/*
 *  /MathJax/config/Accessible-full.js
 *  
 *  Copyright (c) 2010-11 Design Science, Inc.
 *
 *  Part of the MathJax library.
 *  See http://www.mathjax.org for details.
 * 
 *  Licensed under the Apache License, Version 2.0;
 *  you may not use this file except in compliance with the License.
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 */

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

MathJax.Ajax.Preloading(
  "[MathJax]/jax/input/TeX/config.js",
  "[MathJax]/jax/input/MathML/config.js",
  "[MathJax]/jax/output/HTML-CSS/config.js",
  "[MathJax]/jax/output/NativeMML/config.js",
  "[MathJax]/config/MMLorHTML.js",
  "[MathJax]/extensions/tex2jax.js",
  "[MathJax]/extensions/mml2jax.js",
  "[MathJax]/extensions/MathEvents.js",
  "[MathJax]/extensions/MathZoom.js",
  "[MathJax]/extensions/MathMenu.js",
  "[MathJax]/jax/element/mml/jax.js",
  "[MathJax]/extensions/toMathML.js",
  "[MathJax]/extensions/TeX/noErrors.js",
  "[MathJax]/extensions/TeX/noUndefined.js",
  "[MathJax]/jax/input/TeX/jax.js",
  "[MathJax]/extensions/TeX/AMSmath.js",
  "[MathJax]/extensions/TeX/AMSsymbols.js",
  "[MathJax]/jax/input/MathML/jax.js",
  "[MathJax]/jax/output/NativeMML/jax.js",
  "[MathJax]/jax/output/HTML-CSS/jax.js",
  "[MathJax]/jax/output/HTML-CSS/autoload/mtable.js"
);

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

MathJax.Hub.Config({
  menuSettings: {
    zoom: "Double-Click",
    mpContext: true,
    mpMouse: true
  },
  errorSettings: {
    message: ["[Math Error]"]
  }
  
});

MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.0",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/[:"'<>&]/g,"")},formatURL:function(a){return"#"+escape(a)},useLabelIds:true}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js");

MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.0",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.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.0",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",mtextFontInherit:false,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js");

MathJax.OutputJax.NativeMML=MathJax.OutputJax({id:"NativeMML",version:"2.0",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{scale:100,minScaleAdjust:50,styles:{"DIV.MathJax_MathML":{"text-align":"center",margin:".75em 0px"}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.NativeMML.Register("jax/mml")}MathJax.OutputJax.NativeMML.loadComplete("config.js");

(function(c,g){var f="2.0";var a=MathJax.Hub.CombineConfig("MMLorHTML",{prefer:{MSIE:"MML",Firefox:"HTML",Opera:"HTML",Chrome:"HTML",Safari:"HTML",other:"HTML"}});var e={Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4};var b=(g.version==="0.0"||g.versionAtLeast(e[g]||0));var d=(g.isFirefox&&g.versionAtLeast("1.5"))||(g.isMSIE&&g.hasMathPlayer)||(g.isSafari&&g.versionAtLeast("5.0"))||(g.isOpera&&g.versionAtLeast("9.52"));c.Register.StartupHook("End Config",function(){var h=(a.prefer&&typeof(a.prefer)==="object"?a.prefer[MathJax.Hub.Browser]||a.prefer.other||"HTML":a.prefer);if(b||d){if(d&&(h==="MML"||!b)){if(MathJax.OutputJax.NativeMML){MathJax.OutputJax.NativeMML.Register("jax/mml")}else{c.config.jax.unshift("output/NativeMML")}c.Startup.signal.Post("NativeMML output selected")}else{if(MathJax.OutputJax["HTML-CSS"]){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}else{c.config.jax.unshift("output/HTML-CSS")}c.Startup.signal.Post("HTML-CSS output selected")}}else{c.PreProcess.disabled=true;c.prepareScripts.disabled=true;MathJax.Message.Set("Your browser does not support MathJax",null,4000);c.Startup.signal.Post("MathJax not supported")}})})(MathJax.Hub,MathJax.Hub.Browser);MathJax.Ajax.loadComplete("[MathJax]/config/MMLorHTML.js");

MathJax.Extension.tex2jax={version:"2.0",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],balanceBraces:true,skipTags:["script","noscript","style","textarea","pre","code"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c<a;c++){d.push(this.patternQuote(b.inlineMath[c][0]));this.match[b.inlineMath[c][0]]={mode:"",end:b.inlineMath[c][1],pattern:this.endPattern(b.inlineMath[c][1])}}for(c=0,a=b.displayMath.length;c<a;c++){d.push(this.patternQuote(b.displayMath[c][0]));this.match[b.displayMath[c][0]]={mode:"; mode=display",end:b.displayMath[c][1],pattern:this.endPattern(b.displayMath[c][1])}}if(d.length){e.push(d.sort(this.sortLength).join("|"))}if(b.processEnvironments){e.push("\\\\begin\\{([^}]*)\\}")}if(b.processEscapes){e.push("\\\\*\\\\\\$")}if(b.processRefs){e.push("\\\\(eq)?ref\\{[^}]*\\}")}this.start=new RegExp(e.join("|"),"g");this.skipTags=new RegExp("^("+b.skipTags.join("|")+")$","i");this.ignoreClass=new RegExp("(^| )("+b.ignoreClass+")( |$)");this.processClass=new RegExp("(^| )("+b.processClass+")( |$)");return(e.length>0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d<c?-1:1))},scanElement:function(c,b,g){var a,e,d,f;while(c&&c!=b){if(c.nodeName.toLowerCase()==="#text"){if(!g){c=this.scanText(c)}}else{a=(typeof(c.className)==="undefined"?"":c.className);e=(typeof(c.tagName)==="undefined"?"":c.tagName);if(typeof(a)!=="string"){a=String(a)}f=this.processClass.exec(a);if(c.firstChild&&!a.match(/(^| )MathJax/)&&(f||!this.skipTags.exec(e))){d=(g||this.ignoreClass.exec(a))&&!f;this.scanElement(c.firstChild,b,d)}}if(c){c=c.nextSibling}}},scanText:function(b){if(b.nodeValue.replace(/\s+/,"")==""){return b}var a,c;this.search={start:true};this.pattern=this.start;while(b){this.pattern.lastIndex=0;while(b&&b.nodeName.toLowerCase()==="#text"&&(a=this.pattern.exec(b.nodeValue))){if(this.search.start){b=this.startMatch(a,b)}else{b=this.endMatch(a,b)}}if(this.search.matched){b=this.encloseMath(b)}if(b){do{c=b;b=b.nextSibling}while(b&&(b.nodeName.toLowerCase()==="br"||b.nodeName.toLowerCase()==="#comment"));if(!b||b.nodeName!=="#text"){return(this.search.close?this.prevEndMatch():c)}}}return b},startMatch:function(a,b){var f=this.match[a[0]];if(f!=null){this.search={end:f.end,mode:f.mode,pcount:0,open:b,olen:a[0].length,opos:this.pattern.lastIndex-a[0].length};this.switchPattern(f.pattern)}else{if(a[0].substr(0,6)==="\\begin"){this.search={end:"\\end{"+a[1]+"}",mode:"; mode=display",pcount:0,open:b,olen:0,opos:this.pattern.lastIndex-a[0].length,isBeginEnd:true};this.switchPattern(this.endPattern(this.search.end))}else{if(a[0].substr(0,4)==="\\ref"||a[0].substr(0,6)==="\\eqref"){this.search={mode:"",end:"",open:b,pcount:0,olen:0,opos:this.pattern.lastIndex-a[0].length};return this.endMatch([""],b)}else{var d=a[0].substr(0,a[0].length-1),g,c;if(d.length%2===0){c=[d.replace(/\\\\/g,"\\")];g=1}else{c=[d.substr(1).replace(/\\\\/g,"\\"),"$"];g=0}c=MathJax.HTML.Element("span",null,c);var e=MathJax.HTML.TextNode(b.nodeValue.substr(0,a.index));b.nodeValue=b.nodeValue.substr(a.index+a[0].length-g);b.parentNode.insertBefore(c,b);b.parentNode.insertBefore(e,c);this.pattern.lastIndex=g}}}return b},endMatch:function(a,c){var b=this.search;if(a[0]==b.end){if(!b.close||b.pcount===0){b.close=c;b.cpos=this.pattern.lastIndex;b.clen=(b.isBeginEnd?0:a[0].length)}if(b.pcount===0){b.matched=true;c=this.encloseMath(c);this.switchPattern(this.start)}}else{if(a[0]==="{"){b.pcount++}else{if(a[0]==="}"&&b.pcount){b.pcount--}}}return c},prevEndMatch:function(){this.search.matched=true;var a=this.encloseMath(this.search.close);this.switchPattern(this.start);return a},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=(a===this.start)},encloseMath:function(b){var a=this.search,f=a.close,e,c;if(a.cpos===f.length){f=f.nextSibling}else{f=f.splitText(a.cpos)}if(!f){e=f=MathJax.HTML.addText(a.close.parentNode,"")}a.close=f;c=(a.opos?a.open.splitText(a.opos):a.open);while(c.nextSibling&&c.nextSibling!==f){if(c.nextSibling.nodeValue!==null){if(c.nextSibling.nodeName==="#comment"){c.nodeValue+=c.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{c.nodeValue+=c.nextSibling.nodeValue}}else{if(this.msieNewlineBug){c.nodeValue+=(c.nextSibling.nodeName.toLowerCase()==="br"?"\n":" ")}else{c.nodeValue+=" "}}c.parentNode.removeChild(c.nextSibling)}var d=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);if(this.config.preview!=="none"){this.createPreview(a.mode,d)}c=this.createMathTag(a.mode,d);this.search={};this.pattern.lastIndex=0;if(e){e.parentNode.removeChild(e)}return c},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(c,a){var b;if(this.config.preview==="TeX"){b=[this.filterPreview(a)]}else{if(this.config.preview instanceof Array){b=this.config.preview}}if(b){b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b);this.insertNode(b)}},createMathTag:function(c,b){var a=document.createElement("script");a.type="math/tex"+c;MathJax.HTML.setScript(a,b);this.insertNode(a);return a},filterPreview:function(a){return a},msieNewlineBug:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9)};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js");

MathJax.Extension.mml2jax={version:"2.0",config:{preview:"alttext"},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}this.ProcessMathArray(e.getElementsByTagName("math"));if(e.getElementsByTagNameNS){this.ProcessMathArray(e.getElementsByTagNameNS(this.MMLnamespace,"math"))}var d,b;if(document.namespaces){for(d=0,b=document.namespaces.length;d<b;d++){var f=document.namespaces[d];if(f.urn===this.MMLnamespace){this.ProcessMathArray(e.getElementsByTagName(f.name+":math"))}}}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.ProcessMathArray(e.getElementsByTagName(a.nodeName.substr(6)+":math"))}}}}},ProcessMathArray:function(b){var a;if(b.length){if(this.MathTagBug){for(a=b.length-1;a>=0;a--){if(b[a].nodeName==="MATH"){this.ProcessMathFlattened(b[a])}else{this.ProcessMath(b[a])}}}else{for(a=b.length-1;a>=0;a--){this.ProcessMath(b[a])}}}},ProcessMath:function(e){var d=e.parentNode;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;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){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(b,a){var c;if(this.config.preview==="alttext"){var d=b.getAttribute("alttext");if(d!=null){c=[this.filterPreview(d)]}}else{if(this.config.preview instanceof Array){c=this.config.preview}}if(c){c=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},c);a.parentNode.insertBefore(c,a)}},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]);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js");

(function(d,h,l,g,b,j){var p="2.0";var i=MathJax.Extension;var c=i.MathEvents={version:p};var k=d.config.menuSettings;var o={hover:500,frame:{x:3.5,y:5,bwidth:1,bcolor:"#A6D",hwidth:"15px",hcolor:"#83A"},button:{x:-4,y:-3,wx:-2,src:l.fileURL(b.imageDir+"/MenuArrow-15.png")},fadeinInc:0.2,fadeoutInc:0.05,fadeDelay:50,fadeoutStart:400,fadeoutDelay:15*1000,styles:{".MathJax_Hover_Frame":{"border-radius":".25em","-webkit-border-radius":".25em","-moz-border-radius":".25em","-khtml-border-radius":".25em","box-shadow":"0px 0px 15px #83A","-webkit-box-shadow":"0px 0px 15px #83A","-moz-box-shadow":"0px 0px 15px #83A","-khtml-box-shadow":"0px 0px 15px #83A",border:"1px solid #A6D ! important",display:"inline-block",position:"absolute"},".MathJax_Hover_Arrow":{position:"absolute",width:"15px",height:"11px",cursor:"pointer"}}};var m=c.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",Mousedown:function(q){return m.Handler(q,"Mousedown",this)},Mouseup:function(q){return m.Handler(q,"Mouseup",this)},Mousemove:function(q){return m.Handler(q,"Mousemove",this)},Mouseover:function(q){return m.Handler(q,"Mouseover",this)},Mouseout:function(q){return m.Handler(q,"Mouseout",this)},Click:function(q){return m.Handler(q,"Click",this)},DblClick:function(q){return m.Handler(q,"DblClick",this)},Menu:function(q){return m.Handler(q,"ContextMenu",this)},Handler:function(t,r,s){if(l.loadingMathMenu){return m.False(t)}var q=b[s.jaxID];if(!t){t=window.event}t.isContextMenu=(r==="ContextMenu");if(q[r]){return q[r](t,s)}if(i.MathZoom){return i.MathZoom.HandleEvent(t,r,s)}},False:function(q){if(!q){q=window.event}if(q){if(q.preventDefault){q.preventDefault()}if(q.stopPropagation){q.stopPropagation()}q.cancelBubble=true;q.returnValue=false}return false},ContextMenu:function(r,y,u){var w=b[y.jaxID],t=w.getJaxFromMath(y);var z=(w.config.showMathMenu!=null?w:d).config.showMathMenu;if(!z||(k.context!=="MathJax"&&!u)){return}if(c.msieEventBug){r=window.event||r}m.ClearSelection();f.ClearHoverTimer();if(t.hover){if(t.hover.remove){clearTimeout(t.hover.remove);delete t.hover.remove}t.hover.nofade=true}var s=MathJax.Menu;if(s){s.jax=t;var q=s.menu.Find("Show Math As").menu;q.items[1].name=(j[t.inputJax].sourceMenuTitle||"Original Form");q.items[0].hidden=(t.inputJax==="Error");var v=s.menu.Find("Math Settings","MathPlayer");v.hidden=!(t.outputJax==="NativeMML"&&d.Browser.hasMathPlayer);return s.menu.Post(r)}else{if(!l.loadingMathMenu){l.loadingMathMenu=true;var x={pageX:r.pageX,pageY:r.pageY,clientX:r.clientX,clientY:r.clientY};g.Queue(l.Require("[MathJax]/extensions/MathMenu.js"),function(){delete l.loadingMathMenu;if(!MathJax.Menu){MathJax.Menu={}}},["ContextMenu",this,x,y,u])}return m.False(r)}},AltContextMenu:function(s,r){var t=b[r.jaxID];var q=(t.config.showMathMenu!=null?t:d).config.showMathMenu;if(q){q=(t.config.showMathMenuMSIE!=null?t:d).config.showMathMenuMSIE;if(k.context==="MathJax"&&!k.mpContext&&q){if(!c.noContextMenuBug||s.button!==m.RIGHTBUTTON){return}}else{if(!s[m.MENUKEY]||s.button!==m.LEFTBUTTON){return}}return t.ContextMenu(s,r,true)}},ClearSelection:function(){if(c.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(document.selection){setTimeout("document.selection.empty()",0)}},getBBox:function(s){s.appendChild(c.topImg);var r=c.topImg.offsetTop,t=s.offsetHeight-r,q=s.offsetWidth;s.removeChild(c.topImg);return{w:q,h:r,d:t}}};var f=c.Hover={Mouseover:function(s,r){if(k.discoverable||k.zoom==="Hover"){var u=s.fromElement||s.relatedTarget,t=s.toElement||s.target;if(u&&t&&(u.isMathJax!=t.isMathJax||d.getJaxFor(u)!==d.getJaxFor(t))){var q=this.getJaxFromMath(r);if(q.hover){f.ReHover(q)}else{f.HoverTimer(q,r)}return 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A=o.frame.x,z=o.frame.y,x=o.frame.bwidth;if(c.msieBorderWidthBug){x=0}q.hover={opacity:0,id:q.inputID+"-Hover"};var r=h.Element("span",{id:q.hover.id,isMathJax:true,style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{className:"MathJax_Hover_Frame",isMathJax:true,style:{display:"inline-block",position:"absolute",top:this.Px(-y.h-z-x-(y.y||0)),left:this.Px(-A-x+(y.x||0)),width:this.Px(y.w+2*A),height:this.Px(y.h+y.d+2*z),opacity:0,filter:"alpha(opacity=0)"}}]]);var s=h.Element("span",{isMathJax:true,id:q.hover.id+"Menu",style:{display:"inline-block","z-index":1,width:0,height:0,position:"relative"}},[["img",{className:"MathJax_Hover_Arrow",isMathJax:true,math:u,src:o.button.src,onclick:this.HoverMenu,jax:t.id,style:{left:this.Px(y.w+A+x+(y.x||0)+o.button.x),top:this.Px(-y.h-z-x-(y.y||0)-o.button.y),opacity:0,filter:"alpha(opacity=0)"}}]]);if(y.width){r.style.width=s.style.width=y.width;r.style.marginRight=s.style.marginRight="-"+y.width;r.firstChild.style.width=y.width;s.firstChild.style.left="";s.firstChild.style.right=this.Px(o.button.wx)}v.parentNode.insertBefore(r,v);if(w){v.parentNode.insertBefore(s,v)}if(v.style){v.style.position="relative"}this.ReHover(q)},ReHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}q.hover.remove=setTimeout(g(["UnHover",this,q]),o.fadeoutDelay);this.HoverFadeTimer(q,o.fadeinInc)},UnHover:function(q){if(!q.hover.nofade){this.HoverFadeTimer(q,-o.fadeoutInc,o.fadeoutStart)}},HoverFade:function(q){delete 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r=q.versionAtLeast("8.0");c.msieBorderWidthBug=(document.compatMode==="BackCompat");c.msieEventBug=q.isIE9;c.msieAlignBug=(!r||s<8);if(s<9){m.LEFTBUTTON=1}},Safari:function(q){c.safariContextMenuBug=true},Opera:function(q){c.operaPositionBug=true},Konqueror:function(q){c.noContextMenuBug=true}});c.topImg=(c.msieAlignBug?h.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):h.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(c.operaPositionBug){c.topImg.style.border="1px solid"}c.config=o=d.CombineConfig("MathEvents",o);var e=function(){var q=o.styles[".MathJax_Hover_Frame"];q.border=o.frame.bwidth+"px solid "+o.frame.bcolor+" ! important";q["box-shadow"]=q["-webkit-box-shadow"]=q["-moz-box-shadow"]=q["-khtml-box-shadow"]="0px 0px "+o.frame.hwidth+" "+o.frame.hcolor};g.Queue(d.Register.StartupHook("End Config",{}),[e],["getImages",f],["Styles",l,o.styles],["Post",d.Startup.signal,"MathEvents 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(function(a,d,f,c,j){var k="2.0";var i=a.CombineConfig("MathZoom",{styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"font-weight":"normal","font-style":"normal","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","box-shadow":"5px 5px 15px #AAAAAA","-webkit-box-shadow":"5px 5px 15px #AAAAAA","-moz-box-shadow":"5px 5px 15px #AAAAAA","-khtml-box-shadow":"5px 5px 15px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', 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_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"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(n,s){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[s.jaxID];var o=q.getJaxFromMath(s);if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*Math.max(document.body.clientHeight,document.documentElement.clientHeight));var m=d.Element("span",{style:{position:"relative",display:"inline-block",height:0,width:0},id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale,"max-width":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,u=x.firstChild,p=m.firstChild;s.parentNode.insertBefore(m,s);if(u.addEventListener){u.addEventListener("mousedown",this.Remove,true)}if(this.msieTrapEventBug){var w=d.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});m.insertBefore(w,x)}if(this.msieZIndexBug){var t=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=t}var v=q.Zoom(o,u,s,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=v.zH+"px";x.style.width=v.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";x.style.width=(v.zW+this.scrollSize)+"px"}if(x.offsetWidth>l){x.style.width=l+"px";x.style.height=(v.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){x.style.width=Math.min(l,v.zW)+"px"}if(x.offsetWidth<l&&x.offsetHeight<r){x.style.overflow="visible"}this.Position(x,v);if(this.msieTrapEventBug){w.style.height=x.clientHeight+"px";w.style.width=x.clientWidth+"px";w.style.left=(parseFloat(x.style.left)+x.clientLeft)+"px";w.style.top=(parseFloat(x.style.top)+x.clientTop)+"px"}x.style.visibility="";if(this.settings.zoom==="Hover"){p.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",o]);return e(n)},Position:function(p,r){var q=this.Resize(),m=q.x,s=q.y,l=r.mW;var o=-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(n){if(h.onresize){h.onresize(n)}var l=0,q=0,o,p=document.getElementById("MathJax_ZoomFrame"),m=document.getElementById("MathJax_ZoomOverlay");o=p;while(o.offsetParent){l+=o.offsetLeft;o=o.offsetParent}if(h.operaPositionBug){p.style.border="1px solid"}o=p;while(o.offsetParent){q+=o.offsetTop;o=o.offsetParent}if(h.operaPositionBug){p.style.border=""}m.style.left=(-l)+"px";m.style.top=(-q)+"px";if(h.msiePositionBug){setTimeout(h.SetWH,0)}else{h.SetWH()}return{x:l,y:q}},SetWH:function(){var l=document.getElementById("MathJax_ZoomOverlay");l.style.width=l.style.height="1px";var m=document.documentElement||document.body;l.style.width=m.scrollWidth+"px";l.style.height=Math.max(m.clientHeight,m.scrollHeight)+"px"},Remove:function(n){var p=document.getElementById("MathJax_ZoomFrame");if(p){var o=MathJax.OutputJax[p.nextSibling.jaxID];var l=o.getJaxFromMath(p.nextSibling);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);

(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help-v2/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var 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o=this.GetBrackets(m),k=this.GetArgument(m);if(k==="\\frac"){k+="{"+this.GetArgument(k)+"}{"+this.GetArgument(k)+"}"}var l=d.Parse(k,this.stack.env).mml();if(!o){l=h.msqrt.apply(h,l.array())}else{l=h.mroot(l,this.parseRoot(o))}this.Push(l)},Root:function(l){var m=this.GetUpTo(l,"\\of");var k=this.ParseArg(l);this.Push(h.mroot(k,this.parseRoot(m)))},parseRoot:function(p){var l=this.stack.env,k=l.inRoot;l.inRoot=true;var o=d.Parse(p,l);p=o.mml();var m=o.stack.global;if(m.leftRoot||m.upRoot){p=h.mpadded(p);if(m.leftRoot){p.width=m.leftRoot}if(m.upRoot){p.voffset=m.upRoot;p.height=m.upRoot}}l.inRoot=k;return p},MoveRoot:function(k,m){if(!this.stack.env.inRoot){d.Error(k+" can appear only within a root")}if(this.stack.global[m]){d.Error("Multiple use of "+k)}var l=this.GetArgument(k);if(!l.match(/-?[0-9]+/)){d.Error("The argument to "+k+" must be an integer")}l=(l/15)+"em";if(l.substr(0,1)!=="-"){l="+"+l}this.stack.global[m]=l},Accent:function(m,k,p){var o=this.ParseArg(m);var 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m=b.position().With({name:k,move:"vertical"});if(l.charAt(0)==="-"){l=l.slice(1);k={raise:"\\lower",lower:"\\raise"}[k.substr(1)]}if(k==="\\lower"){m.dh="-"+l;m.dd="+"+l}else{m.dh="+"+l;m.dd="-"+l}this.Push(m)},MoveLeftRight:function(k){var n=this.GetDimen(k);var m=(n.charAt(0)==="-"?n.slice(1):"-"+n);if(k==="\\moveleft"){var l=n;n=m;m=l}this.Push(b.position().With({name:k,move:"horizontal",left:h.mspace().With({width:n,mathsize:h.SIZE.NORMAL}),right:h.mspace().With({width:m,mathsize:h.SIZE.NORMAL})}))},Hskip:function(k){this.Push(h.mspace().With({width:this.GetDimen(k),mathsize:h.SIZE.NORMAL}))},Rule:function(m,o){var k=this.GetDimen(m),n=this.GetDimen(m),q=this.GetDimen(m);var l,p={width:k,height:n,depth:q};if(o!=="blank"){if(parseFloat(k)&&parseFloat(n)+parseFloat(q)){p.mathbackground=(this.stack.env.color||"black")}l=h.mpadded(h.mrow()).With(p)}else{l=h.mspace().With(p)}this.Push(l)},MakeBig:function(k,n,l){l*=f.p_height;l=String(l).replace(/(\.\d\d\d).+/,"$1")+"em";var 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l=this.GetArgument(k).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");this.Extension(null,l)},Extension:function(k,l,m){if(k&&!typeof(k)==="string"){k=k.name}l=d.extensionDir+"/"+l;if(!l.match(/\.js$/)){l+=".js"}if(!i.loaded[i.fileURL(l)]){if(k!=null){delete f[m||"macros"][k.replace(/^\\/,"")]}c.RestartAfter(i.Require(l))}},Macro:function(m,p,o,q){if(o){var l=[];if(q!=null){var k=this.GetBrackets(m);l.push(k==null?q:k)}for(var n=l.length;n<o;n++){l.push(this.GetArgument(m))}p=this.SubstituteArgs(l,p)}this.string=this.AddArgs(p,this.string.slice(this.i));this.i=0;if(++this.macroCount>d.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(o<k){var r=l.charAt(o);if(r==="{"){q++;o++}else{if(r==="}"){if(q===0){k=0}else{q--;o++}}else{if(r==="&"&&q===0){d.Error("Extra alignment tab in \\cases text")}else{if(r==="\\"){if(l.substr(o).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){k=0}else{o+=2}}else{o++}}}}}var p=l.substr(this.i,o-this.i);if(!p.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(p));this.i=o}}},Cr:function(k){this.Push(b.cell().With({isCR:true,name:k}))},CrLaTeX:function(k){var o=this.GetBrackets(k,"").replace(/ /g,"");if(o&&!o.match(/^(((\.\d+|\d+(\.\d*)?))(pt|em|ex|mu|mm|cm|in|pc))$/)){d.Error("Bracket argument to "+k+" must be 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l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for 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l=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(l=="\\"){l+=this.GetCS(k)}if(f.delimiter[l]!=null){return this.convertDelimiter(l)}}d.Error("Missing or unrecognized delimiter for "+k)},GetDimen:function(l){var m;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){m=this.GetArgument(l);if(m.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return m.replace(/ /g,"")}}else{m=this.string.slice(this.i);var k=m.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(k){this.i+=k[0].length;return k[1].replace(/ /g,"")}}d.Error("Missing dimension or its units for "+l)},GetUpTo:function(n,o){while(this.nextIsSpace()){this.i++}var m=this.i,l,q,p=0;while(this.i<this.string.length){l=this.i;q=this.string.charAt(this.i++);switch(q){case"\\":q+=this.GetCS();break;case"{":p++;break;case"}":if(p==0){d.Error("Extra close brace while looking for "+o)}p--;break}if(p==0&&q==o){return 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(function(j,b,f,d){var e,h=b.Browser.isMSIE;var g,a,c,i;b.Register.StartupHook("MathZoom Ready",function(){i=MathJax.Extension.MathZoom});j.Augment({config:{styles:{".MathJax_mmlExBox":{display:"block",overflow:"hidden",height:"1px",width:"60ex",padding:0,border:0,margin:0}}},settings:b.config.menuSettings,Config:function(){this.SUPER(arguments).Config.call(this);if(this.settings.scale){this.config.scale=this.settings.scale}if(b.config.displayAlign!=="center"){var m=b.config.displayAlign,k=b.config.displayIndent;var l={"text-align":m+"!important"};l["margin-"+m]=k+"!important";MathJax.Hub.Insert(this.config.styles,{"div.MathJax_MathML":l,"div.MathJax_MathML math":{"text-align":m},"div.MathJax_MathContainer > span":{"text-align":m+"!important"}})}if(!this.require){this.require=[]}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){g=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=g.ContextMenu;this.Mousedown=g.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;if(!h){this.EmExSpan=d.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["div",{className:"MathJax_mmlExBox"}],["span",{className:"MathJax_MathML"}]]);e.math(e.mspace().With({width:"60ex"})).toNativeMML(this.EmExSpan.lastChild)}return f.Styles(this.config.styles)},InitializeMML:function(){this.initialized=true;if(h){try{if(!b.Browser.hasMathPlayer){var k=document.createElement("object");k.id="mathplayer";k.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(k);document.namespaces.add("m","http://www.w3.org/1998/Math/MathML");b.Browser.hasMathPlayer=true}if(!b.Browser.mpImported){document.namespaces.m.doImport("#mathplayer");b.Browser.mpImported=true}}catch(l){alert("MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX     \ncontrols from running.  Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics.")}}else{document.body.appendChild(this.EmExSpan);this.defaultEx=this.EmExSpan.firstChild.offsetWidth/60;this.defaultMEx=this.EmExSpan.lastChild.offsetWidth/60;document.body.removeChild(this.EmExSpan)}},preTranslate:function(l){var r=l.jax[this.id],s,n=r.length,w,p,y,u,x,k,t,q,o;for(s=0;s<n;s++){w=r[s];if(!w.parentNode){continue}if(!this.initialized){this.InitializeMML()}p=w.previousSibling;if(p&&p.className==="MathJax_MathML"){p.parentNode.removeChild(p)}k=w.MathJax.elementJax;x=k.root;k.NativeMML={};var v=(x.Get("display")==="block"?"div":"span");y=d.Element(v,{className:"MathJax_MathML",id:k.inputID+"-Frame"},[["span",{className:"MathJax_MathContainer",isMathJax:true,jaxID:this.id,style:{position:"relative",display:"inline-block","white-space":"nowrap"}},[["span",{isMathJax:true,style:{display:"inline-block"}}]]]]);w.parentNode.insertBefore(y,w);if(!h){w.parentNode.insertBefore(this.EmExSpan.cloneNode(true),w)}}for(s=0;s<n;s++){w=r[s];if(!w.parentNode){continue}k=w.MathJax.elementJax;if(!h){u=w.previousSibling;y=u.previousSibling;t=u.firstChild.offsetWidth/60;q=u.lastChild.offsetWidth/60;if(t===0||t==="NaN"){t=this.defaultEx;q=this.defaultMEx}o=(q>1?t/q:1)*this.config.scale;o=Math.floor(Math.max(this.config.minScaleAdjust/100,o))}else{o=100}k.NativeMML.fontSize=o+"%"}if(!h){for(s=0;s<n;s++){w=r[s];if(!w.parentNode){continue}u=r[s].previousSibling;u.parentNode.removeChild(u)}}},Translate:function(q){if(!q.parentNode){return}var k=q.MathJax.elementJax,r=k.root;var s=document.getElementById(k.inputID+"-Frame"),l=s.firstChild,o=l.firstChild;s.style.fontSize=k.NativeMML.fontSize;try{r.toNativeMML(o)}catch(p){if(p.restart){while(o.firstChild){o.removeChild(o.firstChild)}}throw p}if(h){if(l.addEventListener){for(var m in this.MSIE9events){if(this.MSIE9events.hasOwnProperty(m)){l.addEventListener(m,this.MSIE9event,true)}}}else{var n=(this.config.showMathMenuMSIE!=null?this:b).config;if(n.showMathMenuMSIE&&!this.settings.mpContext&&!this.settings.mpMouse){this.MSIEoverlay(l)}else{l.style.position="";o.firstChild.onmousedown=this.MSIEaltMenu}}}else{l.oncontextmenu=g.Menu;l.onmouseover=g.Mouseover;l.onmouseout=g.Mouseout;l.onmousedown=g.Mousedown;l.onclick=g.Click;l.ondblclick=g.DblClick}},postTranslate:function(l){if(this.forceReflow){var k=(document.styleSheets||[])[0]||{};k.disabled=true;k.disabled=false}},Remove:function(k){var l=k.SourceElement();if(!l){return}l=l.previousSibling;if(!l){return}if(l.className.match(/MathJax_MathML/)){l.parentNode.removeChild(l)}},MMLnamespace:"http://www.w3.org/1998/Math/MathML",MSIEoverlay:function(k){var l=k.firstChild;if(l.nodeName.toLowerCase()==="span"){l=l.firstChild}var m=this.getHoverBBox(null,l,{});d.addElement(k,"span",{style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{isMathJax:true,className:"MathJax_MathPlayer_Overlay",style:{display:"inline-block",position:"absolute",left:c.Px(-m.w),top:c.Px(-m.h-(m.y||0)-1),width:c.Px(m.w),height:c.Px(m.h+m.d),cursor:"pointer","background-color":"white",filter:"alpha(opacity=0)"}}]]);b.Insert(k,{msieMath:l,onmousedown:this.MSIEevent,oncontextmenu:this.MSIEevent,onclick:this.MSIEevent,onmouseup:this.MSIEevent,onmousemove:this.MSIEevent,ondblclick:this.MSIEevent,onmouseover:this.MSIEevent,onmouseout:this.MSIEevent})},MSIEevents:{mousedown:"Mousedown",contextmenu:"ContextMenu",click:"Click",mouseup:"Mouseup",mousemove:"Mousemove",dblclick:"DblClick",mouseover:"Mouseover",mouseout:"Mouseout"},MSIEevent:function(){var l=window.event;var k=j.MSIEevents[l.type];if(j[k]&&j[k](l,this)===false){return false}if(i&&i.HandleEvent(l,k,this)===false){return false}if(l.srcElement.className==="MathJax_MathPlayer_Overlay"&&this.msieMath.fireEvent){if(k==="ContextMenu"||k==="Mouseover"||k==="Mouseout"){this.msieMath.fireEvent("on"+l.type,l)}}return g.False(l)},MSIEaltMenu:function(){var k=this.parentNode.parentNode;while(!k.jaxID){k=k.parentNode}g.AltContextMenu(window.event,k)},MSIE9events:{contextmenu:"Menu",click:"Click",dblclick:"DblClick",mouseup:"False",mouseover:"Mouseover",mouseout:"Mouseout"},MSIE9event:function(l){if(l.type==="contextmenu"&&j.settings.mpContext){return true}if(l.type==="mouseup"&&j.settings.mpMouse){return true}if(l.type==="click"&&j.settings.mpContext){return g.AltContextMenu(l,this)}var k=j.MSIE9events[l.type];return g[k].call(this,l)},getJaxFromMath:function(k){return b.getJaxFor(k.parentNode.nextSibling)},getHoverSpan:function(k,l){return l.firstChild},getHoverBBox:function(k,l,m){return g.getBBox(l.parentNode)},Zoom:function(l,r,p,k,o){l.root.toNativeMML(r);if(this.msieIE8HeightBug){r.style.position="absolute"}var m=p.offsetWidth||p.scrollWidth,s=p.offsetHeight||p.scrollHeight;var q=r.offsetWidth,n=r.offsetHeight;if(this.msieIE8HeightBug){r.style.position=""}return{Y:-g.getBBox(r.parentNode).h,mW:m,mH:s,zW:q,zH:n}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em"}});b.Register.StartupHook("mml Jax Ready",function(){e=MathJax.ElementJax.mml;e.mbase.Augment({toNativeMML:function(p){var n=this.NativeMMLelement(this.type);this.NativeMMLattributes(n);for(var o=0,l=this.data.length;o<l;o++){if(this.data[o]){this.data[o].toNativeMML(n)}else{n.appendChild(this.NativeMMLelement("mrow"))}}p.appendChild(n)},NativeMMLattributes:function(n){var r=this.defaults;var t=(this.attrNames||e.copyAttributeNames),p=e.skipAttributes;if(!this.attrNames){if(this.type==="mstyle"){r=e.math.prototype.defaults}for(var s in r){if(!p[s]&&r.hasOwnProperty(s)){if(this[s]!=null){n.setAttribute(s,this.NativeMMLattribute(this[s]))}}}}for(var o=0,l=t.length;o<l;o++){var q=(this.attr||{})[t[o]];if(q==null){q=this[t[o]]}if(q!=null){n.setAttribute(t[o],this.NativeMMLattribute(q))}}this.NativeMMLclass(n)},NativeMMLclass:function(l){var n=[];if(this["class"]){n.push(this["class"])}if(this.isa(e.TeXAtom)){var m=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(m){n.push("MJX-TeXAtom-"+m)}}if(this.mathvariant&&this.NativeMMLvariants[this.mathvariant]){n.push("MJX"+this.mathvariant)}if(this.arrow){n.push("MJX-arrow")}if(this.variantForm){n.push("MJX-variant")}if(n.length){l.setAttribute("class",n.join(" 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p=this.type;if(this.data[this.sup]==null){p="msub"}if(this.data[this.sub]==null){p="msup"}var n=this.NativeMMLelement(p);this.NativeMMLattributes(n);delete this.data[0].inferred;for(var o=0,l=this.data.length;o<l;o++){if(this.data[o]){this.data[o].toNativeMML(n)}}q.appendChild(n)}});e.munderover.Augment({toNativeMML:function(q){var p=this.type;if(this.data[this.under]==null){p="mover"}if(this.data[this.over]==null){p="munder"}var n=this.NativeMMLelement(p);this.NativeMMLattributes(n);delete this.data[0].inferred;for(var o=0,l=this.data.length;o<l;o++){if(this.data[o]){this.data[o].toNativeMML(n)}}q.appendChild(n)}});if(b.Browser.isFirefox){e.mtable.Augment({toNativeMML:function(l){if(this.width){var m=(this.style||"").replace(/;\s*$/,"").split(";");if(m[0]===""){m.shift()}m.push("width:"+this.width);this.style=m.join(";")}this.SUPER(arguments).toNativeMML.call(this,l)}});if(!b.Browser.versionAtLeast("9.0")){e.mlabeledtr.Augment({toNativeMML:function(p){var n=this.NativeMMLelement("mtr");this.NativeMMLattributes(n);for(var o=1,l=this.data.length;o<l;o++){if(this.data[o]){this.data[o].toNativeMML(n)}else{n.appendChild(this.NativeMMLelement("mrow"))}}p.appendChild(n)}})}var k=MathJax.OutputJax.fontDir+"/HTML-CSS/TeX/otf";j.Augment({config:{styles:{'[mathvariant="double-struck"]':{"font-family":"MathJax_AMS, MathJax_AMS-WEB"},'[mathvariant="script"]':{"font-family":"MathJax_Script, MathJax_Script-WEB"},'[mathvariant="fraktur"]':{"font-family":"MathJax_Fraktur, MathJax_Fraktur-WEB"},'[mathvariant="bold-script"]':{"font-family":"MathJax_Script, MathJax_Caligraphic-WEB","font-weight":"bold"},'[mathvariant="bold-fraktur"]':{"font-family":"MathJax_Fraktur, 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o=0,l=this.data.length;o<l;o++){if(this.data[o]){this.data[o].toNativeMML(n)}else{n.appendChild(this.NativeMMLelement("mrow"))}}p.appendChild(q);if(j.widthBug){p.style.width=q.firstChild.scrollWidth+"px"}}});e.TeXAtom.Augment({toNativeMML:function(m){var l=this.NativeMMLelement("mrow");this.NativeMMLattributes(l);this.data[0].toNativeMML(l);m.appendChild(l)}});e.chars.Augment({toNativeMML:function(l){l.appendChild(document.createTextNode(this.toString()))}});e.entity.Augment({toNativeMML:function(l){l.appendChild(document.createTextNode(this.toString()))}});e.xml.Augment({toNativeMML:function(o){for(var n=0,l=this.data.length;n<l;n++){o.appendChild(this.data[n].cloneNode(true))}}});b.Register.StartupHook("TeX mathchoice Ready",function(){e.TeXmathchoice.Augment({toNativeMML:function(l){this.Core().toNativeMML(l)}})});setTimeout(MathJax.Callback(["loadComplete",j,"jax.js"]),0)});b.Browser.Select({MSIE:function(k){var l=(document.documentMode||0);j.msieIE8HeightBug=(l===8)},Opera:function(k){j.operaPositionBug=true},Firefox:function(k){j.forceReflow=true;j.widthBug=true}});b.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){f.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.OutputJax.NativeMML,MathJax.Hub,MathJax.Ajax,MathJax.HTML);

(function(g,b,d){var f,h=b.Browser.isMobile;var e=MathJax.Object.Subclass({timeout:(h?15:8)*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} []"}},comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,whiteSpace:"nowrap",textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal",fontSizeAdjust:"none"}},[""]);this.text=this.div.firstChild},findFont:function(n,k){if(k&&this.testCollection(k)){return k}for(var l=0,j=n.length;l<j;l++){if(n[l]===k){continue}if(this.testCollection(n[l])){return n[l]}}return null},testCollection:function(j){return this.testFont(this.FontInfo[j])},testFont:function(l){if(l.isWebFont&&d.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(l.weight||"normal");this.div.style.fontStyle=(l.style||"normal")}var k=this.getComparisonWidths(l.testString,l.noStyleChar);if(k){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==k[0]){this.div.style.fontFamily="'"+l.family+"',"+this.comparisonFont[k[2]];if(this.div.offsetWidth==k[1]){return false}}if(this.div.offsetWidth!=k[3]||this.div.offsetHeight!=k[4]){if(l.noStyleChar||!d.FONTDATA||!d.FONTDATA.hasStyleChar){return true}for(var n=0,j=this.testSize.length;n<j;n++){if(this.testStyleChar(l,this.testSize[n])){return true}}}}return false},styleChar:"\uEFFD",versionChar:"\uEFFE",compChar:"\uEFFF",testStyleChar:function(l,o){var r=3+(l.weight?2:0)+(l.style?4:0);var k="",m=0;var q=this.div.style.fontSize;this.div.style.fontSize=o;if(d.msieItalicWidthBug&&l.style==="italic"){this.text.nodeValue=k=this.compChar;m=this.div.offsetWidth}if(d.safariTextNodeBug){this.div.innerHTML=this.compChar+k}else{this.text.nodeValue=this.compChar+k}var j=this.div.offsetWidth-m;if(d.safariTextNodeBug){this.div.innerHTML=this.styleChar+k}else{this.text.nodeValue=this.styleChar+k}var p=Math.floor((this.div.offsetWidth-m)/j+0.5);if(p===r){if(d.safariTextNodeBug){this.div.innerHTML=this.versionChar+k}else{this.text.nodeValue=this.versionChar+k}l.version=Math.floor((this.div.offsetWidth-m)/j+1.5)/2}this.div.style.fontSize=q;return(p===r)},getComparisonWidths:function(o,l){if(d.FONTDATA&&d.FONTDATA.hasStyleChar&&!l){o+=this.styleChar+" "+this.compChar}if(d.safariTextNodeBug){this.div.innerHTML=o}else{this.text.nodeValue=o}this.div.style.fontFamily=this.comparisonFont[0];var k=this.div.offsetWidth;this.div.style.fontFamily=d.webFontDefault;var q=this.div.offsetWidth,n=this.div.offsetHeight;for(var p=1,j=this.comparisonFont.length;p<j;p++){this.div.style.fontFamily=this.comparisonFont[p];if(this.div.offsetWidth!=k){return[k,this.div.offsetWidth,p,q,n]}}return null},loadWebFont:function(k){b.Startup.signal.Post("HTML-CSS Jax - Web-Font "+d.fontInUse+"/"+k.directory);var m=MathJax.Message.File("Web-Font "+d.fontInUse+"/"+k.directory);var j=MathJax.Callback({});var l=MathJax.Callback(["loadComplete",this,k,m,j]);g.timer.start(g,[this.checkWebFont,k,l],0,this.timeout);return j},loadComplete:function(l,o,k,j){MathJax.Message.Clear(o);if(j===g.STATUS.OK){this.webFontLoaded=true;k();return}this.loadError(l);if(b.Browser.isFirefox&&d.allowWebFonts){var m=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){m+=":"+document.location.port}m+="/";if(g.fileURL(d.webfontDir).substr(0,m.length)!==m){this.firefoxFontError(l)}}if(!this.webFontLoaded){d.loadWebFontError(l,k)}else{k()}},loadError:function(j){MathJax.Message.Set("Can't load web font "+d.fontInUse+"/"+j.directory,null,2000);b.Startup.signal.Post(["HTML-CSS Jax - web font error",d.fontInUse+"/"+j.directory,j])},firefoxFontError:function(j){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000);b.Startup.signal.Post("HTML-CSS Jax - Firefox web fonts on remote host error")},checkWebFont:function(j,k,l){if(j.time(l)){return}if(d.Font.testFont(k)){l(j.STATUS.OK)}else{setTimeout(j,j.delay)}},fontFace:function(l){var m=d.allowWebFonts;var o=d.FONTDATA.FONTS[l];if(d.msieFontCSSBug&&!o.family.match(/-Web$/)){o.family+="-Web"}var k=g.fileURL(d.webfontDir+"/"+m);var j=l.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!j.match(/-/)){j+="-Regular"}if(m==="svg"){j+=".svg#"+j}else{j+="."+m}var n={"font-family":o.family,src:"url('"+k+"/"+j+"')"};if(m==="otf"){n.src+=" format('opentype')";k=g.fileURL(d.webfontDir+"/woff");n.src="url('"+k+"/"+j.replace(/otf$/,"woff")+"') format('woff'), "+n.src}else{if(m!=="eot"){n.src+=" format('"+m+"')"}}if(!(d.FontFaceBug&&o.isWebFont)){if(l.match(/-bold/)){n["font-weight"]="bold"}if(l.match(/-italic/)){n["font-style"]="italic"}}return n}});var i,a,c;d.Augment({config:{styles:{".MathJax":{display:"inline","font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none",direction:"ltr",border:0,padding:0,margin:0},".MathJax_Display":{position:"relative",display:"block",width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0 !important",padding:"0 !important",margin:"0 !important","vertical-align":"0 !important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},".MathJax nobr":{"white-space":"nowrap ! important"},".MathJax img":{display:"inline ! 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j=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!j&&this.allowWebFonts){j=this.config.webFont;if(j){this.webFonts=true}}if(!j&&this.config.imageFont){j=this.config.imageFont;this.imgFonts=true}if(j){this.fontInUse=j;this.fontDir+="/"+j;this.webfontDir+="/"+j;this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");b.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{MathJax.Message.Set("Can't find a valid font using ["+this.config.availableFonts.join(", ")+"]",null,3000);this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}};if(MathJax.InputJax.TeX&&MathJax.InputJax.TeX.Definitions){MathJax.InputJax.TeX.Definitions.macros.overline[1]="002D";MathJax.InputJax.TeX.Definitions.macros.underline[1]="002D"}b.Startup.signal.Post("HTML-CSS Jax - no valid 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k=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=k.offsetWidth/5;this.hiddenDiv.removeChild(k);this.startMarker=this.createStrut(this.Element("span"),10,true);this.endMarker=this.addText(this.Element("span"),"x").parentNode;this.HDspan=this.Element("span");if(this.operaHeightBug){this.createStrut(this.HDspan,0)}if(this.msieInlineBlockAlignBug){this.HDimg=this.addElement(this.HDspan,"img",{style:{height:"0px",width:"1px"}});try{this.HDimg.src="about:blank"}catch(j){}}else{this.HDimg=this.createStrut(this.HDspan,0)}this.EmExSpan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["span",{className:"MathJax_ExBox"}],["span",{className:"MathJax"},[["span",{className:"MathJax_EmBox"}]]]]);this.linebreakSpan=this.Element("span",null,[["hr",{style:{width:"100%",size:1,padding:0,border:0,margin:0}}]]);return g.Styles(this.config.styles,["InitializeHTML",this])},removeSTIXfonts:function(l){for(var k=0,j=l.length;k<j;k++){if(l[k]==="STIX"){l.splice(k,1);j--;k--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=l[0]}},PreloadWebFonts:function(){if(!d.allowWebFonts||!d.config.preloadWebFonts){return}for(var k=0,j=d.config.preloadWebFonts.length;k<j;k++){var l=d.FONTDATA.FONTS[d.config.preloadWebFonts[k]];if(!l.available){d.Font.testFont(l)}}},InitializeHTML:function(){this.PreloadWebFonts();document.body.appendChild(this.EmExSpan);document.body.appendChild(this.linebreakSpan);this.defaultEx=this.EmExSpan.firstChild.offsetHeight/60;this.defaultEm=this.EmExSpan.lastChild.firstChild.offsetHeight/60;this.defaultWidth=this.linebreakSpan.firstChild.offsetWidth;document.body.removeChild(this.linebreakSpan);document.body.removeChild(this.EmExSpan)},preTranslate:function(n){var 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q=this.addElement(t,"span");this.createChar(q,[j,k.HW[r][1]],p,n);t.bbox=q.bbox;t.offset=0.65*t.bbox.w;t.scale=p;return}}if(k.stretch){this["extendDelimiter"+k.dir](t,s,k.stretch,p,n)}},extendDelimiterV:function(z,s,D,E,v){var m=this.createStack(z,true);var u=this.createBox(m),t=this.createBox(m);this.createChar(u,(D.top||D.ext),E,v);this.createChar(t,(D.bot||D.ext),E,v);var l={bbox:{w:0,lw:0,rw:0}},C=l,o;var A=u.bbox.h+u.bbox.d+t.bbox.h+t.bbox.d;var q=-u.bbox.h;this.placeBox(u,0,q,true);q-=u.bbox.d;if(D.mid){C=this.createBox(m);this.createChar(C,D.mid,E,v);A+=C.bbox.h+C.bbox.d}if(s>A){l=this.Element("span");this.createChar(l,D.ext,E,v);var B=l.bbox.h+l.bbox.d,j=B-0.05,w,p,x=(D.mid?2:1);p=w=Math.ceil((s-A)/(x*j));if(!D.fullExtenders){j=(s-A)/(x*w)}var 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C={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},l;this.placeBox(o,-o.bbox.lw,0,true);var t=(o.bbox.rw-o.bbox.lw)+(B.bbox.rw-B.bbox.lw)-0.05,s=o.bbox.rw-o.bbox.lw-0.025,u;if(D.mid){C=this.createBox(q);this.createChar(C,D.mid,F,v);t+=C.bbox.w}if(m>t){var E=j.bbox.rw-j.bbox.lw,p=E-0.05,y,r,z=(D.mid?2:1);r=y=Math.ceil((m-t)/(z*p));if(!D.fillExtenders){p=(m-t)/(z*y)}u=(y/(y+1))*(E-p);p=E-u;s-=j.bbox.lw+u;while(z-->0){while(y-->0){if(!this.msieCloneNodeBug){l=j.cloneNode(true)}else{l=this.Element("span");this.createChar(l,D.rep,F,v)}this.placeBox(this.addBox(q,l),s,0,true);s+=p}if(D.mid&&z){this.placeBox(C,s,0,true);s+=C.bbox.w-u;y=r}}}else{u=Math.min(t-m,o.bbox.w/2);s-=u/2;if(D.mid){this.placeBox(C,s,0,true);s+=C.bbox.w}s-=u/2}this.placeBox(B,s,0,true);A.bbox={w:s+B.bbox.rw,lw:0,rw:s+B.bbox.rw,H:Math.max(o.bbox.h,j.bbox.h,B.bbox.h,C.bbox.h),D:Math.max(o.bbox.d,j.bbox.d,B.bbox.d,C.bbox.d),h:j.bbox.h,d:j.bbox.d,exactW:true};A.scale=F;A.isMultiChar=true;this.setStackWidth(q,A.bbox.w)},createChar:function(r,o,l,j){r.isMathJax=true;var q=r,s="",n={fonts:[o[1]],noRemap:true};if(j&&j===f.VARIANT.BOLD){n.fonts=[o[1]+"-bold",o[1]]}if(typeof(o[1])!=="string"){n=o[1]}if(o[0] instanceof Array){for(var 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l=o.remap[w];w=l[0];o=this.FONTDATA.VARIANT[l[1]]}else{if(typeof(o.remap[w])==="string"){r=o.remap[w]+r.substr(A+1);A=0;x=r.length;w=r.charCodeAt(0)}else{w=o.remap[w];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}}}if(this.FONTDATA.REMAP[w]&&!o.noRemap){w=this.FONTDATA.REMAP[w];if(w instanceof Array){o=this.FONTDATA.VARIANT[w[1]];w=w[0]}if(typeof(w)==="string"){r=w+r.substr(A+1);A=0;x=r.length;w=w.charCodeAt(0)}}s=this.lookupChar(o,w);B=s[w];if(k||(!this.checkFont(s,j.style)&&!B[5].img)){if(y.length){this.addText(j,y);y=""}var v=!!j.style.fontFamily||!!z.style.fontStyle||!!z.style.fontWeight||!s.directory||k;k=false;if(j!==z){v=!this.checkFont(s,z.style);j=z}if(v){j=this.addElement(z,"span",{isMathJax:true,subSpan:true})}this.handleFont(j,s,j!==z)}y=this.handleChar(j,s,B,w,y);if(B[0]/1000>z.bbox.h){z.bbox.h=B[0]/1000}if(B[1]/1000>z.bbox.d){z.bbox.d=B[1]/1000}if(z.bbox.w+B[3]/1000<z.bbox.lw){z.bbox.lw=z.bbox.w+B[3]/1000}if(z.bbox.w+B[4]/1000>z.bbox.rw){z.bbox.rw=z.bbox.w+B[4]/1000}z.bbox.w+=B[2]/1000}if(y.length){this.addText(j,y)}if(z.scale&&z.scale!==1){z.bbox.h*=z.scale;z.bbox.d*=z.scale;z.bbox.w*=z.scale;z.bbox.lw*=z.scale;z.bbox.rw*=z.scale}if(r.length==1&&s.skew&&s.skew[w]){z.bbox.skew=s.skew[w]}},checkFont:function(j,k){var l=(k.fontWeight||"normal");if(l.match(/^\d+$/)){l=(parseInt(l)>=600?"bold":"normal")}return(j.family.replace(/'/g,"")===k.fontFamily.replace(/'/g,"")&&(j.style||"normal")===(k.fontStyle||"normal")&&(j.weight||"normal")===l)},handleFont:function(l,j,n){l.style.fontFamily=j.family;if(!j.directory){l.style.fontSize=Math.floor(100/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&j.isWebFont)){var k=j.style||"normal",m=j.weight||"normal";if(k!=="normal"||n){l.style.fontStyle=k}if(m!=="normal"||n){l.style.fontWeight=m}}},handleChar:function(k,j,r,q,p){var o=r[5];if(o.img){return this.handleImg(k,j,r,q,p)}if(o.isUnknown&&this.FONTDATA.DELIMITERS[q]){if(p.length){this.addText(k,p)}var m=k.scale;d.createDelimiter(k,q,0,1,j);k.scale=m;r[0]=k.bbox.h*1000;r[1]=k.bbox.d*1000;r[2]=k.bbox.w*1000;r[3]=k.bbox.lw*1000;r[4]=k.bbox.rw*1000;return""}if(o.c==null){if(q<=65535){o.c=String.fromCharCode(q)}else{var 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q=this.getValues("symmetric","maxsize","minsize");var o=this.HTMLspanElement(),r=this.HTMLgetMu(o),p;var j=d.TeX.axis_height,k=o.scale;if(q.symmetric){p=2*Math.max(m-j,n+j)}else{p=m+n}q.maxsize=d.length2em(q.maxsize,r,o.bbox.h+o.bbox.d);q.minsize=d.length2em(q.minsize,r,o.bbox.h+o.bbox.d);p=Math.max(q.minsize,Math.min(q.maxsize,p));o=this.HTMLcreateSpan(l);d.createDelimiter(o,this.data.join("").charCodeAt(0),p,k);if(q.symmetric){p=(o.bbox.h+o.bbox.d)/2+j}else{p=(o.bbox.h+o.bbox.d)*m/(m+n)}d.positionDelimiter(o,p);this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:function(n,j){this.HTMLremoveColor();var l=this.getValues("maxsize","minsize","mathvariant","fontweight");if((l.fontweight==="bold"||parseInt(l.fontweight)>=600)&&!this.Get("mathvariant",true)){l.mathvariant=f.VARIANT.BOLD}var m=this.HTMLspanElement(),k=this.HTMLgetMu(m),o=m.scale;l.maxsize=d.length2em(l.maxsize,k,m.bbox.w);l.minsize=d.length2em(l.minsize,k,m.bbox.w);j=Math.max(l.minsize,Math.min(l.maxsize,j));m=this.HTMLcreateSpan(n);d.createDelimiter(m,this.data.join("").charCodeAt(0),j,o,l.mathvariant);this.HTMLhandleSpace(m);this.HTMLhandleColor(m);return m}});f.mtext.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));var l=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){l=null}for(var k=0,j=this.data.length;k<j;k++){if(this.data[k]){this.data[k].toHTML(n,l)}}if(!n.bbox){n.bbox={w:0,h:0,d:0,rw:0,lw:0}}if(this.data.join("").length!==1){delete n.bbox.skew}this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});f.merror.Augment({toHTML:function(k){var m=MathJax.HTML.addElement(k,"span",{style:{display:"inline-block"}});k=this.SUPER(arguments).toHTML.call(this,m);var l=d.getHD(m),j=d.getW(m);m.bbox={h:l.h,d:l.d,w:j,lw:0,rw:j,exactW:true};m.id=k.id;k.id=null;return m}});f.ms.Augment({toHTML:f.mbase.HTMLautoload});f.mglyph.Augment({toHTML:f.mbase.HTMLautoload});f.mspace.Augment({toHTML:function(n){n=this.HTMLhandleSize(this.HTMLcreateSpan(n));var l=this.getValues("height","depth","width");var k=this.HTMLgetMu(n);l.mathbackground=this.mathbackground;if(this.background&&!this.mathbackground){l.mathbackground=this.background}var m=d.length2em(l.height,k)/n.scale,o=d.length2em(l.depth,k)/n.scale,j=d.length2em(l.width,k)/n.scale;d.createSpace(n,m,o,j,l.mathbackground);return n}});f.mphantom.Augment({toHTML:function(n,k,p){n=this.HTMLcreateSpan(n);if(this.data[0]!=null){var o=this.data[0].toHTML(n);if(p!=null){d.Remeasured(this.data[0].HTMLstretchV(n,k,p),n)}else{if(k!=null){d.Remeasured(this.data[0].HTMLstretchH(n,k),n)}else{o=d.Measured(o,n)}}n.bbox={w:o.bbox.w,h:o.bbox.h,d:o.bbox.d,lw:0,rw:0,exactW:true};for(var 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s=this.getValues("height","depth","width","lspace","voffset"),q=0,o=0,t=this.HTMLgetMu(r);if(s.lspace){q=this.HTMLlength2em(m,s.lspace,t)}if(s.voffset){o=this.HTMLlength2em(m,s.voffset,t)}d.placeBox(m,q,o);r.bbox={h:m.bbox.h,d:m.bbox.d,w:m.bbox.w,exactW:true,lw:Math.min(0,m.bbox.lw+q),rw:Math.max(m.bbox.w,m.bbox.rw+q),H:Math.max((m.bbox.H==null?-d.BIGDIMEN:m.bbox.H),m.bbox.h+o),D:Math.max((m.bbox.D==null?-d.BIGDIMEN:m.bbox.D),m.bbox.d-o)};if(s.height!==""){r.bbox.h=this.HTMLlength2em(m,s.height,t,"h",0)}if(s.depth!==""){r.bbox.d=this.HTMLlength2em(m,s.depth,t,"d",0)}if(s.width!==""){r.bbox.w=this.HTMLlength2em(m,s.width,t,"w",0)}if(r.bbox.H<=r.bbox.h){delete r.bbox.H}if(r.bbox.D<=r.bbox.d){delete r.bbox.D}var n=/^\s*(\d+(\.\d*)?|\.\d+)\s*(pt|em|ex|mu|px|pc|in|mm|cm)\s*$/;r.bbox.exact=!!((this.data[0]&&this.data[0].data.length==0)||n.exec(s.height)||n.exec(s.width)||n.exec(s.depth));d.setStackWidth(p,r.bbox.w)}this.HTMLhandleSpace(r);this.HTMLhandleColor(r);return 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m=this.data[0].toHTML(k);if(l!=null){this.data[0].HTMLstretchV(k,j,l)}else{if(j!=null){this.data[0].HTMLstretchH(k,j)}}k.bbox=m.bbox}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mfrac.Augment({toHTML:function(C){C=this.HTMLcreateSpan(C);var l=d.createStack(C);var o=d.createBox(l),n=d.createBox(l);d.MeasureSpans([this.HTMLboxChild(0,o),this.HTMLboxChild(1,n)]);var j=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var G=this.HTMLgetScale(),B=j.displaystyle;var F=d.TeX.axis_height*G;if(j.bevelled){var E=(B?0.4:0.15);var r=Math.max(o.bbox.h+o.bbox.d,n.bbox.h+n.bbox.d)+2*E;var D=d.createBox(l);d.createDelimiter(D,47,r);d.placeBox(o,0,(o.bbox.d-o.bbox.h)/2+F+E);d.placeBox(D,o.bbox.w-E/2,(D.bbox.d-D.bbox.h)/2+F);d.placeBox(n,o.bbox.w+D.bbox.w-E,(n.bbox.d-n.bbox.h)/2+F-E)}else{var k=Math.max(o.bbox.w,n.bbox.w);var x=d.thickness2em(j.linethickness,G),z,y,w,s;var 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z=d.TeX.rule_thickness*o,l,k,w,n;if(this.Get("displaystyle")){l=d.TeX.x_height*o}else{l=z}k=Math.max(z+l/4,1.5*d.TeX.min_rule_thickness/this.em);var j=this.HTMLboxChild(0,m);w=j.bbox.h+j.bbox.d+k+z;d.createDelimiter(r,8730,w,o);d.MeasureSpans([j,r]);n=j.bbox.w;var u=0;if(r.isMultiChar||(d.AdjustSurd&&d.imgFonts)){r.bbox.w*=0.95}if(r.bbox.h+r.bbox.d>w){k=((r.bbox.h+r.bbox.d)-(w-z))/2}var A=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!A||n<A.HW[0][0]*o||o<0.75){d.createRule(s,z,0,n)}else{d.createDelimiter(s,d.FONTDATA.RULECHAR,n,o)}w=j.bbox.h+k+z;k=w*d.rfuzz;if(r.isMultiChar){k=d.rfuzz}u=this.HTMLaddRoot(y,r,u,r.bbox.h+r.bbox.d-w,o);d.placeBox(r,u,w-r.bbox.h);d.placeBox(s,u+r.bbox.w,w-s.bbox.h+k);d.placeBox(m,u+r.bbox.w,0);this.HTMLhandleSpace(v);this.HTMLhandleColor(v);return v},HTMLaddRoot:function(l,k,j,n,m){return j}});f.mroot.Augment({toHTML:f.msqrt.prototype.toHTML,HTMLaddRoot:function(r,k,p,n,j){var l=d.createBox(r);if(this.data[1]){var o=this.data[1].toHTML(l);o.style.paddingRight=o.style.paddingLeft="";d.Measured(o,l)}else{l.bbox=this.HTMLzeroBBox()}var m=this.HTMLrootHeight(k.bbox.h+k.bbox.d,j,l)-n;var q=Math.min(l.bbox.w,l.bbox.rw);p=Math.max(q,k.offset);d.placeBox(l,p-q,m);return p-k.offset},HTMLrootHeight:function(l,k,j){return 0.45*(l-0.9*k)+0.6*k+Math.max(0,j.bbox.d-0.075)}});f.mfenced.Augment({toHTML:function(n){n=this.HTMLcreateSpan(n);if(this.data.open){this.data.open.toHTML(n)}if(this.data[0]!=null){this.data[0].toHTML(n)}for(var k=1,j=this.data.length;k<j;k++){if(this.data[k]){if(this.data["sep"+k]){this.data["sep"+k].toHTML(n)}this.data[k].toHTML(n)}}if(this.data.close){this.data.close.toHTML(n)}var p=this.HTMLcomputeBBox(n);var l=n.bbox.h,o=n.bbox.d;for(k=0,j=p.length;k<j;k++){p[k].HTMLstretchV(n,l,o)}if(p.length){this.HTMLcomputeBBox(n,true)}this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n},HTMLcomputeBBox:function(o,n){var k=o.bbox={},p=[];this.HTMLcheckStretchy(this.data.open,k,p,n);this.HTMLcheckStretchy(this.data[0],k,p,n);for(var l=1,j=this.data.length;l<j;l++){if(this.data[l]){this.HTMLcheckStretchy(this.data["sep"+l],k,p,n);this.HTMLcheckStretchy(this.data[l],k,p,n)}}this.HTMLcheckStretchy(this.data.close,k,p,n);this.HTMLcleanBBox(k);return p},HTMLcheckStretchy:function(j,k,m,l){if(j){if(!l&&j.HTMLcanStretch("Vertical")){m.push(j);j=(j.CoreMO()||j)}this.HTMLcombineBBoxes(j,k)}}});f.menclose.Augment({toHTML:f.mbase.HTMLautoload});f.maction.Augment({toHTML:f.mbase.HTMLautoload});f.semantics.Augment({toHTML:function(j){if(this.data[0]!=null){j=this.data[0].toHTML(j);this.spanID=this.data[0].spanID;this.HTMLhandleSpace(j)}return j},HTMLspanElement:function(){return(this.data[0]!=null?this.data[0].HTMLspanElement():null)},HTMLstretchH:function(k,j){return(this.data[0]!=null?this.data[0].HTMLstretchH(k,j):k)},HTMLstretchV:function(k,j,l){return(this.data[0]!=null?this.data[0].HTMLstretchV(k,j,l):k)}});f.munderover.Augment({toHTML:function(K,G,E){var j=this.getValues("displaystyle","accent","accentunder","align");if(!j.displaystyle&&this.data[this.base]!=null&&this.data[this.base].CoreMO().Get("movablelimits")){return f.msubsup.prototype.toHTML.call(this,K)}K=this.HTMLcreateSpan(K);var O=this.HTMLgetScale();var p=d.createStack(K);var q=[],n=[],M=[],v,L,H;for(L=0,H=this.data.length;L<H;L++){if(this.data[L]!=null){v=q[L]=d.createBox(p);n[L]=this.data[L].toHTML(v);if(L==this.base){if(E!=null){this.data[this.base].HTMLstretchV(v,G,E)}else{if(G!=null){this.data[this.base].HTMLstretchH(v,G)}}M[L]=(E==null&&G!=null?false:this.data[L].HTMLcanStretch("Horizontal"))}else{M[L]=this.data[L].HTMLcanStretch("Horizontal")}}}d.MeasureSpans(n);var l=-d.BIGDIMEN,J=l;for(L=0,H=this.data.length;L<H;L++){if(this.data[L]){if(q[L].bbox.w>J){J=q[L].bbox.w}if(!M[L]&&J>l){l=J}}}if(E==null&&G!=null){l=G}else{if(l==-d.BIGDIMEN){l=J}}for(L=J=0,H=this.data.length;L<H;L++){if(this.data[L]){v=q[L];if(M[L]){v.bbox=this.data[L].HTMLstretchH(v,l).bbox}if(v.bbox.w>J){J=v.bbox.w}}}var C=d.TeX.rule_thickness,F=d.FONTDATA.TeX_factor;var o=q[this.base]||{bbox:this.HTMLzeroBBox()};var u,r,z,w,s,B,I,N=0;if(o.bbox.ic){N=1.3*o.bbox.ic+0.05}for(L=0,H=this.data.length;L<H;L++){if(this.data[L]!=null){v=q[L];s=d.TeX.big_op_spacing5*O;var A=(L!=this.base&&j[this.ACCENTS[L]]);if(A&&v.bbox.w<=1/d.em+0.0001){v.bbox.w=v.bbox.rw-v.bbox.lw;v.bbox.noclip=true;if(v.bbox.lw&&!d.zeroWidthBug){v.insertBefore(d.createSpace(v.parentNode,0,0,-v.bbox.lw),v.firstChild)}d.createBlank(v,0,0,v.bbox.rw+0.1)}B={left:0,center:(J-v.bbox.w)/2,right:J-v.bbox.w}[j.align];u=B;r=0;if(L==this.over){if(A){I=Math.max(C*O*F,2.5/this.em);s=0;if(o.bbox.skew){u+=o.bbox.skew}}else{z=d.TeX.big_op_spacing1*O*F;w=d.TeX.big_op_spacing3*O*F;I=Math.max(z,w-Math.max(0,v.bbox.d))}I=Math.max(I,1.5/this.em);u+=N/2;r=o.bbox.h+v.bbox.d+I;v.bbox.h+=s}else{if(L==this.under){if(A){I=3*C*O*F;s=0}else{z=d.TeX.big_op_spacing2*O*F;w=d.TeX.big_op_spacing4*O*F;I=Math.max(z,w-v.bbox.h)}I=Math.max(I,1.5/this.em);u-=N/2;r=-(o.bbox.d+v.bbox.h+I);v.bbox.d+=s}}d.placeBox(v,u,r)}}this.HTMLhandleSpace(K);this.HTMLhandleColor(K);return K},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.msubsup.Augment({toHTML:function(J,H,B){J=this.HTMLcreateSpan(J);var M=this.HTMLgetScale(),G=this.HTMLgetMu(J);var o=d.createStack(J),k,m=[];var n=d.createBox(o);if(this.data[this.base]){m.push(this.data[this.base].toHTML(n));if(B!=null){this.data[this.base].HTMLstretchV(n,H,B)}else{if(H!=null){this.data[this.base].HTMLstretchH(n,H)}}}else{n.bbox=this.HTMLzeroBBox()}var l=(this.data[this.sup]||this.data[this.sub]||this).HTMLgetScale();var K=d.TeX.x_height*M,A=d.TeX.scriptspace*M*0.75;var j,w;if(this.HTMLnotEmpty(this.data[this.sup])){j=d.createBox(o);m.push(this.data[this.sup].toHTML(j))}if(this.HTMLnotEmpty(this.data[this.sub])){w=d.createBox(o);m.push(this.data[this.sub].toHTML(w))}d.MeasureSpans(m);if(j){j.bbox.w+=A;j.bbox.rw=Math.max(j.bbox.w,j.bbox.rw)}if(w){w.bbox.w+=A;w.bbox.rw=Math.max(w.bbox.w,w.bbox.rw)}d.placeBox(n,0,0);var E=d.TeX.sup_drop*l,C=d.TeX.sub_drop*l;var y=n.bbox.h-E,x=n.bbox.d+C,L=0,F;if(n.bbox.ic){n.bbox.w-=n.bbox.ic;L=1.3*n.bbox.ic+0.05}if(this.data[this.base]&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&n.bbox.scale===1&&!this.data[this.base].Get("largeop")){y=x=0}}var I=this.getValues("subscriptshift","superscriptshift");I.subscriptshift=(I.subscriptshift===""?0:d.length2em(I.subscriptshift,G));I.superscriptshift=(I.superscriptshift===""?0:d.length2em(I.superscriptshift,G));if(!j){if(w){x=Math.max(x,d.TeX.sub1*M,w.bbox.h-(4/5)*K,I.subscriptshift);d.placeBox(w,n.bbox.w,-x,w.bbox)}}else{if(!w){k=this.getValues("displaystyle","texprimestyle");F=d.TeX[(k.displaystyle?"sup1":(k.texprimestyle?"sup3":"sup2"))];y=Math.max(y,F*M,j.bbox.d+(1/4)*K,I.superscriptshift);d.placeBox(j,n.bbox.w+L,y,j.bbox)}else{x=Math.max(x,d.TeX.sub2*M);var z=d.TeX.rule_thickness*M;if((y-j.bbox.d)-(w.bbox.h-x)<3*z){x=3*z-y+j.bbox.d+w.bbox.h;E=(4/5)*K-(y-j.bbox.d);if(E>0){y+=E;x-=E}}d.placeBox(j,n.bbox.w+L,Math.max(y,I.superscriptshift));d.placeBox(w,n.bbox.w,-Math.max(x,I.subscriptshift))}}this.HTMLhandleSpace(J);this.HTMLhandleColor(J);return J},HTMLstretchH:f.mbase.HTMLstretchH,HTMLstretchV:f.mbase.HTMLstretchV});f.mmultiscripts.Augment({toHTML:f.mbase.HTMLautoload});f.mtable.Augment({toHTML:f.mbase.HTMLautoload});f["annotation-xml"].Augment({toHTML:f.mbase.HTMLautoload});f.math.Augment({toHTML:function(s,k){var o=this.Get("alttext");if(o&&o!==""){k.setAttribute("aria-label",o)}var l=d.addElement(s,"nobr",{isMathJax:true});s=this.HTMLcreateSpan(l);var q=d.createStack(s),m=d.createBox(q),r;q.style.fontSize=l.parentNode.style.fontSize;l.parentNode.style.fontSize="";if(this.data[0]!=null){if(d.msieColorBug){if(this.background){this.data[0].background=this.background;delete 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t=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(t.indentalignfirst!==f.INDENTALIGN.INDENTALIGN){t.indentalign=t.indentalignfirst}if(t.indentalign===f.INDENTALIGN.AUTO){t.indentalign=this.displayAlign}k.style.textAlign=t.indentalign;if(t.indentshiftfirst!==f.INDENTSHIFT.INDENTSHIFT){t.indentshift=t.indentshiftfirst}if(t.indentshift==="auto"){t.indentshift=this.displayIndent}if(t.indentshift&&t.indentalign!==f.INDENTALIGN.CENTER){s.style[{left:"marginLeft",right:"marginRight"}[t.indentalign]]=d.Em(d.length2em(t.indentshift))}}return s},HTMLspanElement:f.mbase.prototype.HTMLspanElement});f.TeXAtom.Augment({toHTML:function(k){k=this.HTMLcreateSpan(k);if(this.data[0]!=null){if(this.texClass===f.TEXCLASS.VCENTER){var j=d.createStack(k);var l=d.createBox(j);d.Measured(this.data[0].toHTML(l),l);d.placeBox(l,0,d.TeX.axis_height-(l.bbox.h+l.bbox.d)/2+l.bbox.d)}else{k.bbox=this.data[0].toHTML(k).bbox}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return 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j=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/);var k=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var p=(l&&o.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!o.versionAtLeast("5.0"))||(k!=null&&(k[1]<2||(k[1]==2&&k[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!l,safariTextNodeBug:!m,forceReflow:true,allowWebFonts:(l&&!p?"otf":false)});if(j){d.Augment({webFontDefault:(o.isMobile?"sans-serif":"serif")})}if(o.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts,checkWebFontsTwice:true})}if(p){var 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MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="2.0";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a.mtable.Augment({toHTML:function(r){r=this.HTMLcreateSpan(r);if(this.data.length===0){return r}var G=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");var aF=G.width.match(/%$/);var av=b.createStack(r);var aC=this.HTMLgetScale(),ax=this.HTMLgetMu(r),ay=-1;var ao=[],ar=[],ai=[],au=[],at=[],ad,ac,an=-1,ab,am,V,aB,aJ=[];var aj=b.FONTDATA.baselineskip*aC*G.useHeight,E=b.FONTDATA.lineH*aC,L=b.FONTDATA.lineD*aC;for(ad=0,ab=this.data.length;ad<ab;ad++){aB=this.data[ad];V=(aB.type==="mlabeledtr"?ay:0);au[ad]=[];ao[ad]=ar[ad]=0;for(ac=V,am=aB.data.length+V;ac<am;ac++){if(ai[ac]==null){if(ac>an){an=ac}at[ac]=b.createStack(b.createBox(av));ai[ac]=-b.BIGDIMEN}au[ad][ac]=b.createBox(at[ac]);aJ.push(aB.data[ac-V].toHTML(au[ad][ac]))}}b.MeasureSpans(aJ);for(ad=0,ab=this.data.length;ad<ab;ad++){aB=this.data[ad];V=(aB.type==="mlabeledtr"?ay:0);for(ac=V,am=aB.data.length+V;ac<am;ac++){if(aB.data[ac-V].isMultiline){au[ad][ac].style.width="100%"}if(au[ad][ac].bbox.h>ao[ad]){ao[ad]=au[ad][ac].bbox.h}if(au[ad][ac].bbox.d>ar[ad]){ar[ad]=au[ad][ac].bbox.d}if(au[ad][ac].bbox.w>ai[ac]){ai[ac]=au[ad][ac].bbox.w}}}if(ao[0]+ar[0]){ao[0]=Math.max(ao[0],E)}if(ao[au.length-1]+ar[au.length-1]){ar[au.length-1]=Math.max(ar[au.length-1],L)}var aw=G.columnspacing.split(/ /),aL=G.rowspacing.split(/ /),e=G.columnalign.split(/ 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