/*
 *  /MathJax/config/TeX-AMS-MML_HTMLorMML-full.js
 *  
 *  Copyright (c) 2010-2018 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/output/HTML-CSS/config.js",
  "[MathJax]/jax/output/NativeMML/config.js",
  "[MathJax]/jax/output/PreviewHTML/config.js",
  "[MathJax]/config/MMLorHTML.js",
  "[MathJax]/extensions/tex2jax.js",
  "[MathJax]/extensions/mml2jax.js",
  "[MathJax]/extensions/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/output/NativeMML/jax.js",
  "[MathJax]/jax/output/HTML-CSS/jax.js",
  "[MathJax]/jax/output/HTML-CSS/autoload/mtable.js",
  "[MathJax]/jax/output/PreviewHTML/jax.js",
  "[MathJax]/extensions/fast-preview.js",
  "[MathJax]/extensions/AssistiveMML.js",
  "[MathJax]/extensions/a11y/accessibility-menu.js"
);

MathJax.Hub.Config({
  extensions: ['[a11y]/accessibility-menu.js']
});

MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.8",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(/\s/g,"_")},formatURL:function(b,a){return a+"#"+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js");
MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.8",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.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.7.8",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:"2.7.8",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.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.8",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js");
(function(c,g){var f="2.7.0";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:"2.7.8",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},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(c){if(c.nodeValue.replace(/\s+/,"")==""){return c}var b,d,e=0,a;this.search={start:true};this.pattern=this.start;while(c){a=null;this.pattern.lastIndex=e;e=0;while(c&&c.nodeName.toLowerCase()==="#text"&&(b=this.pattern.exec(c.nodeValue))){if(this.search.start){c=this.startMatch(b,c)}else{c=this.endMatch(b,c)}}if(this.search.matched){c=this.encloseMath(c)}else{if(!this.search.start&&!this.search.close){a=this.search}}if(c){do{d=c;c=c.nextSibling}while(c&&this.ignoreTags[c.nodeName.toLowerCase()]!=null);if(!c||c.nodeName!=="#text"){if(!a){return(this.search.close?this.prevEndMatch():d)}c=a.open;e=a.opos+a.olen+(a.blen||0);this.search={start:true};this.pattern=this.start}}}return c},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,blen:a[1].length+3,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)}}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,g=a.close,f,d,c;if(a.cpos===g.length){g=g.nextSibling}else{g=g.splitText(a.cpos)}if(!g){f=g=MathJax.HTML.addText(a.close.parentNode,"")}a.close=g;d=(a.opos?a.open.splitText(a.opos):a.open);while((c=d.nextSibling)&&c!==g){if(c.nodeValue!==null){if(c.nodeName==="#comment"){d.nodeValue+=c.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{d.nodeValue+=c.nodeValue}}else{var h=this.ignoreTags[c.nodeName.toLowerCase()];d.nodeValue+=(h==null?" ":h)}d.parentNode.removeChild(c)}var e=d.nodeValue.substr(a.olen,d.nodeValue.length-a.olen-a.clen);d.parentNode.removeChild(d);if(this.config.preview!=="none"){this.createPreview(a.mode,e)}d=this.createMathTag(a.mode,e);this.search={};this.pattern.lastIndex=0;if(f){f.parentNode.removeChild(f)}return d},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(d,a){var b=MathJax.Hub.config.preRemoveClass;var c=this.config.preview;if(c==="none"){return}if((this.search.close.previousSibling||{}).className===b){return}if(c==="TeX"){c=[this.filterPreview(a)]}if(c){c=MathJax.HTML.Element("span",{className:b},c);this.insertNode(c)}},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}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js");
MathJax.Extension.mml2jax={version:"2.7.8",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&&!j.isMathJax&&!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(g,f){var e=this.config.preview;if(e==="none"){return}var i=false;var c=MathJax.Hub.config.preRemoveClass;if((f.previousSibling||{}).className===c){return}if(e==="mathml"){i=true;if(this.MathTagBug){e="alttext"}else{e=g.cloneNode(true)}}if(e==="alttext"||e==="altimg"){i=true;var d=this.filterPreview(g.getAttribute("alttext"));if(e==="alttext"){if(d!=null){e=MathJax.HTML.TextNode(d)}else{e=null}}else{var a=g.getAttribute("altimg");if(a!=null){var b={width:g.getAttribute("altimg-width"),height:g.getAttribute("altimg-height")};e=MathJax.HTML.Element("img",{src:a,alt:d,style:b})}else{e=null}}}if(e){var h;if(i){h=MathJax.HTML.Element("span",{className:c});h.appendChild(e)}else{h=MathJax.HTML.Element("span",{className:c},e)}f.parentNode.insertBefore(h,f)}},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");
(function(d,h,l,g,m,b,j){var p="2.7.8";var i=MathJax.Extension;var c=i.MathEvents={version:p};var k=d.config.menuSettings;var o={hover:500,frame:{x:3.5,y:5,bwidth:1,bcolor:"#A6D",hwidth:"15px",hcolor:"#83A"},button:{x:-6,y:-3,wx:-2},fadeinInc:0.2,fadeoutInc:0.05,fadeDelay:50,fadeoutStart:400,fadeoutDelay:15*1000,styles:{".MathJax_Hover_Frame":{"border-radius":".25em","-webkit-border-radius":".25em","-moz-border-radius":".25em","-khtml-border-radius":".25em","box-shadow":"0px 0px 15px #83A","-webkit-box-shadow":"0px 0px 15px #83A","-moz-box-shadow":"0px 0px 15px #83A","-khtml-box-shadow":"0px 0px 15px #83A",border:"1px solid #A6D ! important",display:"inline-block",position:"absolute"},".MathJax_Menu_Button .MathJax_Hover_Arrow":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"4px","-webkit-border-radius":"4px","-moz-border-radius":"4px","-khtml-border-radius":"4px","font-family":"'Courier 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A=o.frame.x,z=o.frame.y,x=o.frame.bwidth;if(c.msieBorderWidthBug){x=0}q.hover={opacity:0,id:q.inputID+"-Hover"};var r=h.Element("span",{id:q.hover.id,isMathJax:true,style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{className:"MathJax_Hover_Frame",isMathJax:true,style:{display:"inline-block",position:"absolute",top:this.Px(-y.h-z-x-(y.y||0)),left:this.Px(-A-x+(y.x||0)),width:this.Px(y.w+2*A),height:this.Px(y.h+y.d+2*z),opacity:0,filter:"alpha(opacity=0)"}}]]);var s=h.Element("span",{isMathJax:true,id:q.hover.id+"Menu",className:"MathJax_Menu_Button",style:{display:"inline-block","z-index":1,width:0,height:0,position:"relative"}},[["span",{className:"MathJax_Hover_Arrow",isMathJax:true,math:u,onclick:this.HoverMenu,jax:t.id,style:{left:this.Px(y.w+A+x+(y.x||0)+o.button.x),top:this.Px(-y.h-z-x-(y.y||0)-o.button.y),opacity:0,filter:"alpha(opacity=0)"}},[["span",{isMathJax:true},"\u25BC"]]]]);if(y.width){r.style.width=s.style.width=y.width;r.style.marginRight=s.style.marginRight="-"+y.width;r.firstChild.style.width=y.width;s.firstChild.style.left="";s.firstChild.style.right=this.Px(o.button.wx)}v.parentNode.insertBefore(r,v);if(w){v.parentNode.insertBefore(s,v)}if(v.style){v.style.position="relative"}this.ReHover(q)},ReHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}q.hover.remove=setTimeout(g(["UnHover",this,q]),o.fadeoutDelay);this.HoverFadeTimer(q,o.fadeinInc)},UnHover:function(q){if(!q.hover.nofade){this.HoverFadeTimer(q,-o.fadeoutInc,o.fadeoutStart)}},HoverFade:function(q){delete 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r=q.versionAtLeast("8.0");c.msieBorderWidthBug=(document.compatMode==="BackCompat");c.msieEventBug=q.isIE9;c.msieAlignBug=(!r||s<8);if(s<9){n.LEFTBUTTON=1}},Safari:function(q){c.safariContextMenuBug=true},Opera:function(q){c.operaPositionBug=true},Konqueror:function(q){c.noContextMenuBug=true}});c.topImg=(c.msieAlignBug?h.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):h.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(c.operaPositionBug){c.topImg.style.border="1px solid"}c.config=o=d.CombineConfig("MathEvents",o);var e=function(){var q=o.styles[".MathJax_Hover_Frame"];q.border=o.frame.bwidth+"px solid "+o.frame.bcolor+" ! important";q["box-shadow"]=q["-webkit-box-shadow"]=q["-moz-box-shadow"]=q["-khtml-box-shadow"]="0px 0px "+o.frame.hwidth+" "+o.frame.hcolor};g.Queue(d.Register.StartupHook("End Config",{}),[e],["getImages",f],["Styles",l,o.styles],["Post",d.Startup.signal,"MathEvents 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(function(a,d,f,c,j){var k="2.7.8";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","-webkit-box-sizing":"content-box","-moz-box-sizing":"content-box","box-sizing":"content-box","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 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n,m;if(this.stack.env.font){n={mathvariant:this.stack.env.font}}if(g.remap.hasOwnProperty(o)){o=g.remap[o];if(f(o)){n=o[1];o=o[0]}m=i.mo(i.entity("#x"+o)).With(n)}else{m=i.mo(o).With(n)}if(m.autoDefault("stretchy",true)){m.stretchy=false}if(m.autoDefault("texClass",true)==""){m=i.TeXAtom(m)}this.Push(this.mmlToken(m))},SetFont:function(n,m){this.stack.env.font=m},SetStyle:function(n,m,o,p){this.stack.env.style=m;this.stack.env.level=p;this.Push(b.style().With({styles:{displaystyle:o,scriptlevel:p}}))},SetSize:function(m,n){this.stack.env.size=n;this.Push(b.style().With({styles:{mathsize:n+"em"}}))},Color:function(o){var n=this.GetArgument(o);var m=this.stack.env.color;this.stack.env.color=n;var p=this.ParseArg(o);if(m){this.stack.env.color=m}else{delete this.stack.env.color}this.Push(i.mstyle(p).With({mathcolor:n}))},Spacer:function(m,n){this.Push(i.mspace().With({width:n,mathsize:i.SIZE.NORMAL,scriptlevel:0}))},LeftRight:function(m){this.Push(b[m.substr(1)]().With({delim:this.GetDelimiter(m)}))},Middle:function(m){var n=this.GetDelimiter(m);this.Push(i.TeXAtom().With({texClass:i.TEXCLASS.CLOSE}));if(this.stack.Top().type!=="left"){d.Error(["MisplacedMiddle","%1 must be within \\left and \\right",m])}this.Push(i.mo(n).With({stretchy:true}));this.Push(i.TeXAtom().With({texClass:i.TEXCLASS.OPEN}))},NamedFn:function(n,o){if(!o){o=n.substr(1)}var m=i.mi(o).With({texClass:i.TEXCLASS.OP});this.Push(b.fn(this.mmlToken(m)))},NamedOp:function(n,o){if(!o){o=n.substr(1)}o=o.replace(/&thinsp;/,"\u2006");var m=i.mo(o).With({movablelimits:true,movesupsub:true,form:i.FORM.PREFIX,texClass:i.TEXCLASS.OP});this.Push(this.mmlToken(m))},Limits:function(n,m){var p=this.stack.Prev("nopop");if(!p||(p.Get("texClass")!==i.TEXCLASS.OP&&p.movesupsub==null)){d.Error(["MisplacedLimits","%1 is allowed only on operators",n])}var o=this.stack.Top();if(p.type==="munderover"&&!m){p=o.data[o.data.length-1]=i.msubsup.apply(i.subsup,p.data)}else{if(p.type==="msubsup"&&m){p=o.data[o.data.length-1]=i.munderover.apply(i.underover,p.data)}}p.movesupsub=(m?true:false);p.Core().movablelimits=false;if(p.movablelimits){p.movablelimits=false}},Over:function(o,n,p){var m=b.over().With({name:o});if(n||p){m.open=n;m.close=p}else{if(o.match(/withdelims$/)){m.open=this.GetDelimiter(o);m.close=this.GetDelimiter(o)}}if(o.match(/^\\above/)){m.thickness=this.GetDimen(o)}else{if(o.match(/^\\atop/)||n||p){m.thickness=0}}this.Push(m)},Frac:function(n){var m=this.ParseArg(n);var o=this.ParseArg(n);this.Push(i.mfrac(m,o))},Sqrt:function(p){var q=this.GetBrackets(p),m=this.GetArgument(p);if(m==="\\frac"){m+="{"+this.GetArgument(m)+"}{"+this.GetArgument(m)+"}"}var o=d.Parse(m,this.stack.env).mml();if(!q){o=i.msqrt.apply(i,o.array())}else{o=i.mroot(o,this.parseRoot(q))}this.Push(o)},Root:function(o){var p=this.GetUpTo(o,"\\of");var m=this.ParseArg(o);this.Push(i.mroot(m,this.parseRoot(p)))},parseRoot:function(r){var o=this.stack.env,m=o.inRoot;o.inRoot=true;var q=d.Parse(r,o);r=q.mml();var p=q.stack.global;if(p.leftRoot||p.upRoot){r=i.mpadded(r);if(p.leftRoot){r.width=p.leftRoot}if(p.upRoot){r.voffset=p.upRoot;r.height=p.upRoot}}o.inRoot=m;return r},MoveRoot:function(m,p){if(!this.stack.env.inRoot){d.Error(["MisplacedMoveRoot","%1 can appear only within a root",m])}if(this.stack.global[p]){d.Error(["MultipleMoveRoot","Multiple use of %1",m])}var o=this.GetArgument(m);if(!o.match(/-?[0-9]+/)){d.Error(["IntegerArg","The argument to %1 must be an integer",m])}o=(o/15)+"em";if(o.substr(0,1)!=="-"){o="+"+o}this.stack.global[p]=o},Accent:function(o,m,s){var r=this.ParseArg(o);var q={accent:true};if(this.stack.env.font){q.mathvariant=this.stack.env.font}var n=this.mmlToken(i.mo(i.entity("#x"+m)).With(q));n.stretchy=(s?true:false);var p=(r.isEmbellished()?r.CoreMO():r);if(p.isa(i.mo)){p.movablelimits=false}this.Push(i.TeXAtom(i.munderover(r,null,n).With({accent:true})))},UnderOver:function(o,s,m,q){var r={o:"over",u:"under"}[o.charAt(1)];var p=this.ParseArg(o);if(p.Get("movablelimits")){p.movablelimits=false}if(p.isa(i.munderover)&&p.isEmbellished()){p.Core().With({lspace:0,rspace:0});p=i.mrow(i.mo().With({rspace:0}),p)}var n=i.munderover(p,null,null);n.SetData(n[r],this.mmlToken(i.mo(i.entity("#x"+s)).With({stretchy:true,accent:!q})));if(m){n=i.TeXAtom(n).With({texClass:i.TEXCLASS.OP,movesupsub:true})}this.Push(n.With({subsupOK:true}))},Overset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);n.movablelimits=false;this.Push(i.mover(n,o))},Underset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);n.movablelimits=false;this.Push(i.munder(n,o))},TeXAtom:function(p,r){var q={texClass:r},o;if(r==i.TEXCLASS.OP){q.movesupsub=q.movablelimits=true;var m=this.GetArgument(p);var n=m.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(n){q.mathvariant=i.VARIANT.NORMAL;o=b.fn(this.mmlToken(i.mi(n[1]).With(q)))}else{o=b.fn(i.TeXAtom(d.Parse(m,this.stack.env).mml()).With(q))}}else{o=i.TeXAtom(this.ParseArg(p)).With(q)}this.Push(o)},MmlToken:function(o){var p=this.GetArgument(o),m=this.GetBrackets(o,"").replace(/^\s+/,""),s=this.GetArgument(o),r={attrNames:[]},n;if(!i[p]||!i[p].prototype.isToken){d.Error(["NotMathMLToken","%1 is not a token element",p])}while(m!==""){n=m.match(/^([a-z]+)\s*=\s*('[^']*'|"[^"]*"|[^ ,]*)\s*,?\s*/i);if(!n){d.Error(["InvalidMathMLAttr","Invalid MathML attribute: %1",m])}if(i[p].prototype.defaults[n[1]]==null&&!this.MmlTokenAllow[n[1]]){d.Error(["UnknownAttrForElement","%1 is not a recognized attribute for %2",n[1],p])}var q=this.MmlFilterAttribute(n[1],n[2].replace(/^(['"])(.*)\1$/,"$2"));if(q){if(q.toLowerCase()==="true"){q=true}else{if(q.toLowerCase()==="false"){q=false}}r[n[1]]=q;r.attrNames.push(n[1])}m=m.substr(n[0].length)}this.Push(this.mmlToken(i[p](s).With(r)))},MmlFilterAttribute:function(m,n){return n},MmlTokenAllow:{fontfamily:1,fontsize:1,fontweight:1,fontstyle:1,color:1,background:1,id:1,"class":1,href:1,style:1},Strut:function(m){this.Push(i.mpadded(i.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(o,m,p){var n=this.ParseArg(o);if(m||p){n=i.mpadded(n);if(p){n.height=n.depth=0}if(m){n.width=0}}this.Push(i.TeXAtom(i.mphantom(n)))},Smash:function(o){var n=this.trimSpaces(this.GetBrackets(o,""));var m=i.mpadded(this.ParseArg(o));switch(n){case"b":m.depth=0;break;case"t":m.height=0;break;default:m.height=m.depth=0}this.Push(i.TeXAtom(m))},Lap:function(n){var m=i.mpadded(this.ParseArg(n)).With({width:0});if(n==="\\llap"){m.lspace="-1width"}this.Push(i.TeXAtom(m))},RaiseLower:function(m){var n=this.GetDimen(m);var o=b.position().With({name:m,move:"vertical"});if(n.charAt(0)==="-"){n=n.slice(1);m={raise:"\\lower",lower:"\\raise"}[m.substr(1)]}if(m==="\\lower"){o.dh="-"+n;o.dd="+"+n}else{o.dh="+"+n;o.dd="-"+n}this.Push(o)},MoveLeftRight:function(m){var p=this.GetDimen(m);var o=(p.charAt(0)==="-"?p.slice(1):"-"+p);if(m==="\\moveleft"){var n=p;p=o;o=n}this.Push(b.position().With({name:m,move:"horizontal",left:i.mspace().With({width:p,mathsize:i.SIZE.NORMAL}),right:i.mspace().With({width:o,mathsize:i.SIZE.NORMAL})}))},Hskip:function(m){this.Push(i.mspace().With({width:this.GetDimen(m),mathsize:i.SIZE.NORMAL}))},Rule:function(n,p){var m=this.GetDimen(n),o=this.GetDimen(n),r=this.GetDimen(n);var q={width:m,height:o,depth:r};if(p!=="blank"){q.mathbackground=(this.stack.env.color||"black")}this.Push(i.mspace().With(q))},rule:function(p){var n=this.GetBrackets(p),m=this.GetDimen(p),q=this.GetDimen(p);var o=i.mspace().With({width:m,height:q,mathbackground:(this.stack.env.color||"black")});if(n){o=i.mpadded(o).With({voffset:n});if(n.match(/^\-/)){o.height=n;o.depth="+"+n.substr(1)}else{o.height="+"+n}}this.Push(o)},MakeBig:function(m,p,n){n*=g.p_height;n=String(n).replace(/(\.\d\d\d).+/,"$1")+"em";var o=this.GetDelimiter(m,true);this.Push(i.mstyle(i.TeXAtom(i.mo(o).With({minsize:n,maxsize:n,fence:true,stretchy:true,symmetric:true})).With({texClass:p})).With({scriptlevel:0}))},BuildRel:function(m){var n=this.ParseUpTo(m,"\\over");var o=this.ParseArg(m);this.Push(i.TeXAtom(i.munderover(o,null,n)).With({texClass:i.TEXCLASS.REL}))},HBox:function(m,n){this.Push.apply(this,this.InternalMath(this.GetArgument(m),n))},FBox:function(m){this.Push(i.menclose.apply(i,this.InternalMath(this.GetArgument(m))).With({notation:"box"}))},Not:function(m){this.Push(b.not())},Dots:function(m){this.Push(b.dots().With({ldots:this.mmlToken(i.mo(i.entity("#x2026")).With({stretchy:false})),cdots:this.mmlToken(i.mo(i.entity("#x22EF")).With({stretchy:false}))}))},Require:function(m){var n=this.GetArgument(m).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");this.Extension(null,n)},Extension:function(m,n,o){if(m&&!typeof(m)==="string"){m=m.name}n=d.extensionDir+"/"+n;if(!n.match(/\.js$/)){n+=".js"}if(!j.loaded[j.fileURL(n)]){if(m!=null){delete g[o||"macros"][m.replace(/^\\/,"")]}c.RestartAfter(j.Require(n))}},Macro:function(o,r,q,s){if(q){var n=[];if(s!=null){var m=this.GetBrackets(o);n.push(m==null?s:m)}for(var p=n.length;p<q;p++){n.push(this.GetArgument(o))}r=this.SubstituteArgs(n,r)}this.string=this.AddArgs(r,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(n,p,v,r,u,o,m,w,t){var s=this.GetNext();if(s===""){d.Error(["MissingArgFor","Missing argument for %1",n])}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:true,arraydef:{rowspacing:(o||"4pt"),columnspacing:(u||"1em")}});if(w){q.isCases=true}if(t){q.isNumbered=true;q.arraydef.side=t}if(p||v){q.open=p;q.close=v}if(m==="D"){q.arraydef.displaystyle=true}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:true,name:p}));if(this.stack.Top().isCases){var o=this.string;var t=0,s=-1,q=this.i,n=o.length;while(q<n){var u=o.charAt(q);if(u==="{"){t++;q++}else{if(u==="}"){if(t===0){n=0}else{t--;if(t===0&&s<0){s=q-this.i}q++}}else{if(u==="&"&&t===0){d.Error(["ExtraAlignTab","Extra alignment tab in \\cases text"])}else{if(u==="\\"){if(o.substr(q).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){n=0}else{q+=2}}else{q++}}}}}var r=o.substr(this.i,q-this.i);if(!r.match(/^\s*\\text[^a-zA-Z]/)||s!==r.replace(/\s+$/,"").length-1){this.Push.apply(this,this.InternalMath(r,0));this.i=q}}},Cr:function(m){this.Push(b.cell().With({isCR:true,name:m}))},CrLaTeX:function(o,m){var r;if(!m&&this.string.charAt(this.i)==="["){r=this.GetBrackets(o,"").replace(/ /g,"").replace(/,/,".");if(r&&!this.matchDimen(r)){d.Error(["BracketMustBeDimension","Bracket argument to %1 must be a dimension",o])}}this.Push(b.cell().With({isCR:true,name:o,linebreak:true}));var q=this.stack.Top();if(q.isa(b.array)){if(r&&q.arraydef.rowspacing){var p=q.arraydef.rowspacing.split(/ /);if(!q.rowspacing){q.rowspacing=this.dimen2em(p[0])}while(p.length<q.table.length){p.push(this.Em(q.rowspacing))}p[q.table.length-1]=this.Em(Math.max(0,q.rowspacing+this.dimen2em(r)));q.arraydef.rowspacing=p.join(" ")}}else{if(r){this.Push(i.mspace().With({depth:r}))}this.Push(i.mspace().With({linebreak:i.LINEBREAK.NEWLINE}))}},emPerInch:7.2,pxPerInch:72,matchDimen:function(m){return m.match(/^(-?(?:\.\d+|\d+(?:\.\d*)?))(px|pt|em|ex|mu|pc|in|mm|cm)$/)},dimen2em:function(q){var o=this.matchDimen(q);var n=parseFloat(o[1]||"1"),p=o[2];if(p==="em"){return n}if(p==="ex"){return n*0.43}if(p==="pt"){return n/10}if(p==="pc"){return n*1.2}if(p==="px"){return n*this.emPerInch/this.pxPerInch}if(p==="in"){return n*this.emPerInch}if(p==="cm"){return n*this.emPerInch/2.54}if(p==="mm"){return n*this.emPerInch/25.4}if(p==="mu"){return n/18}return 0},Em:function(n){if(Math.abs(n)<0.0006){return"0em"}return n.toFixed(3).replace(/\.?0+$/,"")+"em"},HLine:function(n,o){if(o==null){o="solid"}var p=this.stack.Top();if(!p.isa(b.array)||p.data.length){d.Error(["Misplaced","Misplaced %1",n])}if(p.table.length==0){p.frame.push("top")}else{var m=(p.arraydef.rowlines?p.arraydef.rowlines.split(/ /):[]);while(m.length<p.table.length){m.push("none")}m[p.table.length-1]=o;p.arraydef.rowlines=m.join(" ")}},HFill:function(m){var n=this.stack.Top();if(n.isa(b.array)){n.hfill.push(n.data.length)}else{d.Error(["UnsupportedHFill","Unsupported use of %1",m])}},BeginEnd:function(o){var p=this.GetArgument(o),r=false;if(p.match(/^\\end\\/)){r=true;p=p.substr(5)}if(p.match(/\\/i)){d.Error(["InvalidEnv","Invalid environment name '%1'",p])}var q=this.envFindName(p);if(!q){d.Error(["UnknownEnv","Unknown environment '%1'",p])}if(!f(q)){q=[q]}var m=(f(q[1])?q[1][0]:q[1]);var n=b.begin().With({name:p,end:m,parse:this});if(o==="\\end"){if(!r&&f(q[1])&&this[q[1][1]]){n=this[q[1][1]].apply(this,[n].concat(q.slice(2)))}else{n=b.end().With({name:p})}}else{if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(q[0]&&this[q[0]]){n=this[q[0]].apply(this,[n].concat(q.slice(2)))}}this.Push(n)},envFindName:function(m){return(g.environment.hasOwnProperty(m)?g.environment[m]:null)},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(n,p,u,s,t,o,m,q){if(!s){s=this.GetArgument("\\begin{"+n.name+"}")}var v=("c"+s).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");s=s.replace(/[^clr]/g,"").split("").join(" ");s=s.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var r=b.array().With({arraydef:{columnalign:s,columnspacing:(t||"1em"),rowspacing:(o||"4pt")}});if(v.match(/[|:]/)){if(v.charAt(0).match(/[|:]/)){r.frame.push("left");r.frame.dashed=v.charAt(0)===":"}if(v.charAt(v.length-1).match(/[|:]/)){r.frame.push("right")}v=v.substr(1,v.length-2);r.arraydef.columnlines=v.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(p){r.open=this.convertDelimiter(p)}if(u){r.close=this.convertDelimiter(u)}if(m==="D"){r.arraydef.displaystyle=true}else{if(m){r.arraydef.displaystyle=false}}if(m==="S"){r.arraydef.scriptlevel=1}if(q){r.arraydef.useHeight=false}this.Push(n);return r},AlignedArray:function(m){var n=this.GetBrackets("\\begin{"+m.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),n)},setArrayAlign:function(n,m){m=this.trimSpaces(m||"");if(m==="t"){n.arraydef.align="baseline 1"}else{if(m==="b"){n.arraydef.align="baseline -1"}else{if(m==="c"){n.arraydef.align="center"}else{if(m){n.arraydef.align=m}}}}return n},convertDelimiter:function(m){if(m){m=(g.delimiter.hasOwnProperty(m)?g.delimiter[m]:null)}if(m==null){return null}if(f(m)){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(n){if(typeof(n)!="string"){return n}var m=n.replace(/^\s+|\s+$/g,"");if(m.match(/\\$/)&&n.match(/ $/)){m+=" "}return m},nextIsSpace:function(){return this.string.charAt(this.i).match(/\s/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){d.Error(["MissingArgFor","Missing argument for %1",n])}return null;case"}":if(!o){d.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"])}return 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x=(z.Get("display")==="block"?"div":"span");A=e.Element(x,{className:"MathJax_MathML",id:n.inputID+"-Frame"},[["span",{className:"MathJax_MathContainer",isMathJax:true,jaxID:this.id,style:{position:"relative",display:"inline-block","white-space":"nowrap"}},[["span",{isMathJax:true,style:{display:"inline-block"}}]]]]);y.parentNode.insertBefore(A,y);if(!i){y.parentNode.insertBefore(this.EmExSpan.cloneNode(true),y)}}for(u=0;u<p;u++){y=t[u];if(!y.parentNode){continue}n=y.MathJax.elementJax;if(!n){continue}if(!i){w=y.previousSibling;v=w.firstChild.offsetWidth/60;s=w.lastChild.offsetWidth/60;if(v===0||v==="NaN"){v=this.defaultEx;s=this.defaultMEx}q=(this.config.matchFontHeight&&s>1?v/s:1);q=Math.floor(Math.max(this.config.minScaleAdjust/100,q)*this.config.scale);n.NativeMML.ex=v;n.NativeMML.mex=s}else{q=100}n.NativeMML.fontSize=q+"%";n.NativeMML.scale=q/100}if(!i){for(u=0;u<p;u++){y=t[u];if(y.parentNode&&y.MathJax.elementJax){y.parentNode.removeChild(y.previousSibling)}}}},Translate:function(s){if(!s.parentNode){return}var m=s.MathJax.elementJax,t=m.root;var u=document.getElementById(m.inputID+"-Frame");if(!u){return}var n=u.firstChild,q=n.firstChild;this.ex=m.NativeMML.ex||this.defaultEx;this.scale=m.NativeMML.scale||1;if(this.scale!==1){u.style.fontSize=m.NativeMML.fontSize}try{t.toNativeMML(q,m)}catch(r){if(r.restart){while(q.firstChild){q.removeChild(q.firstChild)}}throw r}if(i){if(n.addEventListener){for(var o in this.MSIE9events){if(this.MSIE9events.hasOwnProperty(o)){n.addEventListener(o,this.MSIE9event,true)}}}else{var 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false}if(n.srcElement.className==="MathJax_MathPlayer_Overlay"&&this.msieMath.fireEvent){if(m==="ContextMenu"||m==="Mouseover"||m==="Mouseout"){this.msieMath.fireEvent("on"+n.type,n)}}return h.False(n)},MSIEaltMenu:function(){var m=this.parentNode.parentNode;while(!m.jaxID){m=m.parentNode}h.AltContextMenu(window.event,m)},MSIE9events:{contextmenu:"Menu",click:"Click",dblclick:"DblClick",mouseup:"False",mouseover:"Mouseover",mouseout:"Mouseout"},MSIE9event:function(n){if(n.type==="contextmenu"&&l.settings.mpContext){return true}if(n.type==="mouseup"&&l.settings.mpMouse){return true}if(n.type==="click"&&l.settings.mpContext){return h.AltContextMenu(n,this)}var m=l.MSIE9events[n.type];return h[m].call(this,n)},getJaxFromMath:function(m){m=m.parentNode;do{m=m.nextSibling}while(m&&m.nodeName.toLowerCase()!=="script");return c.getJaxFor(m)},getHoverSpan:function(m,n){return n.firstChild},getHoverBBox:function(m,n,o){return 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]){if(this.Get(p,null,1)!==this[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(p==="OP"&&!this.movablelimits){q.push("MJX-fixedlimits")}}}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=(c.Browser.mpNamespace?document.createElement("m:"+o):(document.createElementNS?document.createElementNS(l.MMLnamespace,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;var t=this.data[this.base];if(t&&t.isa(f.TeXAtom)&&t.movablelimits&&!t.Get("displaystyle")){r="msubsup";if(this.data[this.under]==null){r="msup"}if(this.data[this.over]==null){r="msub"}}else{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)}}});f.mn.Augment({NativeMMLremapMinus:function(o){return o.replace(/^-/,"\u2212")},toNativeMML:function(s){var p=this.NativeMMLelement(this.type);this.NativeMMLattributes(p);var r=this.NativeMMLremapMinus;for(var q=0,o=this.data.length;q<o;q++){if(this.data[q]){this.data[q].toNativeMML(p,r);r=null}}s.appendChild(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(p,o){var q=this.toString();if(o){q=o(q)}p.appendChild(document.createTextNode(q))}});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.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(j,b,d){var i,k=b.Browser.isMobile;var h=MathJax.Object.isArray;var e=function(){var m=[].slice.call(arguments,0);m[0][0]=["HTML-CSS",m[0][0]];return MathJax.Message.Set.apply(MathJax.Message,m)};var f=MathJax.Object.Subclass({timeout:(k?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","min-width":0,"max-width":"none",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(r,o){var q=null;if(o&&this.testCollection(o)){q=o}else{for(var p=0,n=r.length;p<n;p++){if(r[p]===o){continue}if(this.testCollection(r[p])){q=r[p];break}}}if(q==="STIX"&&this.testFont(this.FedoraSTIXcheck)){q=null}return q},testCollection:function(n){var m={testString:"() {} []"};m.family={TeX:"MathJax_Size1",STIX:"STIXSizeOneSym"}[n]||n.replace(/-(Math)?/,"")+"MathJax_Size1";if(n==="STIX"){m.noStyleChar=true}return this.testFont(m)},testFont:function(p){if(p.isWebFont&&d.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(p.weight||"normal");this.div.style.fontStyle=(p.style||"normal")}var r=p.familyFixed||p.family;if(!p.isWebFont&&!r.match(/^(STIX|MathJax)|'/)){r=r.replace(/_/g," ").replace(/([a-z])([A-Z])/g,"$1 $2").replace(/ Jax/,"Jax")+"','"+r+"','"+r+"-";if(p.weight){r+="Bold"}if(p.style){r+="Italic"}if(!p.weight&&!p.style){r+="Regular"}p.familyFixed=r="'"+r+"'"}var o=this.getComparisonWidths(p.testString,p.noStyleChar);var s=null;if(o){this.div.style.fontFamily=r+","+this.comparisonFont[0];if(this.div.offsetWidth==o[0]){this.div.style.fontFamily=r+","+this.comparisonFont[o[2]];if(this.div.offsetWidth==o[1]){s=false}}if(s===null&&(this.div.offsetWidth!=o[3]||this.div.offsetHeight!=o[4])){if(!p.noStyleChar&&d.FONTDATA&&d.FONTDATA.hasStyleChar){for(var q=0,n=this.testSize.length;q<n;q++){if(this.testStyleChar(p,this.testSize[q])){s=true;n=0}}}else{s=true}}}if(d.safariTextNodeBug){this.div.innerHTML=""}else{this.text.nodeValue=""}return s},styleChar:"\uEFFD",versionChar:"\uEFFE",compChar:"\uEFFF",testStyleChar:function(p,r){var u=3+(p.weight?2:0)+(p.style?4:0);var o="",q=0;var t=this.div.style.fontSize;this.div.style.fontSize=r;if(d.msieItalicWidthBug&&p.style==="italic"){this.text.nodeValue=o=this.compChar;q=this.div.offsetWidth}if(d.safariTextNodeBug){this.div.innerHTML=this.compChar+o}else{this.text.nodeValue=this.compChar+o}var m=this.div.offsetWidth-q;if(d.safariTextNodeBug){this.div.innerHTML=this.styleChar+o}else{this.text.nodeValue=this.styleChar+o}var s=Math.floor((this.div.offsetWidth-q)/m+0.5);if(s===u){if(d.safariTextNodeBug){this.div.innerHTML=this.versionChar+o}else{this.text.nodeValue=this.versionChar+o}p.version=Math.floor((this.div.offsetWidth-q)/m+1.5)/2}this.div.style.fontSize=t;return(s===u)},getComparisonWidths:function(r,p){if(d.FONTDATA&&d.FONTDATA.hasStyleChar&&!p){r+=this.styleChar+" "+this.compChar}if(d.safariTextNodeBug){this.div.innerHTML=r}else{this.text.nodeValue=r}this.div.style.fontFamily=this.comparisonFont[0];var o=this.div.offsetWidth;this.div.style.fontFamily=d.webFontDefault;var t=this.div.offsetWidth,q=this.div.offsetHeight;for(var s=1,n=this.comparisonFont.length;s<n;s++){this.div.style.fontFamily=this.comparisonFont[s];if(this.div.offsetWidth!=o){return[o,this.div.offsetWidth,s,t,q]}}return null},loadWebFont:function(o){b.Startup.signal.Post("HTML-CSS Jax - Web-Font "+d.fontInUse+"/"+o.directory);var q=e(["LoadWebFont","Loading web-font %1",d.fontInUse+"/"+o.directory]);var m=MathJax.Callback({});var p=MathJax.Callback(["loadComplete",this,o,q,m]);j.timer.start(j,[this.checkWebFont,o,p],0,this.timeout);return m},loadComplete:function(p,r,o,m){MathJax.Message.Clear(r);if(m===j.STATUS.OK){this.webFontLoaded=true;o();return}this.loadError(p);if(b.Browser.isFirefox&&d.allowWebFonts){var q=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){q+=":"+document.location.port}q+="/";if(j.fileURL(d.webfontDir).substr(0,q.length)!==q){this.firefoxFontError(p)}}if(!this.webFontLoaded){d.loadWebFontError(p,o)}else{o()}},loadError:function(m){e(["CantLoadWebFont","Can't load web font %1",d.fontInUse+"/"+m.directory],null,2000);b.Startup.signal.Post("HTML-CSS Jax - web font error for "+d.fontInUse+"/"+m.directory)},firefoxFontError:function(m){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(m,n,o){if(m.time(o)){return}if(d.Font.testFont(n)){o(m.STATUS.OK)}else{setTimeout(m,m.delay)}},fontFace:function(q){var r=d.allowWebFonts;var t=d.FONTDATA.FONTS[q];if(d.msieFontCSSBug&&!t.family.match(/-Web$/)){t.family+="-Web"}if(t.isWebFont){delete t.familyFixed}var m=d.webfontDir+"/"+r;var p=j.fileURL(m);var o=q.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!o.match(/-/)){o+="-Regular"}if(r==="svg"){o+=".svg#"+o}else{o+="."+r}var n=j.fileRev(m+"/"+o.replace(/#.*/,""));var s={"font-family":t.family,src:"url('"+p+"/"+o+n+"')"};if(r==="otf"){o=o.replace(/otf$/,"woff");n=j.fileRev(m+"/"+o);s.src+=" format('opentype')";p=j.fileURL(d.webfontDir+"/woff");s.src="url('"+p+"/"+o+n+"') format('woff'), "+s.src}else{if(r!=="eot"){s.src+=" format('"+r+"')"}}if(!(d.FontFaceBug&&t.isWebFont)){if(q.match(/-bold/)){s["font-weight"]="bold"}if(q.match(/-italic/)){s["font-style"]="italic"}}return s}});var l,a,c;var g=MathJax.Hub.Browser.isMSIE&&(document.documentMode||0)<8;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:focus, body :focus .MathJax":{display:"inline-table"},".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.MathJax_FullWidth":{"text-align":"center",display:(g?"block":"table-cell")+"!important",width:(g?"100%":"10000em")+"!important"},".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","box-sizing":"content-box"},".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_test":{"font-style":"normal","font-weight":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-transform":"none","letter-spacing":"normal","word-spacing":"normal",overflow:"hidden",height:"1px"},".MathJax_test.mjx-test-display":{display:(g?"block":"table")+"!important"},".MathJax_test.mjx-test-inline":{display:"inline!important","margin-right":"-1px"},".MathJax_test.mjx-test-default":{display:"block!important",clear:"both"},".MathJax_ex_box":{display:"inline-block!important",position:"absolute",overflow:"hidden","min-height":0,"max-height":"none",padding:0,border:0,margin:0,width:"1px",height:"60ex"},".MathJax_em_box":{display:"inline-block!important",position:"absolute",overflow:"hidden","min-height":0,"max-height":"none",padding:0,border:0,margin:0,width:"1px",height:"60em"},".mjx-test-inline .MathJax_left_box":{display:"inline-block",width:0,"float":"left"},".mjx-test-inline .MathJax_right_box":{display:"inline-block",width:0,"float":"right"},".mjx-test-display .MathJax_right_box":{display:(g?"block":"table-cell")+"!important",width:(g?"100%":"10000em")+"!important","min-width":0,"max-width":"none",padding:0,border:0,margin:0},".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 o=this.settings,n=this.config,m=o.font;if(this.adjustAvailableFonts){this.adjustAvailableFonts(n.availableFonts)}if(o.scale){n.scale=o.scale}if(m&&m!=="Auto"&&this.fontName[m]){n.availableFonts=[];delete n.fonts;if(h(this.fontName[m])){n.preferredFont=this.fontName[m][0];n.webFont=this.fontName[m][1]}else{n.preferredFont=n.webFont=this.fontName[m]}if(n.preferredFont){n.availableFonts[0]=n.preferredFont}}if(n.fonts){n.availableFonts=n.fonts;n.preferredFont=n.webFont=n.fonts[0];if(n.webFont==="STIX"){n.webFont+="-Web"}}m=this.Font.findFont(n.availableFonts,n.preferredFont);if(!m&&this.allowWebFonts){m=n.webFont;if(m){this.webFonts=true}}if(!m&&this.config.imageFont){m=n.imageFont;this.imgFonts=true}if(m){this.fontInUse=m;this.fontDir+="/"+m;this.webfontDir+="/"+m;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(){l=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=l.ContextMenu;this.Mousedown=l.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 n=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;this.hiddenDiv.removeChild(n);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(m){}}else{this.HDimg=this.createStrut(this.HDspan,0)}this.TestSpan=this.Element("span",{className:"MathJax_test"},[["span",{className:"MathJax_left_box"}],["span",{className:"MathJax_ex_box"}],["span",{className:"MathJax_em_box"}],["span",{className:"MathJax_right_box"}]]);return j.Styles(this.config.styles,["InitializeHTML",this])},removeSTIXfonts:function(p){for(var o=0,n=p.length;o<n;o++){if(p[o]==="STIX"){p.splice(o,1);n--;o--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=p[0]}},PreloadWebFonts:function(){if(!d.allowWebFonts||!d.config.preloadWebFonts){return}for(var o=0,n=d.config.preloadWebFonts.length;o<n;o++){var p=d.FONTDATA.FONTS[d.config.preloadWebFonts[o]];if(!p.available){d.Font.testFont(p)}}},InitializeHTML:function(){this.PreloadWebFonts();this.getDefaultExEm();if(this.defaultEm){return}var m=MathJax.Callback();j.timer.start(j,function(n){if(n.time(m)){b.signal.Post(["HTML-CSS Jax - no default em size"]);return}d.getDefaultExEm();if(d.defaultEm){m()}else{setTimeout(n,n.delay)}},this.defaultEmDelay,this.defaultEmTimeout);return m},defaultEmDelay:100,defaultEmTimeout:1000,getDefaultExEm:function(){var m=document.body.appendChild(this.TestSpan.cloneNode(true));m.className+=" mjx-test-inline mjx-test-default";this.defaultEx=m.childNodes[1].offsetHeight/60;this.defaultEm=m.childNodes[2].offsetHeight/60;this.defaultWidth=Math.max(0,m.lastChild.offsetLeft-m.firstChild.offsetLeft-2);document.body.removeChild(m)},preTranslate:function(s){var r=s.jax[this.id],D,z=r.length,y,G,w,C,u,E,p,F,o,H,v,t=false,A,q=this.config.linebreaks.automatic,x=this.config.linebreaks.width;if(q){t=(x.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)!=null);if(t){x=x.replace(/\s*container\s*/,"")}else{v=this.defaultWidth}if(x===""){x="100%"}}else{v=100000}for(D=0;D<z;D++){G=r[D];if(!G.parentNode){continue}w=G.previousSibling;if(w&&String(w.className).match(/^MathJax(_Display)?( MathJax_Process(ing|ed))?$/)){w.parentNode.removeChild(w)}if(G.MathJax.preview){G.MathJax.preview.style.display="none"}p=G.MathJax.elementJax;if(!p){continue}p.HTMLCSS={display:(p.root.Get("display")==="block")};C=u=this.Element("span",{className:"MathJax",id:p.inputID+"-Frame",isMathJax:true,jaxID:this.id,oncontextmenu:l.Menu,onmousedown:l.Mousedown,onmouseover:l.Mouseover,onmouseout:l.Mouseout,onmousemove:l.Mousemove,onclick:l.Click,ondblclick:l.DblClick,onkeydown:l.Keydown,tabIndex:b.getTabOrder(p)});if(b.Browser.noContextMenu){C.ontouchstart=a.start;C.ontouchend=a.end}if(p.HTMLCSS.display){u=this.Element("div",{className:"MathJax_Display"});u.appendChild(C)}else{if(this.msieDisappearingBug){C.style.display="inline-block"}}u.className+=" MathJax_Processing";G.parentNode.insertBefore(u,G);p.HTMLCSS.span=C;p.HTMLCSS.div=u;E=this.TestSpan.cloneNode(true);E.className+=" mjx-test-"+(p.HTMLCSS.display?"display":"inline");G.parentNode.insertBefore(E,G)}var B=[];for(D=0;D<z;D++){G=r[D];if(!G.parentNode){continue}E=G.previousSibling;u=E.previousSibling;p=G.MathJax.elementJax;if(!p){continue}F=E.childNodes[1].offsetHeight/60;o=E.childNodes[2].offsetHeight/60;A=Math.max(0,p.HTMLCSS.display?E.lastChild.offsetWidth-1:E.lastChild.offsetLeft-E.firstChild.offsetLeft-2);if(F===0||F==="NaN"){B.push(u);p.HTMLCSS.isHidden=true;F=this.defaultEx;o=this.defaultEm;A=this.defaultWidth}if(A===0&&!p.HTMLCSS.display){A=this.defaultWidth}if(t){v=A}H=(this.config.matchFontHeight?F/this.TeX.x_height/o:1);H=Math.floor(Math.max(this.config.minScaleAdjust/100,H)*this.config.scale);p.HTMLCSS.scale=H/100;p.HTMLCSS.fontSize=H+"%";p.HTMLCSS.em=p.HTMLCSS.outerEm=o;this.em=o*H/100;p.HTMLCSS.ex=F;p.HTMLCSS.cwidth=A/this.em;p.HTMLCSS.lineWidth=(q?this.length2em(x,1,v/this.em):1000000)}for(D=0,y=B.length;D<y;D++){this.hiddenDiv.appendChild(B[D]);this.addElement(this.hiddenDiv,"br")}for(D=0;D<z;D++){G=r[D];if(!G.parentNode){continue}p=r[D].MathJax.elementJax;if(!p){continue}G.parentNode.removeChild(G.previousSibling);if(G.MathJax.preview){G.MathJax.preview.style.display=""}}s.HTMLCSSeqn=s.HTMLCSSlast=0;s.HTMLCSSi=-1;s.HTMLCSSchunk=this.config.EqnChunk;s.HTMLCSSdelay=false},PHASE:{I:1,II:2,III:3},Translate:function(n,r){if(!n.parentNode){return}if(r.HTMLCSSdelay){r.HTMLCSSdelay=false;b.RestartAfter(MathJax.Callback.Delay(this.config.EqnChunkDelay))}var m=n.MathJax.elementJax,q=m.root,s=m.HTMLCSS.div,o=m.HTMLCSS.span;if(!document.getElementById(o.id)){return}this.getMetrics(m);if(this.scale!==1){o.style.fontSize=m.HTMLCSS.fontSize}this.initImg(o);this.initHTML(q,o);this.savePreview(n);try{q.setTeXclass();q.toHTML(o,s,this.PHASE.I)}catch(p){if(p.restart){while(o.firstChild){o.removeChild(o.firstChild)}}this.restorePreview(n);throw p}this.restorePreview(n);s.className=s.className.split(/ /)[0]+" MathJax_Processed";b.signal.Post(["New Math Pending",m.inputID]);r.HTMLCSSeqn+=(r.i-r.HTMLCSSi);r.HTMLCSSi=r.i;if(r.HTMLCSSeqn>=r.HTMLCSSlast+r.HTMLCSSchunk){this.postTranslate(r,true);r.HTMLCSSchunk=Math.floor(r.HTMLCSSchunk*this.config.EqnChunkFactor);r.HTMLCSSdelay=true}return false},savePreview:function(m){var n=m.MathJax.preview;if(n){m.MathJax.tmpPreview=document.createElement("span");n.parentNode.replaceChild(m.MathJax.tmpPreview,n)}},restorePreview:function(m){var n=m.MathJax.tmpPreview;if(n){n.parentNode.replaceChild(m.MathJax.preview,n);delete m.MathJax.tmpPreview}},getMetrics:function(m){var n=m.HTMLCSS;this.em=i.mbase.prototype.em=n.em*n.scale;this.outerEm=n.em;this.scale=n.scale;this.cwidth=n.cwidth;this.linebreakWidth=n.lineWidth},postTranslate:function(o,u){var r=o.jax[this.id],v,p,s,q;for(s=o.HTMLCSSlast,q=o.HTMLCSSeqn;s<q;s++){v=r[s];if(v&&v.parentNode&&v.MathJax.elementJax){var n=(v.MathJax.elementJax.HTMLCSS||{}).div;if(n){n.className=n.className.split(/ /)[0]}if(v.MathJax.preview){v.MathJax.preview.innerHTML=""}}}for(s=o.HTMLCSSlast,q=o.HTMLCSSeqn;s<q;s++){v=r[s];if(v&&v.parentNode&&v.MathJax.elementJax){p=v.MathJax.elementJax;this.getMetrics(p);if(p.HTMLCSS.span&&p.HTMLCSS.div){p.root.toHTML(p.HTMLCSS.span,p.HTMLCSS.div,this.PHASE.II)}}}for(s=o.HTMLCSSlast,q=o.HTMLCSSeqn;s<q;s++){v=r[s];if(v&&v.parentNode&&v.MathJax.elementJax){p=v.MathJax.elementJax;this.getMetrics(p);if(p.HTMLCSS.span&&p.HTMLCSS.div){p.root.toHTML(p.HTMLCSS.span,p.HTMLCSS.div,this.PHASE.III);if(p.HTMLCSS.isHidden){v.parentNode.insertBefore(p.HTMLCSS.div,v)}delete p.HTMLCSS.span;delete p.HTMLCSS.div;v.MathJax.state=p.STATE.PROCESSED;b.signal.Post(["New Math",v.MathJax.elementJax.inputID])}}}if(this.forceReflow){var t=(document.styleSheets||[])[0]||{};t.disabled=true;t.disabled=false}o.HTMLCSSlast=o.HTMLCSSeqn},getJaxFromMath:function(m){if(m.parentNode.className.match(/MathJax_Display/)){m=m.parentNode}do{m=m.nextSibling}while(m&&m.nodeName.toLowerCase()!=="script");return b.getJaxFor(m)},getHoverSpan:function(m,n){return m.root.HTMLspanElement()},getHoverBBox:function(m,p,q){var r=p.bbox,o=m.HTMLCSS.outerEm;var n={w:r.w*o,h:r.h*o,d:r.d*o};if(r.width){n.width=r.width}return n},Zoom:function(n,y,x,m,v){y.className="MathJax";y.style.fontSize=n.HTMLCSS.fontSize;var B=y.appendChild(this.TestSpan.cloneNode(true));var q=B.childNodes[2].offsetHeight/60;this.em=i.mbase.prototype.em=q;this.outerEm=q/n.HTMLCSS.scale;B.parentNode.removeChild(B);this.scale=n.HTMLCSS.scale;this.linebreakWidth=n.HTMLCSS.lineWidth;this.cwidth=n.HTMLCSS.cwidth;this.zoomScale=parseInt(b.config.menuSettings.zscale)/100;this.idPostfix="-zoom";n.root.toHTML(y,y);this.idPostfix="";this.zoomScale=1;var z=n.root.HTMLspanElement().bbox,p=z.width;if(p){if(z.tw){m=z.tw*q}if(z.w*q<m){m=z.w*q}y.style.width=Math.floor(m-1.5*d.em)+"px";y.style.display="inline-block";var o=(n.root.id||"MathJax-Span-"+n.root.spanID)+"-zoom";var r=document.getElementById(o).firstChild;while(r&&r.style.width!==p){r=r.nextSibling}if(r){var u=r.offsetWidth;r.style.width="100%";if(u>m){y.style.width=(u+100)+"px"}}}r=y.firstChild.firstChild.style;if(z.H!=null&&z.H>z.h){r.marginTop=d.Em(z.H-Math.max(z.h,d.FONTDATA.lineH))}if(z.D!=null&&z.D>z.d){r.marginBottom=d.Em(z.D-Math.max(z.d,d.FONTDATA.lineD))}if(z.lw<0){r.paddingLeft=d.Em(-z.lw)}if(z.rw>z.w){r.marginRight=d.Em(z.rw-z.w)}y.style.position="absolute";if(!p){x.style.position="absolute"}var w=y.offsetWidth,t=y.offsetHeight,A=x.offsetHeight,s=x.offsetWidth;y.style.position=x.style.position="";return{Y:-l.getBBox(y).h,mW:s,mH:A,zW:w,zH:t}},initImg:function(m){},initHTML:function(n,m){},initFont:function(m){var o=d.FONTDATA.FONTS,n=d.config.availableFonts;if(n&&n.length&&d.Font.testFont(o[m])){o[m].available=true;if(o[m].familyFixed){o[m].family=o[m].familyFixed;delete o[m].familyFixed}return null}if(!this.allowWebFonts){return null}o[m].isWebFont=true;if(d.FontFaceBug){o[m].family=m;if(d.msieFontCSSBug){o[m].family+="-Web"}}return j.Styles({"@font-face":this.Font.fontFace(m)})},Remove:function(m){var n=document.getElementById(m.inputID+"-Frame");if(n){if(m.HTMLCSS.display){n=n.parentNode}n.parentNode.removeChild(n)}delete m.HTMLCSS},getHD:function(n,o){if(n.bbox&&this.config.noReflows&&!o){return{h:n.bbox.h,d:n.bbox.d}}var m=n.style.position;n.style.position="absolute";this.HDimg.style.height="0px";n.appendChild(this.HDspan);var p={h:n.offsetHeight};this.HDimg.style.height=p.h+"px";p.d=n.offsetHeight-p.h;p.h-=p.d;p.h/=this.em;p.d/=this.em;n.removeChild(this.HDspan);n.style.position=m;return p},getW:function(q){var n,p,o=(q.bbox||{}).w,r=q;if(q.bbox&&this.config.noReflows&&q.bbox.exactW!==false){if(!q.bbox.exactW){if(q.style.paddingLeft){o+=this.unEm(q.style.paddingLeft)*(q.scale||1)}if(q.style.paddingRight){o+=this.unEm(q.style.paddingRight)*(q.scale||1)}}return o}if(q.bbox&&q.bbox.exactW){return o}if((q.bbox&&o>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug)||this.negativeBBoxes||!q.firstChild){n=q.offsetWidth;p=q.parentNode.offsetHeight}else{if(q.bbox&&o<0&&this.msieNegativeBBoxBug){n=-q.offsetWidth,p=q.parentNode.offsetHeight}else{var m=q.style.position;q.style.position="absolute";r=this.startMarker;q.insertBefore(r,q.firstChild);q.appendChild(this.endMarker);n=this.endMarker.offsetLeft-r.offsetLeft;q.removeChild(this.endMarker);q.removeChild(r);q.style.position=m}}if(p!=null){q.parentNode.HH=p/this.em}return n/this.em},Measured:function(o,n){var p=o.bbox;if(p.width==null&&p.w&&!p.isMultiline){var m=this.getW(o);p.rw+=m-p.w;p.w=m;p.exactW=true}if(!n){n=o.parentNode}if(!n.bbox){n.bbox=p}return o},Remeasured:function(n,m){m.bbox=this.Measured(n,m).bbox},MeasureSpans:function(q){var t=[],v,s,p,w,n,r,o,u;for(s=0,p=q.length;s<p;s++){v=q[s];if(!v){continue}w=v.bbox;u=this.parentNode(v);if(w.exactW||w.width||w.w===0||w.isMultiline||(this.config.noReflows&&w.exactW!==false)){if(!u.bbox){u.bbox=w}continue}if(this.negativeBBoxes||!v.firstChild||(w.w>=0&&!this.initialSkipBug)||(w.w<0&&this.msieNegativeBBoxBug)){t.push([v])}else{if(this.initialSkipBug){n=this.startMarker.cloneNode(true);r=this.endMarker.cloneNode(true);v.insertBefore(n,v.firstChild);v.appendChild(r);t.push([v,n,r,v.style.position]);v.style.position="absolute"}else{r=this.endMarker.cloneNode(true);v.appendChild(r);t.push([v,null,r])}}}for(s=0,p=t.length;s<p;s++){v=t[s][0];w=v.bbox;u=this.parentNode(v);if((w.w>=0&&!this.initialSkipBug)||this.negativeBBoxes||!v.firstChild){o=v.offsetWidth;u.HH=u.offsetHeight/this.em}else{if(w.w<0&&this.msieNegativeBBoxBug){o=-v.offsetWidth,u.HH=u.offsetHeight/this.em}else{o=t[s][2].offsetLeft-((t[s][1]||{}).offsetLeft||0)}}o/=this.em;w.rw+=o-w.w;w.w=o;w.exactW=true;if(!u.bbox){u.bbox=w}}for(s=0,p=t.length;s<p;s++){v=t[s];if(v[1]){v[1].parentNode.removeChild(v[1]),v[0].style.position=v[3]}if(v[2]){v[2].parentNode.removeChild(v[2])}}},Em:function(n){if(Math.abs(n)<0.0006){return"0em"}return n.toFixed(3).replace(/\.?0+$/,"")+"em"},EmRounded:function(n){if(Math.abs(n)<0.0006){return"0em"}n=(Math.round(n*d.em)+0.05)/d.em;return n.toFixed(3).replace(/\.?0+$/,"")+"em"},unEm:function(n){return parseFloat(n)},Px:function(n){n*=this.em;var o=(n<0?"-":"");return o+Math.abs(n).toFixed(1).replace(/\.?0+$/,"")+"px"},unPx:function(n){return parseFloat(n)/this.em},Percent:function(n){return(100*n).toFixed(1).replace(/\.?0+$/,"")+"%"},length2em:function(t,o,r){if(typeof(t)!=="string"){t=t.toString()}if(t===""){return""}if(t===i.SIZE.NORMAL){return 1}if(t===i.SIZE.BIG){return 2}if(t===i.SIZE.SMALL){return 0.71}if(t==="infinity"){return d.BIGDIMEN}var q=this.FONTDATA.TeX_factor,u=(d.zoomScale||1)/d.em;if(t.match(/mathspace$/)){return d.MATHSPACE[t]*q}var p=t.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var n=parseFloat(p[1]||"1"),s=p[2];if(r==null){r=1}if(o==null){o=1}if(s==="em"){return n*q}if(s==="ex"){return n*d.TeX.x_height*q}if(s==="%"){return n/100*r}if(s==="px"){return n*u}if(s==="pt"){return n/10*q}if(s==="pc"){return n*1.2*q}if(s==="in"){return n*this.pxPerInch*u}if(s==="cm"){return n*this.pxPerInch*u/2.54}if(s==="mm"){return n*this.pxPerInch*u/25.4}if(s==="mu"){return n/18*q*o}return n*r},thickness2em:function(n,m){var o=d.TeX.rule_thickness;if(n===i.LINETHICKNESS.MEDIUM){return o}if(n===i.LINETHICKNESS.THIN){return 0.67*o}if(n===i.LINETHICKNESS.THICK){return 1.67*o}return this.length2em(n,m,o)},border2em:function(n,m){if(n===i.LINETHICKNESS.THIN){n="1px"}if(n===i.LINETHICKNESS.MEDIUM){n="3px"}if(n===i.LINETHICKNESS.THICK){n="5px"}return this.length2em(n,m)},getPadding:function(n){var p={top:0,right:0,bottom:0,left:0},m=false;for(var q in p){if(p.hasOwnProperty(q)){var o=n.style["padding"+q.charAt(0).toUpperCase()+q.substr(1)];if(o){p[q]=this.length2em(o);m=true}}}return(m?p:false)},getBorders:function(r){var o={top:0,right:0,bottom:0,left:0},p={},n=false;for(var s in o){if(o.hasOwnProperty(s)){var m="border"+s.charAt(0).toUpperCase()+s.substr(1);var q=r.style[m+"Style"];if(q){n=true;o[s]=this.border2em(r.style[m+"Width"]||i.LINETHICKNESS.MEDIUM);p[m]=[r.style[m+"Width"],r.style[m+"Style"],r.style[m+"Color"]].join(" ")}}}o.css=p;return(n?o:false)},setBorders:function(m,n){if(n){for(var o in n.css){if(n.css.hasOwnProperty(o)){m.style[o]=n.css[o]}}}},createStrut:function(o,n,p){var m=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:n+"px",width:"1px",marginRight:"-1px"}});if(p){o.insertBefore(m,o.firstChild)}else{o.appendChild(m)}return m},createBlank:function(n,m,o){var p=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(m)}});if(m<0){p.style.marginRight=p.style.width;p.style.width=0}if(o){n.insertBefore(p,n.firstChild)}else{n.appendChild(p)}return p},createShift:function(n,m,p){var o=this.Element("span",{style:{marginLeft:this.Em(m)},isMathJax:true});if(p){n.insertBefore(o,n.firstChild)}else{n.appendChild(o)}return o},createSpace:function(r,p,q,s,o,u){if(p<-q){q=-p}var t=this.Em(p+q),m=this.Em(-q);if(this.msieInlineBlockAlignBug){m=this.Em(d.getHD(r.parentNode,true).d-q)}if(r.isBox||u){var n=(r.scale==null?1:r.scale);r.bbox={exactW:true,h:p*n,d:q*n,w:s*n,rw:s*n,lw:0};r.style.height=t;r.style.verticalAlign=m;r.HH=(p+q)*n}else{r=this.addElement(r,"span",{style:{height:t,verticalAlign:m},isMathJax:true})}if(s>=0){r.style.width=this.Em(s);r.style.display="inline-block";r.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){r.style.height=""}r.style.marginLeft=this.Em(s);if(d.safariNegativeSpaceBug&&r.parentNode.firstChild==r){this.createBlank(r,0,true)}}if(o&&o!==i.COLOR.TRANSPARENT){r.style.backgroundColor=o;r.style.position="relative"}return r},createRule:function(t,p,r,u,n){if(p<-r){r=-p}var o=d.TeX.min_rule_thickness,q=1;if(u>0&&u*this.em<o){u=o/this.em}if(p+r>0&&(p+r)*this.em<o){q=1/(p+r)*(o/this.em);p*=q;r*=q}if(!n){n="solid"}else{n="solid "+n}var m={display:"inline-block",overflow:"hidden",verticalAlign:this.Em(-r)};if(u>p+r){m.borderTop=this.Px(p+r)+" "+n;m.width=this.Em(u);m.height=(this.msieRuleBug&&p+r>0?this.Em(p+r):0)}else{m.borderLeft=this.Px(u)+" "+n;m.width=(this.msieRuleBug&&u>0?this.Em(u):0);m.height=this.Em(p+r)}var s=this.addElement(t,"span",{style:m,noAdjust:true,HH:p+r,isMathJax:true,bbox:{h:p,d:r,w:u,rw:u,lw:0,exactW:true}});if(t.isBox||t.className=="mspace"){t.bbox=s.bbox,t.HH=p+r}return s},createFrame:function(v,s,u,x,z,n){if(s<-u){u=-s}var r=2*z;if(this.msieFrameSizeBug){if(x<r){x=r}if(s+u<r){s=r-u}}if(this.msieBorderWidthBug){r=0}var y=this.Em(s+u-r),m=this.Em(-u-z),q=this.Em(x-r);var o=this.Px(z)+" "+n;var p=this.addElement(v,"span",{style:{border:o,display:"inline-block",overflow:"hidden",width:q,height:y},bbox:{h:s,d:u,w:x,rw:x,lw:0,exactW:true},noAdjust:true,HH:s+u,isMathJax:true});if(m){p.style.verticalAlign=m}return p},parentNode:function(n){var m=n.parentNode;if(m.nodeName.toLowerCase()==="a"){m=m.parentNode}return m},createStack:function(o,q,n){if(this.msiePaddingWidthBug){this.createStrut(o,0)}var p=String(n).match(/%$/);var m=(!p&&n!=null?n:0);o=this.addElement(o,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(p?"100%":this.Em(m)),height:0}});if(!q){o.parentNode.bbox=o.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:m,lw:this.BIGDIMEN,rw:(!p&&n!=null?n:-this.BIGDIMEN)};if(p){o.bbox.width=n}}return o},createBox:function(n,m){var o=this.addElement(n,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(m!=null){o.style.width=m}return o},addBox:function(m,n){n.style.position="absolute";n.isBox=n.isMathJax=true;return m.appendChild(n)},placeBox:function(w,v,u,q){w.isMathJax=true;var z=d.parentNode(w),F=w.bbox,B=z.bbox;if(this.msiePlaceBoxBug){this.addText(w,this.NBSP)}if(this.imgSpaceBug){this.addText(w,this.imgSpace)}var A,I=0;if(w.HH!=null){A=w.HH}else{if(F){var o=w.firstChild;A=Math.max(3,3*(o?o.scale||1:1),F.h+F.d)}else{A=w.offsetHeight/this.em}}if(!w.noAdjust){A+=1;A=Math.round(A*this.em)/this.em;if(this.msieInlineBlockAlignBug){this.addElement(w,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(A)}})}else{this.addElement(w,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(A)}});if(d.chromeHeightBug){A-=(w.lastChild.offsetHeight-Math.round(A*this.em))/this.em}}}if(F){if(this.initialSkipBug){if(F.lw<0){I=F.lw;d.createBlank(w,-I,true)}if(F.rw>F.w){d.createBlank(w,F.rw-F.w+0.1)}}if(!this.msieClipRectBug&&!F.noclip&&!q){var E=3/this.em;var C=(F.H==null?F.h:F.H),n=(F.D==null?F.d:F.D);var G=A-C-E,s=A+n+E,p=-1000,m=F.rw+1000;w.style.clip="rect("+this.Em(G)+" "+this.Em(m)+" "+this.Em(s)+" "+this.Em(p)+")"}}w.style.top=this.Em(-u-A);w.style.left=this.Em(v+I);if(F&&B){if(F.H!=null&&(B.H==null||F.H+u>B.H)){B.H=F.H+u}if(F.D!=null&&(B.D==null||F.D-u>B.D)){B.D=F.D-u}if(F.h+u>B.h){B.h=F.h+u}if(F.d-u>B.d){B.d=F.d-u}if(B.H!=null&&B.H<=B.h){delete B.H}if(B.D!=null&&B.D<=B.d){delete B.D}if(F.w+v>B.w){B.w=F.w+v;if(B.width==null){z.style.width=this.Em(B.w)}}if(F.rw+v>B.rw){B.rw=F.rw+v}if(F.lw+v<B.lw){B.lw=F.lw+v}if(F.width!=null&&!F.isFixed){if(B.width==null){z.style.width=B.width="100%";if(F.minWidth){z.style.minWidth=B.minWidth=F.minWidth}}w.style.width=F.width}if(F.tw){B.tw=F.tw}}},alignBox:function(t,p,s,x,w){if(x==null){x=0}this.placeBox(t,x,s);if(this.msiePlaceBoxBug){var n=t.lastChild;while(n&&n.nodeName!=="#text"){n=n.previousSibling}if(n){t.removeChild(n)}}var v=t.bbox;if(v.isMultiline&&!w){return}var u=v.width!=null&&!v.isFixed;var m=0,q=x-v.w/2,o="50%";if(this.initialSkipBug){m=v.w-v.rw-0.1;q+=v.lw}if(this.msieMarginScaleBug){q=(q*this.em)+"px"}else{q=this.Em(q)}if(u){q=(x===0?"":this.Em(x));o=(50-parseFloat(v.width)/2)+"%"}b.Insert(t.style,({right:{left:"",right:this.Em(m-x)},center:{left:o,marginLeft:q}})[p])},setStackWidth:function(n,m){if(typeof(m)==="number"){n.style.width=this.Em(Math.max(0,m));var o=n.bbox;if(o){o.w=m;o.exactW=true}o=n.parentNode.bbox;if(o){o.w=m;o.exactW=true}}else{n.style.width=n.parentNode.style.width="100%";if(n.bbox){n.bbox.width=m}if(n.parentNode.bbox){n.parentNode.bbox.width=m}}},createDelimiter:function(w,n,p,s,q){if(!n){w.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};w.bbox.rw=w.bbox.w;this.createSpace(w,w.bbox.h,w.bbox.d,w.bbox.w);return}if(!s){s=1}if(!(p instanceof Array)){p=[p,p]}var v=p[1];p=p[0];var o={alias:n};while(o.alias){n=o.alias;o=this.FONTDATA.DELIMITERS[n];if(!o){o={HW:[0,this.FONTDATA.VARIANT[i.VARIANT.NORMAL]]}}}if(o.load){b.RestartAfter(j.Require(this.fontDir+"/fontdata-"+o.load+".js"))}for(var u=0,r=o.HW.length;u<r;u++){if(o.HW[u][0]*s>=p-0.01||(u==r-1&&!o.stretch)){if(o.HW[u][2]){s*=o.HW[u][2]}if(o.HW[u][3]){n=o.HW[u][3]}var t=this.addElement(w,"span");this.createChar(t,[n,o.HW[u][1]],s,q);w.bbox=t.bbox;w.offset=0.65*w.bbox.w;w.scale=s;return}}if(o.stretch){this["extendDelimiter"+o.dir](w,v,o.stretch,s,q)}},extendDelimiterV:function(B,u,F,G,x){var p=this.createStack(B,true);var w=this.createBox(p),v=this.createBox(p);this.createChar(w,(F.top||F.ext),G,x);this.createChar(v,(F.bot||F.ext),G,x);var o={bbox:{w:0,lw:0,rw:0}},E=o,q;var C=w.bbox.h+w.bbox.d+v.bbox.h+v.bbox.d;var s=-w.bbox.h;this.placeBox(w,0,s,true);s-=w.bbox.d;if(F.mid){E=this.createBox(p);this.createChar(E,F.mid,G,x);C+=E.bbox.h+E.bbox.d}if(F.min&&u<C*F.min){u=C*F.min}if(u>C){o=this.Element("span");this.createChar(o,F.ext,G,x);var D=o.bbox.h+o.bbox.d,m=D-0.05,z,r,A=(F.mid?2:1);r=z=Math.min(Math.ceil((u-C)/(A*m)),this.maxStretchyParts);if(!F.fullExtenders){m=(u-C)/(A*z)}var t=(z/(z+1))*(D-m);m=D-t;s+=t+m-o.bbox.h;while(A-->0){while(z-->0){if(!this.msieCloneNodeBug){q=o.cloneNode(true)}else{q=this.Element("span");this.createChar(q,F.ext,G,x)}q.bbox=o.bbox;s-=m;this.placeBox(this.addBox(p,q),0,s,true)}s+=t-o.bbox.d;if(F.mid&&A){this.placeBox(E,0,s-E.bbox.h,true);z=r;s+=-(E.bbox.h+E.bbox.d)+t+m-o.bbox.h}}}else{s+=(C-u)/2;if(F.mid){this.placeBox(E,0,s-E.bbox.h,true);s+=-(E.bbox.h+E.bbox.d)}s+=(C-u)/2}this.placeBox(v,0,s-v.bbox.h,true);s-=v.bbox.h+v.bbox.d;B.bbox={w:Math.max(w.bbox.w,o.bbox.w,v.bbox.w,E.bbox.w),lw:Math.min(w.bbox.lw,o.bbox.lw,v.bbox.lw,E.bbox.lw),rw:Math.max(w.bbox.rw,o.bbox.rw,v.bbox.rw,E.bbox.rw),h:0,d:-s,exactW:true};B.scale=G;B.offset=0.55*B.bbox.w;B.isMultiChar=true;this.setStackWidth(p,B.bbox.w)},extendDelimiterH:function(C,p,F,H,z){var s=this.createStack(C,true);var q=this.createBox(s),D=this.createBox(s);this.createChar(q,(F.left||F.rep),H,z);this.createChar(D,(F.right||F.rep),H,z);var m=this.Element("span");this.createChar(m,F.rep,H,z);var E={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},o;this.placeBox(q,-q.bbox.lw,0,true);var v=(q.bbox.rw-q.bbox.lw)+(D.bbox.rw-D.bbox.lw)-0.05,u=q.bbox.rw-q.bbox.lw-0.025,y;if(F.mid){E=this.createBox(s);this.createChar(E,F.mid,H,z);v+=E.bbox.w}if(F.min&&p<v*F.min){p=v*F.min}if(p>v){var G=m.bbox.rw-m.bbox.lw,r=G-0.05,A,t,B=(F.mid?2:1);t=A=Math.min(Math.ceil((p-v)/(B*r)),this.maxStretchyParts);if(!F.fillExtenders){r=(p-v)/(B*A)}y=(A/(A+1))*(G-r);r=G-y;u-=m.bbox.lw+y;while(B-->0){while(A-->0){if(!this.cloneNodeBug){o=m.cloneNode(true)}else{o=this.Element("span");this.createChar(o,F.rep,H,z)}o.bbox=m.bbox;this.placeBox(this.addBox(s,o),u,0,true);u+=r}if(F.mid&&B){this.placeBox(E,u,0,true);u+=E.bbox.w-y;A=t}}}else{u-=(v-p)/2;if(F.mid){this.placeBox(E,u,0,true);u+=E.bbox.w}u-=(v-p)/2}u-=D.bbox.lw;this.placeBox(D,u,0,true);C.bbox={w:u+D.bbox.rw,lw:0,rw:u+D.bbox.rw,h:Math.max(q.bbox.h,m.bbox.h,D.bbox.h,E.bbox.h),d:Math.max(q.bbox.d,m.bbox.d,D.bbox.d,E.bbox.d),exactW:true};C.scale=H;C.isMultiChar=true;this.setStackWidth(s,C.bbox.w)},createChar:function(u,r,p,n){u.isMathJax=true;var t=u,v="",q={fonts:[r[1]],noRemap:true};if(n&&n===i.VARIANT.BOLD){q.fonts=[r[1]+"-bold",r[1]]}if(typeof(r[1])!=="string"){q=r[1]}if(r[0] instanceof Array){for(var s=0,o=r[0].length;s<o;s++){v+=String.fromCharCode(r[0][s])}}else{v=String.fromCharCode(r[0])}if(r[4]){p*=r[4]}if(p!==1||r[3]){t=this.addElement(u,"span",{style:{fontSize:this.Percent(p)},scale:p,isMathJax:true});this.handleVariant(t,q,v);u.bbox=t.bbox}else{this.handleVariant(u,q,v)}if(r[2]){u.style.marginLeft=this.Em(r[2])}if(r[3]){u.firstChild.style.verticalAlign=this.Em(r[3]);u.bbox.h+=r[3];if(u.bbox.h<0){u.bbox.h=0}}if(r[5]){u.bbox.h+=r[5]}if(r[6]){u.bbox.d+=r[6]}if(this.AccentBug&&u.bbox.w===0){t.firstChild.nodeValue+=this.NBSP}},positionDelimiter:function(n,m){m-=n.bbox.h;n.bbox.d-=m;n.bbox.h+=m;if(m){if(this.safariVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&n.isMultiChar)){if(n.firstChild.style.display===""&&n.style.top!==""){n=n.firstChild;m-=d.unEm(n.style.top)}n.style.position="relative";n.style.top=this.Em(-m)}else{n.style.verticalAlign=this.Em(m);if(d.ffVerticalAlignBug){d.createRule(n.parentNode,n.bbox.h,0,0);delete 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r=q["offset"+w[v].offset];if(r&&y>=w[v].low&&y<=w[v].high){if(w[v].remap&&w[v].remap[y]){y=r+w[v].remap[y]}else{if(w[v].remapOnly){break}y=y-w[v].low+r;if(w[v].add){y+=w[v].add}}if(q["variant"+w[v].offset]){q=this.FONTDATA.VARIANT[q["variant"+w[v].offset]]}break}}}if(q.remap&&q.remap[y]){y=q.remap[y];if(q.remap.variant){q=this.FONTDATA.VARIANT[q.remap.variant]}}else{if(this.FONTDATA.REMAP[y]&&!q.noRemap){y=this.FONTDATA.REMAP[y]}}if(h(y)){q=this.FONTDATA.VARIANT[y[1]];y=y[0]}if(typeof(y)==="string"){t=y+t.substr(C+1);z=t.length;C=-1;continue}u=this.lookupChar(q,y);D=u[y];if(p||(!this.checkFont(u,o.style)&&!D[5].img)){if(A.length){this.addText(o,A);A=""}var x=!!o.style.fontFamily||!!B.style.fontStyle||!!B.style.fontWeight||!u.directory||p;p=false;if(o!==B){x=!this.checkFont(u,B.style);o=B}if(x){o=this.addElement(B,"span",{isMathJax:true,subSpan:true})}this.handleFont(o,u,o!==B)}A=this.handleChar(o,u,D,y,A);if(!(D[5]||{}).space){if(D[0]/1000>B.bbox.h){B.bbox.h=D[0]/1000}if(D[1]/1000>B.bbox.d){B.bbox.d=D[1]/1000}}if(B.bbox.w+D[3]/1000<B.bbox.lw){B.bbox.lw=B.bbox.w+D[3]/1000}if(B.bbox.w+D[4]/1000>B.bbox.rw){B.bbox.rw=B.bbox.w+D[4]/1000}B.bbox.w+=D[2]/1000;if((D[5]||{}).isUnknown){B.bbox.exactW=false}}if(A.length){this.addText(o,A)}if(B.scale&&B.scale!==1){B.bbox.h*=B.scale;B.bbox.d*=B.scale;B.bbox.w*=B.scale;B.bbox.lw*=B.scale;B.bbox.rw*=B.scale}if(d.isChar(t)&&u.skew&&u.skew[y]){B.bbox.skew=u.skew[y]}},checkFont:function(m,n){var o=(n.fontWeight||"normal");if(o.match(/^\d+$/)){o=(parseInt(o)>=600?"bold":"normal")}return(m.family.replace(/'/g,"")===n.fontFamily.replace(/'/g,"")&&(((m.style||"normal")===(n.fontStyle||"normal")&&(m.weight||"normal")===o)||(this.FontFaceBug&&n.fontFamily!=="")))},handleFont:function(o,m,q){o.style.fontFamily=m.family;if(!m.directory){o.style.fontSize=Math.floor(d.config.scale/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&m.isWebFont)){var n=m.style||"normal",p=m.weight||"normal";if(n!=="normal"||q){o.style.fontStyle=n}if(p!=="normal"||q){o.style.fontWeight=p}}},handleChar:function(o,m,u,t,s){var r=u[5];if(r.space){if(s.length){this.addText(o,s)}d.createShift(o,u[2]/1000);return""}if(r.img){return this.handleImg(o,m,u,t,s)}if(r.isUnknown&&this.FONTDATA.DELIMITERS[t]){if(s.length){this.addText(o,s)}var q=o.scale;d.createDelimiter(o,t,0,1,m);if(this.FONTDATA.DELIMITERS[t].dir==="V"){o.style.verticalAlign=this.Em(o.bbox.d);o.bbox.h+=o.bbox.d;o.bbox.d=0}o.scale=q;u[0]=o.bbox.h*1000;u[1]=o.bbox.d*1000;u[2]=o.bbox.w*1000;u[3]=o.bbox.lw*1000;u[4]=o.bbox.rw*1000;return""}if(r.c==null){if(t<=65535){r.c=String.fromCharCode(t)}else{var p=t-65536;r.c=String.fromCharCode((p>>10)+55296)+String.fromCharCode((p&1023)+56320)}}if(d.ffFontOptimizationBug&&u[4]-u[2]>125){o.style.textRendering="optimizeLegibility"}if(r.rfix){this.addText(o,s+r.c);d.createShift(o,r.rfix/1000);return""}if(u[2]||(!this.msieAccentBug&&!this.combiningCharBug)||s.length){return s+r.c}if(this.combiningCharBug){d.addElement(o,"span",{style:{marginLeft:d.Em(u[3]/1000)}},[r.c]);return""}d.createShift(o,u[3]/1000);d.createShift(o,(u[4]-u[3])/1000);this.addText(o,r.c);d.createShift(o,-u[4]/1000);return""},handleImg:function(o,m,r,q,p){return p},lookupChar:function(r,u){var q,o;if(!r.FONTS){var t=this.FONTDATA.FONTS;var s=(r.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(s instanceof Array)){s=[s]}if(r.fonts!=s){r.fonts=s}r.FONTS=[];for(q=0,o=s.length;q<o;q++){if(t[s[q]]){r.FONTS.push(t[s[q]]);t[s[q]].name=s[q]}}}for(q=0,o=r.FONTS.length;q<o;q++){var p=r.FONTS[q];if(typeof(p)==="string"){delete r.FONTS;this.loadFont(p)}if(p[u]){if(p[u].length===5){p[u][5]={}}if(d.allowWebFonts&&!p.available){this.loadWebFont(p)}else{return p}}else{this.findBlock(p,u)}}return this.unknownChar(r,u)},unknownChar:function(m,p){var o=(m.defaultFont||{family:d.config.undefinedFamily});if(m.bold){o.weight="bold"}if(m.italic){o.style="italic"}if(!o[p]){o[p]=[800,200,500,0,500,{isUnknown:true}]}b.signal.Post(["HTML-CSS Jax - unknown char",p,m]);return o},isChar:function(m){if(m.length===1){return true}if(m.length!==2){return false}var o=m.charCodeAt(0);return(o>=55296&&o<56319)},findBlock:function(o,s){if(o.Ranges){for(var r=0,n=o.Ranges.length;r<n;r++){if(s<o.Ranges[r][0]){return}if(s<=o.Ranges[r][1]){var 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n=this.HTMLspanElement();if(n&&(n.parentNode===m||(n.parentNode||{}).parentNode===m)){while(n.firstChild){n.removeChild(n.firstChild)}n.bbox=this.HTMLzeroBBox();n.scale=1;n.isMultChar=n.HH=null;n.style.cssText="";return n}}if(this.href){m=d.addElement(m,"a",{href:this.href,isMathJax:true})}m=d.addElement(m,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){m.style.display="inline-block"}if(this["class"]){m.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}m.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;m.bbox=this.HTMLzeroBBox();this.styles={};if(this.style){m.style.cssText=this.style;if(m.style.fontSize){this.mathsize=m.style.fontSize;m.style.fontSize=""}this.styles={border:d.getBorders(m),padding:d.getPadding(m)};if(this.styles.border){m.style.border=""}if(this.styles.padding){m.style.padding=""}}if(this.href){m.parentNode.bbox=m.bbox}this.HTMLaddAttributes(m);return m},HTMLaddAttributes:function(p){if(this.attrNames){var 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p=q.bbox.h,r=q.bbox.d;for(o=0,n=s.length;o<n;o++){s[o].HTMLstretchV(q,p,r)}if(s.length){this.HTMLcomputeBBox(q,true)}this.HTMLhandleSpace(q);this.HTMLhandleColor(q);return q},HTMLcomputeBBox:function(r,q){var o=r.bbox={},s=[];this.HTMLcheckStretchy(this.data.open,o,s,q);this.HTMLcheckStretchy(this.data[0],o,s,q);for(var p=1,n=this.data.length;p<n;p++){if(this.data[p]){this.HTMLcheckStretchy(this.data["sep"+p],o,s,q);this.HTMLcheckStretchy(this.data[p],o,s,q)}}this.HTMLcheckStretchy(this.data.close,o,s,q);this.HTMLcleanBBox(o);return s},HTMLcheckStretchy:function(m,n,p,o){if(m){if(!o&&m.HTMLcanStretch("Vertical")){p.push(m);m=(m.CoreMO()||m)}this.HTMLcombineBBoxes(m,n)}}});i.menclose.Augment({toHTML:i.mbase.HTMLautoload});i.maction.Augment({toHTML:i.mbase.HTMLautoload});i.semantics.Augment({toHTML:function(n,m,o){n=this.HTMLcreateSpan(n);if(this.data[0]!=null){var p=this.data[0].toHTML(n);if(o!=null){this.data[0].HTMLstretchV(n,m,o)}else{if(m!=null){this.data[0].HTMLstretchH(n,m)}}n.bbox=p.bbox}this.HTMLhandleSpace(n);return n},HTMLstretchH:i.mbase.HTMLstretchH,HTMLstretchV:i.mbase.HTMLstretchV});i.munderover.Augment({toHTML:function(M,I,G){var n=this.getValues("displaystyle","accent","accentunder","align");var q=this.data[this.base];if(!n.displaystyle&&q!=null&&(q.movablelimits||q.CoreMO().Get("movablelimits"))){return i.msubsup.prototype.toHTML.call(this,M)}M=this.HTMLcreateSpan(M);var Q=this.HTMLgetScale();var r=d.createStack(M);var 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w,u,B,A,v,E,K,P=0;q=s[this.base]||{bbox:this.HTMLzeroBBox()};if(q.bbox.ic){P=1.3*q.bbox.ic+0.05}for(N=0,J=this.data.length;N<J;N++){if(this.data[N]!=null){z=s[N];v=d.TeX.big_op_spacing5*Q;var C=(N!=this.base&&n[this.ACCENTS[N]]);if(C&&z.bbox.w<=1/d.em+0.0001){z.bbox.w=z.bbox.rw-z.bbox.lw;z.bbox.noclip=true;if(z.bbox.lw){z.insertBefore(d.createSpace(z.parentNode,0,0,-z.bbox.lw),z.firstChild)}d.createBlank(z,0,0,z.bbox.rw+0.1)}E={left:0,center:(L-z.bbox.w)/2,right:L-z.bbox.w}[n.align];w=E;u=0;if(N==this.over){if(C){K=Math.max(F*Q*H,2.5/this.em);v=0;if(q.bbox.skew){w+=q.bbox.skew;M.bbox.skew=q.bbox.skew;if(w+z.bbox.w>L){M.bbox.skew+=(L-z.bbox.w-w)/2}}}else{B=d.TeX.big_op_spacing1*Q*H;A=d.TeX.big_op_spacing3*Q*H;K=Math.max(B,A-Math.max(0,z.bbox.d))}K=Math.max(K,1.5/this.em);w+=P/2;u=q.bbox.h+z.bbox.d+K;z.bbox.h+=v}else{if(N==this.under){if(C){K=3*F*Q*H;v=0}else{B=d.TeX.big_op_spacing2*Q*H;A=d.TeX.big_op_spacing4*Q*H;K=Math.max(B,A-z.bbox.h)}K=Math.max(K,1.5/this.em);w-=P/2;u=-(q.bbox.d+z.bbox.h+K);z.bbox.d+=v}}d.placeBox(z,w,u)}}this.HTMLhandleSpace(M);this.HTMLhandleColor(M);return 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B=x.bbox.h-H,A=x.bbox.d+G,O=0,I;if(x.bbox.ic){x.bbox.w-=x.bbox.ic;O=1.3*x.bbox.ic+0.05}if(this.data[this.base]&&K==null&&F==null&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(d.isChar(this.data[this.base].data.join(""))&&w[0].scale===1&&!this.data[this.base].Get("largeop")){B=A=0}}var L=this.getValues("subscriptshift","superscriptshift");L.subscriptshift=(L.subscriptshift===""?0:d.length2em(L.subscriptshift,J));L.superscriptshift=(L.superscriptshift===""?0:d.length2em(L.superscriptshift,J));if(!m){if(z){A=Math.max(A,d.TeX.sub1*P,z.bbox.h-(4/5)*N,L.subscriptshift);d.placeBox(z,x.bbox.w,-A,z.bbox)}}else{if(!z){n=this.getValues("displaystyle","texprimestyle");I=d.TeX[(n.displaystyle?"sup1":(n.texprimestyle?"sup3":"sup2"))];B=Math.max(B,I*P,m.bbox.d+(1/4)*N,L.superscriptshift);d.placeBox(m,x.bbox.w+O,B,m.bbox)}else{A=Math.max(A,d.TeX.sub2*P);var C=d.TeX.rule_thickness*P;if((B-m.bbox.d)-(z.bbox.h-A)<3*C){A=3*C-B+m.bbox.d+z.bbox.h;H=(4/5)*N-(B-m.bbox.d);if(H>0){B+=H;A-=H}}d.placeBox(m,x.bbox.w+O,Math.max(B,L.superscriptshift));d.placeBox(z,x.bbox.w,-Math.max(A,L.subscriptshift))}}this.HTMLhandleSpace(M);this.HTMLhandleColor(M);return M},HTMLstretchH:i.mbase.HTMLstretchH,HTMLstretchV:i.mbase.HTMLstretchV});i.mmultiscripts.Augment({toHTML:i.mbase.HTMLautoload});i.mtable.Augment({toHTML:i.mbase.HTMLautoload});i["annotation-xml"].Augment({toHTML:i.mbase.HTMLautoload});i.annotation.Augment({toHTML:function(m){return this.HTMLcreateSpan(m)}});i.math.Augment({toHTML:function(E,B,t){var u,w,x,r,m=E;if(!t||t===d.PHASE.I){var C=d.addElement(E,"nobr",{isMathJax:true});E=this.HTMLcreateSpan(C);var 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A=1/d.em,G=d.em/d.outerEm;d.em/=G;E.bbox.h*=G;E.bbox.d*=G;E.bbox.w*=G;E.bbox.lw*=G;E.bbox.rw*=G;if(E.bbox.H){E.bbox.H*=G}if(E.bbox.D){E.bbox.D*=G}if(r&&r.bbox.width!=null){E.style.minWidth=(r.bbox.minWidth||E.style.width);E.style.width=r.bbox.width;w.style.width=u.style.width="100%";m.className+=" MathJax_FullWidth"}var D=this.HTMLhandleColor(E);if(r){d.createRule(E,(r.bbox.h+A)*G,(r.bbox.d+A)*G,0)}if(!this.isMultiline&&this.Get("display")==="block"&&E.bbox.width==null){var o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(o.indentalignfirst!==i.INDENTALIGN.INDENTALIGN){o.indentalign=o.indentalignfirst}if(o.indentalign===i.INDENTALIGN.AUTO){o.indentalign=this.displayAlign}if(o.indentshiftfirst!==i.INDENTSHIFT.INDENTSHIFT){o.indentshift=o.indentshiftfirst}if(o.indentshift==="auto"){o.indentshift="0"}var F=d.length2em(o.indentshift,1,d.scale*d.cwidth);if(this.displayIndent!=="0"){var y=d.length2em(this.displayIndent,1,d.scale*d.cwidth);F+=(o.indentalign===i.INDENTALIGN.RIGHT?-y:y)}m.style.textAlign=B.style.textAlign=o.indentalign;if(F){b.Insert(E.style,({left:{marginLeft:d.Em(F)},right:{marginRight:d.Em(-F)},center:{marginLeft:d.Em(F),marginRight:d.Em(-F)}})[o.indentalign]);if(D){var v=parseFloat(D.style.marginLeft||"0")+F,s=parseFloat(D.style.marginRight||"0")-F;D.style.marginLeft=d.Em(v);D.style.marginRight=d.Em(s+(o.indentalign==="right"?E.bbox.w+F-E.bbox.w:0));if(d.msieColorBug&&o.indentalign==="right"){if(parseFloat(D.style.marginLeft)>0){var z=MathJax.HTML.addElement(D.parentNode,"span");z.style.marginLeft=d.Em(s+Math.min(0,E.bbox.w+F));D.nextSibling.style.marginRight="0em"}D.nextSibling.style.marginLeft="0em";D.style.marginRight=D.style.marginLeft="0em"}}}}}return E},HTMLspanElement:i.mbase.prototype.HTMLspanElement});i.TeXAtom.Augment({toHTML:function(q,o,s){q=this.HTMLcreateSpan(q);if(this.data[0]!=null){if(this.texClass===i.TEXCLASS.VCENTER){var 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n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(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.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;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="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-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="MJXp-right MJXp-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.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-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.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;p<n;p++){this.PHTMLaddChild(q,"sep"+p,{});this.PHTMLaddChild(q,p,{})}this.PHTMLaddChild(q,"close",{});var o=this.PHTML.h,r=this.PHTML.d;this.PHTMLstretchChild("open",o,r);for(p=0,n=this.data.length;p<n;p++){this.PHTMLstretchChild("sep"+p,o,r);this.PHTMLstretchChild(p,o,r)}this.PHTMLstretchChild("close",o,r);return q}});h.mrow.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var p=this.PHTML.h,r=this.PHTML.d;for(var o=0,n=this.data.length;o<n;o++){this.PHTMLstretchChild(o,p,r)}return q}});h.mstyle.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);this.PHTMLhandleScriptlevel(n);return n}});h.TeXAtom.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);n.className="MJXp-mrow";return n}});h.mtable.Augment({toPreviewHTML:function(E){E=this.PHTMLdefaultSpan(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.PHTML,q=v.PHTMLspanElement();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.PHTMLspanElement();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.PHTML;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({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p<n;p++){this.PHTMLaddChild(q,p,o)}return q}});h.semantics.Augment({toPreviewHTML:function(n){n=this.PHTMLcreateSpan(n);if(this.data[0]){this.data[0].toPreviewHTML(n);MathJax.Hub.Insert(this.data[0].PHTML||{},this.PHTML)}return n}});h.annotation.Augment({toPreviewHTML:function(n){}});h["annotation-xml"].Augment({toPreviewHTML: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.PreviewHTML);
(function(b,g,f){var c=b.config.menuSettings;var e=MathJax.OutputJax;var a=f.isMSIE&&(document.documentMode||0)<8;var d=MathJax.Extension["fast-preview"]={version:"2.7.8",enabled:true,config:b.CombineConfig("fast-preview",{Chunks:{EqnChunk:10000,EqnChunkFactor:1,EqnChunkDelay:0},color:"inherit!important",updateTime:30,updateDelay:6,messageStyle:"none",disabled:f.isMSIE&&!f.versionAtLeast("8.0")}),Config:function(){if(b.config["CHTML-preview"]){MathJax.Hub.Config({"fast-preview":b.config["CHTML-preview"]})}var m,j,k,h,l;var i=this.config;if(!i.disabled&&c.FastPreview==null){b.Config({menuSettings:{FastPreview:true}})}if(c.FastPreview){MathJax.Ajax.Styles({".MathJax_Preview .MJXf-math":{color:i.color}});b.Config({"HTML-CSS":i.Chunks,CommonHTML:i.Chunks,SVG:i.Chunks})}b.Register.MessageHook("Begin Math Output",function(){if(!h&&d.Active()){m=b.processUpdateTime;j=b.processUpdateDelay;k=b.config.messageStyle;b.processUpdateTime=i.updateTime;b.processUpdateDelay=i.updateDelay;b.Config({messageStyle:i.messageStyle});MathJax.Message.Clear(0,0);l=true}});b.Register.MessageHook("End Math Output",function(){if(!h&&l){b.processUpdateTime=m;b.processUpdateDelay=j;b.Config({messageStyle:k});h=true}})},Disable:function(){this.enabled=false},Enable:function(){this.enabled=true},Active:function(){return c.FastPreview&&this.enabled&&!(e[c.renderer]||{}).noFastPreview},Preview:function(h){if(!this.Active()||!h.script.parentNode){return}var i=h.script.MathJax.preview||h.script.previousSibling;if(!i||i.className!==MathJax.Hub.config.preRemoveClass){i=g.Element("span",{className:MathJax.Hub.config.preRemoveClass});h.script.parentNode.insertBefore(i,h.script);h.script.MathJax.preview=i}i.innerHTML="";i.style.color=(a?"black":"inherit");return this.postFilter(i,h)},postFilter:function(j,i){if(!i.math.root.toPreviewHTML){var h=MathJax.Callback.Queue();h.Push(["Require",MathJax.Ajax,"[MathJax]/jax/output/PreviewHTML/config.js"],["Require",MathJax.Ajax,"[MathJax]/jax/output/PreviewHTML/jax.js"]);b.RestartAfter(h.Push({}))}i.math.root.toPreviewHTML(j)},Register:function(h){b.Register.StartupHook(h+" Jax Require",function(){var i=MathJax.InputJax[h];i.postfilterHooks.Add(["Preview",MathJax.Extension["fast-preview"]],50)})}};d.Register("TeX");d.Register("MathML");d.Register("AsciiMath");b.Register.StartupHook("End Config",["Config",d]);b.Startup.signal.Post("fast-preview Ready")})(MathJax.Hub,MathJax.HTML,MathJax.Hub.Browser);MathJax.Ajax.loadComplete("[MathJax]/extensions/fast-preview.js");
(function(a,e,b,f){var c=b.config.menuSettings;var d=MathJax.Extension.AssistiveMML={version:"2.7.8",config:b.CombineConfig("AssistiveMML",{disabled:false,styles:{".MJX_Assistive_MathML":{position:"absolute!important",top:0,left:0,clip:(b.Browser.isMSIE&&(document.documentMode||0)<8?"rect(1px 1px 1px 1px)":"rect(1px, 1px, 1px, 1px)"),padding:"1px 0 0 0!important",border:"0!important",height:"1px!important",width:"1px!important",overflow:"hidden!important",display:"block!important","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none"},".MJX_Assistive_MathML.MJX_Assistive_MathML_Block":{width:"100%!important"}}}),Config:function(){if(!this.config.disabled&&c.assistiveMML==null){b.Config({menuSettings:{assistiveMML:true}})}a.Styles(this.config.styles);b.Register.MessageHook("End Math",function(g){if(c.assistiveMML){return d.AddAssistiveMathML(g[1])}})},AddAssistiveMathML:function(g){var h={jax:b.getAllJax(g),i:0,callback:MathJax.Callback({})};this.HandleMML(h);return h.callback},RemoveAssistiveMathML:function(k){var h=b.getAllJax(k),l;for(var j=0,g=h.length;j<g;j++){l=document.getElementById(h[j].inputID+"-Frame");if(l&&l.getAttribute("data-mathml")){l.removeAttribute("data-mathml");if(l.lastChild&&l.lastChild.className.match(/MJX_Assistive_MathML/)){l.removeChild(l.lastChild)}}}},HandleMML:function(l){var g=l.jax.length,h,i,n,j;while(l.i<g){h=l.jax[l.i];n=document.getElementById(h.inputID+"-Frame");if(h.outputJax!=="NativeMML"&&h.outputJax!=="PlainSource"&&n&&!n.getAttribute("data-mathml")){try{i=h.root.toMathML("").replace(/\n */g,"").replace(/<!--.*?-->/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])});
!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS-MML_HTMLorMML-full.js");
