/*
 *  /MathJax/config/TeX-AMS-MML_HTMLorMML.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/MathZoom.js",
  "[MathJax]/extensions/MathMenu.js",
  "[MathJax]/jax/element/mml/jax.js",
  "[MathJax]/extensions/toMathML.js",
  "[MathJax]/extensions/TeX/noErrors.js",
  "[MathJax]/extensions/TeX/noUndefined.js",
  "[MathJax]/jax/input/TeX/jax.js",
  "[MathJax]/extensions/TeX/AMSmath.js",
  "[MathJax]/extensions/TeX/AMSsymbols.js",
  "[MathJax]/jax/input/MathML/jax.js"
);

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

MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.1.1",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%"}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js");

MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"1.1.4",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:"1.1.5",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",showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#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.id==="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:"1.1.4",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{scale:100,showMathMenu:true,showMathMenuMSIE:true,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){var h="1.1.1";var a=MathJax.Hub.CombineConfig("MMLorHTML",{prefer:{MSIE:"MML",Firefox:"MML",Opera:"HTML",other:"HTML"}});var e={Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4};var b=(c.Browser.version==="0.0"||c.Browser.versionAtLeast(e[c.Browser]||0));var g=false;if(!c.Browser.isIE9){try{new ActiveXObject("MathPlayer.Factory.1");g=true}catch(f){}}var d=(c.Browser.isFirefox&&c.Browser.versionAtLeast("1.5"))||(c.Browser.isMSIE&&g)||(c.Browser.isOpera&&c.Browser.versionAtLeast("9.52"));c.Register.StartupHook("End Config",function(){var i=(a.prefer&&typeof(a.prefer)==="object"?a.prefer[MathJax.Hub.Browser]||a.prefer.other||"HTML":a.prefer);if(b||d){if(d&&(i==="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.Ajax.loadComplete("[MathJax]/config/MMLorHTML.js");

MathJax.Extension.tex2jax={version:"1.1.3",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments: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}this.createPatterns();this.scanElement(a,a.nextSibling)},createPatterns:function(){var d=[],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])}}this.start=new RegExp(d.sort(this.sortLength).join("|")+(b.processEnvironments?"|\\\\begin\\{([^}]*)\\}":"")+(b.processEscapes?"|\\\\*\\\\\\$":""),"g");this.skipTags=new RegExp("^("+b.skipTags.join("|")+")$","i");this.ignoreClass=new RegExp("(^| )("+b.ignoreClass+")( |$)");this.processClass=new RegExp("(^| )("+b.processClass+")( |$)")},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/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,f){var a,e,d;while(c&&c!=b){if(c.nodeName.toLowerCase()==="#text"){if(!f){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)}if(c.firstChild&&!a.match(/(^| )MathJax/)&&!this.skipTags.exec(e)){d=(f||this.ignoreClass.exec(a))&&!this.processClass.exec(a);this.scanElement(c.firstChild,b,d)}}if(c){c=c.nextSibling}}},scanText:function(b){if(b.nodeValue.replace(/\s+/,"")==""){return b}var a,c;this.search={start:true};this.pattern=this.start;while(b){this.pattern.lastIndex=0;while(b&&b.nodeName.toLowerCase()==="#text"&&(a=this.pattern.exec(b.nodeValue))){if(this.search.start){b=this.startMatch(a,b)}else{b=this.endMatch(a,b)}}if(this.search.matched){b=this.encloseMath(b)}if(b){do{c=b;b=b.nextSibling}while(b&&(b.nodeName.toLowerCase()==="br"||b.nodeName.toLowerCase()==="#comment"));if(!b||b.nodeName!=="#text"){return c}}}return b},startMatch:function(a,b){var f=this.match[a[0]];if(f!=null){this.search={end:f.end,mode:f.mode,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",open:b,olen:0,opos:this.pattern.lastIndex-a[0].length,isBeginEnd:true};this.switchPattern(this.endPattern(this.search.end))}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,b){if(a[0]==this.search.end){this.search.close=b;this.search.cpos=this.pattern.lastIndex;this.search.clen=(this.search.isBeginEnd?0:a[0].length);this.search.matched=true;b=this.encloseMath(b);this.switchPattern(this.start)}return b},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=(a===this.start)},encloseMath:function(b){var a=this.search,f=a.close,e,c;if(a.cpos===f.length){f=f.nextSibling}else{f=f.splitText(a.cpos)}if(!f){e=f=MathJax.HTML.addText(a.close.parentNode,"")}a.close=f;c=(a.opos?a.open.splitText(a.opos):a.open);while(c.nextSibling&&c.nextSibling!==f){if(c.nextSibling.nodeValue!==null){if(c.nextSibling.nodeName==="#comment"){c.nodeValue+=c.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{c.nodeValue+=c.nextSibling.nodeValue}}else{if(this.msieNewlineBug){c.nodeValue+=(c.nextSibling.nodeName.toLowerCase()==="br"?"\n":" ")}else{c.nodeValue+=" "}}c.parentNode.removeChild(c.nextSibling)}var d=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);if(this.config.preview!=="none"){this.createPreview(a.mode,d)}c=this.createMathTag(a.mode,d);this.search={};this.pattern.lastIndex=0;if(e){e.parentNode.removeChild(e)}return c},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(c,a){var b;if(this.config.preview==="TeX"){b=[this.filterTeX(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},filterTeX: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:"1.1.2",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=document.getElementsByTagName("html")[0];if(d){for(var c=0,b=d.attributes.length;c<b;c++){var a=d.attributes[c];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.filterText(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)}},filterText: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(a,c,e,b,h){var i="1.1";var g=a.CombineConfig("MathZoom",{delay:400,styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"font-family":"serif","font-size":"85%","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)"}}});var d=function(j){if(!j){j=window.event}if(j){if(j.preventDefault){j.preventDefault()}if(j.stopPropagation){j.stopPropagation()}j.cancelBubble=true;j.returnValue=false}return false};var f=MathJax.Extension.MathZoom={version:i,settings:a.config.menuSettings,HandleEvent:function(l,j,k){if(!l){l=window.event}if(f.settings.CTRL&&!l.ctrlKey){return true}if(f.settings.ALT&&!l.altKey){return true}if(f.settings.CMD&&!l.metaKey){return true}if(f.settings.Shift&&!l.shiftKey){return true}return f[j](l,k)},Click:function(k,j){if(this.settings.zoom==="Click"){return this.Zoom(j,k)}},DblClick:function(k,j){if(this.settings.zoom==="Double-Click"){return this.Zoom(j,k)}},Mouseover:function(k,j){if(this.settings.zoom==="Hover"){f.oldMouseOver=j.onmouseover;j.onmouseover=null;j.onmousemove=this.Mousemove;j.onmouseout=this.Mouseout;return f.Timer(k,j)}},Mouseout:function(j){this.onmouseover=f.oldMouseOver;delete f.oldMouseOver;this.onmousemove=this.onmouseout=null;f.ClearTimer();return d(j)},Mousemove:function(j){return f.Timer(j||window.event,this)},Timer:function(k,j){this.ClearTimer();this.timer=setTimeout(MathJax.Callback(["Zoom",this,j,{}]),g.delay);return d(k)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer);delete this.timer}},Zoom:function(s,l){this.ClearTimer();this.Remove();var v=s.parentNode;if(v.className==="MathJax_MathContainer"){v=v.parentNode}if(v.parentNode.className==="MathJax_MathContainer"){v=v.parentNode.parentNode}var q=(String(v.className).match(/^MathJax_(MathML|Display)$/)?v:s).nextSibling;var m=a.getJaxFor(q),r=m.root;var o=(b&&m.outputJax.isa(b.constructor)?"HTMLCSS":(h&&m.outputJax.isa(h.constructor)?"MathML":null));if(!o){return}var j=Math.floor(0.85*document.body.clientWidth),p=Math.floor(0.85*document.body.clientHeight);var k=c.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":j+"px","max-height":p+"px"}},[["span"]]]]);var x=k.lastChild,u=x.firstChild,n=k.firstChild;s.parentNode.insertBefore(k,s);if(this.msieZIndexBug){var t=c.Element("img",{src:"about:blank",id:"MathJax_ZoomTracker",style:{width:0,height:0,position:"relative"}});document.body.appendChild(k);k.style.position="absolute";k.style.zIndex=g.styles["#MathJax_ZoomOverlay"]["z-index"];k=t}var w=(this["Zoom"+o])(r,u,s);if(this.msiePositionBug){if(this.msieIE8Bug){u.style.position="absolute";x.style.height=u.offsetHeight;u.style.position="";if(x.offsetHeight<=p&&x.offsetWidth<=j){x.style.overflow="visible"}}if(this.msieWidthBug){x.style.width=Math.min(j,w.w)}else{if(w.w>j){x.style.width=j}}if(x.offsetHeight>p){x.style.Height=p+"px"}if(s.nextSibling){s.parentNode.insertBefore(k,s.nextSibling)}else{v.appendChild(k)}}else{if(this.operaPositionBug){x.style.width=Math.min(j,u.offsetWidth)+"px"}}this.Position(x,w,(o==="MathML"&&v.nodeName.toLowerCase()==="div"));x.style.visibility="";if(this.settings.zoom==="Hover"){n.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}}return d(l)},ZoomHTMLCSS:function(o,q,p){q.className="MathJax";b.idPostfix="-zoom";b.getScales(q,q);o.toHTML(q,q);var r=o.HTMLspanElement().bbox;b.idPostfix="";if(r.width&&r.width!=="100%"){var j=Math.floor(0.85*document.body.clientWidth);q.style.width=j+"px";q.style.display="inline-block";var k=(o.id||"MathJax-Span-"+o.spanID)+"-zoom";var l=document.getElementById(k).firstChild;while(l&&l.style.width!==r.width){l=l.nextSibling}if(l){l.style.width="100%"}}q.appendChild(this.topImg);var n=this.topImg.offsetTop;q.removeChild(this.topImg);var m=(this.msieWidthBug?b.getW(p)*b.em:p.offsetWidth);return{w:r.w*b.em,Y:-n,W:m}},ZoomMathML:function(k,l,m){k.toNativeMML(l,l);var n;l.appendChild(this.topImg);n=this.topImg.offsetTop;l.removeChild(this.topImg);var j=(this.ffMMLwidthBug?m.parentNode:m).offsetWidth;return{w:l.offsetWidth,Y:-n,W:j}},Position:function(p,n,r){var k=this.Resize(),m=k.x,l=k.y,j=n.W;if(this.msiePositionBug){j=-j}if(r&&this.ffMMLcenterBug){j=0}var q=-Math.floor((p.offsetWidth-j)/2),o=n.Y;p.style.left=Math.max(q,20-m)+"px";p.style.top=Math.max(o,20-l)+"px"},Resize:function(l){if(f.onresize){f.onresize(l)}var j=0,o=0,n=document.getElementById("MathJax_ZoomFrame"),k=document.getElementById("MathJax_ZoomOverlay");var m=(f.msieZIndexBug?document.getElementById("MathJax_ZoomTracker"):n);if(f.operaPositionBug){n.style.border="1px solid"}if(m.offsetParent){do{j+=m.offsetLeft;o+=m.offsetTop}while(m=m.offsetParent)}if(f.operaPositionBug){n.style.border=""}if(f.msieZIndexBug){n.style.left=j+"px";n.style.top=o+"px"}k.style.left=(-j)+"px";k.style.top=(-o)+"px";if(f.msiePositionBug){setTimeout(f.SetWH,0)}else{f.SetWH()}return{x:j,y:o}},SetWH:function(){var j=document.getElementById("MathJax_ZoomOverlay");j.style.width=j.style.height="1px";j.style.width=document.body.scrollWidth+"px";j.style.height=document.body.scrollHeight+"px"},Remove:function(k){var l=document.getElementById("MathJax_ZoomFrame");if(l){l.parentNode.removeChild(l);l=document.getElementById("MathJax_ZoomTracker");if(l){l.parentNode.removeChild(l)}if(f.operaRefreshBug){var j=c.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(j)}if(window.removeEventListener){removeEventListener("resize",f.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",f.Resize)}else{window.onresize=f.onresize;delete f.onresize}}}return d(k)}};a.Register.StartupHook("HTML-CSS Jax Ready",function(){b=MathJax.OutputJax["HTML-CSS"];b.Augment({HandleEvent:f.HandleEvent})});a.Register.StartupHook("NativeMML Jax Ready",function(){h=MathJax.OutputJax.NativeMML;h.Augment({HandleEvent:f.HandleEvent,MSIEmouseup:function(l,k,j){if(this.trapUp){delete this.trapUp;return true}if(this.MSIEzoomKeys(l)){return true}return false},MSIEclick:function(l,k,j){if(this.trapClick){delete this.trapClick;return true}if(!this.MSIEzoomKeys(l)){return false}if(!this.settings.zoom.match(/Click/)){return false}return(f.Click(l,k)===false)},MSIEdblclick:function(l,k,j){if(!this.MSIEzoomKeys(l)){return false}return(f.DblClick(l,k)===false)},MSIEmouseover:function(l,k,j){if(this.settings.zoom!=="Hover"){return false}f.Timer(l,k);return true},MSIEmouseout:function(l,k,j){if(this.settings.zoom!=="Hover"){return false}f.ClearTimer();return true},MSIEmousemove:function(l,k,j){if(this.settings.zoom!=="Hover"){return false}f.Timer(l,k);return true},MSIEzoomKeys:function(j){if(this.settings.CTRL&&!j.ctrlKey){return false}if(this.settings.CMD&&!j.metaKey){return false}if(this.settings.ALT&&!j.altKey){return false}if(this.settings.Shift&&!j.shiftKey){return false}return true}})});a.Browser.Select({MSIE:function(j){var k=(document.compatMode==="BackCompat");var l=j.versionAtLeast("8.0")&&document.documentMode>7;f.msiePositionBug=true;f.msieWidthBug=!k;f.msieIE8Bug=l;f.msieZIndexBug=!l;f.msieInlineBlockAlignBug=(!l||k);if(document.documentMode>=9){delete g.styles["#MathJax_Zoom"].filter}},Opera:function(j){f.operaPositionBug=true;f.operaRefreshBug=true},Firefox:function(j){f.ffMMLwidthBug=true;f.ffMMLcenterBug=true}});f.topImg=(f.msieInlineBlockAlignBug?c.Element("img",{style:{width:0,height:0},src:"about:blank"}):c.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(f.operaPositionBug){f.topImg.style.border="1px solid"}MathJax.Callback.Queue(["Styles",e,g.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",e,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML);

(function(b,c,f){var k="1.1.4";MathJax.Extension.MathMenu={version:k};var i=b.Browser.isPC,g=b.Browser.isMSIE;var e=(i?null:"5px");var j=b.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",showRenderer:true,showFontMenu:false,showContext: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:(i?"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":e,"-webkit-border-radius":e,"-moz-border-radius":e,"-khtml-border-radius":e,"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:(i?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(i?"-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":(g?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(g?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(i?"1em":".7em")},".MathJax_MenuLabel":{padding:(i?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(i?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(i?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(i?"Highlight":"#606872"),color:(i?"HighlightText":"white")}}});var d=function(l){if(!l){l=window.event}if(l){if(l.preventDefault){l.preventDefault()}if(l.stopPropagation){l.stopPropagation()}l.cancelBubble=true;l.returnValue=false}return false};var a=MathJax.Menu=MathJax.Object.Subclass({version:k,items:[],posted:false,title:null,margin:5,Init:function(l){this.items=[].slice.call(arguments,0)},With:function(l){if(l){b.Insert(this,l)}return this},Post:function(n,v){if(!n){n=window.event}var t=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var l=document.getElementById("MathJax_MenuFrame");if(!l){l=a.Background(this)}var o=c.addElement(l,"div",{onmouseup:a.Mouseup,ondblclick:this.False,ondragstart:this.False,onselectstart:this.False,oncontextmenu:this.False,menuItem:this,className:"MathJax_Menu"},t);for(var q=0,p=this.items.length;q<p;q++){this.items[q].Create(o)}this.posted=true;o.style.width=(o.offsetWidth+2)+"px";var u=n.pageX,s=n.pageY;if(!u&&!s){u=n.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;s=n.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!v){if(u+o.offsetWidth>document.body.offsetWidth-this.margin){u=document.body.offsetWidth-o.offsetWidth-this.margin}a.skipUp=true}else{var r="left",w=v.offsetWidth;u=v.offsetWidth-2;s=0;while(v&&v!==l){u+=v.offsetLeft;s+=v.offsetTop;v=v.parentNode}if(u+o.offsetWidth>document.body.offsetWidth-this.margin){r="right";u=Math.max(this.margin,u-w-o.offsetWidth+6)}if(!i){o.style["borderRadiusTop"+r]=0;o.style["WebkitBorderRadiusTop"+r]=0;o.style["MozBorderRadiusTop"+r]=0;o.style["KhtmlBorderRadiusTop"+r]=0}}o.style.left=u+"px";o.style.top=s+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return this.False(n)},Remove:function(l,m){var n=document.getElementById("MathJax_MenuFrame");if(n){n.parentNode.removeChild(n);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}},Mouseup:function(l,m){if(a.skipUp){delete a.skipUp}else{this.Remove(l,m)}},False:d},{config:j,div:null,Remove:function(l){a.Event(l,this,"Remove")},Mouseover:function(l){a.Event(l,this,"Mouseover")},Mouseout:function(l){a.Event(l,this,"Mouseout")},Mousedown:function(l){a.Event(l,this,"Mousedown")},Mouseup:function(l){a.Event(l,this,"Mouseup")},Mousemove:function(l){a.Event(l,this,"Mousemove")},Event:function(n,o,l){if(!n){n=window.event}var m=o.menuItem;if(m&&m[l]){return m[l](n,o)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(m){var n=c.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:m,onmousedown:this.Remove}]]);var l=n.firstChild;if(m.msieBackgroundBug){l.style.backgroundColor="white";l.style.filter="alpha(opacity=0)";n.width=n.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{l.style.position="fixed"}return n},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var l=document.getElementById("MathJax_MenuFrame");if(l){l=l.firstChild;l.style.width=l.style.height="1px";l.style.width=document.body.scrollWidth+"px";l.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){c.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=c.Cookie.Get("menu")}});var h=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(m){if(!this.hidden){var l={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:this.False,ondragstart:this.False,onselectstart:this.False,onselectend:this.False,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){l.className+=" MathJax_MenuDisabled"}c.addElement(m,"div",l,this.Label(l,m))}},Mouseover:function(q,s){if(!this.disabled){this.Activate(s)}if(!this.menu||!this.menu.posted){var r=document.getElementById("MathJax_MenuFrame").childNodes,n=s.parentNode.childNodes;for(var o=0,l=n.length;o<l;o++){var p=n[o].menuItem;if(p&&p.menu&&p.menu.posted){p.Deactivate(n[o])}}l=r.length-1;while(l>=0&&s.parentNode.menuItem!==r[l].menuItem){r[l].menuItem.posted=false;r[l].parentNode.removeChild(r[l]);l--}if(this.Timer){this.Timer(q,s)}}},Mouseout:function(l,m){if(!this.menu||!this.menu.posted){this.Deactivate(m)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(l,m){return this.Remove(l,m)},Remove:function(l,m){m=m.parentNode.menuItem;return m.Remove(l,m)},Activate:function(l){this.Deactivate(l);l.className+=" MathJax_MenuActive"},Deactivate:function(l){l.className=l.className.replace(/ MathJax_MenuActive/,"")},With:function(l){if(l){b.Insert(this,l)}return this},False:d});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(l,n,m){this.name=l;this.action=n;this.With(m)},Label:function(l,m){return[this.name]},Mouseup:function(l,m){if(!this.disabled){this.Remove(l,m);this.action.call(this,l)}return this.False(l)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(i&&!b.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(l,n){this.name=l;var m=1;if(!(n instanceof a.ITEM)){this.With(n),m++}this.menu=a.apply(a,[].slice.call(arguments,m))},Label:function(l,m){l.onmousemove=a.Mousemove;this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(l,m){if(this.timer){clearTimeout(this.timer)}l={clientX:l.clientX,clientY:l.clientY};this.timer=setTimeout(MathJax.Callback(["Mouseup",this,l,m]),j.delay)},Mouseup:function(n,p){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(n,p)}else{var o=document.getElementById("MathJax_MenuFrame").childNodes,l=o.length-1;while(l>=0){var q=o[l];q.menuItem.posted=false;q.parentNode.removeChild(q);if(q.menuItem===this.menu){break}l--}}}return this.False(n)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(i?"\u25CF":"\u2713"),Init:function(m,l,n){this.name=m;this.variable=l;this.With(n);if(this.value==null){this.value=this.name}},Label:function(m,n){var l={className:"MathJax_MenuRadioCheck"};if(j.settings[this.variable]!==this.value){l={style:{display:"none"}}}return[["span",l,[this.marker]]," "+this.name]},Mouseup:function(p,q){if(!this.disabled){var r=q.parentNode.childNodes;for(var n=0,l=r.length;n<l;n++){var o=r[n].menuItem;if(o&&o.variable===this.variable){r[n].firstChild.style.display="none"}}q.firstChild.display="";j.settings[this.variable]=this.value;a.cookie[this.variable]=j.settings[this.variable];a.saveCookie();if(this.action){this.action.call(a)}}this.Remove(p,q);return this.False(p)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(m,l,n){this.name=m;this.variable=l;this.With(n)},Label:function(m,n){var l={className:"MathJax_MenuCheck"};if(!j.settings[this.variable]){l={style:{display:"none"}}}return[["span",l,[this.marker]]," "+this.name]},Mouseup:function(l,m){if(!this.disabled){m.firstChild.display=(j.settings[this.variable]?"none":"");j.settings[this.variable]=!j.settings[this.variable];a.cookie[this.variable]=j.settings[this.variable];a.saveCookie();if(this.action){this.action.call(a)}}this.Remove(l,m);return this.False(l)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(l,m){this.name=l;this.With(m)},Label:function(l,m){delete l.onmouseover,delete l.onmouseout;delete l.onmousedown;l.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(l,m){delete l.onmouseover,delete l.onmouseout;delete l.onmousedown;l.className+=" MathJax_MenuRule";return null}});a.About=function(){var o=MathJax.OutputJax["HTML-CSS"]||{fontInUse:""};var q=(o.webFonts?"":"local "),m=(o.webFonts?" web":"");var n=(o.imgFonts?"Image":q+o.fontInUse+m)+" fonts";var l=["MathJax.js v"+MathJax.fileversion,["br"]];l.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(l,MathJax.InputJax,"Input Jax");a.About.GetJax(l,MathJax.OutputJax,"Output Jax");a.About.GetJax(l,MathJax.ElementJax,"Element Jax");l.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(l,MathJax.Extension,"Extension",true);l.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[b.Browser+" v"+b.Browser.version+(o.webFonts?" \u2014 "+o.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var r=MathJax.HTML.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+n,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},l],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var s=(document.documentElement||{});var p=window.innerHeight||s.clientHeight||s.scrollHeight||0;if(a.prototype.msieAboutBug){r.style.width="20em";r.style.position="absolute";r.style.left=Math.floor((document.documentElement.scrollWidth-r.offsetWidth)/2)+"px";r.style.top=(Math.floor((p-r.offsetHeight)/3)+document.body.scrollTop)+"px"}else{r.style.marginLeft=Math.floor(-r.offsetWidth/2)+"px";r.style.top=Math.floor((p-r.offsetHeight)/3)+"px"}};a.About.Remove=function(l){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(l,o,n,m){for(var p in o){if(o.hasOwnProperty(p)&&o[p]){if((m&&o[p].version)||(o[p].isa&&o[p].isa(o))){l.push((o[p].id||p)+" "+n+" v"+o[p].version,["br"])}}}return l};a.Help=function(){window.open(j.helpURL,"MathJaxHelp")};a.ShowSource=function(o){if(!o){o=window.event}var n={screenX:o.screenX,screenY:o.screenY};if(!a.jax){return}if(j.settings.format==="MathML"){var l=MathJax.ElementJax.mml;if(l&&typeof(l.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),o)}catch(m){if(!m.restart){throw m}MathJax.Callback.After([this,arguments.callee,n])}}else{if(!f.loadingToMathML){f.loadingToMathML=true;a.ShowSource.Window(o);MathJax.Callback.Queue(f.Require("[MathJax]/extensions/toMathML.js"),function(){delete f.loadingToMathML},[this,arguments.callee,n]);return}}}else{if(a.jax.originalText==null){alert("No TeX form available");return}a.ShowSource.Text(a.jax.originalText,o)}};a.ShowSource.Window=function(m){if(!a.ShowSource.w){var n=[],l=j.windowSettings;for(var o in l){if(l.hasOwnProperty(o)){n.push(o+"="+l[o])}}a.ShowSource.w=window.open("","_blank",n.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(r,q){var n=a.ShowSource.Window(q);r=r.replace(/^\s*/,"").replace(/\s*$/,"");r=r.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");n.document.open();n.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");n.document.write("<table><tr><td><pre>"+r+"</pre></td></tr></table>");n.document.write("</body></html>");n.document.close();var p=n.document.body.firstChild;var o=(n.outerHeight-n.innerHeight)||30,m=(n.outerWidth-n.innerWidth)||30;m=Math.min(Math.floor(0.5*screen.width),p.offsetWidth+m+25);o=Math.min(Math.floor(0.5*screen.height),p.offsetHeight+o+25);n.resizeTo(m,o);if(q&&q.screenX!=null){var l=Math.max(0,Math.min(q.screenX-Math.floor(m/2),screen.width-m-20)),s=Math.max(0,Math.min(q.screenY-Math.floor(o/2),screen.height-o-20));n.moveTo(l,s)}delete a.ShowSource.w};a.Scale=function(){var m=MathJax.OutputJax["HTML-CSS"],l=MathJax.OutputJax.NativeMML;var o=(m?m.config.scale:l.config.scale);var n=prompt("Scale all mathematics (compared to surrounding text) by",o+"%");if(n){if(n.match(/^\s*\d+\s*%?\s*$/)){n=parseInt(n);if(n){if(n!==o){if(m){m.config.scale=n}if(l){l.config.scale=n}a.cookie.scale=n;a.saveCookie();b.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){f.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var l=b.config.outputJax["jax/mml"];if(l[0]!==j.settings.renderer){MathJax.Callback.Queue(["Require",f,"[MathJax]/jax/output/"+j.settings.renderer+"/config.js"],["Post",b.Startup.signal,j.settings.renderer+" output selected"],[function(){var p=MathJax.OutputJax[j.settings.renderer];for(var o=0,n=l.length;o<n;o++){if(l[o]===p){l.splice(o,1);break}}l.unshift(p)}],["Reprocess",b])}};a.Font=function(){var l=MathJax.OutputJax["HTML-CSS"];if(!l){return}document.location.reload()};b.Browser.Select({MSIE:function(l){var m=(document.compatMode==="BackCompat");var n=l.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:(m||!n),msieAboutBug:m});if(document.documentMode>=9){delete j.styles["#MathJax_About"].filter;delete j.styles[".MathJax_Menu"].filter}}});b.Register.StartupHook("End Config",function(){j.settings=b.config.menuSettings;if(!j.settings.format){j.settings.format=(MathJax.InputJax.TeX?"Original":"MathML")}if(typeof(j.settings.showRenderer)!=="undefined"){j.showRenderer=j.settings.showRenderer}if(typeof(j.settings.showFontMenu)!=="undefined"){j.showFontMenu=j.settings.showFontMenu}if(typeof(j.settings.showContext)!=="undefined"){j.showContext=j.settings.showContext}a.getCookie();a.menu=a(h.COMMAND("Show Source",a.ShowSource),h.SUBMENU("Format",h.RADIO("MathML","format"),h.RADIO("Original","format",{value:"Original"})),h.RULE(),h.SUBMENU("Settings",h.SUBMENU("Zoom Trigger",h.RADIO("Hover","zoom",{action:a.Zoom}),h.RADIO("Click","zoom",{action:a.Zoom}),h.RADIO("Double-Click","zoom",{action:a.Zoom}),h.RADIO("No Zoom","zoom",{value:"None"}),h.RULE(),h.LABEL("Trigger Requires:"),h.CHECKBOX((b.Browser.isMac?"Option":"Alt"),"ALT"),h.CHECKBOX("Command","CMD",{hidden:!b.Browser.isMac}),h.CHECKBOX("Control","CTRL",{hidden:b.Browser.isMac}),h.CHECKBOX("Shift","Shift")),h.SUBMENU("Zoom Factor",h.RADIO("125%","zscale"),h.RADIO("133%","zscale"),h.RADIO("150%","zscale"),h.RADIO("175%","zscale"),h.RADIO("200%","zscale"),h.RADIO("250%","zscale"),h.RADIO("300%","zscale"),h.RADIO("400%","zscale")),h.RULE(),h.SUBMENU("Math Renderer",{hidden:!j.showRenderer},h.RADIO("HTML-CSS","renderer",{action:a.Renderer}),h.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"})),h.SUBMENU("Font Preference",{hidden:!j.showFontMenu},h.LABEL("For HTML-CSS:"),h.RADIO("Auto","font",{action:a.Font}),h.RULE(),h.RADIO("TeX (local)","font",{action:a.Font}),h.RADIO("TeX (web)","font",{action:a.Font}),h.RADIO("TeX (image)","font",{action:a.Font}),h.RULE(),h.RADIO("STIX (local)","font",{action:a.Font})),h.SUBMENU("Contextual Menu",{hidden:!j.showContext},h.RADIO("MathJax","context"),h.RADIO("Browser","context")),h.COMMAND("Scale All Math ...",a.Scale)),h.RULE(),h.COMMAND("About MathJax",a.About),h.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(l){a.cookie.showRenderer=j.showRenderer=l;a.saveCookie();a.menu.items[3].menu.item[3].hidden=!l};a.showFontMenu=function(l){a.cookie.showFontMenu=j.showFontMenu=l;a.saveCookie();a.menu.items[3].menu.items[4].hidden=!l};a.showContext=function(l){a.cookie.showContext=j.showContext=l;a.saveCookie();a.menu.items[3].menu.items[5].hidden=!l};MathJax.Callback.Queue(["Styles",f,j.styles],["Post",b.Startup.signal,"MathMenu Ready"],["loadComplete",f,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax);

MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"1.1.1",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.mode){if(!this.root.display&&this.root.mode==="display"){this.root.display="block"}delete this.root.mode}}},{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},PLANE1:String.fromCharCode(55349)});(function(a){var d=false;var b=true;a.mbase=MathJax.Object.Subclass({type:"base",isToken:d,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:b}))}this.Append.apply(this,arguments)},With:function(f){for(var g in f){if(f.hasOwnProperty(g)){this[g]=f[g]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var g=0,f=arguments.length;g<f;g++){this.SetData(this.data.length,arguments[g])}}},SetData:function(f,g){if(g!=null){if(!(g instanceof a.mbase)){g=(this.isToken?a.chars(g):a.mtext(g))}g.parent=this;g.setInherit(this.inheritFromMe?this:this.inherit)}this.data[f]=g},Parent:function(){var f=this.parent;while(f&&f.inferred){f=f.parent}return f},Get:function(g,k){if(typeof(this[g])!=="undefined"){return this[g]}var h=this.Parent();if(h&&h["adjustChild_"+g]!=null){return(h["adjustChild_"+g])(h.childPosition(this))}var j=this.inherit;var f=j;while(j){if(typeof(j[g])!=="undefined"){var i=j.noInherit[this.type];if(!(i&&i[g])){return j[g]}}f=j;j=j.inherit}if(!k){if(this.defaults[g]===a.AUTO){return this.autoDefault(g)}if(this.defaults[g]!==a.INHERIT&&this.defaults[g]!=null){return this.defaults[g]}if(f){return f.defaults[g]}}return null},hasValue:function(f){return(this.Get(f,true)!=null)},getValues:function(){var g={};for(var h=0,f=arguments.length;h<f;h++){g[arguments[h]]=this.Get(arguments[h])}return g},adjustChild_scriptlevel:function(f){return this.Get("scriptlevel")},adjustChild_displaystyle:function(f){return this.Get("displaystyle")},adjustChild_texprimestyle:function(f){return this.Get("texprimestyle")},childPosition:function(h){if(h.parent.inferred){h=h.parent}for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]===h){return g}}return null},setInherit:function(h){if(h!==this.inherit&&this.inherit==null){this.inherit=h;for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]&&this.data[g].setInherit){this.data[g].setInherit(h)}}}},setTeXclass:function(f){this.getPrevClass(f);return(typeof(this.texClass)!=="undefined"?this:f)},getPrevClass:function(f){if(f){this.prevClass=f.Get("texClass");this.prevLevel=f.Get("scriptlevel")}},updateTeXclass:function(f){if(f){this.prevClass=f.prevClass;delete f.prevClass;this.prevLevel=f.prevLevel;delete f.prevLevel;this.texClass=f.Get("texClass")}},texSpacing:function(){var g=(this.prevClass!=null?this.prevClass:a.TEXCLASS.NONE);var f=(this.Get("texClass")||a.TEXCLASS.ORD);if(g===a.TEXCLASS.NONE||f===a.TEXCLASS.NONE){return""}if(g===a.TEXCLASS.VCENTER){g=a.TEXCLASS.ORD}if(f===a.TEXCLASS.VCENTER){f=a.TEXCLASS.ORD}var h=this.TEXSPACE[g][f];if(this.prevLevel>0&&this.Get("scriptlevel")>0&&h>=0){return""}return this.TEXSPACELENGTH[Math.abs(h)]},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(f){return""},isSpacelike:function(){return d},isEmbellished:function(){return d},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var f=0;f<this.data.length;f++){if(!this.data[f].isSpacelike()){return d}}return b},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(f){if(this.data[0]){f=this.data[0].setTeXclass(f);this.updateTeXclass(this.data[0])}return f},setBaseTeXclasses:function(h){this.getPrevClass(h);this.texClass=null;if(this.isEmbellished()){h=this.data[0].setTeXclass(h);this.updateTeXclass(this.Core())}else{if(this.data[0]){this.data[0].setTeXclass()}h=this}for(var g=1,f=this.data.length;g<f;g++){if(this.data[g]){this.data[g].setTeXclass()}}return h},setSeparateTeXclasses:function(h){this.getPrevClass(h);for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]){this.data[g].setTeXclass()}}if(this.isEmbellished()){this.updateTeXclass(this.Core())}return this}});a.mi=a.mbase.Subclass({type:"mi",isToken:b,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.AUTO,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT},autoDefault:function(g){if(g==="mathvariant"){var f=(this.data[0]||"").toString();return(f.length===1||(f.length===2&&f.charCodeAt(0)===this.PLANE1)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""}});a.mn=a.mbase.Subclass({type:"mn",isToken:b,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:b,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:d,separator:d,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:d,symmetric:b,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:d,movablelimits:d,accent:d,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(h,o){var n=this.def;if(!n){if(h==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var l=this.data.join("");var g=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var j=0,f=g.length;j<f;j++){var k=this.OPTABLE[g[j]][l];if(k){n=this.makeDef(k);break}}if(!n){n=this.CheckRange(l)}if(!n&&o){n={}}else{if(!n){n=MathJax.Hub.Insert({},this.defaultDef)}n.form=g[0];this.def=n}}this.useMMLspacing&=~(this.SPACE_ATTR[h]||0);if(n[h]!=null){return n[h]}else{if(!o){return this.defaultDef[h]}}return""},CheckRange:function(k){var l=k.charCodeAt(0);if(k.charAt(0)===a.PLANE1){l=k.charCodeAt(1)+119808-56320}for(var h=0,f=this.RANGES.length;h<f&&this.RANGES[h][0]<=l;h++){if(l<=this.RANGES[h][1]){if(this.RANGES[h][3]){var g=a.optableDir+"/"+this.RANGES[h][3]+".js";this.RANGES[h][3]=null;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(g))}var j=(["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER"])[this.RANGES[h][2]];j=this.OPTABLE.infix[k]=a.mo.OPTYPES[j==="BIN"?"BIN3":j];return this.makeDef(j)}}return null},makeDef:function(g){if(g[2]==null){g[2]=this.defaultDef.texClass}if(!g[3]){g[3]={}}var f=MathJax.Hub.Insert({},g[3]);f.lspace=this.SPACE[g[0]];f.rspace=this.SPACE[g[1]];f.texClass=g[2];return f},getForm:function(){var f=this,h=this.parent,g=this.Parent();while(g&&g.isEmbellished()){f=h;h=g.parent;g=g.Parent()}if(h&&h.type==="mrow"&&h.NonSpaceLength()!==1){if(h.FirstNonSpace()===f){return a.FORM.PREFIX}if(h.LastNonSpace()===f){return a.FORM.POSTFIX}}return a.FORM.INFIX},isEmbellished:function(){return b},lineBreak:function(){var f=this.getValues("linebreak","linebreakstyle");if(f.linebreak===a.LINEBREAK.NEWLINE){if(f.linebreakstyle===a.LINEBREAKSTYLE.INFIXLINEBREAKSTYLE){f.linebreakstyle=this.Get("infixlinebreakstyle")}return f.linebreakstyle}return"none"},setTeXclass:function(f){this.getValues("lspace","rspace");if(this.useMMLspacing){this.texClass=a.TEXCLASS.NONE;return this}this.texClass=this.Get("texClass");if(f){this.prevClass=f.texClass||a.TEXCLASS.ORD;this.prevLevel=f.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)){f.texClass=this.prevClass=a.TEXCLASS.ORD}}return this}});a.mtext=a.mbase.Subclass({type:"mtext",isToken:b,isSpacelike:function(){return b},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:b,isSpacelike:function(){return b},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"0em",height:"0ex",depth:"0ex",linebreak:a.LINEBREAK.AUTO},lineBreak:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE?a.LINEBREAKSTYLE.AFTER:"none")}});a.ms=a.mbase.Subclass({type:"ms",isToken:b,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:b,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:d,isEmbellished:function(){var g=d;for(var h=0,f=this.data.length;h<f;h++){if(this.data[h]==null){continue}if(this.data[h].isEmbellished()){if(g){return d}g=b;this.core=h}else{if(!this.data[h].isSpacelike()){return d}}}return g},NonSpaceLength:function(){var h=0;for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]&&!this.data[g].isSpacelike()){h++}}return h},FirstNonSpace:function(){for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]&&!this.data[g].isSpacelike()){return this.data[g]}}return null},LastNonSpace:function(){for(var f=this.data.length-1;f>=0;f--){if(this.data[0]&&!this.data[f].isSpacelike()){return this.data[f]}}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(h){for(var g=0,f=this.data.length;g<f;g++){if(this.data[g]){h=this.data[g].setTeXclass(h)}}if(this.data[0]){this.updateTeXclass(this.data[0])}return h}});a.mfrac=a.mbase.Subclass({type:"mfrac",num:0,den:1,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:d},adjustChild_displaystyle:function(f){return d},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(!this.Get("displaystyle")||f>0){f++}return f},adjustChild_texprimestyle:function(f){if(f==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:b,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(f){return b}});a.mroot=a.mbase.Subclass({type:"mroot",texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(f){if(f===1){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g===1){f+=2}return f},adjustChild_texprimestyle:function(f){if(f===0){return b}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:b,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(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,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:b,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(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length<this.data.length){g.separators+=g.separators.charAt(g.separators.length-1)}}if(this.data[0]){j=this.data[0].setTeXclass(j)}for(var h=1,f=this.data.length;h<f;h++){if(this.data[h]){if(g.separators!==""){this.SetData("sep"+h,a.mo(g.separators.charAt(h-1)));j=this.data["sep"+h].setTeXclass(j)}j=this.data[h].setTeXclass(j)}}if(g.close!==""){this.SetData("close",a.mo(g.close).With({stretchy:true,texClass:a.TEXCLASS.CLOSE}));j=this.data.close.setTeXclass(j)}this.updateTeXclass(this.data.open);return j}});a.menclose=a.mbase.Subclass({type:"menclose",inferRow:b,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,notation:a.NOTATION.LONGDIV,texClass:a.TEXCLASS.ORD},setTeXclass:a.mbase.setSeparateTeXclasses});a.msubsup=a.mbase.Subclass({type:"msubsup",base:0,sub:1,sup:2,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,subscriptshift:"",superscriptshift:"",texClass:a.AUTO},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}return 0},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}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(f){if(f%2===1){return b}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"],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(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}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:b,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:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},Append:function(){for(var g=0,f=arguments.length;g<f;g++){if(!((arguments[g] instanceof a.mtr)||(arguments[g] instanceof a.mlabeledtr))){arguments[g]=a.mtd(arguments[g])}}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:b,noInherit:{mrow:{rowalign:b,columnalign:b,groupalign:b},mtable:{rowalign:b,columnalign:b,groupalign:b}},Append:function(){for(var g=0,f=arguments.length;g<f;g++){if(!(arguments[g] instanceof a.mtd)){arguments[g]=a.mtd(arguments[g])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtd=a.mbase.Subclass({type:"mtd",inferRow:b,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 b},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:b,noInherit:{mrow:{groupalign:b},mtable:{groupalign:b}}});a.malignmark=a.mbase.Subclass({type:"malignmark",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,edge:a.SIDE.LEFT},isSpacelike:function(){return b}});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(f){return this.selected().setTeXclass(f)}});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:b,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a["annotation-xml"]=a.mbase.Subclass({type:"annotation-xml",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,decimalseparator:".",texprimestyle:d},autoDefault:function(f){if(f==="displaystyle"){return this.Get("display")==="block"}return""},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 f=this.value();if(f<=65535){return String.fromCharCode(f)}return this.PLANE1+String.fromCharCode(f-119808+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 g=0,f=arguments.length;g<f;g++){var h=this.Import(arguments[g]);this.data.push(h);this.div.appendChild(h)}},Import:function(k){if(document.importNode){return document.importNode(k,true)}var g,h,f;if(k.nodeType===1){g=document.createElement(k.nodeName);if(k.className){g.className=iNode.className}for(h=0,f=k.attributes.length;h<f;h++){var j=k.attributes[h];if(j.specified&&j.nodeValue!=null&&j.nodeValue!=""){g.setAttribute(j.nodeName,j.nodeValue)}if(j.nodeName==="style"){g.style.cssText=j.nodeValue}}if(k.className){g.className=k.className}}else{if(k.nodeType===3||k.nodeType===4){g=document.createTextNode(k.nodeValue)}else{if(k.nodeType===8){g=document.createComment(k.nodeValue)}else{return document.createTextNode("")}}}for(h=0,f=k.childNodes.length;h<f;h++){g.appendChild(this.Import(k.childNodes[h]))}return g},value:function(){return this.div},toString:function(){return this.div.innerHTML}});a.TeXAtom=a.mbase.Subclass({type:"texatom",inferRow:b,texClass:a.TEXCLASS.ORD,setTeXclass:function(f){this.getPrevClass(f);this.data[0].setTeXclass();return this}});a.NULL=a.mbase().With({type:"null"});var c=a.TEXCLASS;var e={ORD:[0,0,c.ORD],ORD11:[1,1,c.ORD],ORD21:[2,1,c.ORD],ORD02:[0,2,c.ORD],ORD55:[5,5,c.ORD],OP:[1,2,c.OP,{largeop:true,movablelimits:true,symmetric:true}],OPFIXED:[1,2,c.OP,{largeop:true,movablelimits:true}],INTEGRAL:[0,1,c.OP,{largeop:true,symmetric:true}],INTEGRAL2:[1,2,c.OP,{largeop:true,symmetric:true}],BIN3:[3,3,c.BIN],BIN4:[4,4,c.BIN],BIN01:[0,1,c.BIN],TALLBIN:[4,4,c.BIN,{stretchy:true}],BINOP:[4,4,c.BIN,{largeop:true,movablelimits:true}],REL:[5,5,c.REL],REL1:[1,1,c.REL,{stretchy:true}],REL4:[4,4,c.REL],WIDEREL:[5,5,c.REL,{stretchy:true}],RELACCENT:[5,5,c.REL,{accent:true,stretchy:true}],OPEN:[0,0,c.OPEN,{fence:true,stretchy:true,symmetric:true}],CLOSE:[0,0,c.CLOSE,{fence:true,stretchy:true,symmetric:true}],INNER:[0,0,c.INNER],PUNCT:[0,3,c.PUNCT],ACCENT:[0,0,c.ORD,{accent:true}],WIDEACCENT:[0,0,c.ORD,{accent:true,stretchy:true}]};a.mo.Augment({SPACE:["0em","0.1111em","0.1667em","0.2222em","0.2667em","0.3333em"],RANGES:[[32,127,c.REL,"BasicLatin"],[160,255,c.ORD,"Latin1Supplement"],[256,383,c.ORD],[384,591,c.ORD],[688,767,c.ORD,"SpacingModLetters"],[768,879,c.ORD,"CombDiacritMarks"],[880,1023,c.ORD,"GreekAndCoptic"],[7680,7935,c.ORD],[8192,8303,c.PUNCT,"GeneralPunctuation"],[8304,8351,c.ORD],[8352,8399,c.ORD],[8400,8447,c.ORD,"CombDiactForSymbols"],[8448,8527,c.ORD,"LetterlikeSymbols"],[8528,8591,c.ORD],[8592,8703,c.REL,"Arrows"],[8704,8959,c.BIN,"MathOperators"],[8960,9215,c.ORD,"MiscTechnical"],[9312,9471,c.ORD],[9632,9727,c.ORD,"GeometricShapes"],[9984,10175,c.ORD,"Dingbats"],[10176,10223,c.ORD,"MiscMathSymbolsA"],[10496,10623,c.REL,"SupplementalArrowsB"],[10624,10751,c.ORD,"MiscMathSymbolsB"],[10752,11007,c.BIN,"SuppMathOperators"],[11008,11263,c.ORD],[119808,120831,c.ORD]],OPTABLE:{prefix:{"\u2111":e.ORD11,"\u2113":e.ORD11,"\u211C":e.ORD11,"\u2200":e.ORD21,"\u2202":e.ORD21,"\u2203":e.ORD21,"\u2207":e.ORD21,"\u220F":e.OP,"\u2210":e.OP,"\u2211":e.OP,"\u2212":e.BIN01,"\u2213":e.BIN01,"\u221A":[1,1,c.ORD,{stretchy:true}],"\u2220":e.ORD,"\u222B":e.INTEGRAL,"\u222E":e.INTEGRAL,"\u22C0":e.OP,"\u22C1":e.OP,"\u22C2":e.OP,"\u22C3":e.OP,"\u2308":e.OPEN,"\u230A":e.OPEN,"\u27E8":e.OPEN,"\u2A00":e.OP,"\u2A01":e.OP,"\u2A02":e.OP,"\u2A04":e.OP,"\u2A06":e.OP,"\u00AC":e.ORD21,"\u00B1":e.BIN01,"(":e.OPEN,"+":e.BIN01,"-":e.BIN01,"[":e.OPEN,"{":e.OPEN,"|":e.OPEN},postfix:{"!":[1,0,c.CLOSE],"&":e.ORD,"\u2032":e.ORD02,"\u203E":e.WIDEACCENT,"\u2309":e.CLOSE,"\u230B":e.CLOSE,"\u23DE":e.WIDEACCENT,"\u23DF":e.WIDEACCENT,"\u266D":e.ORD02,"\u266E":e.ORD02,"\u266F":e.ORD02,"\u27E9":e.CLOSE,"\u02C6":e.WIDEACCENT,"\u02C7":e.WIDEACCENT,"\u02D8":e.ACCENT,"\u02D9":e.ACCENT,"\u02DC":e.WIDEACCENT,"\u0302":e.ACCENT,"\u00A8":e.ACCENT,"\u00AF":e.WIDEACCENT,")":e.CLOSE,"]":e.CLOSE,"^":e.WIDEACCENT,_:e.WIDEACCENT,"`":e.ACCENT,"|":e.CLOSE,"}":e.CLOSE,"~":e.WIDEACCENT},infix:{"%":[3,3,c.ORD],"\u2022":e.BIN4,"\u2026":e.INNER,"\u2044":e.TALLBIN,"\u2061":e.ORD,"\u2062":e.ORD,"\u2063":[0,0,c.ORD,{separator:true}],"\u2064":e.ORD,"\u2190":e.RELACCENT,"\u2191":e.WIDEREL,"\u2192":e.RELACCENT,"\u2193":e.WIDEREL,"\u2194":e.RELACCENT,"\u2195":e.WIDEREL,"\u2196":e.WIDEREL,"\u2197":e.WIDEREL,"\u2198":e.WIDEREL,"\u2199":e.WIDEREL,"\u21A6":e.WIDEREL,"\u21A9":e.WIDEREL,"\u21AA":e.WIDEREL,"\u21BC":e.RELACCENT,"\u21BD":e.WIDEREL,"\u21C0":e.RELACCENT,"\u21C1":e.WIDEREL,"\u21CC":e.WIDEREL,"\u21D0":e.WIDEREL,"\u21D1":e.WIDEREL,"\u21D2":e.WIDEREL,"\u21D3":e.WIDEREL,"\u21D4":e.WIDEREL,"\u21D5":e.WIDEREL,"\u2208":e.REL,"\u2209":e.REL,"\u220B":e.REL,"\u2212":e.BIN4,"\u2213":e.BIN4,"\u2215":e.TALLBIN,"\u2216":e.BIN4,"\u2217":e.BIN4,"\u2218":e.BIN4,"\u2219":e.BIN4,"\u221D":e.REL,"\u2223":e.REL,"\u2225":e.REL,"\u2227":e.BIN4,"\u2228":e.BIN4,"\u2229":e.BIN4,"\u222A":e.BIN4,"\u223C":e.REL,"\u2240":e.BIN4,"\u2243":e.REL,"\u2245":e.REL,"\u2248":e.REL,"\u224D":e.REL,"\u2250":e.REL,"\u2260":e.REL,"\u2261":e.REL,"\u2264":e.REL,"\u2265":e.REL,"\u226A":e.REL,"\u226B":e.REL,"\u227A":e.REL,"\u227B":e.REL,"\u2282":e.REL,"\u2283":e.REL,"\u2286":e.REL,"\u2287":e.REL,"\u228E":e.BIN4,"\u2291":e.REL,"\u2292":e.REL,"\u2293":e.BIN4,"\u2294":e.BIN4,"\u2295":e.BIN4,"\u2296":e.BIN4,"\u2297":e.BIN4,"\u2298":e.BIN4,"\u2299":e.BIN4,"\u22A2":e.REL,"\u22A3":e.REL,"\u22A4":e.ORD55,"\u22A5":e.REL,"\u22A8":e.REL,"\u22C4":e.BIN4,"\u22C5":e.BIN4,"\u22C6":e.BIN4,"\u22C8":e.REL,"\u22EE":e.ORD55,"\u22EF":e.INNER,"\u22F1":[5,5,c.INNER],"\u2500":[0,0,c.ORD,{stretchy:true}],"\u25B3":e.BIN4,"\u25B5":e.BIN4,"\u25B9":e.BIN4,"\u25BD":e.BIN4,"\u25BF":e.BIN4,"\u25C3":e.BIN4,"\u2758":[4,4,c.REL,{fence:true,stretchy:true,symmetric:true}],"\u27F5":e.REL1,"\u27F6":e.REL1,"\u27F7":e.REL1,"\u27F8":e.REL1,"\u27F9":e.REL1,"\u27FA":e.REL1,"\u2A2F":e.BIN4,"\u2A3F":e.BIN4,"\u2AAF":e.REL,"\u2AB0":e.REL,"\u00B1":e.BIN4,"\u00B7":e.BIN4,"\u00D7":e.BIN4,"\u00F7":e.BIN4,"*":e.BIN3,"+":e.BIN4,",":[0,3,c.PUNCT,{separator:true}],"-":e.BIN4,".":[3,3,c.ORD],"/":e.ORD11,":":[1,2,c.REL],";":[0,3,c.PUNCT,{separator:true}],"<":e.REL,"=":e.REL,">":e.REL,"?":[1,1,c.CLOSE],"\\":e.ORD,_:e.ORD11,"|":[2,2,c.ORD,{fence:true,stretchy:true,symmetric:true}],"#":e.ORD,"$":e.ORD,"\u002E":[0,3,c.PUNCT,{separator:true}],"\u02B9":e.ORD,"\u02C9":e.ACCENT,"\u02CA":e.ACCENT,"\u02CB":e.ACCENT,"\u0300":e.ACCENT,"\u0301":e.ACCENT,"\u0303":e.WIDEACCENT,"\u0304":e.ACCENT,"\u0306":e.ACCENT,"\u0307":e.ACCENT,"\u0308":e.ACCENT,"\u030C":e.ACCENT,"\u0332":e.WIDEACCENT,"\u0338":e.REL4,"\u2015":[0,0,c.ORD,{stretchy:true}],"\u2017":[0,0,c.ORD,{stretchy:true}],"\u2020":e.BIN3,"\u2021":e.BIN3,"\u20D7":e.ACCENT,"\u2118":e.ORD,"\u2205":e.ORD,"\u221E":e.ORD,"\u2305":e.BIN3,"\u2306":e.BIN3,"\u2322":e.REL4,"\u2323":e.REL4,"\u2329":e.OPEN,"\u232A":e.CLOSE,"\u23AA":e.ORD,"\u23AF":[0,0,c.ORD,{stretchy:true}],"\u23B0":e.OPEN,"\u23B1":e.CLOSE,"\u25EF":e.BIN3,"\u2660":e.ORD,"\u2661":e.ORD,"\u2662":e.ORD,"\u2663":e.ORD,"\u27EE":e.OPEN,"\u27EF":e.CLOSE,"\u27FC":e.REL4,"\u3008":e.OPEN,"\u3009":e.CLOSE,"\uFE37":e.WIDEACCENT,"\uFE38":e.WIDEACCENT}}},{OPTYPES:e})})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js");

MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="1.1.1";var a=MathJax.ElementJax.mml;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.MathMLattributes();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+">"},MathMLattributes:function(){var j=[],g=this.defaults;var c=this.copyAttributes,l=this.skipAttributes;if(this.type==="math"){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}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.quoteHTML(k)+'"')}this[d]=k}}}for(var h=0,f=c.length;h<f;h++){if(this[c[h]]!=null){j.push(c[h]+'="'+this.quoteHTML(this[c[h]])+'"')}}if(j.length){return" "+j.join(" ")}else{return""}},copyAttributes:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],skipAttributes:{texClass:1,useHeight:1,texprimestyle:1},quoteHTML: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.MathMLattributes();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.MathMLattributes();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(c){return c+"<mrow>\n"+this.data[0].toMathML(c+"  ")+"\n"+c+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.quoteHTML(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(){var c="1.1";var a=MathJax.Hub.CombineConfig("TeX.noErrors",{multiLine:true,inlineDelimiters:["",""],style:{"font-family":"serif","font-size":"80%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var b="\u00A0";MathJax.Extension["TeX/noErrors"]={version:c,config:a};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){MathJax.InputJax.TeX.Augment({formatError:function(f,e,g,d){var i=a.inlineDelimiters;var h=(g||a.multiLine);if(!g){e=i[0]+e+i[1]}if(h){e=e.replace(/ /g,b)}else{e=e.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(e).With({isError:true,multiLine:h})}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Config",function(){MathJax.Hub.Config({"HTML-CSS":{styles:{".MathJax .merror":MathJax.Hub.Insert({"font-style":null,"background-color":null,"vertical-align":(MathJax.Hub.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})})})();MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.ElementJax.mml;var b=MathJax.OutputJax["HTML-CSS"];var c=a.math.prototype.toHTML;a.math.Augment({toHTML:function(d,e){if(this.data[0]&&this.data[0].data[0]&&this.data[0].data[0].isError){return this.data[0].data[0].toHTML(d)}return c.call(this,d,e)}});a.merror.Augment({toHTML:function(j){if(!this.isError){return a.mbase.prototype.toHTML.call(this,j)}j=this.HTMLcreateSpan(j);if(this.multiLine){j.style.display="inline-block"}var l=this.data[0].data[0].data.join("").split(/\n/);for(var g=0,e=l.length;g<e;g++){b.addText(j,l[g]);if(g!==e-1){b.addElement(j,"br")}}var n=b.getHD(j.parentNode),d=b.getW(j.parentNode);if(e>1){var k=(n.h+n.d)/2,h=b.TeX.x_height/2;var f=b.config.styles[".MathJax .merror"]["font-size"];if(f&&f.match(/%/)){h*=parseInt(f)/100}j.parentNode.style.verticalAlign=b.Em(n.d+(h-k));n.h=h+k;n.d=k-h}j.bbox={h:n.h,d:n.d,w:d,lw:0,rw:d};return j}});MathJax.Hub.Startup.signal.Post("TeX noErrors Ready")});MathJax.Hub.Register.StartupHook("NativeMML Jax Ready",function(){var b=MathJax.ElementJax.mml;var a=MathJax.Extension["TeX/noErrors"].config;var c=b.math.prototype.toNativeMML;b.math.Augment({toNativeMML:function(d){if(this.data[0]&&this.data[0].data[0]&&this.data[0].data[0].isError){return this.data[0].data[0].toNativeMML(d)}return c.call(this,d)}});b.merror.Augment({toNativeMML:function(g){if(!this.isError){return b.mbase.prototype.toNativeMML.call(this,g)}g=g.appendChild(document.createElement("span"));var h=this.data[0].data[0].data.join("").split(/\n/);for(var f=0,e=h.length;f<e;f++){g.appendChild(document.createTextNode(h[f]));if(f!==e-1){g.appendChild(document.createElement("br"))}}if(this.multiLine){g.style.display="inline-block";if(e>1){g.style.verticalAlign="middle"}}for(var j in a.style){if(a.style.hasOwnProperty(j)){var d=j.replace(/-./g,function(i){return i.charAt(1).toUpperCase()});g.style[d]=a.style[j]}}return g}});MathJax.Hub.Startup.signal.Post("TeX noErrors Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js");

MathJax.Extension["TeX/noUndefined"]={version:"1.1",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(c){this.Push(a.mtext(c).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js");

(function(d){var c=true,f=false,i,h=String.fromCharCode(160);var e=MathJax.Object.Subclass({Init:function(k){this.global={};this.data=[b.start().With({global:this.global})];if(k){this.data[0].env=k}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 i.mbase){n=b.mml(n)}n.global=this.global;o=(this.data.length?this.Top().checkItem(n):c);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=c}if(this.data.length===1&&!l){return this.data[0]}return i.mrow.apply(i,this.data).With((k?{inferred:c}:{}))},checkItem:function(k){if(k.type==="over"&&this.isOpen){k.num=this.mmlData(f);this.data=[]}if(k.type==="cell"&&this.isOpen){d.Error("Misplaced "+k.name)}if(k.isClose&&this[k.type+"Error"]){d.Error(this[k.type+"Error"])}if(!k.isNotStack){return c}this.Push(k.data[0]);return f},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:c,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:c});b.open=b.Subclass({type:"open",isOpen:c,stopError:"Extra open brace or missing close brace",checkItem:function(l){if(l.type==="close"){var k=this.mmlData();return b.mml(i.TeXAtom(k))}return this.SUPER(arguments).checkItem.call(this,l)}});b.close=b.Subclass({type:"close",isClose:c});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 c}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:c,name:"\\over",checkItem:function(m,k){if(m.type==="over"){d.Error("Ambiguous use of "+m.name)}if(m.isClose){var l=i.mfrac(this.num,this.mmlData(f));if(this.thickness!=null){l.linethickness=this.thickness}if(this.open||this.close){l.texClass=i.TEXCLASS.INNER;l.texWithDelims=c;l=i.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:c,delim:"(",stopError:"Extra \\left or missing \\right",checkItem:function(l){if(l.type==="right"){var k=i.mfenced(this.data.length===1?this.data[0]:i.mrow.apply(i,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:c,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:c,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:c});b.style=b.Subclass({type:"style",checkItem:function(l){if(!l.isClose){return this.SUPER(arguments).checkItem.call(this,l)}var k=i.mstyle.apply(i,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=i.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:c,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(l){if(l.isClose&&l.type!=="over"){if(l.isEntry){this.EndEntry();this.clearEnv();return f}if(l.isCR){this.EndEntry();this.EndRow();this.clearEnv();return f}this.EndTable();this.clearEnv();var k=i.mtable.apply(i,this.table).With(this.arraydef);if(this.open||this.close){k=i.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(i.mtd.apply(i,this.data));this.data=[]},EndRow:function(){this.table.push(i.mtr.apply(i,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var k=this.arraydef.rowlines.split(/ /);if(k.length===this.table.length){this.arraydef.frame=k.pop();this.arraydef.rowlines=k.join(" ")}else{if(k.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}},clearEnv:function(){for(var k in this.env){if(this.env.hasOwnProperty(k)){delete this.env[k]}}}});b.cell=b.Subclass({type:"cell",isClose:c});b.mml=b.Subclass({type:"mml",isNotStack:c,Push:function(){for(var l=0,k=arguments.length;l<k;l++){if(arguments[l].type!=="mo"&&arguments[l].isEmbellished()){arguments[l]=i.TeXAtom(arguments[l]).With({isEmbellishedWrapper:c})}}this.data.push.apply(this.data,arguments)},Add:function(){this.data.push.apply(this.data,arguments);return this}});var g={};var j=function(){i=MathJax.ElementJax.mml;MathJax.Hub.Insert(g,{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:i.VARIANT.NORMAL}],hbar:"210F",imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:i.VARIANT.NORMAL}],Re:["211C",{mathvariant:i.VARIANT.NORMAL}],Im:["2111",{mathvariant:i.VARIANT.NORMAL}],partial:["2202",{mathvariant:i.VARIANT.NORMAL}],infty:["221E",{mathvariant:i.VARIANT.NORMAL}],prime:["2032",{mathvariant:i.VARIANT.NORMAL}],emptyset:["2205",{mathvariant:i.VARIANT.NORMAL}],nabla:["2207",{mathvariant:i.VARIANT.NORMAL}],top:["22A4",{mathvariant:i.VARIANT.NORMAL}],bot:["22A5",{mathvariant:i.VARIANT.NORMAL}],angle:["2220",{mathvariant:i.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:i.VARIANT.NORMAL}],backslash:["2216",{mathvariant:i.VARIANT.NORMAL}],forall:["2200",{mathvariant:i.VARIANT.NORMAL}],exists:["2203",{mathvariant:i.VARIANT.NORMAL}],neg:["00AC",{mathvariant:i.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:i.VARIANT.NORMAL}],flat:["266D",{mathvariant:i.VARIANT.NORMAL}],natural:["266E",{mathvariant:i.VARIANT.NORMAL}],sharp:["266F",{mathvariant:i.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:i.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:i.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:i.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:i.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigvee:["22C1",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigwedge:["22C0",{texClass:i.TEXCLASS.OP,movesupsub:c}],biguplus:["2A04",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigcap:["22C2",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigcup:["22C3",{texClass:i.TEXCLASS.OP,movesupsub:c}],"int":["222B",{texClass:i.TEXCLASS.OP}],intop:["222B",{texClass:i.TEXCLASS.OP,movesupsub:c,movablelimits:c}],iint:["222C",{texClass:i.TEXCLASS.OP}],iiint:["222D",{texClass:i.TEXCLASS.OP}],prod:["220F",{texClass:i.TEXCLASS.OP,movesupsub:c}],sum:["2211",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigotimes:["2A02",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigoplus:["2A01",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigodot:["2A00",{texClass:i.TEXCLASS.OP,movesupsub:c}],oint:["222E",{texClass:i.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:i.TEXCLASS.OP,movesupsub:c}],smallint:["222B",{largeop:f}],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:f}],oslash:["2298",{largeop:f}],otimes:["2297",{largeop:f}],ominus:["2296",{largeop:f}],oplus:["2295",{largeop:f}],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:"0338",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",dots:"2026",dotsc:"2026",dotsb:"22EF",dotsm:"22EF",dotsi:"22EF",dotso:"2026",ldotp:["002E",{texClass:i.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:i.TEXCLASS.PUNCT}],colon:["003A",{texClass:i.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:i.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:i.TEXCLASS.ORD}],"\\|":["2225",{texClass:i.TEXCLASS.ORD}],"\\vert":["|",{texClass:i.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",c,0],textstyle:["SetStyle","T",f,0],scriptstyle:["SetStyle","S",f,1],scriptscriptstyle:["SetStyle","SS",f,2],rm:["SetFont",i.VARIANT.NORMAL],mit:["SetFont",i.VARIANT.ITALIC],oldstyle:["SetFont",i.VARIANT.OLDSTYLE],cal:["SetFont",i.VARIANT.CALIGRAPHIC],it:["SetFont",i.VARIANT.ITALIC],bf:["SetFont",i.VARIANT.BOLD],bbFont:["SetFont",i.VARIANT.DOUBLESTRUCK],scr:["SetFont",i.VARIANT.SCRIPT],frak:["SetFont",i.VARIANT.FRAKTUR],sf:["SetFont",i.VARIANT.SANSSERIF],tt:["SetFont",i.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:["NamedOp",0],arccos:["NamedOp",0],arctan:["NamedOp",0],arg:["NamedOp",0],cos:["NamedOp",0],cosh:["NamedOp",0],cot:["NamedOp",0],coth:["NamedOp",0],csc:["NamedOp",0],deg:["NamedOp",0],det:"NamedOp",dim:["NamedOp",0],exp:["NamedOp",0],gcd:"NamedOp",hom:["NamedOp",0],inf:"NamedOp",ker:["NamedOp",0],lg:["NamedOp",0],lim:"NamedOp",liminf:["NamedOp",null,"lim&thinsp;inf"],limsup:["NamedOp",null,"lim&thinsp;sup"],ln:["NamedOp",0],log:["NamedOp",0],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedOp",0],sin:["NamedOp",0],sinh:["NamedOp",0],sup:"NamedOp",tan:["NamedOp",0],tanh:["NamedOp",0],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","203E"],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",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",i.LENGTH.THINMATHSPACE],":":["Spacer",i.LENGTH.THINMATHSPACE],">":["Spacer",i.LENGTH.MEDIUMMATHSPACE],";":["Spacer",i.LENGTH.THICKMATHSPACE],"!":["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",i.LENGTH.THINMATHSPACE],negthinspace:["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",i.TEXCLASS.ORD,0.85],Big:["MakeBig",i.TEXCLASS.ORD,1.15],bigg:["MakeBig",i.TEXCLASS.ORD,1.45],Bigg:["MakeBig",i.TEXCLASS.ORD,1.75],bigl:["MakeBig",i.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",i.TEXCLASS.OPEN,1.15],biggl:["MakeBig",i.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",i.TEXCLASS.OPEN,1.75],bigr:["MakeBig",i.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",i.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",i.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",i.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",i.TEXCLASS.REL,0.85],Bigm:["MakeBig",i.TEXCLASS.REL,1.15],biggm:["MakeBig",i.TEXCLASS.REL,1.45],Biggm:["MakeBig",i.TEXCLASS.REL,1.75],mathord:["TeXAtom",i.TEXCLASS.ORD],mathop:["TeXAtom",i.TEXCLASS.OP],mathopen:["TeXAtom",i.TEXCLASS.OPEN],mathclose:["TeXAtom",i.TEXCLASS.CLOSE],mathbin:["TeXAtom",i.TEXCLASS.BIN],mathrel:["TeXAtom",i.TEXCLASS.REL],mathpunct:["TeXAtom",i.TEXCLASS.PUNCT],mathinner:["TeXAtom",i.TEXCLASS.INNER],vcenter:["TeXAtom",i.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"],eqalign:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"Cr",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",i.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",i.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\rm mod}"],pmod:["Macro","\\pod{{\\rm mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}{\\rm 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"],not:["Macro","\\mathrel{\\rlap{\\kern.5em\\notChar}}"]," ":["Macro","\\text{ }"],space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],def:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Macro","",1],nonumber:["Macro",""],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],require:"Require"},environment:{array:["Array"],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",i.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",i.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"){g.macros[l]=["Macro",k[l]]}else{g.macros[l]=["Macro"].concat(k[l])}}}}};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);this.Parse();this.Push(b.stop())},Parse:function(){var k;while(this.i<this.string.length){k=this.string.charAt(this.i++);if(g.special[k]){this[g.special[k]](k)}else{if(g.letter.test(k)){this.Variable(k)}else{if(g.digit.test(k)){this.Number(k)}else{this.Other(k)}}}}},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(q){var k=this.GetCS(),p,n;if(g.macros[k]){var m=g.macros[k];if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,["\\"+k].concat(m.slice(1)))}else{if(g.mathchar0mi[k]){p=g.mathchar0mi[k];n={mathvariant:i.VARIANT.ITALIC};if(p instanceof Array){n=p[1];p=p[0]}this.Push(this.mmlToken(i.mi(i.entity("#x"+p)).With(n)))}else{if(g.mathchar0mo[k]){p=g.mathchar0mo[k];n={stretchy:f};if(p instanceof Array){n=p[1];n.stretchy=f;p=p[0]}this.Push(this.mmlToken(i.mo(i.entity("#x"+p)).With(n)))}else{if(g.mathchar7[k]){p=g.mathchar7[k];n={mathvariant:i.VARIANT.NORMAL};if(p instanceof Array){n=p[1];p=p[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.entity("#x"+p)).With(n)))}else{if(g.delimiter["\\"+k]!=null){var o=g.delimiter["\\"+k];n={};if(o instanceof Array){n=o[1];o=o[0]}if(o.length===4){o=i.entity("#x"+o)}else{o=i.chars(o)}this.Push(this.mmlToken(i.mo(o).With({fence:f,stretchy:f}).With(n)))}else{this.csUndefined("\\"+k)}}}}}},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(i.mi(i.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(g.number);if(l){k=i.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=i.mo(i.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(i.mtext(i.chars(h)))},Space:function(k){},Superscript:function(m){var k,l=this.stack.Prev();if(!l){l=i.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=i.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){l=i.munderover(l,null,null).With({movesupsub:c})}k=l.over}else{l=i.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){var k,l=this.stack.Prev();if(!l){l=i.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]){l=i.munderover(l,null,null).With({movesupsub:c})}k=l.under}else{l=i.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:String.fromCharCode(8242),SMARTQUOTE:String.fromCharCode(8217),Prime:function(m){var l=this.stack.Prev();if(!l){l=i.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(i.mo(i.chars(k)).With({isPrime:c,variantForm:d.isSTIX}));this.Push(i.msubsup(l,null,k))},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(g.remap[m]){m=g.remap[m];if(m instanceof Array){l=m[1];m=m[0]}k=i.mo(i.entity("#x"+m))}else{k=i.mo(m)}if(k.autoDefault("texClass",true)==""){k=i.TeXAtom(k)}this.Push(this.mmlToken(k.With(l)))},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(i.mstyle(n).With({mathcolor:l}))},Spacer:function(k,l){this.Push(i.mspace().With({width:l,mathsize:i.SIZE.NORMAL,scriptlevel:1}))},LeftRight:function(k){this.Push(b[k.substr(1)]().With({delim:this.GetDelimiter(k)}))},NamedOp:function(m,l,o){var n=(l!=null&&l===0?f:c);if(!o){o=m.substr(1)}l=((l||l==null)?c:f);o=o.replace(/&thinsp;/,String.fromCharCode(8198));var k=i.mo(o).With({movablelimits:l,movesupsub:n,form:i.FORM.PREFIX,texClass:i.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!==i.TEXCLASS.OP){d.Error(l+" is allowed only on operators")}m.movesupsub=(k?c:f);m.movablelimits=f},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(i.mfrac(k,m))},Sqrt:function(l){var m=this.GetBrackets(l),k=this.ParseArg(l);if(m==""){k=i.msqrt.apply(i,k.array())}else{k=i.mroot(k,this.parseRoot(m))}this.Push(k)},Root:function(l){var m=this.GetUpTo(l,"\\of");var k=this.ParseArg(l);this.Push(i.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=i.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(i.mo(i.entity("#x"+k)).With(n));l.stretchy=(p?c:f);this.Push(i.munderover(o,null,l).With({accent:c}))},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=i.munderover(n,null,null);if(k){l.movesupsub=c}l.data[l[o]]=this.mmlToken(i.mo(i.entity("#x"+p)).With({stretchy:c,accent:(o=="under")}));this.Push(l)},Overset:function(k){var m=this.ParseArg(k),l=this.ParseArg(k);this.Push(i.munderover(l,null,m))},Underset:function(k){var m=this.ParseArg(k),l=this.ParseArg(k);this.Push(i.munderover(l,m,null))},TeXAtom:function(n,p){var o={texClass:p},m;if(p==i.TEXCLASS.OP){o.movesupsub=o.movablelimits=c;var k=this.GetArgument(n);var l=k.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(l){m=this.mmlToken(i.mo(l[1]).With({movablelimits:c,movesupsub:c,mathvariant:i.VARIANT.NORMAL,form:i.FORM.PREFIX,texClass:i.TEXCLASS.OP}));m.useMMLspacing&=~m.SPACE_ATTR.form}else{m=i.TeXAtom(d.Parse(k,this.stack.env).mml()).With(o)}}else{m=i.TeXAtom(this.ParseArg(n)).With(o)}this.Push(m)},Strut:function(k){this.Push(i.mpadded(i.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(l,k,m){var n=i.mphantom(this.ParseArg(l));if(k||m){n=i.mpadded(n);if(m){n.height=n.depth=0}if(k){n.width=0}}this.Push(n)},Smash:function(m){var l=this.trimSpaces(this.GetBrackets(m));var k=i.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(k)},Lap:function(l){var k=i.mpadded(this.ParseArg(l)).With({width:0});if(l==="\\llap"){k.lspace="-1 width"}this.Push(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:i.mspace().With({width:n,mathsize:i.SIZE.NORMAL,scriptlevel:1}),right:i.mspace().With({width:m,mathsize:i.SIZE.NORMAL,scriptlevel:1})}))},Hskip:function(k){this.Push(i.mspace().With({width:this.GetDimen(k),mathsize:i.SIZE.NORMAL,scriptlevel:0}))},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"){l=i.mpadded(i.mrow()).With(p);if(parseFloat(k)&&parseFloat(n)+parseFloat(q)){l=i.mstyle(l).With({mathbackground:(this.stack.env.color||"black")})}}else{l=i.mspace().With(p)}this.Push(l)},MakeBig:function(k,n,l){l*=g.p_height;l=String(l).replace(/(\.\d\d\d).+/,"$1")+"em";var m=this.GetDelimiter(k);this.Push(i.TeXAtom(i.mo(m).With({minsize:l,maxsize:l,scriptlevel:0,fence:c,stretchy:c,symmetric:c})).With({texClass:n}))},BuildRel:function(k){var l=this.ParseUpTo(k,"\\over");var m=this.ParseArg(k);this.Push(i.TeXAtom(i.munderover(m,null,l)).With({mclass:i.TEXCLASS.REL}))},HBox:function(k,l){this.Push.apply(this,this.InternalMath(this.GetArgument(k),l))},FBox:function(k){this.Push(i.menclose.apply(i,this.InternalMath(this.GetArgument(k))).With({notation:"box"}))},Require:function(k){var l=this.GetArgument(k);this.Extension(null,l)},Extension:function(k,l,m){if(k&&!typeof(k)==="string"){k=k.name}l=d.extensionDir+"/"+l;if(!l.match(/\.js$/)){l+=".js"}if(!MathJax.Ajax.loaded[MathJax.Ajax.fileURL(l)]){if(k!=null){delete g[m||"macros"][k.replace(/^\\/,"")]}MathJax.Hub.RestartAfter(MathJax.Ajax.Require(l))}},Macro:function(l,o,n){if(n){var k=[];for(var m=0;m<n;m++){k.push(this.GetArgument(l))}o=this.SubstituteArgs(k,o)}this.string=this.AddArgs(o,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,q,m,k){var r=this.GetNext();if(r===""){d.Error("Missing argument for "+l)}if(r==="{"){this.i++}else{this.string=r+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:c,arraydef:{rowspacing:(m||"4pt"),columnspacing:(q||"1em")}});if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=c}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(k){this.Push(b.cell().With({isEntry:c,name:k}))},Cr:function(k){this.Push(b.cell().With({isCR:c,name:k}))},HLine:function(l,m){if(m==null){m="solid"}var n=this.stack.Top();if(n.type!=="array"||n.data.length){d.Error("Misplaced "+l)}if(n.table.length==0){n.arraydef.frame=m}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+'"')}if(!g.environment[m]){d.Error('Unknown environment "'+m+'"')}if(++this.macroCount>d.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}var n=g.environment[m];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)}))},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(m,o,t,r,s,n,k,p){if(!r){r=this.GetArgument("\\begin{"+m.name+"}")}var u=("c"+r).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");r=r.replace(/[^clr]/g,"").split("").join(" ");r=r.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var q=b.array().With({arraydef:{columnalign:r,columnspacing:(s||"1em"),rowspacing:(n||"4pt")}});if(u.match(/[|:]/)){var l=(u.charAt(0)+u.charAt(u.length-1)).replace(/[^|:]/g,"");if(l!==""){q.arraydef.frame={"|":"solid",":":"dashed"}[l.charAt(0)];q.arraydef.framespacing=".5em .5ex"}u=u.substr(1,u.length-2);q.arraydef.columnlines=u.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(o){q.open=this.convertDelimiter(o)}if(t){q.close=this.convertDelimiter(t)}if(k==="D"){q.arraydef.displaystyle=c}if(k==="S"){q.arraydef.scriptlevel=1}if(p){q.arraydef.useHeight=f}this.Push(m);return q},convertDelimiter:function(k){if(k){k=g.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/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){if(this.GetNext()!="["){return""}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(g.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:f};if(s!=null){p.scriptlevel=s}if(this.stack.env.font){p.mathvariant=this.stack.env.font}if(!q.match(/\$|\\\(/)){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(i.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="$";l=o}}}else{if(r==="\\"){r=q.charAt(o++);if(r==="("&&n===""){if(l<o-2){m.push(this.InternalText(q.slice(l,o-2),p))}n=")";l=o}else{if(r===")"&&n===")"){m.push(i.TeXAtom(d.Parse(q.slice(l,o-2)).mml().With(p)));n="";l=o}}}}}if(n!==""){d.Error("Math not terminated in text box")}if(l<q.length){m.push(this.InternalText(q.slice(l),p))}return m},InternalText:function(l,k){l=l.replace(/^\s+/,h).replace(/\s+$/,h);return i.mtext(i.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]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:g,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},Translate:function(k){var l,n=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");if(MathJax.Hub.Browser.isKonqueror){n=n.replace(/&lt;/g,"<").replace(/&gt;/g,">").replace(/&amp;/g,"&")}var o=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);n=d.prefilterMath(n,o,k);try{l=d.Parse(n).mml()}catch(m){if(!m.texError){throw m}l=this.formatError(m,n,o,k)}if(l.inferred){l=i.apply(MathJax.ElementJax,l.data)}else{l=i(l)}if(o){l.root.display="block"}return this.postfilterMath(l,o,k)},prefilterMath:function(l,m,k){return l.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(m,l,n,k){return i.merror(m.message.replace(/\n.*/,""))},Error:function(k){throw MathJax.Hub.Insert(Error(k),{texError:c})},Macro:function(k,l,m){g.macros[k]=["Macro"].concat([].slice.call(arguments,1))},combineRelations:function(l){for(var n=0,k=l.data.length;n<k;n++){if(l.data[n]){if(l.isa(i.mrow)){while(n+1<k&&l.data[n+1]&&l.data[n].isa(i.mo)&&l.data[n+1].isa(i.mo)&&l.data[n].Get("texClass")===i.TEXCLASS.REL&&l.data[n+1].Get("texClass")===i.TEXCLASS.REL){l.data[n].Append.apply(l.data[n],l.data[n+1].data);l.data.splice(n+1,1);k--}}if(!l.data[n].isToken){this.combineRelations(l.data[n])}}}}});d.loadComplete("jax.js")})(MathJax.InputJax.TeX);

MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var e="1.1";var a=MathJax.ElementJax.mml;var f=MathJax.InputJax.TeX;var c=f.Definitions;var d=f.Stack.Item;var b=function(g){return g.join("em ")+"em"};MathJax.Hub.Insert(c,{macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",a.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",a.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",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",a.ALIGN.LEFT],shoveright:["HandleShove",a.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",b([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",b([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",b([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:["Array",null,null,null,"rlrlrlrlrlrl",b([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18]),".5em","D"],gathered:["Array",null,null,null,"c",null,".5em","D"],subarray:["Array",null,null,null,null,b([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",b([1/3]),".2em","S",1]},delimiter:{"\\lvert":["2223",{texClass:a.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:a.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:a.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:a.TEXCLASS.CLOSE}]}});f.Parse.Augment({HandleTag:function(h){var g=this.trimSpaces(this.GetArgument(h));if(g==="*"){g=this.GetArgument(h)}else{g="("+g+")"}if(this.stack.global.notag){f.Error(h+" not allowed in "+this.stack.global.notag+" environment")}if(this.stack.global.tag){f.Error("Multiple "+h)}this.stack.global.tag=a.mtd.apply(a,this.InternalMath(g))},HandleNoTag:function(g){if(this.stack.global.tag){delete this.stack.global.tag}},HandleDeclareOp:function(h){var g="";var i=this.trimSpaces(this.GetArgument(h));if(i=="*"){g="\\limits";i=this.trimSpaces(this.GetArgument(h))}if(i.charAt(0)=="\\"){i=i.substr(1)}var j=this.GetArgument(h);j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");f.Definitions.macros[i]=["Macro","\\mathop{\\rm "+j+"}"+g]},HandleOperatorName:function(h){var g="\\nolimits";var i=this.trimSpaces(this.GetArgument(h));if(i=="*"){g="\\limits";i=this.trimSpaces(this.GetArgument(h))}i=i.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+i+"}"+g+" "+this.string.slice(this.i);this.i=0},HandleShove:function(h,g){var i=this.stack.Top();if(i.type!=="multline"||i.data.length){f.Error(h+" must come at the beginning of the line")}i.data.shove=g},CFrac:function(j){var g=this.trimSpaces(this.GetBrackets(j)),i=this.GetArgument(j),k=this.GetArgument(j);var h=a.mfrac(f.Parse("\\strut\\textstyle{"+i+"}",this.stack.env).mml(),f.Parse("\\strut\\textstyle{"+k+"}",this.stack.env).mml());g=({l:a.ALIGN.LEFT,r:a.ALIGN.RIGHT,"":""})[g];if(g==null){f.Error("Illegal alignment specified in "+j)}if(g){h.numalign=h.denomalign=g}this.Push(h)},Genfrac:function(h,j,o,l,g){if(j==null){j=this.GetDelimiterArg(h)}else{j=this.convertDelimiter(j)}if(o==null){o=this.GetDelimiterArg(h)}else{o=this.convertDelimiter(o)}if(l==null){l=this.GetArgument(h)}if(g==null){g=this.trimSpaces(this.GetArgument(h))}var k=this.ParseArg(h);var n=this.ParseArg(h);var i=a.mfrac(k,n);if(l!==""){i.linethickness=l}if(j||o){i=a.mfenced(i).With({open:j,close:o})}if(g!==""){var m=(["D","T","S","SS"])[g];if(m==null){f.Error("Bad math style for "+h)}i=a.mstyle(i);if(m==="D"){i.displaystyle=true;i.scriptlevel=0}else{i.displaystyle=false;i.scriptlevel=g-1}}this.Push(i)},Multline:function(h,g){this.Push(h);return d.multline().With({arraydef:{displaystyle:true,rowspacing:".5em",width:f.config.MultLineWidth,columnwidth:"100%",side:f.config.TagSide,minlabelspacing:f.config.TagIndent}})},AMSarray:function(i,h,g,k,j){this.Push(i);k=k.replace(/[^clr]/g,"").split("").join(" ");k=k.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return d.AMSarray(i.name,h,g,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:k,columnspacing:(j||"1em"),rowspacing:"3pt",side:f.config.TagSide,minlabelspacing:f.config.TagIndent}})},AlignAt:function(i,h,g){var j=this.GetArgument("\\begin{"+i.name+"}");if(j.match(/[^0-9]/)){f.Error("Argument to \\begin{"+i.name+"} must me a positive integer")}align="";spacing=[];while(j>0){align+="rl";spacing.push("0em 0em");j--}spacing=spacing.join(" ");if(g){return this.AMSarray(i,h,g,align,spacing)}return this.Array(i,null,null,align,spacing,".5em","D")},MultiIntegral:function(g,k){var j=this.GetNext();if(j==="\\"){var h=this.i;j=this.GetArgument(g);this.i=h;if(j==="\\limits"){if(g==="\\idotsint"){k="\\!\\!\\mathop{\\,\\,"+k+"}"}else{k="\\!\\!\\!\\mathop{\\,\\,\\,"+k+"}"}}}this.string=k+" "+this.string.slice(this.i);this.i=0},xArrow:function(i,m,k,g){var j={width:"+"+(k+g)+"mu",lspace:k+"mu"};var n=this.GetBrackets(i),o=this.ParseArg(i);var p=a.mo(a.chars(String.fromCharCode(m))).With({stretchy:true,texClass:a.TEXCLASS.REL});var h=a.munderover(p);h.SetData(h.over,a.mpadded(o).With(j).With({voffset:".15em"}));if(n){n=f.Parse(n,this.stack.env).mml();h.SetData(h.under,a.mpadded(n).With(j).With({voffset:"-.24em"}))}this.Push(h)},GetDelimiterArg:function(g){var h=this.trimSpaces(this.GetArgument(g));if(h==""){return null}if(!c.delimiter[h]){f.Error("Missing or unrecognized delimiter for "+g)}return this.convertDelimiter(h)}});d.multline=d.array.Subclass({type:"multline",EndEntry:function(){var g=a.mtd.apply(a,this.data);if(this.data.shove){g.columnalign=this.data.shove}this.row.push(g);this.data=[]},EndRow:function(){if(this.row.length!=1){f.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 h=this.table.length-1,j;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=a.ALIGN.LEFT}if(!this.table[h][0].columnalign){this.table[h][0].columnalign=a.ALIGN.RIGHT}var g=a.mtr;if(this.global.tag){this.table[0]=[this.global.tag].concat(this.table[0]);delete this.global.tag;g=a.mlabeledtr}this.table[0]=g.apply(a,this.table[0]);for(j=1,h=this.table.length;j<h;j++){this.table[j]=a.mtr.apply(a,this.table[j])}}}});d.AMSarray=d.array.Subclass({type:"AMSarray",Init:function(j,i,h,g){this.SUPER(arguments).Init.apply(this);this.numbered=i;this.save_notag=g.global.notag;g.global.notag=(h?null:j)},EndRow:function(){var g=a.mtr;if(this.global.tag){this.row=[this.global.tag].concat(this.row);g=a.mlabeledtr;delete this.global.tag}this.table.push(g.apply(a,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notag=this.save_notag}});d.start.Augment({oldCheckItem:d.start.prototype.checkItem,checkItem:function(h){if(h.type==="stop"){var g=this.mmlData();if(this.global.tag){var j=[this.global.tag,a.mtd(g)];delete this.global.tag;var i={side:f.config.TagSide,minlabelspacing:f.config.TagIndent,columnalign:g.displayAlign};if(g.displayAlign===a.INDENTALIGN.LEFT){i.width="100%";if(g.displayIndent&&!String(g.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){i.columnwidth=g.displayIndent+" fit";i.columnspacing="0";j=[j[0],a.mtd(),j[1]]}}else{if(g.displayAlign===a.INDENTALIGN.RIGHT){i.width="100%";if(g.displayIndent&&!String(g.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){i.columnwidth="fit "+g.displayIndent;i.columnspacing="0";j[2]=a.mtd()}}}g=a.mtable(a.mlabeledtr.apply(a,j)).With(i)}return d.mml(g)}return this.SUPER(arguments).checkItem.call(this,h)}});MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js");

MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b="1.1.2";var a=MathJax.ElementJax.mml;MathJax.Hub.Insert(MathJax.InputJax.TeX.Definitions,{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",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":"250C","\\urcorner":"2510","\\llcorner":"2514","\\lrcorner":"2518"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}});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.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.Startup.signal.Post("TeX AMSsymbols Ready")});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(f){var g;if(typeof f!=="string"){g=f.parentNode}else{if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}f=f.replace(/^\s*(?:\/\/)?<!(--)?\[CDATA\[((.|\n)*)(\/\/)?\]\]\1>\s*$/,"$2");f=f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);g=b.ParseXML(f);if(g==null){b.Error("Error parsing MathML")}}var e=g.getElementsByTagName("parsererror")[0];if(e){b.Error("Error parsing MathML: "+e.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,""))}if(g.childNodes.length!==1){b.Error("MathML must be formed by a single element")}if(g.firstChild.nodeName.toLowerCase()==="html"){var d=g.getElementsByTagName("h1")[0];if(d&&d.textContent==="XML parsing error"&&d.nextSibling){b.Error("Error parsing MathML: "+String(d.nextSibling.nodeValue).replace(/fatal parsing error: /,""))}}if(g.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")!=="math"){b.Error("MathML must be formed by a <math> element, not <"+g.firstChild.nodeName+">")}this.mml=this.MakeMML(g.firstChild)},MakeMML:function(h){var l=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");if(!(a[l]&&a[l].isa&&a[l].isa(a.mbase))){return a.merror("Unknown node type: "+l)}var d=a[l](),k,j,e,n;for(k=0,j=h.attributes.length;k<j;k++){e=h.attributes[k].name;if(e=="xlink:href"){e="href"}if(e.match(/:/)){continue}n=h.attributes[k].value;if(n.toLowerCase()==="true"){n=true}else{if(n.toLowerCase()==="false"){n=false}}d[e]=n}for(k=0,j=h.childNodes.length;k<j;k++){var f=h.childNodes[k];if(f.nodeName==="#comment"){continue}if(f.nodeName==="#text"){if(d.isToken&&!d.mmlSelfClosing){var o=this.trimSpace(f.nodeValue);if(d.isa(a.mo)&&o.length===1&&this.Remap[o.charAt(0)]){o=this.Remap[o.charAt(0)]}o=o.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);d.Append(a.chars(o))}else{if(f.nodeValue.match(/\S/)){b.Error("Unexpected text node: '"+f.nodeValue+"'")}}}else{if(d.type==="annotation-xml"){d.Append(a.xml(f))}else{var g=this.MakeMML(f);d.Append(g);if(g.mmlSelfClosing&&g.data.length){d.Append.apply(d,g.data);g.data=[]}}}}if(b.config.useMathMLspacing){d.useMMLspacing=8}return d},trimSpace:function(d){return d.replace(/^[ \t\n\r]+/,"").replace(/[ \t\n\r]+$/,"").replace(/[ \t\n\r][ \t\n\r]+/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},Remap:{"\u0027":"\u2032","\u002A":"\u2217","\u002D":"\u2212"}},{loaded:[]});b.Augment({Translate:function(d){if(!this.ParseXML){this.ParseXML=this.createParser()}var e,g;if(d.firstChild&&d.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){g=this.prefilterMathML(d.firstChild)}else{g=d.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");if(c.isMSIE){g=g.replace(/(&nbsp;)+$/,"")}else{if(c.isKonqueror){g=g.replace(/&lt;/g,"<").replace(/&gt;/g,">").replace(/&amp;/g,"&")}}g=this.prefilterMath(g,d)}try{e=b.Parse(g).mml}catch(f){if(!f.mathmlError){throw f}e=this.formatError(f,g,d)}return a(e)},prefilterMath:function(e,d){return e},prefilterMathML:function(d){return d},formatError:function(f,e,d){return a.merror(f.message.replace(/\n.*/,""))},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({mmlSelfClossing:true})}});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/TeX-AMS-MML_HTMLorMML.js");