;p++){q.appendChild(this.data[p].cloneNode(true))}}});f.mi.Augment({toNativeMML:function(p){this.SUPER(arguments).toNativeMML.call(this,p);if(l.miItalicBug){if(this.Get("mathvariant")===f.VARIANT.NORMAL){var o=p.lastChild;o.setAttribute("mathvariant",f.VARIANT.NORMAL)}}}});f.mo.Augment({toNativeMML:function(t){this.SUPER(arguments).toNativeMML.call(this,t);if(l.webkitMoSpacingBug){var o=0,s=0,v=this.parent;if(v&&v.type==="mrow"&&(v.inferred||!v.isEmbellished())){var q=this.getValues("lspace","rspace");o=q.lspace,s=q.rspace;if(l.NAMEDSPACE[o]){o=l.NAMEDSPACE[o]}if(l.NAMEDSPACE[s]){s=l.NAMEDSPACE[s]}}var u=t.lastChild;var r=e.Element("span");r.style.cssText=(u.getAttribute("style")||"");r.style.setProperty("-webkit-margin-start",o);r.style.setProperty("-webkit-margin-end",s);u.setAttribute("style",r.style.cssText)}}});f.mmultiscripts.Augment({toNativeMML:function(s){if(!l.mmultiscriptsBug||this.data.length===0){this.SUPER(arguments).toNativeMML.call(this,s);return}var q=this.NativeMMLelement("mrow");this.NativeMMLattributes(q);if(this.data[0]){this.data[0].toNativeMML(q)}else{q.appendChild(this.NativeMMLelement("mrow"))}var t=q.removeChild(q.lastChild);var p=this.data.length,r,o;for(r=1;r<p;r+=2){if(this.data[r].type==="mprescripts"){break}o=this.NativeMMLelement("msubsup");o.appendChild(t);if(this.data[r]){this.data[r].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}if(r+1<p&&this.data[r+1]){this.data[r+1].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}t=o}q.appendChild(t);for(r++;r<p;r+=2){o=this.NativeMMLelement("msubsup");o.appendChild(this.NativeMMLelement("mrow"));if(this.data[r]){this.data[r].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}if(r+1<p&&this.data[r+1]){this.data[r+1].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}q.insertBefore(o,t)}s.appendChild(q)}});c.Register.StartupHook("TeX mathchoice Ready",function(){f.TeXmathchoice.Augment({toNativeMML:function(o){this.Core().toNativeMML(o)}})});setTimeout(MathJax.Callback(["loadComplete",l,"jax.js"]),0)});c.Browser.Select({MSIE:function(m){var n=(document.documentMode||0);l.msieIE8HeightBug=(n===8)},Opera:function(m){l.operaPositionBug=true;l.stretchyMoBug=true;l.tableLabelBug=true;l.mfencedBug=true;l.miBug=true;l.mmultiscriptsBug=true},Firefox:function(m){var n=m.versionAtLeast("29.0");l.ffTableWidthBug=!m.versionAtLeast("13.0");l.forceReflow=!n;l.widthBug=!n;l.mtdWidthBug=true;l.handlesVariants=n;l.spaceWidthBug=!m.versionAtLeast("20.0");l.tableSpacingBug=!m.versionAtLeast("33.0");l.tableLabelBug=true;l.mfencedBug=true},Chrome:function(m){l.tableSpacingBug=true;l.tableLabelBug=true;l.mfencedBug=true},Safari:function(m){l.tableSpacingBug=true;l.tableLabelBug=true;l.mfencedBug=true;l.miItalicBug=true;l.webkitMoSpacingBug=true;l.spaceWidthBug=true;l.mmultiscriptsBug=true}});c.Register.StartupHook("End Cookie",function(){if(c.config.menuSettings.zoom!=="None"){g.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.OutputJax.NativeMML,MathJax.Hub,MathJax.Ajax,MathJax.HTML);
(function(h,b,d){var g,i=b.Browser.isMobile;var e=function(){var k=[].slice.call(arguments,0);k[0][0]=["HTML-CSS",k[0][0]];return MathJax.Message.Set.apply(MathJax.Message,k)};var f=MathJax.Object.Subclass({timeout:(i?15:8)*1000,comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],FedoraSTIXcheck:{family:"STIXSizeOneSym",testString:"abcABC",noStyleChar:true},Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",width:0,height:0,overflow:"hidden",padding:0,border:0,margin:0}},[["div",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,whiteSpace:"nowrap",textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal",fontSizeAdjust:"none"}},[""]]]).firstChild;this.text=this.div.firstChild},findFont:function(p,l){var o=null;if(l&&this.testCollection(l)){o=l}else{for(var n=0,k=p.length;n<k;n++){if(p[n]===l){continue}if(this.testCollection(p[n])){o=p[n];break}}}if(o==="STIX"&&this.testFont(this.FedoraSTIXcheck)){o=null}return o},testCollection:function(l){var k={testString:"() {} []"};k.family={TeX:"MathJax_Size1",STIX:"STIXSizeOneSym"}[l]||l.replace(/-(Math)?/,"")+"MathJax_Size1";if(l==="STIX"){k.noStyleChar=true}return this.testFont(k)},testFont:function(n){if(n.isWebFont&&d.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(n.weight||"normal");this.div.style.fontStyle=(n.style||"normal")}var p=n.familyFixed||n.family;if(!p.match(/^(STIX|MathJax)|'/)){p=p.replace(/_/g," ").replace(/([a-z])([A-Z])/g,"$1 $2").replace(/ Jax/,"Jax")+"','"+p+"','"+p+"-";if(n.weight){p+="Bold"}if(n.style){p+="Italic"}if(!n.weight&&!n.style){p+="Regular"}n.familyFixed=p="'"+p+"'"}var l=this.getComparisonWidths(n.testString,n.noStyleChar);var q=null;if(l){this.div.style.fontFamily=p+","+this.comparisonFont[0];if(this.div.offsetWidth==l[0]){this.div.style.fontFamily=p+","+this.comparisonFont[l[2]];if(this.div.offsetWidth==l[1]){q=false}}if(q===null&&(this.div.offsetWidth!=l[3]||this.div.offsetHeight!=l[4])){if(!n.noStyleChar&&d.FONTDATA&&d.FONTDATA.hasStyleChar){for(var o=0,k=this.testSize.length;o<k;o++){if(this.testStyleChar(n,this.testSize[o])){q=true;k=0}}}else{q=true}}}if(d.safariTextNodeBug){this.div.innerHTML=""}else{this.text.nodeValue=""}return q},styleChar:"\uEFFD",versionChar:"\uEFFE",compChar:"\uEFFF",testStyleChar:function(m,p){var s=3+(m.weight?2:0)+(m.style?4:0);var l="",o=0;var r=this.div.style.fontSize;this.div.style.fontSize=p;if(d.msieItalicWidthBug&&m.style==="italic"){this.text.nodeValue=l=this.compChar;o=this.div.offsetWidth}if(d.safariTextNodeBug){this.div.innerHTML=this.compChar+l}else{this.text.nodeValue=this.compChar+l}var k=this.div.offsetWidth-o;if(d.safariTextNodeBug){this.div.innerHTML=this.styleChar+l}else{this.text.nodeValue=this.styleChar+l}var q=Math.floor((this.div.offsetWidth-o)/k+0.5);if(q===s){if(d.safariTextNodeBug){this.div.innerHTML=this.versionChar+l}else{this.text.nodeValue=this.versionChar+l}m.version=Math.floor((this.div.offsetWidth-o)/k+1.5)/2}this.div.style.fontSize=r;return(q===s)},getComparisonWidths:function(p,n){if(d.FONTDATA&&d.FONTDATA.hasStyleChar&&!n){p+=this.styleChar+" "+this.compChar}if(d.safariTextNodeBug){this.div.innerHTML=p}else{this.text.nodeValue=p}this.div.style.fontFamily=this.comparisonFont[0];var l=this.div.offsetWidth;this.div.style.fontFamily=d.webFontDefault;var r=this.div.offsetWidth,o=this.div.offsetHeight;for(var q=1,k=this.comparisonFont.length;q<k;q++){this.div.style.fontFamily=this.comparisonFont[q];if(this.div.offsetWidth!=l){return[l,this.div.offsetWidth,q,r,o]}}return null},loadWebFont:function(l){b.Startup.signal.Post("HTML-CSS Jax - Web-Font "+d.fontInUse+"/"+l.directory);var o=e(["LoadWebFont","Loading web-font %1",d.fontInUse+"/"+l.directory]);var k=MathJax.Callback({});var m=MathJax.Callback(["loadComplete",this,l,o,k]);h.timer.start(h,[this.checkWebFont,l,m],0,this.timeout);return k},loadComplete:function(m,p,l,k){MathJax.Message.Clear(p);if(k===h.STATUS.OK){this.webFontLoaded=true;l();return}this.loadError(m);if(b.Browser.isFirefox&&d.allowWebFonts){var o=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){o+=":"+document.location.port}o+="/";if(h.fileURL(d.webfontDir).substr(0,o.length)!==o){this.firefoxFontError(m)}}if(!this.webFontLoaded){d.loadWebFontError(m,l)}else{l()}},loadError:function(k){e(["CantLoadWebFont","Can't load web font %1",d.fontInUse+"/"+k.directory],null,2000);b.Startup.signal.Post(["HTML-CSS Jax - web font error",d.fontInUse+"/"+k.directory,k])},firefoxFontError:function(k){e(["FirefoxCantLoadWebFont","Firefox can't load web fonts from a remote host"],null,3000);b.Startup.signal.Post("HTML-CSS Jax - Firefox web fonts on remote host error")},checkWebFont:function(k,l,m){if(k.time(m)){return}if(d.Font.testFont(l)){m(k.STATUS.OK)}else{setTimeout(k,k.delay)}},fontFace:function(o){var p=d.allowWebFonts;var r=d.FONTDATA.FONTS[o];if(d.msieFontCSSBug&&!r.family.match(/-Web$/)){r.family+="-Web"}var k=d.webfontDir+"/"+p;var n=h.fileURL(k);var m=o.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!m.match(/-/)){m+="-Regular"}if(p==="svg"){m+=".svg#"+m}else{m+="."+p}var l=h.fileRev(k+"/"+m.replace(/#.*/,""));var q={"font-family":r.family,src:"url('"+n+"/"+m+l+"')"};if(p==="otf"){m=m.replace(/otf$/,"woff");l=h.fileRev(k+"/"+m);q.src+=" format('opentype')";n=h.fileURL(d.webfontDir+"/woff");q.src="url('"+n+"/"+m+l+"') format('woff'), "+q.src}else{if(p!=="eot"){q.src+=" format('"+p+"')"}}if(!(d.FontFaceBug&&r.isWebFont)){if(o.match(/-bold/)){q["font-weight"]="bold"}if(o.match(/-italic/)){q["font-style"]="italic"}}return q}});var j,a,c;d.Augment({config:{styles:{".MathJax":{display:"inline","font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none",direction:"ltr","max-width":"none","max-height":"none","min-width":0,"min-height":0,border:0,padding:0,margin:0},".MathJax_Display":{position:"relative",display:"block!important","text-indent":0,"max-width":"none","max-height":"none","min-width":0,"min-height":0,width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","min-width":0,"min-height":0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0!important",padding:"0!important",margin:"0!important","vertical-align":"0!important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},".MathJax nobr":{"white-space":"nowrap!important"},".MathJax img":{display:"inline!important","float":"none!important"},".MathJax *":{transition:"none","-webkit-transition":"none","-moz-transition":"none","-ms-transition":"none","-o-transition":"none"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax_Processed":{display:"none!important"},".MathJax_ExBox":{display:"block!important",overflow:"hidden",width:"1px",height:"60ex","min-height":0,"max-height":"none"},".MathJax .MathJax_EmBox":{display:"block!important",overflow:"hidden",width:"1px",height:"60em","min-height":0,"max-height":"none"},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity=0)"},".MathJax .MathJax_HitBox *":{filter:"none",opacity:1,background:"transparent"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",opacity:1,background:"transparent"},"@font-face":{"font-family":"MathJax_Blank",src:"url('about:blank')"}}},settings:b.config.menuSettings,Font:null,webFontDefault:"MathJax_Blank",allowWebFonts:"otf",maxStretchyParts:1000,fontName:{TeXLocal:"TeX",TeXWeb:["","TeX"],TeXImage:["",""],STIXLocal:["STIX","STIX-Web"],STIXWeb:"STIX-Web",AsanaMathWeb:"Asana-Math",GyrePagellaWeb:"Gyre-Pagella",GyreTermesWeb:"Gyre-Termes",LatinModernWeb:"Latin-Modern",NeoEulerWeb:"Neo-Euler"},fontInUse:"generic",FONTDATA:{TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]},"-generic-variant":{},"-largeOp":{},"-smallOp":{}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}},Config:function(){if(!this.require){this.require=[]}this.Font=f();this.SUPER(arguments).Config.call(this);var m=this.settings,l=this.config,k=m.font;if(this.adjustAvailableFonts){this.adjustAvailableFonts(l.availableFonts)}if(m.scale){l.scale=m.scale}if(k&&k!=="Auto"&&this.fontName[k]){l.availableFonts=[];delete l.fonts;if(this.fontName[k] instanceof Array){l.preferredFont=this.fontName[k][0];l.webFont=this.fontName[k][1]}else{l.preferredFont=l.webFont=this.fontName[k]}if(l.preferredFont){l.availableFonts[0]=l.preferredFont}}if(l.fonts){l.availableFonts=l.fonts;l.preferredFont=l.webFont=l.fonts[0];if(l.webFont==="STIX"){l.webFont+="-Web"}}k=this.Font.findFont(l.availableFonts,l.preferredFont);if(!k&&this.allowWebFonts){k=l.webFont;if(k){this.webFonts=true}}if(!k&&this.config.imageFont){k=l.imageFont;this.imgFonts=true}if(k){this.fontInUse=k;this.fontDir+="/"+k;this.webfontDir+="/"+k;this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");b.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{e(["CantFindFontUsing","Can't find a valid font using %1","["+this.config.availableFonts.join(", ")+"]"],null,3000);b.Startup.signal.Post("HTML-CSS Jax - no valid font")}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;this.hiddenDiv=this.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=this.addElement(this.hiddenDiv,"div",{id:"MathJax_Hidden"});var l=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=l.offsetWidth/5;this.hiddenDiv.removeChild(l);this.startMarker=this.createStrut(this.Element("span"),10,true);this.endMarker=this.addText(this.Element("span"),"x").parentNode;this.HDspan=this.Element("span");if(this.operaHeightBug){this.createStrut(this.HDspan,0)}if(this.msieInlineBlockAlignBug){this.HDimg=this.addElement(this.HDspan,"img",{style:{height:"0px",width:"1px"}});try{this.HDimg.src="about:blank"}catch(k){}}else{this.HDimg=this.createStrut(this.HDspan,0)}this.EmExSpan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["span",{className:"MathJax_ExBox"}],["span",{className:"MathJax"},[["span",{className:"MathJax_EmBox"}]]]]);this.linebreakSpan=this.Element("span",null,[["hr",{style:{width:"100%",size:1,padding:0,border:0,margin:0}}]]);return h.Styles(this.config.styles,["InitializeHTML",this])},removeSTIXfonts:function(n){for(var l=0,k=n.length;l<k;l++){if(n[l]==="STIX"){n.splice(l,1);k--;l--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=n[0]}},PreloadWebFonts:function(){if(!d.allowWebFonts||!d.config.preloadWebFonts){return}for(var l=0,k=d.config.preloadWebFonts.length;l<k;l++){var n=d.FONTDATA.FONTS[d.config.preloadWebFonts[l]];if(!n.available){d.Font.testFont(n)}}},InitializeHTML:function(){this.PreloadWebFonts();this.getDefaultExEm();if(this.defaultEm){return}var k=MathJax.Callback();h.timer.start(h,function(l){if(l.time(k)){b.signal.Post(["HTML-CSS Jax - no default em size"]);return}d.getDefaultExEm();if(d.defaultEm){k()}else{setTimeout(l,l.delay)}},this.defaultEmDelay,this.defaultEmTimeout);return k},defaultEmDelay:100,defaultEmTimeout:1000,getDefaultExEm:function(){document.body.appendChild(this.EmExSpan);document.body.appendChild(this.linebreakSpan);this.defaultEx=this.EmExSpan.firstChild.offsetHeight/60;this.defaultEm=this.EmExSpan.lastChild.firstChild.offsetHeight/60;this.defaultWidth=this.linebreakSpan.firstChild.offsetWidth;document.body.removeChild(this.linebreakSpan);document.body.removeChild(this.EmExSpan)},preTranslate:function(p){var o=p.jax[this.id],y,v=o.length,B,t,x,r,z,l,A,k,C,s,q=false,w,n=this.config.linebreaks.automatic,u=this.config.linebreaks.width;if(n){q=(u.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)!=null);if(q){u=u.replace(/\s*container\s*/,"")}else{s=this.defaultWidth}if(u===""){u="100%"}}else{s=100000}for(y=0;y<v;y++){B=o[y];if(!B.parentNode){continue}t=B.previousSibling;if(t&&String(t.className).match(/^MathJax(_Display)?( MathJax_Processing)?$/)){t.parentNode.removeChild(t)}l=B.MathJax.elementJax;if(!l){continue}l.HTMLCSS={display:(l.root.Get("display")==="block")};x=r=this.Element("span",{className:"MathJax",id:l.inputID+"-Frame",isMathJax:true,jaxID:this.id,oncontextmenu:j.Menu,onmousedown:j.Mousedown,onmouseover:j.Mouseover,onmouseout:j.Mouseout,onmousemove:j.Mousemove,onclick:j.Click,ondblclick:j.DblClick});if(b.Browser.noContextMenu){x.ontouchstart=a.start;x.ontouchend=a.end}if(l.HTMLCSS.display){r=this.Element("div",{className:"MathJax_Display"});r.appendChild(x)}else{if(this.msieDisappearingBug){x.style.display="inline-block"}}r.className+=" MathJax_Processing";B.parentNode.insertBefore(r,B);B.parentNode.insertBefore(this.EmExSpan.cloneNode(true),B);r.parentNode.insertBefore(this.linebreakSpan.cloneNode(true),r)}for(y=0;y<v;y++){B=o[y];if(!B.parentNode){continue}z=B.previousSibling;r=z.previousSibling;l=B.MathJax.elementJax;if(!l){continue}A=z.firstChild.offsetHeight/60;k=z.lastChild.firstChild.offsetHeight/60;w=r.previousSibling.firstChild.offsetWidth;if(q){s=w}if(A===0||A==="NaN"){this.hiddenDiv.appendChild(r);l.HTMLCSS.isHidden=true;A=this.defaultEx;k=this.defaultEm;w=this.defaultWidth;if(q){s=w}}C=(this.config.matchFontHeight?A/this.TeX.x_height/k:1);C=Math.floor(Math.max(this.config.minScaleAdjust/100,C)*this.config.scale);l.HTMLCSS.scale=C/100;l.HTMLCSS.fontSize=C+"%";l.HTMLCSS.em=l.HTMLCSS.outerEm=k;this.em=k*C/100;l.HTMLCSS.ex=A;l.HTMLCSS.cwidth=w/this.em;l.HTMLCSS.lineWidth=(n?this.length2em(u,1,s/this.em):1000000)}for(y=0;y<v;y++){B=o[y];if(!B.parentNode){continue}z=o[y].previousSibling;l=o[y].MathJax.elementJax;if(!l){continue}x=z.previousSibling;if(!l.HTMLCSS.isHidden){x=x.previousSibling}x.parentNode.removeChild(x);z.parentNode.removeChild(z)}p.HTMLCSSeqn=p.HTMLCSSlast=0;p.HTMLCSSi=-1;p.HTMLCSSchunk=this.config.EqnChunk;p.HTMLCSSdelay=false},PHASE:{I:1,II:2,III:3},Translate:function(l,p){if(!l.parentNode){return}if(p.HTMLCSSdelay){p.HTMLCSSdelay=false;b.RestartAfter(MathJax.Callback.Delay(this.config.EqnChunkDelay))}var k=l.MathJax.elementJax,o=k.root,m=document.getElementById(k.inputID+"-Frame"),q=(k.HTMLCSS.display?(m||{}).parentNode:m);if(!q){return}this.getMetrics(k);if(this.scale!==1){m.style.fontSize=k.HTMLCSS.fontSize}this.initImg(m);this.initHTML(o,m);this.savePreview(l);try{o.setTeXclass();k.HTMLCSS.span=m;k.HTMLCSS.div=q;o.toHTML(m,q,this.PHASE.I)}catch(n){if(n.restart){while(m.firstChild){m.removeChild(m.firstChild)}}this.restorePreview(l);throw n}this.restorePreview(l);if(k.HTMLCSS.isHidden){l.parentNode.insertBefore(q,l)}q.className=q.className.split(/ /)[0]+" MathJax_Processed";b.signal.Post(["New Math Pending",k.inputID]);p.HTMLCSSeqn+=(p.i-p.HTMLCSSi);p.HTMLCSSi=p.i;if(p.HTMLCSSeqn>=p.HTMLCSSlast+p.HTMLCSSchunk){this.postTranslate(p,true);p.HTMLCSSchunk=Math.floor(p.HTMLCSSchunk*this.config.EqnChunkFactor);p.HTMLCSSdelay=true}return false},savePreview:function(k){var l=k.MathJax.preview;if(l){k.MathJax.tmpPreview=document.createElement("span");l.parentNode.replaceChild(k.MathJax.tmpPreview,l)}},restorePreview:function(k){var l=k.MathJax.tmpPreview;if(l){l.parentNode.replaceChild(k.MathJax.preview,l);delete k.MathJax.tmpPreview}},getMetrics:function(k){var l=k.HTMLCSS;this.em=g.mbase.prototype.em=l.em*l.scale;this.outerEm=l.em;this.scale=l.scale;this.cwidth=l.cwidth;this.linebreakWidth=l.lineWidth},postTranslate:function(s,p){var l=s.jax[this.id],o,n,r,k;for(r=s.HTMLCSSlast,k=s.HTMLCSSeqn;r<k;r++){o=l[r];if(o&&o.MathJax.elementJax){n=o.MathJax.elementJax;this.getMetrics(n);n.root.toHTML(n.HTMLCSS.span,n.HTMLCSS.div,this.PHASE.II)}}for(r=s.HTMLCSSlast,k=s.HTMLCSSeqn;r<k;r++){o=l[r];if(o&&o.MathJax.elementJax){n=o.MathJax.elementJax;this.getMetrics(n);n.root.toHTML(n.HTMLCSS.span,n.HTMLCSS.div,this.PHASE.III);delete n.HTMLCSS.span;delete n.HTMLCSS.div;o.MathJax.state=n.STATE.PROCESSED;b.signal.Post(["New 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h.Styles({"@font-face":this.Font.fontFace(k)})},Remove:function(k){var l=document.getElementById(k.inputID+"-Frame");if(l){if(k.HTMLCSS.display){l=l.parentNode}l.parentNode.removeChild(l)}delete k.HTMLCSS},getHD:function(l){if(l.bbox&&this.config.noReflows){return{h:l.bbox.h,d:l.bbox.d}}var k=l.style.position;l.style.position="absolute";this.HDimg.style.height="0px";l.appendChild(this.HDspan);var m={h:l.offsetHeight};this.HDimg.style.height=m.h+"px";m.d=l.offsetHeight-m.h;m.h-=m.d;m.h/=this.em;m.d/=this.em;l.removeChild(this.HDspan);l.style.position=k;return m},getW:function(o){var l,n,m=(o.bbox||{}).w,p=o;if(o.bbox&&this.config.noReflows&&o.bbox.exactW!==false){if(!o.bbox.exactW){if(o.style.paddingLeft){m+=this.unEm(o.style.paddingLeft)*(o.scale||1)}if(o.style.paddingRight){m+=this.unEm(o.style.paddingRight)*(o.scale||1)}}return m}if(o.bbox&&o.bbox.exactW){return 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k.toFixed(3).replace(/\.?0+$/,"")+"em"},EmRounded:function(k){k=(Math.round(k*d.em)+0.05)/d.em;if(Math.abs(k)<0.0006){return"0em"}return k.toFixed(3).replace(/\.?0+$/,"")+"em"},unEm:function(k){return parseFloat(k)},Px:function(k){k*=this.em;var l=(k<0?"-":"");return l+Math.abs(k).toFixed(1).replace(/\.?0+$/,"")+"px"},unPx:function(k){return parseFloat(k)/this.em},Percent:function(k){return(100*k).toFixed(1).replace(/\.?0+$/,"")+"%"},length2em:function(r,l,p){if(typeof(r)!=="string"){r=r.toString()}if(r===""){return""}if(r===g.SIZE.NORMAL){return 1}if(r===g.SIZE.BIG){return 2}if(r===g.SIZE.SMALL){return 0.71}if(r==="infinity"){return d.BIGDIMEN}var o=this.FONTDATA.TeX_factor,s=(d.zoomScale||1)/d.em;if(r.match(/mathspace$/)){return d.MATHSPACE[r]*o}var n=r.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var k=parseFloat(n[1]||"1"),q=n[2];if(p==null){p=1}if(l==null){l=1}if(q==="em"){return k*o}if(q==="ex"){return k*d.TeX.x_height*o}if(q==="%"){return k/100*p}if(q==="px"){return k*s}if(q==="pt"){return k/10*o}if(q==="pc"){return k*1.2*o}if(q==="in"){return k*this.pxPerInch*s}if(q==="cm"){return k*this.pxPerInch*s/2.54}if(q==="mm"){return k*this.pxPerInch*s/25.4}if(q==="mu"){return k/18*o*l}return k*p},thickness2em:function(l,k){var m=d.TeX.rule_thickness;if(l===g.LINETHICKNESS.MEDIUM){return m}if(l===g.LINETHICKNESS.THIN){return 0.67*m}if(l===g.LINETHICKNESS.THICK){return 1.67*m}return this.length2em(l,k,m)},getPadding:function(l){var n={top:0,right:0,bottom:0,left:0},k=false;for(var o in n){if(n.hasOwnProperty(o)){var m=l.style["padding"+o.charAt(0).toUpperCase()+o.substr(1)];if(m){n[o]=this.length2em(m);k=true}}}return(k?n:false)},getBorders:function(p){var m={top:0,right:0,bottom:0,left:0},n={},l=false;for(var q in m){if(m.hasOwnProperty(q)){var k="border"+q.charAt(0).toUpperCase()+q.substr(1);var o=p.style[k+"Style"];if(o){l=true;m[q]=this.length2em(p.style[k+"Width"]);n[k]=[p.style[k+"Width"],p.style[k+"Style"],p.style[k+"Color"]].join(" ")}}}m.css=n;return(l?m:false)},setBorders:function(k,l){if(l){for(var m in l.css){if(l.css.hasOwnProperty(m)){k.style[m]=l.css[m]}}}},createStrut:function(m,l,n){var k=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:l+"px",width:"1px",marginRight:"-1px"}});if(n){m.insertBefore(k,m.firstChild)}else{m.appendChild(k)}return k},createBlank:function(l,k,m){var n=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(k)}});if(k<0){n.style.marginRight=n.style.width;n.style.width=0}if(m){l.insertBefore(n,l.firstChild)}else{l.appendChild(n)}return n},createShift:function(l,k,n){var m=this.Element("span",{style:{marginLeft:this.Em(k)},isMathJax:true});if(n){l.insertBefore(m,l.firstChild)}else{l.appendChild(m)}return m},createSpace:function(p,n,o,q,m,s){if(n<-o){o=-n}var r=this.Em(n+o),k=this.Em(-o);if(this.msieInlineBlockAlignBug){k=this.Em(d.getHD(p.parentNode).d-o)}if(p.isBox||s){var l=(p.scale==null?1:p.scale);p.bbox={exactW:true,h:n*l,d:o*l,w:q*l,rw:q*l,lw:0};p.style.height=r;p.style.verticalAlign=k;p.HH=(n+o)*l}else{p=this.addElement(p,"span",{style:{height:r,verticalAlign:k},isMathJax:true})}if(q>=0){p.style.width=this.Em(q);p.style.display="inline-block";p.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){p.style.height=""}p.style.marginLeft=this.Em(q);if(d.safariNegativeSpaceBug&&p.parentNode.firstChild==p){this.createBlank(p,0,true)}}if(m&&m!==g.COLOR.TRANSPARENT){p.style.backgroundColor=m;p.style.position="relative"}return p},createRule:function(r,n,p,s,l){if(n<-p){p=-n}var m=d.TeX.min_rule_thickness,o=1;if(s>0&&s*this.em<m){s=m/this.em}if(n+p>0&&(n+p)*this.em<m){o=1/(n+p)*(m/this.em);n*=o;p*=o}if(!l){l="solid"}else{l="solid "+l}l=this.Em(s)+" "+l;var t=(o===1?this.Em(n+p):m+"px"),k=this.Em(-p);var q=this.addElement(r,"span",{style:{borderLeft:l,display:"inline-block",overflow:"hidden",width:0,height:t,verticalAlign:k},bbox:{h:n,d:p,w:s,rw:s,lw:0,exactW:true},noAdjust:true,HH:n+p,isMathJax:true});if(this.msieRuleBug&&s>0){q.style.width=this.Em(s)}if(r.isBox||r.className=="mspace"){r.bbox=q.bbox,r.HH=n+p}return q},createFrame:function(s,q,r,u,x,l){if(q<-r){r=-q}var p=2*x;if(this.msieFrameSizeBug){if(u<p){u=p}if(q+r<p){q=p-r}}if(this.msieBorderWidthBug){p=0}var v=this.Em(q+r-p),k=this.Em(-r-x),o=this.Em(u-p);var m=this.Em(x)+" "+l;var n=this.addElement(s,"span",{style:{border:m,display:"inline-block",overflow:"hidden",width:o,height:v},bbox:{h:q,d:r,w:u,rw:u,lw:0,exactW:true},noAdjust:true,HH:q+r,isMathJax:true});if(k){n.style.verticalAlign=k}return n},parentNode:function(l){var k=l.parentNode;if(k.nodeName.toLowerCase()==="a"){k=k.parentNode}return k},createStack:function(m,o,l){if(this.msiePaddingWidthBug){this.createStrut(m,0)}var n=String(l).match(/%$/);var k=(!n&&l!=null?l:0);m=this.addElement(m,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(n?"100%":this.Em(k)),height:0}});if(!o){m.parentNode.bbox=m.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:k,lw:this.BIGDIMEN,rw:(!n&&l!=null?l:-this.BIGDIMEN)};if(n){m.bbox.width=l}}return m},createBox:function(l,k){var m=this.addElement(l,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(k!=null){m.style.width=k}return m},addBox:function(k,l){l.style.position="absolute";l.isBox=l.isMathJax=true;return k.appendChild(l)},placeBox:function(u,s,q,o){u.isMathJax=true;var v=d.parentNode(u),C=u.bbox,z=v.bbox;if(this.msiePlaceBoxBug){this.addText(u,this.NBSP)}if(this.imgSpaceBug){this.addText(u,this.imgSpace)}var w,F=0;if(u.HH!=null){w=u.HH}else{if(C){w=Math.max(3,C.h+C.d)}else{w=u.offsetHeight/this.em}}if(!u.noAdjust){w+=1;w=Math.round(w*this.em)/this.em;if(this.msieInlineBlockAlignBug){this.addElement(u,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(w)}})}else{this.addElement(u,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(w)}});if(d.chromeHeightBug){w-=(u.lastChild.offsetHeight-Math.round(w*this.em))/this.em}}}if(C){if(this.initialSkipBug){if(C.lw<0){F=C.lw;d.createBlank(u,-F,true)}if(C.rw>C.w){d.createBlank(u,C.rw-C.w+0.1)}}if(!this.msieClipRectBug&&!C.noclip&&!o){var B=3/this.em;var A=(C.H==null?C.h:C.H),m=(C.D==null?C.d:C.D);var E=w-A-B,p=w+m+B,n=-1000,k=1000;u.style.clip="rect("+this.Em(E)+" "+this.Em(k)+" "+this.Em(p)+" 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k=0,p=v-u.w/2,n="50%";if(this.initialSkipBug){k=u.w-u.rw-0.1;p+=u.lw}if(this.msieMarginScaleBug){p=(p*this.em)+"px"}else{p=this.Em(p)}if(t){p=(v===0?"":this.Em(v));n=(50-parseFloat(u.width)/2)+"%"}b.Insert(s.style,({right:{left:"",right:this.Em(k-v)},center:{left:n,marginLeft:p}})[o])},setStackWidth:function(l,k){if(typeof(k)==="number"){l.style.width=this.Em(Math.max(0,k));var m=l.bbox;if(m){m.w=k;m.exactW=true}m=l.parentNode.bbox;if(m){m.w=k;m.exactW=true}}else{l.style.width=l.parentNode.style.width="100%";if(l.bbox){l.bbox.width=k}if(l.parentNode.bbox){l.parentNode.bbox.width=k}}},createDelimiter:function(u,k,n,q,o){if(!k){u.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};u.bbox.rw=u.bbox.w;this.createSpace(u,u.bbox.h,u.bbox.d,u.bbox.w);return}if(!q){q=1}if(!(n instanceof Array)){n=[n,n]}var t=n[1];n=n[0];var l={alias:k};while(l.alias){k=l.alias;l=this.FONTDATA.DELIMITERS[k];if(!l){l={HW:[0,this.FONTDATA.VARIANT[g.VARIANT.NORMAL]]}}}if(l.load){b.RestartAfter(h.Require(this.fontDir+"/fontdata-"+l.load+".js"))}for(var s=0,p=l.HW.length;s<p;s++){if(l.HW[s][0]*q>=n-0.01||(s==p-1&&!l.stretch)){if(l.HW[s][2]){q*=l.HW[s][2]}if(l.HW[s][3]){k=l.HW[s][3]}var r=this.addElement(u,"span");this.createChar(r,[k,l.HW[s][1]],q,o);u.bbox=r.bbox;u.offset=0.65*u.bbox.w;u.scale=q;return}}if(l.stretch){this["extendDelimiter"+l.dir](u,t,l.stretch,q,o)}},extendDelimiterV:function(A,t,E,F,w){var o=this.createStack(A,true);var v=this.createBox(o),u=this.createBox(o);this.createChar(v,(E.top||E.ext),F,w);this.createChar(u,(E.bot||E.ext),F,w);var m={bbox:{w:0,lw:0,rw:0}},D=m,p;var B=v.bbox.h+v.bbox.d+u.bbox.h+u.bbox.d;var r=-v.bbox.h;this.placeBox(v,0,r,true);r-=v.bbox.d;if(E.mid){D=this.createBox(o);this.createChar(D,E.mid,F,w);B+=D.bbox.h+D.bbox.d}if(E.min&&t<B*E.min){t=B*E.min}if(t>B){m=this.Element("span");this.createChar(m,E.ext,F,w);var C=m.bbox.h+m.bbox.d,l=C-0.05,x,q,z=(E.mid?2:1);q=x=Math.min(Math.ceil((t-B)/(z*l)),this.maxStretchyParts);if(!E.fullExtenders){l=(t-B)/(z*x)}var 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l=this.Element("span");this.createChar(l,E.rep,G,y);var D={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},m;this.placeBox(p,-p.bbox.lw,0,true);var u=(p.bbox.rw-p.bbox.lw)+(C.bbox.rw-C.bbox.lw)-0.05,t=p.bbox.rw-p.bbox.lw-0.025,v;if(E.mid){D=this.createBox(r);this.createChar(D,E.mid,G,y);u+=D.bbox.w}if(E.min&&o<u*E.min){o=u*E.min}if(o>u){var F=l.bbox.rw-l.bbox.lw,q=F-0.05,z,s,A=(E.mid?2:1);s=z=Math.min(Math.ceil((o-u)/(A*q)),this.maxStretchyParts);if(!E.fillExtenders){q=(o-u)/(A*z)}v=(z/(z+1))*(F-q);q=F-v;t-=l.bbox.lw+v;while(A-->0){while(z-->0){if(!this.cloneNodeBug){m=l.cloneNode(true)}else{m=this.Element("span");this.createChar(m,E.rep,G,y)}m.bbox=l.bbox;this.placeBox(this.addBox(r,m),t,0,true);t+=q}if(E.mid&&A){this.placeBox(D,t,0,true);t+=D.bbox.w-v;z=s}}}else{t-=(u-o)/2;if(E.mid){this.placeBox(D,t,0,true);t+=D.bbox.w}t-=(u-o)/2}this.placeBox(C,t,0,true);B.bbox={w:t+C.bbox.rw,lw:0,rw:t+C.bbox.rw,H:Math.max(p.bbox.h,l.bbox.h,C.bbox.h,D.bbox.h),D:Math.max(p.bbox.d,l.bbox.d,C.bbox.d,D.bbox.d),h:l.bbox.h,d:l.bbox.d,exactW:true};B.scale=G;B.isMultiChar=true;this.setStackWidth(r,B.bbox.w)},createChar:function(s,p,n,k){s.isMathJax=true;var r=s,t="",o={fonts:[p[1]],noRemap:true};if(k&&k===g.VARIANT.BOLD){o.fonts=[p[1]+"-bold",p[1]]}if(typeof(p[1])!=="string"){o=p[1]}if(p[0] instanceof Array){for(var q=0,l=p[0].length;q<l;q++){t+=String.fromCharCode(p[0][q])}}else{t=String.fromCharCode(p[0])}if(p[4]){n*=p[4]}if(n!==1||p[3]){r=this.addElement(s,"span",{style:{fontSize:this.Percent(n)},scale:n,isMathJax:true});this.handleVariant(r,o,t);s.bbox=r.bbox}else{this.handleVariant(s,o,t)}if(p[2]){s.style.marginLeft=this.Em(p[2])}if(p[3]){s.firstChild.style.verticalAlign=this.Em(p[3]);s.bbox.h+=p[3];if(s.bbox.h<0){s.bbox.h=0}}if(p[5]){s.bbox.h+=p[5]}if(p[6]){s.bbox.d+=p[6]}if(this.AccentBug&&s.bbox.w===0){r.firstChild.nodeValue+=this.NBSP}},positionDelimiter:function(l,k){k-=l.bbox.h;l.bbox.d-=k;l.bbox.h+=k;if(k){if(this.safariVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&l.isMultiChar)){if(l.firstChild.style.display===""&&l.style.top!==""){l=l.firstChild;k-=d.unEm(l.style.top)}l.style.position="relative";l.style.top=this.Em(-k)}else{l.style.verticalAlign=this.Em(k);if(d.ffVerticalAlignBug){d.createRule(l.parentNode,l.bbox.h,0,0);delete 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v=!!k.style.fontFamily||!!z.style.fontStyle||!!z.style.fontWeight||!s.directory||l;l=false;if(k!==z){v=!this.checkFont(s,z.style);k=z}if(v){k=this.addElement(z,"span",{isMathJax:true,subSpan:true})}this.handleFont(k,s,k!==z)}y=this.handleChar(k,s,B,w,y);if(!(B[5]||{}).space){if(B[0]/1000>z.bbox.h){z.bbox.h=B[0]/1000}if(B[1]/1000>z.bbox.d){z.bbox.d=B[1]/1000}}if(z.bbox.w+B[3]/1000<z.bbox.lw){z.bbox.lw=z.bbox.w+B[3]/1000}if(z.bbox.w+B[4]/1000>z.bbox.rw){z.bbox.rw=z.bbox.w+B[4]/1000}z.bbox.w+=B[2]/1000;if((B[5]||{}).isUnknown){z.bbox.exactW=false}}if(y.length){this.addText(k,y)}if(z.scale&&z.scale!==1){z.bbox.h*=z.scale;z.bbox.d*=z.scale;z.bbox.w*=z.scale;z.bbox.lw*=z.scale;z.bbox.rw*=z.scale}if(r.length==1&&s.skew&&s.skew[w]){z.bbox.skew=s.skew[w]}},checkFont:function(k,l){var m=(l.fontWeight||"normal");if(m.match(/^\d+$/)){m=(parseInt(m)>=600?"bold":"normal")}return(k.family.replace(/'/g,"")===l.fontFamily.replace(/'/g,"")&&(k.style||"normal")===(l.fontStyle||"normal")&&(k.weight||"normal")===m)},handleFont:function(m,k,o){m.style.fontFamily=k.family;if(!k.directory){m.style.fontSize=Math.floor(d.config.scale/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&k.isWebFont)){var l=k.style||"normal",n=k.weight||"normal";if(l!=="normal"||o){m.style.fontStyle=l}if(n!=="normal"||o){m.style.fontWeight=n}}},handleChar:function(l,k,s,r,q){var p=s[5];if(p.space){if(q.length){this.addText(l,q)}d.createShift(l,s[2]/1000);return""}if(p.img){return this.handleImg(l,k,s,r,q)}if(p.isUnknown&&this.FONTDATA.DELIMITERS[r]){if(q.length){this.addText(l,q)}var o=l.scale;d.createDelimiter(l,r,0,1,k);if(this.FONTDATA.DELIMITERS[r].dir==="V"){l.style.verticalAlign=this.Em(l.bbox.d);l.bbox.h+=l.bbox.d;l.bbox.d=0}l.scale=o;s[0]=l.bbox.h*1000;s[1]=l.bbox.d*1000;s[2]=l.bbox.w*1000;s[3]=l.bbox.lw*1000;s[4]=l.bbox.rw*1000;return""}if(p.c==null){if(r<=65535){p.c=String.fromCharCode(r)}else{var m=r-65536;p.c=String.fromCharCode((m>>10)+55296)+String.fromCharCode((m&1023)+56320)}}if(p.rfix){this.addText(l,q+p.c);d.createShift(l,p.rfix/1000);return""}if(s[2]||!this.msieAccentBug||q.length){return q+p.c}d.createShift(l,s[3]/1000);d.createShift(l,(s[4]-s[3])/1000);this.addText(l,p.c);d.createShift(l,-s[4]/1000);return""},handleImg:function(l,k,p,o,m){return m},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof 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k=MathJax.Callback.Queue();k.Push(["Require",h,this.fontDir+"/"+l]);if(this.imgFonts){if(!MathJax.isPacked){l=l.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}k.Push(["Require",h,this.webfontDir+"/png/"+l])}b.RestartAfter(k.Push({}))},loadWebFont:function(k){k.available=k.isWebFont=true;if(d.FontFaceBug){k.family=k.name;if(d.msieFontCSSBug){k.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(k))},loadWebFontError:function(l,k){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");l.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");e(["WebFontNotAvailable","Web-Fonts not available -- using image fonts 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t=e.Element("span",{},[["span",{className:"MJXc-over"}]]);t.firstChild.appendChild(q.lastChild);if(q.childNodes.length>(this.data[this.under]?1:0)){t.firstChild.appendChild(q.firstChild)}this.data[this.over].CHTMLhandleScriptlevel(t.firstChild.firstChild);if(r!=null){if(p.vec){t.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}r=r-p.d+0.1;if(u.t!=null){r+=u.t-u.h}t.firstChild.firstChild.style.marginBottom=g.Em(r)}if(q.firstChild){q.insertBefore(t,q.firstChild)}else{q.appendChild(t)}}if(this.data[this.under]){q.lastChild.firstChild.style.marginLeft=s.l=q.lastChild.firstChild.marginRight=s.r=0;this.data[this.under].CHTMLhandleScriptlevel(q.lastChild)}o.w=Math.max(0.8*p.w,0.8*s.w,u.w);o.h=0.8*(p.h+p.d+(r||0))+u.h;o.d=u.d+0.8*(s.h+s.d);return q}});h.msubsup.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.CHTML.h-0.4),u=Math.max(0.2,s.CHTML.d+0.1);var t=this.CHTML;if(n&&p){var r=e.Element("span",{className:"MJXc-script-box",style:{height:g.Em(o+n.CHTML.h*0.8+u+p.CHTML.d*0.8),"vertical-align":g.Em(-u-p.CHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.CHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.CHTML.h-0.05))}}]]]]]]);p.CHTMLhandleScriptlevel(r.firstChild);n.CHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.CHTML.h,n.CHTML.h*0.8+o);t.d=Math.max(s.CHTML.d,p.CHTML.d*0.8+u);t.w=s.CHTML.w+Math.max(n.CHTML.w,p.CHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.CHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.CHTML.h,n.CHTML.h*0.8+o);t.d=Math.max(s.CHTML.d,n.CHTML.d*0.8-o);t.w=s.CHTML.w+n.CHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.CHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.CHTML.h,p.CHTML.h*0.8-u);t.d=Math.max(s.CHTML.d,p.CHTML.d*0.8+u);t.w=s.CHTML.w+p.CHTML.w+0.07}}}return q}});h.mfrac.Augment({toCommonHTML:function(r){r=this.CHTMLdefaultSpan(r,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].CHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].CHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXc-box",style:{"margin-top":"-.8em"}},[["span",{className:"MJXc-denom"},[["span",{},[["span",{className:"MJXc-rule"}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.CHTMLbboxFor(0),p=this.CHTMLbboxFor(1),v=this.CHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-0.9);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}return r}});h.msqrt.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});this.CHTMLlayoutRoot(n,n.firstChild);return n},CHTMLlayoutRoot:function(u,n){var v=this.CHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXc-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXc-root"},[["span",{className:"MJXc-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXc-right MJXc-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.CHTML.h=v.h+0.18;this.CHTML.d=v.d;this.CHTML.w=v.w+p;return u}});h.mroot.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});var p=this.CHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.CHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXc-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.CHTML.w+=Math.max(0,p.w*0.8+s);this.CHTML.h=Math.max(this.CHTML.h,p.h*0.8+o);return q},CHTMLlayoutRoot:h.msqrt.prototype.CHTMLlayoutRoot});h.mfenced.Augment({toCommonHTML:function(q){q=this.CHTMLcreateSpan(q);this.CHTMLhandleStyle(q);this.CHTMLhandleColor(q);this.addFakeNodes();this.CHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;p<n;p++){this.CHTMLaddChild(q,"sep"+p,{});this.CHTMLaddChild(q,p,{})}this.CHTMLaddChild(q,"close",{});var o=this.CHTML.h,r=this.CHTML.d;this.CHTMLstretchChild("open",o,r);for(p=0,n=this.data.length;p<n;p++){this.CHTMLstretchChild("sep"+p,o,r);this.CHTMLstretchChild(p,o,r)}this.CHTMLstretchChild("close",o,r);return q}});h.mrow.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q);var p=this.CHTML.h,r=this.CHTML.d;for(var o=0,n=this.data.length;o<n;o++){this.CHTMLstretchChild(o,p,r)}return q}});h.mstyle.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n);this.CHTMLhandleScriptlevel(n);return n}});h.TeXAtom.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n);n.className="MJXc-mrow";return n}});h.mtable.Augment({toCommonHTML:function(E){E=this.CHTMLdefaultSpan(E,{noBBox:true});var r=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","width");var u=MathJax.Hub.SplitList,F,A,D,z;var N=u(r.columnspacing),w=u(r.rowspacing),L=u(r.columnalign),t=u(r.rowalign);for(F=0,A=N.length;F<A;F++){N[F]=g.length2em(N[F])}for(F=0,A=w.length;F<A;F++){w[F]=g.length2em(w[F])}var K=e.Element("span");while(E.firstChild){K.appendChild(E.firstChild)}E.appendChild(K);var y=0,s=0;for(F=0,A=this.data.length;F<A;F++){var v=this.data[F];if(v){var J=g.arrayEntry(w,F-1),C=g.arrayEntry(t,F);var x=v.CHTML,q=v.CHTMLspanElement();q.style.verticalAlign=C;var B=(v.type==="mlabeledtr"?1:0);for(D=0,z=v.data.length;D<z-B;D++){var p=v.data[D+B];if(p){var M=g.arrayEntry(N,D-1),G=g.arrayEntry(L,D);var I=p.CHTMLspanElement();if(D){x.w+=M;I.style.paddingLeft=g.Em(M)}if(F){I.style.paddingTop=g.Em(J)}I.style.textAlign=G}}y+=x.h+x.d;if(F){y+=J}if(x.w>s){s=x.w}}}var o=this.CHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({CHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.CHTMLcreateSpan(q);this.CHTMLhandleStyle(q);this.CHTMLhandleColor(q);if(this.isToken){this.CHTMLhandleToken(q)}for(var p=1,n=this.data.length;p<n;p++){this.CHTMLaddChild(q,p,o)}return q}});h.semantics.Augment({toCommonHTML:function(n){n=this.CHTMLcreateSpan(n);if(this.data[0]){this.data[0].toCommonHTML(n);MathJax.Hub.Insert(this.data[0].CHTML||{},this.CHTML)}return n}});h.annotation.Augment({toCommonHTML:function(n){}});h["annotation-xml"].Augment({toCommonHTML:function(n){}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",g,"jax.js"]),0)})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){i.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.CommonHTML);
(function(a,d){var b=a.config.menuSettings;var c=MathJax.Extension["CHTML-preview"]={version:"2.5.0",config:a.CombineConfig("CHTML-preview",{Chunks:{EqnChunk:10000,EqnChunkFactor:1,EqnChunkDelay:0},color:"inherit!important",updateTime:30,updateDelay:6,messageStyle:"none",disabled:false}),Config:function(){a.Config({"HTML-CSS":this.config.Chunks,SVG:this.config.Chunks});MathJax.Ajax.Styles({".MathJax_Preview .MJXc-math":{color:this.config.color}});var j,g,h,e,i;var f=this.config;if(!f.disabled&&b.CHTMLpreview==null){a.Config({menuSettings:{CHTMLpreview:true}})}a.Register.MessageHook("Begin Math Output",function(){if(!e&&b.CHTMLpreview&&b.renderer!=="CommonHTML"){j=a.processUpdateTime;g=a.processUpdateDelay;h=a.config.messageStyle;a.processUpdateTime=f.updateTime;a.processUpdateDelay=f.updateDelay;a.Config({messageStyle:f.messageStyle});MathJax.Message.Clear(0,0);i=true}});a.Register.MessageHook("End Math Output",function(){if(!e&&i){a.processUpdateTime=j;a.processUpdateDelay=g;a.Config({messageStyle:h});e=true}})},Preview:function(e){if(!b.CHTMLpreview||b.renderer==="CommonHTML"){return}var f=e.script.MathJax.preview||e.script.previousSibling;if(!f||f.className!==MathJax.Hub.config.preRemoveClass){f=d.Element("span",{className:MathJax.Hub.config.preRemoveClass});e.script.parentNode.insertBefore(f,e.script);e.script.MathJax.preview=f}f.innerHTML="";f.style.color="inherit";return this.postFilter(f,e)},postFilter:function(g,f){if(!f.math.root.toCommonHTML){var e=MathJax.Callback.Queue();e.Push(["Require",MathJax.Ajax,"[MathJax]/jax/output/CommonHTML/config.js"],["Require",MathJax.Ajax,"[MathJax]/jax/output/CommonHTML/jax.js"]);a.RestartAfter(e.Push({}))}f.math.root.toCommonHTML(g)},Register:function(e){a.Register.StartupHook(e+" Jax Require",function(){var f=MathJax.InputJax[e];f.postfilterHooks.Add(["Preview",MathJax.Extension["CHTML-preview"]],50)})}};c.Register("TeX");c.Register("MathML");c.Register("AsciiMath");a.Register.StartupHook("End Config",["Config",c]);a.Startup.signal.Post("CHTML-preview Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/CHTML-preview.js");
MathJax.Ajax.loadComplete("[MathJax]/config/TeX-MML-AM_HTMLorMML-full.js");
