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

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

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

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

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

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

MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.0",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js");

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

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

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

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

MathJax.Extension.mml2jax={version:"2.0",config:{preview:"alttext"},MMLnamespace:"http://www.w3.org/1998/Math/MathML",PreProcess:function(e){if(!this.configured){this.config=MathJax.Hub.CombineConfig("mml2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.InitBrowser();this.configured=true}if(typeof(e)==="string"){e=document.getElementById(e)}if(!e){e=document.body}this.ProcessMathArray(e.getElementsByTagName("math"));if(e.getElementsByTagNameNS){this.ProcessMathArray(e.getElementsByTagNameNS(this.MMLnamespace,"math"))}var d,b;if(document.namespaces){for(d=0,b=document.namespaces.length;d<b;d++){var f=document.namespaces[d];if(f.urn===this.MMLnamespace){this.ProcessMathArray(e.getElementsByTagName(f.name+":math"))}}}else{var c=document.getElementsByTagName("html")[0];if(c){for(d=0,b=c.attributes.length;d<b;d++){var a=c.attributes[d];if(a.nodeName.substr(0,6)==="xmlns:"&&a.nodeValue===this.MMLnamespace){this.ProcessMathArray(e.getElementsByTagName(a.nodeName.substr(6)+":math"))}}}}},ProcessMathArray:function(b){var a;if(b.length){if(this.MathTagBug){for(a=b.length-1;a>=0;a--){if(b[a].nodeName==="MATH"){this.ProcessMathFlattened(b[a])}else{this.ProcessMath(b[a])}}}else{for(a=b.length-1;a>=0;a--){this.ProcessMath(b[a])}}}},ProcessMath:function(e){var d=e.parentNode;var a=document.createElement("script");a.type="math/mml";d.insertBefore(a,e);if(this.AttributeBug){var b=this.OuterHTML(e);if(this.CleanupHTML){b=b.replace(/<\?import .*?>/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/&nbsp;/g,"&#xA0;")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"</math>";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c="<!--"+e.nodeValue+"-->"}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b<a;b++){var d=e.attributes[b];if(d.specified){c+=" "+d.nodeName.toLowerCase().replace(/xmlns:xmlns/,"xmlns")+"=";var f=d.nodeValue;if(f==null&&d.nodeName==="style"&&e.style){f=e.style.cssText}c+='"'+this.quoteHTML(f)+'"'}}c+=">";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b<a;b++){c+=this.OuterHTML(e.childNodes[b])}c+="</"+e.nodeName.toLowerCase()+">"}}}return c},OuterHTML:function(d){if(d.nodeName.charAt(0)==="#"){return this.NodeHTML(d)}if(!this.AttributeBug){return d.outerHTML}var c=this.NodeHTML(d);for(var b=0,a=d.childNodes.length;b<a;b++){c+=this.OuterHTML(d.childNodes[b])}c+="</"+d.nodeName.toLowerCase()+">";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&#x26;").replace(/</g,"&lt;").replace(/>/g,"&gt;").replace(/"/g,"&quot;")},createPreview:function(b,a){var c;if(this.config.preview==="alttext"){var d=b.getAttribute("alttext");if(d!=null){c=[this.filterPreview(d)]}}else{if(this.config.preview instanceof Array){c=this.config.preview}}if(c){c=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},c);a.parentNode.insertBefore(c,a)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"<math><mi>x</mi><mspace /></math>"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="&lt;"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js");

(function(d,h,l,g,b,j){var p="2.0";var i=MathJax.Extension;var c=i.MathEvents={version:p};var k=d.config.menuSettings;var o={hover:500,frame:{x:3.5,y:5,bwidth:1,bcolor:"#A6D",hwidth:"15px",hcolor:"#83A"},button:{x:-4,y:-3,wx:-2,src:l.fileURL(b.imageDir+"/MenuArrow-15.png")},fadeinInc:0.2,fadeoutInc:0.05,fadeDelay:50,fadeoutStart:400,fadeoutDelay:15*1000,styles:{".MathJax_Hover_Frame":{"border-radius":".25em","-webkit-border-radius":".25em","-moz-border-radius":".25em","-khtml-border-radius":".25em","box-shadow":"0px 0px 15px #83A","-webkit-box-shadow":"0px 0px 15px #83A","-moz-box-shadow":"0px 0px 15px #83A","-khtml-box-shadow":"0px 0px 15px #83A",border:"1px solid #A6D ! important",display:"inline-block",position:"absolute"},".MathJax_Hover_Arrow":{position:"absolute",width:"15px",height:"11px",cursor:"pointer"}}};var m=c.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",Mousedown:function(q){return m.Handler(q,"Mousedown",this)},Mouseup:function(q){return m.Handler(q,"Mouseup",this)},Mousemove:function(q){return m.Handler(q,"Mousemove",this)},Mouseover:function(q){return m.Handler(q,"Mouseover",this)},Mouseout:function(q){return m.Handler(q,"Mouseout",this)},Click:function(q){return m.Handler(q,"Click",this)},DblClick:function(q){return m.Handler(q,"DblClick",this)},Menu:function(q){return m.Handler(q,"ContextMenu",this)},Handler:function(t,r,s){if(l.loadingMathMenu){return m.False(t)}var q=b[s.jaxID];if(!t){t=window.event}t.isContextMenu=(r==="ContextMenu");if(q[r]){return q[r](t,s)}if(i.MathZoom){return i.MathZoom.HandleEvent(t,r,s)}},False:function(q){if(!q){q=window.event}if(q){if(q.preventDefault){q.preventDefault()}if(q.stopPropagation){q.stopPropagation()}q.cancelBubble=true;q.returnValue=false}return false},ContextMenu:function(r,y,u){var w=b[y.jaxID],t=w.getJaxFromMath(y);var z=(w.config.showMathMenu!=null?w:d).config.showMathMenu;if(!z||(k.context!=="MathJax"&&!u)){return}if(c.msieEventBug){r=window.event||r}m.ClearSelection();f.ClearHoverTimer();if(t.hover){if(t.hover.remove){clearTimeout(t.hover.remove);delete t.hover.remove}t.hover.nofade=true}var s=MathJax.Menu;if(s){s.jax=t;var q=s.menu.Find("Show Math As").menu;q.items[1].name=(j[t.inputJax].sourceMenuTitle||"Original Form");q.items[0].hidden=(t.inputJax==="Error");var v=s.menu.Find("Math Settings","MathPlayer");v.hidden=!(t.outputJax==="NativeMML"&&d.Browser.hasMathPlayer);return s.menu.Post(r)}else{if(!l.loadingMathMenu){l.loadingMathMenu=true;var x={pageX:r.pageX,pageY:r.pageY,clientX:r.clientX,clientY:r.clientY};g.Queue(l.Require("[MathJax]/extensions/MathMenu.js"),function(){delete l.loadingMathMenu;if(!MathJax.Menu){MathJax.Menu={}}},["ContextMenu",this,x,y,u])}return m.False(r)}},AltContextMenu:function(s,r){var t=b[r.jaxID];var q=(t.config.showMathMenu!=null?t:d).config.showMathMenu;if(q){q=(t.config.showMathMenuMSIE!=null?t:d).config.showMathMenuMSIE;if(k.context==="MathJax"&&!k.mpContext&&q){if(!c.noContextMenuBug||s.button!==m.RIGHTBUTTON){return}}else{if(!s[m.MENUKEY]||s.button!==m.LEFTBUTTON){return}}return t.ContextMenu(s,r,true)}},ClearSelection:function(){if(c.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(document.selection){setTimeout("document.selection.empty()",0)}},getBBox:function(s){s.appendChild(c.topImg);var r=c.topImg.offsetTop,t=s.offsetHeight-r,q=s.offsetWidth;s.removeChild(c.topImg);return{w:q,h:r,d:t}}};var f=c.Hover={Mouseover:function(s,r){if(k.discoverable||k.zoom==="Hover"){var u=s.fromElement||s.relatedTarget,t=s.toElement||s.target;if(u&&t&&(u.isMathJax!=t.isMathJax||d.getJaxFor(u)!==d.getJaxFor(t))){var q=this.getJaxFromMath(r);if(q.hover){f.ReHover(q)}else{f.HoverTimer(q,r)}return m.False(s)}}},Mouseout:function(s,r){if(k.discoverable||k.zoom==="Hover"){var u=s.fromElement||s.relatedTarget,t=s.toElement||s.target;if(u&&t&&(u.isMathJax!=t.isMathJax||d.getJaxFor(u)!==d.getJaxFor(t))){var q=this.getJaxFromMath(r);if(q.hover){f.UnHover(q)}else{f.ClearHoverTimer()}return m.False(s)}}},Mousemove:function(s,r){if(k.discoverable||k.zoom==="Hover"){var q=this.getJaxFromMath(r);if(q.hover){return}if(f.lastX==s.clientX&&f.lastY==s.clientY){return}f.lastX=s.clientX;f.lastY=s.clientY;f.HoverTimer(q,r);return m.False(s)}},HoverTimer:function(q,r){this.ClearHoverTimer();this.hoverTimer=setTimeout(g(["Hover",this,q,r]),o.hover)},ClearHoverTimer:function(){if(this.hoverTimer){clearTimeout(this.hoverTimer);delete this.hoverTimer}},Hover:function(q,u){if(i.MathZoom&&i.MathZoom.Hover({},u)){return}var t=b[q.outputJax],v=t.getHoverSpan(q,u),y=t.getHoverBBox(q,v,u),w=(t.config.showMathMenu!=null?t:d).config.showMathMenu;var A=o.frame.x,z=o.frame.y,x=o.frame.bwidth;if(c.msieBorderWidthBug){x=0}q.hover={opacity:0,id:q.inputID+"-Hover"};var r=h.Element("span",{id:q.hover.id,isMathJax:true,style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{className:"MathJax_Hover_Frame",isMathJax:true,style:{display:"inline-block",position:"absolute",top:this.Px(-y.h-z-x-(y.y||0)),left:this.Px(-A-x+(y.x||0)),width:this.Px(y.w+2*A),height:this.Px(y.h+y.d+2*z),opacity:0,filter:"alpha(opacity=0)"}}]]);var s=h.Element("span",{isMathJax:true,id:q.hover.id+"Menu",style:{display:"inline-block","z-index":1,width:0,height:0,position:"relative"}},[["img",{className:"MathJax_Hover_Arrow",isMathJax:true,math:u,src:o.button.src,onclick:this.HoverMenu,jax:t.id,style:{left:this.Px(y.w+A+x+(y.x||0)+o.button.x),top:this.Px(-y.h-z-x-(y.y||0)-o.button.y),opacity:0,filter:"alpha(opacity=0)"}}]]);if(y.width){r.style.width=s.style.width=y.width;r.style.marginRight=s.style.marginRight="-"+y.width;r.firstChild.style.width=y.width;s.firstChild.style.left="";s.firstChild.style.right=this.Px(o.button.wx)}v.parentNode.insertBefore(r,v);if(w){v.parentNode.insertBefore(s,v)}if(v.style){v.style.position="relative"}this.ReHover(q)},ReHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}q.hover.remove=setTimeout(g(["UnHover",this,q]),o.fadeoutDelay);this.HoverFadeTimer(q,o.fadeinInc)},UnHover:function(q){if(!q.hover.nofade){this.HoverFadeTimer(q,-o.fadeoutInc,o.fadeoutStart)}},HoverFade:function(q){delete q.hover.timer;q.hover.opacity=Math.max(0,Math.min(1,q.hover.opacity+q.hover.inc));q.hover.opacity=Math.floor(1000*q.hover.opacity)/1000;var s=document.getElementById(q.hover.id),r=document.getElementById(q.hover.id+"Menu");s.firstChild.style.opacity=q.hover.opacity;s.firstChild.style.filter="alpha(opacity="+Math.floor(100*q.hover.opacity)+")";if(r){r.firstChild.style.opacity=q.hover.opacity;r.firstChild.style.filter=s.style.filter}if(q.hover.opacity===1){return}if(q.hover.opacity>0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){var q=new Image();q.src=o.button.src}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.last<a.delay);a.last=q;if(s){a.timeout=setTimeout(a.menu,a.delay,r,this);r.preventDefault()}},end:function(q){if(a.timeout){clearTimeout(a.timeout);delete a.timeout;a.last=0;q.preventDefault();return m.Handler((q.touches[0]||q.touch),"DblClick",this)}},menu:function(r,q){delete a.timeout;a.last=0;return m.Handler((r.touches[0]||r.touch),"ContextMenu",q)}};if(d.Browser.isMobile){var n=o.styles[".MathJax_Hover_Arrow"];n.width="25px";n.height="18px";o.button.x=-6}d.Browser.Select({MSIE:function(q){var s=(document.documentMode||0);var r=q.versionAtLeast("8.0");c.msieBorderWidthBug=(document.compatMode==="BackCompat");c.msieEventBug=q.isIE9;c.msieAlignBug=(!r||s<8);if(s<9){m.LEFTBUTTON=1}},Safari:function(q){c.safariContextMenuBug=true},Opera:function(q){c.operaPositionBug=true},Konqueror:function(q){c.noContextMenuBug=true}});c.topImg=(c.msieAlignBug?h.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):h.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(c.operaPositionBug){c.topImg.style.border="1px solid"}c.config=o=d.CombineConfig("MathEvents",o);var e=function(){var q=o.styles[".MathJax_Hover_Frame"];q.border=o.frame.bwidth+"px solid "+o.frame.bcolor+" ! important";q["box-shadow"]=q["-webkit-box-shadow"]=q["-moz-box-shadow"]=q["-khtml-box-shadow"]="0px 0px "+o.frame.hwidth+" "+o.frame.hcolor};g.Queue(d.Register.StartupHook("End Config",{}),[e],["getImages",f],["Styles",l,o.styles],["Post",d.Startup.signal,"MathEvents Ready"],["loadComplete",l,"[MathJax]/extensions/MathEvents.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.Callback,MathJax.OutputJax,MathJax.InputJax);

(function(a,d,f,c,j){var k="2.0";var i=a.CombineConfig("MathZoom",{styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"font-weight":"normal","font-style":"normal","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","box-shadow":"5px 5px 15px #AAAAAA","-webkit-box-shadow":"5px 5px 15px #AAAAAA","-moz-box-shadow":"5px 5px 15px #AAAAAA","-khtml-box-shadow":"5px 5px 15px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_ZoomOverlay":{position:"absolute",left:0,top:0,"z-index":300,display:"inline-block",width:"100%",height:"100%",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"},"#MathJax_ZoomEventTrap":{position:"absolute",left:0,top:0,"z-index":302,display:"inline-block",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"}}});var e,b,g;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){g=MathJax.Extension.MathEvents.Event;e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var h=MathJax.Extension.MathZoom={version:k,settings:a.config.menuSettings,scrollSize:18,HandleEvent:function(n,l,m){if(h.settings.CTRL&&!n.ctrlKey){return true}if(h.settings.ALT&&!n.altKey){return true}if(h.settings.CMD&&!n.metaKey){return true}if(h.settings.Shift&&!n.shiftKey){return true}if(!h[l]){return true}return h[l](n,m)},Click:function(m,l){if(this.settings.zoom==="Click"){return this.Zoom(m,l)}},DblClick:function(m,l){if(this.settings.zoom==="Double-Click"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(n,s){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[s.jaxID];var o=q.getJaxFromMath(s);if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*Math.max(document.body.clientHeight,document.documentElement.clientHeight));var m=d.Element("span",{style:{position:"relative",display:"inline-block",height:0,width:0},id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale,"max-width":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,u=x.firstChild,p=m.firstChild;s.parentNode.insertBefore(m,s);if(u.addEventListener){u.addEventListener("mousedown",this.Remove,true)}if(this.msieTrapEventBug){var w=d.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});m.insertBefore(w,x)}if(this.msieZIndexBug){var t=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=t}var v=q.Zoom(o,u,s,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=v.zH+"px";x.style.width=v.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";x.style.width=(v.zW+this.scrollSize)+"px"}if(x.offsetWidth>l){x.style.width=l+"px";x.style.height=(v.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){x.style.width=Math.min(l,v.zW)+"px"}if(x.offsetWidth<l&&x.offsetHeight<r){x.style.overflow="visible"}this.Position(x,v);if(this.msieTrapEventBug){w.style.height=x.clientHeight+"px";w.style.width=x.clientWidth+"px";w.style.left=(parseFloat(x.style.left)+x.clientLeft)+"px";w.style.top=(parseFloat(x.style.top)+x.clientTop)+"px"}x.style.visibility="";if(this.settings.zoom==="Hover"){p.onmouseover=this.Remove}if(window.addEventListener){addEventListener("resize",this.Resize,false)}else{if(window.attachEvent){attachEvent("onresize",this.Resize)}else{this.onresize=window.onresize;window.onresize=this.Resize}}a.signal.Post(["math zoomed",o]);return e(n)},Position:function(p,r){var q=this.Resize(),m=q.x,s=q.y,l=r.mW;var o=-Math.floor((p.offsetWidth-l)/2),n=r.Y;p.style.left=Math.max(o,10-m)+"px";p.style.top=Math.max(n,10-s)+"px";if(!h.msiePositionBug){h.SetWH()}},Resize:function(n){if(h.onresize){h.onresize(n)}var l=0,q=0,o,p=document.getElementById("MathJax_ZoomFrame"),m=document.getElementById("MathJax_ZoomOverlay");o=p;while(o.offsetParent){l+=o.offsetLeft;o=o.offsetParent}if(h.operaPositionBug){p.style.border="1px solid"}o=p;while(o.offsetParent){q+=o.offsetTop;o=o.offsetParent}if(h.operaPositionBug){p.style.border=""}m.style.left=(-l)+"px";m.style.top=(-q)+"px";if(h.msiePositionBug){setTimeout(h.SetWH,0)}else{h.SetWH()}return{x:l,y:q}},SetWH:function(){var l=document.getElementById("MathJax_ZoomOverlay");l.style.width=l.style.height="1px";var m=document.documentElement||document.body;l.style.width=m.scrollWidth+"px";l.style.height=Math.max(m.clientHeight,m.scrollHeight)+"px"},Remove:function(n){var p=document.getElementById("MathJax_ZoomFrame");if(p){var o=MathJax.OutputJax[p.nextSibling.jaxID];var l=o.getJaxFromMath(p.nextSibling);a.signal.Post(["math unzoomed",l]);p.parentNode.removeChild(p);p=document.getElementById("MathJax_ZoomTracker");if(p){p.parentNode.removeChild(p)}if(h.operaRefreshBug){var m=d.addElement(document.body,"div",{style:{position:"fixed",left:0,top:0,width:"100%",height:"100%",backgroundColor:"white",opacity:0},id:"MathJax_OperaDiv"});document.body.removeChild(m)}if(window.removeEventListener){removeEventListener("resize",h.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",h.Resize)}else{window.onresize=h.onresize;delete h.onresize}}}return e(n)}};a.Browser.Select({MSIE:function(l){var n=(document.documentMode||0);var m=(n>=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML);

(function(c,g,k,f,b){var p="2.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:j};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var o=c.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help-v2/user/",closeImg:k.fileURL(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(n?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(q){this.items=[].slice.call(arguments,0)},With:function(q){if(q){c.Insert(this,q)}return this},Post:function(r,B){if(!r){r=window.event}var z=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var q=document.getElementById("MathJax_MenuFrame");if(!q){q=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax])}var s=g.addElement(q,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"},z);for(var u=0,t=this.items.length;u<t;u++){this.items[u].Create(s)}if(a.isMobile){g.addElement(s,"span",{className:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:o.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;s.style.width=(s.offsetWidth+2)+"px";var A=r.pageX,w=r.pageY;if(!A&&!w){A=r.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;w=r.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+s.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-s.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(s.offsetWidth/2));w-=20}a.skipUp=r.isContextMenu}else{var v="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);w=0;while(B&&B!==q){A+=B.offsetLeft;w+=B.offsetTop;B=B.parentNode}if(A+s.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){v="right";A=Math.max(this.margin,A-C-s.offsetWidth+6)}if(!n){s.style["borderRadiusTop"+v]=0;s.style["WebkitBorderRadiusTop"+v]=0;s.style["MozBorderRadiusTop"+v]=0;s.style["KhtmlBorderRadiusTop"+v]=0}}s.style.left=A+"px";s.style.top=w+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(r)},Remove:function(q,r){j.Post(["unpost",a.jax]);var s=document.getElementById("MathJax_MenuFrame");if(s){s.parentNode.removeChild(s);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(q)},Find:function(r){var t=[].slice.call(arguments,1);for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){if(t.length){if(!this.items[s].menu){return null}return this.items[s].menu.Find.apply(this.items[s].menu,t)}return this.items[s]}}return null},IndexOf:function(r){for(var s=0,q=this.items.length;s<q;s++){if(this.items[s].name===r){return s}}return null}},{config:o,div:null,Close:function(q){return a.Event(q,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(q){return a.Event(q,this,"Remove")},Mouseover:function(q){return a.Event(q,this,"Mouseover")},Mouseout:function(q){return a.Event(q,this,"Mouseout")},Mousedown:function(q){return a.Event(q,this,"Mousedown")},Mouseup:function(q){return a.Event(q,this,"Mouseup")},Touchstart:function(q){return a.Event(q,this,"Touchstart")},Touchend:function(q){return a.Event(q,this,"Touchend")},Event:function(s,u,q,t){if(a.skipMouseover&&q==="Mouseover"&&!t){return h(s)}if(a.skipUp){if(q.match(/Mouseup|Touchend/)){delete a.skipUp;return h(s)}if(q==="Touchstart"||(q==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!s){s=window.event}var r=u.menuItem;if(r&&r[q]){return r[q](s,u)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(r){var s=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:r,onmousedown:this.Remove}]]);var q=s.firstChild;if(r.msieBackgroundBug){q.style.backgroundColor="white";q.style.filter="alpha(opacity=0)"}if(r.msieFixedPositionBug){s.width=s.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{q.style.position="fixed"}return s},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var q=document.getElementById("MathJax_MenuFrame");if(q){q=q.firstChild;q.style.width=q.style.height="1px";q.style.width=document.body.scrollWidth+"px";q.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 q=new Image();q.src=o.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(r){if(!this.hidden){var q={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){q.className+=" MathJax_MenuDisabled"}g.addElement(r,"div",q,this.Label(q,r))}},Mouseover:function(u,w){if(!this.disabled){this.Activate(w)}if(!this.menu||!this.menu.posted){var v=document.getElementById("MathJax_MenuFrame").childNodes,r=w.parentNode.childNodes;for(var s=0,q=r.length;s<q;s++){var t=r[s].menuItem;if(t&&t.menu&&t.menu.posted){t.Deactivate(r[s])}}q=v.length-1;while(q>=0&&w.parentNode.menuItem!==v[q].menuItem){v[q].menuItem.posted=false;v[q].parentNode.removeChild(v[q]);q--}if(this.Timer&&!a.isMobile){this.Timer(u,w)}}},Mouseout:function(q,r){if(!this.menu||!this.menu.posted){this.Deactivate(r)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(q,r){return this.Remove(q,r)},Touchstart:function(q,r){return this.TouchEvent(q,r,"Mousedown")},Touchend:function(q,r){return this.TouchEvent(q,r,"Mouseup")},TouchEvent:function(r,s,q){if(this!==m.lastItem){if(m.lastMenu){a.Event(r,m.lastMenu,"Mouseout")}a.Event(r,s,"Mouseover",true);m.lastItem=this;m.lastMenu=s}if(this.nativeTouch){return null}a.Event(r,s,q);return false},Remove:function(q,r){r=r.parentNode.menuItem;return r.Remove(q,r)},Activate:function(q){this.Deactivate(q);q.className+=" MathJax_MenuActive"},Deactivate:function(q){q.className=q.className.replace(/ MathJax_MenuActive/,"")},With:function(q){if(q){c.Insert(this,q)}return this}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(q,s,r){this.name=q;this.action=s;this.With(r)},Label:function(q,r){return[this.name]},Mouseup:function(q,r){if(!this.disabled){this.Remove(q,r);j.Post(["command",this]);this.action.call(this,q)}return h(q)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(q,s){this.name=q;var r=1;if(!(s instanceof a.ITEM)){this.With(s),r++}this.menu=a.apply(a,[].slice.call(arguments,r))},Label:function(q,r){this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(q,r){if(this.timer){clearTimeout(this.timer)}q={clientX:q.clientX,clientY:q.clientY};this.timer=setTimeout(f(["Mouseup",this,q,r]),o.delay)},Touchend:function(r,t){var s=this.menu.posted;var q=this.SUPER(arguments).Touchend.apply(this,arguments);if(s){this.Deactivate(t);delete m.lastItem;delete m.lastMenu}return q},Mouseup:function(r,t){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(r,t)}else{var s=document.getElementById("MathJax_MenuFrame").childNodes,q=s.length-1;while(q>=0){var u=s[q];u.menuItem.posted=false;u.parentNode.removeChild(u);if(u.menuItem===this.menu){break}q--}}}return h(r)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(r,q,s){this.name=r;this.variable=q;this.With(s);if(this.value==null){this.value=this.name}},Label:function(r,s){var q={className:"MathJax_MenuRadioCheck"};if(o.settings[this.variable]!==this.value){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(t,u){if(!this.disabled){var v=u.parentNode.childNodes;for(var r=0,q=v.length;r<q;r++){var s=v[r].menuItem;if(s&&s.variable===this.variable){v[r].firstChild.style.display="none"}}u.firstChild.display="";o.settings[this.variable]=this.value;a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(t,u);if(this.action&&!this.disabled){this.action.call(a,this)}return h(t)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(r,q,s){this.name=r;this.variable=q;this.With(s)},Label:function(r,s){var q={className:"MathJax_MenuCheck"};if(!o.settings[this.variable]){q={style:{display:"none"}}}return[["span",q,[this.marker]]," "+this.name]},Mouseup:function(q,r){if(!this.disabled){r.firstChild.display=(o.settings[this.variable]?"none":"");o.settings[this.variable]=!o.settings[this.variable];a.cookie[this.variable]=o.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(q,r);if(this.action&&!this.disabled){this.action.call(a,this)}return h(q)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(q,r){this.name=q;this.With(r)},Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(q,r){delete q.onmouseover,delete q.onmouseout;delete q.onmousedown;q.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{fontInUse:""};var v=(t.webFonts?"":"local "),r=(t.webFonts?" web":"");var s=(t.imgFonts?"Image":v+t.fontInUse+r)+" fonts";if(s==="local  fonts"&&b.SVG){s="web SVG fonts"}var q=["MathJax.js v"+MathJax.fileversion,["br"]];q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.InputJax,"Input Jax");a.About.GetJax(q,MathJax.OutputJax,"Output Jax");a.About.GetJax(q,MathJax.ElementJax,"Element Jax");q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(q,MathJax.Extension,"Extension",true);q.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(t.webFonts&&!t.imgFonts?" \u2014 "+t.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var w=g.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"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"}},q],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var x=(document.documentElement||{});var u=window.innerHeight||x.clientHeight||x.scrollHeight||0;if(a.prototype.msieAboutBug){w.style.width="20em";w.style.position="absolute";w.style.left=Math.floor((document.documentElement.scrollWidth-w.offsetWidth)/2)+"px";w.style.top=(Math.floor((u-w.offsetHeight)/3)+document.body.scrollTop)+"px"}else{w.style.marginLeft=Math.floor(-w.offsetWidth/2)+"px";w.style.top=Math.floor((u-w.offsetHeight)/3)+"px"}};a.About.Remove=function(q){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(r,w,u,t){var v=[];for(var x in w){if(w.hasOwnProperty(x)&&w[x]){if((t&&w[x].version)||(w[x].isa&&w[x].isa(w))){v.push((w[x].id||x)+" "+u+" v"+w[x].version)}}}v.sort();for(var s=0,q=v.length;s<q;s++){r.push(v[s],["br"])}return r};a.Help=function(){window.open(o.helpURL,"MathJaxHelp")};a.ShowSource=function(t){if(!t){t=window.event}var s={screenX:t.screenX,screenY:t.screenY};if(!a.jax){return}if(this.format==="MathML"){var q=MathJax.ElementJax.mml;if(q&&typeof(q.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),t)}catch(r){if(!r.restart){throw r}f.After([this,a.ShowSource,s])}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(t);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!q.mbase.prototype.toMathML){q.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,s]);return}}}else{if(a.jax.originalText==null){alert("No original form available");return}a.ShowSource.Text(a.jax.originalText,t)}};a.ShowSource.Window=function(r){if(!a.ShowSource.w){var s=[],q=o.windowSettings;for(var t in q){if(q.hasOwnProperty(t)){s.push(t+"="+q[t])}}a.ShowSource.w=window.open("","_blank",s.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(z,v){var s=a.ShowSource.Window(v);z=z.replace(/^\s*/,"").replace(/\s*$/,"");z=z.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");if(a.isMobile){s.document.open();s.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<pre>"+z+"</pre>");s.document.write("<hr><input type='button' value='Close' onclick='window.close()' />");s.document.write("</body></html>");s.document.close()}else{s.document.open();s.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");s.document.write("<table><tr><td><pre>"+z+"</pre></td></tr></table>");s.document.write("</body></html>");s.document.close();var u=s.document.body.firstChild;var t=(s.outerHeight-s.innerHeight)||30,r=(s.outerWidth-s.innerWidth)||30;r=Math.min(Math.floor(0.5*screen.width),u.offsetWidth+r+25);t=Math.min(Math.floor(0.5*screen.height),u.offsetHeight+t+25);s.resizeTo(r,t);if(v&&v.screenX!=null){var q=Math.max(0,Math.min(v.screenX-Math.floor(r/2),screen.width-r-20)),A=Math.max(0,Math.min(v.screenY-Math.floor(t/2),screen.height-t-20));s.moveTo(q,A)}}delete a.ShowSource.w};a.Scale=function(){var r=b["HTML-CSS"],q=b.NativeMML;var t=(r?r.config.scale:q.config.scale);var s=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");if(s){if(s.match(/^\s*\d+\s*%?\s*$/)){s=parseInt(s);if(s){if(s!==t){if(r){r.config.scale=s}if(q){q.config.scale=s}a.cookie.scale=s;a.saveCookie();c.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var r=c.outputJax["jax/mml"];if(r[0]!==o.settings.renderer){var u=c.Browser,t,q=a.Renderer.Messages,s;switch(o.settings.renderer){case"NativeMML":if(!o.settings.warnedMML){if(u.isChrome||(u.isSafari&&!u.versionAtLeast("5.0"))){t=q.MML.WebKit}else{if(u.isMSIE){if(!u.hasMathPlayer){t=q.MML.MSIE}}else{t=q.MML[u]}}s="warnedMML"}break;case"SVG":if(!o.settings.warnedSVG){if(u.isMSIE&&!e){t=q.SVG.MSIE}}break}if(t){t+="\n\nSwitch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)";a.cookie.renderer=r[0].id;a.saveCookie();if(!confirm(t)){return}if(s){a.cookie[s]=o.settings[s]=true}a.cookie.renderer=o.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,o.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:"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:"Internet Explorer requires the MathPlayer plugin in order to process MathML output.",Opera:"Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly.",Firefox:"Your browser's native MathML does not implement all the features used by MathJax, so some expressions my render improperly."},SVG:{MSIE:"SVG is not implemented in Internet Explorer prior to IE9, or when the browser is emulating IE8 or below. Switching to SVG output will cause the mathemtics to not display properly."}};a.Font=function(){var q=b["HTML-CSS"];if(!q){return}document.location.reload()};a.MPEvents=function(s){var r=o.settings.discoverable,q=a.MPEvents.Messages;if(!e){if(o.settings.mpMouse&&!confirm(q.IE8warning)){delete a.cookie.mpContext;delete o.settings.mpContext;delete a.cookie.mpMouse;delete o.settings.mpMouse;a.saveCookie();return}o.settings.mpContext=o.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=o.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!r&&s.name==="Menu Events"&&o.settings.mpContext){alert(q.IE9warning)}}};a.MPEvents.Messages={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:"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(q){var r=(document.compatMode==="BackCompat");var s=q.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:true,msieFixedPositionBug:(r||!s),msieAboutBug:r});if(e){delete o.styles["#MathJax_About"].filter;delete o.styles[".MathJax_Menu"].filter}},Firefox:function(q){a.skipMouseover=q.isMobile&&q.versionAtLeast("6.0");a.skipMousedown=q.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;c.Register.StartupHook("End Config",function(){o.settings=c.config.menuSettings;if(typeof(o.settings.showRenderer)!=="undefined"){o.showRenderer=o.settings.showRenderer}if(typeof(o.settings.showFontMenu)!=="undefined"){o.showFontMenu=o.settings.showFontMenu}if(typeof(o.settings.showContext)!=="undefined"){o.showContext=o.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU("Show Math As",m.COMMAND("MathML Code",a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND("Original Form",a.ShowSource,{nativeTouch:true}),m.RULE(),m.CHECKBOX("Show TeX hints in MathML","texHints")),m.RULE(),m.SUBMENU("Math Settings",m.SUBMENU("Zoom Trigger",m.RADIO("Hover","zoom",{action:a.Zoom}),m.RADIO("Click","zoom",{action:a.Zoom}),m.RADIO("Double-Click","zoom",{action:a.Zoom}),m.RADIO("No Zoom","zoom",{value:"None"}),m.RULE(),m.LABEL("Trigger Requires:"),m.CHECKBOX((c.Browser.isMac?"Option":"Alt"),"ALT"),m.CHECKBOX("Command","CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX("Control","CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX("Shift","Shift")),m.SUBMENU("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("Math Renderer",{hidden:!o.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||!o.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL("Let MathPlayer Handle:"),m.CHECKBOX("Menu Events","mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse Events","mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX("Mouse and Menu Events","mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU("Font Preference",{hidden:!o.showFontMenu},m.LABEL("For HTML-CSS:"),m.RADIO("Auto","font",{action:a.Font}),m.RULE(),m.RADIO("TeX (local)","font",{action:a.Font}),m.RADIO("TeX (web)","font",{action:a.Font}),m.RADIO("TeX (image)","font",{action:a.Font}),m.RULE(),m.RADIO("STIX (local)","font",{action:a.Font})),m.SUBMENU("Contextual Menu",{hidden:!o.showContext},m.RADIO("MathJax","context"),m.RADIO("Browser","context")),m.COMMAND("Scale All Math ...",a.Scale),m.RULE().With({hidden:!o.showDiscoverable,name:"discover_rule"}),m.CHECKBOX("Highlight on Hover","discoverable",{hidden:!o.showDiscoverable})),m.RULE(),m.COMMAND("About MathJax",a.About),m.COMMAND("MathJax Help",a.Help));if(a.isMobile){(function(){var r=o.settings;var q=a.menu.Find("Math Settings","Zoom Trigger").menu;q.items[0].disabled=q.items[1].disabled=true;if(r.zoom==="Hover"||r.zoom=="Click"){r.zoom="None"}q.items=q.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}});a.showRenderer=function(q){a.cookie.showRenderer=o.showRenderer=q;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!q};a.showMathPlayer=function(q){a.cookie.showMathPlayer=o.showMathPlayer=q;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!q};a.showFontMenu=function(q){a.cookie.showFontMenu=o.showFontMenu=q;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!q};a.showContext=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!q};a.showDiscoverable=function(q){a.cookie.showContext=o.showContext=q;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!q;a.menu.Find("Math Settings","discover_rule").hidden=!q};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,o.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:"2.0",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",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},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"]});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor: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}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e<d;e++){this.SetData(this.data.length,arguments[e])}}},SetData:function(d,e){if(e!=null){if(!(e instanceof a.mbase)){e=(this.isToken?a.chars(e):a.mtext(e))}e.parent=this;e.setInherit(this.inheritFromMe?this:this.inherit)}this.data[d]=e},Parent:function(){var d=this.parent;while(d&&d.inferred){d=d.parent}return d},Get:function(e,j){if(this[e]!=null){return this[e]}if(this.attr&&this.attr[e]!=null){return this.attr[e]}var f=this.Parent();if(f&&f["adjustChild_"+e]!=null){return(f["adjustChild_"+e])(f.childPosition(this))}var i=this.inherit;var d=i;while(i){var h=i[e];if(h==null&&i.attr){h=i.attr[e]}if(h!=null&&!i.noInheritAttribute[e]){var g=i.noInherit[this.type];if(!(g&&g[e])){return h}}d=i;i=i.inherit}if(!j){if(this.defaults[e]===a.AUTO){return this.autoDefault(e)}if(this.defaults[e]!==a.INHERIT&&this.defaults[e]!=null){return this.defaults[e]}if(d){return d.defaults[e]}}return null},hasValue:function(d){return(this.Get(d,true)!=null)},getValues:function(){var e={};for(var f=0,d=arguments.length;f<d;f++){e[arguments[f]]=this.Get(arguments[f])}return e},adjustChild_scriptlevel:function(d){return this.Get("scriptlevel")},adjustChild_displaystyle:function(d){return this.Get("displaystyle")},adjustChild_texprimestyle:function(d){return this.Get("texprimestyle")},childPosition:function(f){if(f.parent.inferred){f=f.parent}for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]===f){return e}}return null},setInherit:function(f){if(f!==this.inherit&&this.inherit==null){this.inherit=f;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].setInherit){this.data[e].setInherit(f)}}}},setTeXclass:function(d){this.getPrevClass(d);return(typeof(this.texClass)!=="undefined"?this:d)},getPrevClass:function(d){if(d){this.prevClass=d.Get("texClass");this.prevLevel=d.Get("scriptlevel")}},updateTeXclass:function(d){if(d){this.prevClass=d.prevClass;delete d.prevClass;this.prevLevel=d.prevLevel;delete d.prevLevel;this.texClass=d.Get("texClass")}},texSpacing:function(){var e=(this.prevClass!=null?this.prevClass:a.TEXCLASS.NONE);var d=(this.Get("texClass")||a.TEXCLASS.ORD);if(e===a.TEXCLASS.NONE||d===a.TEXCLASS.NONE){return""}if(e===a.TEXCLASS.VCENTER){e=a.TEXCLASS.ORD}if(d===a.TEXCLASS.VCENTER){d=a.TEXCLASS.ORD}var f=this.TEXSPACE[e][d];if(this.prevLevel>0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},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(d){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 e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].hasNewline()){return true}}return false},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var e=0,d=this.data.length;e<d;e++){if(!this.data[e].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(d){if(this.data[0]){d=this.data[0].setTeXclass(d);this.updateTeXclass(this.data[0])}return d},setBaseTeXclasses:function(f){this.getPrevClass(f);this.texClass=null;if(this.isEmbellished()){f=this.data[0].setTeXclass(f);this.updateTeXclass(this.Core())}else{if(this.data[0]){this.data[0].setTeXclass()}f=this}for(var e=1,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].setTeXclass()}}return f},setSeparateTeXclasses:function(f){this.getPrevClass(f);for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].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},autoDefault:function(e){if(e==="mathvariant"){var d=(this.data[0]||"").toString();return(d.length===1||(d.length===2&&d.charCodeAt(0)>=55296&&d.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});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}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:true,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(f,l){var k=this.def;if(!k){if(f==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var j=this.data.join("");var e=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var g=0,d=e.length;g<d;g++){var h=this.OPTABLE[e[g]][j];if(h){k=this.makeDef(h);break}}if(!k){k=this.CheckRange(j)}if(!k&&l){k={}}else{if(!k){k=MathJax.Hub.Insert({},this.defaultDef)}k.form=e[0];this.def=k}}this.useMMLspacing&=~(this.SPACE_ATTR[f]||0);if(k[f]!=null){return k[f]}else{if(!l){return this.defaultDef[f]}}return""},CheckRange:function(h){var j=h.charCodeAt(0);if(j>=55296&&j<56320){j=(((j-55296)<<10)+(h.charCodeAt(1)-56320))+65536}for(var f=0,d=this.RANGES.length;f<d&&this.RANGES[f][0]<=j;f++){if(j<=this.RANGES[f][1]){if(this.RANGES[f][3]){var e=a.optableDir+"/"+this.RANGES[f][3]+".js";this.RANGES[f][3]=null;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(e))}var g=a.TEXCLASSNAMES[this.RANGES[f][2]];g=this.OPTABLE.infix[h]=a.mo.OPTYPES[g==="BIN"?"BIN3":g];return this.makeDef(g)}}return null},makeDef:function(e){if(e[2]==null){e[2]=this.defaultDef.texClass}if(!e[3]){e[3]={}}var d=MathJax.Hub.Insert({},e[3]);d.lspace=this.SPACE[e[0]];d.rspace=this.SPACE[e[1]];d.texClass=e[2];if(d.texClass===a.TEXCLASS.REL&&(this.movablelimits||this.data.join("").match(/^[a-z]+$/i))){d.texClass=a.TEXCLASS.OP}return d},getForm:function(){var d=this,f=this.parent,e=this.Parent();while(e&&e.isEmbellished()){d=f;f=e.parent;e=e.Parent()}if(f&&f.type==="mrow"&&f.NonSpaceLength()!==1){if(f.FirstNonSpace()===d){return a.FORM.PREFIX}if(f.LastNonSpace()===d){return a.FORM.POSTFIX}}return a.FORM.INFIX},isEmbellished:function(){return true},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)},setTeXclass:function(d){this.getValues("lspace","rspace");if(this.useMMLspacing){this.texClass=a.TEXCLASS.NONE;return this}this.texClass=this.Get("texClass");if(this.texClass===a.TEXCLASS.NONE){return d}if(d){this.prevClass=d.texClass||a.TEXCLASS.ORD;this.prevLevel=d.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)){d.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}});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},hasNewline:function(){return(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,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,isEmbellished:function(){var e=false;for(var f=0,d=this.data.length;f<d;f++){if(this.data[f]==null){continue}if(this.data[f].isEmbellished()){if(e){return false}e=true;this.core=f}else{if(!this.data[f].isSpacelike()){return false}}}return e},NonSpaceLength:function(){var f=0;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){f++}}return f},FirstNonSpace:function(){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},LastNonSpace:function(){for(var d=this.data.length-1;d>=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}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(f){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){f=this.data[e].setTeXclass(f)}}if(this.data[0]){this.updateTeXclass(this.data[0])}return f}});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(d){return false},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(!this.Get("displaystyle")||d>0){d++}return d},adjustChild_texprimestyle:function(d){if(d==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(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===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,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},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(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length<this.data.length){e.separators+=e.separators.charAt(e.separators.length-1)}}if(this.data[0]){g=this.data[0].setTeXclass(g)}for(var f=1,d=this.data.length;f<d;f++){if(this.data[f]){if(e.separators!==""){this.SetData("sep"+f,a.mo(e.separators.charAt(f-1)));g=this.data["sep"+f].setTeXclass(g)}g=this.data[f].setTeXclass(g)}}if(e.close!==""){this.SetData("close",a.mo(e.close).With({stretchy:true,texClass:a.TEXCLASS.CLOSE}));g=this.data.close.setTeXclass(g)}this.updateTeXclass(this.data.open);return g}});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,linebreakContainer:true,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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}return 0},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===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(d){if(d%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(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===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:{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 e=0,d=arguments.length;e<d;e++){if(!((arguments[e] instanceof a.mtr)||(arguments[e] instanceof a.mlabeledtr))){arguments[e]=a.mtd(arguments[e])}}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 e=0,d=arguments.length;e<d;e++){if(!(arguments[e] instanceof a.mtd)){arguments[e]=a.mtd(arguments[e])}}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(d){return this.selected().setTeXclass(d)}});a.semantics=a.mbase.Subclass({type:"semantics",isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{definitionURL:null,encoding:null},setTeXclass:a.mbase.setChildTeXclass});a.annotation=a.mbase.Subclass({type:"annotation",isToken: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,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(d){if(d==="displaystyle"){return this.Get("display")==="block"}return""},linebreakContainer:true,setTeXclass:a.mbase.setChildTeXclass});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 d=this.value();if(d<=65535){return String.fromCharCode(d)}d-=65536;return String.fromCharCode((d>>10)+55296)+String.fromCharCode((d&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 e=0,d=arguments.length;e<d;e++){var f=this.Import(arguments[e]);this.data.push(f);this.div.appendChild(f)}},Import:function(h){if(document.importNode){return document.importNode(h,true)}var e,f,d;if(h.nodeType===1){e=document.createElement(h.nodeName);if(h.className){e.className=iNode.className}for(f=0,d=h.attributes.length;f<d;f++){var g=h.attributes[f];if(g.specified&&g.nodeValue!=null&&g.nodeValue!=""){e.setAttribute(g.nodeName,g.nodeValue)}if(g.nodeName==="style"){e.style.cssText=g.nodeValue}}if(h.className){e.className=h.className}}else{if(h.nodeType===3||h.nodeType===4){e=document.createTextNode(h.nodeValue)}else{if(h.nodeType===8){e=document.createComment(h.nodeValue)}else{return document.createTextNode("")}}}for(f=0,d=h.childNodes.length;f<d;f++){e.appendChild(this.Import(h.childNodes[f]))}return e},value:function(){return this.div},toString:function(){return this.div.innerHTML}});a.TeXAtom=a.mbase.Subclass({type:"texatom",inferRow:true,texClass:a.TEXCLASS.ORD,setTeXclass:function(d){this.getPrevClass(d);this.data[0].setTeXclass();return this}});a.NULL=a.mbase().With({type:"null"});var b=a.TEXCLASS;var c={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":c.ORD21,"\u2202":c.ORD21,"\u2203":c.ORD21,"\u2207":c.ORD21,"\u220F":c.OP,"\u2210":c.OP,"\u2211":c.OP,"\u2212":c.BIN01,"\u2213":c.BIN01,"\u221A":[1,1,b.ORD,{stretchy:true}],"\u2220":c.ORD,"\u222B":c.INTEGRAL,"\u222E":c.INTEGRAL,"\u22C0":c.OP,"\u22C1":c.OP,"\u22C2":c.OP,"\u22C3":c.OP,"\u2308":c.OPEN,"\u230A":c.OPEN,"\u27E8":c.OPEN,"\u27EE":c.OPEN,"\u2A00":c.OP,"\u2A01":c.OP,"\u2A02":c.OP,"\u2A04":c.OP,"\u2A06":c.OP,"\u00AC":c.ORD21,"\u00B1":c.BIN01,"(":c.OPEN,"+":c.BIN01,"-":c.BIN01,"[":c.OPEN,"{":c.OPEN,"|":c.OPEN},postfix:{"!":[1,0,b.CLOSE],"&":c.ORD,"\u2032":c.ORD02,"\u203E":c.WIDEACCENT,"\u2309":c.CLOSE,"\u230B":c.CLOSE,"\u23DE":c.WIDEACCENT,"\u23DF":c.WIDEACCENT,"\u266D":c.ORD02,"\u266E":c.ORD02,"\u266F":c.ORD02,"\u27E9":c.CLOSE,"\u27EF":c.CLOSE,"\u02C6":c.WIDEACCENT,"\u02C7":c.WIDEACCENT,"\u02C9":c.WIDEACCENT,"\u02CA":c.ACCENT,"\u02CB":c.ACCENT,"\u02D8":c.ACCENT,"\u02D9":c.ACCENT,"\u02DC":c.WIDEACCENT,"\u0302":c.WIDEACCENT,"\u00A8":c.ACCENT,"\u00AF":c.WIDEACCENT,")":c.CLOSE,"]":c.CLOSE,"^":c.WIDEACCENT,_:c.WIDEACCENT,"`":c.ACCENT,"|":c.CLOSE,"}":c.CLOSE,"~":c.WIDEACCENT},infix:{"":c.ORD,"%":[3,3,b.ORD],"\u2022":c.BIN4,"\u2026":c.INNER,"\u2044":c.TALLBIN,"\u2061":c.ORD,"\u2062":c.ORD,"\u2063":[0,0,b.ORD,{linebreakstyle:"after",separator:true}],"\u2064":c.ORD,"\u2190":c.WIDEREL,"\u2191":c.RELSTRETCH,"\u2192":c.WIDEREL,"\u2193":c.RELSTRETCH,"\u2194":c.WIDEREL,"\u2195":c.RELSTRETCH,"\u2196":c.RELSTRETCH,"\u2197":c.RELSTRETCH,"\u2198":c.RELSTRETCH,"\u2199":c.RELSTRETCH,"\u21A6":c.WIDEREL,"\u21A9":c.WIDEREL,"\u21AA":c.WIDEREL,"\u21BC":c.WIDEREL,"\u21BD":c.WIDEREL,"\u21C0":c.WIDEREL,"\u21C1":c.WIDEREL,"\u21CC":c.WIDEREL,"\u21D0":c.WIDEREL,"\u21D1":c.RELSTRETCH,"\u21D2":c.WIDEREL,"\u21D3":c.RELSTRETCH,"\u21D4":c.WIDEREL,"\u21D5":c.RELSTRETCH,"\u2208":c.REL,"\u2209":c.REL,"\u220B":c.REL,"\u2212":c.BIN4,"\u2213":c.BIN4,"\u2215":c.TALLBIN,"\u2216":c.BIN4,"\u2217":c.BIN4,"\u2218":c.BIN4,"\u2219":c.BIN4,"\u221D":c.REL,"\u2223":c.REL,"\u2225":c.REL,"\u2227":c.BIN4,"\u2228":c.BIN4,"\u2229":c.BIN4,"\u222A":c.BIN4,"\u223C":c.REL,"\u2240":c.BIN4,"\u2243":c.REL,"\u2245":c.REL,"\u2248":c.REL,"\u224D":c.REL,"\u2250":c.REL,"\u2260":c.REL,"\u2261":c.REL,"\u2264":c.REL,"\u2265":c.REL,"\u226A":c.REL,"\u226B":c.REL,"\u227A":c.REL,"\u227B":c.REL,"\u2282":c.REL,"\u2283":c.REL,"\u2286":c.REL,"\u2287":c.REL,"\u228E":c.BIN4,"\u2291":c.REL,"\u2292":c.REL,"\u2293":c.BIN4,"\u2294":c.BIN4,"\u2295":c.BIN4,"\u2296":c.BIN4,"\u2297":c.BIN4,"\u2298":c.BIN4,"\u2299":c.BIN4,"\u22A2":c.REL,"\u22A3":c.REL,"\u22A4":c.ORD55,"\u22A5":c.REL,"\u22A8":c.REL,"\u22C4":c.BIN4,"\u22C5":c.BIN4,"\u22C6":c.BIN4,"\u22C8":c.REL,"\u22EE":c.ORD55,"\u22EF":c.INNER,"\u22F1":[5,5,b.INNER],"\u25B3":c.BIN4,"\u25B5":c.BIN4,"\u25B9":c.BIN4,"\u25BD":c.BIN4,"\u25BF":c.BIN4,"\u25C3":c.BIN4,"\u2758":c.REL,"\u27F5":c.WIDEREL,"\u27F6":c.WIDEREL,"\u27F7":c.WIDEREL,"\u27F8":c.WIDEREL,"\u27F9":c.WIDEREL,"\u27FA":c.WIDEREL,"\u27FC":c.WIDEREL,"\u2A2F":c.BIN4,"\u2A3F":c.BIN4,"\u2AAF":c.REL,"\u2AB0":c.REL,"\u00B1":c.BIN4,"\u00B7":c.BIN4,"\u00D7":c.BIN4,"\u00F7":c.BIN4,"*":c.BIN3,"+":c.BIN4,",":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"-":c.BIN4,".":[3,3,b.ORD],"/":c.ORD11,":":[1,2,b.REL],";":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"<":c.REL,"=":c.REL,">":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c});a.mo.prototype.OPTABLE.infix["^"]=c.WIDEREL;a.mo.prototype.OPTABLE.infix._=c.WIDEREL})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js");

MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.0";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=[];var 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){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"){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");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.arrow){e.push("MJX-arrow")}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((1/18)*RegExp.$1).toFixed(3).replace(/\.?0+$/,"")+"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(e){e=String(e).split("");for(var f=0,d=e.length;f<d;f++){var h=e[f].charCodeAt(0);if(h<32||h>126){e[f]="&#x"+h.toString(16).toUpperCase()+";"}else{var g={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[e[f]];if(g){e[f]=g}}}return e.join("")}});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="2.0";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:"2.0",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 e=MathJax.Object.Subclass({Init:function(l,k){this.global={isInner:k};this.data=[b.start(this.global)];if(l){this.data[0].env=l}this.env=this.data[0].env},Push:function(){var l,k,n,o;for(l=0,k=arguments.length;l<k;l++){n=arguments[l];if(n instanceof h.mbase){n=b.mml(n)}n.global=this.global;o=(this.data.length?this.Top().checkItem(n):true);if(o instanceof Array){this.Pop();this.Push.apply(this,o)}else{if(o instanceof b){this.Pop();this.Push(o)}else{if(o){this.data.push(n);if(n.env){for(var p in this.env){if(this.env.hasOwnProperty(p)){n.env[p]=this.env[p]}}this.env=n.env}else{n.env=this.env}}}}}},Pop:function(){var k=this.data.pop();if(!k.isOpen){delete k.env}this.env=(this.data.length?this.Top().env:{});return k},Top:function(k){if(k==null){k=1}if(this.data.length<k){return null}return this.data[this.data.length-k]},Prev:function(k){var l=this.Top();if(k){return l.data[l.data.length-1]}else{return l.Pop()}},toString:function(){return"stack[\n  "+this.data.join("\n  ")+"\n]"}});var b=e.Item=MathJax.Object.Subclass({type:"base",closeError:"Extra close brace or missing open brace",rightError:"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(k,l){if(k==null){k=true}if(this.data.length===1&&!l){return this.data[0]}return h.mrow.apply(h,this.data).With((k?{inferred:true}:{}))},checkItem:function(k){if(k.type==="over"&&this.isOpen){k.num=this.mmlData(false);this.data=[]}if(k.type==="cell"&&this.isOpen){if(k.linebreak){return false}d.Error("Misplaced "+k.name)}if(k.isClose&&this[k.type+"Error"]){d.Error(this[k.type+"Error"])}if(!k.isNotStack){return true}this.Push(k.data[0]);return false},With:function(k){for(var l in k){if(k.hasOwnProperty(l)){this[l]=k[l]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:true,Init:function(k){this.SUPER(arguments).Init.call(this);this.global=k},checkItem:function(k){if(k.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,k)}});b.stop=b.Subclass({type:"stop",isClose:true});b.open=b.Subclass({type:"open",isOpen:true,stopError:"Extra open brace or missing close brace",checkItem:function(l){if(l.type==="close"){var k=this.mmlData();return b.mml(h.TeXAtom(k))}return this.SUPER(arguments).checkItem.call(this,l)}});b.close=b.Subclass({type:"close",isClose:true});b.subsup=b.Subclass({type:"subsup",stopError:"Missing superscript or subscript argument",checkItem:function(l){var k=["","subscript","superscript"][this.position];if(l.type==="open"||l.type==="left"){return true}if(l.type==="mml"){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("Missing open brace for "+k)}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:true,name:"\\over",checkItem:function(m,k){if(m.type==="over"){d.Error("Ambiguous use of "+m.name)}if(m.isClose){var l=h.mfrac(this.num,this.mmlData(false));if(this.thickness!=null){l.linethickness=this.thickness}if(this.open||this.close){l.texClass=h.TEXCLASS.INNER;l.texWithDelims=true;l=h.mfenced(l).With({open:this.open,close:this.close})}return[b.mml(l),m]}return this.SUPER(arguments).checkItem.call(this,m)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:true,delim:"(",stopError:"Extra \\left or missing \\right",checkItem:function(l){if(l.type==="right"){var k=h.mfenced(this.data.length===1?this.data[0]:h.mrow.apply(h,this.data));return b.mml(k.With({open:this.delim,close: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(k){if(k.type==="end"){if(k.name!==this.name){d.Error("\\begin{"+this.name+"} ended with \\end{"+k.name+"}")}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(k.type==="stop"){d.Error("Missing \\end{"+this.name+"}")}return this.SUPER(arguments).checkItem.call(this,k)}});b.end=b.Subclass({type:"end",isClose:true});b.style=b.Subclass({type:"style",checkItem:function(l){if(!l.isClose){return this.SUPER(arguments).checkItem.call(this,l)}var k=h.mstyle.apply(h,this.data).With(this.styles);return[b.mml(k),l]}});b.position=b.Subclass({type:"position",checkItem:function(l){if(l.isClose){d.Error("Missing box for "+this.name)}if(l.isNotStack){var k=l.mmlData();switch(this.move){case"vertical":k=h.mpadded(k).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(k)];case"horizontal":return[b.mml(this.left),l,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,l)}});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(l){if(l.isClose&&l.type!=="over"){if(l.isEntry){this.EndEntry();this.clearEnv();return false}if(l.isCR){this.EndEntry();this.EndRow();this.clearEnv();return false}this.EndTable();this.clearEnv();var k=h.mtable.apply(h,this.table).With(this.arraydef);if(this.frame.length===4){k.frame=(this.frame.dashed?"dashed":"solid")}else{if(this.frame.length){k.hasFrame=true;if(this.arraydef.rowlines){this.arraydef.rowlines=this.arraydef.rowlines.replace(/none( none)+$/,"none")}k=h.menclose(k).With({notation:this.frame.join(" "),isFrame:true});if((this.arraydef.columnlines||"none")!="none"||(this.arraydef.rowlines||"none")!="none"){k.padding=0}}}if(this.open||this.close){k=h.mfenced(k).With({open:this.open,close:this.close})}k=b.mml(k);if(this.requireClose){if(l.type==="close"){return k}d.Error("Missing close brace")}return[k,l]}return this.SUPER(arguments).checkItem.call(this,l)},EndEntry:function(){this.row.push(h.mtd.apply(h,this.data));this.data=[]},EndRow:function(){this.table.push(h.mtr.apply(h,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var k=this.arraydef.rowlines.split(/ /);if(k.length===this.table.length){this.frame.push("bottom");k.pop();this.arraydef.rowlines=k.join(" ")}else{if(k.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}if(this.rowspacing){var l=this.arraydef.rowspacing.split(/ /);while(l.length<this.table.length){l.push(this.rowspacing)}this.arraydef.rowspacing=l.join(" ")}},clearEnv:function(){for(var k in this.env){if(this.env.hasOwnProperty(k)){delete this.env[k]}}}});b.cell=b.Subclass({type:"cell",isClose:true});b.mml=b.Subclass({type:"mml",isNotStack:true,Add:function(){this.data.push.apply(this.data,arguments);return this}});b.fn=b.Subclass({type:"fn",checkItem:function(l){if(this.data[0]){if(l.type!=="mml"||!l.data[0]){return[this.data[0],l]}if(l.data[0].isa(h.mspace)){return[this.data[0],l]}var k=l.data[0];if(k.isEmbellished()){k=k.CoreMO()}if([0,0,1,1,0,1,1,0,0,0][k.Get("texClass")]){return[this.data[0],l]}return[this.data[0],h.mo(h.entity("#x2061")).With({texClass:h.TEXCLASS.NONE}),l]}return this.SUPER(arguments).checkItem.apply(this,arguments)}});b.not=b.Subclass({type:"not",checkItem:function(l){var k,m;if(l.type==="open"||l.type==="left"){return true}if(l.type==="mml"&&l.data[0].type.match(/^(mo|mi|mtext)$/)){k=l.data[0],m=k.data.join("");if(m.length===1&&!k.movesupsub){m=b.not.remap[m.charCodeAt(0)];if(m){k.SetData(0,h.chars(String.fromCharCode(m)))}else{k.Append(h.chars("\u0338"))}return l}}k=h.mpadded(h.mtext("\u29F8")).With({width:0});k=h.TeXAtom(k).With({texClass:h.TEXCLASS.REL});return[k,l]}});b.not.remap={8712:8713,8715:8716,8739:8740,8741:8742,8764:8769,126:8769,8771:8772,8773:8775,8776:8777,61:8800,8801:8802,60:8814,62:8815,8804:8816,8805:8817,8818:8820,8819:8821,8822:8824,8823:8825,8826:8832,8827:8833,8834:8836,8835:8837,8838:8840,8839:8841,8866:8876,8872:8877,8873:8878,8875:8879,8828:8928,8829:8929,8849:8930,8850:8931,8882:8938,8883:8939,8884:8940,8885:8941,8707:8708};b.dots=b.Subclass({type:"dots",checkItem:function(l){if(l.type==="open"||l.type==="left"){return true}var m=this.ldots;if(l.type==="mml"&&l.data[0].isEmbellished()){var k=l.data[0].CoreMO().Get("texClass");if(k===h.TEXCLASS.BIN||k===h.TEXCLASS.REL){m=this.cdots}}return[m,l]}});var f={Add:function(k,n,m){if(!n){n=this}for(var l in k){if(k.hasOwnProperty(l)){if(typeof k[l]==="object"&&!(k[l] instanceof Array)&&(typeof n[l]==="object"||typeof n[l]==="function")){this.Add(k[l],n[l],k[l],m)}else{if(!n[l]||!n[l].isUser||!m){n[l]=k[l]}}}}return n}};var j=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","\u2019":"Prime"},remap:{"-":"2212","*":"2217"},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",aleph:["2135",{mathvariant:h.VARIANT.NORMAL}],hbar:"210F",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}],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}],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",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","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",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","\\mathbin{\\mmlToken{mo}{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],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",begin:"Begin",end:"End",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,".1em"],eqnarray:["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",h.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],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 k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){f.macros[l]=["Macro",k[l]]}else{f.macros[l]=["Macro"].concat(k[l])}f.macros[l].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k,!!m);this.Parse();this.Push(b.stop())},Parse:function(){var l,k;while(this.i<this.string.length){l=this.string.charAt(this.i++);k=l.charCodeAt(0);if(k>=55296&&k<56320){l+=this.string.charAt(this.i++)}if(f.special[l]){this[f.special[l]](l)}else{if(f.letter.test(l)){this.Variable(l)}else{if(f.digit.test(l)){this.Number(l)}else{this.Other(l)}}}}},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(k){return k},ControlSequence:function(n){var k=this.GetCS(),m=this.csFindMacro(k);if(m){if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,[n+k].concat(m.slice(1)))}else{if(f.mathchar0mi[k]){this.csMathchar0mi(k,f.mathchar0mi[k])}else{if(f.mathchar0mo[k]){this.csMathchar0mo(k,f.mathchar0mo[k])}else{if(f.mathchar7[k]){this.csMathchar7(k,f.mathchar7[k])}else{if(f.delimiter["\\"+k]!=null){this.csDelimiter(k,f.delimiter["\\"+k])}else{this.csUndefined(n+k)}}}}}},csFindMacro:function(k){return f.macros[k]},csMathchar0mi:function(k,m){var l={mathvariant:h.VARIANT.ITALIC};if(m instanceof Array){l=m[1];m=m[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csMathchar0mo:function(k,m){var l={stretchy:false};if(m instanceof Array){l=m[1];l.stretchy=false;m=m[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+m)).With(l)))},csMathchar7:function(k,m){var l={mathvariant:h.VARIANT.NORMAL};if(m instanceof Array){l=m[1];m=m[0]}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+m)).With(l)))},csDelimiter:function(k,m){var l={};if(m instanceof Array){l=m[1];m=m[0]}if(m.length===4){m=h.entity("#x"+m)}else{m=h.chars(m)}this.Push(this.mmlToken(h.mo(m).With({fence:false,stretchy:false}).With(l)))},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(f.number);if(l){k=h.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=h.mo(h.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(h.mtext(h.chars(g)))},Space:function(k){},Superscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=h.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.over}else{l=h.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var k,l=this.stack.Prev();if(!l){l=h.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){if(l.movablelimits&&l.isa(h.mi)){l=this.mi2mo(l)}l=h.munderover(l,null,null).With({movesupsub:true})}k=l.under}else{l=h.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(m){var l=this.stack.Prev();if(!l){l=h.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(h.mo(h.chars(k)).With({isPrime:true}));this.Push(h.msup(l,k))},mi2mo:function(k){var l=h.mo();l.Append.apply(l,k.data);var m;for(m in l.defaults){if(l.defaults.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}for(m in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(m)&&k[m]!=null){l[m]=k[m]}}return l},Comment:function(k){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(k){d.Error("You can't use 'macro parameter character #' in math mode")},Other:function(m){var l={stretchy:false},k;if(this.stack.env.font){l.mathvariant=this.stack.env.font}if(f.remap[m]){m=f.remap[m];if(m instanceof Array){l=m[1];m=m[0]}k=h.mo(h.entity("#x"+m)).With(l)}else{k=h.mo(m).With(l)}if(k.autoDefault("texClass",true)==""){k=h.TeXAtom(k)}this.Push(this.mmlToken(k))},SetFont:function(l,k){this.stack.env.font=k},SetStyle:function(l,k,m,n){this.stack.env.style=k;this.stack.env.level=n;this.Push(b.style().With({styles:{displaystyle:m,scriptlevel:n}}))},SetSize:function(k,l){this.stack.env.size=l;this.Push(b.style().With({styles:{mathsize:l+"em"}}))},Color:function(m){var l=this.GetArgument(m);var k=this.stack.env.color;this.stack.env.color=l;var n=this.ParseArg(m);if(k){this.stack.env.color}else{delete this.stack.env.color}this.Push(h.mstyle(n).With({mathcolor:l}))},Spacer:function(k,l){this.Push(h.mspace().With({width:l,mathsize:h.SIZE.NORMAL,scriptlevel:0}))},LeftRight:function(k){this.Push(b[k.substr(1)]().With({delim:this.GetDelimiter(k)}))},Middle:function(k){var l=this.GetDelimiter(k);if(this.stack.Top().type!=="left"){d.Error(k+" must be within \\left and \\right")}this.Push(h.mo(l).With({stretchy:true}))},NamedFn:function(l,m){if(!m){m=l.substr(1)}var k=h.mi(m).With({texClass:h.TEXCLASS.OP});this.Push(b.fn(this.mmlToken(k)))},NamedOp:function(l,m){if(!m){m=l.substr(1)}m=m.replace(/&thinsp;/,"\u2006");var k=h.mo(m).With({movablelimits:true,movesupsub:true,form:h.FORM.PREFIX,texClass:h.TEXCLASS.OP});k.useMMLspacing&=~k.SPACE_ATTR.form;this.Push(this.mmlToken(k))},Limits:function(l,k){var m=this.stack.Prev("nopop");if(m.texClass!==h.TEXCLASS.OP){d.Error(l+" is allowed only on operators")}m.movesupsub=(k?true:false);m.movablelimits=false},Over:function(m,l,n){var k=b.over().With({name:m});if(l||n){k.open=l;k.close=n}else{if(m.match(/withdelims$/)){k.open=this.GetDelimiter(m);k.close=this.GetDelimiter(m)}}if(m.match(/^\\above/)){k.thickness=this.GetDimen(m)}else{if(m.match(/^\\atop/)||l||n){k.thickness=0}}this.Push(k)},Frac:function(l){var k=this.ParseArg(l);var m=this.ParseArg(l);this.Push(h.mfrac(k,m))},Sqrt:function(m){var o=this.GetBrackets(m),k=this.GetArgument(m);if(k==="\\frac"){k+="{"+this.GetArgument(k)+"}{"+this.GetArgument(k)+"}"}var l=d.Parse(k,this.stack.env).mml();if(!o){l=h.msqrt.apply(h,l.array())}else{l=h.mroot(l,this.parseRoot(o))}this.Push(l)},Root:function(l){var m=this.GetUpTo(l,"\\of");var k=this.ParseArg(l);this.Push(h.mroot(k,this.parseRoot(m)))},parseRoot:function(p){var l=this.stack.env,k=l.inRoot;l.inRoot=true;var o=d.Parse(p,l);p=o.mml();var m=o.stack.global;if(m.leftRoot||m.upRoot){p=h.mpadded(p);if(m.leftRoot){p.width=m.leftRoot}if(m.upRoot){p.voffset=m.upRoot;p.height=m.upRoot}}l.inRoot=k;return p},MoveRoot:function(k,m){if(!this.stack.env.inRoot){d.Error(k+" can appear only within a root")}if(this.stack.global[m]){d.Error("Multiple use of "+k)}var l=this.GetArgument(k);if(!l.match(/-?[0-9]+/)){d.Error("The argument to "+k+" must be an integer")}l=(l/15)+"em";if(l.substr(0,1)!=="-"){l="+"+l}this.stack.global[m]=l},Accent:function(m,k,p){var o=this.ParseArg(m);var n={accent:true};if(this.stack.env.font){n.mathvariant=this.stack.env.font}var l=this.mmlToken(h.mo(h.entity("#x"+k)).With(n));l.stretchy=(p?true:false);this.Push(h.TeXAtom(h.munderover(o,null,l).With({accent:true})))},UnderOver:function(m,p,k){var o={o:"over",u:"under"}[m.charAt(1)];var n=this.ParseArg(m);if(n.Get("movablelimits")){n.movablelimits=false}var l=h.munderover(n,null,null);if(k){l.movesupsub=true}l.data[l[o]]=this.mmlToken(h.mo(h.entity("#x"+p)).With({stretchy:true,accent:(o=="under")}));this.Push(l)},Overset:function(k){var m=this.ParseArg(k),l=this.ParseArg(k);this.Push(h.mover(l,m))},Underset:function(k){var m=this.ParseArg(k),l=this.ParseArg(k);this.Push(h.munder(l,m))},TeXAtom:function(n,p){var o={texClass:p},m;if(p==h.TEXCLASS.OP){o.movesupsub=o.movablelimits=true;var k=this.GetArgument(n);var l=k.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(l){o.mathvariant=h.VARIANT.NORMAL;m=b.fn(this.mmlToken(h.mi(l[1]).With(o)))}else{m=b.fn(h.TeXAtom(d.Parse(k,this.stack.env).mml()).With(o))}}else{m=h.TeXAtom(this.ParseArg(n)).With(o)}this.Push(m)},MmlToken:function(m){var n=this.GetArgument(m),k=this.GetBrackets(m,"").replace(/^\s+/,""),p=this.GetArgument(m),o={attrNames:[]},l;if(!h[n]||!h[n].prototype.isToken){d.Error(n+" is not a token element")}while(k!==""){l=k.match(/^([a-z]+)\s*=\s*('[^']*'|"[^"]*"|[^ ]*)\s*/i);if(!l){d.Error("Invalid MathML attribute: "+k)}if(!h[n].prototype.defaults[l[1]]&&!this.MmlTokenAllow[l[1]]){d.Error(l[1]+" is not a recognized attribute for "+n)}o[l[1]]=l[2].replace(/^(['"])(.*)\1$/,"$2");o.attrNames.push(l[1]);k=k.substr(l[0].length)}this.Push(this.mmlToken(h[n](p).With(o)))},MmlTokenAllow:{fontfamily:1,fontsize:1,fontweight:1,fontstyle:1,color:1,background:1,id:1,"class":1,href:1,style:1},Strut:function(k){this.Push(h.mpadded(h.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(l,k,m){var n=h.mphantom(this.ParseArg(l));if(k||m){n=h.mpadded(n);if(m){n.height=n.depth=0}if(k){n.width=0}}this.Push(h.TeXAtom(n))},Smash:function(m){var l=this.trimSpaces(this.GetBrackets(m,""));var k=h.mpadded(this.ParseArg(m));switch(l){case"b":k.depth=0;break;case"t":k.height=0;break;default:k.height=k.depth=0}this.Push(h.TeXAtom(k))},Lap:function(l){var k=h.mpadded(this.ParseArg(l)).With({width:0});if(l==="\\llap"){k.lspace="-1 width"}this.Push(h.TeXAtom(k))},RaiseLower:function(k){var l=this.GetDimen(k);var m=b.position().With({name:k,move:"vertical"});if(l.charAt(0)==="-"){l=l.slice(1);k={raise:"\\lower",lower:"\\raise"}[k.substr(1)]}if(k==="\\lower"){m.dh="-"+l;m.dd="+"+l}else{m.dh="+"+l;m.dd="-"+l}this.Push(m)},MoveLeftRight:function(k){var n=this.GetDimen(k);var m=(n.charAt(0)==="-"?n.slice(1):"-"+n);if(k==="\\moveleft"){var l=n;n=m;m=l}this.Push(b.position().With({name:k,move:"horizontal",left:h.mspace().With({width:n,mathsize:h.SIZE.NORMAL}),right:h.mspace().With({width:m,mathsize:h.SIZE.NORMAL})}))},Hskip:function(k){this.Push(h.mspace().With({width:this.GetDimen(k),mathsize:h.SIZE.NORMAL}))},Rule:function(m,o){var k=this.GetDimen(m),n=this.GetDimen(m),q=this.GetDimen(m);var l,p={width:k,height:n,depth:q};if(o!=="blank"){if(parseFloat(k)&&parseFloat(n)+parseFloat(q)){p.mathbackground=(this.stack.env.color||"black")}l=h.mpadded(h.mrow()).With(p)}else{l=h.mspace().With(p)}this.Push(l)},MakeBig:function(k,n,l){l*=f.p_height;l=String(l).replace(/(\.\d\d\d).+/,"$1")+"em";var m=this.GetDelimiter(k);this.Push(h.TeXAtom(h.mo(m).With({minsize:l,maxsize:l,scriptlevel:0,fence:true,stretchy:true,symmetric:true})).With({texClass:n}))},BuildRel:function(k){var l=this.ParseUpTo(k,"\\over");var m=this.ParseArg(k);this.Push(h.TeXAtom(h.munderover(m,null,l)).With({mclass:h.TEXCLASS.REL}))},HBox:function(k,l){this.Push.apply(this,this.InternalMath(this.GetArgument(k),l))},FBox:function(k){this.Push(h.menclose.apply(h,this.InternalMath(this.GetArgument(k))).With({notation:"box"}))},Not:function(k){this.Push(b.not())},Dots:function(k){this.Push(b.dots().With({ldots:this.mmlToken(h.mo(h.entity("#x2026")).With({stretchy:false})),cdots:this.mmlToken(h.mo(h.entity("#x22EF")).With({stretchy:false}))}))},Require:function(k){var l=this.GetArgument(k).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");this.Extension(null,l)},Extension:function(k,l,m){if(k&&!typeof(k)==="string"){k=k.name}l=d.extensionDir+"/"+l;if(!l.match(/\.js$/)){l+=".js"}if(!i.loaded[i.fileURL(l)]){if(k!=null){delete f[m||"macros"][k.replace(/^\\/,"")]}c.RestartAfter(i.Require(l))}},Macro:function(m,p,o,q){if(o){var l=[];if(q!=null){var k=this.GetBrackets(m);l.push(k==null?q:k)}for(var n=l.length;n<o;n++){l.push(this.GetArgument(m))}p=this.SubstituteArgs(l,p)}this.string=this.AddArgs(p,this.string.slice(this.i));this.i=0;if(++this.macroCount>d.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,r,m,k,t){var q=this.GetNext();if(q===""){d.Error("Missing argument for "+l)}if(q==="{"){this.i++}else{this.string=q+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:true,arraydef:{rowspacing:(m||"4pt"),columnspacing:(r||"1em")}});if(t){o.isCases=true}if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=true}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(n){this.Push(b.cell().With({isEntry:true,name:n}));if(this.stack.Top().isCases){var l=this.string;var q=0,o=this.i,k=l.length;while(o<k){var r=l.charAt(o);if(r==="{"){q++;o++}else{if(r==="}"){if(q===0){k=0}else{q--;o++}}else{if(r==="&"&&q===0){d.Error("Extra alignment tab in \\cases text")}else{if(r==="\\"){if(l.substr(o).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){k=0}else{o+=2}}else{o++}}}}}var p=l.substr(this.i,o-this.i);if(!p.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(p));this.i=o}}},Cr:function(k){this.Push(b.cell().With({isCR:true,name:k}))},CrLaTeX:function(k){var o=this.GetBrackets(k,"").replace(/ /g,"");if(o&&!o.match(/^(((\.\d+|\d+(\.\d*)?))(pt|em|ex|mu|mm|cm|in|pc))$/)){d.Error("Bracket argument to "+k+" must be a dimension")}this.Push(b.cell().With({isCR:true,name:k,linebreak:true}));var m=this.stack.Top();if(m.isa(b.array)){if(o&&m.arraydef.rowspacing){var l=m.arraydef.rowspacing.split(/ /);if(!m.rowspacing){m.rowspacing=this.dimen2em(l[0])}while(l.length<m.table.length){l.push(m.rowspacing)}l[m.table.length-1]=(m.rowspacing+this.dimen2em(o))+"em";m.arraydef.rowspacing=l.join(" ")}}else{if(o){this.Push(h.mspace().With({depth:o}))}this.Push(h.mo().With({linebreak:h.LINEBREAK.NEWLINE}))}},emPerInch:7.2,dimen2em:function(o){var l=o.match(/^((?:\.\d+|\d+(?:\.\d*)?))(pt|em|ex|mu|pc|in|mm|cm)/);var k=parseFloat(l[1]||"1"),n=l[2];if(n==="em"){return k}if(n==="ex"){return k*0.43}if(n==="pt"){return k/10}if(n==="pc"){return k*1.2}if(n==="in"){return k*this.emPerInch}if(n==="cm"){return k*this.emPerInch/2.54}if(n==="mm"){return k*this.emPerInch/25.4}if(n==="mu"){return k/18}return 0},HLine:function(l,m){if(m==null){m="solid"}var n=this.stack.Top();if(!n.isa(b.array)||n.data.length){d.Error("Misplaced "+l)}if(n.table.length==0){n.frame.push("top")}else{var k=(n.arraydef.rowlines?n.arraydef.rowlines.split(/ /):[]);while(k.length<n.table.length){k.push("none")}k[n.table.length-1]=m;n.arraydef.rowlines=k.join(" ")}},Begin:function(l){var m=this.GetArgument(l);if(m.match(/[^a-z*]/i)){d.Error('Invalid environment name "'+m+'"')}var n=this.envFindName(m);if(!n){d.Error('Unknown environment "'+m+'"')}if(++this.macroCount>d.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},envFindName:function(k){return f.environment[k]},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(l,n,s,q,r,m,k,o){if(!q){q=this.GetArgument("\\begin{"+l.name+"}")}var t=("c"+q).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");q=q.replace(/[^clr]/g,"").split("").join(" ");q=q.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var p=b.array().With({arraydef:{columnalign:q,columnspacing:(r||"1em"),rowspacing:(m||"4pt")}});if(t.match(/[|:]/)){if(t.charAt(0).match(/[|:]/)){p.frame.push("left");p.frame.dashed=t.charAt(0)===":"}if(t.charAt(t.length-1).match(/[|:]/)){p.frame.push("right")}t=t.substr(1,t.length-2);p.arraydef.columnlines=t.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(n){p.open=this.convertDelimiter(n)}if(s){p.close=this.convertDelimiter(s)}if(k==="D"){p.arraydef.displaystyle=true}if(k==="S"){p.arraydef.scriptlevel=1}if(o){p.arraydef.useHeight=false}this.Push(l);return p},AlignedArray:function(k){var l=this.GetBrackets("\\begin{"+k.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),l)},setArrayAlign:function(l,k){k=this.trimSpaces(k||"");if(k==="t"){l.arraydef.align="baseline 1"}else{if(k==="b"){l.arraydef.align="baseline -1"}else{if(k==="c"){l.arraydef.align="center"}else{if(k){l.arraydef.align=k}}}}return l},convertDelimiter:function(k){if(k){k=f.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":n++;break;case"}":if(n==0){d.Error("Extra close brace")}if(--n==0){return this.string.slice(k,this.i-1)}break}}d.Error("Missing close brace");break}return this.string.charAt(this.i++)},GetBrackets:function(l,n){if(this.GetNext()!="["){return n}var k=++this.i,m=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":m++;break;case"\\":this.i++;break;case"}":if(m--<=0){d.Error("Extra close brace while looking for ']'")}break;case"]":if(m==0){return this.string.slice(k,this.i-1)}break}}d.Error("Couldn't find closing ']' for argument to "+l)},GetDelimiter:function(k){while(this.nextIsSpace()){this.i++}var l=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(l=="\\"){l+=this.GetCS(k)}if(f.delimiter[l]!=null){return this.convertDelimiter(l)}}d.Error("Missing or unrecognized delimiter for "+k)},GetDimen:function(l){var m;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){m=this.GetArgument(l);if(m.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return m.replace(/ /g,"")}}else{m=this.string.slice(this.i);var k=m.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(k){this.i+=k[0].length;return k[1].replace(/ /g,"")}}d.Error("Missing dimension or its units for "+l)},GetUpTo:function(n,o){while(this.nextIsSpace()){this.i++}var m=this.i,l,q,p=0;while(this.i<this.string.length){l=this.i;q=this.string.charAt(this.i++);switch(q){case"\\":q+=this.GetCS();break;case"{":p++;break;case"}":if(p==0){d.Error("Extra close brace while looking for "+o)}p--;break}if(p==0&&q==o){return this.string.slice(m,l)}}d.Error("Couldn't find "+o+" for "+n)},ParseArg:function(k){return d.Parse(this.GetArgument(k),this.stack.env).mml()},ParseUpTo:function(k,l){return d.Parse(this.GetUpTo(k,l),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="$";l=o}}}else{if(r==="}"&&n==="}"){m.push(h.TeXAtom(d.Parse(q.slice(l,o),{}).mml().With(p)));n="";l=o}else{if(r==="\\"){if(n===""&&q.substr(o).match(/^(eq)?ref\s*\{/)){if(l<o-1){m.push(this.InternalText(q.slice(l,o-1),p))}n="}";l=o-1}else{r=q.charAt(o++);if(r==="("&&n===""){if(l<o-2){m.push(this.InternalText(q.slice(l,o-2),p))}n=")";l=o}else{if(r===")"&&n===")"){m.push(h.TeXAtom(d.Parse(q.slice(l,o-2),{}).mml().With(p)));n="";l=o}}}}}}}if(n!==""){d.Error("Math not terminated in text box")}if(l<q.length){m.push(this.InternalText(q.slice(l),p))}return m},InternalText:function(l,k){l=l.replace(/^\s+/,g).replace(/\s+$/,g);return h.mtext(h.chars(l)).With(k)},SubstituteArgs:function(l,k){var o="";var n="";var p;var m=0;while(m<k.length){p=k.charAt(m++);if(p==="\\"){o+=p+k.charAt(m++)}else{if(p==="#"){p=k.charAt(m++);if(p==="#"){o+=p}else{if(!p.match(/[1-9]/)||p>l.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:"TeX Commands",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(k){var l,m=false,o=MathJax.HTML.getScript(k);var q=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var p={math:o,display:q,script:k};this.prefilterHooks.Execute(p);o=p.math;try{l=d.Parse(o).mml()}catch(n){if(!n.texError){throw n}l=this.formatError(n,o,q,k);m=true}if(l.inferred){l=h.apply(MathJax.ElementJax,l.data)}else{l=h(l)}if(q){l.root.display="block"}if(m){l.texError=true}p.math=l;this.postfilterHooks.Execute(p);return p.math},prefilterMath:function(l,m,k){return l},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(n,m,o,k){var l=n.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",l,m,o,k]);return h.merror(l)},Error:function(k){throw c.Insert(Error(k),{texError:true})},Macro:function(k,l,m){f.macros[k]=["Macro"].concat([].slice.call(arguments,1));f.macros[k].isUser=true},combineRelations:function(o){var p,k,n,l;for(p=0,k=o.data.length;p<k;p++){if(o.data[p]){if(o.isa(h.mrow)){while(p+1<k&&(n=o.data[p])&&(l=o.data[p+1])&&n.isa(h.mo)&&l.isa(h.mo)&&n.Get("texClass")===h.TEXCLASS.REL&&l.Get("texClass")===h.TEXCLASS.REL){if(n.variantForm==l.variantForm&&n.Get("mathvariant")==l.Get("mathvariant")&&n.style==l.style&&n["class"]==l["class"]&&!n.id&&!l.id){n.Append.apply(n,l.data);o.data.splice(p+1,1);k--}else{n.rspace=l.lspace="0pt";p++}}}if(!o.data[p].isToken){this.combineRelations(o.data[p])}}}}});d.prefilterHooks.Add(function(k){k.math=d.prefilterMath(k.math,k.display,k.script)});d.postfilterHooks.Add(function(k){k.math=d.postfilterMath(k.math,k.display,k.script)});d.loadComplete("jax.js")})(MathJax.InputJax.TeX,MathJax.Hub,MathJax.Ajax);

MathJax.Extension["TeX/AMSmath"]={version:"2.0",number:0,startNumber:0,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(h){return h.join("em ")+"em"};d.Add({macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",b.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",b.LENGTH.NEGATIVETHICKMATHSPACE],intI:["Macro","\\mathchoice{\\!}{}{}{}\\!\\!\\int"],iiiint:["MultiIntegral","\\int\\intI\\intI\\intI"],idotsint:["MultiIntegral","\\int\\cdots\\int"],dddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}}",1],ddddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}\\mathord{.}}",1],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:["Macro","\\mathop{\\rm inj\\,lim}"],projlim:["Macro","\\mathop{\\rm proj\\,lim}"],varliminf:["Macro","\\mathop{\\underline{\\rm lim}}"],varlimsup:["Macro","\\mathop{\\overline{\\rm lim}}"],varinjlim:["Macro","\\mathop{\\underrightarrow{\\rm lim\\Rule{-1pt}{0pt}{1pt}}\\Rule{0pt}{0pt}{.45em}}"],varprojlim:["Macro","\\mathop{\\underleftarrow{\\rm 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([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",c([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],multline:["Multline",null,true],"multline*":["Multline",null,false],split:["AMSarray",null,false,false,"rl",c([5/18])],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([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18]),".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]},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(j+" not allowed in "+k.notags+" environment")}if(k.tag){g.Error("Multiple "+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(!f.refUpdate){if(j.label){g.Error("Multiple "+i+"'s")}j.label=h;if(f.labels[h]||f.eqlabels[h]){g.Error("Label '"+h+"' mutiply defined")}f.eqlabels[h]="???"}},HandleRef:function(j,l){var i=this.GetArgument(j);var k=f.labels[i]||f.eqlabels[i];if(!k){k="??";f.badref=!f.refUpdate}var h=k;if(l){h=a.formatTag(h)}if(a.useLabelIds){k=i}this.Push(b.mrow.apply(b,this.InternalMath(h)).With({href:a.formatURL(a.formatID(k)),"class":"MathJax_ref"}))},HandleDeclareOp:function(i){var h=(this.GetStar()?"\\limits":"");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()?"\\limits":"\\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(i+" must come at the beginning of the line")}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("Illegal alignment specified in "+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=b.mfenced(j).With({open:k,close:p})}if(h!==""){var n=(["D","T","S","SS"])[h];if(n==null){g.Error("Bad math style for "+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("Argument to \\begin{"+k.name+"} must me a positive integer")}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("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("Missing or unrecognized delimiter for "+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 i=this.global,h=i.tag;i.tagged=true;if(i.label){f.eqlabels[i.label]=i.tagID;if(a.useLabelIds){h.id=a.formatID(i.label)}}delete i.tag;delete i.tagID;delete i.label;return h}});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(){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("multline rows must have exactly one column")}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},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}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.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.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={}}};MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js");

MathJax.Extension["TeX/AMSsymbols"]={version:"2.0"};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",{variantForm:true}],varnothing:["2205",{variantForm:true}],blacktriangle:"25B2",triangledown:"25BD",blacktriangledown:"25BC",square:"25A1",Box:"25A1",blacksquare:"25A0",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",{variantForm:true}],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",shortmid:["2223",{variantForm:true}],smallfrown:"2322",shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C0",blacktriangleright:"25B6",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.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){b["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}};if(a.msieIE6){MathJax.Hub.Insert(b["-TeX-variant"].remap,{8592:[58049,"-WinIE6"],8594:[58048,"-WinIE6"],8739:[58050,"-WinIE6"],8741:[58051,"-WinIE6"],8764:[58052,"-WinIE6"],9651:[58067,"-WinIE6"]})}}if(a.fontInUse==="STIX"){MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX.Definitions;c.mathchar0mi.varnothing="2205";c.mathchar0mi.hslash="210F";c.mathchar0mi.blacktriangle="25B4";c.mathchar0mi.blacktriangledown="25BE";c.mathchar0mi.square="25FB";c.mathchar0mi.blacksquare="25FC";c.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];c.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];c.mathchar0mo.blacktriangleleft="25C2";c.mathchar0mo.blacktriangleright="25B8";c.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(b["-STIX-variant"],{remap:{10887:57360,10888:57359,8816:57361,8817:57358,8928:57419,8929:57423,8840:57366,8841:57368}})})}});MathJax.Hub.Register.StartupHook("SVG Jax Ready",function(){var b=MathJax.OutputJax.SVG;var a=b.FONTDATA.VARIANT;a["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}}});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js");

(function(b,c){var a;b.Parse=MathJax.Object.Subclass({Init:function(d){this.Parse(d)},Parse:function(g){var h;if(typeof g!=="string"){h=g.parentNode}else{if(g.match(/^<[a-z]+:/i)&&!g.match(/^<[^<>]* xmlns:/)){g=g.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var d=g.match(/^(<math( ('.*?'|".*?"|[^>])+)>)/i);if(d&&d[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){g=d[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+g.substr(d[0].length)}g=g.replace(/^\s*(?:\/\/)?<!(--)?\[CDATA\[((.|\n)*)(\/\/)?\]\]\1>\s*$/,"$2");g=g.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);h=b.ParseXML(g);if(h==null){b.Error("Error parsing MathML")}}var f=h.getElementsByTagName("parsererror")[0];if(f){b.Error("Error parsing MathML: "+f.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,""))}if(h.childNodes.length!==1){b.Error("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){b.Error("Error parsing MathML: "+String(e.nextSibling.nodeValue).replace(/fatal parsing error: /,""))}}if(h.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")!=="math"){b.Error("MathML must be formed by a <math> element, not <"+h.firstChild.nodeName+">")}this.mml=this.MakeMML(h.firstChild)},MakeMML:function(g){var h=String(g.getAttribute("class")||"");var e,f=g.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var d=(h.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(d){e=this.TeXAtom(d[2])}else{if(!(a[f]&&a[f].isa&&a[f].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",f]);return a.merror("Unknown node type: "+f)}else{e=a[f]()}}this.AddAttributes(e,g);this.CheckClass(e,h);this.AddChildren(e,g);if(b.config.useMathMLspacing){e.useMMLspacing=8}return e},TeXAtom:function(e){var d=a.TeXAtom().With({texClass:a.TEXCLASS[e]});if(d.texClass===a.TEXCLASS.OP){d.movesupsub=d.movablelimits=true}return d},CheckClass:function(e,g){g=g.split(/ /);var h=[];for(var f=0,d=g.length;f<d;f++){if(g[f].substr(0,4)==="MJX-"){if(g[f]==="MJX-arrow"){e.arrow=true}else{if(g[f]==="MJX-variant"){e.variantForm=true;if(!MathJax.Extension["TeX/AMSsymbols"]){MathJax.Hub.RestartAfter(MathJax.Ajax.Require("[MathJax]/extensions/TeX/AMSsymbols.js"))}}else{if(g[f].substr(0,11)!=="MJX-TeXAtom"){e.mathvariant=g[f].substr(3);if(e.mathvariant==="-tex-caligraphic-bold"||e.mathvariant==="-tex-oldstyle-bold"){if(!MathJax.Extension["TeX/boldsymbol"]){MathJax.Hub.RestartAfter(MathJax.Ajax.Require("[MathJax]/extensions/TeX/boldsymbol.js"))}}}}}}else{h.push(g[f])}}if(h.length){e["class"]=h.join(" ")}else{delete e["class"]}},AddAttributes:function(f,h){f.attr={};f.attrNames=[];for(var g=0,d=h.attributes.length;g<d;g++){var e=h.attributes[g].name;if(e=="xlink:href"){e="href"}if(e.match(/:/)){continue}var j=h.attributes[g].value;if(j.toLowerCase()==="true"){j=true}else{if(j.toLowerCase()==="false"){j=false}}if(f.defaults[e]!=null||a.copyAttributes[e]){f[e]=j}else{f.attr[e]=j}f.attrNames.push(e)}},AddChildren:function(f,h){for(var g=0,d=h.childNodes.length;g<d;g++){var k=h.childNodes[g];if(k.nodeName==="#comment"){continue}if(k.nodeName==="#text"){if(f.isToken&&!f.mmlSelfClosing){var j=k.nodeValue.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);f.Append(a.chars(this.trimSpace(j)))}else{if(k.nodeValue.match(/\S/)){b.Error("Unexpected text node: '"+k.nodeValue+"'")}}}else{if(f.type==="annotation-xml"){f.Append(a.xml(k))}else{var e=this.MakeMML(k);f.Append(e);if(e.mmlSelfClosing&&e.data.length){f.Append.apply(f,e.data);e.data=[]}}}}},trimSpace:function(d){return d.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/  +/g," ")},replaceEntity:function(f,e){if(e.match(/^(lt|amp|quot)$/)){return f}if(b.Parse.Entity[e]){return b.Parse.Entity[e]}var g=e.charAt(0).toLowerCase();var d=e.match(/^[a-zA-Z](fr|scr|opf)$/);if(d){g=d[1]}if(!b.Parse.loaded[g]){b.Parse.loaded[g]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(b.entityDir+"/"+g+".js"))}return f}},{loaded:[]});b.Augment({sourceMenuTitle:"Original MathML",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(d){if(!this.ParseXML){this.ParseXML=this.createParser()}var e,g,h={script:d};if(d.firstChild&&d.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){h.math=d.firstChild;this.prefilterHooks.Execute(h);g=h.math}else{g=MathJax.HTML.getScript(d);if(c.isMSIE){g=g.replace(/(&nbsp;)+$/,"")}h.math=g;this.prefilterHooks.Execute(h);g=h.math}try{e=b.Parse(g).mml}catch(f){if(!f.mathmlError){throw f}e=this.formatError(f,g,d)}h.math=a(e);this.postfilterHooks.Execute(h);return h.math},prefilterMath:function(e,d){return e},prefilterMathML:function(e,d){return e},formatError:function(g,f,d){var e=g.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",e,f,d]);return a.merror(e)},Error:function(d){throw MathJax.Hub.Insert(Error(d),{mathmlError:true})},parseDOM:function(d){return this.parser.parseFromString(d,"text/xml")},parseMS:function(d){return(this.parser.loadXML(d)?this.parser:null)},parseDIV:function(d){this.div.innerHTML=d.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2></$1>");return this.div},parseError:function(d){return null},createParser:function(){if(window.DOMParser){this.parser=new DOMParser();return(this.parseDOM)}else{if(window.ActiveXObject){var e=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var f=0,d=e.length;f<d&&!this.parser;f++){try{this.parser=new ActiveXObject(e[f])}catch(g){}}if(!this.parser){alert("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.");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)},Startup:function(){a=MathJax.ElementJax.mml;a.mspace.Augment({mmlSelfClosing:true});a.none.Augment({mmlSelfClosing:true});a.mprescripts.Augment({mmlSelfClosing:true})}});b.prefilterHooks.Add(function(d){d.math=(typeof(d.math)==="string"?b.prefilterMath(d.math,d.script):b.prefilterMathML(d.math,d.script))});b.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"};b.loadComplete("jax.js")})(MathJax.InputJax.MathML,MathJax.Hub.Browser);

MathJax.Ajax.loadComplete("[MathJax]/config/Accessible.js");
