/*
 *  /MathJax/config/TeX-AMS-texvc_HTML.js
 *
 *  Copyright (c) 2010-11 Design Science, Inc.
 *
 *  wiki2jax.js and TeX/texvc.js also
 *  Copyright (c) 2010-2011 http://en.wikipedia.org/User:Nageh
 *
 *  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
 *
 * Various customized logic!
 * - custom conversion helpers
 * - some custom texvc commands ('texvc.js')
 * - heuristic detection of inline vs display maths (displays are in a <dd>) (ConvertMath())
 * - workaround for \scriptstyle / \scriptscriptstyle font-size hack used on Wikipedia
 * - partial hacks for \oiint an d\oiiint. (needs font fixes?)
 * - hack to support \color commands -> drop for MathJax 2.0 which has this natively?
 * - custom render settings (mathJax.js config?)
 * - support for user hooks -> find a way to generalize this for site JS too
 * - support for wikEd, ajaxPreview (mathJax.Init() in loader)
 * - conditional loading
 * - some misc
 */

MathJax.Ajax.Preloading(
  "[MathJax]/jax/input/TeX/config.js",
  "[MathJax]/jax/output/HTML-CSS/config.js",
  "[MathJax]/jax/element/mml/jax.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]/extensions/TeX/boldsymbol.js",
  "[MathJax]/extensions/TeX/mathchoice.js",
  "[MathJax]/jax/output/HTML-CSS/jax.js",
  "[MathJax]/jax/output/HTML-CSS/autoload/mtable.js",
  "[MathJax]/extensions/wiki2jax.js",
  "[MathJax]/extensions/TeX/texvc.js"
);

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

MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.1.1",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%"}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js");

MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.4",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:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#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"}}}});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.id==="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("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.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.1",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g<f;g++){this.SetData(this.data.length,arguments[g])}}},SetData:function(f,g){if(g!=null){if(!(g instanceof a.mbase)){g=(this.isToken?a.chars(g):a.mtext(g))}g.parent=this;g.setInherit(this.inheritFromMe?this:this.inherit)}this.data[f]=g},Parent:function(){var f=this.parent;while(f&&f.inferred){f=f.parent}return f},Get:function(g,k){if(typeof(this[g])!=="undefined"){return this[g]}var h=this.Parent();if(h&&h["adjustChild_"+g]!=null){return(h["adjustChild_"+g])(h.childPosition(this))}var j=this.inherit;var f=j;while(j){if(typeof(j[g])!=="undefined"){var i=j.noInherit[this.type];if(!(i&&i[g])){return j[g]}}f=j;j=j.inherit}if(!k){if(this.defaults[g]===a.AUTO){return this.autoDefault(g)}if(this.defaults[g]!==a.INHERIT&&this.defaults[g]!=null){return this.defaults[g]}if(f){return f.defaults[g]}}return null},hasValue:function(f){return(this.Get(f,true)!=null)},getValues:function(){var g={};for(var h=0,f=arguments.length;h<f;h++){g[arguments[h]]=this.Get(arguments[h])}return g},adjustChild_scriptlevel:function(f){return this.Get("scriptlevel")},adjustChild_displaystyle:function(f){return this.Get("displaystyle")},adjustChild_texprimestyle:function(f){return this.Get("texprimestyle")},childPosition:function(h){if(h.parent.inferred){h=h.parent}for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]===h){return g}}return null},setInherit:function(h){if(h!==this.inherit&&this.inherit==null){this.inherit=h;for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]&&this.data[g].setInherit){this.data[g].setInherit(h)}}}},setTeXclass:function(f){this.getPrevClass(f);return(typeof(this.texClass)!=="undefined"?this:f)},getPrevClass:function(f){if(f){this.prevClass=f.Get("texClass");this.prevLevel=f.Get("scriptlevel")}},updateTeXclass:function(f){if(f){this.prevClass=f.prevClass;delete f.prevClass;this.prevLevel=f.prevLevel;delete f.prevLevel;this.texClass=f.Get("texClass")}},texSpacing:function(){var g=(this.prevClass!=null?this.prevClass:a.TEXCLASS.NONE);var f=(this.Get("texClass")||a.TEXCLASS.ORD);if(g===a.TEXCLASS.NONE||f===a.TEXCLASS.NONE){return""}if(g===a.TEXCLASS.VCENTER){g=a.TEXCLASS.ORD}if(f===a.TEXCLASS.VCENTER){f=a.TEXCLASS.ORD}var h=this.TEXSPACE[g][f];if(this.prevLevel>0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var f=0;f<this.data.length;f++){if(!this.data[f].isSpacelike()){return d}}return b},childEmbellished:function(){return(this.data[0]&&this.data[0].isEmbellished())},childCore:function(){return this.data[0]},childCoreMO:function(){return(this.data[0]?this.data[0].CoreMO():null)},setChildTeXclass:function(f){if(this.data[0]){f=this.data[0].setTeXclass(f);this.updateTeXclass(this.data[0])}return f},setBaseTeXclasses:function(h){this.getPrevClass(h);this.texClass=null;if(this.isEmbellished()){h=this.data[0].setTeXclass(h);this.updateTeXclass(this.Core())}else{if(this.data[0]){this.data[0].setTeXclass()}h=this}for(var g=1,f=this.data.length;g<f;g++){if(this.data[g]){this.data[g].setTeXclass()}}return h},setSeparateTeXclasses:function(h){this.getPrevClass(h);for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]){this.data[g].setTeXclass()}}if(this.isEmbellished()){this.updateTeXclass(this.Core())}return this}});a.mi=a.mbase.Subclass({type:"mi",isToken:b,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.AUTO,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT},autoDefault:function(g){if(g==="mathvariant"){var f=(this.data[0]||"").toString();return(f.length===1||(f.length===2&&f.charCodeAt(0)===this.PLANE1)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:b,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:b,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:d,separator:d,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:d,symmetric:b,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:d,movablelimits:d,accent:d,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(h,o){var n=this.def;if(!n){if(h==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var l=this.data.join("");var g=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var j=0,f=g.length;j<f;j++){var k=this.OPTABLE[g[j]][l];if(k){n=this.makeDef(k);break}}if(!n){n=this.CheckRange(l)}if(!n&&o){n={}}else{if(!n){n=MathJax.Hub.Insert({},this.defaultDef)}n.form=g[0];this.def=n}}this.useMMLspacing&=~(this.SPACE_ATTR[h]||0);if(n[h]!=null){return n[h]}else{if(!o){return this.defaultDef[h]}}return""},CheckRange:function(k){var l=k.charCodeAt(0);if(k.charAt(0)===a.PLANE1){l=k.charCodeAt(1)+119808-56320}for(var h=0,f=this.RANGES.length;h<f&&this.RANGES[h][0]<=l;h++){if(l<=this.RANGES[h][1]){if(this.RANGES[h][3]){var g=a.optableDir+"/"+this.RANGES[h][3]+".js";this.RANGES[h][3]=null;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(g))}var j=(["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER"])[this.RANGES[h][2]];j=this.OPTABLE.infix[k]=a.mo.OPTYPES[j==="BIN"?"BIN3":j];return this.makeDef(j)}}return null},makeDef:function(g){if(g[2]==null){g[2]=this.defaultDef.texClass}if(!g[3]){g[3]={}}var f=MathJax.Hub.Insert({},g[3]);f.lspace=this.SPACE[g[0]];f.rspace=this.SPACE[g[1]];f.texClass=g[2];return f},getForm:function(){var f=this,h=this.parent,g=this.Parent();while(g&&g.isEmbellished()){f=h;h=g.parent;g=g.Parent()}if(h&&h.type==="mrow"&&h.NonSpaceLength()!==1){if(h.FirstNonSpace()===f){return a.FORM.PREFIX}if(h.LastNonSpace()===f){return a.FORM.POSTFIX}}return a.FORM.INFIX},isEmbellished:function(){return b},lineBreak:function(){var f=this.getValues("linebreak","linebreakstyle");if(f.linebreak===a.LINEBREAK.NEWLINE){if(f.linebreakstyle===a.LINEBREAKSTYLE.INFIXLINEBREAKSTYLE){f.linebreakstyle=this.Get("infixlinebreakstyle")}return f.linebreakstyle}return"none"},setTeXclass:function(f){this.getValues("lspace","rspace");if(this.useMMLspacing){this.texClass=a.TEXCLASS.NONE;return this}this.texClass=this.Get("texClass");if(this.texClass===a.TEXCLASS.NONE){return f}if(f){this.prevClass=f.texClass||a.TEXCLASS.ORD;this.prevLevel=f.Get("scriptlevel")}else{this.prevClass=a.TEXCLASS.NONE}if(this.texClass===a.TEXCLASS.BIN&&(this.prevClass===a.TEXCLASS.NONE||this.prevClass===a.TEXCLASS.BIN||this.prevClass===a.TEXCLASS.OP||this.prevClass===a.TEXCLASS.REL||this.prevClass===a.TEXCLASS.OPEN||this.prevClass===a.TEXCLASS.PUNCT)){this.texClass=a.TEXCLASS.ORD}else{if(this.prevClass===a.TEXCLASS.BIN&&(this.texClass===a.TEXCLASS.REL||this.texClass===a.TEXCLASS.CLOSE||this.texClass===a.TEXCLASS.PUNCT)){f.texClass=this.prevClass=a.TEXCLASS.ORD}}return this}});a.mtext=a.mbase.Subclass({type:"mtext",isToken:b,isSpacelike:function(){return b},texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mspace=a.mbase.Subclass({type:"mspace",isToken:b,isSpacelike:function(){return b},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"0em",height:"0ex",depth:"0ex",linebreak:a.LINEBREAK.AUTO},lineBreak:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE?a.LINEBREAKSTYLE.AFTER:"none")}});a.ms=a.mbase.Subclass({type:"ms",isToken:b,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,lquote:'"',rquote:'"'}});a.mglyph=a.mbase.Subclass({type:"mglyph",isToken:b,texClass:a.TEXCLASS.ORD,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,alt:"",src:"",width:a.AUTO,height:a.AUTO,valign:"0em"}});a.mrow=a.mbase.Subclass({type:"mrow",isSpacelike:a.mbase.childrenSpacelike,inferred:d,isEmbellished:function(){var g=d;for(var h=0,f=this.data.length;h<f;h++){if(this.data[h]==null){continue}if(this.data[h].isEmbellished()){if(g){return d}g=b;this.core=h}else{if(!this.data[h].isSpacelike()){return d}}}return g},NonSpaceLength:function(){var h=0;for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]&&!this.data[g].isSpacelike()){h++}}return h},FirstNonSpace:function(){for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]&&!this.data[g].isSpacelike()){return this.data[g]}}return null},LastNonSpace:function(){for(var f=this.data.length-1;f>=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return 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MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c="1.0";var a=MathJax.ElementJax.mml;var e=MathJax.InputJax.TeX;var b=e.Definitions;var d={};d[a.VARIANT.NORMAL]=a.VARIANT.BOLD;d[a.VARIANT.ITALIC]=a.VARIANT.BOLDITALIC;d[a.VARIANT.FRAKTUR]=a.VARIANT.BOLDFRAKTUR;d[a.VARIANT.SCRIPT]=a.VARIANT.BOLDSCRIPT;d[a.VARIANT.SANSSERIF]=a.VARIANT.BOLDSANSSERIF;d["-tex-caligraphic"]="-tex-caligraphic-bold";d["-tex-oldstyle"]="-tex-oldstyle-bold";b.macros.boldsymbol="Boldsymbol";e.Parse.Augment({mmlToken:function(g){if(this.stack.env.boldsymbol){var f=g.Get("mathvariant");if(f==null){g.mathvariant=a.VARIANT.BOLD}else{g.mathvariant=(d[f]||f)}}return g},Boldsymbol:function(i){var f=this.stack.env.boldsymbol,g=this.stack.env.font;this.stack.env.boldsymbol=true;this.stack.env.font=null;var h=this.ParseArg(i);this.stack.env.font=g;this.stack.env.boldsymbol=f;this.Push(h)}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var c=a.FONTDATA.FONTS;var b=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){c["MathJax_Caligraphic-bold"]="Caligraphic/Bold/Main.js";b["-tex-caligraphic-bold"]={fonts:["MathJax_Caligraphic-bold","MathJax_Main-bold","MathJax_Main","MathJax_Math","MathJax_Size1"],offsetA:65,variantA:"bold-italic"};b["-tex-oldstyle-bold"]={fonts:["MathJax_Caligraphic-bold","MathJax_Main-bold","MathJax_Main","MathJax_Math","MathJax_Size1"]};if(a.msieCheckGreek&&a.Font.testFont({family:"MathJax_Greek",weight:"bold",style:"italic",testString:a.msieCheckGreek})){b["bold-italic"].offsetG=913;b["bold-italic"].variantG="-Greek-Bold-Italic";b["-Greek-Bold-Italic"]={fonts:["MathJax_Greek-bold-italic"]};c["MathJax_Greek-bold-italic"]="Greek/BoldItalic/Main.js"}if(MathJax.Hub.Browser.isChrome&&!MathJax.Hub.Browser.versionAtLeast("5.0")){b["-tex-caligraphic-bold"].remap={84:[58096,"-WinChrome"]}}}else{if(a.fontInUse==="STIX"){b["-tex-caligraphic-bold"]={fonts:["STIXGeneral-bold-italic","STIXNonUnicode-bold-italic","STIXNonUnicode","STIXGeneral","STIXSizeOneSym"],offsetA:57927,noLowerCase:1};b["-tex-oldstyle-bold"]={fonts:["STIXGeneral-bold","STIXNonUnicode-bold","STIXGeneral","STIXSizeOneSym"],offsetN:57955,remap:{57956:57959,57957:57963,57958:57967,57959:57971,57960:57975,57961:57979,57962:57983,57963:57987,57964:57991}}}}MathJax.Hub.Startup.signal.Post("TeX boldsymbol Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/boldsymbol.js");

MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c="1.0";var a=MathJax.ElementJax.mml;var d=MathJax.InputJax.TeX;var b=d.Definitions;b.macros.mathchoice="MathChoice";d.Parse.Augment({MathChoice:function(f){var i=this.ParseArg(f),e=this.ParseArg(f),g=this.ParseArg(f),h=this.ParseArg(f);this.Push(a.TeXmathchoice(i,e,g,h))}});a.TeXmathchoice=a.mbase.Subclass({type:"TeXmathchoice",choice:function(){var e=this.getValues("displaystyle","scriptlevel");if(e.scriptlevel>0){return Math.min(3,e.scriptlevel+1)}return(e.displaystyle?0:1)},setTeXclass:function(e){return this.Core().setTeXclass(e)},isSpacelike:function(){return this.Core().isSpacelike()},isEmbellished:function(){return this.Core().isEmbellished()},Core:function(){return this.data[this.choice()]},toHTML:function(e){e=this.HTMLcreateSpan(e);e.bbox=this.Core().toHTML(e).bbox;return e}});MathJax.Hub.Startup.signal.Post("TeX mathchoice Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/mathchoice.js");

(function(c,d,e){var a;var b=MathJax.Object.Subclass({timeout:5*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} []"}},comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal"}},[""]);this.text=this.div.firstChild},findFont:function(j,g){if(g&&this.testCollection(g)){return g}for(var h=0,f=j.length;h<f;h++){if(j[h]===g){continue}if(this.testCollection(j[h])){return j[h]}}return null},testCollection:function(f){return this.testFont(this.FontInfo[f])},testFont:function(h){if(h.isWebFont&&e.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(h.weight||"normal");this.div.style.fontStyle=(h.style||"normal")}var g=this.getComparisonWidths(h.testString,h.noStyleChar);if(g){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==g[0]){this.div.style.fontFamily="'"+h.family+"',"+this.comparisonFont[g[2]];if(this.div.offsetWidth==g[1]){return false}}if(this.div.offsetWidth!=g[3]){if(h.noStyleChar||!e.FONTDATA||!e.FONTDATA.hasStyleChar){return true}for(var j=0,f=this.testSize.length;j<f;j++){if(this.testStyleChar(h,this.testSize[j])){return true}}}}return false},styleChar:String.fromCharCode(61437),versionChar:String.fromCharCode(61438),compChar:String.fromCharCode(61439),testStyleChar:function(h,j){var m=3+(h.weight?2:0)+(h.style?4:0);var g="",i=0;var l=this.div.style.fontSize;this.div.style.fontSize=j;if(e.msieItalicWidthBug&&h.style==="italic"){this.text.nodeValue=g=this.compChar;i=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+g}else{this.text.nodeValue=this.compChar+g}var f=this.div.offsetWidth-i;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+g}else{this.text.nodeValue=this.styleChar+g}var k=Math.floor((this.div.offsetWidth-i)/f+0.5);if(k===m){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+g}else{this.text.nodeValue=this.versionChar+g}h.version=Math.floor((this.div.offsetWidth-i)/f+1.5)/2}this.div.style.fontSize=l;return(k===m)},getComparisonWidths:function(j,h){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!h){j+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=j}else{this.text.nodeValue=j}this.div.style.fontFamily=this.comparisonFont[0];var g=this.div.offsetWidth,l=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];l=this.div.offsetWidth}for(var k=1,f=this.comparisonFont.length;k<f;k++){this.div.style.fontFamily=this.comparisonFont[k];if(this.div.offsetWidth!=g){return[g,this.div.offsetWidth,k,l]}}return null},loadWebFont:function(g){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+g.directory);var i=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+g.directory);var f=MathJax.Callback({});var h=MathJax.Callback(["loadComplete",this,g,i,f]);c.timer.start(c,[this.checkWebFont,g,h],1,this.timeout);return f},loadComplete:function(h,j,g,f){MathJax.Message.Clear(j);if(f===c.STATUS.OK){g();return}this.loadError(h);if(d.Browser.isFirefox&&e.allowWebFonts){var i=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){i+=":"+document.location.port}i+="/";if(c.fileURL(e.webfontDir).substr(0,i.length)!==i){this.firefoxFontError(h)}}e.loadWebFontError(h,g)},loadError:function(f){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+f.directory,null,2000)},firefoxFontError:function(f){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(f,g,h){if(f.time(h)){return}if(e.Font.testFont(g)){h(f.STATUS.OK)}else{setTimeout(f,f.delay)}},fontFace:function(h){var i=e.allowWebFonts;var k=e.FONTDATA.FONTS[h];if(e.msieFontCSSBug&&!k.family.match(/-Web$/)){k.family+="-Web"}var g=c.fileURL(e.webfontDir+"/"+i);var f=h.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!f.match(/-/)){f+="-Regular"}if(i==="svg"){f+=".svg#"+f}else{f+="."+i}var j={"font-family":k.family,src:"url('"+g+"/"+f+"')"};if(i==="svg"){j.src+=" format('svg')"}if(!(e.FontFaceBug&&k.isWebFont)){if(h.match(/-bold/)){j["font-weight"]="bold"}if(h.match(/-italic/)){j["font-style"]="italic"}}return j}});e.Augment({config:{styles:{".MathJax":{display:"inline","font-family":"serif","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",border:0,padding:0,margin:0},".MathJax_Display":{position:"relative",display:"block",width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0 !important",padding:"0 !important",margin:"0 !important","vertical-align":"0 !important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},".MathJax nobr":{"white-space":"nowrap"},".MathJax img":{display:"inline ! important"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax .MathJax_HitBox":{cursor:"text"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",background:"transparent"}}},settings:d.config.menuSettings,LEFTBUTTON:(d.Browser.isMSIE?1:0),MENUKEY:"altKey",Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var g=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(g.scale){this.config.scale=g.scale}if(g.font&&g.font!=="Auto"){if(g.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(g.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(g.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(g.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var f=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!f&&this.allowWebFonts){f=this.config.webFont;if(f){this.webFonts=true}}if(!f&&this.config.imageFont){f=this.config.imageFont;this.imgFonts=true}if(f){this.fontInUse=f;this.fontDir+="/"+f;this.webfontDir+="/"+f;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");d.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{MathJax.Message.Set("Can't find a valid font using ["+this.config.availableFonts.join(", ")+"]",null,3000);this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}};if(MathJax.InputJax.TeX&&MathJax.InputJax.TeX.Definitions){MathJax.InputJax.TeX.Definitions.macros.overline[1]="002D";MathJax.InputJax.TeX.Definitions.macros.underline[1]="002D"}d.Startup.signal.Post("HTML-CSS Jax - no valid font")}},Startup:function(){var h=[],l=this.FONTDATA.VARIANT.normal.fonts;if(!(l instanceof Array)){l=[l]}for(var g=0,f=l.length;g<f;g++){h[g]=this.FONTDATA.FONTS[l[g]].family;if(!h[g]){h[g]=l[g]}}this.config.styles[".MathJax .math span"]=this.config.styles["#MathJax_getScales"]={"font-family":h.join(",")};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 k=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=k.offsetWidth/5;this.hiddenDiv.removeChild(k);this.startMarker=e.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(j){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.HDMspan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}});if(this.msieInlineBlockAlignBug){this.HDMimg=this.addElement(this.HDMspan,"img",{style:{height:"0px",width:"1px","max-width":"none","max-height":"none",border:0,padding:0,margin:0}});try{this.HDMimg.src="about:blank"}catch(j){}}else{this.HDMimg=e.createStrut(this.HDMspan,0);this.HDMimg.style.marginRight=""}this.marginCheck=e.Element("span",null,[["span",{style:{display:"inline-block",width:"5em"}}]]);this.marginMove=e.addElement(this.marginCheck,"span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}});return c.Styles(this.config.styles,["PreloadWebFonts",this])},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var g=0,f=e.config.preloadWebFonts.length;g<f;g++){var h=e.FONTDATA.FONTS[e.config.preloadWebFonts[g]];if(!h.available){e.Font.testFont(h)}}},Translate:function(l){if(!l.parentNode){return}var j=l.previousSibling;if(j&&String(j.className).match(/^MathJax(_MathML|_Display)?$/)){j.parentNode.removeChild(j)}var m=l.MathJax.elementJax.root,n,f,h;n=f=h=this.Element("span",{className:"MathJax",oncontextmenu:this.ContextMenu,onmousedown:this.Mousedown,onmouseover:this.Mouseover,onclick:this.Click,ondblclick:this.DblClick});var i=(m.Get("display")==="block");if(i){f=h=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});f.appendChild(n)}f.setAttribute("role","textbox");f.setAttribute("aria-readonly","true");if(this.useProcessingFrame){h=this.Element((i?"div":"span"),{className:"MathJax_Processing"});h.appendChild(f)}l.parentNode.insertBefore(h,l);var g;try{this.getScales(n);g=(this.em===0||String(this.em)==="NaN")}catch(k){g=true}if(g){this.hiddenDiv.appendChild(h);this.getScales(n)}this.initImg(n);this.initHTML(m,n);m.setTeXclass();try{m.toHTML(n,f)}catch(k){if(k.restart){h.parentNode.removeChild(h)}throw k}if(g){l.parentNode.insertBefore(h,l)}if(this.useProcessingFrame){h.parentNode.replaceChild(f,h)}},ContextMenu:function(i,j){if(e.config.showMathMenu&&(e.settings.context==="MathJax"||j)){if(e.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(!i||e.msieEventBug){i=window.event}var f=MathJax.Menu;if(f){var h=(this.parentNode.className==="MathJax_Display"?this.parentNode:this);f.jax=d.getJaxFor(h.nextSibling);f.menu.items[1].menu.items[1].name=(f.jax.inputJax.id==="MathML"?"Original":f.jax.inputJax.id);return f.menu.Post(i)}else{if(!c.loadingMathMenu){c.loadingMathMenu=true;var g={pageX:i.pageX,pageY:i.pageY,clientX:i.clientX,clientY:i.clientY};MathJax.Callback.Queue(c.Require("[MathJax]/extensions/MathMenu.js"),function(){delete c.loadingMathMenu},[this,arguments.callee,g,j])}if(!i){i=window.event}if(i.preventDefault){i.preventDefault()}if(i.stopPropagation){i.stopPropagation()}i.cancelBubble=true;i.returnValue=false;return false}}},Mousedown:function(f){if(e.config.showMathMenu){if(!f){f=window.event}if(e.settings.context==="MathJax"){if(!e.noContextMenuBug||f.button!==2){return}}else{if(!f[e.MENUKEY]||f.button!==e.LEFTBUTTON){return}}return e.ContextMenu.call(this,f,true)}},Mouseover:function(f){e.HandleEvent(f,"Mouseover",this)},Click:function(f){e.HandleEvent(f,"Click",this)},DblClick:function(f){e.HandleEvent(f,"DblClick",this)},HandleEvent:function(h,f,g){},initImg:function(f){},initHTML:function(g,f){},initFont:function(f){var h=e.FONTDATA.FONTS,g=e.config.availableFonts;if(g&&g.length&&e.Font.testFont(h[f])){h[f].available=true;return null}if(!this.allowWebFonts){return null}h[f].isWebFont=true;if(e.FontFaceBug){h[f].family=f;if(e.msieFontCSSBug){h[f].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(f)})},Remove:function(f){var g=f.SourceElement();if(!g){return}g=g.previousSibling;if(!g){return}if(g.className.match(/^MathJax/)){g.parentNode.removeChild(g)}},getScales:function(h){h.parentNode.insertBefore(this.HDMspan,h);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var g=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var f=this.outerEm=this.HDMspan.offsetWidth/60;this.scale=Math.floor(Math.max(this.config.minScaleAdjust/100,(g/this.TeX.x_height)/f)*this.config.scale);h.style.fontSize=this.HDMspan.style.fontSize=this.scale+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&f===this.em&&this.scale!==100){this.em=a.mbase.prototype.em=f*this.scale/100}h.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(h)},getMarginScale:function(f){return 1},getMSIEmarginScale:function(h){h.appendChild(this.marginCheck);var f=this.marginCheck.offsetWidth,g=this.marginMove.offsetWidth;var i=g/(2*g-f);h.removeChild(this.marginCheck);return i},getHD:function(g){var f=g.style.position;g.style.position="absolute";this.HDimg.style.height="0px";g.appendChild(this.HDspan);var h={h:g.offsetHeight};this.HDimg.style.height=h.h+"px";h.d=g.offsetHeight-h.h;h.h-=h.d;h.h/=this.em;h.d/=this.em;g.removeChild(this.HDspan);g.style.position=f;return h},getW:function(i){var g=i.offsetWidth,h=(i.bbox?i.bbox.w:-1),j=i;if((h<0||this.negativeSkipBug)&&g>=0){if(this.negativeSkipBug){var f=i.style.position;i.style.position="absolute";j=this.startMarker;if(i.firstChild){i.insertBefore(j,i.firstChild)}else{i.appendChild(j)}j=this.startMarker}i.appendChild(this.endMarker);g=this.endMarker.offsetLeft-j.offsetLeft;i.removeChild(this.endMarker);if(this.negativeSkipBug){i.removeChild(j);i.style.position=f}}return g/this.em},Measured:function(h,g){if(h.bbox.width==null&&h.bbox.w&&!h.bbox.isMultiline){var f=this.getW(h);h.bbox.rw+=f-h.bbox.w;h.bbox.w=f}if(!g){g=h.parentNode}if(!g.bbox){g.bbox=h.bbox}return h},Remeasured:function(g,f){f.bbox=this.Measured(g,f).bbox},Em:function(f){if(Math.abs(f)<0.0006){return"0em"}return f.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(f){return(100*f).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(f){return this.Percent(this.length2em(f))},length2em:function(k,i){if(typeof(k)!=="string"){k=k.toString()}if(k===""){return""}if(k===a.SIZE.NORMAL){return 1}if(k===a.SIZE.BIG){return 2}if(k===a.SIZE.SMALL){return 0.71}if(k==="infinity"){return e.BIGDIMEN}var h=this.FONTDATA.TeX_factor;if(k.match(/mathspace$/)){return e.MATHSPACE[k]*h}var g=k.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var f=parseFloat(g[1]||"1"),j=g[2];if(i==null){i=1}if(j==="em"){return f*h}if(j==="ex"){return f*e.TeX.x_height*h}if(j==="%"){return f/100*i}if(j==="px"){return f/e.em}if(j==="pt"){return f/10*h}if(j==="pc"){return f*1.2*h}if(j==="in"){return f*this.pxPerInch/e.em}if(j==="cm"){return f*this.pxPerInch/e.em/2.54}if(j==="mm"){return f*this.pxPerInch/e.em/25.4}if(j==="mu"){return f/18*h}return f*h*i},thickness2em:function(f){var g=e.TeX.rule_thickness;if(f===a.LINETHICKNESS.MEDIUM){return g}if(f===a.LINETHICKNESS.THIN){return 0.67*g}if(f===a.LINETHICKNESS.THICK){return 1.67*g}return this.length2em(f,g)},createStrut:function(i,g,j){var f=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:g+"px",width:"1px",marginRight:"-1px"}});if(j){i.insertBefore(f,i.firstChild)}else{i.appendChild(f)}return f},createBlank:function(g,f,h){var i=this.Element("span",{style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(f)}});if(h){g.insertBefore(i,g.firstChild)}else{g.appendChild(i)}return i},createShift:function(g,f,i){var h=this.Element("span",{style:{marginLeft:this.Em(f)}});if(i){g.insertBefore(h,g.firstChild)}else{g.appendChild(h)}return h},createSpace:function(k,j,m,f,g){var i=this.Em(Math.max(0,j+m)),l=this.Em(-m);if(this.msieInlineBlockAlignBug){l=this.Em(e.getHD(k.parentNode).d-m)}if(k.isBox||k.className=="mspace"){k.bbox={h:j*k.scale,d:m*k.scale,w:f*k.scale,rw:f*k.scale,lw:0};k.style.height=i;k.style.verticalAlign=l}else{k=this.addElement(k,"span",{style:{height:i,verticalAlign:l}})}if(f>=0){k.style.width=this.Em(f);k.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){k.style.height=""}k.style.marginLeft=this.Em(f);if(e.safariNegativeSpaceBug&&k.parentNode.firstChild==k){this.createBlank(k,0,true)}}if(g&&g!==a.COLOR.TRANSPARENT){k.style.backgroundColor=g}return k},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em<j){p=j/this.em}if(k+m>0&&(k+m)*this.em<j){var l=1/(k+m)*(j/this.em);k*=l;m*=l}if(!i){i="solid"}else{i="solid "+i}i=this.Em(p)+" "+i;var q=this.Em(k+m),g=this.Em(-m);var n=this.addElement(o,"span",{style:{borderLeft:i,display:"inline-block",overflow:"hidden",width:0,height:q,verticalAlign:g},bbox:{h:k,d:m,w:p,rw:p,lw:0},noAdjust:true});if(p>0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(o,m,n,p,r,g){var l=(this.msieBorderWidthBug?0:2*r);var q=this.Em(m+n-l),f=this.Em(-n-r),k=this.Em(p-l);var i=this.Em(r)+" "+g;var j=this.addElement(o,"span",{style:{border:i,display:"inline-block",overflow:"hidden",width:k,height:q},bbox:{h:m,d:n,w:p,rw:p,lw:0},noAdjust:true});if(f){j.style.verticalAlign=f}return j},createStack:function(h,j,g){if(this.msiePaddingWidthBug){this.createStrut(h,0)}var i=String(g).match(/%$/);var f=(!i&&g!=null?g:0);h=this.addElement(h,"span",{noAdjust:true,style:{display:"inline-block",position:"relative",width:(i?"100%":this.Em(f)),height:0}});if(!j){h.parentNode.bbox=h.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:(!i&&g!=null?g:-this.BIGDIMEN)};if(i){h.bbox.width=g}}return h},createBox:function(g,f){var h=this.addElement(g,"span",{style:{position:"absolute"},isBox:true});if(f!=null){h.style.width=f}return h},addBox:function(f,g){g.style.position="absolute";g.isBox=true;return f.appendChild(g)},placeBox:function(n,m,k,i){var o=n.parentNode,v=n.bbox,q=o.bbox;if(this.msiePlaceBoxBug){this.addText(n,this.NBSP)}if(this.imgSpaceBug){this.addText(n,this.imgSpace)}var p=n.offsetHeight/this.em+1,z=0;if(n.noAdjust){p-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(n,"img",{className:"MathJax_strut",border:0,src:"about:blank",style:{width:0,height:this.Em(p)}})}else{this.addElement(n,"span",{style:{display:"inline-block",width:0,height:this.Em(p)}})}}n.style.top=this.Em(-k-p);n.style.left=this.Em(m+z);if(v){if(this.negativeSkipBug){if(v.lw<0){z=v.lw;e.createBlank(n,-z,true);h=0}if(v.rw>v.w){e.createBlank(n,v.rw-v.w+0.1)}}if(!this.msieClipRectBug&&!v.noclip&&!i){var u=3/this.em;var s=(v.H==null?v.h:v.H),g=(v.D==null?v.d:v.D);var w=p-s-u,j=p+g+u,h=v.lw-3*u,f=1000;if(v.isFixed){f=v.width-h}n.style.clip="rect("+this.Em(w)+" "+this.Em(f)+" "+this.Em(j)+" "+this.Em(h)+")"}}if(v&&q){if(v.H!=null&&(q.H==null||v.H+k>q.H)){q.H=v.H+k}if(v.D!=null&&(q.D==null||v.D-k>q.D)){q.D=v.D-k}if(v.h+k>q.h){q.h=v.h+k}if(v.d-k>q.d){q.d=v.d-k}if(q.H!=null&&q.H<=q.h){delete q.H}if(q.D!=null&&q.D<=q.d){delete q.D}if(v.w+m>q.w){q.w=v.w+m;if(q.width==null){o.style.width=this.Em(q.w)}}if(v.rw+m>q.rw){q.rw=v.rw+m}if(v.lw+m<q.lw){q.lw=v.lw+m}if(v.width!=null&&!v.isFixed){if(q.width==null){o.style.width=q.width="100%"}n.style.width=v.width}}},alignBox:function(h,n,m){this.placeBox(h,0,m);var j=h.bbox;if(j.isMultiline){return}var g=j.width!=null&&!j.isFixed;var i=0,k=-j.w/2,f="50%";if(this.negativeSkipBug){i=j.w-j.rw-0.1;k+=j.lw}k=this.Em(k*this.msieMarginScale);if(g){k="";f=(50-parseFloat(j.width)/2)+"%"}d.Insert(h.style,({right:{left:"",right:this.Em(i)},center:{left:f,marginLeft:k}})[n])},setStackWidth:function(g,f){if(typeof(f)==="number"){g.style.width=this.Em(Math.max(0,f));if(g.bbox){g.bbox.w=f}if(g.parentNode.bbox){g.parentNode.bbox.w=f}}else{g.style.width=g.parentNode.style.width="100%";if(g.bbox){g.bbox.width=f}if(g.parentNode.bbox){g.parentNode.bbox.width=f}}},createDelimiter:function(q,f,h,l,j){if(!f){q.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};q.bbox.rw=q.bbox.w;this.createSpace(q,q.bbox.h,q.bbox.d,q.bbox.w);return}if(!l){l=1}if(!(h instanceof Array)){h=[h,h]}var p=h[1];h=h[0];var g={alias:f};while(g.alias){f=g.alias;g=this.FONTDATA.DELIMITERS[f];if(!g){g={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}for(var o=0,k=g.HW.length;o<k;o++){if(g.HW[o][0]*l>=h-0.01||(o==k-1&&!g.stretch)){if(g.HW[o][2]){l*=g.HW[o][2]}if(g.HW[o][3]){f=g.HW[o][3]}var n=this.addElement(q,"span");this.createChar(n,[f,g.HW[o][1]],l,j);q.bbox=n.bbox;q.offset=0.65*q.bbox.w;q.scale=l;return}}if(g.stretch){this["extendDelimiter"+g.dir](q,p,g.stretch,l,j)}},extendDelimiterV:function(v,p,A,B,s){var i=this.createStack(v,true);var r=this.createBox(i),q=this.createBox(i);this.createChar(r,(A.top||A.ext),B,s);this.createChar(q,(A.bot||A.ext),B,s);var g={bbox:{w:0,lw:0,rw:0}},z=g,j;var w=r.bbox.h+r.bbox.d+q.bbox.h+q.bbox.d;var m=-r.bbox.h;this.placeBox(r,0,m,true);m-=r.bbox.d;if(A.mid){z=this.createBox(i);this.createChar(z,A.mid,B,s);w+=z.bbox.h+z.bbox.d}if(p>w){g=this.Element("span");this.createChar(g,A.ext,B,s);var x=g.bbox.h+g.bbox.d,f=x-0.05,t,l,u=(A.mid?2:1);l=t=Math.ceil((p-w)/(u*f));if(!A.fullExtenders){f=(p-w)/(u*t)}var o=(t/(t+1))*(x-f);f=x-o;m+=o+f-g.bbox.h;while(u-->0){while(t-->0){if(!this.msieCloneNodeBug){j=g.cloneNode(true)}else{j=this.Element("span");this.createChar(j,A.ext,B,s)}m-=f;this.placeBox(this.addBox(i,j),0,m,true)}m+=o-g.bbox.d;if(A.mid&&u){this.placeBox(z,0,m-z.bbox.h,true);t=l;m+=-(z.bbox.h+z.bbox.d)+o+f-g.bbox.h}}}else{m+=(w-p)/2;if(A.mid){this.placeBox(z,0,m-z.bbox.h,true);m+=-(z.bbox.h+z.bbox.d)}m+=(w-p)/2}this.placeBox(q,0,m-q.bbox.h,true);m-=q.bbox.h+q.bbox.d;v.bbox={w:Math.max(r.bbox.w,g.bbox.w,q.bbox.w,z.bbox.w),lw:Math.min(r.bbox.lw,g.bbox.lw,q.bbox.lw,z.bbox.lw),rw:Math.max(r.bbox.rw,g.bbox.rw,q.bbox.rw,z.bbox.rw),h:0,d:-m};v.scale=B;v.offset=0.55*v.bbox.w;v.isMultiChar=true;this.setStackWidth(i,v.bbox.w)},extendDelimiterH:function(u,h,z,B,r){var l=this.createStack(u,true);var i=this.createBox(l),v=this.createBox(l);this.createChar(i,(z.left||z.rep),B,r);this.createChar(v,(z.right||z.rep),B,r);var f=this.Element("span");this.createChar(f,z.rep,B,r);var y={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},g;this.placeBox(i,-i.bbox.lw,0,true);var p=(i.bbox.rw-i.bbox.lw)+(v.bbox.rw-v.bbox.lw)-0.05,o=i.bbox.rw-i.bbox.lw-0.025,q;if(z.mid){y=this.createBox(l);this.createChar(y,z.mid,B,r);p+=y.bbox.w}if(h>p){var A=f.bbox.rw-f.bbox.lw,j=A-0.05,s,m,t=(z.mid?2:1);m=s=Math.ceil((h-p)/(t*j));j=(h-p)/(t*s);q=(s/(s+1))*(A-j);j=A-q;o-=f.bbox.lw+q;while(t-->0){while(s-->0){if(!this.msieCloneNodeBug){g=f.cloneNode(true)}else{g=this.Element("span");this.createChar(g,z.rep,B,r)}this.placeBox(this.addBox(l,g),o,0,true);o+=j}if(z.mid&&t){this.placeBox(y,o,0,true);o+=y.bbox.w-q;s=m}}}else{q=Math.min(p-h,i.bbox.w/2);o-=q/2;if(z.mid){this.placeBox(y,o,0,true);o+=y.bbox.w}o-=q/2}this.placeBox(v,o,0,true);u.bbox={w:o+v.bbox.rw,lw:0,rw:o+v.bbox.rw,H:Math.max(i.bbox.h,f.bbox.h,v.bbox.h,y.bbox.h),D:Math.max(i.bbox.d,f.bbox.d,v.bbox.d,y.bbox.d),h:f.bbox.h,d:f.bbox.d};u.scale=B;u.isMultiChar=true;this.setStackWidth(l,u.bbox.w)},createChar:function(o,k,h,f){var n=o,p="",j={fonts:[k[1]],noRemap:true};if(f&&f===a.VARIANT.BOLD){j.fonts=[k[1]+"-bold",k[1]]}if(typeof(k[1])!=="string"){j=k[1]}if(k[0] instanceof Array){for(var l=0,g=k[0].length;l<g;l++){p+=String.fromCharCode(k[0][l])}}else{p=String.fromCharCode(k[0])}if(h!==1){n=this.addElement(o,"span",{style:{fontSize:this.Percent(h)},scale:h});this.handleVariant(n,j,p);o.bbox=n.bbox}else{this.handleVariant(o,j,p)}if(k[2]){o.style.marginLeft=this.Em(k[2])}if(this.AccentBug&&o.bbox.w===0){n.firstChild.nodeValue+=this.NBSP;e.createSpace(o,0,0,-o.offsetWidth/e.em)}},positionDelimiter:function(g,f){f-=g.bbox.h;g.bbox.d-=f;g.bbox.h+=f;if(f){if(this.safariVerticalAlignBug||this.msieVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&g.isMultiChar)){if(g.firstChild.style.display===""&&g.style.top!==""){g=g.firstChild;f-=parseFloat(g.style.top)}g.style.position="relative";g.style.top=this.Em(-f)}else{g.style.verticalAlign=this.Em(f);if(e.ffVerticalAlignBug){e.createRule(g.parentNode,g.bbox.h,0,0)}}}},handleVariant:function(v,j,o){var u="",s,y,p,g,x,z,f=v;if(o.length===0){return}if(!v.bbox){v.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!j){j=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}z=j;for(var w=0,t=o.length;w<t;w++){j=z;s=o.charCodeAt(w);y=o.charAt(w);if(y===this.PLANE1){w++;s=o.charCodeAt(w)+119808-56320;if(this.FONTDATA.RemapPlane1){var A=this.FONTDATA.RemapPlane1(s,j);s=A.n;j=A.variant}}else{var q,l,r=this.FONTDATA.RANGES;for(q=0,l=r.length;q<l;q++){if(r[q].name==="alpha"&&j.noLowerCase){continue}var k=j["offset"+r[q].offset];if(k&&s>=r[q].low&&s<=r[q].high){if(r[q].remap&&r[q].remap[s]){s=k+r[q].remap[s]}else{s=s-r[q].low+k;if(r[q].add){s+=r[q].add}}if(j["variant"+r[q].offset]){j=this.FONTDATA.VARIANT[j["variant"+r[q].offset]]}break}}}if(j.remap&&j.remap[s]){if(j.remap[s] instanceof Array){var h=j.remap[s];s=h[0];j=this.FONTDATA.VARIANT[h[1]]}else{s=j.remap[s];if(j.remap.variant){j=this.FONTDATA.VARIANT[j.remap.variant]}}}if(this.FONTDATA.REMAP[s]&&!j.noRemap){s=this.FONTDATA.REMAP[s]}p=this.lookupChar(j,s);y=p[s];if(j!==x&&!y[5].img){if(u.length){this.addText(f,u);u=""}f=v;x=g;if(j!==x){if(x){f=this.addElement(v,"span")}else{g=j}}this.handleFont(f,p,f!==v);x=j}u=this.handleChar(f,p,y,s,u);if(y[0]/1000>v.bbox.h){v.bbox.h=y[0]/1000}if(y[1]/1000>v.bbox.d){v.bbox.d=y[1]/1000}if(v.bbox.w+y[3]/1000<v.bbox.lw){v.bbox.lw=v.bbox.w+y[3]/1000}if(v.bbox.w+y[4]/1000>v.bbox.rw){v.bbox.rw=v.bbox.w+y[4]/1000}v.bbox.w+=y[2]/1000}if(u.length){this.addText(f,u)}if(v.scale&&v.scale!==1){v.bbox.h*=v.scale;v.bbox.d*=v.scale;v.bbox.w*=v.scale;v.bbox.lw*=v.scale;v.bbox.rw*=v.scale}if(o.length==1&&p.skew&&p.skew[s]){v.bbox.skew=p.skew[s]}},handleFont:function(h,f,j){h.style.fontFamily=f.family;if(!(e.FontFaceBug&&f.isWebFont)){var g=f.style||"normal",i=f.weight||"normal";if(g!=="normal"||j){h.style.fontStyle=g}if(i!=="normal"||j){h.style.fontWeight=i}}},handleChar:function(g,f,l,k,j){var i=l[5];if(i.img){return this.handleImg(g,f,l,k,j)}if(i.isUnknown&&this.FONTDATA.DELIMITERS[k]){var h=g.scale;e.createDelimiter(g,k,0,1,f);g.scale=h;l[0]=g.bbox.h*1000;l[1]=g.bbox.d*1000;l[2]=g.bbox.w*1000;l[3]=g.bbox.lw*1000;l[4]=g.bbox.rw*1000;return""}if(i.c==null){if(k<=65535){i.c=String.fromCharCode(k)}else{i.c=this.PLANE1+String.fromCharCode(k-119808+56320)}}if(l[2]||!this.msieAccentBug||j.length){return j+i.c}e.createShift(g,l[3]/1000);e.createShift(g,(l[4]-l[3])/1000);this.addText(g,i.c);e.createShift(g,-l[4]/1000);return""},handleImg:function(g,f,j,i,h){return h},lookupChar:function(j,p){var h,f;if(!j.FONTS){var o=this.FONTDATA.FONTS;var l=(j.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(l instanceof Array)){l=[l]}if(j.fonts!=l){j.fonts=l}j.FONTS=[];for(h=0,f=l.length;h<f;h++){if(o[l[h]]){j.FONTS.push(o[l[h]]);o[l[h]].name=l[h]}}}for(h=0,f=j.FONTS.length;h<f;h++){var g=j.FONTS[h];if(typeof(g)==="string"){delete j.FONTS;this.loadFont(g)}if(g[p]){if(g[p].length===5){g[p][5]={}}if(e.allowWebFonts&&!g.available){this.loadWebFont(g)}else{return g}}else{this.findBlock(g,p)}}var k=(j.defaultFont||{family:e.config.undefinedFamily});if(j.bold){k.weight="bold"}if(j.italic){k.style="italic"}k[p]=[800,200,500,0,500,{isUnknown:true}];return k},findBlock:function(g,n){if(g.Ranges){for(var l=0,f=g.Ranges.length;l<f;l++){if(n<g.Ranges[l][0]){return}if(n<=g.Ranges[l][1]){var k=g.Ranges[l][2];for(var h=g.Ranges.length-1;h>=0;h--){if(g.Ranges[h][2]==k){g.Ranges.splice(h,1)}}this.loadFont(g.directory+"/"+k+".js")}}}},loadFont:function(g){var f=MathJax.Callback.Queue();f.Push(["Require",c,this.fontDir+"/"+g]);if(this.imgFonts){if(!MathJax.isPacked){g=g.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}f.Push(["Require",c,this.webfontDir+"/png/"+g])}d.RestartAfter(f.Push({}))},loadWebFont:function(f){f.available=f.isWebFont=true;if(e.FontFaceBug){f.family=f.name;if(e.msieFontCSSBug){f.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(f))},loadWebFontError:function(g,f){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");g.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts 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g=k.bbox={},l=[];this.HTMLcheckStretchy(this.data.open,g,l,j);this.HTMLcheckStretchy(this.data[0],g,l,j);for(var h=1,f=this.data.length;h<f;h++){if(this.data[h]){this.HTMLcheckStretchy(this.data["sep"+h],g,l,j);this.HTMLcheckStretchy(this.data[h],g,l,j)}}this.HTMLcheckStretchy(this.data.close,g,l,j);this.HTMLcleanBBox(g);return l},HTMLcheckStretchy:function(f,g,i,h){if(f){if(!h&&f.HTMLcanStretch("Vertical")){i.push(f);f=(f.CoreMO()||f)}this.HTMLcombineBBoxes(f,g)}}});a.menclose.Augment({toHTML:a.mbase.HTMLautoload});a.maction.Augment({toHTML:a.mbase.HTMLautoload});a.semantics.Augment({toHTML:function(f){if(this.data[0]!=null){f=this.data[0].toHTML(f);this.spanID=this.data[0].spanID;this.HTMLhandleSpace(f)}return f},HTMLspanElement:function(){return(this.data[0]!=null?this.data[0].HTMLspanElement():null)},HTMLstretchH:function(g,f){return(this.data[0]!=null?this.data[0].HTMLstretchH(g,f):g)},HTMLstretchV:function(g,f,i){return(this.data[0]!=null?this.data[0].HTMLstretchV(g,f,i):g)}});a.munderover.Augment({toHTML:function(G,B,z){var f=this.getValues("displaystyle","accent","accentunder","align");if(!f.displaystyle&&this.data[this.base]!=null&&this.data[this.base].Get("movablelimits")){return a.msubsup.prototype.toHTML.call(this,G)}G=this.HTMLcreateSpan(G);var K=this.HTMLgetScale();var j=e.createStack(G);var l=[],I=[],q,H,C,g=-e.BIGDIMEN,F=g;for(H=0,C=this.data.length;H<C;H++){if(this.data[H]!=null){q=l[H]=e.createBox(j);e.Measured(this.data[H].toHTML(q),q);if(H==this.base){if(z!=null){e.Remeasured(this.data[this.base].HTMLstretchV(q,B,z),q)}else{if(B!=null){e.Remeasured(this.data[this.base].HTMLstretchH(q,B),q)}}I[H]=(z==null&&B!=null?false:this.data[H].HTMLcanStretch("Horizontal"))}else{I[H]=this.data[H].HTMLcanStretch("Horizontal")}if(q.bbox.w>F){F=q.bbox.w}if(!I[H]&&F>g){g=F}}}if(z==null&&B!=null){g=B}else{if(g==-e.BIGDIMEN){g=F}}for(H=F=0,C=this.data.length;H<C;H++){if(this.data[H]){q=l[H];if(I[H]){q.bbox=this.data[H].HTMLstretchH(q,g).bbox}if(q.bbox.w>F){F=q.bbox.w}}}var w=e.TeX.rule_thickness,A=e.FONTDATA.TeX_factor;var h=l[this.base]||{bbox:this.HTMLzeroBBox()},J=(h.bbox.ic||0);var p,n,s,r,o,v,E;for(H=0,C=this.data.length;H<C;H++){if(this.data[H]!=null){q=l[H];o=e.TeX.big_op_spacing5*K;var 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G=this.HTMLgetScale();var j=e.createStack(C),g;var i=e.createBox(j);this.HTMLmeasureChild(this.base,i);if(this.data[this.base]){if(w!=null){e.Remeasured(this.data[this.base].HTMLstretchV(i,A,w),i)}else{if(A!=null){e.Remeasured(this.data[this.base].HTMLstretchH(i,A),i)}}}e.placeBox(i,0,0);var h=(this.data[this.sup]||this.data[this.sub]||this).HTMLgetScale();var E=e.TeX.x_height*G,o=e.TeX.scriptspace*G*0.75;var f,k;if(this.HTMLnotEmpty(this.data[this.sup])){f=e.createBox(j);e.Measured(this.data[this.sup].toHTML(f),f);f.bbox.w+=o;f.bbox.rw=Math.max(f.bbox.w,f.bbox.rw)}if(this.HTMLnotEmpty(this.data[this.sub])){k=e.createBox(j);e.Measured(this.data[this.sub].toHTML(k),k);k.bbox.w+=o;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}var y=e.TeX.sup_drop*h,x=e.TeX.sub_drop*h;var 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n=e.TeX.rule_thickness*G;if((m-f.bbox.d)-(k.bbox.h-l)<3*n){l=3*n-m+f.bbox.d+k.bbox.h;y=(4/5)*E-(m-f.bbox.d);if(y>0){m+=y;l-=y}}e.placeBox(f,i.bbox.w+o,Math.max(m,B.superscriptshift));e.placeBox(k,i.bbox.w+o-F,-Math.max(l,B.subscriptshift))}}this.HTMLhandleSpace(C);this.HTMLhandleColor(C);return C},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload});a.mtable.Augment({toHTML:a.mbase.HTMLautoload});a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload});a.math.Augment({toHTML:function(n,g){var k=this.Get("alttext");if(k){g.setAttribute("aria-label",k)}var h=e.addElement(n,"nobr");n=this.HTMLcreateSpan(h);var l=e.createStack(n),i=e.createBox(l),m;l.style.fontSize=h.parentNode.style.fontSize;h.parentNode.style.fontSize="";if(this.data[0]!=null){if(e.msieColorBug){if(this.background){this.data[0].background=this.background;delete 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o=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(o.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){o.indentalign=o.indentalignfirst}if(o.indentalign===a.INDENTALIGN.AUTO){o.indentalign=this.displayAlign}g.style.textAlign=o.indentalign;if(o.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){o.indentshift=o.indentshiftfirst}if(o.indentshift==="auto"){o.indentshift=this.displayIndent}if(o.indentshift&&o.indentalign!==a.INDENTALIGN.CENTER){n.style[{left:"marginLeft",right:"marginRight"}[o.indentalign]]=e.Em(e.length2em(o.indentshift))}}return n}});a.TeXAtom.Augment({toHTML:function(g){g=this.HTMLcreateSpan(g);if(this.data[0]!=null){if(this.texClass===a.TEXCLASS.VCENTER){var f=e.createStack(g);var h=e.createBox(f);e.Measured(this.data[0].toHTML(h),h);e.placeBox(h,0,e.TeX.axis_height-(h.bbox.h+h.bbox.d)/2+h.bbox.d)}else{g.bbox=this.data[0].toHTML(g).bbox}}this.HTMLhandleSpace(g);this.HTMLhandleColor(g);return 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g=j.versionAtLeast("3.1");j.isMobile=(navigator.appVersion.match(/Mobile/i)!=null);var f=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var k=(g&&j.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!j.versionAtLeast("5.0"))||(f!=null&&(f[1]<2||(f[1]==2&&f[2]<2)))));e.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},useProcessingFrame:true,rfuzz:0.011,AccentBug:true,AdjustSurd:true,safariContextMenuBug:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!g,safariTextNodeBug:!h,safariWebFontSerif:["serif"],allowWebFonts:(g&&!k?"otf":false)});if(k){var i=d.config["HTML-CSS"];if(i){i.availableFonts=[];i.preferredFont=null}else{d.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(f){e.Augment({useProcessingFrame:true,rfuzz:0.011,AccentBug:true,AdjustSurd:true,allowWebFonts:(f.versionAtLeast("4.0")?"otf":"svg"),safariNegativeSpaceBug:true,safariWebFontSerif:[""]})},Opera:function(f){f.isMini=(navigator.appVersion.match("Opera Mini")!=null);e.config.styles[".MathJax .merror"]["vertical-align"]=null;e.Augment({useProcessingFrame:true,operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:f.versionAtLeast("10.61"),negativeSkipBug:true,zeroWidthBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(f.versionAtLeast("10.0")&&!f.isMini?"otf":false),adjustAvailableFonts:function(j){for(var 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MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="1.1";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a.mtable.Augment({toHTML:function(X){X=this.HTMLcreateSpan(X);if(this.data.length===0){return X}var aJ=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");var r=aJ.width.match(/%$/);var ag=b.createStack(X);var am=this.HTMLgetScale();var aH=-1;var w=[],I=[],l=[],O=[],K=[],aF,aE,v=-1,aC,t,ay,R;var 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/),au=[];for(aF=0,aC=al.length;aF<aC;aF++){al[aF]=b.length2em(al[aF])}for(aF=0,aC=S.length;aF<aC;aF++){S[aF]=b.length2em(S[aF])}while(al.length<v){al.push(al[al.length-1])}while(ah.length<=v){ah.push(ah[ah.length-1])}while(N.length<v){N.push(N[N.length-1])}while(ap.length<=v){ap.push(ap[ap.length-1])}while(S.length<O.length){S.push(S[S.length-1])}while(L.length<=O.length){L.push(L[L.length-1])}while(k.length<O.length){k.push(k[k.length-1])}if(K[aH]){ah[aH]=(aJ.side.substr(0,1)==="l"?"left":"right");al[aH]=-l[aH]}for(aF=0,aC=O.length;aF<aC;aF++){R=this.data[aF];au[aF]=[];if(R.rowalign){L[aF]=R.rowalign}if(R.columnalign){au[aF]=R.columnalign.split(/ /);while(au[aF].length<=v){au[aF].push(au[aF][au[aF].length-1])}}}var az=w[0]+I[O.length-1];for(aF=0,aC=O.length-1;aF<aC;aF++){az+=Math.max((w[aF]+I[aF]?aL:0),I[aF]+w[aF+1]+S[aF])}var ac=0,aa=0,aA,aI=az;if(aJ.frame!=="none"||(aJ.columnlines+aJ.rowlines).match(/solid|dashed/)){ac=b.length2em(aJ.framespacing.split(/[, 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aq,aw=0,U=0,V=0,aB=0,aG=0,o=[],B=[],ai=1;if(aJ.equalcolumns&&aJ.width!=="auto"){if(r){aq=(100/(v+1)).toFixed(2).replace(/\.?0+$/,"")+"%";for(aF=0,aC=Math.min(v+1,ap.length);aF<aC;aF++){ap[aF]=aq}aq=0;aw=1;aG=v+1;for(aF=0,aC=Math.min(v+1,al.length);aF<aC;aF++){aq+=al[aF]}}else{aq=b.length2em(aJ.width);for(aF=0,aC=Math.min(v+1,al.length);aF<aC;aF++){aq-=al[aF]}aq/=v+1;for(aF=0,aC=Math.min(v+1,ap.length);aF<aC;aF++){l[aF]=aq}}}else{for(aF=0,aC=Math.min(v+1,ap.length);aF<aC;aF++){if(ap[aF]==="auto"){U+=l[aF]}else{if(ap[aF]==="fit"){B[aG]=aF;aG++;U+=l[aF]}else{if(ap[aF].match(/%$/)){o[aB]=aF;aB++;V+=l[aF];aw+=b.length2em(ap[aF],1)}else{l[aF]=b.length2em(ap[aF]);U+=l[aF]}}}}if(r){aq=0;for(aF=0,aC=Math.min(v,al.length);aF<aC;aF++){aq+=al[aF]}if(aw>0.98){ai=0.98/aw;aw=0.98}}else{if(aJ.width==="auto"){if(aw>0.98){ai=V/(U+V);aq=U+V}else{aq=U/(1-aw)}}else{aq=b.length2em(aJ.width);for(aF=0,aC=Math.min(v+1,al.length);aF<aC;aF++){aq-=al[aF]}}for(aF=0,aC=o.length;aF<aC;aF++){l[o[aF]]=b.length2em(ap[o[aF]],aq*ai);U+=l[o[aF]]}if(Math.abs(aq-U)>0.01){if(aG&&aq>U){aq=(aq-U)/aG;for(aF=0,aC=B.length;aF<aC;aF++){l[B[aF]]+=aq}}else{aq=aq/U;for(aE=0;aE<=v;aE++){l[aE]*=aq}}}if(aJ.equalcolumns){var ad=Math.max.apply(Math,l);for(aE=0;aE<=v;aE++){l[aE]=ad}}}}if(aJ.equalrows){var T=Math.max.apply(Math,w),ao=Math.max.apply(Math,I);for(aF=0,aC=O.length;aF<aC;aF++){ay=((T+ao)-(w[aF]+I[aF]))/2;w[aF]+=ay;I[aF]+=ay}}var ar=h,n,u,aD;ay=(K[aH]?aH:0);for(aE=ay;aE<=v;aE++){for(aF=0,aC=O.length;aF<aC;aF++){if(O[aF][aE]){ay=(this.data[aF].type==="mlabeledtr"?aH:0);var ak=this.data[aF].data[aE-ay];if(ak.HTMLcanStretch("Horizontal")){O[aF][aE].bbox=ak.HTMLstretchH(K[aE],l[aE]).bbox}else{if(ak.HTMLcanStretch("Vertical")){var z=ak.CoreMO();var ab=z.symmetric;z.symmetric=false;O[aF][aE].bbox=ak.HTMLstretchV(K[aE],w[aF],I[aF]).bbox;z.symmetric=ab}}aD=ak.rowalign||this.data[aF].rowalign||L[aF];n=({top:w[aF]-O[aF][aE].bbox.h,bottom:O[aF][aE].bbox.d-I[aF],center:((w[aF]-I[aF])-(O[aF][aE].bbox.h-O[aF][aE].bbox.d))/2,baseline:0,axis:0})[aD];aD=(ak.columnalign||au[aF][aE]||ah[aE]);b.alignBox(O[aF][aE],aD,ar+n)}if(aF<O.length-1){ar-=Math.max((w[aF]+I[aF]?aL:0),I[aF]+w[aF+1]+S[aF])}}ar=h}if(r){var 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E=b.createStack(X,false,"100%");b.addBox(E,ag);b.alignBox(ag,Q.indentalign,0);if(Q.indentshift&&Q.indentalign!==a.INDENTALIGN.CENTER){ag.style[{left:"Left",right:"Right"}[Q.indentalign]]=b.Em(b.length2em(Q.indentshift))}K[aH].parentNode.parentNode.removeChild(K[aH].parentNode);b.addBox(E,K[aH]);b.alignBox(K[aH],ah[aH],0);if(b.msieRelativeWidthBug){ag.style.top=K[aH].style.top=""}if(r){ag.style.width=aJ.width;X.bbox.width="100%"}K[aH].style.marginRight=K[aH].style.marginLeft=b.Em(b.length2em(aJ.minlabelspacing))}if(!r){this.HTMLhandleSpace(X)}var aj=this.HTMLhandleColor(X);if(aj&&r){if(!d){d=b.createFrame(ag,aI,0,aA,0,"none");b.addBox(ag,d);b.placeBox(d,0,ax,true);d.style.width="100%"}d.style.backgroundColor=aj.style.backgroundColor;d.parentNode.insertBefore(d,d.parentNode.firstChild);aj.parentNode.removeChild(aj)}return X},HTMLhandleSpace:function(d){d.style.paddingLeft=d.style.paddingRight=".1667em"}});a.mtd.Augment({toHTML:function(e,d,g){e=this.HTMLcreateSpan(e);if(this.data[0]){var f=b.Measured(this.data[0].toHTML(e),e);if(g!=null){b.Remeasured(this.data[0].HTMLstretchV(e,d,g),e)}else{if(d!=null){b.Remeasured(this.data[0].HTMLstretchH(e,d),e)}}e.bbox=f.bbox}this.HTMLhandleSpace(e);this.HTMLhandleColor(e);return e},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});MathJax.Hub.Startup.signal.Post("HTML-CSS mtable Ready");MathJax.Ajax.loadComplete(b.autoloadDir+"/mtable.js")});

MathJax.Extension.wiki2jax = {
  version: "1.0",

  config: {
    element: null,    // The ID of the element to be processed
                      //   (defaults to full document)

    preview: "TeX"    // Set to "none" to prevent preview strings from being inserted
                      //   or to an array that specifies an HTML snippet to use for
                      //   the preview.
  },

  PreProcess: function (element) {
    if (!this.configured) {
      MathJax.Hub.Insert(this.config,(MathJax.Hub.config.wiki2jax||{}));
      if (this.config.Augment) {MathJax.Hub.Insert(this,this.config.Augment)}
      if (typeof(this.config.previewTeX) !== "undefined" && !this.config.previewTeX)
        {this.config.preview = "none"} // backward compatibility for previewTeX parameter
      this.previewClass = MathJax.Hub.config.preRemoveClass;
      this.configured = true;
    }
    var span, i;
    if ((!element || element == document.body) && mathJax.span) {  // dirty hack
      span = mathJax.span;
      i = mathJax.spanIndex;
    }
    else {
      if (typeof(element) === "string") {element = document.getElementById(element)}
      if (!element) {element = this.config.element || document.body}
      span = element.getElementsByTagName("span");
      i = span.length-1;
    }
    for (; i >= 0; i--)
      if (span[i].className === "tex") this.ConvertMath(span[i])
  },

  ConvertMath: function (node) {
    var parent = node.parentNode,
        mode = parent.tagName === "DD" && parent.firstChild === parent.lastChild ? "; mode=display" : "",
        tex = node.innerHTML.substring(node.innerHTML[0]=='$',node.innerHTML.length-(node.innerHTML[node.innerHTML.length-1]=='$'));

    tex = tex.replace(/&lt;/g,"<").replace(/&gt;/g,">").replace(/&amp;/g,"&").replace(/&nbsp;/g," ");
    tex = tex.replace(/\\iiint([^!]*)!\\!\\!\\!\\!.*\\subset\\!\\supset/g,"\\iiint$1mkern-2.5em\\subset\\!\\supset").replace(/\\iint([^!]*)!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!(.*)\\subset\\!\\supset/g,"\\iint$1mkern-1.65em$2\\subset\\!\\!\\supset").replace(/\\int\\!\\!\\!(\\!)+\\int\\!\\!\\!(\\!)+\\int([^!]*)!\\!\\!\\!\\!.*\\bigcirc(\\,)*/g,"\\iiint$3mkern-2.5em\\subset\\!\\supset").replace(/\\int\\!\\!\\!(\\!)+\\int([^!]*)!\\!\\!\\!\\!\\!\\!\\!\\!(.*)\\bigcirc(\\,)*/g,"\\iint$2mkern-1.65em$3\\subset\\!\\!\\supset");
    if (mode === "") {
      tex = tex.replace(/ *\\scriptstyle(\W)/g,"\\textstyle$1").replace(/ *\\scriptscriptstyle(\W)/g,"\\scriptstyle$1");
      if (parent.firstChild === node) tex = "\\displaystyle "+tex;
    }

    var i;
    while ((i = tex.search(/\\color{/)) != -1) {
      var braces = 0;
      for (i += 6; i < tex.length; i++) {
        if (tex[i] == '{') braces++;
        else if (tex[i] == '}') {
          if (braces-- == 0)
            break;
        }
      }
      tex = (tex.substring(0, i) + "}" + tex.substring(i, tex.length)).replace(/\\color{(\w*)}/, "\\textcolor{$1}{");
    }

    var script = document.createElement("script");
    script.type = "math/tex" + mode;
    if (MathJax.Hub.Browser.isMSIE) {script.text = tex}
      else {script.appendChild(document.createTextNode(tex))}

    if (node.nextSibling) {parent.insertBefore(script,node.nextSibling)}
      else {parent.appendChild(script)}
    if (this.config.preview !== "none") {this.createPreview(node)}
    parent.removeChild(node);
  },

  createPreview: function (node) {
    var preview;
    if (this.config.preview === "TeX") {preview = [this.filterTeX(node.innerHTML)]}
    else if (this.config.preview instanceof Array) {preview = this.config.preview}
    if (preview) {
      preview = MathJax.HTML.Element("span",{className: MathJax.Hub.config.preRemoveClass},preview);
      node.parentNode.insertBefore(preview,node);
    }
  },

  filterTeX: function (tex) {return tex}

};

MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.wiki2jax]);
MathJax.Ajax.loadComplete("[MathJax]/extensions/wiki2jax.js");

MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () {
  var VERSION = "1.0";

  var MML = MathJax.ElementJax.mml;

  MathJax.Hub.Insert(MathJax.InputJax.TeX.Definitions,{

    mathchar0mi: {
      // Lowercase Greek letters
      thetasym:     '03B8',  // theta
      koppa:        '03DF',
      stigma:       '03DB',
      coppa:        '03D9',  // archaic koppa

      // Ord symbols
      C:            ['0043',{mathvariant: MML.VARIANT.DOUBLESTRUCK}],
      cnums:        ['0043',{mathvariant: MML.VARIANT.DOUBLESTRUCK}],
      Complex:      ['0043',{mathvariant: MML.VARIANT.DOUBLESTRUCK}],
      N:            ['004E',{mathvariant: MML.VARIANT.DOUBLESTRUCK}],
      natnums:      ['004E',{mathvariant: MML.VARIANT.DOUBLESTRUCK}],
      R:            ['0052',{mathvariant: MML.VARIANT.DOUBLESTRUCK}],
      reals:        ['0052',{mathvariant: MML.VARIANT.DOUBLESTRUCK}],
      Reals:        ['0052',{mathvariant: MML.VARIANT.DOUBLESTRUCK}],
      Z:            ['005A',{mathvariant: MML.VARIANT.DOUBLESTRUCK}],
      sect:         '00A7',  // S
      P:            '00B6',
      alef:         ['2135',{mathvariant: MML.VARIANT.NORMAL}],  // aleph
      alefsym:      ['2135',{mathvariant: MML.VARIANT.NORMAL}],  // aleph
      weierp:       ['2118',{mathvariant: MML.VARIANT.NORMAL}],  // wp
      real:         ['211C',{mathvariant: MML.VARIANT.NORMAL}],  // Re
      part:         ['2202',{mathvariant: MML.VARIANT.NORMAL}],  // partial
      infin:        ['221E',{mathvariant: MML.VARIANT.NORMAL}],  // infty
      empty:        ['2205',{mathvariant: MML.VARIANT.NORMAL}],  // emptyset
      O:            ['2205',{mathvariant: MML.VARIANT.NORMAL}],  // emptyset (but should probably be Swedish O)
      ang:          ['2220',{mathvariant: MML.VARIANT.NORMAL}],  // angle
      exist:        ['2203',{mathvariant: MML.VARIANT.NORMAL}],  // exists
      clubs:        ['2663',{mathvariant: MML.VARIANT.NORMAL}],  // clubsuit
      diamonds:     ['2662',{mathvariant: MML.VARIANT.NORMAL}],  // diamondsuit
      hearts:       ['2661',{mathvariant: MML.VARIANT.NORMAL}],  // heartsuit
      spades:       ['2660',{mathvariant: MML.VARIANT.NORMAL}],  // spadesuit
      textvisiblespace: '2423'
    },

    mathchar0mo: {
      // Binary operators
      and:          '2227',  // land
      or:           '2228',  // lor
      bull:         '2219',  // bullet
      plusmn:       '00B1',  // pm
      sdot:         '22C5',  // cdot

      // Binary relations
      sup:          '2283',  // supset
      sub:          '2282',  // subset
      supe:         '2287',  // supseteq
      sube:         '2286',  // subseteq
      isin:         '2208',  // in

      hAar:               '21D4',  // Leftrightarrow [sic]
      hArr:               '21D4',  // Leftrightarrow
      Harr:               '21D4',  // Leftrightarrow
      Lrarr:              '21D4',  // Leftrightarrow
      lrArr:              '21D4',  // Leftrightarrow
      lArr:               '21D0',  // Leftarrow
      Larr:               '21D0',  // Leftarrow
      rArr:               '21D2',  // Rightarrow
      Rarr:               '21D2',  // Rightarrow
      harr:               '2194',  // leftrightarrow
      lrarr:              '2194',  // leftrightarrow
      larr:               '2190',  // leftarrow
      gets:               '2190',  // leftarrow
      rarr:               '2192',   // rightarrow

      // big ops
      oiint:              ['222F',{texClass: MML.TEXCLASS.OP}],  // not part of texvc but nice to have
      oiiint:             ['2230',{texClass: MML.TEXCLASS.OP}]
    },

    mathchar7: {
      // Uppercase Greek letters
      Alpha:        '0391',
      Beta:         '0392',
      Epsilon:      '0395',
      Zeta:         '0396',
      Eta:          '0397',
      Iota:         '0399',
      Kappa:        '039A',
      Mu:           '039C',
      Nu:           '039D',
      Omicron:      '039F',
      Rho:          '03A1',
      Tau:          '03A4',
      Chi:          '03A7',

      Koppa:        '03DE',
      Stigma:       '03DA',
      Coppa:        '03D8',  // archaic Koppa
    },

    delimiter: {
      '\\uarr':           '2191',  // uparrow
      '\\darr':           '2193',  // downarrow
      '\\Uarr':           '21D1',  // Uparrow
      '\\uArr':           '21D1',  // Uparrow
      '\\Darr':           '21D3',  // Downarrow
      '\\dArr':           '21D3',  // Downarrow
      '\\rang':           '27E9',  // rangle
      '\\lang':           '27E8'   // langle
    },

    macros: {
      sgn:                ['NamedOp',0],
      textcolor:          ['Macro','\\color{#1}',1],
      bold:               ['Macro','{\\boldsymbol #1}',1]  // boldsymbol
    }

  });
});

MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function () {
  MathJax.Hub.Startup.signal.Post("TeX texvc Ready");
});

MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/texvc.js");

MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS-texvc_HTML.js");