/*
 *  /MathJax/config/TeX-MML-AM_CHTML-full.js
 *  
 *  Copyright (c) 2010-2016 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/CommonHTML/jax.js",
  "[MathJax]/jax/output/CommonHTML/autoload/mtable.js",
  "[MathJax]/jax/output/PreviewHTML/jax.js",
  "[MathJax]/extensions/fast-preview.js",
  "[MathJax]/extensions/AssistiveMML.js"
);

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

MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.0",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/[:"'<>&]/g,"")},formatURL:function(b,a){return a+"#"+escape(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js");
MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.0",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js");
MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.7.0",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:"2.7.0",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:"2.7.0",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:"2.7.0",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"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c<a;c++){d.push(this.patternQuote(b.inlineMath[c][0]));this.match[b.inlineMath[c][0]]={mode:"",end:b.inlineMath[c][1],pattern:this.endPattern(b.inlineMath[c][1])}}for(c=0,a=b.displayMath.length;c<a;c++){d.push(this.patternQuote(b.displayMath[c][0]));this.match[b.displayMath[c][0]]={mode:"; mode=display",end:b.displayMath[c][1],pattern:this.endPattern(b.displayMath[c][1])}}if(d.length){e.push(d.sort(this.sortLength).join("|"))}if(b.processEnvironments){e.push("\\\\begin\\{([^}]*)\\}")}if(b.processEscapes){e.push("\\\\*\\\\\\$")}if(b.processRefs){e.push("\\\\(eq)?ref\\{[^}]*\\}")}this.start=new RegExp(e.join("|"),"g");this.skipTags=new RegExp("^("+b.skipTags.join("|")+")$","i");var f=[];if(MathJax.Hub.config.preRemoveClass){f.push(MathJax.Hub.config.preRemoveClass)}if(b.ignoreClass){f.push(b.ignoreClass)}this.ignoreClass=(f.length?new RegExp("(^| )("+f.join("|")+")( |$)"):/^$/);this.processClass=new RegExp("(^| )("+b.processClass+")( |$)");return(e.length>0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d<c?-1:1))},scanElement:function(c,b,g){var a,e,d,f;while(c&&c!=b){if(c.nodeName.toLowerCase()==="#text"){if(!g){c=this.scanText(c)}}else{a=(typeof(c.className)==="undefined"?"":c.className);e=(typeof(c.tagName)==="undefined"?"":c.tagName);if(typeof(a)!=="string"){a=String(a)}f=this.processClass.exec(a);if(c.firstChild&&!a.match(/(^| )MathJax/)&&(f||!this.skipTags.exec(e))){d=(g||this.ignoreClass.exec(a))&&!f;this.scanElement(c.firstChild,b,d)}}if(c){c=c.nextSibling}}},scanText:function(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&&this.ignoreTags[b.nodeName.toLowerCase()]!=null);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,g=a.close,f,d,c;if(a.cpos===g.length){g=g.nextSibling}else{g=g.splitText(a.cpos)}if(!g){f=g=MathJax.HTML.addText(a.close.parentNode,"")}a.close=g;d=(a.opos?a.open.splitText(a.opos):a.open);while((c=d.nextSibling)&&c!==g){if(c.nodeValue!==null){if(c.nodeName==="#comment"){d.nodeValue+=c.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{d.nodeValue+=c.nodeValue}}else{var h=this.ignoreTags[c.nodeName.toLowerCase()];d.nodeValue+=(h==null?" ":h)}d.parentNode.removeChild(c)}var e=d.nodeValue.substr(a.olen,d.nodeValue.length-a.olen-a.clen);d.parentNode.removeChild(d);if(this.config.preview!=="none"){this.createPreview(a.mode,e)}d=this.createMathTag(a.mode,e);this.search={};this.pattern.lastIndex=0;if(f){f.parentNode.removeChild(f)}return d},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(d,a){var b=MathJax.Hub.config.preRemoveClass;var c=this.config.preview;if(c==="none"){return}if((this.search.close.previousSibling||{}).className===b){return}if(c==="TeX"){c=[this.filterPreview(a)]}if(c){c=MathJax.HTML.Element("span",{className:b},c);this.insertNode(c)}},createMathTag:function(c,b){var a=document.createElement("script");a.type="math/tex"+c;MathJax.HTML.setScript(a,b);this.insertNode(a);return a},filterPreview:function(a){return a}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js");
MathJax.Extension.mml2jax={version:"2.7.0",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(g,f){var e=this.config.preview;if(e==="none"){return}var i=false;var c=MathJax.Hub.config.preRemoveClass;if((f.previousSibling||{}).className===c){return}if(e==="mathml"){i=true;if(this.MathTagBug){e="alttext"}else{e=g.cloneNode(true)}}if(e==="alttext"||e==="altimg"){i=true;var d=this.filterPreview(g.getAttribute("alttext"));if(e==="alttext"){if(d!=null){e=MathJax.HTML.TextNode(d)}else{e=null}}else{var a=g.getAttribute("altimg");if(a!=null){var b={width:g.getAttribute("altimg-width"),height:g.getAttribute("altimg-height")};e=MathJax.HTML.Element("img",{src:a,alt:d,style:b})}else{e=null}}}if(e){var h;if(i){h=MathJax.HTML.Element("span",{className:c});h.appendChild(e)}else{h=MathJax.HTML.Element("span",{className:c},e)}f.parentNode.insertBefore(h,f)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"<math><mi>x</mi><mspace /></math>"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="&lt;"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax],5);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js");
MathJax.Extension.asciimath2jax={version:"2.7.0",config:{delimiters:[["`","`"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"asciimath2jax_ignore",processClass:"asciimath2jax_process",preview:"AsciiMath"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},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&&this.ignoreTags[b.nodeName.toLowerCase()]!=null);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,g=a.close,f,d,c;if(a.cpos===g.length){g=g.nextSibling}else{g=g.splitText(a.cpos)}if(!g){f=g=MathJax.HTML.addText(a.close.parentNode,"")}a.close=g;d=(a.opos?a.open.splitText(a.opos):a.open);while((c=d.nextSibling)&&c!==g){if(c.nodeValue!==null){if(c.nodeName==="#comment"){d.nodeValue+=c.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{d.nodeValue+=d.nextSibling.nodeValue}}else{var h=this.ignoreTags[c.nodeName.toLowerCase()];d.nodeValue+=(h==null?" ":h)}d.parentNode.removeChild(c)}var e=d.nodeValue.substr(a.olen,d.nodeValue.length-a.olen-a.clen);d.parentNode.removeChild(d);if(this.config.preview!=="none"){this.createPreview(a.mode,e)}d=this.createMathTag(a.mode,e);this.search={};this.pattern.lastIndex=0;if(f){f.parentNode.removeChild(f)}return d},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(d,a){var b=MathJax.Hub.config.preRemoveClass;var c=this.config.preview;if(c==="none"){return}if((this.search.close.previousSibling||{}).className===b){return}if(c==="AsciiMath"){c=[this.filterPreview(a)]}if(c){c=MathJax.HTML.Element("span",{className:b},c);this.insertNode(c)}},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}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.asciimath2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/asciimath2jax.js");
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(function(a,d,f,c,j){var k="2.7.0";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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g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;N<K;N++){this.items[N].Create(v)}if(g.isMobile){o.addElement(v,"span",{className:"MathJax_MenuClose",menu:E,ontouchstart:g.Close,ontouchend:n,onmousedown:g.Close,onmouseup:n},[["span",{},"\u00D7"]])}I.appendChild(v);this.posted=true;if(v.offsetWidth){v.style.width=(v.offsetWidth+2)+"px"}var H=M.pageX,F=M.pageY;var u=document.body.getBoundingClientRect();var C=(window.getComputedStyle?window.getComputedStyle(document.body):{marginLeft:"0px"});var A=u.right-Math.min(0,u.left)+parseFloat(C.marginLeft);if(!H&&!F&&"clientX" in M){H=M.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;F=M.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!E){var L=g.CurrentNode()||M.target;if((M.type==="keydown"||(!H&&!F))&&L){var P=window.pageXOffset||document.documentElement.scrollLeft;var O=window.pageYOffset||document.documentElement.scrollTop;var 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(function(d,c,j){var i,h="\u00A0";var k=function(m){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",m]].concat([].slice.call(arguments,1)))};var f=MathJax.Object.isArray;var e=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o<n;o++){p=arguments[o];if(!p){continue}if(p instanceof i.mbase){p=b.mml(p)}p.global=this.global;q=(this.data.length?this.Top().checkItem(p):true);if(q instanceof Array){this.Pop();this.Push.apply(this,q)}else{if(q instanceof b){this.Pop();this.Push(q)}else{if(q){this.data.push(p);if(p.env){if(p.copyEnv!==false){for(var r in this.env){if(this.env.hasOwnProperty(r)){p.env[r]=this.env[r]}}}this.env=p.env}else{p.env=this.env}}}}}},Pop:function(){var m=this.data.pop();if(!m.isOpen){delete m.env}this.env=(this.data.length?this.Top().env:{});return 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i.mrow.apply(i,this.data).With((m?{inferred:true}:{}))},checkItem:function(m){if(m.type==="over"&&this.isOpen){m.num=this.mmlData(false);this.data=[]}if(m.type==="cell"&&this.isOpen){if(m.linebreak){return false}d.Error(["Misplaced","Misplaced %1",m.name])}if(m.isClose&&this[m.type+"Error"]){d.Error(this[m.type+"Error"])}if(!m.isNotStack){return true}this.Push(m.data[0]);return false},With:function(m){for(var n in m){if(m.hasOwnProperty(n)){this[n]=m[n]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:true,Init:function(m){this.SUPER(arguments).Init.call(this);this.global=m},checkItem:function(m){if(m.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,m)}});b.stop=b.Subclass({type:"stop",isClose:true});b.open=b.Subclass({type:"open",isOpen:true,stopError:["ExtraOpenMissingClose","Extra open brace or missing close brace"],checkItem:function(n){if(n.type==="close"){var 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b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,m)){d.Error(this[["","subError","supError"][this.position]])}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:true,name:"\\over",checkItem:function(o,m){if(o.type==="over"){d.Error(["AmbiguousUseOf","Ambiguous use of %1",o.name])}if(o.isClose){var n=i.mfrac(this.num,this.mmlData(false));if(this.thickness!=null){n.linethickness=this.thickness}if(this.open||this.close){n.texWithDelims=true;n=d.fixedFence(this.open,n,this.close)}return[b.mml(n),o]}return this.SUPER(arguments).checkItem.call(this,o)},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(m){if(m.type==="right"){return b.mml(d.fenced(this.delim,this.mmlData(),m.delim))}return this.SUPER(arguments).checkItem.call(this,m)}});b.right=b.Subclass({type:"right",isClose:true,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:true,checkItem:function(m){if(m.type==="end"){if(m.name!==this.name){d.Error(["EnvBadEnd","\\begin{%1} ended with \\end{%2}",this.name,m.name])}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(m.type==="stop"){d.Error(["EnvMissingEnd","Missing \\end{%1}",this.name])}return this.SUPER(arguments).checkItem.call(this,m)}});b.end=b.Subclass({type:"end",isClose:true});b.style=b.Subclass({type:"style",checkItem:function(n){if(!n.isClose){return this.SUPER(arguments).checkItem.call(this,n)}var m=i.mstyle.apply(i,this.data).With(this.styles);return[b.mml(m),n]}});b.position=b.Subclass({type:"position",checkItem:function(n){if(n.isClose){d.Error(["MissingBoxFor","Missing box for %1",this.name])}if(n.isNotStack){var m=n.mmlData();switch(this.move){case"vertical":m=i.mpadded(m).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(m)];case"horizontal":return[b.mml(this.left),n,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,n)}});b.array=b.Subclass({type:"array",isOpen:true,copyEnv:false,arraydef:{},Init:function(){this.table=[];this.row=[];this.frame=[];this.hfill=[];this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(n){if(n.isClose&&n.type!=="over"){if(n.isEntry){this.EndEntry();this.clearEnv();return false}if(n.isCR){this.EndEntry();this.EndRow();this.clearEnv();return false}this.EndTable();this.clearEnv();var o=this.arraydef.scriptlevel;delete this.arraydef.scriptlevel;var m=i.mtable.apply(i,this.table).With(this.arraydef);if(this.frame.length===4){m.frame=(this.frame.dashed?"dashed":"solid")}else{if(this.frame.length){m.hasFrame=true;if(this.arraydef.rowlines){this.arraydef.rowlines=this.arraydef.rowlines.replace(/none( 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m=i.mtr;if(this.isNumbered&&this.row.length===3){this.row.unshift(this.row.pop());m=i.mlabeledtr}this.table.push(m.apply(i,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 m=this.arraydef.rowlines.split(/ /);if(m.length===this.table.length){this.frame.push("bottom");m.pop();this.arraydef.rowlines=m.join(" ")}else{if(m.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}if(this.rowspacing){var n=this.arraydef.rowspacing.split(/ /);while(n.length<this.table.length){n.push(this.rowspacing+"em")}this.arraydef.rowspacing=n.join(" ")}},clearEnv:function(){for(var m in this.env){if(this.env.hasOwnProperty(m)){delete this.env[m]}}}});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(n){if(this.data[0]){if(n.isOpen){return true}if(n.type!=="fn"){if(n.type!=="mml"||!n.data[0]){return[this.data[0],n]}if(n.data[0].isa(i.mspace)){return[this.data[0],n]}var m=n.data[0];if(m.isEmbellished()){m=m.CoreMO()}if([0,0,1,1,0,1,1,0,0,0][m.Get("texClass")]){return[this.data[0],n]}}return[this.data[0],i.mo(i.entity("#x2061")).With({texClass:i.TEXCLASS.NONE}),n]}return this.SUPER(arguments).checkItem.apply(this,arguments)}});b.not=b.Subclass({type:"not",checkItem:function(n){var m,o;if(n.type==="open"||n.type==="left"){return true}if(n.type==="mml"&&n.data[0].type.match(/^(mo|mi|mtext)$/)){m=n.data[0],o=m.data.join("");if(o.length===1&&!m.movesupsub){o=b.not.remap[o.charCodeAt(0)];if(o){m.SetData(0,i.chars(String.fromCharCode(o)))}else{m.Append(i.chars("\u0338"))}return 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n=o.movesupsub,m=o.sub;if((o.type==="msubsup"&&o.data[o.sub])||(o.type==="munderover"&&o.data[o.under]&&!o.subsupOK)){d.Error(["DoubleSubscripts","Double subscripts: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.under]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.under}else{o=i.msubsup(o,null,null);m=o.sub}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(o){var n=this.stack.Prev();if(!n){n=i.mi()}if(n.type==="msubsup"&&n.data[n.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=["","\u2032","\u2033","\u2034","\u2057"][m.length]||m;this.Push(b.prime(n,this.mmlToken(i.mo(m))))},mi2mo:function(m){var n=i.mo();n.Append.apply(n,m.data);var o;for(o in n.defaults){if(n.defaults.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}for(o in i.copyAttributes){if(i.copyAttributes.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}n.lspace=n.rspace="0";n.useMMLspacing&=~(n.SPACE_ATTR.lspace|n.SPACE_ATTR.rspace);return n},Comment:function(m){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(m){d.Error(["CantUseHash1","You can't use 'macro parameter character #' in math mode"])},Other:function(o){var n,m;if(this.stack.env.font){n={mathvariant:this.stack.env.font}}if(g.remap[o]){o=g.remap[o];if(f(o)){n=o[1];o=o[0]}m=i.mo(i.entity("#x"+o)).With(n)}else{m=i.mo(o).With(n)}if(m.autoDefault("stretchy",true)){m.stretchy=false}if(m.autoDefault("texClass",true)==""){m=i.TeXAtom(m)}this.Push(this.mmlToken(m))},SetFont:function(n,m){this.stack.env.font=m},SetStyle:function(n,m,o,p){this.stack.env.style=m;this.stack.env.level=p;this.Push(b.style().With({styles:{displaystyle:o,scriptlevel:p}}))},SetSize:function(m,n){this.stack.env.size=n;this.Push(b.style().With({styles:{mathsize:n+"em"}}))},Color:function(o){var n=this.GetArgument(o);var m=this.stack.env.color;this.stack.env.color=n;var p=this.ParseArg(o);if(m){this.stack.env.color}else{delete this.stack.env.color}this.Push(i.mstyle(p).With({mathcolor:n}))},Spacer:function(m,n){this.Push(i.mspace().With({width:n,mathsize:i.SIZE.NORMAL,scriptlevel:0}))},LeftRight:function(m){this.Push(b[m.substr(1)]().With({delim:this.GetDelimiter(m)}))},Middle:function(m){var n=this.GetDelimiter(m);this.Push(i.TeXAtom().With({texClass:i.TEXCLASS.CLOSE}));if(this.stack.Top().type!=="left"){d.Error(["MisplacedMiddle","%1 must be within \\left and \\right",m])}this.Push(i.mo(n).With({stretchy:true}));this.Push(i.TeXAtom().With({texClass:i.TEXCLASS.OPEN}))},NamedFn:function(n,o){if(!o){o=n.substr(1)}var m=i.mi(o).With({texClass:i.TEXCLASS.OP});this.Push(b.fn(this.mmlToken(m)))},NamedOp:function(n,o){if(!o){o=n.substr(1)}o=o.replace(/&thinsp;/,"\u2006");var m=i.mo(o).With({movablelimits:true,movesupsub:true,form:i.FORM.PREFIX,texClass:i.TEXCLASS.OP});m.useMMLspacing&=~m.SPACE_ATTR.form;this.Push(this.mmlToken(m))},Limits:function(n,m){var p=this.stack.Prev("nopop");if(!p||(p.Get("texClass")!==i.TEXCLASS.OP&&p.movesupsub==null)){d.Error(["MisplacedLimits","%1 is allowed only on operators",n])}var o=this.stack.Top();if(p.type==="munderover"&&!m){p=o.data[o.data.length-1]=i.msubsup.apply(i.subsup,p.data)}else{if(p.type==="msubsup"&&m){p=o.data[o.data.length-1]=i.munderover.apply(i.underover,p.data)}}p.movesupsub=(m?true:false);p.Core().movablelimits=false;if(p.movablelimits){p.movablelimits=false}},Over:function(o,n,p){var m=b.over().With({name:o});if(n||p){m.open=n;m.close=p}else{if(o.match(/withdelims$/)){m.open=this.GetDelimiter(o);m.close=this.GetDelimiter(o)}}if(o.match(/^\\above/)){m.thickness=this.GetDimen(o)}else{if(o.match(/^\\atop/)||n||p){m.thickness=0}}this.Push(m)},Frac:function(n){var m=this.ParseArg(n);var o=this.ParseArg(n);this.Push(i.mfrac(m,o))},Sqrt:function(p){var q=this.GetBrackets(p),m=this.GetArgument(p);if(m==="\\frac"){m+="{"+this.GetArgument(m)+"}{"+this.GetArgument(m)+"}"}var o=d.Parse(m,this.stack.env).mml();if(!q){o=i.msqrt.apply(i,o.array())}else{o=i.mroot(o,this.parseRoot(q))}this.Push(o)},Root:function(o){var p=this.GetUpTo(o,"\\of");var m=this.ParseArg(o);this.Push(i.mroot(m,this.parseRoot(p)))},parseRoot:function(r){var o=this.stack.env,m=o.inRoot;o.inRoot=true;var q=d.Parse(r,o);r=q.mml();var p=q.stack.global;if(p.leftRoot||p.upRoot){r=i.mpadded(r);if(p.leftRoot){r.width=p.leftRoot}if(p.upRoot){r.voffset=p.upRoot;r.height=p.upRoot}}o.inRoot=m;return r},MoveRoot:function(m,p){if(!this.stack.env.inRoot){d.Error(["MisplacedMoveRoot","%1 can appear only within a root",m])}if(this.stack.global[p]){d.Error(["MultipleMoveRoot","Multiple use of %1",m])}var o=this.GetArgument(m);if(!o.match(/-?[0-9]+/)){d.Error(["IntegerArg","The argument to %1 must be an integer",m])}o=(o/15)+"em";if(o.substr(0,1)!=="-"){o="+"+o}this.stack.global[p]=o},Accent:function(o,m,s){var r=this.ParseArg(o);var q={accent:true};if(this.stack.env.font){q.mathvariant=this.stack.env.font}var n=this.mmlToken(i.mo(i.entity("#x"+m)).With(q));n.stretchy=(s?true:false);var p=(r.isEmbellished()?r.CoreMO():r);if(p.isa(i.mo)){p.movablelimits=false}this.Push(i.TeXAtom(i.munderover(r,null,n).With({accent:true})))},UnderOver:function(o,s,m,q){var r={o:"over",u:"under"}[o.charAt(1)];var p=this.ParseArg(o);if(p.Get("movablelimits")){p.movablelimits=false}if(p.isa(i.munderover)&&p.isEmbellished()){p.Core().With({lspace:0,rspace:0});p=i.mrow(i.mo().With({rspace:0}),p)}var n=i.munderover(p,null,null);n.SetData(n[r],this.mmlToken(i.mo(i.entity("#x"+s)).With({stretchy:true,accent:!q})));if(m){n=i.TeXAtom(n).With({texClass:i.TEXCLASS.OP,movesupsub:true})}this.Push(n.With({subsupOK:true}))},Overset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);if(n.movablelimits){n.movablelimits=false}this.Push(i.mover(n,o))},Underset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);if(n.movablelimits){n.movablelimits=false}this.Push(i.munder(n,o))},TeXAtom:function(p,r){var q={texClass:r},o;if(r==i.TEXCLASS.OP){q.movesupsub=q.movablelimits=true;var m=this.GetArgument(p);var n=m.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(n){q.mathvariant=i.VARIANT.NORMAL;o=b.fn(this.mmlToken(i.mi(n[1]).With(q)))}else{o=b.fn(i.TeXAtom(d.Parse(m,this.stack.env).mml()).With(q))}}else{o=i.TeXAtom(this.ParseArg(p)).With(q)}this.Push(o)},MmlToken:function(o){var p=this.GetArgument(o),m=this.GetBrackets(o,"").replace(/^\s+/,""),s=this.GetArgument(o),r={attrNames:[]},n;if(!i[p]||!i[p].prototype.isToken){d.Error(["NotMathMLToken","%1 is not a token element",p])}while(m!==""){n=m.match(/^([a-z]+)\s*=\s*('[^']*'|"[^"]*"|[^ ,]*)\s*,?\s*/i);if(!n){d.Error(["InvalidMathMLAttr","Invalid MathML attribute: %1",m])}if(i[p].prototype.defaults[n[1]]==null&&!this.MmlTokenAllow[n[1]]){d.Error(["UnknownAttrForElement","%1 is not a recognized attribute for 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m=i.mpadded(this.ParseArg(n)).With({width:0});if(n==="\\llap"){m.lspace="-1width"}this.Push(i.TeXAtom(m))},RaiseLower:function(m){var n=this.GetDimen(m);var o=b.position().With({name:m,move:"vertical"});if(n.charAt(0)==="-"){n=n.slice(1);m={raise:"\\lower",lower:"\\raise"}[m.substr(1)]}if(m==="\\lower"){o.dh="-"+n;o.dd="+"+n}else{o.dh="+"+n;o.dd="-"+n}this.Push(o)},MoveLeftRight:function(m){var p=this.GetDimen(m);var o=(p.charAt(0)==="-"?p.slice(1):"-"+p);if(m==="\\moveleft"){var n=p;p=o;o=n}this.Push(b.position().With({name:m,move:"horizontal",left:i.mspace().With({width:p,mathsize:i.SIZE.NORMAL}),right:i.mspace().With({width:o,mathsize:i.SIZE.NORMAL})}))},Hskip:function(m){this.Push(i.mspace().With({width:this.GetDimen(m),mathsize:i.SIZE.NORMAL}))},Rule:function(o,q){var m=this.GetDimen(o),p=this.GetDimen(o),s=this.GetDimen(o);var n,r={width:m,height:p,depth:s};if(q!=="blank"){if(parseFloat(m)&&parseFloat(p)+parseFloat(s)){r.mathbackground=(this.stack.env.color||"black")}n=i.mpadded(i.mrow()).With(r)}else{n=i.mspace().With(r)}this.Push(n)},MakeBig:function(m,p,n){n*=g.p_height;n=String(n).replace(/(\.\d\d\d).+/,"$1")+"em";var o=this.GetDelimiter(m,true);this.Push(i.TeXAtom(i.mo(o).With({minsize:n,maxsize:n,fence:true,stretchy:true,symmetric:true})).With({texClass:p}))},BuildRel:function(m){var n=this.ParseUpTo(m,"\\over");var o=this.ParseArg(m);this.Push(i.TeXAtom(i.munderover(o,null,n)).With({texClass:i.TEXCLASS.REL}))},HBox:function(m,n){this.Push.apply(this,this.InternalMath(this.GetArgument(m),n))},FBox:function(m){this.Push(i.menclose.apply(i,this.InternalMath(this.GetArgument(m))).With({notation:"box"}))},Not:function(m){this.Push(b.not())},Dots:function(m){this.Push(b.dots().With({ldots:this.mmlToken(i.mo(i.entity("#x2026")).With({stretchy:false})),cdots:this.mmlToken(i.mo(i.entity("#x22EF")).With({stretchy:false}))}))},Require:function(m){var n=this.GetArgument(m).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");this.Extension(null,n)},Extension:function(m,n,o){if(m&&!typeof(m)==="string"){m=m.name}n=d.extensionDir+"/"+n;if(!n.match(/\.js$/)){n+=".js"}if(!j.loaded[j.fileURL(n)]){if(m!=null){delete g[o||"macros"][m.replace(/^\\/,"")]}c.RestartAfter(j.Require(n))}},Macro:function(o,r,q,s){if(q){var n=[];if(s!=null){var m=this.GetBrackets(o);n.push(m==null?s:m)}for(var p=n.length;p<q;p++){n.push(this.GetArgument(o))}r=this.SubstituteArgs(n,r)}this.string=this.AddArgs(r,this.string.slice(this.i));this.i=0;if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(n,p,v,r,u,o,m,w,t){var s=this.GetNext();if(s===""){d.Error(["MissingArgFor","Missing argument for %1",n])}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:true,arraydef:{rowspacing:(o||"4pt"),columnspacing:(u||"1em")}});if(w){q.isCases=true}if(t){q.isNumbered=true;q.arraydef.side=t}if(p||v){q.open=p;q.close=v}if(m==="D"){q.arraydef.displaystyle=true}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:true,name:p}));if(this.stack.Top().isCases){var o=this.string;var s=0,q=this.i,n=o.length;while(q<n){var t=o.charAt(q);if(t==="{"){s++;q++}else{if(t==="}"){if(s===0){n=0}else{s--;q++}}else{if(t==="&"&&s===0){d.Error(["ExtraAlignTab","Extra alignment tab in \\cases text"])}else{if(t==="\\"){if(o.substr(q).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){n=0}else{q+=2}}else{q++}}}}}var r=o.substr(this.i,q-this.i);if(!r.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(r,0));this.i=q}}},Cr:function(m){this.Push(b.cell().With({isCR:true,name:m}))},CrLaTeX:function(m){var q;if(this.string.charAt(this.i)==="["){q=this.GetBrackets(m,"").replace(/ /g,"").replace(/,/,".");if(q&&!this.matchDimen(q)){d.Error(["BracketMustBeDimension","Bracket argument to %1 must be a dimension",m])}}this.Push(b.cell().With({isCR:true,name:m,linebreak:true}));var p=this.stack.Top();if(p.isa(b.array)){if(q&&p.arraydef.rowspacing){var o=p.arraydef.rowspacing.split(/ 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p=this.stack.Top();if(!p.isa(b.array)||p.data.length){d.Error(["Misplaced","Misplaced %1",n])}if(p.table.length==0){p.frame.push("top")}else{var m=(p.arraydef.rowlines?p.arraydef.rowlines.split(/ /):[]);while(m.length<p.table.length){m.push("none")}m[p.table.length-1]=o;p.arraydef.rowlines=m.join(" ")}},HFill:function(m){var n=this.stack.Top();if(n.isa(b.array)){n.hfill.push(n.data.length)}else{d.Error(["UnsupportedHFill","Unsupported use of %1",m])}},BeginEnd:function(o){var p=this.GetArgument(o),r=false;if(p.match(/^\\end\\/)){r=true;p=p.substr(5)}if(p.match(/\\/i)){d.Error(["InvalidEnv","Invalid environment name '%1'",p])}var q=this.envFindName(p);if(!q){d.Error(["UnknownEnv","Unknown environment '%1'",p])}if(!f(q)){q=[q]}var m=(f(q[1])?q[1][0]:q[1]);var n=b.begin().With({name:p,end:m,parse:this});if(o==="\\end"){if(!r&&f(q[1])&&this[q[1][1]]){n=this[q[1][1]].apply(this,[n].concat(q.slice(2)))}else{n=b.end().With({name:p})}}else{if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(q[0]&&this[q[0]]){n=this[q[0]].apply(this,[n].concat(q.slice(2)))}}this.Push(n)},envFindName:function(m){return g.environment[m]},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(n,p,u,s,t,o,m,q){if(!s){s=this.GetArgument("\\begin{"+n.name+"}")}var v=("c"+s).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");s=s.replace(/[^clr]/g,"").split("").join(" ");s=s.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var 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w=s[u.n];v.text+=w.c;v.className=s.className;if(x.h<w[0]+k){x.t=x.h=w[0]+k}if(x.d<w[1]+a){x.b=x.d=w[1]+a}if(x.l>x.w+w[3]){x.l=x.w+w[3]}if(x.r<x.w+w[4]){x.r=x.w+w[4]}x.w+=w[2]*(u.rscale||1);if(r==1&&s.skew&&s.skew[u.n]){x.skew=s.skew[u.n]}if(w[5].rfix){this.flushText(t,v).style.marginRight=h.Em(w[5].rfix/1000)}},space:function(s,r,u,t){if(s.w){if(t.text===""){t.className=s.font.className}this.flushText(r,t).style.marginRight=h.Em(s.w);u.w+=s.w}},unknown:function(s,r,v,t){(this["char"])(s,r,v,t,0);var u=s.font[s.n];if(u[5].a){t.a=u[5].a;if(v.a==null||t.a>v.a){v.a=t.a}}r=this.flushText(r,t,s.style);r.style.width=h.Em(u[2])},flushText:function(s,t,r){s=h.addElement(s,"mjx-charbox",{className:t.className,style:r},[t.text]);if(t.a){s.style.paddingBottom=h.Em(t.a)}t.text="";t.className=null;t.a=0;t.flushed=true;return s}},handleText:function(t,w,s,v){if(t.childNodes.length===0){h.addElement(t,"mjx-char");v=h.BBOX.empty(v)}if(typeof(s)==="string"){s=this.FONTDATA.VARIANT[s]}if(!s){s=this.FONTDATA.VARIANT[i.VARIANT.NORMAL]}var r={text:w,i:0,length:w.length},u=[];if(s.style&&r.length){u.push(this.styledText(s,w))}else{while(r.i<r.length){var x=this.getUnicode(r);u.push.apply(u,this.getCharList(s,x))}}if(u.length){this.addCharList(t.firstChild,u,v)}v.clean();if(v.d<0){v.D=v.d;v.d=0}if(v.h-v.a){t.firstChild.style[v.h-v.a<0?"marginTop":"paddingTop"]=this.EmRounded(v.h-v.a)}if(v.d>-v.b){t.firstChild.style.paddingBottom=this.EmRounded(v.d+v.b)}return v},createDelimiter:function(w,r,t,z,u){if(!r){var A=this.BBOX.zero();A.w=A.r=this.TEX.nulldelimiterspace;h.addElement(w,"mjx-box",{style:{width:A.w}});return A}if(!(t instanceof Array)){t=[t,t]}var y=t[1];t=t[0];var s={alias:r};while(s.alias){r=s.alias;s=this.FONTDATA.DELIMITERS[r];if(!s){s={HW:[0,this.FONTDATA.VARIANT[i.VARIANT.NORMAL]]}}}if(s.load){c.RestartAfter(j.Require(this.fontDir+"/TeX/fontdata-"+s.load+".js"))}for(var x=0,v=s.HW.length;x<v;x++){if(s.HW[x][0]>=t-0.01||(x==v-1&&!s.stretch)){if(s.HW[x][3]){r=s.HW[x][3]}A=this.createChar(w,[r,s.HW[x][1]],(s.HW[x][2]||1),u);A.offset=0.6*A.w;if(z){A.scale=z.scale;z.rscale=z.rscale}return A}}if(!s.stretch){return A}return this["extendDelimiter"+s.dir](w,y,s.stretch,z,u)},extendDelimiterV:function(D,w,O,v,B){D=h.addElement(D,"mjx-delim-v");var M=h.Element("span");var A,z,N,u,G,s,E,x,F=1,L;G=this.createChar(M,(O.top||O.ext),1,B);A=M.removeChild(M.firstChild);s=this.createChar(M,(O.bot||O.ext),1,B);z=M.removeChild(M.firstChild);E=x=h.BBOX.zero();var 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r=h.BBOX({w:Math.max(G.w,x.w,s.w,E.w),l:Math.min(G.l,x.l,s.l,E.l),r:Math.max(G.r,x.r,s.r,E.r),h:w-s.d,d:s.d,t:w-s.d,b:s.d});r.offset=0.5*r.w;if(v){r.scale=v.scale;r.rscale=v.rscale}return r},extendDelimiterH:function(E,r,O,u,C){E=h.addElement(E,"mjx-delim-h");var M=h.Element("span");var s,L,N,t,J,B,v,F,y,G=1;B=this.createChar(M,(O.left||O.rep),1,C);s=M.removeChild(M.firstChild);v=this.createChar(M,(O.right||O.rep),1,C);L=M.removeChild(M.firstChild);y=this.createChar(M,O.rep,1,C);t=M.removeChild(M.firstChild);s.style.marginLeft=h.Em(-B.l);L.style.marginRight=h.Em(v.r-v.w);E.appendChild(s);var P=h.BBOX.zero();P.h=Math.max(B.h,v.h,y.h);P.d=Math.max(B.D||B.d,v.D||v.d,y.D||y.d);var x=(B.r-B.l)+(v.r-v.l)-q;if(O.mid){F=this.createChar(M,O.mid,1,C);N=M.removeChild(M.firstChild);N.style.marginleft=h.Em(-F.l);N.style.marginRight=h.Em(F.r-F.w);x+=F.r-F.l+q;G=2;if(F.h>P.h){P.h=F.h}if(F.d>P.d){P.d=F.d}}if(O.min&&r<x*O.min){r=x*O.min}P.w=P.r=r;if(r>x){var A=y.r-y.l,I=A-q;var 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r=this.Core();if(r&&r!==this){s=r.CHTMLcanStretch(v,t,u)}}this.CHTML.stretch=s;return s},CHTMLstretchV:function(r,s){this.CHTML.updateFrom(this.Core().CHTMLstretchV(r,s));return this.CHTML},CHTMLstretchH:function(s,r){this.CHTML.updateFrom(this.CHTMLstretchCoreH(s,r));return this.CHTML},CHTMLstretchCoreH:function(s,r){return this.Core().CHTMLstretchH(this.CHTMLcoreNode(s),r)},CHTMLcreateNode:function(r){if(!this.CHTML){this.CHTML={}}this.CHTML=h.BBOX.zero();if(this.href){r=h.addElement(r,"a",{href:this.href,isMathJax:true})}if(!this.CHTMLnodeID){this.CHTMLnodeID=h.GetID()}var s=(this.id||"MJXc-Node-"+this.CHTMLnodeID)+h.idPostfix;return this.CHTMLhandleAttributes(h.addElement(r,"mjx-"+this.type,{id:s}))},CHTMLnodeElement:function(){if(!this.CHTMLnodeID){return null}return document.getElementById((this.id||"MJXc-Node-"+this.CHTMLnodeID)+h.idPostfix)},CHTMLlength2em:function(s,r){return h.length2em(s,r,this.CHTML.scale)},CHTMLhandleAttributes:function(u){if(this["class"]){if(u.className){u.className+=" "+this["class"]}else{u.className=this["class"]}}if(this.attrNames){var y=this.attrNames,t=i.nocopyAttributes,x=c.config.ignoreMMLattributes;var v=(this.type==="mstyle"?i.math.prototype.defaults:this.defaults);for(var s=0,r=y.length;s<r;s++){var w=y[s];if(x[w]==false||(!t[w]&&!x[w]&&v[w]==null&&typeof(u[w])==="undefined")){u.setAttribute(w,this.attr[w])}}}return u},CHTMLhandleScale:function(u){var w=1,t=this.parent,v=(t?t.CHTML.scale:1);var r=this.getValues("scriptlevel","fontsize");r.mathsize=this.Get("mathsize",null,!this.isToken);if(r.scriptlevel!==0){if(r.scriptlevel>2){r.scriptlevel=2}w=Math.pow(this.Get("scriptsizemultiplier"),r.scriptlevel);r.scriptminsize=h.length2em(this.Get("scriptminsize"),0.8,1);if(w<r.scriptminsize){w=r.scriptminsize}}if(this.removedStyles&&this.removedStyles.fontSize&&!r.fontsize){r.fontsize=this.removedStyles.fontSize}if(r.fontsize&&!this.mathsize){r.mathsize=r.fontsize}if(r.mathsize!==1){w*=h.length2em(r.mathsize,1,1)}var s=this.CHTMLvariant;if(s&&s.style&&s.style["font-family"]){w*=(h.config.scale/100)/h.scale}this.CHTML.scale=w;v=this.CHTML.rscale=w/v;if(Math.abs(v-1)<0.001){v=1}if(u&&v!==1){u.style.fontSize=h.Percent(v)}return w},CHTMLhandleStyle:function(u){if(!this.style){return}var t=u.style;t.cssText=this.style;this.removedStyles={};for(var s=0,r=h.removeStyles.length;s<r;s++){var v=h.removeStyles[s];if(t[v]){this.removedStyles[v]=t[v];t[v]=""}}},CHTMLhandleBBox:function(v){var s=this.CHTML,u=v.style;if(this.data.length===1&&(this.data[0].CHTML||{}).pwidth){s.pwidth=this.data[0].CHTML.pwidth;s.mwidth=this.data[0].CHTML.mwidth;u.width="100%"}else{if(s.pwidth){s.mwidth=h.Em(s.w);u.width="100%"}else{if(s.w<0){u.width="0px";u.marginRight=h.Em(s.w)}}}if(!this.style){return}for(var t=0,r=h.BBOX.styleAdjust.length;t<r;t++){var w=h.BBOX.styleAdjust[t];if(w&&u[w[0]]){s.adjust(u[w[0]],w[1],w[2],w[3])}}},CHTMLhandleColor:function(r){if(this.mathcolor){r.style.color=this.mathcolor}else{if(this.color){r.style.color=this.color}}if(this.mathbackground){r.style.backgroundColor=this.mathbackground}else{if(this.background){r.style.backgroundColor=this.background}}},CHTMLhandleSpace:function(r){if(!this.useMMLspacing){var s=this.texSpacing();if(s!==""){this.CHTML.L=this.CHTMLlength2em(s);r.className+=" 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s=r.mathvariant;if(this.variantForm){s="-TeX-variant"}if(r.family&&!r.hasVariant){if(!r.weight&&r.mathvariant.match(/bold/)){r.weight="bold"}if(!r.style&&r.mathvariant.match(/italic/)){r.style="italic"}this.CHTMLvariant={fonts:[],noRemap:true,cache:{},style:{"font-family":r.family,"font-weight":r.weight||"normal","font-style":r.style||"normal"}};return}if(r.weight==="bold"){s={normal:i.VARIANT.BOLD,italic:i.VARIANT.BOLDITALIC,fraktur:i.VARIANT.BOLDFRAKTUR,script:i.VARIANT.BOLDSCRIPT,"sans-serif":i.VARIANT.BOLDSANSSERIF,"sans-serif-italic":i.VARIANT.SANSSERIFBOLDITALIC}[s]||s}else{if(r.weight==="normal"){s={bold:i.VARIANT.normal,"bold-italic":i.VARIANT.ITALIC,"bold-fraktur":i.VARIANT.FRAKTUR,"bold-script":i.VARIANT.SCRIPT,"bold-sans-serif":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.SANSSERIFITALIC}[s]||s}}if(r.style==="italic"){s={normal:i.VARIANT.ITALIC,bold:i.VARIANT.BOLDITALIC,"sans-serif":i.VARIANT.SANSSERIFITALIC,"bold-sans-serif":i.VARIANT.SANSSERIFBOLDITALIC}[s]||s}else{if(r.style==="normal"){s={italic:i.VARIANT.NORMAL,"bold-italic":i.VARIANT.BOLD,"sans-serif-italic":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.BOLDSANSSERIF}[s]||s}}this.CHTMLvariant=h.FONTDATA.VARIANT[s]||h.FONTDATA.VARIANT[i.VARIANT.NORMAL]},CHTMLbboxFor:function(r){if(this.data[r]&&this.data[r].CHTML){return this.data[r].CHTML}return h.BBOX.zero()},CHTMLdrawBBox:function(s,t){if(!t){t=this.CHTML}var r=h.Element("mjx-box",{style:{opacity:0.25,"margin-left":h.Em(-(t.w+(t.R||0)))}},[["mjx-box",{style:{height:h.Em(t.h),width:h.Em(t.w),"background-color":"red"}}],["mjx-box",{style:{height:h.Em(t.d),width:h.Em(t.w),"margin-left":h.Em(-t.w),"vertical-align":h.Em(-t.d),"background-color":"green"}}]]);if(s.nextSibling){s.parentNode.insertBefore(r,s.nextSibling)}else{s.parentNode.appendChild(r)}},CHTMLnotEmpty:function(r){while(r&&r.data.length<2&&(r.type==="mrow"||r.type==="texatom")){r=r.data[0]}return !!r}},{CHTMLautoload:function(){var r=h.autoloadDir+"/"+this.type+".js";c.RestartAfter(j.Require(r))},CHTMLautoloadFile:function(r){var s=h.autoloadDir+"/"+r+".js";c.RestartAfter(j.Require(s))},CHTMLstretchV:function(r,s){this.Core().CHTMLstretchV(r,s);this.toCommonHTML(this.CHTMLnodeElement(),{stretch:true});return this.CHTML},CHTMLstretchH:function(s,r){this.CHTMLstretchCoreH(s,r);this.toCommonHTML(s,{stretch:true});return this.CHTML}});i.chars.Augment({toCommonHTML:function(s,r){if(r==null){r={}}var t=this.toString();if(r.remap){t=r.remap(t,r.remapchars)}this.CHTMLhandleText(s,t,r.variant||this.parent.CHTMLvariant)}});i.entity.Augment({toCommonHTML:function(s,r){if(r==null){r={}}var t=this.toString();if(r.remapchars){t=r.remap(t,r.remapchars)}this.CHTMLhandleText(s,t,r.variant||this.parent.CHTMLvariant)}});i.math.Augment({toCommonHTML:function(w){w=this.CHTMLdefaultNode(w);if(this.CHTML.w<0){w.parentNode.style.width="0px";w.parentNode.style.marginRight=h.Em(this.CHTML.w)}var u=this.Get("alttext");if(u&&!w.getAttribute("aria-label")){w.setAttribute("aria-label",u)}if(this.CHTML.pwidth){w.parentNode.style.minWidth=this.CHTML.mwidth||h.Em(this.CHTML.w);w.parentNode.className="mjx-full-width "+w.parentNode.className;w.style.width=this.CHTML.pwidth}else{if(!this.isMultiline&&this.Get("display")==="block"){var t=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(t.indentalignfirst!==i.INDENTALIGN.INDENTALIGN){t.indentalign=t.indentalignfirst}if(t.indentalign===i.INDENTALIGN.AUTO){t.indentalign=o.displayAlign}if(t.indentshiftfirst!==i.INDENTSHIFT.INDENTSHIFT){t.indentshift=t.indentshiftfirst}if(t.indentshift==="auto"){t.indentshift="0"}var s=this.CHTMLlength2em(t.indentshift,h.cwidth);if(o.displayIndent!=="0"){var r=this.CHTMLlength2em(o.displayIndent,h.cwidth);s+=(t.indentalign===i.INDENTALIGN.RIGHT?-r:r)}var v=w.parentNode.parentNode.style;w.parentNode.style.textAlign=v.textAlign=t.indentalign;if(s){s*=h.em/h.outerEm;c.Insert(v,({left:{marginLeft:h.Em(s)},right:{marginRight:h.Em(-s)},center:{marginLeft:h.Em(s),marginRight:h.Em(-s)}})[t.indentalign])}}}return w}});i.mi.Augment({toCommonHTML:function(r){r=this.CHTMLdefaultNode(r);var t=this.CHTML,s=this.data.join("");if(t.skew!=null&&s.length!==1){delete t.skew}if(t.r>t.w&&s.length===1&&!this.CHTMLvariant.noIC){t.ic=t.r-t.w;t.w=t.r;r.lastChild.style.paddingRight=h.Em(t.ic)}return r}});i.mn.Augment({CHTMLremapMinus:function(r){return r.replace(/^-/,"\u2212")},toCommonHTML:function(r){r=this.CHTMLdefaultNode(r,{childOptions:{remap:this.CHTMLremapMinus}});var t=this.CHTML,s=this.data.join("");if(t.skew!=null&&s.length!==1){delete t.skew}if(t.r>t.w&&s.length===1&&!this.CHTMLvariant.noIC){t.ic=t.r-t.w;t.w=t.r;r.lastChild.style.paddingRight=h.Em(t.ic)}return r}});i.mo.Augment({toCommonHTML:function(u){u=this.CHTMLcreateNode(u);this.CHTMLhandleStyle(u);this.CHTMLgetVariant();this.CHTMLhandleScale(u);h.BBOX.empty(this.CHTML);var s=this.getValues("displaystyle","largeop");s.variant=this.CHTMLvariant;s.text=this.data.join("");if(s.text==""){if(this.fence){u.style.width=h.Em(h.TEX.nulldelimiterspace)}}else{this.CHTMLadjustAccent(s);this.CHTMLadjustVariant(s);for(var t=0,r=this.data.length;t<r;t++){this.CHTMLaddChild(u,t,{childOptions:{variant:s.mathvariant,remap:this.remap,remapchars:s.remapchars}})}if(s.text.length!==1){delete this.CHTML.skew}else{if(this.CHTML.w===0&&this.CHTML.l<0){this.CHTMLfixCombiningChar(u)}}if(s.largeop){this.CHTMLcenterOp(u)}}this.CHTML.clean();this.CHTMLhandleBBox(u);this.CHTMLhandleSpace(u);this.CHTMLhandleColor(u);return u},CHTMLhandleSpace:function(u){if(this.useMMLspacing){var s=this.getValues("scriptlevel","lspace","rspace");s.lspace=Math.max(0,this.CHTMLlength2em(s.lspace));s.rspace=Math.max(0,this.CHTMLlength2em(s.rspace));if(s.scriptlevel>0){if(!this.hasValue("lspace")){s.lspace=0.15}if(!this.hasValue("rspace")){s.rspace=0.15}}var r=this,t=this.Parent();while(t&&t.isEmbellished()&&t.Core()===r){r=t;t=t.Parent();u=r.CHTMLnodeElement()}if(s.lspace){u.style.paddingLeft=h.Em(s.lspace)}if(s.rspace){u.style.paddingRight=h.Em(s.rspace)}this.CHTML.L=s.lspace;this.CHTML.R=s.rspace}else{this.SUPER(arguments).CHTMLhandleSpace.apply(this,arguments)}},CHTMLadjustAccent:function(t){var s=this.CoreParent();t.parent=s;if(t.text.length===1&&s&&s.isa(i.munderover)&&this.CoreText(s.data[s.base]).length===1){var u=s.data[s.over],r=s.data[s.under];if(u&&this===u.CoreMO()&&s.Get("accent")){t.remapchars=h.FONTDATA.REMAPACCENT}else{if(r&&this===r.CoreMO()&&s.Get("accentunder")){t.remapchars=h.FONTDATA.REMAPACCENTUNDER}}}},CHTMLadjustVariant:function(s){var r=s.parent,t=(r&&r.isa(i.msubsup)&&this!==r.data[r.base]);if(s.largeop){s.mathvariant=(s.displaystyle?"-largeOp":"-smallOp")}if(t){s.remapchars=this.remapChars;if(s.text.match(/['`"\u00B4\u2032-\u2037\u2057]/)){s.mathvariant="-TeX-variant"}}},CHTMLfixCombiningChar:function(r){r=r.firstChild;var s=h.Element("mjx-box",{style:{width:".25em","margin-left":"-.25em"}});r.insertBefore(s,r.firstChild)},CHTMLcenterOp:function(r){var t=this.CHTML;var s=(t.h-t.d)/2-h.TEX.axis_height;if(Math.abs(s)>0.001){r.style.verticalAlign=h.Em(-s)}t.h-=s;t.d+=s;if(t.r>t.w){t.ic=t.r-t.w;t.w=t.r;r.style.paddingRight=h.Em(t.ic)}},CHTMLcanStretch:function(v,t,u){if(!this.Get("stretchy")){return false}var w=this.data.join("");if(w.length!==1){return false}var s={text:w};this.CHTMLadjustAccent(s);if(s.remapchars){w=s.remapchars[w]||w}w=h.FONTDATA.DELIMITERS[w.charCodeAt(0)];var r=(w&&w.dir===v.substr(0,1));if(r){r=(this.CHTML.h!==t||this.CHTML.d!==u||!!this.Get("minsize",true)||!!this.Get("maxsize",true));if(r){this.CHTML.stretch=true}}return r},CHTMLstretchV:function(u,x){var v=this.CHTMLnodeElement(),w=this.CHTML;var s=this.getValues("symmetric","maxsize","minsize");var t,r=h.TEX.axis_height;if(s.symmetric){t=2*Math.max(u-r,x+r)}else{t=u+x}s.maxsize=this.CHTMLlength2em(s.maxsize,w.h+w.d);s.minsize=this.CHTMLlength2em(s.minsize,w.h+w.d);t=Math.max(s.minsize,Math.min(s.maxsize,t));if(t!==w.sH){if(t!=s.minsize){t=[Math.max(t*h.TEX.delimiterfactor/1000,t-h.TEX.delimitershortfall),t]}while(v.firstChild){v.removeChild(v.firstChild)}this.CHTML=w=h.createDelimiter(v,this.data.join("").charCodeAt(0),t,w);w.sH=(t instanceof Array?t[1]:t);if(s.symmetric){t=(w.h+w.d)/2+r}else{t=(w.h+w.d)*u/(u+x)}t-=w.h;if(Math.abs(t)>0.05){v.style.verticalAlign=h.Em(t);w.h+=t;w.d-=t;w.t+=t;w.b-=t}}return this.CHTML},CHTMLstretchH:function(t,r){var u=this.CHTML;var s=this.getValues("maxsize","minsize","mathvariant","fontweight");if((s.fontweight==="bold"||(this.removedStyles||{}).fontWeight==="bold"||parseInt(s.fontweight)>=600)&&!this.Get("mathvariant",true)){s.mathvariant=i.VARIANT.BOLD}s.maxsize=this.CHTMLlength2em(s.maxsize,u.w);s.minsize=this.CHTMLlength2em(s.minsize,u.w);r=Math.max(s.minsize,Math.min(s.maxsize,r));if(r!==u.sW){while(t.firstChild){t.removeChild(t.firstChild)}this.CHTML=u=h.createDelimiter(t,this.data.join("").charCodeAt(0),r,u,s.mathvariant);u.sW=r}return this.CHTML}});i.mtext.Augment({CHTMLgetVariant:function(){if(h.config.mtextFontInherit||this.Parent().type==="merror"){var t=(h.config.scale/100)/h.scale;var s={cache:{},fonts:[],className:"MJXc-font-inherit",rscale:t,style:{"font-size":h.Percent(t)}};var r=this.Get("mathvariant");if(r.match(/bold/)){s.style["font-weight"]="bold"}if(r.match(/italic|-tex-mathit/)){s.style["font-style"]="italic"}if(r==="monospace"){s.className+=" MJXc-monospace-font"}if(r==="double-struck"){s.className+=" MJXc-double-struck-font"}if(r.match(/fraktur/)){s.className+=" MJXc-fraktur-font"}if(r.match(/sans-serif/)){s.className+=" MJXc-sans-serif-font"}if(r.match(/script/)){s.className+=" MJXc-script-font"}this.CHTMLvariant=s}else{this.SUPER(arguments).CHTMLgetVariant.call(this)}}});i.merror.Augment({toCommonHTML:function(r){r=this.CHTMLdefaultNode(r);var s=this.CHTML;s.rescale(0.9);s.h+=3/h.em;if(s.h>s.t){s.t=s.h}s.d+=3/h.em;if(s.d>s.b){s.b=s.d}s.w+=8/h.em;s.r=s.w;s.l=0;return r}});i.mspace.Augment({toCommonHTML:function(u){u=this.CHTMLcreateNode(u);this.CHTMLhandleStyle(u);this.CHTMLhandleScale(u);var s=this.getValues("height","depth","width");var r=this.CHTMLlength2em(s.width),t=this.CHTMLlength2em(s.height),x=this.CHTMLlength2em(s.depth);var v=this.CHTML;v.w=v.r=r;v.h=v.t=t;v.d=v.b=x;v.l=0;if(r<0){u.style.marginRight=h.Em(r);r=0}u.style.width=h.Em(r);u.style.height=h.Em(Math.max(0,t+x));if(x){u.style.verticalAlign=h.Em(-x)}this.CHTMLhandleBBox(u);this.CHTMLhandleColor(u);return u}});i.mpadded.Augment({toCommonHTML:function(s,E){var r;if(E&&E.stretch){s=s.firstChild;r=s.firstChild}else{s=this.CHTMLdefaultNode(s,{childNodes:"mjx-box",forceChild:true});r=s.firstChild;s=h.addElement(s,"mjx-block");s.appendChild(r);h.addElement(s,"mjx-strut")}var v=this.CHTMLbboxFor(0);var C=this.getValues("width","height","depth","lspace","voffset");var A=0,z=0,B=v.w,t=v.h,u=v.d;r.style.width=0;r.style.margin=h.Em(-t)+" 0 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u}});i.munderover.Augment({toCommonHTML:function(v,F){var D=this.getValues("displaystyle","accent","accentunder","align");var t=this.data[this.base];if(!D.displaystyle&&t!=null&&(t.movablelimits||t.CoreMO().Get("movablelimits"))){return i.msubsup.prototype.toCommonHTML.call(this,v,s)}var A,y,r=[],s=false;if(F&&F.stretch){if(this.data[this.base]){t=h.getNode(v,"mjx-op")}if(this.data[this.under]){A=h.getNode(v,"mjx-under")}if(this.data[this.over]){y=h.getNode(v,"mjx-over")}r[0]=t;r[1]=A||y;r[2]=y;s=true}else{var x=["mjx-op","mjx-under","mjx-over"];if(this.over===1){x[1]=x[2]}v=this.CHTMLdefaultNode(v,{childNodes:x,noBBox:true,forceChild:true,minChildren:2});r[0]=t=v.removeChild(v.firstChild);r[1]=A=y=v.removeChild(v.firstChild);if(v.firstChild){r[2]=y=v.removeChild(v.firstChild)}}var w=[],u=this.CHTMLgetBBoxes(w,r,D);var E=w[this.base],B=this.CHTML;B.w=u;B.h=E.h;B.d=E.d;var z=t,C=0;if(E.ic){C=1.3*E.ic+0.05}if(this.data[this.over]){z=this.CHTMLaddOverscript(y,w,D,C,t,s)}if(this.data[this.under]){this.CHTMLaddUnderscript(A,w,D,C,v,z,s)}else{if(!s){v.appendChild(z)}}this.CHTMLplaceBoxes(t,A,y,D,w);return v},CHTMLgetBBoxes:function(z,v,u){var x,s=this.data.length,y,t=-n,r=t;for(x=0;x<s;x++){z[x]=this.CHTMLbboxFor(x);z[x].x=z[x].y=0;if(this.data[x]){z[x].stretch=this.data[x].CHTMLcanStretch("Horizontal")}y=(x===this.base?1:z[x].rscale);if(x!==this.base){delete z[x].L;delete z[x].R}r=Math.max(r,y*(z[x].w+(z[x].L||0)+(z[x].R||0)));if(!z[x].stretch&&r>t){t=r}}if(t===-n){t=r}for(x=0;x<s;x++){if(z[x].stretch){y=(x===this.base?1:z[x].rscale);z[x]=this.data[x].CHTMLstretchH(v[x].firstChild,t/y);z[x].x=z[x].y=0;r=Math.max(r,y*(z[x].w+(z[x].L||0)+(z[x].R||0)))}}if(!z[this.base]){z[this.base]=h.BBOX.empty()}return r},CHTMLaddOverscript:function(A,y,E,D,s,r){var C=this.CHTML;var x,w,v=h.TEX.big_op_spacing5,u;var z=y[this.over],F=y[this.base],t=z.rscale;if(!r){var B=h.Element("mjx-stack");B.appendChild(A);B.appendChild(s)}if(z.D){z.d=z.D}if(z.d<0){A.firstChild.style.verticalAlign="top";A.style.height=h.Em(z.h+z.d)}z.x=0;if(E.accent){if(z.w<0.001){z.x+=(z.r-z.l)/2}u=h.TEX.rule_thickness;v=0;if(F.skew){z.x+=t*F.skew;C.skew=t*F.skew;if(z.x+t*z.w>C.w){C.skew+=(C.w-(z.x+t*z.w))/2}}}else{x=h.TEX.big_op_spacing1;w=h.TEX.big_op_spacing3;u=Math.max(x,w-Math.max(0,t*z.d))}z.x+=D/2;z.y=C.h+u+v+t*z.d;if(u){A.style.paddingBottom=h.Em(u/t)}if(v){A.style.paddingTop=h.Em(v/t)}return B},CHTMLaddUnderscript:function(A,y,D,C,s,z,r){var B=this.CHTML;var x,w,v=h.TEX.big_op_spacing5,u;var E=y[this.under],t=E.rscale;if(!r){h.addElement(s,"mjx-itable",{},[["mjx-row",{},[["mjx-cell"]]],["mjx-row"]]);s.firstChild.firstChild.firstChild.appendChild(z);s.firstChild.lastChild.appendChild(A)}if(E.D){E.d=E.D}if(E.d<0){A.firstChild.style.verticalAlign="top";s.firstChild.style.marginBottom=h.Em(E.d)}if(D.accentunder){u=2*h.TEX.rule_thickness;v=0}else{x=h.TEX.big_op_spacing2;w=h.TEX.big_op_spacing4;u=Math.max(x,w-t*E.h)}E.x=-C/2;E.y=-(B.d+u+v+t*E.h);if(u){A.style.paddingTop=h.Em(u/t)}if(v){A.style.paddingBottom=h.Em(v/t)}},CHTMLplaceBoxes:function(r,A,z,D,y){var s=this.CHTML.w,x,u=y.length,v;var C=h.BBOX.zero();C.scale=this.CHTML.scale;C.rscale=this.CHTML.rscale;y[this.base].x=y[this.base].y=0;var E=n;for(x=0;x<u;x++){v=(x===this.base?1:y[x].rscale);var B=v*(y[x].w+(y[x].L||0)+(y[x].R||0));y[x].x+={left:0,center:(s-B)/2,right:s-B}[D.align];if(y[x].x<E){E=y[x].x}}for(x=0;x<u;x++){if(this.data[x]){v=(x===this.base?1:y[x].rscale);if(y[x].x-E){var t=(x===this.base?r:x===this.over?z:A);t.style.paddingLeft=h.Em((y[x].x-E)/v)}C.combine(y[x],y[x].x-E,y[x].y)}}this.CHTML=C},CHTMLstretchV:i.mbase.CHTMLstretchV,CHTMLstretchH:i.mbase.CHTMLstretchH,CHTMLchildNode:function(t,s){var r=["mjx-op","mjx-under","mjx-over"];if(this.over===1){r[1]=r[2]}return h.getNode(t,r[s])}});i.msubsup.Augment({toCommonHTML:function(S,C){var A=this.getValues("displaystyle","subscriptshift","superscriptshift","texprimestyle");var D,H,z;if(C&&C.stretch){if(this.data[this.base]){D=h.getNode(S,"mjx-base")}if(this.data[this.sub]){H=h.getNode(S,"mjx-sub")}if(this.data[this.sup]){z=h.getNode(S,"mjx-sup")}E=h.getNode(S,"mjx-stack")}else{var K=["mjx-base","mjx-sub","mjx-sup"];if(this.sup===1){K[1]=K[2]}S=this.CHTMLdefaultNode(S,{childNodes:K,noBBox:true,forceChild:true,minChildren:3});D=S.childNodes[this.base];H=S.childNodes[this.sub];z=S.childNodes[this.sup];if(!this.CHTMLnotEmpty(this.data[this.sub])){S.removeChild(H);H=null}if(!this.CHTMLnotEmpty(this.data[this.sup])){S.removeChild(z);z=null}if(S.childNodes.length===3){var E=h.addElement(S,"mjx-stack");E.appendChild(z);E.appendChild(H)}}var F=[],G=h.BBOX.empty(this.CHTML);for(var V=0,T=this.data.length;V<T;V++){F[V]=this.CHTMLbboxFor(V)}var y=F[this.base]||h.BBOX.empty(),P=F[this.sub],W=F[this.sup];var B=(H?P.rscale:1),w=(z?W.rscale:1);G.combine(y,0,0);var X=h.TEX.x_height,N=h.TEX.scriptspace;var Q=h.TEX.sup_drop*w,O=h.TEX.sub_drop*B;var L=y.h-Q,J=y.d+O,Y=0,R;if(y.ic){G.w-=y.ic;D.style.marginRight=h.Em(-y.ic);Y=1.3*y.ic+0.05}var U=this.data[this.base];if(U){if((U.type==="mrow"||U.type==="mstyle")&&U.data.length===1){U=U.data[0]}if(U.type==="mi"||U.type==="mo"){if(U.data.join("").length===1&&y.rscale===1&&!y.sH&&!U.Get("largeop")){L=J=0}}}A.subscriptshift=(A.subscriptshift===""?0:this.CHTMLlength2em(A.subscriptshift));A.superscriptshift=(A.superscriptshift===""?0:this.CHTMLlength2em(A.superscriptshift));var I=G.w;if(H){P.w+=N}if(z){W.w+=N}if(!z){if(H){J=Math.max(J,h.TEX.sub1,B*P.h-(4/5)*X,A.subscriptshift);H.style.verticalAlign=h.Em(-J/B);H.style.paddingRight=h.Em(N/B);G.combine(P,I,-J)}}else{if(!H){R=h.TEX[(A.displaystyle?"sup1":(A.texprimestyle?"sup3":"sup2"))];L=Math.max(L,R,w*W.d+(1/4)*X,A.superscriptshift);z.style.verticalAlign=h.Em(L/w);z.style.paddingLeft=h.Em(Y/w);z.style.paddingRight=h.Em(N/w);G.combine(W,I+Y,L)}else{J=Math.max(J,h.TEX.sub2);var M=h.TEX.rule_thickness;if((L-w*W.d)-(B*P.h-J)<3*M){J=3*M-L+w*W.d+B*P.h;Q=(4/5)*X-(L-w*W.d);if(Q>0){L+=Q;J-=Q}}L=Math.max(L,A.superscriptshift);J=Math.max(J,A.subscriptshift);H.style.paddingRight=h.Em(N/B);z.style.paddingBottom=h.Em(L/w+J/B-W.d-P.h/B*w);z.style.paddingLeft=h.Em(Y/w);z.style.paddingRight=h.Em(N/w);E.style.verticalAlign=h.Em(-J);G.combine(W,I+Y,L);G.combine(P,I,-J)}}G.clean();return S},CHTMLstretchV:i.mbase.CHTMLstretchV,CHTMLstretchH:i.mbase.CHTMLstretchH,CHTMLchildNode:function(t,s){var r=["mjx-base","mjx-sub","mjx-sup"];if(this.over===1){r[1]=r[2]}return h.getNode(t,r[s])}});i.mfrac.Augment({toCommonHTML:function(M){M=this.CHTMLdefaultNode(M,{childNodes:["mjx-numerator","mjx-denominator"],childOptions:{autowidth:true},forceChild:true,noBBox:true,minChildren:2});var w=this.getValues("linethickness","displaystyle","numalign","denomalign","bevelled");var N=w.displaystyle;var C=M.firstChild,s=M.lastChild;var x=h.addElement(M,"mjx-box");x.appendChild(C);x.appendChild(s);M.appendChild(x);if(w.numalign!=="center"){C.style.textAlign=w.numalign}if(w.denomalign!=="center"){s.style.textAlign=w.denomalign}var O=this.CHTMLbboxFor(0),A=this.CHTMLbboxFor(1),B=h.BBOX.empty(this.CHTML),E=O.rscale,y=A.rscale;w.linethickness=Math.max(0,h.thickness2em(w.linethickness||"0",B.scale));var L=h.TEX.min_rule_thickness/h.em,S=h.TEX.axis_height;var I=w.linethickness,K,J,G,F;if(w.bevelled){x.className+=" MJXc-bevelled";var R=(N?0.4:0.15);var D=Math.max(E*(O.h+O.d),y*(A.h+A.d))+2*R;var Q=h.Element("mjx-bevel");x.insertBefore(Q,s);var r=h.createDelimiter(Q,47,D);G=E*(O.d-O.h)/2+S+R;F=y*(A.d-A.h)/2+S-R;if(G){C.style.verticalAlign=h.Em(G/E)}if(F){s.style.verticalAlign=h.Em(F/y)}Q.style.marginLeft=Q.style.marginRight=h.Em(-R/2);B.combine(O,0,G);B.combine(r,E*O.w-R/2,0);B.combine(A,E*O.w+r.w-R,F);B.clean()}else{x.className+=" 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false}});i.msqrt.Augment({toCommonHTML:function(v){v=this.CHTMLdefaultNode(v,{childNodes:["mjx-box","mjx-root"],forceChild:true,noBBox:true});var u=v.firstChild||h.Element("mjx-box");var D=h.addElement(v,"mjx-box");D.appendChild(u);var E=this.CHTMLbboxFor(0),B=h.BBOX.empty(this.CHTML);var F=h.TEX.rule_thickness,w=h.TEX.surd_height,s=F,r,C;if(this.Get("displaystyle")){s=h.TEX.x_height}r=F+s/4;C=E.h+E.d+r+F;var y=h.Element("mjx-surd");D.insertBefore(y,u);var z=h.createDelimiter(y,8730,[C-0.04,C]);if(z.h+z.d>C){r=((z.h+z.d)-(C-F))/2}C=E.h+r+F;var A=this.CHTMLaddRoot(v,z,z.h+z.d-C);u.style.paddingTop=h.Em(r);u.style.borderTop=h.Px(w*E.scale,1)+" solid";D.style.paddingTop=h.Em(2*F-w);E.h+=r+2*F;B.combine(z,A,C-z.h);B.combine(E,A+z.w,0);B.clean();return v},CHTMLaddRoot:function(){return 0}});i.mroot.Augment({toCommonHTML:i.msqrt.prototype.toCommonHTML,CHTMLaddRoot:function(z,t,u){if(!this.data[1]){return}var y=this.CHTML,A=this.data[1].CHTML,v=z.firstChild;var r=A.rscale;var s=this.CHTMLrootHeight(A,t,r)-u;var x=Math.min(A.w,A.r);var B=Math.max(x,t.offset/r);if(s){v.style.verticalAlign=h.Em(s/r)}if(B>x){v.firstChild.style.paddingLeft=h.Em(B-x)}B-=t.offset/r;v.style.width=h.Em(B);y.combine(A,0,s);return B*r},CHTMLrootHeight:function(t,r,s){return 0.45*(r.h+r.d-0.9)+r.offset+Math.max(0,t.d-0.075)}});i.mfenced.Augment({toCommonHTML:function(u){u=this.CHTMLcreateNode(u);this.CHTMLhandleStyle(u);this.CHTMLhandleScale(u);this.CHTMLaddChild(u,"open",{});for(var t=0,r=this.data.length;t<r;t++){this.CHTMLaddChild(u,"sep"+t,{});this.CHTMLaddChild(u,t,{})}this.CHTMLaddChild(u,"close",{});var s=this.CHTML.h,v=this.CHTML.d;this.CHTMLstretchChildV("open",s,v);for(t=0,r=this.data.length;t<r;t++){this.CHTMLstretchChildV("sep"+t,s,v);this.CHTMLstretchChildV(t,s,v)}this.CHTMLstretchChildV("close",s,v);this.CHTMLhandleSpace(u);this.CHTMLhandleBBox(u);this.CHTMLhandleColor(u);return u}});i.mrow.Augment({toCommonHTML:function(v,s){s=s||{};v=this.CHTMLdefaultNode(v);var y=this.CHTML,u=y.h,w=y.d,x;for(var t=0,r=this.data.length;t<r;t++){this.CHTMLstretchChildV(t,u,w);if(this.data[t]&&this.data[t].CHTML&&this.data[t].CHTML.w<0){x=true}}if(this.CHTMLlineBreaks()){this.CHTMLmultiline(v);if(s.autowidth){v.style.width=""}}else{if(x&&y.w){v.style.width=h.Em(Math.max(0,y.w))}if(y.w<0){v.style.marginRight=h.Em(y.w)}}return v},CHTMLlineBreaks:function(){if(!this.parent.linebreakContainer){return false}return(l.automatic&&this.CHTML.w>h.linebreakWidth)||this.hasNewline()},CHTMLstretchV:function(r,s){this.CHTMLstretchChildV(this.CoreIndex(),r,s);return this.CHTML},CHTMLstretchH:function(s,r){this.CHTMLstretchChildH(this.CoreIndex(),r,s);return this.CHTML}});i.mstyle.Augment({toCommonHTML:function(r){r=this.CHTMLdefaultNode(r);if(this.scriptlevel&&this.data[0]){this.CHTML.rescale(this.data[0].CHTML.rscale)}return r}});i.TeXAtom.Augment({toCommonHTML:function(w,u){if(!u||!u.stretch){w=this.CHTMLdefaultNode(w)}if(this.texClass===i.TEXCLASS.VCENTER){var r=h.TEX.axis_height,t=this.CHTML;var s=r-(t.h+t.d)/2+t.d;if(Math.abs(s)>0.001){w.style.verticalAlign=h.Em(s);t.h+=s;t.t+=s;t.d-=s;t.b-=s}}return w},CHTMLstretchV:function(r,s){this.CHTML.updateFrom(this.Core().CHTMLstretchV(r,s));this.toCommonHTML(this.CHTMLnodeElement(),{stretch:true});return this.CHTML},CHTMLstretchH:function(s,r){this.CHTML.updateFrom(this.CHTMLstretchCoreH(s,r));this.toCommonHTML(s,{stretch:true});return this.CHTML}});i.semantics.Augment({toCommonHTML:function(r){r=this.CHTMLcreateNode(r);if(this.data[0]){this.data[0].toCommonHTML(r);this.CHTML.updateFrom(this.data[0].CHTML);this.CHTMLhandleBBox(r)}return r}});i.annotation.Augment({toCommonHTML:function(r){return this.CHTMLcreateNode(r)}});i["annotation-xml"].Augment({toCommonHTML:i.mbase.CHTMLautoload});i.ms.Augment({toCommonHTML:i.mbase.CHTMLautoload});i.mglyph.Augment({toCommonHTML:i.mbase.CHTMLautoload});i.menclose.Augment({toCommonHTML:i.mbase.CHTMLautoload});i.maction.Augment({toCommonHTML:i.mbase.CHTMLautoload});i.mmultiscripts.Augment({toCommonHTML:i.mbase.CHTMLautoload});i.mtable.Augment({toCommonHTML:i.mbase.CHTMLautoload});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",h,"jax.js"]),0)})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(c.config.menuSettings.zoom!=="None"){j.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.CommonHTML);
MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var g="2.7.0";var b=MathJax.ElementJax.mml,a=MathJax.Hub.config,e=MathJax.OutputJax.CommonHTML,d=MathJax.Hub.SplitList;var c=-1,f=1000000;b.mtable.Augment({toCommonHTML:function(l){var m={rows:[],labels:[],labeled:false};l=this.CHTMLdefaultNode(l,{noBBox:true,childOptions:m});var k=e.Element("mjx-table");while(l.firstChild){k.appendChild(l.firstChild)}l.appendChild(k);var h=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","width","side","minlabelspacing","useHeight");var j=e.TEX.min_rule_thickness/e.em;m.t=e.Px(j*this.CHTML.scale,1);this.CHTMLgetBoxSizes(h,m);this.CHTMLgetAttributes(h,m);this.CHTMLadjustCells(h,m);if(h.frame){k.style.border=m.t+" "+h.frame}this.CHTMLalignV(h,m,l);this.CHTMLcolumnWidths(h,m,l);this.CHTMLstretchCells(h,m);if(m.labeled){this.CHTMLaddLabels(h,m,l,k)}var i=this.CHTML;i.w=i.r=m.R;i.h=i.t=m.T-m.B;i.d=i.b=m.B;if(!h.frame&&!i.pwidth){l.style.padding="0 "+e.Em(1/6);i.L=i.R=1/6}this.CHTMLhandleSpace(l);this.CHTMLhandleBBox(l);this.CHTMLhandleColor(l);return l},CHTMLgetBoxSizes:function(z,k){var r=e.FONTDATA.lineH*z.useHeight,t=e.FONTDATA.lineD*z.useHeight;var y=[],h=[],l=[],w=-1,q,n;for(q=0,n=this.data.length;q<n;q++){var B=this.data[q],A=(B.type==="mtr"?0:c);y[q]=r;h[q]=t;for(var p=A,v=B.data.length+A;p<v;p++){if(l[p]==null){l[p]=-f;if(p>w){w=p}}var u=B.data[p-A].CHTML;if(u.h>y[q]){y[q]=u.h}if(u.d>h[q]){h[q]=u.d}if(u.w>l[p]){l[p]=u.w}}}if(z.equalrows){k.HD=true;var x=Math.max.apply(Math,y);var o=Math.max.apply(Math,h);for(q=0,n=y.length;q<n;q++){y[q]=x;h[q]=o}}k.H=y;k.D=h;k.W=l,k.J=w},CHTMLgetAttributes:function(v,j){var l=d(v.columnspacing),x=d(v.rowspacing),t=d(v.columnalign),r=d(v.rowalign),k=d(v.columnlines),w=d(v.rowlines),o=d(v.columnwidth),n=[],q,p,u=j.J,s=j.rows.length-1;for(q=0,p=l.length;q<p;q++){l[q]=this.CHTMLlength2em(l[q])}for(q=0,p=x.length;q<p;q++){x[q]=this.CHTMLlength2em(x[q])}while(l.length<u){l.push(l[l.length-1])}while(t.length<=u){t.push(t[t.length-1])}while(k.length<u){k.push(k[k.length-1])}while(o.length<=u){o.push(o[o.length-1])}while(x.length<s){x.push(x[x.length-1])}while(r.length<=s){r.push(r[r.length-1])}while(w.length<s){w.push(w[w.length-1])}t[c]=(v.side.substr(0,1)==="l"?"left":"right");for(q=0;q<=s;q++){var y=this.data[q];n[q]=[];if(y.rowalign){r[q]=y.rowalign}if(y.columnalign){n[q]=d(y.columnalign);while(n[q].length<=u){n[q].push(n[q][n[q].length-1])}}}var h=d(v.framespacing);if(h.length!=2){h=d(this.defaults.framespacing)}h[0]=Math.max(0,this.CHTMLlength2em(h[0]));h[1]=Math.max(0,this.CHTMLlength2em(h[1]));if(v.columnlines.replace(/none/g,"").replace(/ /g,"")!==""||v.rowlines.replace(/none/g,"").replace(/ /g,"")!==""){v.fspace=true}if(v.frame===b.LINES.NONE){delete v.frame}else{v.fspace=true}if(v.frame){h[0]=Math.max(0,h[0]);h[1]=Math.max(0,h[1])}if(v.fspace){l[u]=h[0];x[s]=h[1]}else{l[u]=x[s]=0}k[u]=w[s]=b.LINES.NONE;j.CSPACE=l;j.RSPACE=x;j.CALIGN=t;j.RALIGN=r;j.CLINES=k;j.RLINES=w;j.CWIDTH=o;j.RCALIGN=n;j.FSPACE=h},CHTMLadjustCells:function(k,q){var P=q.rows,U=q.CSPACE,n=q.CLINES,w=q.RSPACE,E=q.RLINES,S=q.CALIGN,p=q.RALIGN,F=q.RCALIGN;U[q.J]*=2;w[P.length-1]*=2;var o="0",G,r,y,J,l,N,Q=0;if(k.fspace){Q=q.FSPACE[1];o=e.Em(q.FSPACE[1])}q.RHD=[];q.RH=[];for(var O=0,I=P.length;O<I;O++){var v=P[O],u=this.data[O];G=w[O]/2;J=null;y="0";if(E[O]!==b.LINES.NONE&&E[O]!==""){J=q.t+" "+E[O]}q.RH[O]=Q+q.H[O];Q=Math.max(0,G);q.RHD[O]=q.RH[O]+Q+q.D[O];G=e.Em(Q);if(k.fspace){y=e.Em(q.FSPACE[0])}for(var K=0,x=v.length;K<x;K++){var C=(u.type==="mtr"?0:c);cell=v[K].style;l=u.data[K-C].CHTML;r=U[K]/2;if(n[K]!==b.LINES.NONE){cell.borderRight=q.t+" "+n[K];r-=1/e.em/2}r=e.Em(Math.max(0,r));cell.padding=o+" "+r+" 0px "+y;if(J){cell.borderBottom=J}y=r;N=(u.data[K-C].rowalign||this.data[O].rowalign||p[O]);var z=Math.max(1,l.h),A=Math.max(0.2,l.d),h=(q.H[O]+q.D[O])-(z+A),t=v[K].firstChild.style;if(N===b.ALIGN.TOP){if(h){t.marginBottom=e.Em(h)}cell.verticalAlign="top"}else{if(N===b.ALIGN.BOTTOM){cell.verticalAlign="bottom";if(h){t.marginTop=e.Em(h)}}else{if(N===b.ALIGN.CENTER){if(h){t.marginTop=t.marginBottom=e.Em(h/2)}cell.verticalAlign="middle"}else{if(z!==q.H[O]){t.marginTop=e.Em(q.H[O]-z)}}}}N=(u.data[K-C].columnalign||F[O][K]||S[K]);if(N!==b.ALIGN.CENTER){cell.textAlign=N}}v.node.style.height=e.Em(q.RHD[O]);o=G}U[q.J]/=2;w[P.length-1]/=2},CHTMLalignV:function(w,k,o){var m,t=k.rows.length,v=k.H,j=k.D,x=k.RSPACE;if(typeof(w.align)!=="string"){w.align=String(w.align)}if(w.align.match(/(top|bottom|center|baseline|axis)( 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n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var 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 s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var 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]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;p<n;p++){this.PHTMLaddChild(q,"sep"+p,{});this.PHTMLaddChild(q,p,{})}this.PHTMLaddChild(q,"close",{});var o=this.PHTML.h,r=this.PHTML.d;this.PHTMLstretchChild("open",o,r);for(p=0,n=this.data.length;p<n;p++){this.PHTMLstretchChild("sep"+p,o,r);this.PHTMLstretchChild(p,o,r)}this.PHTMLstretchChild("close",o,r);return q}});h.mrow.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var p=this.PHTML.h,r=this.PHTML.d;for(var o=0,n=this.data.length;o<n;o++){this.PHTMLstretchChild(o,p,r)}return q}});h.mstyle.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);this.PHTMLhandleScriptlevel(n);return n}});h.TeXAtom.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);n.className="MJXp-mrow";return n}});h.mtable.Augment({toPreviewHTML:function(E){E=this.PHTMLdefaultSpan(E,{noBBox:true});var r=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","width");var u=MathJax.Hub.SplitList,F,A,D,z;var N=u(r.columnspacing),w=u(r.rowspacing),L=u(r.columnalign),t=u(r.rowalign);for(F=0,A=N.length;F<A;F++){N[F]=g.length2em(N[F])}for(F=0,A=w.length;F<A;F++){w[F]=g.length2em(w[F])}var K=e.Element("span");while(E.firstChild){K.appendChild(E.firstChild)}E.appendChild(K);var y=0,s=0;for(F=0,A=this.data.length;F<A;F++){var v=this.data[F];if(v){var J=g.arrayEntry(w,F-1),C=g.arrayEntry(t,F);var x=v.PHTML,q=v.PHTMLspanElement();q.style.verticalAlign=C;var B=(v.type==="mlabeledtr"?1:0);for(D=0,z=v.data.length;D<z-B;D++){var p=v.data[D+B];if(p){var M=g.arrayEntry(N,D-1),G=g.arrayEntry(L,D);var I=p.PHTMLspanElement();if(D){x.w+=M;I.style.paddingLeft=g.Em(M)}if(F){I.style.paddingTop=g.Em(J)}I.style.textAlign=G}}y+=x.h+x.d;if(F){y+=J}if(x.w>s){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p<n;p++){this.PHTMLaddChild(q,p,o)}return q}});h.semantics.Augment({toPreviewHTML:function(n){n=this.PHTMLcreateSpan(n);if(this.data[0]){this.data[0].toPreviewHTML(n);MathJax.Hub.Insert(this.data[0].PHTML||{},this.PHTML)}return n}});h.annotation.Augment({toPreviewHTML:function(n){}});h["annotation-xml"].Augment({toPreviewHTML:function(n){}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",g,"jax.js"]),0)})});MathJax.Hub.Register.StartupHook("End 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