/*
 *  /MathJax/config/TeX-AMS-MML_SVG.js
 *  
 *  Copyright (c) 2010-2014 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/output/SVG/config.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.Hub.Config({"v1.0-compatible":false});

MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.4.0",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:"2.4.0",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.SVG=MathJax.OutputJax({id:"SVG",version:"2.4.0",directory:MathJax.OutputJax.directory+"/SVG",extensionDir:MathJax.OutputJax.extensionDir+"/SVG",autoloadDir:MathJax.OutputJax.directory+"/SVG/autoload",fontDir:MathJax.OutputJax.directory+"/SVG/fonts",config:{scale:100,minScaleAdjust:50,font:"TeX",blacker:10,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",addMMLclasses:false,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},merrorStyle:{fontSize:"90%",color:"#C00",background:"#FF8",border:"1px solid #C00",padding:"3px"},styles:{".MathJax_SVG_Display":{"text-align":"center",margin:"1em 0em"},".MathJax_SVG .MJX-monospace":{"font-family":"monospace"},".MathJax_SVG .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_SVG_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",padding:"3px 4px","z-index":401}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.SVG.Register("jax/mml")}MathJax.OutputJax.SVG.loadComplete("config.js");
MathJax.Extension.tex2jax={version:"2.4.0",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],balanceBraces:true,skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c<a;c++){d.push(this.patternQuote(b.inlineMath[c][0]));this.match[b.inlineMath[c][0]]={mode:"",end:b.inlineMath[c][1],pattern:this.endPattern(b.inlineMath[c][1])}}for(c=0,a=b.displayMath.length;c<a;c++){d.push(this.patternQuote(b.displayMath[c][0]));this.match[b.displayMath[c][0]]={mode:"; mode=display",end:b.displayMath[c][1],pattern:this.endPattern(b.displayMath[c][1])}}if(d.length){e.push(d.sort(this.sortLength).join("|"))}if(b.processEnvironments){e.push("\\\\begin\\{([^}]*)\\}")}if(b.processEscapes){e.push("\\\\*\\\\\\$")}if(b.processRefs){e.push("\\\\(eq)?ref\\{[^}]*\\}")}this.start=new RegExp(e.join("|"),"g");this.skipTags=new RegExp("^("+b.skipTags.join("|")+")$","i");var f=[];if(MathJax.Hub.config.preRemoveClass){f.push(MathJax.Hub.config.preRemoveClass)}if(b.ignoreClass){f.push(b.ignoreClass)}this.ignoreClass=(f.length?new RegExp("(^| )("+f.join("|")+")( |$)"):/^$/);this.processClass=new RegExp("(^| )("+b.processClass+")( |$)");return(e.length>0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d<c?-1:1))},scanElement:function(c,b,g){var a,e,d,f;while(c&&c!=b){if(c.nodeName.toLowerCase()==="#text"){if(!g){c=this.scanText(c)}}else{a=(typeof(c.className)==="undefined"?"":c.className);e=(typeof(c.tagName)==="undefined"?"":c.tagName);if(typeof(a)!=="string"){a=String(a)}f=this.processClass.exec(a);if(c.firstChild&&!a.match(/(^| )MathJax/)&&(f||!this.skipTags.exec(e))){d=(g||this.ignoreClass.exec(a))&&!f;this.scanElement(c.firstChild,b,d)}}if(c){c=c.nextSibling}}},scanText:function(b){if(b.nodeValue.replace(/\s+/,"")==""){return b}var a,c;this.search={start:true};this.pattern=this.start;while(b){this.pattern.lastIndex=0;while(b&&b.nodeName.toLowerCase()==="#text"&&(a=this.pattern.exec(b.nodeValue))){if(this.search.start){b=this.startMatch(a,b)}else{b=this.endMatch(a,b)}}if(this.search.matched){b=this.encloseMath(b)}if(b){do{c=b;b=b.nextSibling}while(b&&(b.nodeName.toLowerCase()==="br"||b.nodeName.toLowerCase()==="#comment"));if(!b||b.nodeName!=="#text"){return(this.search.close?this.prevEndMatch():c)}}}return b},startMatch:function(a,b){var f=this.match[a[0]];if(f!=null){this.search={end:f.end,mode:f.mode,pcount:0,open:b,olen:a[0].length,opos:this.pattern.lastIndex-a[0].length};this.switchPattern(f.pattern)}else{if(a[0].substr(0,6)==="\\begin"){this.search={end:"\\end{"+a[1]+"}",mode:"; mode=display",pcount:0,open:b,olen:0,opos:this.pattern.lastIndex-a[0].length,isBeginEnd:true};this.switchPattern(this.endPattern(this.search.end))}else{if(a[0].substr(0,4)==="\\ref"||a[0].substr(0,6)==="\\eqref"){this.search={mode:"",end:"",open:b,pcount:0,olen:0,opos:this.pattern.lastIndex-a[0].length};return this.endMatch([""],b)}else{var d=a[0].substr(0,a[0].length-1),g,c;if(d.length%2===0){c=[d.replace(/\\\\/g,"\\")];g=1}else{c=[d.substr(1).replace(/\\\\/g,"\\"),"$"];g=0}c=MathJax.HTML.Element("span",null,c);var e=MathJax.HTML.TextNode(b.nodeValue.substr(0,a.index));b.nodeValue=b.nodeValue.substr(a.index+a[0].length-g);b.parentNode.insertBefore(c,b);b.parentNode.insertBefore(e,c);this.pattern.lastIndex=g}}}return b},endMatch:function(a,c){var b=this.search;if(a[0]==b.end){if(!b.close||b.pcount===0){b.close=c;b.cpos=this.pattern.lastIndex;b.clen=(b.isBeginEnd?0:a[0].length)}if(b.pcount===0){b.matched=true;c=this.encloseMath(c);this.switchPattern(this.start)}}else{if(a[0]==="{"){b.pcount++}else{if(a[0]==="}"&&b.pcount){b.pcount--}}}return c},prevEndMatch:function(){this.search.matched=true;var a=this.encloseMath(this.search.close);this.switchPattern(this.start);return a},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=(a===this.start)},encloseMath:function(b){var a=this.search,f=a.close,e,c;if(a.cpos===f.length){f=f.nextSibling}else{f=f.splitText(a.cpos)}if(!f){e=f=MathJax.HTML.addText(a.close.parentNode,"")}a.close=f;c=(a.opos?a.open.splitText(a.opos):a.open);while(c.nextSibling&&c.nextSibling!==f){if(c.nextSibling.nodeValue!==null){if(c.nextSibling.nodeName==="#comment"){c.nodeValue+=c.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{c.nodeValue+=c.nextSibling.nodeValue}}else{if(this.msieNewlineBug){c.nodeValue+=(c.nextSibling.nodeName.toLowerCase()==="br"?"\n":" ")}else{c.nodeValue+=" "}}c.parentNode.removeChild(c.nextSibling)}var d=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);if(this.config.preview!=="none"){this.createPreview(a.mode,d)}c=this.createMathTag(a.mode,d);this.search={};this.pattern.lastIndex=0;if(e){e.parentNode.removeChild(e)}return c},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(c,a){var b=this.config.preview;if(b==="none"){return}if(b==="TeX"){b=[this.filterPreview(a)]}if(b){b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b);this.insertNode(b)}},createMathTag:function(c,b){var a=document.createElement("script");a.type="math/tex"+c;MathJax.HTML.setScript(a,b);this.insertNode(a);return a},filterPreview:function(a){return a},msieNewlineBug:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9)};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js");
MathJax.Extension.mml2jax={version:"2.4.0",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&&!h[e].prefix===!c){f.push(h[e])}}},ProcessMathArray:function(c){var b,a=c.length;if(a){if(this.MathTagBug){for(b=0;b<a;b++){if(c[b].nodeName==="MATH"){this.ProcessMathFlattened(c[b])}else{this.ProcessMath(c[b])}}}else{for(b=0;b<a;b++){this.ProcessMath(c[b])}}}},ProcessMath:function(e){var d=e.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var a=document.createElement("script");a.type="math/mml";d.insertBefore(a,e);if(this.AttributeBug){var b=this.OuterHTML(e);if(this.CleanupHTML){b=b.replace(/<\?import .*?>/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/&nbsp;/g,"&#xA0;")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"</math>";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c="<!--"+e.nodeValue+"-->"}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b<a;b++){var d=e.attributes[b];if(d.specified&&d.nodeName.substr(0,10)!=="_moz-math-"){c+=" "+d.nodeName.toLowerCase().replace(/xmlns:xmlns/,"xmlns")+"=";var f=d.nodeValue;if(f==null&&d.nodeName==="style"&&e.style){f=e.style.cssText}c+='"'+this.quoteHTML(f)+'"'}}c+=">";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b<a;b++){c+=this.OuterHTML(e.childNodes[b])}c+="</"+e.nodeName.toLowerCase()+">"}}}return c},OuterHTML:function(d){if(d.nodeName.charAt(0)==="#"){return this.NodeHTML(d)}if(!this.AttributeBug){return d.outerHTML}var c=this.NodeHTML(d);for(var b=0,a=d.childNodes.length;b<a;b++){c+=this.OuterHTML(d.childNodes[b])}c+="</"+d.nodeName.toLowerCase()+">";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&#x26;").replace(/</g,"&lt;").replace(/>/g,"&gt;").replace(/\"/g,"&quot;")},createPreview:function(f,b){var g=this.config.preview;if(g==="none"){return}var a=false;if(g==="mathml"){a=true;if(this.MathTagBug){g="alttext"}else{g=f.cloneNode(false)}}if(g==="alttext"||g==="altimg"){a=true;var c=this.filterPreview(f.getAttribute("alttext"));if(g==="alttext"){if(c!=null){g=MathJax.HTML.TextNode(c)}else{g=null}}else{var h=f.getAttribute("altimg");if(h!=null){var e={width:f.getAttribute("altimg-width"),height:f.getAttribute("altimg-height")};g=MathJax.HTML.Element("img",{src:h,alt:c,style:e})}else{g=null}}}if(g){var d;if(a){d=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass});d.appendChild(g)}else{d=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},g)}b.parentNode.insertBefore(d,b)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"<math><mi>x</mi><mspace /></math>"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="&lt;"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax],5);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js");
(function(d,h,l,g,m,b,j){var q="2.4.0";var i=MathJax.Extension;var c=i.MathEvents={version:q};var k=d.config.menuSettings;var p={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.urlRev(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 n=c.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",Mousedown:function(r){return n.Handler(r,"Mousedown",this)},Mouseup:function(r){return n.Handler(r,"Mouseup",this)},Mousemove:function(r){return n.Handler(r,"Mousemove",this)},Mouseover:function(r){return n.Handler(r,"Mouseover",this)},Mouseout:function(r){return n.Handler(r,"Mouseout",this)},Click:function(r){return n.Handler(r,"Click",this)},DblClick:function(r){return n.Handler(r,"DblClick",this)},Menu:function(r){return n.Handler(r,"ContextMenu",this)},Handler:function(u,s,t){if(l.loadingMathMenu){return n.False(u)}var r=b[t.jaxID];if(!u){u=window.event}u.isContextMenu=(s==="ContextMenu");if(r[s]){return r[s](u,t)}if(i.MathZoom){return i.MathZoom.HandleEvent(u,s,t)}},False:function(r){if(!r){r=window.event}if(r){if(r.preventDefault){r.preventDefault()}else{r.returnValue=false}if(r.stopPropagation){r.stopPropagation()}r.cancelBubble=true}return false},ContextMenu:function(u,F,x){var C=b[F.jaxID],w=C.getJaxFromMath(F);var G=(C.config.showMathMenu!=null?C:d).config.showMathMenu;if(!G||(k.context!=="MathJax"&&!x)){return}if(c.msieEventBug){u=window.event||u}n.ClearSelection();f.ClearHoverTimer();if(w.hover){if(w.hover.remove){clearTimeout(w.hover.remove);delete w.hover.remove}w.hover.nofade=true}var v=MathJax.Menu;var H,E;if(v){if(v.loadingDomain){return n.False(u)}H=m.loadDomain("MathMenu");if(!H){v.jax=w;var s=v.menu.Find("Show Math As").menu;s.items[0].name=w.sourceMenuTitle;s.items[0].format=(w.sourceMenuFormat||"MathML");s.items[1].name=j[w.inputJax].sourceMenuTitle;s.items[5].disabled=!j[w.inputJax].annotationEncoding;var B=s.items[2];B.disabled=true;var r=B.menu.items;annotationList=MathJax.Hub.Config.semanticsAnnotations;for(var A=0,z=r.length;A<z;A++){var t=r[A].name[1];if(w.root&&w.root.getAnnotation(t)!==null){B.disabled=false;r[A].hidden=false}else{r[A].hidden=true}}var y=v.menu.Find("Math Settings","MathPlayer");y.hidden=!(w.outputJax==="NativeMML"&&d.Browser.hasMathPlayer);return v.menu.Post(u)}v.loadingDomain=true;E=function(){delete v.loadingDomain}}else{if(l.loadingMathMenu){return n.False(u)}l.loadingMathMenu=true;H=l.Require("[MathJax]/extensions/MathMenu.js");E=function(){delete l.loadingMathMenu;if(!MathJax.Menu){MathJax.Menu={}}}}var D={pageX:u.pageX,pageY:u.pageY,clientX:u.clientX,clientY:u.clientY};g.Queue(H,E,["ContextMenu",n,D,F,x]);return n.False(u)},AltContextMenu:function(t,s){var u=b[s.jaxID];var r=(u.config.showMathMenu!=null?u:d).config.showMathMenu;if(r){r=(u.config.showMathMenuMSIE!=null?u:d).config.showMathMenuMSIE;if(k.context==="MathJax"&&!k.mpContext&&r){if(!c.noContextMenuBug||t.button!==n.RIGHTBUTTON){return}}else{if(!t[n.MENUKEY]||t.button!==n.LEFTBUTTON){return}}return u.ContextMenu(t,s,true)}},ClearSelection:function(){if(c.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(document.selection){setTimeout("document.selection.empty()",0)}},getBBox:function(t){t.appendChild(c.topImg);var s=c.topImg.offsetTop,u=t.offsetHeight-s,r=t.offsetWidth;t.removeChild(c.topImg);return{w:r,h:s,d:u}}};var f=c.Hover={Mouseover:function(t,s){if(k.discoverable||k.zoom==="Hover"){var v=t.fromElement||t.relatedTarget,u=t.toElement||t.target;if(v&&u&&(v.isMathJax!=u.isMathJax||d.getJaxFor(v)!==d.getJaxFor(u))){var r=this.getJaxFromMath(s);if(r.hover){f.ReHover(r)}else{f.HoverTimer(r,s)}return n.False(t)}}},Mouseout:function(t,s){if(k.discoverable||k.zoom==="Hover"){var v=t.fromElement||t.relatedTarget,u=t.toElement||t.target;if(v&&u&&(v.isMathJax!=u.isMathJax||d.getJaxFor(v)!==d.getJaxFor(u))){var r=this.getJaxFromMath(s);if(r.hover){f.UnHover(r)}else{f.ClearHoverTimer()}return n.False(t)}}},Mousemove:function(t,s){if(k.discoverable||k.zoom==="Hover"){var r=this.getJaxFromMath(s);if(r.hover){return}if(f.lastX==t.clientX&&f.lastY==t.clientY){return}f.lastX=t.clientX;f.lastY=t.clientY;f.HoverTimer(r,s);return n.False(t)}},HoverTimer:function(r,s){this.ClearHoverTimer();this.hoverTimer=setTimeout(g(["Hover",this,r,s]),p.hover)},ClearHoverTimer:function(){if(this.hoverTimer){clearTimeout(this.hoverTimer);delete this.hoverTimer}},Hover:function(r,v){if(i.MathZoom&&i.MathZoom.Hover({},v)){return}var u=b[r.outputJax],w=u.getHoverSpan(r,v),z=u.getHoverBBox(r,w,v),x=(u.config.showMathMenu!=null?u:d).config.showMathMenu;var B=p.frame.x,A=p.frame.y,y=p.frame.bwidth;if(c.msieBorderWidthBug){y=0}r.hover={opacity:0,id:r.inputID+"-Hover"};var s=h.Element("span",{id:r.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(-z.h-A-y-(z.y||0)),left:this.Px(-B-y+(z.x||0)),width:this.Px(z.w+2*B),height:this.Px(z.h+z.d+2*A),opacity:0,filter:"alpha(opacity=0)"}}]]);var t=h.Element("span",{isMathJax:true,id:r.hover.id+"Menu",style:{display:"inline-block","z-index":1,width:0,height:0,position:"relative"}},[["img",{className:"MathJax_Hover_Arrow",isMathJax:true,math:v,src:p.button.src,onclick:this.HoverMenu,jax:u.id,style:{left:this.Px(z.w+B+y+(z.x||0)+p.button.x),top:this.Px(-z.h-A-y-(z.y||0)-p.button.y),opacity:0,filter:"alpha(opacity=0)"}}]]);if(z.width){s.style.width=t.style.width=z.width;s.style.marginRight=t.style.marginRight="-"+z.width;s.firstChild.style.width=z.width;t.firstChild.style.left="";t.firstChild.style.right=this.Px(p.button.wx)}w.parentNode.insertBefore(s,w);if(x){w.parentNode.insertBefore(t,w)}if(w.style){w.style.position="relative"}this.ReHover(r)},ReHover:function(r){if(r.hover.remove){clearTimeout(r.hover.remove)}r.hover.remove=setTimeout(g(["UnHover",this,r]),p.fadeoutDelay);this.HoverFadeTimer(r,p.fadeinInc)},UnHover:function(r){if(!r.hover.nofade){this.HoverFadeTimer(r,-p.fadeoutInc,p.fadeoutStart)}},HoverFade:function(r){delete r.hover.timer;r.hover.opacity=Math.max(0,Math.min(1,r.hover.opacity+r.hover.inc));r.hover.opacity=Math.floor(1000*r.hover.opacity)/1000;var t=document.getElementById(r.hover.id),s=document.getElementById(r.hover.id+"Menu");t.firstChild.style.opacity=r.hover.opacity;t.firstChild.style.filter="alpha(opacity="+Math.floor(100*r.hover.opacity)+")";if(s){s.firstChild.style.opacity=r.hover.opacity;s.firstChild.style.filter=t.style.filter}if(r.hover.opacity===1){return}if(r.hover.opacity>0){this.HoverFadeTimer(r,r.hover.inc);return}t.parentNode.removeChild(t);if(s){s.parentNode.removeChild(s)}if(r.hover.remove){clearTimeout(r.hover.remove)}delete r.hover},HoverFadeTimer:function(r,t,s){r.hover.inc=t;if(!r.hover.timer){r.hover.timer=setTimeout(g(["HoverFade",this,r]),(s||p.fadeDelay))}},HoverMenu:function(r){if(!r){r=window.event}return b[this.jax].ContextMenu(r,this.math,true)},ClearHover:function(r){if(r.hover.remove){clearTimeout(r.hover.remove)}if(r.hover.timer){clearTimeout(r.hover.timer)}f.ClearHoverTimer();delete r.hover},Px:function(r){if(Math.abs(r)<0.006){return"0px"}return r.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var r=new Image();r.src=p.button.src}}};var a=c.Touch={last:0,delay:500,start:function(s){var r=new Date().getTime();var t=(r-a.last<a.delay&&a.up);a.last=r;a.up=false;if(t){a.timeout=setTimeout(a.menu,a.delay,s,this);s.preventDefault()}},end:function(s){var r=new Date().getTime();a.up=(r-a.last<a.delay);if(a.timeout){clearTimeout(a.timeout);delete a.timeout;a.last=0;a.up=false;s.preventDefault();return n.Handler((s.touches[0]||s.touch),"DblClick",this)}},menu:function(s,r){delete a.timeout;a.last=0;a.up=false;return n.Handler((s.touches[0]||s.touch),"ContextMenu",r)}};if(d.Browser.isMobile){var o=p.styles[".MathJax_Hover_Arrow"];o.width="25px";o.height="18px";p.button.x=-6}d.Browser.Select({MSIE:function(r){var t=(document.documentMode||0);var s=r.versionAtLeast("8.0");c.msieBorderWidthBug=(document.compatMode==="BackCompat");c.msieEventBug=r.isIE9;c.msieAlignBug=(!s||t<8);if(t<9){n.LEFTBUTTON=1}},Safari:function(r){c.safariContextMenuBug=true},Opera:function(r){c.operaPositionBug=true},Konqueror:function(r){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=p=d.CombineConfig("MathEvents",p);var e=function(){var r=p.styles[".MathJax_Hover_Frame"];r.border=p.frame.bwidth+"px solid "+p.frame.bcolor+" ! important";r["box-shadow"]=r["-webkit-box-shadow"]=r["-moz-box-shadow"]=r["-khtml-box-shadow"]="0px 0px "+p.frame.hwidth+" "+p.frame.hcolor};g.Queue(d.Register.StartupHook("End Config",{}),[e],["getImages",f],["Styles",l,p.styles],["Post",d.Startup.signal,"MathEvents Ready"],["loadComplete",l,"[MathJax]/extensions/MathEvents.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.Callback,MathJax.Localization,MathJax.OutputJax,MathJax.InputJax);
(function(a,d,f,c,j){var k="2.4.0";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_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");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);
(function(c,g,k,f,b){var q="2.4.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:q,signal:j};var o=function(r){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",r]].concat([].slice.call(arguments,1)))};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var p=c.CombineConfig("MathMenu",{delay:150,closeImg:k.urlRev(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},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_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(n?"1em":".7em"),left:"auto"},".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 a=MathJax.Menu=MathJax.Object.Subclass({version:q,items:[],posted:false,title:null,margin:5,Init:function(r){this.items=[].slice.call(arguments,0)},With:function(r){if(r){c.Insert(this,r)}return this},Post:function(s,C,A){if(!s){s=window.event}var r=document.getElementById("MathJax_MenuFrame");if(!r){r=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax]);a.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var t=g.Element("div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"});if(!A){MathJax.Localization.setCSS(t)}for(var v=0,u=this.items.length;v<u;v++){this.items[v].Create(t)}if(a.isMobile){g.addElement(t,"span",{className:"MathJax_Menu_Close",menu:C,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:p.closeImg,style:{width:"100%",height:"100%"}}]])}r.appendChild(t);this.posted=true;t.style.width=(t.offsetWidth+2)+"px";var B=s.pageX,z=s.pageY;if(!B&&!z){B=s.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;z=s.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!C){if(B+t.offsetWidth>document.body.offsetWidth-this.margin){B=document.body.offsetWidth-t.offsetWidth-this.margin}if(a.isMobile){B=Math.max(5,B-Math.floor(t.offsetWidth/2));z-=20}a.skipUp=s.isContextMenu}else{var w="left",D=C.offsetWidth;B=(a.isMobile?30:D-2);z=0;while(C&&C!==r){B+=C.offsetLeft;z+=C.offsetTop;C=C.parentNode}if(!a.isMobile){if((a.isRTL&&B-D-t.offsetWidth>this.margin)||(!a.isRTL&&B+t.offsetWidth>document.body.offsetWidth-this.margin)){w="right";B=Math.max(this.margin,B-D-t.offsetWidth+6)}}if(!n){t.style["borderRadiusTop"+w]=0;t.style["WebkitBorderRadiusTop"+w]=0;t.style["MozBorderRadiusTop"+w]=0;t.style["KhtmlBorderRadiusTop"+w]=0}}t.style.left=B+"px";t.style.top=z+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(s)},Remove:function(r,s){j.Post(["unpost",a.jax]);var t=document.getElementById("MathJax_MenuFrame");if(t){t.parentNode.removeChild(t);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(r)},Find:function(r){return this.FindN(1,r,[].slice.call(arguments,1))},FindId:function(r){return this.FindN(0,r,[].slice.call(arguments,1))},FindN:function(v,s,u){for(var t=0,r=this.items.length;t<r;t++){if(this.items[t].name[v]===s){if(u.length){if(!this.items[t].menu){return null}return this.items[t].menu.FindN(v,u[0],u.slice(1))}return this.items[t]}}return null},IndexOf:function(r){return this.IndexOfN(1,r)},IndexOfId:function(r){return this.IndexOfN(0,r)},IndexOfN:function(u,s){for(var t=0,r=this.items.length;t<r;t++){if(this.items[t].name[u]===s){return t}}return null}},{config:p,div:null,Close:function(r){return a.Event(r,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(r){return a.Event(r,this,"Remove")},Mouseover:function(r){return a.Event(r,this,"Mouseover")},Mouseout:function(r){return a.Event(r,this,"Mouseout")},Mousedown:function(r){return a.Event(r,this,"Mousedown")},Mouseup:function(r){return a.Event(r,this,"Mouseup")},Touchstart:function(r){return a.Event(r,this,"Touchstart")},Touchend:function(r){return a.Event(r,this,"Touchend")},Event:function(t,v,r,u){if(a.skipMouseover&&r==="Mouseover"&&!u){return h(t)}if(a.skipUp){if(r.match(/Mouseup|Touchend/)){delete a.skipUp;return h(t)}if(r==="Touchstart"||(r==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!t){t=window.event}var s=v.menuItem;if(s&&s[r]){return s[r](t,v)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(s){var t=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:s,onmousedown:this.Remove}]]);var r=t.firstChild;if(a.msieBackgroundBug){r.style.backgroundColor="white";r.style.filter="alpha(opacity=0)"}if(a.msieFixedPositionBug){t.width=t.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{r.style.position="fixed"}return t},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var r=document.getElementById("MathJax_MenuFrame");if(r){r=r.firstChild;r.style.width=r.style.height="1px";r.style.width=document.body.scrollWidth+"px";r.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var r=new Image();r.src=p.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(s){if(!this.hidden){var r={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){r.className+=" MathJax_MenuDisabled"}g.addElement(s,"div",r,this.Label(r,s))}},Name:function(){return o(this.name[0],this.name[1])},Mouseover:function(v,x){if(!this.disabled){this.Activate(x)}if(!this.menu||!this.menu.posted){var w=document.getElementById("MathJax_MenuFrame").childNodes,s=x.parentNode.childNodes;for(var t=0,r=s.length;t<r;t++){var u=s[t].menuItem;if(u&&u.menu&&u.menu.posted){u.Deactivate(s[t])}}r=w.length-1;while(r>=0&&x.parentNode.menuItem!==w[r].menuItem){w[r].menuItem.posted=false;w[r].parentNode.removeChild(w[r]);r--}if(this.Timer&&!a.isMobile){this.Timer(v,x)}}},Mouseout:function(r,s){if(!this.menu||!this.menu.posted){this.Deactivate(s)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(r,s){return this.Remove(r,s)},Touchstart:function(r,s){return this.TouchEvent(r,s,"Mousedown")},Touchend:function(r,s){return this.TouchEvent(r,s,"Mouseup")},TouchEvent:function(s,t,r){if(this!==m.lastItem){if(m.lastMenu){a.Event(s,m.lastMenu,"Mouseout")}a.Event(s,t,"Mouseover",true);m.lastItem=this;m.lastMenu=t}if(this.nativeTouch){return null}a.Event(s,t,r);return false},Remove:function(r,s){s=s.parentNode.menuItem;return s.Remove(r,s)},Activate:function(r){this.Deactivate(r);r.className+=" MathJax_MenuActive"},Deactivate:function(r){r.className=r.className.replace(/ MathJax_MenuActive/,"")},With:function(r){if(r){c.Insert(this,r)}return this},isRTL:function(){return a.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(r,t,s){if(!(r instanceof Array)){r=[r,r]}this.name=r;this.action=t;this.With(s)},Label:function(r,s){return[this.Name()]},Mouseup:function(r,s){if(!this.disabled){this.Remove(r,s);j.Post(["command",this]);this.action.call(this,r)}return h(r)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),markerRTL:(n&&!c.Browser.isSafari?"\u25B0":"\u25C2"),Init:function(r,t){if(!(r instanceof Array)){r=[r,r]}this.name=r;var s=1;if(!(t instanceof a.ITEM)){this.With(t),s++}this.menu=a.apply(a,[].slice.call(arguments,s))},Label:function(r,s){this.menu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(r,s){if(this.timer){clearTimeout(this.timer)}r={clientX:r.clientX,clientY:r.clientY};this.timer=setTimeout(f(["Mouseup",this,r,s]),p.delay)},Touchend:function(s,u){var t=this.menu.posted;var r=this.SUPER(arguments).Touchend.apply(this,arguments);if(t){this.Deactivate(u);delete m.lastItem;delete m.lastMenu}return r},Mouseup:function(s,u){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(s,u,this.ltr)}else{var t=document.getElementById("MathJax_MenuFrame").childNodes,r=t.length-1;while(r>=0){var v=t[r];v.menuItem.posted=false;v.parentNode.removeChild(v);if(v.menuItem===this.menu){break}r--}}}return h(s)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(s,r,t){if(!(s instanceof Array)){s=[s,s]}this.name=s;this.variable=r;this.With(t);if(this.value==null){this.value=this.name[0]}},Label:function(s,t){var r={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(p.settings[this.variable]!==this.value){r={style:{display:"none"}}}return[["span",r,[this.marker]]," "+this.Name()]},Mouseup:function(u,v){if(!this.disabled){var w=v.parentNode.childNodes;for(var s=0,r=w.length;s<r;s++){var t=w[s].menuItem;if(t&&t.variable===this.variable){w[s].firstChild.style.display="none"}}v.firstChild.display="";p.settings[this.variable]=this.value;a.cookie[this.variable]=p.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(u,v);if(this.action&&!this.disabled){this.action.call(a,this)}return h(u)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(s,r,t){if(!(s instanceof Array)){s=[s,s]}this.name=s;this.variable=r;this.With(t)},Label:function(s,t){var r={className:"MathJax_MenuCheck"+this.rtlClass()};if(!p.settings[this.variable]){r={style:{display:"none"}}}return[["span",r,[this.marker]]," "+this.Name()]},Mouseup:function(r,s){if(!this.disabled){s.firstChild.display=(p.settings[this.variable]?"none":"");p.settings[this.variable]=!p.settings[this.variable];a.cookie[this.variable]=p.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(r,s);if(this.action&&!this.disabled){this.action.call(a,this)}return h(r)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(r,s){if(!(r instanceof Array)){r=[r,r]}this.name=r;this.With(s)},Label:function(r,s){delete r.onmouseover,delete r.onmouseout;delete r.onmousedown;r.className+=" MathJax_MenuLabel";return[this.Name()]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(r,s){delete r.onmouseover,delete r.onmouseout;delete r.onmousedown;r.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{};var s=(t.imgFonts?"image":(t.fontInUse?(t.webFonts?"web":"local")+" "+t.fontInUse:(b.SVG?"web SVG":"generic")))+" fonts";var x=(!t.webFonts||t.imgFonts?null:t.allowWebFonts.replace(/otf/,"woff or otf")+" fonts");var r=["MathJax.js v"+MathJax.fileversion,["br"]];r.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(r,MathJax.InputJax,["InputJax","%1 Input Jax v%2"]);a.About.GetJax(r,MathJax.OutputJax,["OutputJax","%1 Output Jax v%2"]);a.About.GetJax(r,MathJax.ElementJax,["ElementJax","%1 Element Jax v%2"]);r.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(r,MathJax.Extension,["Extension","%1 Extension v%2"],true);r.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(x?" \u2014 "+o(x.replace(/ /g,""),x):"")]]);a.About.div=a.Background(a.About);var v=g.addElement(a.About.div,"div",{id:"MathJax_About"},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],o(s.replace(/ /g,""),"using "+s),["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},r],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]],["img",{src:p.closeImg,style:{width:"21px",height:"21px",position:"absolute",top:".2em",right:".2em"},onclick:a.About.Remove}]]);MathJax.Localization.setCSS(v);var w=(document.documentElement||{});var u=window.innerHeight||w.clientHeight||w.scrollHeight||0;if(a.prototype.msieAboutBug){v.style.width="20em";v.style.position="absolute";v.style.left=Math.floor((document.documentElement.scrollWidth-v.offsetWidth)/2)+"px";v.style.top=(Math.floor((u-v.offsetHeight)/3)+document.body.scrollTop)+"px"}else{v.style.marginLeft=Math.floor(-v.offsetWidth/2)+"px";v.style.top=Math.floor((u-v.offsetHeight)/3)+"px"}};a.About.Remove=function(r){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(s,x,v,u){var w=[];for(var y in x){if(x.hasOwnProperty(y)&&x[y]){if((u&&x[y].version)||(x[y].isa&&x[y].isa(x))){w.push(o(v[0],v[1],(x[y].id||y),x[y].version))}}}w.sort();for(var t=0,r=w.length;t<r;t++){s.push(w[t],["br"])}return s};a.Help=function(){k.Require("[MathJax]/extensions/HelpDialog.js",function(){MathJax.Extension.Help.Dialog()})};a.ShowSource=function(v){if(!v){v=window.event}var u={screenX:v.screenX,screenY:v.screenY};if(!a.jax){return}if(this.format==="MathML"){var s=MathJax.ElementJax.mml;if(s&&typeof(s.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML("",a.jax),v)}catch(t){if(!t.restart){throw t}f.After([this,a.ShowSource,u],t.restart)}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(v);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!s.mbase.prototype.toMathML){s.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,u]);return}}}else{if(this.format==="Error"){a.ShowSource.Text(a.jax.errorText,v)}else{if(p.semanticsAnnotations[this.format]){var r=a.jax.root.getAnnotation(this.format);if(r.data[0]){a.ShowSource.Text(r.data[0].toString())}}else{if(a.jax.originalText==null){alert(o("NoOriginalForm","No original form available"));return}a.ShowSource.Text(a.jax.originalText,v)}}}};a.ShowSource.Window=function(s){if(!a.ShowSource.w){var t=[],r=p.windowSettings;for(var u in r){if(r.hasOwnProperty(u)){t.push(u+"="+r[u])}}a.ShowSource.w=window.open("","_blank",t.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(v,t){var r=a.ShowSource.Window(t);delete a.ShowSource.w;v=v.replace(/^\s*/,"").replace(/\s*$/,"");v=v.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");var u=o("EqSource","MathJax Equation Source");if(a.isMobile){r.document.open();r.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>"+u+"</title></head><body style='font-size:85%'>");r.document.write("<pre>"+v+"</pre>");r.document.write("<hr><input type='button' value='"+o("Close","Close")+"' onclick='window.close()' />");r.document.write("</body></html>");r.document.close()}else{r.document.open();r.document.write("<html><head><title>"+u+"</title></head><body style='font-size:85%'>");r.document.write("<table><tr><td><pre>"+v+"</pre></td></tr></table>");r.document.write("</body></html>");r.document.close();var s=r.document.body.firstChild;setTimeout(function(){var A=(r.outerHeight-r.innerHeight)||30,z=(r.outerWidth-r.innerWidth)||30,w,D;z=Math.max(100,Math.min(Math.floor(0.5*screen.width),s.offsetWidth+z+25));A=Math.max(40,Math.min(Math.floor(0.5*screen.height),s.offsetHeight+A+25));if(a.prototype.msieHeightBug){A+=35}r.resizeTo(z,A);var C;try{C=t.screenX}catch(B){}if(t&&C!=null){w=Math.max(0,Math.min(t.screenX-Math.floor(z/2),screen.width-z-20));D=Math.max(0,Math.min(t.screenY-Math.floor(A/2),screen.height-A-20));r.moveTo(w,D)}},50)}};a.Scale=function(){var s=b["HTML-CSS"],r=b.NativeMML,v=b.SVG;var u=(s||r||v||{config:{scale:100}}).config.scale;var t=prompt(o("ScaleMath","Scale all mathematics (compared to surrounding text) by"),u+"%");if(t){if(t.match(/^\s*\d+(\.\d*)?\s*%?\s*$/)){t=parseFloat(t);if(t){if(t!==u){if(s){s.config.scale=t}if(r){r.config.scale=t}if(v){v.config.scale=t}a.cookie.scale=t;a.saveCookie();c.Reprocess()}}else{alert(o("NonZeroScale","The scale should not be zero"))}}else{alert(o("PercentScale","The scale should be a percentage (e.g., 120%%)"))}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var s=c.outputJax["jax/mml"];if(s[0]!==p.settings.renderer){var v=c.Browser,u,r=a.Renderer.Messages,t;switch(p.settings.renderer){case"NativeMML":if(!p.settings.warnedMML){if(v.isChrome&&v.version.substr(0,3)!=="24."){u=r.MML.WebKit}else{if(v.isSafari&&!v.versionAtLeast("5.0")){u=r.MML.WebKit}else{if(v.isMSIE){if(!v.hasMathPlayer){u=r.MML.MSIE}}else{u=r.MML[v]}}}t="warnedMML"}break;case"SVG":if(!p.settings.warnedSVG){if(v.isMSIE&&!e){u=r.SVG.MSIE}}break}if(u){u=o(u[0],u[1]);u+="\n\n";u+=o("SwitchAnyway","Switch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)");a.cookie.renderer=s[0].id;a.saveCookie();if(!confirm(u)){a.cookie.renderer=p.settings.renderer=g.Cookie.Get("menu").renderer;a.saveCookie();return}if(t){a.cookie.warned=p.settings.warned=true}a.cookie.renderer=p.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,p.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:["WebkitNativeMMLWarning","Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable."],MSIE:["MSIENativeMMLWarning","Internet Explorer requires the MathPlayer plugin in order to process MathML output."],Opera:["OperaNativeMMLWarning","Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly."],Safari:["SafariNativeMMLWarning","Your browser's native MathML does not implement all the features used by MathJax, so some expressions may not render properly."],Firefox:["FirefoxNativeMMLWarning","Your browser's native MathML does not implement all the features used by MathJax, so some expressions may not render properly."]},SVG:{MSIE:["MSIESVGWarning","SVG is not implemented in Internet Explorer prior to IE9 or when it is emulating IE8 or below. Switching to SVG output will cause the mathematics to not display properly."]}};a.Font=function(){var r=b["HTML-CSS"];if(!r){return}document.location.reload()};a.Locale=function(){MathJax.Localization.setLocale(p.settings.locale);MathJax.Hub.Queue(["Reprocess",MathJax.Hub])};a.LoadLocale=function(){var r=prompt(o("LoadURL","Load translation data from this URL:"));if(r){if(!r.match(/\.js$/)){alert(o("BadURL","The URL should be for a javascript file that defines MathJax translation data.  Javascript file names should end with '.js'"))}k.Require(r,function(s){if(s!=k.STATUS.OK){alert(o("BadData","Failed to load translation data from %1",r))}})}};a.MPEvents=function(t){var s=p.settings.discoverable,r=a.MPEvents.Messages;if(!e){if(p.settings.mpMouse&&!confirm(o.apply(o,r.IE8warning))){delete a.cookie.mpContext;delete p.settings.mpContext;delete a.cookie.mpMouse;delete p.settings.mpMouse;a.saveCookie();return}p.settings.mpContext=p.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=p.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!s&&t.name[1]==="Menu Events"&&p.settings.mpContext){alert(o.apply(o,r.IE9warning))}}};a.MPEvents.Messages={IE8warning:["IE8warning","This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?"],IE9warning:["IE9warning","The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead."]};c.Browser.Select({MSIE:function(r){var s=(document.compatMode==="BackCompat");var t=r.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(s||!t),msieAboutBug:s,msieHeightBug:((document.documentMode||0)<9)});if(e){delete p.styles["#MathJax_About"].filter;delete p.styles[".MathJax_Menu"].filter}},Firefox:function(r){a.skipMouseover=r.isMobile&&r.versionAtLeast("6.0");a.skipMousedown=r.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;a.CreateLocaleMenu=function(){if(!a.menu){return}var w=a.menu.Find("Language").menu,t=w.items;var s=[],y=MathJax.Localization.strings;for(var x in y){if(y.hasOwnProperty(x)){s.push(x)}}s=s.sort();w.items=[];for(var u=0,r=s.length;u<r;u++){var v=y[s[u]].menuTitle;if(v){v+=" ("+s[u]+")"}else{v=s[u]}w.items.push(m.RADIO([s[u],v],"locale",{action:a.Locale}))}w.items.push(t[t.length-2],t[t.length-1])};a.CreateAnnotationMenu=function(){if(!a.menu){return}var t=a.menu.Find("Show Math As","Annotation").menu;var s=p.semanticsAnnotations;for(var r in s){if(s.hasOwnProperty(r)){t.items.push(m.COMMAND([r,r],a.ShowSource,{hidden:true,nativeTouch:true,format:r}))}}};c.Register.StartupHook("End Config",function(){p.settings=c.config.menuSettings;if(typeof(p.settings.showRenderer)!=="undefined"){p.showRenderer=p.settings.showRenderer}if(typeof(p.settings.showFontMenu)!=="undefined"){p.showFontMenu=p.settings.showFontMenu}if(typeof(p.settings.showContext)!=="undefined"){p.showContext=p.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU(["Show","Show Math As"],m.COMMAND(["MathMLcode","MathML Code"],a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND(["Original","Original Form"],a.ShowSource,{nativeTouch:true}),m.SUBMENU(["Annotation","Annotation"],{disabled:true}),m.RULE(),m.CHECKBOX(["texHints","Show TeX hints in MathML"],"texHints"),m.CHECKBOX(["semantics","Add original form as annotation"],"semantics")),m.RULE(),m.SUBMENU(["Settings","Math Settings"],m.SUBMENU(["ZoomTrigger","Zoom Trigger"],m.RADIO(["Hover","Hover"],"zoom",{action:a.Zoom}),m.RADIO(["Click","Click"],"zoom",{action:a.Zoom}),m.RADIO(["DoubleClick","Double-Click"],"zoom",{action:a.Zoom}),m.RADIO(["NoZoom","No Zoom"],"zoom",{value:"None"}),m.RULE(),m.LABEL(["TriggerRequires","Trigger Requires:"]),m.CHECKBOX((c.Browser.isMac?["Option","Option"]:["Alt","Alt"]),"ALT"),m.CHECKBOX(["Command","Command"],"CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX(["Control","Control"],"CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX(["Shift","Shift"],"Shift")),m.SUBMENU(["ZoomFactor","Zoom Factor"],m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU(["Renderer","Math Renderer"],{hidden:!p.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!p.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL(["MPHandles","Let MathPlayer Handle:"]),m.CHECKBOX(["MenuEvents","Menu Events"],"mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX(["MouseEvents","Mouse Events"],"mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX(["MenuAndMouse","Mouse and Menu Events"],"mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU(["FontPrefs","Font Preference"],{hidden:!p.showFontMenu},m.LABEL(["ForHTMLCSS","For HTML-CSS:"]),m.RADIO(["Auto","Auto"],"font",{action:a.Font}),m.RULE(),m.RADIO(["TeXLocal","TeX (local)"],"font",{action:a.Font}),m.RADIO(["TeXWeb","TeX (web)"],"font",{action:a.Font}),m.RADIO(["TeXImage","TeX (image)"],"font",{action:a.Font}),m.RULE(),m.RADIO(["STIXLocal","STIX (local)"],"font",{action:a.Font}),m.RADIO(["STIXWeb","STIX (web)"],"font",{action:a.Font}),m.RULE(),m.RADIO(["AsanaMathWeb","Asana Math (web)"],"font",{action:a.Font}),m.RADIO(["GyrePagellaWeb","Gyre Pagella (web)"],"font",{action:a.Font}),m.RADIO(["GyreTermesWeb","Gyre Termes (web)"],"font",{action:a.Font}),m.RADIO(["LatinModernWeb","Latin Modern (web)"],"font",{action:a.Font}),m.RADIO(["NeoEulerWeb","Neo Euler (web)"],"font",{action:a.Font})),m.SUBMENU(["ContextMenu","Contextual Menu"],{hidden:!p.showContext},m.RADIO("MathJax","context"),m.RADIO(["Browser","Browser"],"context")),m.COMMAND(["Scale","Scale All Math ..."],a.Scale),m.RULE().With({hidden:!p.showDiscoverable,name:["","discover_rule"]}),m.CHECKBOX(["Discoverable","Highlight on Hover"],"discoverable",{hidden:!p.showDiscoverable})),m.SUBMENU(["Locale","Language"],{hidden:!p.showLocale,ltr:true},m.RADIO("en","locale",{action:a.Locale}),m.RULE().With({hidden:!p.showLocaleURL,name:["","localURL_rule"]}),m.COMMAND(["LoadLocale","Load from URL ..."],a.LoadLocale,{hidden:!p.showLocaleURL})),m.RULE(),m.COMMAND(["About","About MathJax"],a.About),m.COMMAND(["Help","MathJax Help"],a.Help));if(a.isMobile){(function(){var s=p.settings;var r=a.menu.Find("Math Settings","Zoom Trigger").menu;r.items[0].disabled=r.items[1].disabled=true;if(s.zoom==="Hover"||s.zoom=="Click"){s.zoom="None"}r.items=r.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}a.CreateLocaleMenu();a.CreateAnnotationMenu()});a.showRenderer=function(r){a.cookie.showRenderer=p.showRenderer=r;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!r};a.showMathPlayer=function(r){a.cookie.showMathPlayer=p.showMathPlayer=r;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!r};a.showFontMenu=function(r){a.cookie.showFontMenu=p.showFontMenu=r;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!r};a.showContext=function(r){a.cookie.showContext=p.showContext=r;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!r};a.showDiscoverable=function(r){a.cookie.showDiscoverable=p.showDiscoverable=r;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!r;a.menu.Find("Math Settings","discover_rule").hidden=!r};a.showLocale=function(r){a.cookie.showLocale=p.showLocale=r;a.saveCookie();a.menu.Find("Language").hidden=!r};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,p.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax);
MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"2.4.0",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){if(arguments.length===1&&arguments[0].type==="math"){this.root=arguments[0]}else{this.root=MathJax.ElementJax.mml.math.apply(this,arguments)}if(this.root.attr&&this.root.attr.mode){if(!this.root.display&&this.root.attr.mode==="display"){this.root.display="block";this.root.attrNames.push("display")}delete this.root.attr.mode;for(var b=0,a=this.root.attrNames.length;b<a;b++){if(this.root.attrNames[b]==="mode"){this.root.attrNames.splice(b,1);break}}}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",UPDIAGONALARROW:"updiagonalarrow",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",PHASORANGLE:"phasorangle",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],Error:function(d,e){var c=this.merror(d),b=MathJax.Localization.fontDirection(),a=MathJax.Localization.fontFamily();if(e){c=c.With(e)}if(b||a){c=this.mstyle(c);if(b){c.dir=b}if(a){c.style.fontFamily="font-family: "+a}}return c}});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true,notParent:true}))}this.Append.apply(this,arguments)},With:function(e){for(var f in e){if(e.hasOwnProperty(f)){this[f]=e[f]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var f=0,e=arguments.length;f<e;f++){this.SetData(this.data.length,arguments[f])}}},SetData:function(e,f){if(f!=null){if(!(f instanceof a.mbase)){f=(this.isToken||this.isChars?a.chars(f):a.mtext(f))}f.parent=this;f.setInherit(this.inheritFromMe?this:this.inherit)}this.data[e]=f},Parent:function(){var e=this.parent;while(e&&e.notParent){e=e.parent}return e},Get:function(f,k){if(this[f]!=null){return this[f]}if(this.attr&&this.attr[f]!=null){return this.attr[f]}var g=this.Parent();if(g&&g["adjustChild_"+f]!=null){return(g["adjustChild_"+f])(this.childPosition(),k)}var j=this.inherit;var e=j;while(j){var i=j[f];if(i==null&&j.attr){i=j.attr[f]}if(i!=null&&j.noInheritAttribute&&!j.noInheritAttribute[f]){var h=j.noInherit[this.type];if(!(h&&h[f])){return i}}e=j;j=j.inherit}if(!k){if(this.defaults[f]===a.AUTO){return this.autoDefault(f)}if(this.defaults[f]!==a.INHERIT&&this.defaults[f]!=null){return this.defaults[f]}if(e){return e.defaults[f]}}return null},hasValue:function(e){return(this.Get(e,true)!=null)},getValues:function(){var f={};for(var g=0,e=arguments.length;g<e;g++){f[arguments[g]]=this.Get(arguments[g])}return f},adjustChild_scriptlevel:function(f,e){return this.Get("scriptlevel",e)},adjustChild_displaystyle:function(f,e){return this.Get("displaystyle",e)},adjustChild_texprimestyle:function(f,e){return this.Get("texprimestyle",e)},childPosition:function(){var h=this,g=h.parent;while(g.notParent){h=g;g=h.parent}for(var f=0,e=g.data.length;f<e;f++){if(g.data[f]===h){return f}}return null},setInherit:function(g){if(g!==this.inherit&&this.inherit==null){this.inherit=g;for(var f=0,e=this.data.length;f<e;f++){if(this.data[f]&&this.data[f].setInherit){this.data[f].setInherit(g)}}}},setTeXclass:function(e){this.getPrevClass(e);return(typeof(this.texClass)!=="undefined"?this:e)},getPrevClass:function(e){if(e){this.prevClass=e.Get("texClass");this.prevLevel=e.Get("scriptlevel")}},updateTeXclass:function(e){if(e){this.prevClass=e.prevClass;delete e.prevClass;this.prevLevel=e.prevLevel;delete e.prevLevel;this.texClass=e.Get("texClass")}},texSpacing:function(){var f=(this.prevClass!=null?this.prevClass:a.TEXCLASS.NONE);var e=(this.Get("texClass")||a.TEXCLASS.ORD);if(f===a.TEXCLASS.NONE||e===a.TEXCLASS.NONE){return""}if(f===a.TEXCLASS.VCENTER){f=a.TEXCLASS.ORD}if(e===a.TEXCLASS.VCENTER){e=a.TEXCLASS.ORD}var g=this.TEXSPACE[f][e];if(this.prevLevel>0&&this.Get("scriptlevel")>0&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var f=0,e=this.data.length;f<e;f++){if(this.data[f]&&this.data[f].hasNewline()){return true}}return false},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"},getAnnotation:function(){return null}},{childrenSpacelike:function(){for(var f=0,e=this.data.length;f<e;f++){if(!this.data[f].isSpacelike()){return false}}return true},childEmbellished:function(){return(this.data[0]&&this.data[0].isEmbellished())},childCore:function(){return this.data[0]},childCoreMO:function(){return(this.data[0]?this.data[0].CoreMO():null)},setChildTeXclass:function(e){if(this.data[0]){e=this.data[0].setTeXclass(e);this.updateTeXclass(this.data[0])}return e},setBaseTeXclasses:function(g){this.getPrevClass(g);this.texClass=null;if(this.data[0]){if(this.isEmbellished()||this.data[0].isa(a.mi)){g=this.data[0].setTeXclass(g);this.updateTeXclass(this.Core())}else{this.data[0].setTeXclass();g=this}}else{g=this}for(var f=1,e=this.data.length;f<e;f++){if(this.data[f]){this.data[f].setTeXclass()}}return g},setSeparateTeXclasses:function(g){this.getPrevClass(g);for(var f=0,e=this.data.length;f<e;f++){if(this.data[f]){this.data[f].setTeXclass()}}if(this.isEmbellished()){this.updateTeXclass(this.Core())}return this}});a.mi=a.mbase.Subclass({type:"mi",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.AUTO,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT},autoDefault:function(f){if(f==="mathvariant"){var e=(this.data[0]||"").toString();return(e.length===1||(e.length===2&&e.charCodeAt(0)>=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h<e;h++){var j=this.OPTABLE[f[h]][k];if(j){l=this.makeDef(j);break}}if(!l){l=this.CheckRange(k)}if(!l&&n){l={}}else{if(!l){l=MathJax.Hub.Insert({},this.defaultDef)}l.form=f[0];this.def=l}}this.useMMLspacing&=~(this.SPACE_ATTR[g]||0);if(l[g]!=null){return l[g]}else{if(!n){return this.defaultDef[g]}}return""},CheckRange:function(j){var k=j.charCodeAt(0);if(k>=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g<e&&this.RANGES[g][0]<=k;g++){if(k<=this.RANGES[g][1]){if(this.RANGES[g][3]){var f=a.optableDir+"/"+this.RANGES[g][3]+".js";this.RANGES[g][3]=null;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(f))}var h=a.TEXCLASSNAMES[this.RANGES[g][2]];h=this.OPTABLE.infix[j]=a.mo.OPTYPES[h==="BIN"?"BIN3":h];return this.makeDef(h)}}return null},makeDef:function(f){if(f[2]==null){f[2]=this.defaultDef.texClass}if(!f[3]){f[3]={}}var e=MathJax.Hub.Insert({},f[3]);e.lspace=this.SPACE[f[0]];e.rspace=this.SPACE[f[1]];e.texClass=f[2];if(e.texClass===a.TEXCLASS.REL&&(this.movablelimits||this.data.join("").match(/^[a-z]+$/i))){e.texClass=a.TEXCLASS.OP}return e},getForm:function(){var e=this,g=this.parent,f=this.Parent();while(f&&f.isEmbellished()){e=g;g=f.parent;f=f.Parent()}if(g&&g.type==="mrow"&&g.NonSpaceLength()!==1){if(g.FirstNonSpace()===e){return a.FORM.PREFIX}if(g.LastNonSpace()===e){return a.FORM.POSTFIX}}return a.FORM.INFIX},isEmbellished:function(){return true},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)},setTeXclass:function(f){var e=this.getValues("form","lspace","rspace","fence");if(this.useMMLspacing){this.texClass=a.TEXCLASS.NONE;return this}if(e.fence&&!this.texClass){if(e.form===a.FORM.PREFIX){this.texClass=a.TEXCLASS.OPEN}if(e.form===a.FORM.POSTFIX){this.texClass=a.TEXCLASS.CLOSE}}this.texClass=this.Get("texClass");if(this.data.join("")==="\u2061"){if(f){f.texClass=a.TEXCLASS.OP;f.fnOP=true}this.texClass=this.prevClass=a.TEXCLASS.NONE;return f}return this.adjustTeXclass(f)},adjustTeXclass:function(e){if(this.texClass===a.TEXCLASS.NONE){return e}if(e){if(e.autoOP&&(this.texClass===a.TEXCLASS.BIN||this.texClass===a.TEXCLASS.REL)){e.texClass=a.TEXCLASS.ORD}this.prevClass=e.texClass||a.TEXCLASS.ORD;this.prevLevel=e.Get("scriptlevel")}else{this.prevClass=a.TEXCLASS.NONE}if(this.texClass===a.TEXCLASS.BIN&&(this.prevClass===a.TEXCLASS.NONE||this.prevClass===a.TEXCLASS.BIN||this.prevClass===a.TEXCLASS.OP||this.prevClass===a.TEXCLASS.REL||this.prevClass===a.TEXCLASS.OPEN||this.prevClass===a.TEXCLASS.PUNCT)){this.texClass=a.TEXCLASS.ORD}else{if(this.prevClass===a.TEXCLASS.BIN&&(this.texClass===a.TEXCLASS.REL||this.texClass===a.TEXCLASS.CLOSE||this.texClass===a.TEXCLASS.PUNCT)){e.texClass=this.prevClass=a.TEXCLASS.ORD}}return this}});a.mtext=a.mbase.Subclass({type:"mtext",isToken:true,isSpacelike:function(){return true},texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mspace=a.mbase.Subclass({type:"mspace",isToken:true,isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"0em",height:"0ex",depth:"0ex",linebreak:a.LINEBREAK.AUTO},hasDimAttr:function(){return(this.hasValue("width")||this.hasValue("height")||this.hasValue("depth"))},hasNewline:function(){return(!this.hasDimAttr()&&this.Get("linebreak")===a.LINEBREAK.NEWLINE)}});a.ms=a.mbase.Subclass({type:"ms",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,lquote:'"',rquote:'"'}});a.mglyph=a.mbase.Subclass({type:"mglyph",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,alt:"",src:"",width:a.AUTO,height:a.AUTO,valign:"0em"}});a.mrow=a.mbase.Subclass({type:"mrow",isSpacelike:a.mbase.childrenSpacelike,inferred:false,notParent:false,isEmbellished:function(){var f=false;for(var g=0,e=this.data.length;g<e;g++){if(this.data[g]==null){continue}if(this.data[g].isEmbellished()){if(f){return false}f=true;this.core=g}else{if(!this.data[g].isSpacelike()){return false}}}return f},NonSpaceLength:function(){var g=0;for(var f=0,e=this.data.length;f<e;f++){if(this.data[f]&&!this.data[f].isSpacelike()){g++}}return g},FirstNonSpace:function(){for(var f=0,e=this.data.length;f<e;f++){if(this.data[f]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},LastNonSpace:function(){for(var e=this.data.length-1;e>=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);for(f=0;f<e;f++){if(this.data[f]){g=this.data[f].setTeXclass(g)}}this.texClass=a.TEXCLASS.INNER;return this}else{for(f=0;f<e;f++){if(this.data[f]){g=this.data[f].setTeXclass(g)}}if(this.data[0]){this.updateTeXclass(this.data[0])}return g}},getAnnotation:function(e){if(this.data.length!=1){return null}return this.data[0].getAnnotation(e)}});a.mfrac=a.mbase.Subclass({type:"mfrac",num:0,den:1,linebreakContainer:true,texClass:a.TEXCLASS.INNER,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,linethickness:a.LINETHICKNESS.MEDIUM,numalign:a.ALIGN.CENTER,denomalign:a.ALIGN.CENTER,bevelled:false},adjustChild_displaystyle:function(e){return false},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(!this.Get("displaystyle")||e>0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){delete this.scriptlevel;var e=this.Get("scriptlevel");this.scriptlevel=f;f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(h){this.getPrevClass(h);var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}));this.data.open.useMMLspacing&=~this.data.open.SPACE_ATTR.form;h=this.data.open.setTeXclass(h)}if(f.separators!==""){while(f.separators.length<this.data.length){f.separators+=f.separators.charAt(f.separators.length-1)}}if(this.data[0]){h=this.data[0].setTeXclass(h)}for(var g=1,e=this.data.length;g<e;g++){if(this.data[g]){if(f.separators!==""){this.SetData("sep"+g,a.mo(f.separators.charAt(g-1)).With({separator:true}));h=this.data["sep"+g].setTeXclass(h)}h=this.data[g].setTeXclass(h)}}if(f.close!==""){this.SetData("close",a.mo(f.close).With({fence:true,form:a.FORM.POSTFIX,texClass:a.TEXCLASS.CLOSE}));this.data.close.useMMLspacing&=~this.data.close.SPACE_ATTR.form;h=this.data.close.setTeXclass(h)}this.updateTeXclass(this.data.open);this.texClass=a.TEXCLASS.INNER;return h}});a.menclose=a.mbase.Subclass({type:"menclose",inferRow:true,linebreakContainer:true,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,notation:a.NOTATION.LONGDIV,texClass:a.TEXCLASS.ORD},setTeXclass:a.mbase.setSeparateTeXclasses});a.msubsup=a.mbase.Subclass({type:"msubsup",base:0,sub:1,sup:2,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,subscriptshift:"",superscriptshift:"",texClass:a.AUTO},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}return 0},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f<e;f++){if(!((arguments[f] instanceof a.mtr)||(arguments[f] instanceof a.mlabeledtr))){arguments[f]=a.mtd(arguments[f])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtr=a.mbase.Subclass({type:"mtr",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{rowalign:true,columnalign:true,groupalign:true},mtable:{rowalign:true,columnalign:true,groupalign:true}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f<e;f++){if(!(arguments[f] instanceof a.mtd)){arguments[f]=a.mtd(arguments[f])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtd=a.mbase.Subclass({type:"mtd",inferRow:true,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowspan:1,columnspan:1,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},setTeXclass:a.mbase.setSeparateTeXclasses});a.maligngroup=a.mbase.Subclass({type:"malign",isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{groupalign:true},mtable:{groupalign:true}}});a.malignmark=a.mbase.Subclass({type:"malignmark",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,edge:a.SIDE.LEFT},isSpacelike:function(){return true}});a.mlabeledtr=a.mtr.Subclass({type:"mlabeledtr"});a.maction=a.mbase.Subclass({type:"maction",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,actiontype:a.ACTIONTYPE.TOGGLE,selection:1},selected:function(){return this.data[this.Get("selection")-1]||a.NULL},isEmbellished:function(){return this.selected().isEmbellished()},isSpacelike:function(){return this.selected().isSpacelike()},Core:function(){return this.selected().Core()},CoreMO:function(){return this.selected().CoreMO()},setTeXclass:function(e){if(this.Get("actiontype")===a.ACTIONTYPE.TOOLTIP&&this.data[1]){this.data[1].setTeXclass()}return this.selected().setTeXclass(e)}});a.semantics=a.mbase.Subclass({type:"semantics",notParent:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{definitionURL:null,encoding:null},setTeXclass:a.mbase.setChildTeXclass,getAnnotation:function(g){var l=MathJax.Hub.config.MathMenu.semanticsAnnotations[g];if(l){for(var h=0,e=this.data.length;h<e;h++){var k=this.data[h].Get("encoding");if(k){for(var f=0,o=l.length;f<o;f++){if(l[f]===k){return this.data[h]}}}}}return null}});a.annotation=a.mbase.Subclass({type:"annotation",isChars:true,linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a["annotation-xml"]=a.mbase.Subclass({type:"annotation-xml",linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a.math=a.mstyle.Subclass({type:"math",defaults:{mathvariant:a.VARIANT.NORMAL,mathsize:a.SIZE.NORMAL,mathcolor:"",mathbackground:a.COLOR.TRANSPARENT,dir:"ltr",scriptlevel:0,displaystyle:a.AUTO,display:"inline",maxwidth:"",overflow:a.OVERFLOW.LINEBREAK,altimg:"","altimg-width":"","altimg-height":"","altimg-valign":"",alttext:"",cdgroup:"",scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8px",infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,lineleading:"1ex",indentshift:"auto",indentalign:a.INDENTALIGN.AUTO,indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,decimalseparator:".",texprimestyle:false},autoDefault:function(e){if(e==="displaystyle"){return this.Get("display")==="block"}return""},linebreakContainer:true,setTeXclass:a.mbase.setChildTeXclass,getAnnotation:function(e){if(this.data.length!=1){return null}return this.data[0].getAnnotation(e)}});a.chars=a.mbase.Subclass({type:"chars",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){return this.data.join("")},toString:function(){return this.data.join("")}});a.entity=a.mbase.Subclass({type:"entity",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){if(this.data[0].substr(0,2)==="#x"){return parseInt(this.data[0].substr(2),16)}else{if(this.data[0].substr(0,1)==="#"){return parseInt(this.data[0].substr(1))}else{return 0}}},toString:function(){var e=this.value();if(e<=65535){return String.fromCharCode(e)}e-=65536;return String.fromCharCode((e>>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f<e;f++){var g=this.Import(arguments[f]);this.data.push(g);this.div.appendChild(g)}},Import:function(j){if(document.importNode){return document.importNode(j,true)}var f,g,e;if(j.nodeType===1){f=document.createElement(j.nodeName);for(g=0,e=j.attributes.length;g<e;g++){var h=j.attributes[g];if(h.specified&&h.nodeValue!=null&&h.nodeValue!=""){f.setAttribute(h.nodeName,h.nodeValue)}if(h.nodeName==="style"){f.style.cssText=h.nodeValue}}if(j.className){f.className=j.className}}else{if(j.nodeType===3||j.nodeType===4){f=document.createTextNode(j.nodeValue)}else{if(j.nodeType===8){f=document.createComment(j.nodeValue)}else{return document.createTextNode("")}}}for(g=0,e=j.childNodes.length;g<e;g++){f.appendChild(this.Import(j.childNodes[g]))}return f},value:function(){return this.div},toString:function(){return this.div.innerHTML}});a.TeXAtom=a.mbase.Subclass({type:"texatom",inferRow:true,notParent:true,texClass:a.TEXCLASS.ORD,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,isEmbellished:a.mbase.childEmbellished,setTeXclass:function(e){this.data[0].setTeXclass();return this.adjustTeXclass(e)},adjustTeXclass:a.mo.prototype.adjustTeXclass});a.NULL=a.mbase().With({type:"null"});var b=a.TEXCLASS;var d={ORD:[0,0,b.ORD],ORD11:[1,1,b.ORD],ORD21:[2,1,b.ORD],ORD02:[0,2,b.ORD],ORD55:[5,5,b.ORD],OP:[1,2,b.OP,{largeop:true,movablelimits:true,symmetric:true}],OPFIXED:[1,2,b.OP,{largeop:true,movablelimits:true}],INTEGRAL:[0,1,b.OP,{largeop:true,symmetric:true}],INTEGRAL2:[1,2,b.OP,{largeop:true,symmetric:true}],BIN3:[3,3,b.BIN],BIN4:[4,4,b.BIN],BIN01:[0,1,b.BIN],BIN5:[5,5,b.BIN],TALLBIN:[4,4,b.BIN,{stretchy:true}],BINOP:[4,4,b.BIN,{largeop:true,movablelimits:true}],REL:[5,5,b.REL],REL1:[1,1,b.REL,{stretchy:true}],REL4:[4,4,b.REL],RELSTRETCH:[5,5,b.REL,{stretchy:true}],RELACCENT:[5,5,b.REL,{accent:true}],WIDEREL:[5,5,b.REL,{accent:true,stretchy:true}],OPEN:[0,0,b.OPEN,{fence:true,stretchy:true,symmetric:true}],CLOSE:[0,0,b.CLOSE,{fence:true,stretchy:true,symmetric:true}],INNER:[0,0,b.INNER],PUNCT:[0,3,b.PUNCT],ACCENT:[0,0,b.ORD,{accent:true}],WIDEACCENT:[0,0,b.ORD,{accent:true,stretchy:true}]};a.mo.Augment({SPACE:["0em","0.1111em","0.1667em","0.2222em","0.2667em","0.3333em"],RANGES:[[32,127,b.REL,"BasicLatin"],[160,255,b.ORD,"Latin1Supplement"],[256,383,b.ORD],[384,591,b.ORD],[688,767,b.ORD,"SpacingModLetters"],[768,879,b.ORD,"CombDiacritMarks"],[880,1023,b.ORD,"GreekAndCoptic"],[7680,7935,b.ORD],[8192,8303,b.PUNCT,"GeneralPunctuation"],[8304,8351,b.ORD],[8352,8399,b.ORD],[8400,8447,b.ORD,"CombDiactForSymbols"],[8448,8527,b.ORD,"LetterlikeSymbols"],[8528,8591,b.ORD],[8592,8703,b.REL,"Arrows"],[8704,8959,b.BIN,"MathOperators"],[8960,9215,b.ORD,"MiscTechnical"],[9312,9471,b.ORD],[9472,9631,b.ORD],[9632,9727,b.ORD,"GeometricShapes"],[9984,10175,b.ORD,"Dingbats"],[10176,10223,b.ORD,"MiscMathSymbolsA"],[10224,10239,b.REL,"SupplementalArrowsA"],[10496,10623,b.REL,"SupplementalArrowsB"],[10624,10751,b.ORD,"MiscMathSymbolsB"],[10752,11007,b.BIN,"SuppMathOperators"],[11008,11263,b.ORD,"MiscSymbolsAndArrows"],[119808,120831,b.ORD]],OPTABLE:{prefix:{"\u2200":d.ORD21,"\u2202":d.ORD21,"\u2203":d.ORD21,"\u2207":d.ORD21,"\u220F":d.OP,"\u2210":d.OP,"\u2211":d.OP,"\u2212":d.BIN01,"\u2213":d.BIN01,"\u221A":[1,1,b.ORD,{stretchy:true}],"\u2220":d.ORD,"\u222B":d.INTEGRAL,"\u222E":d.INTEGRAL,"\u22C0":d.OP,"\u22C1":d.OP,"\u22C2":d.OP,"\u22C3":d.OP,"\u2308":d.OPEN,"\u230A":d.OPEN,"\u27E8":d.OPEN,"\u27EE":d.OPEN,"\u2A00":d.OP,"\u2A01":d.OP,"\u2A02":d.OP,"\u2A04":d.OP,"\u2A06":d.OP,"\u00AC":d.ORD21,"\u00B1":d.BIN01,"(":d.OPEN,"+":d.BIN01,"-":d.BIN01,"[":d.OPEN,"{":d.OPEN,"|":d.OPEN},postfix:{"!":[1,0,b.CLOSE],"&":d.ORD,"\u2032":d.ORD02,"\u203E":d.WIDEACCENT,"\u2309":d.CLOSE,"\u230B":d.CLOSE,"\u23DE":d.WIDEACCENT,"\u23DF":d.WIDEACCENT,"\u266D":d.ORD02,"\u266E":d.ORD02,"\u266F":d.ORD02,"\u27E9":d.CLOSE,"\u27EF":d.CLOSE,"\u02C6":d.WIDEACCENT,"\u02C7":d.WIDEACCENT,"\u02C9":d.WIDEACCENT,"\u02CA":d.ACCENT,"\u02CB":d.ACCENT,"\u02D8":d.ACCENT,"\u02D9":d.ACCENT,"\u02DC":d.WIDEACCENT,"\u0302":d.WIDEACCENT,"\u00A8":d.ACCENT,"\u00AF":d.WIDEACCENT,")":d.CLOSE,"]":d.CLOSE,"^":d.WIDEACCENT,_:d.WIDEACCENT,"`":d.ACCENT,"|":d.CLOSE,"}":d.CLOSE,"~":d.WIDEACCENT},infix:{"":d.ORD,"%":[3,3,b.ORD],"\u2022":d.BIN4,"\u2026":d.INNER,"\u2044":d.TALLBIN,"\u2061":d.ORD,"\u2062":d.ORD,"\u2063":[0,0,b.ORD,{linebreakstyle:"after",separator:true}],"\u2064":d.ORD,"\u2190":d.WIDEREL,"\u2191":d.RELSTRETCH,"\u2192":d.WIDEREL,"\u2193":d.RELSTRETCH,"\u2194":d.WIDEREL,"\u2195":d.RELSTRETCH,"\u2196":d.RELSTRETCH,"\u2197":d.RELSTRETCH,"\u2198":d.RELSTRETCH,"\u2199":d.RELSTRETCH,"\u21A6":d.WIDEREL,"\u21A9":d.WIDEREL,"\u21AA":d.WIDEREL,"\u21BC":d.WIDEREL,"\u21BD":d.WIDEREL,"\u21C0":d.WIDEREL,"\u21C1":d.WIDEREL,"\u21CC":d.WIDEREL,"\u21D0":d.WIDEREL,"\u21D1":d.RELSTRETCH,"\u21D2":d.WIDEREL,"\u21D3":d.RELSTRETCH,"\u21D4":d.WIDEREL,"\u21D5":d.RELSTRETCH,"\u2208":d.REL,"\u2209":d.REL,"\u220B":d.REL,"\u2212":d.BIN4,"\u2213":d.BIN4,"\u2215":d.TALLBIN,"\u2216":d.BIN4,"\u2217":d.BIN4,"\u2218":d.BIN4,"\u2219":d.BIN4,"\u221D":d.REL,"\u2223":d.REL,"\u2225":d.REL,"\u2227":d.BIN4,"\u2228":d.BIN4,"\u2229":d.BIN4,"\u222A":d.BIN4,"\u223C":d.REL,"\u2240":d.BIN4,"\u2243":d.REL,"\u2245":d.REL,"\u2248":d.REL,"\u224D":d.REL,"\u2250":d.REL,"\u2260":d.REL,"\u2261":d.REL,"\u2264":d.REL,"\u2265":d.REL,"\u226A":d.REL,"\u226B":d.REL,"\u227A":d.REL,"\u227B":d.REL,"\u2282":d.REL,"\u2283":d.REL,"\u2286":d.REL,"\u2287":d.REL,"\u228E":d.BIN4,"\u2291":d.REL,"\u2292":d.REL,"\u2293":d.BIN4,"\u2294":d.BIN4,"\u2295":d.BIN4,"\u2296":d.BIN4,"\u2297":d.BIN4,"\u2298":d.BIN4,"\u2299":d.BIN4,"\u22A2":d.REL,"\u22A3":d.REL,"\u22A4":d.ORD55,"\u22A5":d.REL,"\u22A8":d.REL,"\u22C4":d.BIN4,"\u22C5":d.BIN4,"\u22C6":d.BIN4,"\u22C8":d.REL,"\u22EE":d.ORD55,"\u22EF":d.INNER,"\u22F1":[5,5,b.INNER],"\u25B3":d.BIN4,"\u25B5":d.BIN4,"\u25B9":d.BIN4,"\u25BD":d.BIN4,"\u25BF":d.BIN4,"\u25C3":d.BIN4,"\u2758":d.REL,"\u27F5":d.WIDEREL,"\u27F6":d.WIDEREL,"\u27F7":d.WIDEREL,"\u27F8":d.WIDEREL,"\u27F9":d.WIDEREL,"\u27FA":d.WIDEREL,"\u27FC":d.WIDEREL,"\u2A2F":d.BIN4,"\u2A3F":d.BIN4,"\u2AAF":d.REL,"\u2AB0":d.REL,"\u00B1":d.BIN4,"\u00B7":d.BIN4,"\u00D7":d.BIN4,"\u00F7":d.BIN4,"*":d.BIN3,"+":d.BIN4,",":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"-":d.BIN4,".":[3,3,b.ORD],"/":d.ORD11,":":[1,2,b.REL],";":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"<":d.REL,"=":d.REL,">":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js");
MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.4.0";var a=MathJax.ElementJax.mml;SETTINGS=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[],h=(this.isToken?"":k+(g?"":"  "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken&&!this.isChars){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"&&(!this.attr||!this.attr.xmlns)){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close"||d==="form");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)&&SETTINGS.texHints){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return RegExp.$2+((1/18)*RegExp.$3).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(f){f=String(f).split("");for(var g=0,d=f.length;g<d;g++){var k=f[g].charCodeAt(0);if(k<=55295||57344<=k){if(k<32||k>126){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[f[g]];if(j){f[g]=j}}}else{if(g+1<d){var h=f[g+1].charCodeAt(0);var e=(((k-55296)<<10)+(h-56320)+65536);f[g]="&#x"+e.toString(16).toUpperCase()+";";f[g+1]="";g++}else{f[g]=""}}}return f.join("")}});a.math.Augment({toMathML:function(c,d){var f;if(c==null){c=""}if(d&&d.originalText&&SETTINGS.semantics){f=MathJax.InputJax[d.inputJax].annotationEncoding}var k=(this.data[0]&&this.data[0].data.length>1);var n=this.type,j=this.toMathMLattributes();var h=[],l=c+(f?"    ":"")+(k?"  ":"");for(var g=0,e=this.data.length;g<e;g++){if(this.data[g]){h.push(this.data[g].toMathML(l))}else{h.push(l+"<mrow />")}}if(h.length===0||(h.length===1&&h[0]==="")){if(!f){return"<"+n+j+" />"}h.push(l+"<mrow />")}if(f){if(k){h.unshift(c+"    <mrow>");h.push(c+"    </mrow>")}h.unshift(c+"  <semantics>");h.push(c+'    <annotation encoding="'+f+'">'+d.originalText+"</annotation>");h.push(c+"  </semantics>")}return c+"<"+n+j+">\n"+h.join("\n")+"\n"+c+"</"+n+">"}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+"  "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+"  "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();if(!c&&this.data[0].data.length===1){return d.substr(2)+this.data[0].toMathML(d)}return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+"  ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js");
(function(b,e){var d="2.4.0";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Config",function(){b.Config({"HTML-CSS":{styles:{".MathJax .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.call(this,j,k)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.call(this,p)}p=this.HTMLcreateSpan(p);p.className="noError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var o=0,l=r.length;o<l;o++){h.addText(p,r[o]);if(o!==l-1){h.addElement(p,"br",{isMathJax:true})}}var q=h.getHD(p.parentNode),k=h.getW(p.parentNode);if(l>1){var n=(q.h+q.d)/2,j=h.TeX.x_height/2;p.parentNode.style.verticalAlign=h.Em(q.d+(j-n));q.h=j+n;q.d=n-j}p.bbox={h:q.h,d:q.d,w:k,lw:0,rw:k};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.call(this,i,j)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.call(this,n)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l<j;l++){e.addText(n,o[l]);if(l!==j-1){e.addElement(n,"br",{isMathJax:true})}}if(j>1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.call(this,j)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.call(this,n)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l<k;l++){n.appendChild(document.createTextNode(o[l]));if(l!==k-1){n.appendChild(document.createElement("br"))}}if(this.multiLine){n.style.display="inline-block";if(k>1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js");
MathJax.Extension["TeX/noUndefined"]={version:"2.4.0",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js");
(function(d,c,i){var h,g="\u00A0";var j=function(l){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",l]].concat([].slice.call(arguments,1)))};var e=MathJax.Object.Subclass({Init:function(m,l){this.global={isInner:l};this.data=[b.start(this.global)];if(m){this.data[0].env=m}this.env=this.data[0].env},Push:function(){var n,l,o,p;for(n=0,l=arguments.length;n<l;n++){o=arguments[n];if(!o){continue}if(o instanceof h.mbase){o=b.mml(o)}o.global=this.global;p=(this.data.length?this.Top().checkItem(o):true);if(p instanceof Array){this.Pop();this.Push.apply(this,p)}else{if(p instanceof b){this.Pop();this.Push(p)}else{if(p){this.data.push(o);if(o.env){for(var q in this.env){if(this.env.hasOwnProperty(q)){o.env[q]=this.env[q]}}this.env=o.env}else{o.env=this.env}}}}}},Pop:function(){var l=this.data.pop();if(!l.isOpen){delete l.env}this.env=(this.data.length?this.Top().env:{});return l},Top:function(l){if(l==null){l=1}if(this.data.length<l){return null}return this.data[this.data.length-l]},Prev:function(l){var m=this.Top();if(l){return m.data[m.data.length-1]}else{return m.Pop()}},toString:function(){return"stack[\n  "+this.data.join("\n  ")+"\n]"}});var b=e.Item=MathJax.Object.Subclass({type:"base",endError:["ExtraOpenMissingClose","Extra open brace or missing close brace"],closeError:["ExtraCloseMissingOpen","Extra close brace or missing open brace"],rightError:["MissingLeftExtraRight","Missing \\left or extra \\right"],Init:function(){if(this.isOpen){this.env={}}this.data=[];this.Push.apply(this,arguments)},Push:function(){this.data.push.apply(this.data,arguments)},Pop:function(){return this.data.pop()},mmlData:function(l,m){if(l==null){l=true}if(this.data.length===1&&!m){return this.data[0]}return h.mrow.apply(h,this.data).With((l?{inferred:true}:{}))},checkItem:function(l){if(l.type==="over"&&this.isOpen){l.num=this.mmlData(false);this.data=[]}if(l.type==="cell"&&this.isOpen){if(l.linebreak){return false}d.Error(["Misplaced","Misplaced %1",l.name])}if(l.isClose&&this[l.type+"Error"]){d.Error(this[l.type+"Error"])}if(!l.isNotStack){return true}this.Push(l.data[0]);return false},With:function(l){for(var m in l){if(l.hasOwnProperty(m)){this[m]=l[m]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:true,Init:function(l){this.SUPER(arguments).Init.call(this);this.global=l},checkItem:function(l){if(l.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,l)}});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(m){if(m.type==="close"){var l=this.mmlData();return b.mml(h.TeXAtom(l))}return this.SUPER(arguments).checkItem.call(this,m)}});b.close=b.Subclass({type:"close",isClose:true});b.prime=b.Subclass({type:"prime",checkItem:function(l){if(this.data[0].type!=="msubsup"){return[h.msup(this.data[0],this.data[1]),l]}this.data[0].SetData(this.data[0].sup,this.data[1]);return[this.data[0],l]}});b.subsup=b.Subclass({type:"subsup",stopError:["MissingScript","Missing superscript or subscript argument"],supError:["MissingOpenForSup","Missing open brace for superscript"],subError:["MissingOpenForSub","Missing open brace for subscript"],checkItem:function(l){if(l.type==="open"||l.type==="left"){return true}if(l.type==="mml"){if(this.primes){if(this.position!==2){this.data[0].SetData(2,this.primes)}else{l.data[0]=h.mrow(this.primes.With({variantForm:true}),l.data[0])}}this.data[0].SetData(this.position,l.data[0]);return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,l)){d.Error(this[["","subError","supError"][this.position]])}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:true,name:"\\over",checkItem:function(n,l){if(n.type==="over"){d.Error(["AmbiguousUseOf","Ambiguous use of %1",n.name])}if(n.isClose){var m=h.mfrac(this.num,this.mmlData(false));if(this.thickness!=null){m.linethickness=this.thickness}if(this.open||this.close){m.texClass=h.TEXCLASS.INNER;m.texWithDelims=true;m=d.fenced(this.open,m,this.close)}return[b.mml(m),n]}return this.SUPER(arguments).checkItem.call(this,n)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:true,delim:"(",stopError:["ExtraLeftMissingRight","Extra \\left or missing \\right"],checkItem:function(l){if(l.type==="right"){return b.mml(d.fenced(this.delim,this.mmlData(),l.delim))}return this.SUPER(arguments).checkItem.call(this,l)}});b.right=b.Subclass({type:"right",isClose:true,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:true,checkItem:function(l){if(l.type==="end"){if(l.name!==this.name){d.Error(["EnvBadEnd","\\begin{%1} ended with \\end{%2}",this.name,l.name])}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(l.type==="stop"){d.Error(["EnvMissingEnd","Missing \\end{%1}",this.name])}return this.SUPER(arguments).checkItem.call(this,l)}});b.end=b.Subclass({type:"end",isClose:true});b.style=b.Subclass({type:"style",checkItem:function(m){if(!m.isClose){return this.SUPER(arguments).checkItem.call(this,m)}var l=h.mstyle.apply(h,this.data).With(this.styles);return[b.mml(l),m]}});b.position=b.Subclass({type:"position",checkItem:function(m){if(m.isClose){d.Error(["MissingBoxFor","Missing box for %1",this.name])}if(m.isNotStack){var l=m.mmlData();switch(this.move){case"vertical":l=h.mpadded(l).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(l)];case"horizontal":return[b.mml(this.left),m,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,m)}});b.array=b.Subclass({type:"array",isOpen:true,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.frame=[];this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(m){if(m.isClose&&m.type!=="over"){if(m.isEntry){this.EndEntry();this.clearEnv();return false}if(m.isCR){this.EndEntry();this.EndRow();this.clearEnv();return false}this.EndTable();this.clearEnv();var l=h.mtable.apply(h,this.table).With(this.arraydef);if(this.frame.length===4){l.frame=(this.frame.dashed?"dashed":"solid")}else{if(this.frame.length){l.hasFrame=true;if(this.arraydef.rowlines){this.arraydef.rowlines=this.arraydef.rowlines.replace(/none( none)+$/,"none")}l=h.menclose(l).With({notation:this.frame.join(" "),isFrame:true});if((this.arraydef.columnlines||"none")!="none"||(this.arraydef.rowlines||"none")!="none"){l.padding=0}}}if(this.open||this.close){l=d.fenced(this.open,l,this.close)}l=b.mml(l);if(this.requireClose){if(m.type==="close"){return l}d.Error(["MissingCloseBrace","Missing close brace"])}return[l,m]}return this.SUPER(arguments).checkItem.call(this,m)},EndEntry:function(){this.row.push(h.mtd.apply(h,this.data));this.data=[]},EndRow:function(){this.table.push(h.mtr.apply(h,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var l=this.arraydef.rowlines.split(/ /);if(l.length===this.table.length){this.frame.push("bottom");l.pop();this.arraydef.rowlines=l.join(" ")}else{if(l.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}if(this.rowspacing){var m=this.arraydef.rowspacing.split(/ /);while(m.length<this.table.length){m.push(this.rowspacing+"em")}this.arraydef.rowspacing=m.join(" ")}},clearEnv:function(){for(var l in this.env){if(this.env.hasOwnProperty(l)){delete this.env[l]}}}});b.cell=b.Subclass({type:"cell",isClose:true});b.mml=b.Subclass({type:"mml",isNotStack:true,Add:function(){this.data.push.apply(this.data,arguments);return this}});b.fn=b.Subclass({type:"fn",checkItem:function(m){if(this.data[0]){if(m.type!=="mml"||!m.data[0]){return[this.data[0],m]}if(m.data[0].isa(h.mspace)){return[this.data[0],m]}var l=m.data[0];if(l.isEmbellished()){l=l.CoreMO()}if([0,0,1,1,0,1,1,0,0,0][l.Get("texClass")]){return[this.data[0],m]}return[this.data[0],h.mo(h.entity("#x2061")).With({texClass:h.TEXCLASS.NONE}),m]}return this.SUPER(arguments).checkItem.apply(this,arguments)}});b.not=b.Subclass({type:"not",checkItem:function(m){var l,n;if(m.type==="open"||m.type==="left"){return true}if(m.type==="mml"&&m.data[0].type.match(/^(mo|mi|mtext)$/)){l=m.data[0],n=l.data.join("");if(n.length===1&&!l.movesupsub){n=b.not.remap[n.charCodeAt(0)];if(n){l.SetData(0,h.chars(String.fromCharCode(n)))}else{l.Append(h.chars("\u0338"))}return m}}l=h.mpadded(h.mtext("\u29F8")).With({width:0});l=h.TeXAtom(l).With({texClass:h.TEXCLASS.REL});return[l,m]}});b.not.remap={8592:8602,8594:8603,8596:8622,8656:8653,8658:8655,8660:8654,8712:8713,8715:8716,8739:8740,8741:8742,8764:8769,126:8769,8771:8772,8773:8775,8776:8777,8781:8813,61:8800,8801:8802,60:8814,62:8815,8804:8816,8805:8817,8818:8820,8819:8821,8822:8824,8823:8825,8826:8832,8827:8833,8834:8836,8835:8837,8838:8840,8839:8841,8866:8876,8872:8877,8873:8878,8875:8879,8828:8928,8829:8929,8849:8930,8850:8931,8882:8938,8883:8939,8884:8940,8885:8941,8707:8708};b.dots=b.Subclass({type:"dots",checkItem:function(m){if(m.type==="open"||m.type==="left"){return true}var n=this.ldots;if(m.type==="mml"&&m.data[0].isEmbellished()){var l=m.data[0].CoreMO().Get("texClass");if(l===h.TEXCLASS.BIN||l===h.TEXCLASS.REL){n=this.cdots}}return[n,m]}});var f={Add:function(l,o,n){if(!o){o=this}for(var m in l){if(l.hasOwnProperty(m)){if(typeof l[m]==="object"&&!(l[m] instanceof Array)&&(typeof o[m]==="object"||typeof o[m]==="function")){this.Add(l[m],o[m],l[m],n)}else{if(!o[m]||!o[m].isUser||!n){o[m]=l[m]}}}}return o}};var k=function(){h=MathJax.ElementJax.mml;c.Insert(f,{letter:/[a-z]/i,digit:/[0-9.]/,number:/^(?:[0-9]+(?:\{,\}[0-9]{3})*(?:\.[0-9]*)*|\.[0-9]+)/,special:{"\\":"ControlSequence","{":"Open","}":"Close","~":"Tilde","^":"Superscript",_:"Subscript"," ":"Space","\t":"Space","\r":"Space","\n":"Space","'":"Prime","%":"Comment","&":"Entry","#":"Hash","\u00A0":"Space","\u2019":"Prime"},remap:{"-":"2212","*":"2217","`":"2018"},mathchar0mi:{alpha:"03B1",beta:"03B2",gamma:"03B3",delta:"03B4",epsilon:"03F5",zeta:"03B6",eta:"03B7",theta:"03B8",iota:"03B9",kappa:"03BA",lambda:"03BB",mu:"03BC",nu:"03BD",xi:"03BE",omicron:"03BF",pi:"03C0",rho:"03C1",sigma:"03C3",tau:"03C4",upsilon:"03C5",phi:"03D5",chi:"03C7",psi:"03C8",omega:"03C9",varepsilon:"03B5",vartheta:"03D1",varpi:"03D6",varrho:"03F1",varsigma:"03C2",varphi:"03C6",S:["00A7",{mathvariant:h.VARIANT.NORMAL}],aleph:["2135",{mathvariant:h.VARIANT.NORMAL}],hbar:["210F",{variantForm:true}],imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:h.VARIANT.NORMAL}],Re:["211C",{mathvariant:h.VARIANT.NORMAL}],Im:["2111",{mathvariant:h.VARIANT.NORMAL}],partial:["2202",{mathvariant:h.VARIANT.NORMAL}],infty:["221E",{mathvariant:h.VARIANT.NORMAL}],prime:["2032",{mathvariant:h.VARIANT.NORMAL,variantForm:true}],emptyset:["2205",{mathvariant:h.VARIANT.NORMAL}],nabla:["2207",{mathvariant:h.VARIANT.NORMAL}],top:["22A4",{mathvariant:h.VARIANT.NORMAL}],bot:["22A5",{mathvariant:h.VARIANT.NORMAL}],angle:["2220",{mathvariant:h.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:h.VARIANT.NORMAL}],backslash:["2216",{mathvariant:h.VARIANT.NORMAL,variantForm:true}],forall:["2200",{mathvariant:h.VARIANT.NORMAL}],exists:["2203",{mathvariant:h.VARIANT.NORMAL}],neg:["00AC",{mathvariant:h.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:h.VARIANT.NORMAL}],flat:["266D",{mathvariant:h.VARIANT.NORMAL}],natural:["266E",{mathvariant:h.VARIANT.NORMAL}],sharp:["266F",{mathvariant:h.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:h.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:h.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:h.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:h.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:h.TEXCLASS.OP,movesupsub:true}],bigvee:["22C1",{texClass:h.TEXCLASS.OP,movesupsub:true}],bigwedge:["22C0",{texClass:h.TEXCLASS.OP,movesupsub:true}],biguplus:["2A04",{texClass:h.TEXCLASS.OP,movesupsub:true}],bigcap:["22C2",{texClass:h.TEXCLASS.OP,movesupsub:true}],bigcup:["22C3",{texClass:h.TEXCLASS.OP,movesupsub:true}],"int":["222B",{texClass:h.TEXCLASS.OP}],intop:["222B",{texClass:h.TEXCLASS.OP,movesupsub:true,movablelimits:true}],iint:["222C",{texClass:h.TEXCLASS.OP}],iiint:["222D",{texClass:h.TEXCLASS.OP}],prod:["220F",{texClass:h.TEXCLASS.OP,movesupsub:true}],sum:["2211",{texClass:h.TEXCLASS.OP,movesupsub:true}],bigotimes:["2A02",{texClass:h.TEXCLASS.OP,movesupsub:true}],bigoplus:["2A01",{texClass:h.TEXCLASS.OP,movesupsub:true}],bigodot:["2A00",{texClass:h.TEXCLASS.OP,movesupsub:true}],oint:["222E",{texClass:h.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:h.TEXCLASS.OP,movesupsub:true}],smallint:["222B",{largeop:false}],triangleleft:"25C3",triangleright:"25B9",bigtriangleup:"25B3",bigtriangledown:"25BD",wedge:"2227",land:"2227",vee:"2228",lor:"2228",cap:"2229",cup:"222A",ddagger:"2021",dagger:"2020",sqcap:"2293",sqcup:"2294",uplus:"228E",amalg:"2A3F",diamond:"22C4",bullet:"2219",wr:"2240",div:"00F7",odot:["2299",{largeop:false}],oslash:["2298",{largeop:false}],otimes:["2297",{largeop:false}],ominus:["2296",{largeop:false}],oplus:["2295",{largeop:false}],mp:"2213",pm:"00B1",circ:"2218",bigcirc:"25EF",setminus:["2216",{variantForm:true}],cdot:"22C5",ast:"2217",times:"00D7",star:"22C6",propto:"221D",sqsubseteq:"2291",sqsupseteq:"2292",parallel:"2225",mid:"2223",dashv:"22A3",vdash:"22A2",leq:"2264",le:"2264",geq:"2265",ge:"2265",lt:"003C",gt:"003E",succ:"227B",prec:"227A",approx:"2248",succeq:"2AB0",preceq:"2AAF",supset:"2283",subset:"2282",supseteq:"2287",subseteq:"2286","in":"2208",ni:"220B",notin:"2209",owns:"220B",gg:"226B",ll:"226A",sim:"223C",simeq:"2243",perp:"22A5",equiv:"2261",asymp:"224D",smile:"2323",frown:"2322",ne:"2260",neq:"2260",cong:"2245",doteq:"2250",bowtie:"22C8",models:"22A8",notChar:"29F8",Leftrightarrow:"21D4",Leftarrow:"21D0",Rightarrow:"21D2",leftrightarrow:"2194",leftarrow:"2190",gets:"2190",rightarrow:"2192",to:"2192",mapsto:"21A6",leftharpoonup:"21BC",leftharpoondown:"21BD",rightharpoonup:"21C0",rightharpoondown:"21C1",nearrow:"2197",searrow:"2198",nwarrow:"2196",swarrow:"2199",rightleftharpoons:"21CC",hookrightarrow:"21AA",hookleftarrow:"21A9",longleftarrow:"27F5",Longleftarrow:"27F8",longrightarrow:"27F6",Longrightarrow:"27F9",Longleftrightarrow:"27FA",longleftrightarrow:"27F7",longmapsto:"27FC",ldots:"2026",cdots:"22EF",vdots:"22EE",ddots:"22F1",dotsc:"2026",dotsb:"22EF",dotsm:"22EF",dotsi:"22EF",dotso:"2026",ldotp:["002E",{texClass:h.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:h.TEXCLASS.PUNCT}],colon:["003A",{texClass:h.TEXCLASS.PUNCT}]},mathchar7:{Gamma:"0393",Delta:"0394",Theta:"0398",Lambda:"039B",Xi:"039E",Pi:"03A0",Sigma:"03A3",Upsilon:"03A5",Phi:"03A6",Psi:"03A8",Omega:"03A9",_:"005F","#":"0023","$":"0024","%":"0025","&":"0026",And:"0026"},delimiter:{"(":"(",")":")","[":"[","]":"]","<":"27E8",">":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim&thinsp;inf"],limsup:["NamedOp","lim&thinsp;sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","00B4"],grave:["Accent","0060"],ddot:["Accent","00A8"],tilde:["Accent","007E"],bar:["Accent","00AF"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","005E"],vec:["Accent","2192"],dot:["Accent","02D9"],widetilde:["Accent","007E",1],widehat:["Accent","005E",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro",'\\mmlToken{mo}[lspace="thickmathspace" rspace="thickmathspace"]{mod}'],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it\\text{#1}}",1],textbf:["Macro","\\mathord{\\bf\\text{#1}}",1],textsf:["Macro","\\mathord{\\sf\\text{#1}}",1],texttt:["Macro","\\mathord{\\tt\\text{#1}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde","\u00A0":"Tilde",begin:"BeginEnd",end:"BeginEnd",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".2em","T"],equation:[null,"Equation"],"equation*":[null,"Equation"],eqnarray:["ExtensionEnv",null,"AMSmath"],"eqnarray*":["ExtensionEnv",null,"AMSmath"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var l=this.config.Macros;for(var m in l){if(l.hasOwnProperty(m)){if(typeof(l[m])==="string"){f.macros[m]=["Macro",l[m]]}else{f.macros[m]=["Macro"].concat(l[m])}f.macros[m].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(m,n){this.string=m;this.i=0;this.macroCount=0;var l;if(n){l={};for(var o in n){if(n.hasOwnProperty(o)){l[o]=n[o]}}}this.stack=d.Stack(l,!!n);this.Parse();this.Push(b.stop())},Parse:function(){var m,l;while(this.i<this.string.length){m=this.string.charAt(this.i++);l=m.charCodeAt(0);if(l>=55296&&l<56320){m+=this.string.charAt(this.i++)}if(f.special[m]){this[f.special[m]](m)}else{if(f.letter.test(m)){this.Variable(m)}else{if(f.digit.test(m)){this.Number(m)}else{this.Other(m)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(l){return l},ControlSequence:function(o){var l=this.GetCS(),n=this.csFindMacro(l);if(n){if(!(n instanceof Array)){n=[n]}var m=n[0];if(!(m instanceof Function)){m=this[m]}m.apply(this,[o+l].concat(n.slice(1)))}else{if(f.mathchar0mi[l]){this.csMathchar0mi(l,f.mathchar0mi[l])}else{if(f.mathchar0mo[l]){this.csMathchar0mo(l,f.mathchar0mo[l])}else{if(f.mathchar7[l]){this.csMathchar7(l,f.mathchar7[l])}else{if(f.delimiter["\\"+l]!=null){this.csDelimiter(l,f.delimiter["\\"+l])}else{this.csUndefined(o+l)}}}}}},csFindMacro:function(l){return f.macros[l]},csMathchar0mi:function(l,n){var m={mathvariant:h.VARIANT.ITALIC};if(n instanceof Array){m=n[1];n=n[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+n)).With(m)))},csMathchar0mo:function(l,n){var m={stretchy:false};if(n instanceof Array){m=n[1];m.stretchy=false;n=n[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+n)).With(m)))},csMathchar7:function(l,n){var m={mathvariant:h.VARIANT.NORMAL};if(n instanceof Array){m=n[1];n=n[0]}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+n)).With(m)))},csDelimiter:function(l,n){var m={};if(n instanceof Array){m=n[1];n=n[0]}if(n.length===4){n=h.entity("#x"+n)}else{n=h.chars(n)}this.Push(this.mmlToken(h.mo(n).With({fence:false,stretchy:false}).With(m)))},csUndefined:function(l){d.Error(["UndefinedControlSequence","Undefined control sequence %1",l])},Variable:function(m){var l={};if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(m)).With(l)))},Number:function(o){var l,m=this.string.slice(this.i-1).match(f.number);if(m){l=h.mn(m[0].replace(/[{}]/g,""));this.i+=m[0].length-1}else{l=h.mo(h.chars(o))}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(l))},Open:function(l){this.Push(b.open())},Close:function(l){this.Push(b.close())},Tilde:function(l){this.Push(h.mtext(h.chars(g)))},Space:function(l){},Superscript:function(p){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var l,o,m,n=this.stack.Top();if(n.type==="prime"){m=n.data[0];o=n.data[1];this.stack.Pop()}else{m=this.stack.Prev();if(!m){m=h.mi("")}}if(m.isEmbellishedWrapper){m=m.data[0].data[0]}if(m.type==="msubsup"){if(m.data[m.sup]){d.Error(["DoubleExponent","Double exponent: use braces to clarify"])}l=m.sup}else{if(m.movesupsub){if(m.type!=="munderover"||m.data[m.over]){if(m.movablelimits&&m.isa(h.mi)){m=this.mi2mo(m)}m=h.munderover(m,null,null).With({movesupsub:true})}l=m.over}else{m=h.msubsup(m,null,null);l=m.sup}}this.Push(b.subsup(m).With({position:l,primes:o}))},Subscript:function(p){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var l,o,m,n=this.stack.Top();if(n.type==="prime"){m=n.data[0];o=n.data[1];this.stack.Pop()}else{m=this.stack.Prev();if(!m){m=h.mi("")}}if(m.isEmbellishedWrapper){m=m.data[0].data[0]}if(m.type==="msubsup"){if(m.data[m.sub]){d.Error(["DoubleSubscripts","Double subscripts: use braces to clarify"])}l=m.sub}else{if(m.movesupsub){if(m.type!=="munderover"||m.data[m.under]){if(m.movablelimits&&m.isa(h.mi)){m=this.mi2mo(m)}m=h.munderover(m,null,null).With({movesupsub:true})}l=m.under}else{m=h.msubsup(m,null,null);l=m.sub}}this.Push(b.subsup(m).With({position:l,primes:o}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(n){var m=this.stack.Prev();if(!m){m=h.mi()}if(m.type==="msubsup"&&m.data[m.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var l="";this.i--;do{l+=this.PRIME;this.i++,n=this.GetNext()}while(n==="'"||n===this.SMARTQUOTE);l=["","\u2032","\u2033","\u2034","\u2057"][l.length]||l;this.Push(b.prime(m,this.mmlToken(h.mo(l))))},mi2mo:function(l){var m=h.mo();m.Append.apply(m,l.data);var n;for(n in m.defaults){if(m.defaults.hasOwnProperty(n)&&l[n]!=null){m[n]=l[n]}}for(n in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(n)&&l[n]!=null){m[n]=l[n]}}return m},Comment:function(l){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(l){d.Error(["CantUseHash1","You can't use 'macro parameter character #' in math mode"])},Other:function(n){var m,l;if(this.stack.env.font){m={mathvariant:this.stack.env.font}}if(f.remap[n]){n=f.remap[n];if(n instanceof Array){m=n[1];n=n[0]}l=h.mo(h.entity("#x"+n)).With(m)}else{l=h.mo(n).With(m)}if(l.autoDefault("stretchy",true)){l.stretchy=false}if(l.autoDefault("texClass",true)==""){l=h.TeXAtom(l)}this.Push(this.mmlToken(l))},SetFont:function(m,l){this.stack.env.font=l},SetStyle:function(m,l,n,o){this.stack.env.style=l;this.stack.env.level=o;this.Push(b.style().With({styles:{displaystyle:n,scriptlevel:o}}))},SetSize:function(l,m){this.stack.env.size=m;this.Push(b.style().With({styles:{mathsize:m+"em"}}))},Color:function(n){var m=this.GetArgument(n);var l=this.stack.env.color;this.stack.env.color=m;var o=this.ParseArg(n);if(l){this.stack.env.color}else{delete this.stack.env.color}this.Push(h.mstyle(o).With({mathcolor:m}))},Spacer:function(l,m){this.Push(h.mspace().With({width:m,mathsize:h.SIZE.NORMAL,scriptlevel:0}))},LeftRight:function(l){this.Push(b[l.substr(1)]().With({delim:this.GetDelimiter(l)}))},Middle:function(l){var m=this.GetDelimiter(l);if(this.stack.Top().type!=="left"){d.Error(["MisplacedMiddle","%1 must be within \\left and \\right",l])}this.Push(h.mo(m).With({stretchy:true}))},NamedFn:function(m,n){if(!n){n=m.substr(1)}var l=h.mi(n).With({texClass:h.TEXCLASS.OP});this.Push(b.fn(this.mmlToken(l)))},NamedOp:function(m,n){if(!n){n=m.substr(1)}n=n.replace(/&thinsp;/,"\u2006");var l=h.mo(n).With({movablelimits:true,movesupsub:true,form:h.FORM.PREFIX,texClass:h.TEXCLASS.OP});l.useMMLspacing&=~l.SPACE_ATTR.form;this.Push(this.mmlToken(l))},Limits:function(m,l){var n=this.stack.Prev("nopop");if(!n||n.texClass!==h.TEXCLASS.OP){d.Error(["MisplacedLimits","%1 is allowed only on operators",m])}n.movesupsub=(l?true:false);n.movablelimits=false},Over:function(n,m,o){var l=b.over().With({name:n});if(m||o){l.open=m;l.close=o}else{if(n.match(/withdelims$/)){l.open=this.GetDelimiter(n);l.close=this.GetDelimiter(n)}}if(n.match(/^\\above/)){l.thickness=this.GetDimen(n)}else{if(n.match(/^\\atop/)||m||o){l.thickness=0}}this.Push(l)},Frac:function(m){var l=this.ParseArg(m);var n=this.ParseArg(m);this.Push(h.mfrac(l,n))},Sqrt:function(o){var p=this.GetBrackets(o),l=this.GetArgument(o);if(l==="\\frac"){l+="{"+this.GetArgument(l)+"}{"+this.GetArgument(l)+"}"}var m=d.Parse(l,this.stack.env).mml();if(!p){m=h.msqrt.apply(h,m.array())}else{m=h.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(m){var o=this.GetUpTo(m,"\\of");var l=this.ParseArg(m);this.Push(h.mroot(l,this.parseRoot(o)))},parseRoot:function(q){var m=this.stack.env,l=m.inRoot;m.inRoot=true;var p=d.Parse(q,m);q=p.mml();var o=p.stack.global;if(o.leftRoot||o.upRoot){q=h.mpadded(q);if(o.leftRoot){q.width=o.leftRoot}if(o.upRoot){q.voffset=o.upRoot;q.height=o.upRoot}}m.inRoot=l;return q},MoveRoot:function(l,o){if(!this.stack.env.inRoot){d.Error(["MisplacedMoveRoot","%1 can appear only within a root",l])}if(this.stack.global[o]){d.Error(["MultipleMoveRoot","Multiple use of %1",l])}var m=this.GetArgument(l);if(!m.match(/-?[0-9]+/)){d.Error(["IntegerArg","The argument to %1 must be an integer",l])}m=(m/15)+"em";if(m.substr(0,1)!=="-"){m="+"+m}this.stack.global[o]=m},Accent:function(n,l,q){var p=this.ParseArg(n);var o={accent:true};if(this.stack.env.font){o.mathvariant=this.stack.env.font}var m=this.mmlToken(h.mo(h.entity("#x"+l)).With(o));m.stretchy=(q?true:false);this.Push(h.TeXAtom(h.munderover(p,null,m).With({accent:true})))},UnderOver:function(n,q,l){var p={o:"over",u:"under"}[n.charAt(1)];var o=this.ParseArg(n);if(o.Get("movablelimits")){o.movablelimits=false}var m=h.munderover(o,null,null);if(l){m.movesupsub=true}m.data[m[p]]=this.mmlToken(h.mo(h.entity("#x"+q)).With({stretchy:true,accent:(p=="under")}));this.Push(m)},Overset:function(l){var n=this.ParseArg(l),m=this.ParseArg(l);this.Push(h.mover(m,n))},Underset:function(l){var n=this.ParseArg(l),m=this.ParseArg(l);this.Push(h.munder(m,n))},TeXAtom:function(o,q){var p={texClass:q},n;if(q==h.TEXCLASS.OP){p.movesupsub=p.movablelimits=true;var l=this.GetArgument(o);var m=l.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(m){p.mathvariant=h.VARIANT.NORMAL;n=b.fn(this.mmlToken(h.mi(m[1]).With(p)))}else{n=b.fn(h.TeXAtom(d.Parse(l,this.stack.env).mml()).With(p))}}else{n=h.TeXAtom(this.ParseArg(o)).With(p)}this.Push(n)},MmlToken:function(n){var o=this.GetArgument(n),l=this.GetBrackets(n,"").replace(/^\s+/,""),r=this.GetArgument(n),q={attrNames:[]},m;if(!h[o]||!h[o].prototype.isToken){d.Error(["NotMathMLToken","%1 is not a token element",o])}while(l!==""){m=l.match(/^([a-z]+)\s*=\s*(\'[^']*'|"[^"]*"|[^ ]*)\s*/i);if(!m){d.Error(["InvalidMathMLAttr","Invalid MathML attribute: %1",l])}if(!h[o].prototype.defaults[m[1]]&&!this.MmlTokenAllow[m[1]]){d.Error(["UnknownAttrForElement","%1 is not a recognized attribute for %2",m[1],o])}var p=this.MmlFilterAttribute(m[1],m[2].replace(/^(['"])(.*)\1$/,"$2"));if(p){if(p.toLowerCase()==="true"){p=true}else{if(p.toLowerCase()==="false"){p=false}}q[m[1]]=p;q.attrNames.push(m[1])}l=l.substr(m[0].length)}this.Push(this.mmlToken(h[o](r).With(q)))},MmlFilterAttribute:function(l,m){return m},MmlTokenAllow:{fontfamily:1,fontsize:1,fontweight:1,fontstyle:1,color:1,background:1,id:1,"class":1,href:1,style:1},Strut:function(l){this.Push(h.mpadded(h.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(m,l,n){var o=h.mphantom(this.ParseArg(m));if(l||n){o=h.mpadded(o);if(n){o.height=o.depth=0}if(l){o.width=0}}this.Push(h.TeXAtom(o))},Smash:function(n){var m=this.trimSpaces(this.GetBrackets(n,""));var l=h.mpadded(this.ParseArg(n));switch(m){case"b":l.depth=0;break;case"t":l.height=0;break;default:l.height=l.depth=0}this.Push(h.TeXAtom(l))},Lap:function(m){var l=h.mpadded(this.ParseArg(m)).With({width:0});if(m==="\\llap"){l.lspace="-1width"}this.Push(h.TeXAtom(l))},RaiseLower:function(l){var m=this.GetDimen(l);var n=b.position().With({name:l,move:"vertical"});if(m.charAt(0)==="-"){m=m.slice(1);l={raise:"\\lower",lower:"\\raise"}[l.substr(1)]}if(l==="\\lower"){n.dh="-"+m;n.dd="+"+m}else{n.dh="+"+m;n.dd="-"+m}this.Push(n)},MoveLeftRight:function(l){var o=this.GetDimen(l);var n=(o.charAt(0)==="-"?o.slice(1):"-"+o);if(l==="\\moveleft"){var m=o;o=n;n=m}this.Push(b.position().With({name:l,move:"horizontal",left:h.mspace().With({width:o,mathsize:h.SIZE.NORMAL}),right:h.mspace().With({width:n,mathsize:h.SIZE.NORMAL})}))},Hskip:function(l){this.Push(h.mspace().With({width:this.GetDimen(l),mathsize:h.SIZE.NORMAL}))},Rule:function(n,p){var l=this.GetDimen(n),o=this.GetDimen(n),r=this.GetDimen(n);var m,q={width:l,height:o,depth:r};if(p!=="blank"){if(parseFloat(l)&&parseFloat(o)+parseFloat(r)){q.mathbackground=(this.stack.env.color||"black")}m=h.mpadded(h.mrow()).With(q)}else{m=h.mspace().With(q)}this.Push(m)},MakeBig:function(l,o,m){m*=f.p_height;m=String(m).replace(/(\.\d\d\d).+/,"$1")+"em";var n=this.GetDelimiter(l,true);this.Push(h.TeXAtom(h.mo(n).With({minsize:m,maxsize:m,fence:true,stretchy:true,symmetric:true})).With({texClass:o}))},BuildRel:function(l){var m=this.ParseUpTo(l,"\\over");var n=this.ParseArg(l);this.Push(h.TeXAtom(h.munderover(n,null,m)).With({mclass:h.TEXCLASS.REL}))},HBox:function(l,m){this.Push.apply(this,this.InternalMath(this.GetArgument(l),m))},FBox:function(l){this.Push(h.menclose.apply(h,this.InternalMath(this.GetArgument(l))).With({notation:"box"}))},Not:function(l){this.Push(b.not())},Dots:function(l){this.Push(b.dots().With({ldots:this.mmlToken(h.mo(h.entity("#x2026")).With({stretchy:false})),cdots:this.mmlToken(h.mo(h.entity("#x22EF")).With({stretchy:false}))}))},Require:function(l){var m=this.GetArgument(l).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");this.Extension(null,m)},Extension:function(l,m,n){if(l&&!typeof(l)==="string"){l=l.name}m=d.extensionDir+"/"+m;if(!m.match(/\.js$/)){m+=".js"}if(!i.loaded[i.fileURL(m)]){if(l!=null){delete f[n||"macros"][l.replace(/^\\/,"")]}c.RestartAfter(i.Require(m))}},Macro:function(n,q,p,r){if(p){var m=[];if(r!=null){var l=this.GetBrackets(n);m.push(l==null?r:l)}for(var o=m.length;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(m,o,t,q,s,n,l,u){var r=this.GetNext();if(r===""){d.Error(["MissingArgFor","Missing argument for %1",m])}if(r==="{"){this.i++}else{this.string=r+"}"+this.string.slice(this.i+1);this.i=0}var p=b.array().With({requireClose:true,arraydef:{rowspacing:(n||"4pt"),columnspacing:(s||"1em")}});if(u){p.isCases=true}if(o||t){p.open=o;p.close=t}if(l==="D"){p.arraydef.displaystyle=true}if(q!=null){p.arraydef.columnalign=q}this.Push(p)},Entry:function(o){this.Push(b.cell().With({isEntry:true,name:o}));if(this.stack.Top().isCases){var n=this.string;var r=0,p=this.i,l=n.length;while(p<l){var s=n.charAt(p);if(s==="{"){r++;p++}else{if(s==="}"){if(r===0){l=0}else{r--;p++}}else{if(s==="&"&&r===0){d.Error(["ExtraAlignTab","Extra alignment tab in \\cases text"])}else{if(s==="\\"){if(n.substr(p).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){l=0}else{p+=2}}else{p++}}}}}var q=n.substr(this.i,p-this.i);if(!q.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(q));this.i=p}}},Cr:function(l){this.Push(b.cell().With({isCR:true,name:l}))},CrLaTeX:function(l){var p;if(this.string.charAt(this.i)==="["){p=this.GetBrackets(l,"").replace(/ /g,"");if(p&&!p.match(/^((-?(\.\d+|\d+(\.\d*)?))(pt|em|ex|mu|mm|cm|in|pc))$/)){d.Error(["BracketMustBeDimension","Bracket argument to %1 must be a dimension",l])}}this.Push(b.cell().With({isCR:true,name:l,linebreak:true}));var o=this.stack.Top();if(o.isa(b.array)){if(p&&o.arraydef.rowspacing){var m=o.arraydef.rowspacing.split(/ /);if(!o.rowspacing){o.rowspacing=this.dimen2em(m[0])}while(m.length<o.table.length){m.push(this.Em(o.rowspacing))}m[o.table.length-1]=this.Em(Math.max(0,o.rowspacing+this.dimen2em(p)));o.arraydef.rowspacing=m.join(" ")}}else{if(p){this.Push(h.mspace().With({depth:p}))}this.Push(h.mspace().With({linebreak:h.LINEBREAK.NEWLINE}))}},emPerInch:7.2,dimen2em:function(p){var n=p.match(/^(-?(?:\.\d+|\d+(?:\.\d*)?))(pt|em|ex|mu|pc|in|mm|cm)/);var l=parseFloat(n[1]||"1"),o=n[2];if(o==="em"){return l}if(o==="ex"){return l*0.43}if(o==="pt"){return l/10}if(o==="pc"){return l*1.2}if(o==="in"){return l*this.emPerInch}if(o==="cm"){return l*this.emPerInch/2.54}if(o==="mm"){return l*this.emPerInch/25.4}if(o==="mu"){return l/18}return 0},Em:function(l){if(Math.abs(l)<0.0006){return"0em"}return l.toFixed(3).replace(/\.?0+$/,"")+"em"},HLine:function(m,n){if(n==null){n="solid"}var o=this.stack.Top();if(!o.isa(b.array)||o.data.length){d.Error(["Misplaced","Misplaced %1",m])}if(o.table.length==0){o.frame.push("top")}else{var l=(o.arraydef.rowlines?o.arraydef.rowlines.split(/ /):[]);while(l.length<o.table.length){l.push("none")}l[o.table.length-1]=n;o.arraydef.rowlines=l.join(" ")}},BeginEnd:function(n){var o=this.GetArgument(n),q=false;if(o.match(/^\\end\\/)){q=true;o=o.substr(5)}if(o.match(/\\/i)){d.Error(["InvalidEnv","Invalid environment name '%1'",o])}var p=this.envFindName(o);if(!p){d.Error(["UnknownEnv","Unknown environment '%1'",o])}if(!(p instanceof Array)){p=[p]}var l=(p[1] instanceof Array?p[1][0]:p[1]);var m=b.begin().With({name:o,end:l,parse:this});if(n==="\\end"){if(!q&&p[1] instanceof Array&&this[p[1][1]]){m=this[p[1][1]].apply(this,[m].concat(p.slice(2)))}else{m=b.end().With({name:o})}}else{if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}}this.Push(m)},envFindName:function(l){return f.environment[l]},Equation:function(l,m){return m},ExtensionEnv:function(m,l){this.Extension(m.name,l,"environment")},Array:function(m,o,t,r,s,n,l,p){if(!r){r=this.GetArgument("\\begin{"+m.name+"}")}var u=("c"+r).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");r=r.replace(/[^clr]/g,"").split("").join(" ");r=r.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var q=b.array().With({arraydef:{columnalign:r,columnspacing:(s||"1em"),rowspacing:(n||"4pt")}});if(u.match(/[|:]/)){if(u.charAt(0).match(/[|:]/)){q.frame.push("left");q.frame.dashed=u.charAt(0)===":"}if(u.charAt(u.length-1).match(/[|:]/)){q.frame.push("right")}u=u.substr(1,u.length-2);q.arraydef.columnlines=u.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(o){q.open=this.convertDelimiter(o)}if(t){q.close=this.convertDelimiter(t)}if(l==="D"){q.arraydef.displaystyle=true}else{if(l){q.arraydef.displaystyle=false}}if(l==="S"){q.arraydef.scriptlevel=1}if(p){q.arraydef.useHeight=false}this.Push(m);return q},AlignedArray:function(l){var m=this.GetBrackets("\\begin{"+l.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),m)},setArrayAlign:function(m,l){l=this.trimSpaces(l||"");if(l==="t"){m.arraydef.align="baseline 1"}else{if(l==="b"){m.arraydef.align="baseline -1"}else{if(l==="c"){m.arraydef.align="center"}else{if(l){m.arraydef.align=l}}}}return m},convertDelimiter:function(l){if(l){l=f.delimiter[l]}if(l==null){return null}if(l instanceof Array){l=l[0]}if(l.length===4){l=String.fromCharCode(parseInt(l,16))}return l},trimSpaces:function(l){if(typeof(l)!="string"){return l}return l.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/\s/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var l=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(l){this.i+=l[1].length;return l[1]}else{this.i++;return" "}},GetArgument:function(m,n){switch(this.GetNext()){case"":if(!n){d.Error(["MissingArgFor","Missing argument for %1",m])}return null;case"}":if(!n){d.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"])}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var l=++this.i,o=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":o++;break;case"}":if(--o==0){return this.string.slice(l,this.i-1)}break}}d.Error(["MissingCloseBrace","Missing close brace"]);break}return this.string.charAt(this.i++)},GetBrackets:function(m,o){if(this.GetNext()!="["){return o}var l=++this.i,n=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":n++;break;case"\\":this.i++;break;case"}":if(n--<=0){d.Error(["ExtraCloseLooking","Extra close brace while looking for %1","']'"])}break;case"]":if(n==0){return this.string.slice(l,this.i-1)}break}}d.Error(["MissingCloseBracket","Couldn't find closing ']' for argument to %1",m])},GetDelimiter:function(l,m){while(this.nextIsSpace()){this.i++}var n=this.string.charAt(this.i);this.i++;if(this.i<=this.string.length){if(n=="\\"){n+=this.GetCS(l)}else{if(n==="{"&&m){this.i--;n=this.GetArgument(l)}}if(f.delimiter[n]!=null){return this.convertDelimiter(n)}}d.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",l])},GetDimen:function(m){var n;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){n=this.GetArgument(m);if(n.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return n.replace(/ /g,"")}}else{n=this.string.slice(this.i);var l=n.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(l){this.i+=l[0].length;return l[1].replace(/ /g,"")}}d.Error(["MissingDimOrUnits","Missing dimension or its units for %1",m])},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(["ExtraCloseLooking","Extra close brace while looking for %1",o])}p--;break}if(p==0&&q==o){return this.string.slice(m,l)}}d.Error(["TokenNotFoundForCommand","Couldn't find %1 for %2",o,n])},ParseArg:function(l){return d.Parse(this.GetArgument(l),this.stack.env).mml()},ParseUpTo:function(l,m){return d.Parse(this.GetUpTo(l,m),this.stack.env).mml()},InternalMath:function(q,s){var p={displaystyle:false};if(s!=null){p.scriptlevel=s}if(this.stack.env.font){p.mathvariant=this.stack.env.font}if(!q.match(/\\?\$|\\\(|\\(eq)?ref\s*\{/)){return[this.InternalText(q,p)]}var o=0,l=0,r,n="";var m=[];while(o<q.length){r=q.charAt(o++);if(r==="$"){if(n==="$"){m.push(h.TeXAtom(d.Parse(q.slice(l,o-1),{}).mml().With(p)));n="";l=o}else{if(n===""){if(l<o-1){m.push(this.InternalText(q.slice(l,o-1),p))}n="$";l=o}}}else{if(r==="}"&&n==="}"){m.push(h.TeXAtom(d.Parse(q.slice(l,o),{}).mml().With(p)));n="";l=o}else{if(r==="\\"){if(n===""&&q.substr(o).match(/^(eq)?ref\s*\{/)){if(l<o-1){m.push(this.InternalText(q.slice(l,o-1),p))}n="}";l=o-1}else{r=q.charAt(o++);if(r==="("&&n===""){if(l<o-2){m.push(this.InternalText(q.slice(l,o-2),p))}n=")";l=o}else{if(r===")"&&n===")"){m.push(h.TeXAtom(d.Parse(q.slice(l,o-2),{}).mml().With(p)));n="";l=o}else{if(r==="$"&&n===""){o--;q=q.substr(0,o-1)+q.substr(o)}}}}}}}}if(n!==""){d.Error(["MathNotTerminated","Math not terminated in text box"])}if(l<q.length){m.push(this.InternalText(q.slice(l),p))}return m},InternalText:function(m,l){m=m.replace(/^\s+/,g).replace(/\s+$/,g);return h.mtext(h.chars(m)).With(l)},SubstituteArgs:function(m,l){var p="";var o="";var q;var n=0;while(n<l.length){q=l.charAt(n++);if(q==="\\"){p+=q+l.charAt(n++)}else{if(q==="#"){q=l.charAt(n++);if(q==="#"){p+=q}else{if(!q.match(/[1-9]/)||q>m.length){d.Error(["IllegalMacroParam","Illegal macro parameter reference"])}o=this.AddArgs(this.AddArgs(o,p),m[q-1]);p=""}}else{p+=q}}}return this.AddArgs(o,p)},AddArgs:function(m,l){if(l.match(/^[a-z]/i)&&m.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){m+=" "}if(m.length+l.length>d.config.MAXBUFFER){d.Error(["MaxBufferSize","MathJax internal buffer size exceeded; is there a recursive macro call?"])}return m+l}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:k,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:["TeXCommands","TeX Commands"],annotationEncoding:"application/x-tex",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(l){var m,n=false,p=MathJax.HTML.getScript(l);var r=(l.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var q={math:p,display:r,script:l};this.prefilterHooks.Execute(q);p=q.math;try{m=d.Parse(p).mml()}catch(o){if(!o.texError){throw o}m=this.formatError(o,p,r,l);n=true}if(m.inferred){m=h.apply(MathJax.ElementJax,m.data)}else{m=h(m)}if(r){m.root.display="block"}if(n){m.texError=true}q.math=m;this.postfilterHooks.Execute(q);return q.math},prefilterMath:function(m,n,l){return m},postfilterMath:function(m,n,l){this.combineRelations(m.root);return m},formatError:function(o,n,p,l){var m=o.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",m,n,p,l]);return h.Error(m)},Error:function(l){if(l instanceof Array){l=j.apply(j,l)}throw c.Insert(Error(l),{texError:true})},Macro:function(l,m,n){f.macros[l]=["Macro"].concat([].slice.call(arguments,1));f.macros[l].isUser=true},fenced:function(n,m,o){var l=h.mrow().With({open:n,close:o,texClass:h.TEXCLASS.INNER});if(n){l.Append(h.mo(n).With({fence:true,stretchy:true,texClass:h.TEXCLASS.OPEN}))}if(m.type==="mrow"){l.Append.apply(l,m.data)}else{l.Append(m)}if(o){l.Append(h.mo(o).With({fence:true,stretchy:true,texClass:h.TEXCLASS.CLOSE}))}return l},combineRelations:function(p){var q,l,o,n;for(q=0,l=p.data.length;q<l;q++){if(p.data[q]){if(p.isa(h.mrow)){while(q+1<l&&(o=p.data[q])&&(n=p.data[q+1])&&o.isa(h.mo)&&n.isa(h.mo)&&o.Get("texClass")===h.TEXCLASS.REL&&n.Get("texClass")===h.TEXCLASS.REL){if(o.variantForm==n.variantForm&&o.Get("mathvariant")==n.Get("mathvariant")&&o.style==n.style&&o["class"]==n["class"]&&!o.id&&!n.id){o.Append.apply(o,n.data);p.data.splice(q+1,1);l--}else{o.rspace=n.lspace="0pt";q++}}}if(!p.data[q].isToken){this.combineRelations(p.data[q])}}}}});d.prefilterHooks.Add(function(l){l.math=d.prefilterMath(l.math,l.display,l.script)});d.postfilterHooks.Add(function(l){l.math=d.postfilterMath(l.math,l.display,l.script)});d.loadComplete("jax.js")})(MathJax.InputJax.TeX,MathJax.Hub,MathJax.Ajax);
MathJax.Extension["TeX/AMSmath"]={version:"2.4.0",number:0,startNumber:0,IDs:{},eqIDs:{},labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,g=MathJax.InputJax.TeX,f=MathJax.Extension["TeX/AMSmath"];var d=g.Definitions,e=g.Stack.Item,a=g.config.equationNumbers;var c=function(j){var l=[];for(var k=0,h=j.length;k<h;k++){l[k]=g.Parse.prototype.Em(j[k])}return l.join(" ")};d.Add({mathchar0mo:{iiiint:["2A0C",{texClass:b.TEXCLASS.OP}]},macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",b.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",b.LENGTH.NEGATIVETHICKMATHSPACE],idotsint:["MultiIntegral","\\int\\cdots\\int"],dddot:["Accent","20DB"],ddddot:["Accent","20DC"],sideset:["Macro","\\mathop{\\mathop{\\rlap{\\phantom{#3}}}\\nolimits#1\\!\\mathop{#3}\\nolimits#2}",3],boxed:["Macro","\\fbox{$\\displaystyle{#1}$}",1],tag:"HandleTag",notag:"HandleNoTag",label:"HandleLabel",ref:"HandleRef",eqref:["HandleRef",true],substack:["Macro","\\begin{subarray}{c}#1\\end{subarray}",1],injlim:["NamedOp","inj&thinsp;lim"],projlim:["NamedOp","proj&thinsp;lim"],varliminf:["Macro","\\mathop{\\underline{\\mmlToken{mi}{lim}}}"],varlimsup:["Macro","\\mathop{\\overline{\\mmlToken{mi}{lim}}}"],varinjlim:["Macro","\\mathop{\\underrightarrow{\\mmlToken{mi}{lim}\\Rule{-1pt}{0pt}{1pt}}\\Rule{0pt}{0pt}{.45em}}"],varprojlim:["Macro","\\mathop{\\underleftarrow{\\mmlToken{mi}{lim}\\Rule{-1pt}{0pt}{1pt}}\\Rule{0pt}{0pt}{.45em}}"],DeclareMathOperator:"HandleDeclareOp",operatorname:"HandleOperatorName",genfrac:"Genfrac",frac:["Genfrac","","","",""],tfrac:["Genfrac","","","",1],dfrac:["Genfrac","","","",0],binom:["Genfrac","(",")","0em",""],tbinom:["Genfrac","(",")","0em",1],dbinom:["Genfrac","(",")","0em",0],cfrac:"CFrac",shoveleft:["HandleShove",b.ALIGN.LEFT],shoveright:["HandleShove",b.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",c([0,2,0,2,0,2,0,2,0,2,0])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",c([0,2,0,2,0,2,0,2,0,2,0])],multline:["Multline",null,true],"multline*":["Multline",null,false],split:["AMSarray",null,false,false,"rl",c([0])],gather:["AMSarray",null,true,true,"c"],"gather*":["AMSarray",null,false,true,"c"],alignat:["AlignAt",null,true,true],"alignat*":["AlignAt",null,false,true],alignedat:["AlignAt",null,false,false],aligned:["AlignedArray",null,null,null,"rlrlrlrlrlrl",c([0,2,0,2,0,2,0,2,0,2,0]),".5em","D"],gathered:["AlignedArray",null,null,null,"c",null,".5em","D"],subarray:["Array",null,null,null,null,c([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",c([1/3]),".2em","S",1],equation:["EquationBegin","Equation",true],"equation*":["EquationBegin","EquationStar",false],eqnarray:["AMSarray",null,true,true,"rcl",b.LENGTH.THICKMATHSPACE,".5em"],"eqnarray*":["AMSarray",null,false,true,"rcl",b.LENGTH.THICKMATHSPACE,".5em"]},delimiter:{"\\lvert":["2223",{texClass:b.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:b.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:b.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:b.TEXCLASS.CLOSE}]}},null,true);g.Parse.Augment({HandleTag:function(j){var l=this.GetStar();var i=this.trimSpaces(this.GetArgument(j)),h=i;if(!l){i=a.formatTag(i)}var k=this.stack.global;k.tagID=h;if(k.notags){g.Error(["CommandNotAllowedInEnv","%1 not allowed in %2 environment",j,k.notags])}if(k.tag){g.Error(["MultipleCommand","Multiple %1",j])}k.tag=b.mtd.apply(b,this.InternalMath(i)).With({id:a.formatID(h)})},HandleNoTag:function(h){if(this.stack.global.tag){delete this.stack.global.tag}this.stack.global.notag=true},HandleLabel:function(i){var j=this.stack.global,h=this.GetArgument(i);if(h===""){return}if(!f.refUpdate){if(j.label){g.Error(["MultipleCommand","Multiple %1",i])}j.label=h;if(f.labels[h]||f.eqlabels[h]){g.Error(["MultipleLabel","Label '%1' multiply defined",h])}f.eqlabels[h]={tag:"???",id:""}}},HandleRef:function(j,l){var i=this.GetArgument(j);var k=f.labels[i]||f.eqlabels[i];if(!k){k={tag:"???",id:""};f.badref=!f.refUpdate}var h=k.tag;if(l){h=a.formatTag(h)}this.Push(b.mrow.apply(b,this.InternalMath(h)).With({href:a.formatURL(k.id),"class":"MathJax_ref"}))},HandleDeclareOp:function(i){var h=(this.GetStar()?"":"\\nolimits");var j=this.trimSpaces(this.GetArgument(i));if(j.charAt(0)=="\\"){j=j.substr(1)}var k=this.GetArgument(i);k=k.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");g.Definitions.macros[j]=["Macro","\\mathop{\\rm "+k+"}"+h]},HandleOperatorName:function(i){var h=(this.GetStar()?"":"\\nolimits");var j=this.trimSpaces(this.GetArgument(i));j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+j+"}"+h+" "+this.string.slice(this.i);this.i=0},HandleShove:function(i,h){var j=this.stack.Top();if(j.type!=="multline"||j.data.length){g.Error(["CommandAtTheBeginingOfLine","%1 must come at the beginning of the line",i])}j.data.shove=h},CFrac:function(k){var h=this.trimSpaces(this.GetBrackets(k,"")),j=this.GetArgument(k),l=this.GetArgument(k);var i=b.mfrac(g.Parse("\\strut\\textstyle{"+j+"}",this.stack.env).mml(),g.Parse("\\strut\\textstyle{"+l+"}",this.stack.env).mml());h=({l:b.ALIGN.LEFT,r:b.ALIGN.RIGHT,"":""})[h];if(h==null){g.Error(["IllegalAlign","Illegal alignment specified in %1",k])}if(h){i.numalign=i.denomalign=h}this.Push(i)},Genfrac:function(i,k,p,m,h){if(k==null){k=this.GetDelimiterArg(i)}else{k=this.convertDelimiter(k)}if(p==null){p=this.GetDelimiterArg(i)}else{p=this.convertDelimiter(p)}if(m==null){m=this.GetArgument(i)}if(h==null){h=this.trimSpaces(this.GetArgument(i))}var l=this.ParseArg(i);var o=this.ParseArg(i);var j=b.mfrac(l,o);if(m!==""){j.linethickness=m}if(k||p){j=g.fenced(k,j,p)}if(h!==""){var n=(["D","T","S","SS"])[h];if(n==null){g.Error(["BadMathStyleFor","Bad math style for %1",i])}j=b.mstyle(j);if(n==="D"){j.displaystyle=true;j.scriptlevel=0}else{j.displaystyle=false;j.scriptlevel=h-1}}this.Push(j)},Multline:function(i,h){this.Push(i);this.checkEqnEnv();return e.multline(h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",width:g.config.MultLineWidth,columnwidth:"100%",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AMSarray:function(j,i,h,l,k){this.Push(j);if(h){this.checkEqnEnv()}l=l.replace(/[^clr]/g,"").split("").join(" ");l=l.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return e.AMSarray(j.name,i,h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:l,columnspacing:(k||"1em"),rowspacing:"3pt",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AlignAt:function(k,i,h){var p,j,o="",m=[];if(!h){j=this.GetBrackets("\\begin{"+k.name+"}")}p=this.GetArgument("\\begin{"+k.name+"}");if(p.match(/[^0-9]/)){g.Error(["PositiveIntegerArg","Argument to %1 must me a positive integer","\\begin{"+k.name+"}"])}while(p>0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error(["ErroneousNestingEq","Erroneous nesting of equation structures"])}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i)},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]==null){g.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",h])}return this.convertDelimiter(i)},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h).With({id:a.formatID(i.tagID)})}},getTag:function(){var l=this.global,j=l.tag;l.tagged=true;if(l.label){if(a.useLabelIds){j.id=a.formatID(l.label)}f.eqlabels[l.label]={tag:l.tagID,id:j.id}}if(document.getElementById(j.id)||f.IDs[j.id]||f.eqIDs[j.id]){var k=0,h;do{k++;h=j.id+"_"+k}while(document.getElementById(h)||f.IDs[h]||f.eqIDs[h]);j.id=h;if(l.label){f.eqlabels[l.label].id=h}}f.eqIDs[j.id]=1;this.clearTag();return j},clearTag:function(){var h=this.global;delete h.tag;delete h.tagID;delete h.label},fixInitialMO:function(l){for(var k=0,h=l.length;k<h;k++){if(l[k]&&(l[k].type!=="mspace"&&(l[k].type!=="texatom"||(l[k].data[0]&&l[k].data[0].data.length)))){if(l[k].isEmbellished()){var j=l[k].CoreMO();j.form=b.FORM.INFIX;j.lspace=b.LENGTH.MEDIUMMATHSPACE}break}}}});e.multline=e.array.Subclass({type:"multline",Init:function(i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(i&&a.autoNumber!=="none");this.save={notag:h.global.notag};h.global.tagged=!i&&!h.global.forcetag},EndEntry:function(){if(this.table.length){this.fixInitialMO(this.data)}var h=b.mtd.apply(b,this.data);if(this.data.shove){h.columnalign=this.data.shove}this.row.push(h);this.data=[]},EndRow:function(){if(this.row.length!=1){g.Error(["MultlineRowsOneCol","The rows within the %1 environment must have exactly one column","multline"])}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var j=this.table.length-1,l,k=-1;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=b.ALIGN.LEFT}if(!this.table[j][0].columnalign){this.table[j][0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){k=(this.arraydef.side==="left"?0:this.table.length-1);this.table[k]=[this.getTag()].concat(this.table[k])}for(l=0,j=this.table.length;l<j;l++){var h=(l===k?b.mlabeledtr:b.mtr);this.table[l]=h.apply(b,this.table[l])}}this.global.notag=this.save.notag}});e.AMSarray=e.array.Subclass({type:"AMSarray",Init:function(k,j,i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(j&&a.autoNumber!=="none");this.save={notags:h.global.notags,notag:h.global.notag};h.global.notags=(i?null:k);h.global.tagged=!j&&!h.global.forcetag},EndEntry:function(){if(this.row.length){this.fixInitialMO(this.data)}this.row.push(b.mtd.apply(b,this.data));this.data=[]},EndRow:function(){var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.row=[this.getTag()].concat(this.row);h=b.mlabeledtr}else{this.clearTag()}if(this.numbered){delete this.global.notag}this.table.push(h.apply(b,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notags=this.save.notags;this.global.notag=this.save.notag}});e.start.Augment({oldCheckItem:e.start.prototype.checkItem,checkItem:function(j){if(j.type==="stop"){var h=this.mmlData(),i=this.global;if(f.display&&!i.tag&&!i.tagged&&!i.isInner&&(a.autoNumber==="all"||i.forcetag)){this.autoTag()}if(i.tag){var l=[this.getTag(),b.mtd(h)];var k={side:g.config.TagSide,minlabelspacing:g.config.TagIndent,columnalign:h.displayAlign};if(h.displayAlign===b.INDENTALIGN.LEFT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth=h.displayIndent+" fit";k.columnspacing="0";l=[l[0],b.mtd(),l[1]]}}else{if(h.displayAlign===b.INDENTALIGN.RIGHT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth="fit "+h.displayIndent;k.columnspacing="0";l[2]=b.mtd()}}}h=b.mtable(b.mlabeledtr.apply(b,l)).With(k)}return e.mml(h)}return this.oldCheckItem.call(this,j)}});g.prefilterHooks.Add(function(h){f.display=h.display;f.number=f.startNumber;f.eqlabels=f.eqIDs={};f.badref=false;if(f.refUpdate){f.number=h.script.MathJax.startNumber}});g.postfilterHooks.Add(function(h){h.script.MathJax.startNumber=f.startNumber;f.startNumber=f.number;MathJax.Hub.Insert(f.IDs,f.eqIDs);MathJax.Hub.Insert(f.labels,f.eqlabels);if(f.badref&&!h.math.texError){f.refs.push(h.script)}});MathJax.Hub.Register.MessageHook("Begin Math Input",function(){f.refs=[];f.refUpdate=false});MathJax.Hub.Register.MessageHook("End Math Input",function(k){if(f.refs.length){f.refUpdate=true;for(var j=0,h=f.refs.length;j<h;j++){f.refs[j].MathJax.state=MathJax.ElementJax.STATE.UPDATE}return MathJax.Hub.processInput({scripts:f.refs,start:new Date().getTime(),i:0,j:0,jax:{},jaxIDs:[]})}return null});g.resetEquationNumbers=function(i,h){f.startNumber=(i||0);if(!h){f.labels=f.IDs={}}};MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js");
MathJax.Extension["TeX/AMSsymbols"]={version:"2.4.0"};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var a=MathJax.ElementJax.mml,b=MathJax.InputJax.TeX.Definitions;b.Add({mathchar0mi:{digamma:"03DD",varkappa:"03F0",varGamma:["0393",{mathvariant:a.VARIANT.ITALIC}],varDelta:["0394",{mathvariant:a.VARIANT.ITALIC}],varTheta:["0398",{mathvariant:a.VARIANT.ITALIC}],varLambda:["039B",{mathvariant:a.VARIANT.ITALIC}],varXi:["039E",{mathvariant:a.VARIANT.ITALIC}],varPi:["03A0",{mathvariant:a.VARIANT.ITALIC}],varSigma:["03A3",{mathvariant:a.VARIANT.ITALIC}],varUpsilon:["03A5",{mathvariant:a.VARIANT.ITALIC}],varPhi:["03A6",{mathvariant:a.VARIANT.ITALIC}],varPsi:["03A8",{mathvariant:a.VARIANT.ITALIC}],varOmega:["03A9",{mathvariant:a.VARIANT.ITALIC}],beth:"2136",gimel:"2137",daleth:"2138",backprime:["2035",{variantForm:true}],hslash:"210F",varnothing:["2205",{variantForm:true}],blacktriangle:"25B4",triangledown:["25BD",{variantForm:true}],blacktriangledown:"25BE",square:"25FB",Box:"25FB",blacksquare:"25FC",lozenge:"25CA",Diamond:"25CA",blacklozenge:"29EB",circledS:["24C8",{mathvariant:a.VARIANT.NORMAL}],bigstar:"2605",sphericalangle:"2222",measuredangle:"2221",nexists:"2204",complement:"2201",mho:"2127",eth:["00F0",{mathvariant:a.VARIANT.NORMAL}],Finv:"2132",diagup:"2571",Game:"2141",diagdown:"2572",Bbbk:["006B",{mathvariant:a.VARIANT.DOUBLESTRUCK}],yen:"00A5",circledR:"00AE",checkmark:"2713",maltese:"2720"},mathchar0mo:{dotplus:"2214",ltimes:"22C9",smallsetminus:"2216",rtimes:"22CA",Cap:"22D2",doublecap:"22D2",leftthreetimes:"22CB",Cup:"22D3",doublecup:"22D3",rightthreetimes:"22CC",barwedge:"22BC",curlywedge:"22CF",veebar:"22BB",curlyvee:"22CE",doublebarwedge:"2A5E",boxminus:"229F",circleddash:"229D",boxtimes:"22A0",circledast:"229B",boxdot:"22A1",circledcirc:"229A",boxplus:"229E",centerdot:"22C5",divideontimes:"22C7",intercal:"22BA",leqq:"2266",geqq:"2267",leqslant:"2A7D",geqslant:"2A7E",eqslantless:"2A95",eqslantgtr:"2A96",lesssim:"2272",gtrsim:"2273",lessapprox:"2A85",gtrapprox:"2A86",approxeq:"224A",lessdot:"22D6",gtrdot:"22D7",lll:"22D8",llless:"22D8",ggg:"22D9",gggtr:"22D9",lessgtr:"2276",gtrless:"2277",lesseqgtr:"22DA",gtreqless:"22DB",lesseqqgtr:"2A8B",gtreqqless:"2A8C",doteqdot:"2251",Doteq:"2251",eqcirc:"2256",risingdotseq:"2253",circeq:"2257",fallingdotseq:"2252",triangleq:"225C",backsim:"223D",thicksim:["223C",{variantForm:true}],backsimeq:"22CD",thickapprox:["2248",{variantForm:true}],subseteqq:"2AC5",supseteqq:"2AC6",Subset:"22D0",Supset:"22D1",sqsubset:"228F",sqsupset:"2290",preccurlyeq:"227C",succcurlyeq:"227D",curlyeqprec:"22DE",curlyeqsucc:"22DF",precsim:"227E",succsim:"227F",precapprox:"2AB7",succapprox:"2AB8",vartriangleleft:"22B2",lhd:"22B2",vartriangleright:"22B3",rhd:"22B3",trianglelefteq:"22B4",unlhd:"22B4",trianglerighteq:"22B5",unrhd:"22B5",vDash:"22A8",Vdash:"22A9",Vvdash:"22AA",smallsmile:["2323",{variantForm:true}],shortmid:["2223",{variantForm:true}],smallfrown:["2322",{variantForm:true}],shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C2",blacktriangleright:"25B8",therefore:"2234",because:"2235",eqsim:"2242",vartriangle:["25B3",{variantForm:true}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:true}],ngeqslant:["2A88",{variantForm:true}],nleqq:["2270",{variantForm:true}],ngeqq:["2271",{variantForm:true}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:true}],gvertneqq:["2269",{variantForm:true}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:true}],nsucceq:["22E1",{variantForm:true}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:true}],nshortparallel:["2226",{variantForm:true}],nmid:"2224",nparallel:"2226",nvdash:"22AC",nvDash:"22AD",nVdash:"22AE",nVDash:"22AF",ntriangleleft:"22EA",ntriangleright:"22EB",ntrianglelefteq:"22EC",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigarrow:"21DD",leadsto:"21DD",dashrightarrow:"21E2",dashleftarrow:"21E0",nleftarrow:"219A",nrightarrow:"219B",nLeftarrow:"21CD",nRightarrow:"21CF",nleftrightarrow:"21AE",nLeftrightarrow:"21CE"},delimiter:{"\\ulcorner":"231C","\\urcorner":"231D","\\llcorner":"231E","\\lrcorner":"231F"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}},null,true);var c=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":c,"\u2323":c,"\u25B3":c,"\uE006":c,"\uE007":c,"\uE00C":c,"\uE00D":c,"\uE00E":c,"\uE00F":c,"\uE010":c,"\uE011":c,"\uE016":c,"\uE017":c,"\uE018":c,"\uE019":c,"\uE01A":c,"\uE01B":c,"\uE04B":c,"\uE04F":c}}});MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js");
(function(c,d){var a;var b=function(e){return MathJax.Localization._.apply(MathJax.Localization,[["MathML",e]].concat([].slice.call(arguments,1)))};c.Parse=MathJax.Object.Subclass({Init:function(e){this.Parse(e)},Parse:function(g){var h;if(typeof g!=="string"){h=g.parentNode}else{h=c.ParseXML(this.preProcessMath.call(this,g));if(h==null){c.Error(["ErrorParsingMathML","Error parsing MathML"])}}var f=h.getElementsByTagName("parsererror")[0];if(f){c.Error(["ParsingError","Error parsing MathML: %1",f.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,"")])}if(h.childNodes.length!==1){c.Error(["MathMLSingleElement","MathML must be formed by a single element"])}if(h.firstChild.nodeName.toLowerCase()==="html"){var e=h.getElementsByTagName("h1")[0];if(e&&e.textContent==="XML parsing error"&&e.nextSibling){c.Error(["ParsingError","Error parsing MathML: %1",String(e.nextSibling.nodeValue).replace(/fatal parsing error: /,"")])}}if(h.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")!=="math"){c.Error(["MathMLRootElement","MathML must be formed by a <math> element, not %1","<"+h.firstChild.nodeName+">"])}this.mml=this.MakeMML(h.firstChild)},MakeMML:function(h){var i=String(h.getAttribute("class")||"");var f,g=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e[2])}else{if(!(a[g]&&a[g].isa&&a[g].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",g]);return a.Error(b("UnknownNodeType","Unknown node type: %1",g))}else{f=a[g]()}}this.AddAttributes(f,h);this.CheckClass(f,f["class"]);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(f){var e=a.TeXAtom().With({texClass:a.TEXCLASS[f]});if(e.texClass===a.TEXCLASS.OP){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||"").split(/ /);var j=[];for(var g=0,e=h.length;g<e;g++){if(h[g].substr(0,4)==="MJX-"){if(h[g]==="MJX-arrow"){if(!f.notation.match("/"+a.NOTATION.UPDIAGONALARROW+"/")){f.notation+=" "+a.NOTATION.UPDIAGONALARROW}}else{if(h[g]==="MJX-variant"){f.variantForm=true;if(!MathJax.Extension["TeX/AMSsymbols"]){MathJax.Hub.RestartAfter(MathJax.Ajax.Require("[MathJax]/extensions/TeX/AMSsymbols.js"))}}else{if(h[g].substr(0,11)!=="MJX-TeXAtom"){f.mathvariant=h[g].substr(3);if(f.mathvariant==="-tex-caligraphic-bold"||f.mathvariant==="-tex-oldstyle-bold"){if(!MathJax.Extension["TeX/boldsymbol"]){MathJax.Hub.RestartAfter(MathJax.Ajax.Require("[MathJax]/extensions/TeX/boldsymbol.js"))}}}}}}else{j.push(h[g])}}if(j.length){f["class"]=j.join(" ")}else{delete f["class"]}},AddAttributes:function(g,j){g.attr={};g.attrNames=[];for(var h=0,e=j.attributes.length;h<e;h++){var f=j.attributes[h].name;if(f=="xlink:href"){f="href"}if(f.match(/:/)){continue}if(f.match(/^_moz-math-((column|row)(align|line)|font-style)$/)){continue}var k=j.attributes[h].value;k=this.filterAttribute(f,k);if(k!=null){if(k.toLowerCase()==="true"){k=true}else{if(k.toLowerCase()==="false"){k=false}}if(g.defaults[f]!=null||a.copyAttributes[f]){g[f]=k}else{g.attr[f]=k}g.attrNames.push(f)}}},filterAttribute:function(e,f){return f},AddChildren:function(e,g){for(var k=0,j=g.childNodes.length;k<j;k++){var f=g.childNodes[k];if(f.nodeName==="#comment"){continue}if(f.nodeName==="#text"){if((e.isToken||e.isChars)&&!e.mmlSelfClosing){var o=f.nodeValue.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);e.Append(a.chars(this.trimSpace(o)))}else{if(f.nodeValue.match(/\S/)){c.Error(["UnexpectedTextNode","Unexpected text node: %1","'"+f.nodeValue+"'"])}}}else{if(e.type==="annotation-xml"){e.Append(a.xml(f))}else{var h=this.MakeMML(f);e.Append(h);if(h.mmlSelfClosing&&h.data.length){e.Append.apply(e,h.data);h.data=[]}}}}if(e.type==="mrow"&&e.data.length>=2){var l=e.data[0],n=e.data[e.data.length-1];if(l.type==="mo"&&l.Get("fence")&&n.type==="mo"&&n.Get("fence")){if(l.data[0]){e.open=l.data.join("")}if(n.data[0]){e.close=n.data.join("")}}}},preProcessMath:function(f){if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var e=f.match(/^(<math( ('.*?'|".*?"|[^>])+)>)/i);if(e&&e[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){f=e[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+f.substr(e[0].length)}if(f.match(/^<math/i)&&!f.match(/^<[^<>]* xmlns=/)){f=f.replace(/^<(math)/i,'<math xmlns="http://www.w3.org/1998/Math/MathML"')}f=f.replace(/^\s*(?:\/\/)?<!(--)?\[CDATA\[((.|\n)*)(\/\/)?\]\]\1>\s*$/,"$2");return f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/  +/g," ")},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity[f]){return c.Parse.Entity[f]}var h=f.charAt(0).toLowerCase();var e=f.match(/^[a-zA-Z](fr|scr|opf)$/);if(e){h=e[1]}if(!c.Parse.loaded[h]){c.Parse.loaded[h]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+"/"+h+".js"))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:["OriginalMathML","Original MathML"],prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){i.math=e.firstChild;this.prefilterHooks.Execute(i);h=i.math}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/(&nbsp;)+$/,"")}i.math=h;this.prefilterHooks.Execute(i);h=i.math}try{f=c.Parse(h).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);this.postfilterHooks.Execute(i);return i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",f,g,e]);return a.Error(f)},Error:function(e){if(e instanceof Array){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,"text/xml")},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML=e.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2></$1>");return this.div},parseError:function(e){return null},createMSParser:function(){var j=null;var f=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var g=0,e=f.length;g<e&&!j;g++){try{j=new ActiveXObject(f[g])}catch(h){}}return j},createParser:function(){if(window.DOMParser){this.parser=new DOMParser();return(this.parseDOM)}else{if(window.ActiveXObject){this.parser=this.createMSParser();if(!this.parser){MathJax.Localization.Try(this.parserCreationError);return(this.parseError)}this.parser.async=false;return(this.parseMS)}}this.div=MathJax.Hub.Insert(document.createElement("div"),{style:{visibility:"hidden",overflow:"hidden",height:"1px",position:"absolute",top:0}});if(!document.body.firstChild){document.body.appendChild(this.div)}else{document.body.insertBefore(this.div,document.body.firstChild)}return(this.parseDIV)},parserCreationError:function(){alert(b("CantCreateXMLParser","MathJax can't create an XML parser for MathML.  Check that\nthe 'Script ActiveX controls marked safe for scripting' security\nsetting is enabled (use the Internet Options item in the Tools\nmenu, and select the Security panel, then press the Custom Level\nbutton to check this).\n\nMathML equations will not be able to be processed by MathJax."))},Startup:function(){a=MathJax.ElementJax.mml;a.mspace.Augment({mmlSelfClosing:true});a.none.Augment({mmlSelfClosing:true});a.mprescripts.Augment({mmlSelfClosing:true})}});c.prefilterHooks.Add(function(e){e.math=(typeof(e.math)==="string"?c.prefilterMath(e.math,e.script):c.prefilterMathML(e.math,e.script))});c.Parse.Entity={ApplyFunction:"\u2061",Backslash:"\u2216",Because:"\u2235",Breve:"\u02D8",Cap:"\u22D2",CenterDot:"\u00B7",CircleDot:"\u2299",CircleMinus:"\u2296",CirclePlus:"\u2295",CircleTimes:"\u2297",Congruent:"\u2261",ContourIntegral:"\u222E",Coproduct:"\u2210",Cross:"\u2A2F",Cup:"\u22D3",CupCap:"\u224D",Dagger:"\u2021",Del:"\u2207",Delta:"\u0394",Diamond:"\u22C4",DifferentialD:"\u2146",DotEqual:"\u2250",DoubleDot:"\u00A8",DoubleRightTee:"\u22A8",DoubleVerticalBar:"\u2225",DownArrow:"\u2193",DownLeftVector:"\u21BD",DownRightVector:"\u21C1",DownTee:"\u22A4",Downarrow:"\u21D3",Element:"\u2208",EqualTilde:"\u2242",Equilibrium:"\u21CC",Exists:"\u2203",ExponentialE:"\u2147",FilledVerySmallSquare:"\u25AA",ForAll:"\u2200",Gamma:"\u0393",Gg:"\u22D9",GreaterEqual:"\u2265",GreaterEqualLess:"\u22DB",GreaterFullEqual:"\u2267",GreaterLess:"\u2277",GreaterSlantEqual:"\u2A7E",GreaterTilde:"\u2273",Hacek:"\u02C7",Hat:"\u005E",HumpDownHump:"\u224E",HumpEqual:"\u224F",Im:"\u2111",ImaginaryI:"\u2148",Integral:"\u222B",Intersection:"\u22C2",InvisibleComma:"\u2063",InvisibleTimes:"\u2062",Lambda:"\u039B",Larr:"\u219E",LeftAngleBracket:"\u27E8",LeftArrow:"\u2190",LeftArrowRightArrow:"\u21C6",LeftCeiling:"\u2308",LeftDownVector:"\u21C3",LeftFloor:"\u230A",LeftRightArrow:"\u2194",LeftTee:"\u22A3",LeftTriangle:"\u22B2",LeftTriangleEqual:"\u22B4",LeftUpVector:"\u21BF",LeftVector:"\u21BC",Leftarrow:"\u21D0",Leftrightarrow:"\u21D4",LessEqualGreater:"\u22DA",LessFullEqual:"\u2266",LessGreater:"\u2276",LessSlantEqual:"\u2A7D",LessTilde:"\u2272",Ll:"\u22D8",Lleftarrow:"\u21DA",LongLeftArrow:"\u27F5",LongLeftRightArrow:"\u27F7",LongRightArrow:"\u27F6",Longleftarrow:"\u27F8",Longleftrightarrow:"\u27FA",Longrightarrow:"\u27F9",Lsh:"\u21B0",MinusPlus:"\u2213",NestedGreaterGreater:"\u226B",NestedLessLess:"\u226A",NotDoubleVerticalBar:"\u2226",NotElement:"\u2209",NotEqual:"\u2260",NotExists:"\u2204",NotGreater:"\u226F",NotGreaterEqual:"\u2271",NotLeftTriangle:"\u22EA",NotLeftTriangleEqual:"\u22EC",NotLess:"\u226E",NotLessEqual:"\u2270",NotPrecedes:"\u2280",NotPrecedesSlantEqual:"\u22E0",NotRightTriangle:"\u22EB",NotRightTriangleEqual:"\u22ED",NotSubsetEqual:"\u2288",NotSucceeds:"\u2281",NotSucceedsSlantEqual:"\u22E1",NotSupersetEqual:"\u2289",NotTilde:"\u2241",NotVerticalBar:"\u2224",Omega:"\u03A9",OverBar:"\u203E",OverBrace:"\u23DE",PartialD:"\u2202",Phi:"\u03A6",Pi:"\u03A0",PlusMinus:"\u00B1",Precedes:"\u227A",PrecedesEqual:"\u2AAF",PrecedesSlantEqual:"\u227C",PrecedesTilde:"\u227E",Product:"\u220F",Proportional:"\u221D",Psi:"\u03A8",Rarr:"\u21A0",Re:"\u211C",ReverseEquilibrium:"\u21CB",RightAngleBracket:"\u27E9",RightArrow:"\u2192",RightArrowLeftArrow:"\u21C4",RightCeiling:"\u2309",RightDownVector:"\u21C2",RightFloor:"\u230B",RightTee:"\u22A2",RightTeeArrow:"\u21A6",RightTriangle:"\u22B3",RightTriangleEqual:"\u22B5",RightUpVector:"\u21BE",RightVector:"\u21C0",Rightarrow:"\u21D2",Rrightarrow:"\u21DB",Rsh:"\u21B1",Sigma:"\u03A3",SmallCircle:"\u2218",Sqrt:"\u221A",Square:"\u25A1",SquareIntersection:"\u2293",SquareSubset:"\u228F",SquareSubsetEqual:"\u2291",SquareSuperset:"\u2290",SquareSupersetEqual:"\u2292",SquareUnion:"\u2294",Star:"\u22C6",Subset:"\u22D0",SubsetEqual:"\u2286",Succeeds:"\u227B",SucceedsEqual:"\u2AB0",SucceedsSlantEqual:"\u227D",SucceedsTilde:"\u227F",SuchThat:"\u220B",Sum:"\u2211",Superset:"\u2283",SupersetEqual:"\u2287",Supset:"\u22D1",Therefore:"\u2234",Theta:"\u0398",Tilde:"\u223C",TildeEqual:"\u2243",TildeFullEqual:"\u2245",TildeTilde:"\u2248",UnderBar:"\u005F",UnderBrace:"\u23DF",Union:"\u22C3",UnionPlus:"\u228E",UpArrow:"\u2191",UpDownArrow:"\u2195",UpTee:"\u22A5",Uparrow:"\u21D1",Updownarrow:"\u21D5",Upsilon:"\u03A5",Vdash:"\u22A9",Vee:"\u22C1",VerticalBar:"\u2223",VerticalTilde:"\u2240",Vvdash:"\u22AA",Wedge:"\u22C0",Xi:"\u039E",acute:"\u00B4",aleph:"\u2135",alpha:"\u03B1",amalg:"\u2A3F",and:"\u2227",ang:"\u2220",angmsd:"\u2221",angsph:"\u2222",ape:"\u224A",backprime:"\u2035",backsim:"\u223D",backsimeq:"\u22CD",beta:"\u03B2",beth:"\u2136",between:"\u226C",bigcirc:"\u25EF",bigodot:"\u2A00",bigoplus:"\u2A01",bigotimes:"\u2A02",bigsqcup:"\u2A06",bigstar:"\u2605",bigtriangledown:"\u25BD",bigtriangleup:"\u25B3",biguplus:"\u2A04",blacklozenge:"\u29EB",blacktriangle:"\u25B4",blacktriangledown:"\u25BE",blacktriangleleft:"\u25C2",bowtie:"\u22C8",boxdl:"\u2510",boxdr:"\u250C",boxminus:"\u229F",boxplus:"\u229E",boxtimes:"\u22A0",boxul:"\u2518",boxur:"\u2514",bsol:"\u005C",bull:"\u2022",cap:"\u2229",check:"\u2713",chi:"\u03C7",circ:"\u02C6",circeq:"\u2257",circlearrowleft:"\u21BA",circlearrowright:"\u21BB",circledR:"\u00AE",circledS:"\u24C8",circledast:"\u229B",circledcirc:"\u229A",circleddash:"\u229D",clubs:"\u2663",colon:"\u003A",comp:"\u2201",ctdot:"\u22EF",cuepr:"\u22DE",cuesc:"\u22DF",cularr:"\u21B6",cup:"\u222A",curarr:"\u21B7",curlyvee:"\u22CE",curlywedge:"\u22CF",dagger:"\u2020",daleth:"\u2138",ddarr:"\u21CA",deg:"\u00B0",delta:"\u03B4",digamma:"\u03DD",div:"\u00F7",divideontimes:"\u22C7",dot:"\u02D9",doteqdot:"\u2251",dotplus:"\u2214",dotsquare:"\u22A1",dtdot:"\u22F1",ecir:"\u2256",efDot:"\u2252",egs:"\u2A96",ell:"\u2113",els:"\u2A95",empty:"\u2205",epsi:"\u03B5",epsiv:"\u03F5",erDot:"\u2253",eta:"\u03B7",eth:"\u00F0",flat:"\u266D",fork:"\u22D4",frown:"\u2322",gEl:"\u2A8C",gamma:"\u03B3",gap:"\u2A86",gimel:"\u2137",gnE:"\u2269",gnap:"\u2A8A",gne:"\u2A88",gnsim:"\u22E7",gt:"\u003E",gtdot:"\u22D7",harrw:"\u21AD",hbar:"\u210F",hellip:"\u2026",hookleftarrow:"\u21A9",hookrightarrow:"\u21AA",imath:"\u0131",infin:"\u221E",intcal:"\u22BA",iota:"\u03B9",jmath:"\u0237",kappa:"\u03BA",kappav:"\u03F0",lEg:"\u2A8B",lambda:"\u03BB",lap:"\u2A85",larrlp:"\u21AB",larrtl:"\u21A2",lbrace:"\u007B",lbrack:"\u005B",le:"\u2264",leftleftarrows:"\u21C7",leftthreetimes:"\u22CB",lessdot:"\u22D6",lmoust:"\u23B0",lnE:"\u2268",lnap:"\u2A89",lne:"\u2A87",lnsim:"\u22E6",longmapsto:"\u27FC",looparrowright:"\u21AC",lowast:"\u2217",loz:"\u25CA",lt:"\u003C",ltimes:"\u22C9",ltri:"\u25C3",macr:"\u00AF",malt:"\u2720",mho:"\u2127",mu:"\u03BC",multimap:"\u22B8",nLeftarrow:"\u21CD",nLeftrightarrow:"\u21CE",nRightarrow:"\u21CF",nVDash:"\u22AF",nVdash:"\u22AE",natur:"\u266E",nearr:"\u2197",nharr:"\u21AE",nlarr:"\u219A",not:"\u00AC",nrarr:"\u219B",nu:"\u03BD",nvDash:"\u22AD",nvdash:"\u22AC",nwarr:"\u2196",omega:"\u03C9",omicron:"\u03BF",or:"\u2228",osol:"\u2298",period:"\u002E",phi:"\u03C6",phiv:"\u03D5",pi:"\u03C0",piv:"\u03D6",prap:"\u2AB7",precnapprox:"\u2AB9",precneqq:"\u2AB5",precnsim:"\u22E8",prime:"\u2032",psi:"\u03C8",rarrtl:"\u21A3",rbrace:"\u007D",rbrack:"\u005D",rho:"\u03C1",rhov:"\u03F1",rightrightarrows:"\u21C9",rightthreetimes:"\u22CC",ring:"\u02DA",rmoust:"\u23B1",rtimes:"\u22CA",rtri:"\u25B9",scap:"\u2AB8",scnE:"\u2AB6",scnap:"\u2ABA",scnsim:"\u22E9",sdot:"\u22C5",searr:"\u2198",sect:"\u00A7",sharp:"\u266F",sigma:"\u03C3",sigmav:"\u03C2",simne:"\u2246",smile:"\u2323",spades:"\u2660",sub:"\u2282",subE:"\u2AC5",subnE:"\u2ACB",subne:"\u228A",supE:"\u2AC6",supnE:"\u2ACC",supne:"\u228B",swarr:"\u2199",tau:"\u03C4",theta:"\u03B8",thetav:"\u03D1",tilde:"\u02DC",times:"\u00D7",triangle:"\u25B5",triangleq:"\u225C",upsi:"\u03C5",upuparrows:"\u21C8",veebar:"\u22BB",vellip:"\u22EE",weierp:"\u2118",xi:"\u03BE",yen:"\u00A5",zeta:"\u03B6",zigrarr:"\u21DD"};c.loadComplete("jax.js")})(MathJax.InputJax.MathML,MathJax.Hub.Browser);
MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS-MML_SVG.js");