text: /*
   *  /MathJax/config/TeX-MML-AM_CHTML.js
   *  
   *  Copyright (c) 2010-2015 The MathJax Consortium
   *
   *  Part of the MathJax library.
   *  See http://www.mathjax.org for details.
   * 
   *  Licensed under the Apache License, Version 2.0;
   *  you may not use this file except in compliance with the License.
   *
   *      http://www.apache.org/licenses/LICENSE-2.0
   */
  
  MathJax.Ajax.Preloading(
    "[MathJax]/jax/input/TeX/config.js",
    "[MathJax]/jax/input/MathML/config.js",
    "[MathJax]/jax/input/AsciiMath/config.js",
    "[MathJax]/jax/output/CommonHTML/config.js",
    "[MathJax]/jax/output/PreviewHTML/config.js",
    "[MathJax]/extensions/tex2jax.js",
    "[MathJax]/extensions/mml2jax.js",
    "[MathJax]/extensions/asciimath2jax.js",
    "[MathJax]/extensions/MathEvents.js",
    "[MathJax]/extensions/MathZoom.js",
    "[MathJax]/extensions/MathMenu.js",
    "[MathJax]/jax/element/mml/jax.js",
    "[MathJax]/extensions/toMathML.js",
    "[MathJax]/extensions/TeX/noErrors.js",
    "[MathJax]/extensions/TeX/noUndefined.js",
    "[MathJax]/jax/input/TeX/jax.js",
    "[MathJax]/extensions/TeX/AMSmath.js",
    "[MathJax]/extensions/TeX/AMSsymbols.js",
    "[MathJax]/jax/input/MathML/jax.js",
    "[MathJax]/jax/input/AsciiMath/jax.js",
    "[MathJax]/jax/output/PreviewHTML/jax.js",
    "[MathJax]/extensions/fast-preview.js",
    "[MathJax]/extensions/AssistiveMML.js"
  );
  
  MathJax.Hub.Config({"v1.0-compatible":false});
  
  MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.6.1",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/[:"'<>&]/g,"")},formatURL:function(a){return"#"+escape(a)},useLabelIds:true}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js");
  MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.6.1",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js");
  MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.6.0",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{fixphi:true,useMathMLspacing:true,displaystyle:true,decimalsign:"."}});MathJax.InputJax.AsciiMath.Register("math/asciimath");MathJax.InputJax.AsciiMath.loadComplete("config.js");
  MathJax.OutputJax.CommonHTML=MathJax.OutputJax({id:"CommonHTML",version:"2.6.1",directory:MathJax.OutputJax.directory+"/CommonHTML",extensionDir:MathJax.OutputJax.extensionDir+"/CommonHTML",autoloadDir:MathJax.OutputJax.directory+"/CommonHTML/autoload",fontDir:MathJax.OutputJax.directory+"/CommonHTML/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{matchFontHeight:true,scale:100,minScaleAdjust:50,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Cambria Math','Arial Unicode MS',serif",EqnChunk:(MathJax.Hub.Browser.isMobile?20:100),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.CommonHTML.Register("jax/mml")}MathJax.OutputJax.CommonHTML.loadComplete("config.js");
  MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.6.1",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");
  MathJax.Extension.tex2jax={version:"2.6.0",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],balanceBraces:true,skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c<a;c++){d.push(this.patternQuote(b.inlineMath[c][0]));this.match[b.inlineMath[c][0]]={mode:"",end:b.inlineMath[c][1],pattern:this.endPattern(b.inlineMath[c][1])}}for(c=0,a=b.displayMath.length;c<a;c++){d.push(this.patternQuote(b.displayMath[c][0]));this.match[b.displayMath[c][0]]={mode:"; mode=display",end:b.displayMath[c][1],pattern:this.endPattern(b.displayMath[c][1])}}if(d.length){e.push(d.sort(this.sortLength).join("|"))}if(b.processEnvironments){e.push("\\\\begin\\{([^}]*)\\}")}if(b.processEscapes){e.push("\\\\*\\\\\\$")}if(b.processRefs){e.push("\\\\(eq)?ref\\{[^}]*\\}")}this.start=new RegExp(e.join("|"),"g");this.skipTags=new RegExp("^("+b.skipTags.join("|")+")$","i");var f=[];if(MathJax.Hub.config.preRemoveClass){f.push(MathJax.Hub.config.preRemoveClass)}if(b.ignoreClass){f.push(b.ignoreClass)}this.ignoreClass=(f.length?new RegExp("(^| )("+f.join("|")+")( |$)"):/^$/);this.processClass=new RegExp("(^| )("+b.processClass+")( |$)");return(e.length>0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d<c?-1:1))},scanElement:function(c,b,g){var a,e,d,f;while(c&&c!=b){if(c.nodeName.toLowerCase()==="#text"){if(!g){c=this.scanText(c)}}else{a=(typeof(c.className)==="undefined"?"":c.className);e=(typeof(c.tagName)==="undefined"?"":c.tagName);if(typeof(a)!=="string"){a=String(a)}f=this.processClass.exec(a);if(c.firstChild&&!a.match(/(^| )MathJax/)&&(f||!this.skipTags.exec(e))){d=(g||this.ignoreClass.exec(a))&&!f;this.scanElement(c.firstChild,b,d)}}if(c){c=c.nextSibling}}},scanText:function(b){if(b.nodeValue.replace(/\s+/,"")==""){return b}var a,c;this.search={start:true};this.pattern=this.start;while(b){this.pattern.lastIndex=0;while(b&&b.nodeName.toLowerCase()==="#text"&&(a=this.pattern.exec(b.nodeValue))){if(this.search.start){b=this.startMatch(a,b)}else{b=this.endMatch(a,b)}}if(this.search.matched){b=this.encloseMath(b)}if(b){do{c=b;b=b.nextSibling}while(b&&(b.nodeName.toLowerCase()==="br"||b.nodeName.toLowerCase()==="#comment"));if(!b||b.nodeName!=="#text"){return(this.search.close?this.prevEndMatch():c)}}}return b},startMatch:function(a,b){var f=this.match[a[0]];if(f!=null){this.search={end:f.end,mode:f.mode,pcount:0,open:b,olen:a[0].length,opos:this.pattern.lastIndex-a[0].length};this.switchPattern(f.pattern)}else{if(a[0].substr(0,6)==="\\begin"){this.search={end:"\\end{"+a[1]+"}",mode:"; mode=display",pcount:0,open:b,olen:0,opos:this.pattern.lastIndex-a[0].length,isBeginEnd:true};this.switchPattern(this.endPattern(this.search.end))}else{if(a[0].substr(0,4)==="\\ref"||a[0].substr(0,6)==="\\eqref"){this.search={mode:"",end:"",open:b,pcount:0,olen:0,opos:this.pattern.lastIndex-a[0].length};return this.endMatch([""],b)}else{var d=a[0].substr(0,a[0].length-1),g,c;if(d.length%2===0){c=[d.replace(/\\\\/g,"\\")];g=1}else{c=[d.substr(1).replace(/\\\\/g,"\\"),"$"];g=0}c=MathJax.HTML.Element("span",null,c);var e=MathJax.HTML.TextNode(b.nodeValue.substr(0,a.index));b.nodeValue=b.nodeValue.substr(a.index+a[0].length-g);b.parentNode.insertBefore(c,b);b.parentNode.insertBefore(e,c);this.pattern.lastIndex=g}}}return b},endMatch:function(a,c){var b=this.search;if(a[0]==b.end){if(!b.close||b.pcount===0){b.close=c;b.cpos=this.pattern.lastIndex;b.clen=(b.isBeginEnd?0:a[0].length)}if(b.pcount===0){b.matched=true;c=this.encloseMath(c);this.switchPattern(this.start)}}else{if(a[0]==="{"){b.pcount++}else{if(a[0]==="}"&&b.pcount){b.pcount--}}}return c},prevEndMatch:function(){this.search.matched=true;var a=this.encloseMath(this.search.close);this.switchPattern(this.start);return a},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=(a===this.start)},encloseMath:function(b){var a=this.search,f=a.close,e,c;if(a.cpos===f.length){f=f.nextSibling}else{f=f.splitText(a.cpos)}if(!f){e=f=MathJax.HTML.addText(a.close.parentNode,"")}a.close=f;c=(a.opos?a.open.splitText(a.opos):a.open);while(c.nextSibling&&c.nextSibling!==f){if(c.nextSibling.nodeValue!==null){if(c.nextSibling.nodeName==="#comment"){c.nodeValue+=c.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{c.nodeValue+=c.nextSibling.nodeValue}}else{if(this.msieNewlineBug){c.nodeValue+=(c.nextSibling.nodeName.toLowerCase()==="br"?"\n":" ")}else{c.nodeValue+=" "}}c.parentNode.removeChild(c.nextSibling)}var d=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);if(this.config.preview!=="none"){this.createPreview(a.mode,d)}c=this.createMathTag(a.mode,d);this.search={};this.pattern.lastIndex=0;if(e){e.parentNode.removeChild(e)}return c},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(c,a){var b=this.config.preview;if(b==="none"){return}if(b==="TeX"){b=[this.filterPreview(a)]}if(b){b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b);this.insertNode(b)}},createMathTag:function(c,b){var a=document.createElement("script");a.type="math/tex"+c;MathJax.HTML.setScript(a,b);this.insertNode(a);return a},filterPreview:function(a){return a},msieNewlineBug:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9)};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js");
  MathJax.Extension.mml2jax={version:"2.6.0",config:{preview:"mathml"},MMLnamespace:"http://www.w3.org/1998/Math/MathML",PreProcess:function(e){if(!this.configured){this.config=MathJax.Hub.CombineConfig("mml2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.InitBrowser();this.configured=true}if(typeof(e)==="string"){e=document.getElementById(e)}if(!e){e=document.body}var h=[];this.PushMathElements(h,e,"math");this.PushMathElements(h,e,"math",this.MMLnamespace);var d,b;if(typeof(document.namespaces)!=="undefined"){try{for(d=0,b=document.namespaces.length;d<b;d++){var f=document.namespaces[d];if(f.urn===this.MMLnamespace){this.PushMathElements(h,e,f.name+":math")}}}catch(g){}}else{var c=document.getElementsByTagName("html")[0];if(c){for(d=0,b=c.attributes.length;d<b;d++){var a=c.attributes[d];if(a.nodeName.substr(0,6)==="xmlns:"&&a.nodeValue===this.MMLnamespace){this.PushMathElements(h,e,a.nodeName.substr(6)+":math")}}}}this.ProcessMathArray(h)},PushMathElements:function(f,d,a,c){var h,g=MathJax.Hub.config.preRemoveClass;if(c){if(!d.getElementsByTagNameNS){return}h=d.getElementsByTagNameNS(c,a)}else{h=d.getElementsByTagName(a)}for(var e=0,b=h.length;e<b;e++){var j=h[e].parentNode;if(j&&j.className!==g&&!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(f,b){var g=this.config.preview;if(g==="none"){return}var a=false;if(g==="mathml"){a=true;if(this.MathTagBug){g="alttext"}else{g=f.cloneNode(true)}}if(g==="alttext"||g==="altimg"){a=true;var c=this.filterPreview(f.getAttribute("alttext"));if(g==="alttext"){if(c!=null){g=MathJax.HTML.TextNode(c)}else{g=null}}else{var h=f.getAttribute("altimg");if(h!=null){var e={width:f.getAttribute("altimg-width"),height:f.getAttribute("altimg-height")};g=MathJax.HTML.Element("img",{src:h,alt:c,style:e})}else{g=null}}}if(g){var d;if(a){d=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass});d.appendChild(g)}else{d=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},g)}b.parentNode.insertBefore(d,b)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"<math><mi>x</mi><mspace /></math>"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="&lt;"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax],5);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js");
  MathJax.Extension.asciimath2jax={version:"2.6.0",config:{delimiters:[["`","`"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"asciimath2jax_ignore",processClass:"asciimath2jax_process",preview:"AsciiMath"},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("asciimath2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}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=[],c,a,b=this.config;this.match={};if(b.delimiters.length===0){return false}for(c=0,a=b.delimiters.length;c<a;c++){d.push(this.patternQuote(b.delimiters[c][0]));this.match[b.delimiters[c][0]]={mode:"",end:b.delimiters[c][1],pattern:this.endPattern(b.delimiters[c][1])}}this.start=new RegExp(d.sort(this.sortLength).join("|"),"g");this.skipTags=new RegExp("^("+b.skipTags.join("|")+")$","i");var e=[];if(MathJax.Hub.config.preRemoveClass){e.push(MathJax.Hub.config.preRemoveClass)}if(b.ignoreClass){e.push(b.ignoreClass)}this.ignoreClass=(e.length?new RegExp("(^| )("+e.join("|")+")( |$)"):/^$/);this.processClass=new RegExp("(^| )("+b.processClass+")( |$)");return true},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d<c?-1:1))},scanElement:function(c,b,g){var a,e,d,f;while(c&&c!=b){if(c.nodeName.toLowerCase()==="#text"){if(!g){c=this.scanText(c)}}else{a=(typeof(c.className)==="undefined"?"":c.className);e=(typeof(c.tagName)==="undefined"?"":c.tagName);if(typeof(a)!=="string"){a=String(a)}f=this.processClass.exec(a);if(c.firstChild&&!a.match(/(^| )MathJax/)&&(f||!this.skipTags.exec(e))){d=(g||this.ignoreClass.exec(a))&&!f;this.scanElement(c.firstChild,b,d)}}if(c){c=c.nextSibling}}},scanText:function(b){if(b.nodeValue.replace(/\s+/,"")==""){return b}var a,c;this.search={start:true};this.pattern=this.start;while(b){this.pattern.lastIndex=0;while(b&&b.nodeName.toLowerCase()==="#text"&&(a=this.pattern.exec(b.nodeValue))){if(this.search.start){b=this.startMatch(a,b)}else{b=this.endMatch(a,b)}}if(this.search.matched){b=this.encloseMath(b)}if(b){do{c=b;b=b.nextSibling}while(b&&(b.nodeName.toLowerCase()==="br"||b.nodeName.toLowerCase()==="#comment"));if(!b||b.nodeName!=="#text"){return c}}}return b},startMatch:function(a,b){var c=this.match[a[0]];if(c!=null){this.search={end:c.end,mode:c.mode,open:b,olen:a[0].length,opos:this.pattern.lastIndex-a[0].length};this.switchPattern(c.pattern)}return b},endMatch:function(a,b){if(a[0]==this.search.end){this.search.close=b;this.search.cpos=this.pattern.lastIndex;this.search.clen=(this.search.isBeginEnd?0:a[0].length);this.search.matched=true;b=this.encloseMath(b);this.switchPattern(this.start)}return b},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=(a===this.start)},encloseMath:function(b){var a=this.search,f=a.close,e,c;if(a.cpos===f.length){f=f.nextSibling}else{f=f.splitText(a.cpos)}if(!f){e=f=MathJax.HTML.addText(a.close.parentNode,"")}a.close=f;c=(a.opos?a.open.splitText(a.opos):a.open);while(c.nextSibling&&c.nextSibling!==f){if(c.nextSibling.nodeValue!==null){if(c.nextSibling.nodeName==="#comment"){c.nodeValue+=c.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{c.nodeValue+=c.nextSibling.nodeValue}}else{if(this.msieNewlineBug){c.nodeValue+=(c.nextSibling.nodeName.toLowerCase()==="br"?"\n":" ")}else{c.nodeValue+=" "}}c.parentNode.removeChild(c.nextSibling)}var d=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);if(this.config.preview!=="none"){this.createPreview(a.mode,d)}c=this.createMathTag(a.mode,d);this.search={};this.pattern.lastIndex=0;if(e){e.parentNode.removeChild(e)}return c},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(c,a){var b=this.config.preview;if(b==="none"){return}if(b==="AsciiMath"){b=[this.filterPreview(a)]}if(b){b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b);this.insertNode(b)}},createMathTag:function(c,a){var b=document.createElement("script");b.type="math/asciimath"+c;MathJax.HTML.setScript(b,a);this.insertNode(b);return b},filterPreview:function(a){return a},msieNewlineBug:(MathJax.Hub.Browser.isMSIE&&(document.documentMode||0)<9)};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.asciimath2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/asciimath2jax.js");
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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 q.hover.timer;q.hover.opacity=Math.max(0,Math.min(1,q.hover.opacity+q.hover.inc));q.hover.opacity=Math.floor(1000*q.hover.opacity)/1000;var s=document.getElementById(q.hover.id),r=document.getElementById(q.hover.id+"Menu");s.firstChild.style.opacity=q.hover.opacity;s.firstChild.style.filter="alpha(opacity="+Math.floor(100*q.hover.opacity)+")";if(r){r.firstChild.style.opacity=q.hover.opacity;r.firstChild.style.filter=s.style.filter}if(q.hover.opacity===1){return}if(q.hover.opacity>0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.last<a.delay&&a.up);a.last=q;a.up=false;if(s){a.timeout=setTimeout(a.menu,a.delay,r,this);r.preventDefault()}},end:function(r){var q=new Date().getTime();a.up=(q-a.last<a.delay);if(a.timeout){clearTimeout(a.timeout);delete a.timeout;a.last=0;a.up=false;r.preventDefault();return n.Handler((r.touches[0]||r.touch),"DblClick",this)}},menu:function(r,q){delete a.timeout;a.last=0;a.up=false;return n.Handler((r.touches[0]||r.touch),"ContextMenu",q)}};d.Browser.Select({MSIE:function(q){var s=(document.documentMode||0);var 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="2.6.0";var i=a.CombineConfig("MathZoom",{styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"font-weight":"normal","font-style":"normal","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","-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', Positive='true')"},"#MathJax_ZoomOverlay":{position:"absolute",left:0,top:0,"z-index":300,display:"inline-block",width:"100%",height:"100%",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"},"#MathJax_ZoomFrame":{position:"relative",display:"inline-block",height:0,width:0},"#MathJax_ZoomEventTrap":{position:"absolute",left:0,top:0,"z-index":302,display:"inline-block",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"}}});var e,b,g;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){g=MathJax.Extension.MathEvents.Event;e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var h=MathJax.Extension.MathZoom={version:k,settings:a.config.menuSettings,scrollSize:18,HandleEvent:function(n,l,m){if(h.settings.CTRL&&!n.ctrlKey){return true}if(h.settings.ALT&&!n.altKey){return true}if(h.settings.CMD&&!n.metaKey){return true}if(h.settings.Shift&&!n.shiftKey){return true}if(!h[l]){return true}return h[l](n,m)},Click:function(m,l){if(this.settings.zoom==="Click"){return this.Zoom(m,l)}},DblClick:function(m,l){if(this.settings.zoom==="Double-Click"||this.settings.zoom==="DoubleClick"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(o,u){this.Remove();b.ClearHoverTimer();g.ClearSelection();var s=MathJax.OutputJax[u.jaxID];var p=s.getJaxFromMath(u);if(p.hover){b.UnHover(p)}var q=this.findContainer(u);var l=Math.floor(0.85*q.clientWidth),t=Math.max(document.body.clientHeight,document.documentElement.clientHeight);if(this.getOverflow(q)!=="visible"){t=Math.min(q.clientHeight,t)}t=Math.floor(0.85*t);var n=d.Element("span",{id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var z=n.lastChild,w=z.firstChild,r=n.firstChild;u.parentNode.insertBefore(n,u);u.parentNode.insertBefore(u,n);if(w.addEventListener){w.addEventListener("mousedown",this.Remove,true)}var m=z.offsetWidth||z.clientWidth;l-=m;t-=m;z.style.maxWidth=l+"px";z.style.maxHeight=t+"px";if(this.msieTrapEventBug){var y=d.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});n.insertBefore(y,z)}if(this.msieZIndexBug){var v=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});n.style.position="relative";n.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];n=v}var x=s.Zoom(p,w,u,l,t);if(this.msiePositionBug){if(this.msieSizeBug){z.style.height=x.zH+"px";z.style.width=x.zW+"px"}if(z.offsetHeight>t){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m<l&&z.offsetHeight-m<t){z.style.overflow="visible"}this.Position(z,x);if(this.msieTrapEventBug){y.style.height=z.clientHeight+"px";y.style.width=z.clientWidth+"px";y.style.left=(parseFloat(z.style.left)+z.clientLeft)+"px";y.style.top=(parseFloat(z.style.top)+z.clientTop)+"px"}z.style.visibility="";if(this.settings.zoom==="Hover"){r.onmouseover=this.Remove}if(window.addEventListener){addEventListener("resize",this.Resize,false)}else{if(window.attachEvent){attachEvent("onresize",this.Resize)}else{this.onresize=window.onresize;window.onresize=this.Resize}}a.signal.Post(["math zoomed",p]);return e(o)},Position:function(p,r){p.style.display="none";var q=this.Resize(),m=q.x,s=q.y,l=r.mW;p.style.display="";var o=-l-Math.floor((p.offsetWidth-l)/2),n=r.Y;p.style.left=Math.max(o,10-m)+"px";p.style.top=Math.max(n,10-s)+"px";if(!h.msiePositionBug){h.SetWH()}},Resize:function(m){if(h.onresize){h.onresize(m)}var q=document.getElementById("MathJax_ZoomFrame"),l=document.getElementById("MathJax_ZoomOverlay");var o=h.getXY(q),n=h.findContainer(q);if(h.getOverflow(n)!=="visible"){l.scroll_parent=n;var p=h.getXY(n);o.x-=p.x;o.y-=p.y;p=h.getBorder(n);o.x-=p.x;o.y-=p.y}l.style.left=(-o.x)+"px";l.style.top=(-o.y)+"px";if(h.msiePositionBug){setTimeout(h.SetWH,0)}else{h.SetWH()}return o},SetWH:function(){var l=document.getElementById("MathJax_ZoomOverlay");if(!l){return}l.style.display="none";var m=l.scroll_parent||document.documentElement||document.body;l.style.width=m.scrollWidth+"px";l.style.height=Math.max(m.clientHeight,m.scrollHeight)+"px";l.style.display=""},findContainer:function(l){l=l.parentNode;while(l.parentNode&&l!==document.body&&h.getOverflow(l)==="visible"){l=l.parentNode}return l},getOverflow:(window.getComputedStyle?function(l){return getComputedStyle(l).overflow}:function(l){return(l.currentStyle||{overflow:"visible"}).overflow}),getBorder:function(o){var m={thin:1,medium:2,thick:3};var n=(window.getComputedStyle?getComputedStyle(o):(o.currentStyle||{borderLeftWidth:0,borderTopWidth:0}));var l=n.borderLeftWidth,p=n.borderTopWidth;if(m[l]){l=m[l]}else{l=parseInt(l)}if(m[p]){p=m[p]}else{p=parseInt(p)}return{x:l,y:p}},getXY:function(o){var l=0,n=0,m;m=o;while(m.offsetParent){l+=m.offsetLeft;m=m.offsetParent}if(h.operaPositionBug){o.style.border="1px solid"}m=o;while(m.offsetParent){n+=m.offsetTop;m=m.offsetParent}if(h.operaPositionBug){o.style.border=""}return{x:l,y:n}},Remove:function(n){var p=document.getElementById("MathJax_ZoomFrame");if(p){var o=MathJax.OutputJax[p.previousSibling.jaxID];var l=o.getJaxFromMath(p.previousSibling);a.signal.Post(["math unzoomed",l]);p.parentNode.removeChild(p);p=document.getElementById("MathJax_ZoomTracker");if(p){p.parentNode.removeChild(p)}if(h.operaRefreshBug){var m=d.addElement(document.body,"div",{style:{position:"fixed",left:0,top:0,width:"100%",height:"100%",backgroundColor:"white",opacity:0},id:"MathJax_OperaDiv"});document.body.removeChild(m)}if(window.removeEventListener){removeEventListener("resize",h.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",h.Resize)}else{window.onresize=h.onresize;delete h.onresize}}}return e(n)}};a.Browser.Select({MSIE:function(l){var n=(document.documentMode||0);var m=(n>=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML);
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h=f.merror.prototype.toCommonHTML;f.merror.Augment({toCommonHTML:function(n){if(!this.isError){return h.apply(this,arguments)}n=g.addElement(n,"mjx-noError");var p=this.data[0].data[0].data.join("").split(/\n/);for(var k=0,j=p.length;k<j;k++){i.addText(n,p[k]);if(k!==j-1){g.addElement(n,"br",{isMathJax:true})}}var o=this.CHTML=g.BBOX.zero();o.w=(n.offsetWidth)/g.em;if(j>1){var l=1.2*j/2;o.h=l+0.25;o.d=l-0.25;n.style.verticalAlign=g.Em(0.45-l)}else{o.h=1;o.d=0.2+2/g.em}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js");
  MathJax.Extension["TeX/noUndefined"]={version:"2.6.0",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js");
  (function(d,c,i){var h,g="\u00A0";var j=function(l){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",l]].concat([].slice.call(arguments,1)))};var e=MathJax.Object.Subclass({Init:function(m,l){this.global={isInner:l};this.data=[b.start(this.global)];if(m){this.data[0].env=m}this.env=this.data[0].env},Push:function(){var n,l,o,p;for(n=0,l=arguments.length;n<l;n++){o=arguments[n];if(!o){continue}if(o instanceof h.mbase){o=b.mml(o)}o.global=this.global;p=(this.data.length?this.Top().checkItem(o):true);if(p instanceof Array){this.Pop();this.Push.apply(this,p)}else{if(p instanceof b){this.Pop();this.Push(p)}else{if(p){this.data.push(o);if(o.env){for(var q in this.env){if(this.env.hasOwnProperty(q)){o.env[q]=this.env[q]}}this.env=o.env}else{o.env=this.env}}}}}},Pop:function(){var l=this.data.pop();if(!l.isOpen){delete l.env}this.env=(this.data.length?this.Top().env:{});return l},Top:function(l){if(l==null){l=1}if(this.data.length<l){return null}return this.data[this.data.length-l]},Prev:function(l){var m=this.Top();if(l){return m.data[m.data.length-1]}else{return m.Pop()}},toString:function(){return"stack[\n  "+this.data.join("\n  ")+"\n]"}});var b=e.Item=MathJax.Object.Subclass({type:"base",endError:["ExtraOpenMissingClose","Extra open brace or missing close brace"],closeError:["ExtraCloseMissingOpen","Extra close brace or missing open brace"],rightError:["MissingLeftExtraRight","Missing \\left or extra \\right"],Init:function(){if(this.isOpen){this.env={}}this.data=[];this.Push.apply(this,arguments)},Push:function(){this.data.push.apply(this.data,arguments)},Pop:function(){return this.data.pop()},mmlData:function(l,m){if(l==null){l=true}if(this.data.length===1&&!m){return this.data[0]}return h.mrow.apply(h,this.data).With((l?{inferred:true}:{}))},checkItem:function(l){if(l.type==="over"&&this.isOpen){l.num=this.mmlData(false);this.data=[]}if(l.type==="cell"&&this.isOpen){if(l.linebreak){return false}d.Error(["Misplaced","Misplaced 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this.SUPER(arguments).checkItem.call(this,m)}});b.close=b.Subclass({type:"close",isClose:true});b.prime=b.Subclass({type:"prime",checkItem:function(l){if(this.data[0].type!=="msubsup"){return[h.msup(this.data[0],this.data[1]),l]}this.data[0].SetData(this.data[0].sup,this.data[1]);return[this.data[0],l]}});b.subsup=b.Subclass({type:"subsup",stopError:["MissingScript","Missing superscript or subscript argument"],supError:["MissingOpenForSup","Missing open brace for superscript"],subError:["MissingOpenForSub","Missing open brace for subscript"],checkItem:function(l){if(l.type==="open"||l.type==="left"){return true}if(l.type==="mml"){if(this.primes){if(this.position!==2){this.data[0].SetData(2,this.primes)}else{l.data[0]=h.mrow(this.primes.With({variantForm:true}),l.data[0])}}this.data[0].SetData(this.position,l.data[0]);if(this.movesupsub!=null){this.data[0].movesupsub=this.movesupsub}return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,l)){d.Error(this[["","subError","supError"][this.position]])}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:true,name:"\\over",checkItem:function(n,l){if(n.type==="over"){d.Error(["AmbiguousUseOf","Ambiguous use of %1",n.name])}if(n.isClose){var m=h.mfrac(this.num,this.mmlData(false));if(this.thickness!=null){m.linethickness=this.thickness}if(this.open||this.close){m.texWithDelims=true;m=d.fixedFence(this.open,m,this.close)}return[b.mml(m),n]}return this.SUPER(arguments).checkItem.call(this,n)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:true,delim:"(",stopError:["ExtraLeftMissingRight","Extra \\left or missing \\right"],checkItem:function(l){if(l.type==="right"){return b.mml(d.fenced(this.delim,this.mmlData(),l.delim))}return this.SUPER(arguments).checkItem.call(this,l)}});b.right=b.Subclass({type:"right",isClose:true,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:true,checkItem:function(l){if(l.type==="end"){if(l.name!==this.name){d.Error(["EnvBadEnd","\\begin{%1} ended with \\end{%2}",this.name,l.name])}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(l.type==="stop"){d.Error(["EnvMissingEnd","Missing \\end{%1}",this.name])}return this.SUPER(arguments).checkItem.call(this,l)}});b.end=b.Subclass({type:"end",isClose:true});b.style=b.Subclass({type:"style",checkItem:function(m){if(!m.isClose){return this.SUPER(arguments).checkItem.call(this,m)}var l=h.mstyle.apply(h,this.data).With(this.styles);return[b.mml(l),m]}});b.position=b.Subclass({type:"position",checkItem:function(m){if(m.isClose){d.Error(["MissingBoxFor","Missing box for %1",this.name])}if(m.isNotStack){var l=m.mmlData();switch(this.move){case"vertical":l=h.mpadded(l).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(l)];case"horizontal":return[b.mml(this.left),m,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,m)}});b.array=b.Subclass({type:"array",isOpen:true,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.frame=[];this.hfill=[];this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(m){if(m.isClose&&m.type!=="over"){if(m.isEntry){this.EndEntry();this.clearEnv();return false}if(m.isCR){this.EndEntry();this.EndRow();this.clearEnv();return false}this.EndTable();this.clearEnv();var n=this.arraydef.scriptlevel;delete this.arraydef.scriptlevel;var l=h.mtable.apply(h,this.table).With(this.arraydef);if(this.frame.length===4){l.frame=(this.frame.dashed?"dashed":"solid")}else{if(this.frame.length){l.hasFrame=true;if(this.arraydef.rowlines){this.arraydef.rowlines=this.arraydef.rowlines.replace(/none( 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l=h.mtr;if(this.isNumbered&&this.row.length===3){this.row.unshift(this.row.pop());l=h.mlabeledtr}this.table.push(l.apply(h,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var l=this.arraydef.rowlines.split(/ /);if(l.length===this.table.length){this.frame.push("bottom");l.pop();this.arraydef.rowlines=l.join(" ")}else{if(l.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}if(this.rowspacing){var m=this.arraydef.rowspacing.split(/ /);while(m.length<this.table.length){m.push(this.rowspacing+"em")}this.arraydef.rowspacing=m.join(" ")}},clearEnv:function(){for(var l in this.env){if(this.env.hasOwnProperty(l)){delete this.env[l]}}}});b.cell=b.Subclass({type:"cell",isClose:true});b.mml=b.Subclass({type:"mml",isNotStack:true,Add:function(){this.data.push.apply(this.data,arguments);return this}});b.fn=b.Subclass({type:"fn",checkItem:function(m){if(this.data[0]){if(m.isOpen){return true}if(m.type!=="fn"){if(m.type!=="mml"||!m.data[0]){return[this.data[0],m]}if(m.data[0].isa(h.mspace)){return[this.data[0],m]}var l=m.data[0];if(l.isEmbellished()){l=l.CoreMO()}if([0,0,1,1,0,1,1,0,0,0][l.Get("texClass")]){return[this.data[0],m]}}return[this.data[0],h.mo(h.entity("#x2061")).With({texClass:h.TEXCLASS.NONE}),m]}return this.SUPER(arguments).checkItem.apply(this,arguments)}});b.not=b.Subclass({type:"not",checkItem:function(m){var l,n;if(m.type==="open"||m.type==="left"){return true}if(m.type==="mml"&&m.data[0].type.match(/^(mo|mi|mtext)$/)){l=m.data[0],n=l.data.join("");if(n.length===1&&!l.movesupsub){n=b.not.remap[n.charCodeAt(0)];if(n){l.SetData(0,h.chars(String.fromCharCode(n)))}else{l.Append(h.chars("\u0338"))}return 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clarify"])}if(n.type!=="msubsup"){if(m){if(n.type!=="munderover"||n.data[n.under]){if(n.movablelimits&&n.isa(h.mi)){n=this.mi2mo(n)}n=h.munderover(n,null,null).With({movesupsub:true})}l=n.under}else{n=h.msubsup(n,null,null);l=n.sub}}this.Push(b.subsup(n).With({position:l,primes:p,movesupsub:m}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(n){var m=this.stack.Prev();if(!m){m=h.mi()}if(m.type==="msubsup"&&m.data[m.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var l="";this.i--;do{l+=this.PRIME;this.i++,n=this.GetNext()}while(n==="'"||n===this.SMARTQUOTE);l=["","\u2032","\u2033","\u2034","\u2057"][l.length]||l;this.Push(b.prime(m,this.mmlToken(h.mo(l))))},mi2mo:function(l){var m=h.mo();m.Append.apply(m,l.data);var n;for(n in m.defaults){if(m.defaults.hasOwnProperty(n)&&l[n]!=null){m[n]=l[n]}}for(n in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(n)&&l[n]!=null){m[n]=l[n]}}m.lspace=m.rspace="0";m.useMMLspacing&=~(m.SPACE_ATTR.lspace|m.SPACE_ATTR.rspace);return m},Comment:function(l){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(l){d.Error(["CantUseHash1","You can't use 'macro parameter character #' in math mode"])},Other:function(n){var m,l;if(this.stack.env.font){m={mathvariant:this.stack.env.font}}if(f.remap[n]){n=f.remap[n];if(n instanceof Array){m=n[1];n=n[0]}l=h.mo(h.entity("#x"+n)).With(m)}else{l=h.mo(n).With(m)}if(l.autoDefault("stretchy",true)){l.stretchy=false}if(l.autoDefault("texClass",true)==""){l=h.TeXAtom(l)}this.Push(this.mmlToken(l))},SetFont:function(m,l){this.stack.env.font=l},SetStyle:function(m,l,n,o){this.stack.env.style=l;this.stack.env.level=o;this.Push(b.style().With({styles:{displaystyle:n,scriptlevel:o}}))},SetSize:function(l,m){this.stack.env.size=m;this.Push(b.style().With({styles:{mathsize:m+"em"}}))},Color:function(n){var m=this.GetArgument(n);var l=this.stack.env.color;this.stack.env.color=m;var o=this.ParseArg(n);if(l){this.stack.env.color}else{delete this.stack.env.color}this.Push(h.mstyle(o).With({mathcolor:m}))},Spacer:function(l,m){this.Push(h.mspace().With({width:m,mathsize:h.SIZE.NORMAL,scriptlevel:0}))},LeftRight:function(l){this.Push(b[l.substr(1)]().With({delim:this.GetDelimiter(l)}))},Middle:function(l){var m=this.GetDelimiter(l);if(this.stack.Top().type!=="left"){d.Error(["MisplacedMiddle","%1 must be within \\left and \\right",l])}this.Push(h.mo(m).With({stretchy:true}))},NamedFn:function(m,n){if(!n){n=m.substr(1)}var l=h.mi(n).With({texClass:h.TEXCLASS.OP});this.Push(b.fn(this.mmlToken(l)))},NamedOp:function(m,n){if(!n){n=m.substr(1)}n=n.replace(/&thinsp;/,"\u2006");var l=h.mo(n).With({movablelimits:true,movesupsub:true,form:h.FORM.PREFIX,texClass:h.TEXCLASS.OP});l.useMMLspacing&=~l.SPACE_ATTR.form;this.Push(this.mmlToken(l))},Limits:function(m,l){var o=this.stack.Prev("nopop");if(!o||(o.Get("texClass")!==h.TEXCLASS.OP&&o.movesupsub==null)){d.Error(["MisplacedLimits","%1 is allowed only on operators",m])}var n=this.stack.Top();if(o.type==="munderover"&&!l){o=n.data[n.data.length-1]=h.msubsup.apply(h.subsup,o.data)}else{if(o.type==="msubsup"&&l){o=n.data[n.data.length-1]=h.munderover.apply(h.underover,o.data)}}o.movesupsub=(l?true:false);o.Core().movablelimits=false;if(o.movablelimits){o.movablelimits=false}},Over:function(n,m,o){var l=b.over().With({name:n});if(m||o){l.open=m;l.close=o}else{if(n.match(/withdelims$/)){l.open=this.GetDelimiter(n);l.close=this.GetDelimiter(n)}}if(n.match(/^\\above/)){l.thickness=this.GetDimen(n)}else{if(n.match(/^\\atop/)||m||o){l.thickness=0}}this.Push(l)},Frac:function(m){var l=this.ParseArg(m);var n=this.ParseArg(m);this.Push(h.mfrac(l,n))},Sqrt:function(o){var p=this.GetBrackets(o),l=this.GetArgument(o);if(l==="\\frac"){l+="{"+this.GetArgument(l)+"}{"+this.GetArgument(l)+"}"}var m=d.Parse(l,this.stack.env).mml();if(!p){m=h.msqrt.apply(h,m.array())}else{m=h.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(m){var o=this.GetUpTo(m,"\\of");var l=this.ParseArg(m);this.Push(h.mroot(l,this.parseRoot(o)))},parseRoot:function(q){var m=this.stack.env,l=m.inRoot;m.inRoot=true;var p=d.Parse(q,m);q=p.mml();var o=p.stack.global;if(o.leftRoot||o.upRoot){q=h.mpadded(q);if(o.leftRoot){q.width=o.leftRoot}if(o.upRoot){q.voffset=o.upRoot;q.height=o.upRoot}}m.inRoot=l;return q},MoveRoot:function(l,o){if(!this.stack.env.inRoot){d.Error(["MisplacedMoveRoot","%1 can appear only within a root",l])}if(this.stack.global[o]){d.Error(["MultipleMoveRoot","Multiple use of %1",l])}var m=this.GetArgument(l);if(!m.match(/-?[0-9]+/)){d.Error(["IntegerArg","The argument to %1 must be an integer",l])}m=(m/15)+"em";if(m.substr(0,1)!=="-"){m="+"+m}this.stack.global[o]=m},Accent:function(n,l,q){var p=this.ParseArg(n);var o={accent:true};if(this.stack.env.font){o.mathvariant=this.stack.env.font}var m=this.mmlToken(h.mo(h.entity("#x"+l)).With(o));m.stretchy=(q?true:false);this.Push(h.TeXAtom(h.munderover(p,null,m).With({accent:true})))},UnderOver:function(n,r,l,p){var q={o:"over",u:"under"}[n.charAt(1)];var o=this.ParseArg(n);if(o.Get("movablelimits")){o.movablelimits=false}if(o.isa(h.munderover)&&o.isEmbellished()){o.Core().With({lspace:0,rspace:0});o=h.mrow(h.mo().With({rspace:0}),o)}var m=h.munderover(o,null,null);m.SetData(m[q],this.mmlToken(h.mo(h.entity("#x"+r)).With({stretchy:true,accent:!p})));if(l){m=h.TeXAtom(m).With({texClass:h.TEXCLASS.OP,movesupsub:true})}this.Push(m.With({subsupOK:true}))},Overset:function(l){var n=this.ParseArg(l),m=this.ParseArg(l);if(m.movablelimits){m.movablelimits=false}this.Push(h.mover(m,n))},Underset:function(l){var n=this.ParseArg(l),m=this.ParseArg(l);if(m.movablelimits){m.movablelimits=false}this.Push(h.munder(m,n))},TeXAtom:function(o,q){var p={texClass:q},n;if(q==h.TEXCLASS.OP){p.movesupsub=p.movablelimits=true;var l=this.GetArgument(o);var m=l.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(m){p.mathvariant=h.VARIANT.NORMAL;n=b.fn(this.mmlToken(h.mi(m[1]).With(p)))}else{n=b.fn(h.TeXAtom(d.Parse(l,this.stack.env).mml()).With(p))}}else{n=h.TeXAtom(this.ParseArg(o)).With(p)}this.Push(n)},MmlToken:function(n){var o=this.GetArgument(n),l=this.GetBrackets(n,"").replace(/^\s+/,""),r=this.GetArgument(n),q={attrNames:[]},m;if(!h[o]||!h[o].prototype.isToken){d.Error(["NotMathMLToken","%1 is not a token element",o])}while(l!==""){m=l.match(/^([a-z]+)\s*=\s*('[^']*'|"[^"]*"|[^ ,]*)\s*,?\s*/i);if(!m){d.Error(["InvalidMathMLAttr","Invalid MathML attribute: %1",l])}if(h[o].prototype.defaults[m[1]]==null&&!this.MmlTokenAllow[m[1]]){d.Error(["UnknownAttrForElement","%1 is not a recognized attribute for %2",m[1],o])}var p=this.MmlFilterAttribute(m[1],m[2].replace(/^(['"])(.*)\1$/,"$2"));if(p){if(p.toLowerCase()==="true"){p=true}else{if(p.toLowerCase()==="false"){p=false}}q[m[1]]=p;q.attrNames.push(m[1])}l=l.substr(m[0].length)}this.Push(this.mmlToken(h[o](r).With(q)))},MmlFilterAttribute:function(l,m){return m},MmlTokenAllow:{fontfamily:1,fontsize:1,fontweight:1,fontstyle:1,color:1,background:1,id:1,"class":1,href:1,style:1},Strut:function(l){this.Push(h.mpadded(h.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(m,l,n){var o=h.mphantom(this.ParseArg(m));if(l||n){o=h.mpadded(o);if(n){o.height=o.depth=0}if(l){o.width=0}}this.Push(h.TeXAtom(o))},Smash:function(n){var m=this.trimSpaces(this.GetBrackets(n,""));var l=h.mpadded(this.ParseArg(n));switch(m){case"b":l.depth=0;break;case"t":l.height=0;break;default:l.height=l.depth=0}this.Push(h.TeXAtom(l))},Lap:function(m){var l=h.mpadded(this.ParseArg(m)).With({width:0});if(m==="\\llap"){l.lspace="-1width"}this.Push(h.TeXAtom(l))},RaiseLower:function(l){var m=this.GetDimen(l);var n=b.position().With({name:l,move:"vertical"});if(m.charAt(0)==="-"){m=m.slice(1);l={raise:"\\lower",lower:"\\raise"}[l.substr(1)]}if(l==="\\lower"){n.dh="-"+m;n.dd="+"+m}else{n.dh="+"+m;n.dd="-"+m}this.Push(n)},MoveLeftRight:function(l){var o=this.GetDimen(l);var n=(o.charAt(0)==="-"?o.slice(1):"-"+o);if(l==="\\moveleft"){var m=o;o=n;n=m}this.Push(b.position().With({name:l,move:"horizontal",left:h.mspace().With({width:o,mathsize:h.SIZE.NORMAL}),right:h.mspace().With({width:n,mathsize:h.SIZE.NORMAL})}))},Hskip:function(l){this.Push(h.mspace().With({width:this.GetDimen(l),mathsize:h.SIZE.NORMAL}))},Rule:function(n,p){var l=this.GetDimen(n),o=this.GetDimen(n),r=this.GetDimen(n);var m,q={width:l,height:o,depth:r};if(p!=="blank"){if(parseFloat(l)&&parseFloat(o)+parseFloat(r)){q.mathbackground=(this.stack.env.color||"black")}m=h.mpadded(h.mrow()).With(q)}else{m=h.mspace().With(q)}this.Push(m)},MakeBig:function(l,o,m){m*=f.p_height;m=String(m).replace(/(\.\d\d\d).+/,"$1")+"em";var n=this.GetDelimiter(l,true);this.Push(h.TeXAtom(h.mo(n).With({minsize:m,maxsize:m,fence:true,stretchy:true,symmetric:true})).With({texClass:o}))},BuildRel:function(l){var m=this.ParseUpTo(l,"\\over");var n=this.ParseArg(l);this.Push(h.TeXAtom(h.munderover(n,null,m)).With({texClass:h.TEXCLASS.REL}))},HBox:function(l,m){this.Push.apply(this,this.InternalMath(this.GetArgument(l),m))},FBox:function(l){this.Push(h.menclose.apply(h,this.InternalMath(this.GetArgument(l))).With({notation:"box"}))},Not:function(l){this.Push(b.not())},Dots:function(l){this.Push(b.dots().With({ldots:this.mmlToken(h.mo(h.entity("#x2026")).With({stretchy:false})),cdots:this.mmlToken(h.mo(h.entity("#x22EF")).With({stretchy:false}))}))},Require:function(l){var m=this.GetArgument(l).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");this.Extension(null,m)},Extension:function(l,m,n){if(l&&!typeof(l)==="string"){l=l.name}m=d.extensionDir+"/"+m;if(!m.match(/\.js$/)){m+=".js"}if(!i.loaded[i.fileURL(m)]){if(l!=null){delete f[n||"macros"][l.replace(/^\\/,"")]}c.RestartAfter(i.Require(m))}},Macro:function(n,q,p,r){if(p){var m=[];if(r!=null){var l=this.GetBrackets(n);m.push(l==null?r:l)}for(var o=m.length;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(m,o,u,q,t,n,l,v,s){var r=this.GetNext();if(r===""){d.Error(["MissingArgFor","Missing argument for %1",m])}if(r==="{"){this.i++}else{this.string=r+"}"+this.string.slice(this.i+1);this.i=0}var p=b.array().With({requireClose:true,arraydef:{rowspacing:(n||"4pt"),columnspacing:(t||"1em")}});if(v){p.isCases=true}if(s){p.isNumbered=true;p.arraydef.side=s}if(o||u){p.open=o;p.close=u}if(l==="D"){p.arraydef.displaystyle=true}if(q!=null){p.arraydef.columnalign=q}this.Push(p)},Entry:function(o){this.Push(b.cell().With({isEntry:true,name:o}));if(this.stack.Top().isCases){var n=this.string;var r=0,p=this.i,l=n.length;while(p<l){var s=n.charAt(p);if(s==="{"){r++;p++}else{if(s==="}"){if(r===0){l=0}else{r--;p++}}else{if(s==="&"&&r===0){d.Error(["ExtraAlignTab","Extra alignment tab in \\cases text"])}else{if(s==="\\"){if(n.substr(p).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){l=0}else{p+=2}}else{p++}}}}}var q=n.substr(this.i,p-this.i);if(!q.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(q,0));this.i=p}}},Cr:function(l){this.Push(b.cell().With({isCR:true,name:l}))},CrLaTeX:function(l){var p;if(this.string.charAt(this.i)==="["){p=this.GetBrackets(l,"").replace(/ /g,"").replace(/,/,".");if(p&&!this.matchDimen(p)){d.Error(["BracketMustBeDimension","Bracket argument to %1 must be a dimension",l])}}this.Push(b.cell().With({isCR:true,name:l,linebreak:true}));var o=this.stack.Top();if(o.isa(b.array)){if(p&&o.arraydef.rowspacing){var m=o.arraydef.rowspacing.split(/ /);if(!o.rowspacing){o.rowspacing=this.dimen2em(m[0])}while(m.length<o.table.length){m.push(this.Em(o.rowspacing))}m[o.table.length-1]=this.Em(Math.max(0,o.rowspacing+this.dimen2em(p)));o.arraydef.rowspacing=m.join(" ")}}else{if(p){this.Push(h.mspace().With({depth:p}))}this.Push(h.mspace().With({linebreak:h.LINEBREAK.NEWLINE}))}},emPerInch:7.2,pxPerInch:72,matchDimen:function(l){return l.match(/^(-?(?:\.\d+|\d+(?:\.\d*)?))(px|pt|em|ex|mu|pc|in|mm|cm)$/)},dimen2em:function(p){var n=this.matchDimen(p);var l=parseFloat(n[1]||"1"),o=n[2];if(o==="em"){return l}if(o==="ex"){return l*0.43}if(o==="pt"){return l/10}if(o==="pc"){return l*1.2}if(o==="px"){return l*this.emPerInch/this.pxPerInch}if(o==="in"){return l*this.emPerInch}if(o==="cm"){return l*this.emPerInch/2.54}if(o==="mm"){return l*this.emPerInch/25.4}if(o==="mu"){return l/18}return 0},Em:function(l){if(Math.abs(l)<0.0006){return"0em"}return l.toFixed(3).replace(/\.?0+$/,"")+"em"},HLine:function(m,n){if(n==null){n="solid"}var o=this.stack.Top();if(!o.isa(b.array)||o.data.length){d.Error(["Misplaced","Misplaced %1",m])}if(o.table.length==0){o.frame.push("top")}else{var l=(o.arraydef.rowlines?o.arraydef.rowlines.split(/ /):[]);while(l.length<o.table.length){l.push("none")}l[o.table.length-1]=n;o.arraydef.rowlines=l.join(" ")}},HFill:function(l){var m=this.stack.Top();if(m.isa(b.array)){m.hfill.push(m.data.length)}else{d.Error(["UnsupportedHFill","Unsupported use of %1",l])}},BeginEnd:function(n){var o=this.GetArgument(n),q=false;if(o.match(/^\\end\\/)){q=true;o=o.substr(5)}if(o.match(/\\/i)){d.Error(["InvalidEnv","Invalid environment name '%1'",o])}var p=this.envFindName(o);if(!p){d.Error(["UnknownEnv","Unknown environment '%1'",o])}if(!(p instanceof Array)){p=[p]}var l=(p[1] instanceof Array?p[1][0]:p[1]);var m=b.begin().With({name:o,end:l,parse:this});if(n==="\\end"){if(!q&&p[1] instanceof Array&&this[p[1][1]]){m=this[p[1][1]].apply(this,[m].concat(p.slice(2)))}else{m=b.end().With({name:o})}}else{if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}}this.Push(m)},envFindName:function(l){return f.environment[l]},Equation:function(l,m){return m},ExtensionEnv:function(m,l){this.Extension(m.name,l,"environment")},Array:function(m,o,t,r,s,n,l,p){if(!r){r=this.GetArgument("\\begin{"+m.name+"}")}var u=("c"+r).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");r=r.replace(/[^clr]/g,"").split("").join(" ");r=r.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var 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n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var 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q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var 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]){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0;var 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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:"2.6.0",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()){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:"2.6.1",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"&&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":"")});j.innerHTML=i;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])});
  MathJax.Ajax.loadComplete("[MathJax]/config/TeX-MML-AM_CHTML.js");
  