/*
 *  /MathJax/config/AM_HTMLorMML.js
 *  
 *  Copyright (c) 2010-2015 The MathJax Consortium
 *
 *  Part of the MathJax library.
 *  See http://www.mathjax.org for details.
 * 
 *  Licensed under the Apache License, Version 2.0;
 *  you may not use this file except in compliance with the License.
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 */

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

MathJax.Ajax.Preloading(
  "[MathJax]/jax/input/AsciiMath/config.js",
  "[MathJax]/jax/output/HTML-CSS/config.js",
  "[MathJax]/jax/output/NativeMML/config.js",
  "[MathJax]/jax/output/CommonHTML/config.js",
  "[MathJax]/config/MMLorHTML.js",
  "[MathJax]/extensions/asciimath2jax.js",
  "[MathJax]/extensions/MathEvents.js",
  "[MathJax]/extensions/MathZoom.js",
  "[MathJax]/extensions/MathMenu.js",
  "[MathJax]/jax/element/mml/jax.js",
  "[MathJax]/extensions/toMathML.js",
  "[MathJax]/jax/input/AsciiMath/jax.js",
  "[MathJax]/jax/output/CommonHTML/jax.js",
  "[MathJax]/extensions/CHTML-preview.js"
);

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

MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.5.0",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{fixphi:true,useMathMLspacing:true,displaystyle:true,decimalsign:"."}});MathJax.InputJax.AsciiMath.Register("math/asciimath");MathJax.InputJax.AsciiMath.loadComplete("config.js");
MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.5.3",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:{noReflows:true,matchFontHeight:true,scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",mtextFontInherit:false,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"},".MathJax .MJX-monospace":{"font-family":"monospace"},".MathJax .MJX-sans-serif":{"font-family":"sans-serif"},"#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","z-index":401}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set(["MathJaxNotSupported","Your browser does not support MathJax"],null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js");
MathJax.OutputJax.NativeMML=MathJax.OutputJax({id:"NativeMML",version:"2.5.1",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{matchFontHeight:true,scale:100,minScaleAdjust:50,styles:{"div.MathJax_MathML":{"text-align":"center",margin:".75em 0px"}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.NativeMML.Register("jax/mml")}MathJax.OutputJax.NativeMML.loadComplete("config.js");
MathJax.OutputJax.CommonHTML=MathJax.OutputJax({id:"CommonHTML",version:"2.5.0",directory:MathJax.OutputJax.directory+"/CommonHTML",extensionDir:MathJax.OutputJax.extensionDir+"/CommonHTML",config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.CommonHTML.Register("jax/mml")}MathJax.OutputJax.CommonHTML.loadComplete("config.js");
(function(c,g){var f="2.5.0";var a=MathJax.Hub.CombineConfig("MMLorHTML",{prefer:{MSIE:"MML",Firefox:"HTML",Opera:"HTML",Chrome:"HTML",Safari:"HTML",other:"HTML"}});var e={Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4};var b=(g.version==="0.0"||g.versionAtLeast(e[g]||0));var d=(g.isFirefox&&g.versionAtLeast("1.5"))||(g.isMSIE&&g.hasMathPlayer)||(g.isSafari&&g.versionAtLeast("5.0"))||(g.isOpera&&g.versionAtLeast("9.52"));c.Register.StartupHook("End Config",function(){var h=(a.prefer&&typeof(a.prefer)==="object"?a.prefer[MathJax.Hub.Browser]||a.prefer.other||"HTML":a.prefer);if(b||d){if(d&&(h==="MML"||!b)){if(MathJax.OutputJax.NativeMML){MathJax.OutputJax.NativeMML.Register("jax/mml")}else{c.config.jax.unshift("output/NativeMML")}c.Startup.signal.Post("NativeMML output selected")}else{if(MathJax.OutputJax["HTML-CSS"]){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}else{c.config.jax.unshift("output/HTML-CSS")}c.Startup.signal.Post("HTML-CSS output selected")}}else{c.PreProcess.disabled=true;c.prepareScripts.disabled=true;MathJax.Message.Set(["MathJaxNotSupported","Your browser does not support MathJax"],null,4000);c.Startup.signal.Post("MathJax not supported")}})})(MathJax.Hub,MathJax.Hub.Browser);MathJax.Ajax.loadComplete("[MathJax]/config/MMLorHTML.js");
MathJax.Extension.asciimath2jax={version:"2.5.0",config:{delimiters:[["`","`"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"asciimath2jax_ignore",processClass:"asciimath2jax_process",preview:"AsciiMath"},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("asciimath2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],c,a,b=this.config;this.match={};if(b.delimiters.length===0){return false}for(c=0,a=b.delimiters.length;c<a;c++){d.push(this.patternQuote(b.delimiters[c][0]));this.match[b.delimiters[c][0]]={mode:"",end:b.delimiters[c][1],pattern:this.endPattern(b.delimiters[c][1])}}this.start=new RegExp(d.sort(this.sortLength).join("|"),"g");this.skipTags=new RegExp("^("+b.skipTags.join("|")+")$","i");var e=[];if(MathJax.Hub.config.preRemoveClass){e.push(MathJax.Hub.config.preRemoveClass)}if(b.ignoreClass){e.push(b.ignoreClass)}this.ignoreClass=(e.length?new RegExp("(^| )("+e.join("|")+")( |$)"):/^$/);this.processClass=new RegExp("(^| )("+b.processClass+")( |$)");return true},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d<c?-1:1))},scanElement:function(c,b,g){var a,e,d,f;while(c&&c!=b){if(c.nodeName.toLowerCase()==="#text"){if(!g){c=this.scanText(c)}}else{a=(typeof(c.className)==="undefined"?"":c.className);e=(typeof(c.tagName)==="undefined"?"":c.tagName);if(typeof(a)!=="string"){a=String(a)}f=this.processClass.exec(a);if(c.firstChild&&!a.match(/(^| )MathJax/)&&(f||!this.skipTags.exec(e))){d=(g||this.ignoreClass.exec(a))&&!f;this.scanElement(c.firstChild,b,d)}}if(c){c=c.nextSibling}}},scanText:function(b){if(b.nodeValue.replace(/\s+/,"")==""){return b}var a,c;this.search={start:true};this.pattern=this.start;while(b){this.pattern.lastIndex=0;while(b&&b.nodeName.toLowerCase()==="#text"&&(a=this.pattern.exec(b.nodeValue))){if(this.search.start){b=this.startMatch(a,b)}else{b=this.endMatch(a,b)}}if(this.search.matched){b=this.encloseMath(b)}if(b){do{c=b;b=b.nextSibling}while(b&&(b.nodeName.toLowerCase()==="br"||b.nodeName.toLowerCase()==="#comment"));if(!b||b.nodeName!=="#text"){return c}}}return b},startMatch:function(a,b){var c=this.match[a[0]];if(c!=null){this.search={end:c.end,mode:c.mode,open:b,olen:a[0].length,opos:this.pattern.lastIndex-a[0].length};this.switchPattern(c.pattern)}return b},endMatch:function(a,b){if(a[0]==this.search.end){this.search.close=b;this.search.cpos=this.pattern.lastIndex;this.search.clen=(this.search.isBeginEnd?0:a[0].length);this.search.matched=true;b=this.encloseMath(b);this.switchPattern(this.start)}return b},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=(a===this.start)},encloseMath:function(b){var a=this.search,f=a.close,e,c;if(a.cpos===f.length){f=f.nextSibling}else{f=f.splitText(a.cpos)}if(!f){e=f=MathJax.HTML.addText(a.close.parentNode,"")}a.close=f;c=(a.opos?a.open.splitText(a.opos):a.open);while(c.nextSibling&&c.nextSibling!==f){if(c.nextSibling.nodeValue!==null){if(c.nextSibling.nodeName==="#comment"){c.nodeValue+=c.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{c.nodeValue+=c.nextSibling.nodeValue}}else{if(this.msieNewlineBug){c.nodeValue+=(c.nextSibling.nodeName.toLowerCase()==="br"?"\n":" ")}else{c.nodeValue+=" "}}c.parentNode.removeChild(c.nextSibling)}var d=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);if(this.config.preview!=="none"){this.createPreview(a.mode,d)}c=this.createMathTag(a.mode,d);this.search={};this.pattern.lastIndex=0;if(e){e.parentNode.removeChild(e)}return c},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(c,a){var b=this.config.preview;if(b==="none"){return}if(b==="AsciiMath"){b=[this.filterPreview(a)]}if(b){b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b);this.insertNode(b)}},createMathTag:function(c,a){var b=document.createElement("script");b.type="math/asciimath"+c;MathJax.HTML.setScript(b,a);this.insertNode(b);return b},filterPreview:function(a){return a},msieNewlineBug:(MathJax.Hub.Browser.isMSIE&&(document.documentMode||0)<9)};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.asciimath2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/asciimath2jax.js");
(function(d,h,l,g,m,b,j){var q="2.5.0";var i=MathJax.Extension;var c=i.MathEvents={version:q};var k=d.config.menuSettings;var p={hover:500,frame:{x:3.5,y:5,bwidth:1,bcolor:"#A6D",hwidth:"15px",hcolor:"#83A"},button:{x:-4,y:-3,wx:-2,src:l.urlRev(b.imageDir+"/MenuArrow-15.png")},fadeinInc:0.2,fadeoutInc:0.05,fadeDelay:50,fadeoutStart:400,fadeoutDelay:15*1000,styles:{".MathJax_Hover_Frame":{"border-radius":".25em","-webkit-border-radius":".25em","-moz-border-radius":".25em","-khtml-border-radius":".25em","box-shadow":"0px 0px 15px #83A","-webkit-box-shadow":"0px 0px 15px #83A","-moz-box-shadow":"0px 0px 15px #83A","-khtml-box-shadow":"0px 0px 15px #83A",border:"1px solid #A6D ! important",display:"inline-block",position:"absolute"},".MathJax_Hover_Arrow":{position:"absolute",width:"15px",height:"11px",cursor:"pointer"}}};var n=c.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",Mousedown:function(r){return n.Handler(r,"Mousedown",this)},Mouseup:function(r){return n.Handler(r,"Mouseup",this)},Mousemove:function(r){return n.Handler(r,"Mousemove",this)},Mouseover:function(r){return n.Handler(r,"Mouseover",this)},Mouseout:function(r){return n.Handler(r,"Mouseout",this)},Click:function(r){return n.Handler(r,"Click",this)},DblClick:function(r){return n.Handler(r,"DblClick",this)},Menu:function(r){return n.Handler(r,"ContextMenu",this)},Handler:function(u,s,t){if(l.loadingMathMenu){return n.False(u)}var r=b[t.jaxID];if(!u){u=window.event}u.isContextMenu=(s==="ContextMenu");if(r[s]){return r[s](u,t)}if(i.MathZoom){return i.MathZoom.HandleEvent(u,s,t)}},False:function(r){if(!r){r=window.event}if(r){if(r.preventDefault){r.preventDefault()}else{r.returnValue=false}if(r.stopPropagation){r.stopPropagation()}r.cancelBubble=true}return false},ContextMenu:function(u,F,x){var C=b[F.jaxID],w=C.getJaxFromMath(F);var G=(C.config.showMathMenu!=null?C:d).config.showMathMenu;if(!G||(k.context!=="MathJax"&&!x)){return}if(c.msieEventBug){u=window.event||u}n.ClearSelection();f.ClearHoverTimer();if(w.hover){if(w.hover.remove){clearTimeout(w.hover.remove);delete w.hover.remove}w.hover.nofade=true}var v=MathJax.Menu;var H,E;if(v){if(v.loadingDomain){return n.False(u)}H=m.loadDomain("MathMenu");if(!H){v.jax=w;var s=v.menu.Find("Show Math As").menu;s.items[0].name=w.sourceMenuTitle;s.items[0].format=(w.sourceMenuFormat||"MathML");s.items[1].name=j[w.inputJax].sourceMenuTitle;s.items[5].disabled=!j[w.inputJax].annotationEncoding;var B=s.items[2];B.disabled=true;var r=B.menu.items;annotationList=MathJax.Hub.Config.semanticsAnnotations;for(var A=0,z=r.length;A<z;A++){var t=r[A].name[1];if(w.root&&w.root.getAnnotation(t)!==null){B.disabled=false;r[A].hidden=false}else{r[A].hidden=true}}var y=v.menu.Find("Math Settings","MathPlayer");y.hidden=!(w.outputJax==="NativeMML"&&d.Browser.hasMathPlayer);return v.menu.Post(u)}v.loadingDomain=true;E=function(){delete v.loadingDomain}}else{if(l.loadingMathMenu){return n.False(u)}l.loadingMathMenu=true;H=l.Require("[MathJax]/extensions/MathMenu.js");E=function(){delete l.loadingMathMenu;if(!MathJax.Menu){MathJax.Menu={}}}}var D={pageX:u.pageX,pageY:u.pageY,clientX:u.clientX,clientY:u.clientY};g.Queue(H,E,["ContextMenu",n,D,F,x]);return n.False(u)},AltContextMenu:function(t,s){var u=b[s.jaxID];var r=(u.config.showMathMenu!=null?u:d).config.showMathMenu;if(r){r=(u.config.showMathMenuMSIE!=null?u:d).config.showMathMenuMSIE;if(k.context==="MathJax"&&!k.mpContext&&r){if(!c.noContextMenuBug||t.button!==n.RIGHTBUTTON){return}}else{if(!t[n.MENUKEY]||t.button!==n.LEFTBUTTON){return}}return u.ContextMenu(t,s,true)}},ClearSelection:function(){if(c.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(document.selection){setTimeout("document.selection.empty()",0)}},getBBox:function(t){t.appendChild(c.topImg);var s=c.topImg.offsetTop,u=t.offsetHeight-s,r=t.offsetWidth;t.removeChild(c.topImg);return{w:r,h:s,d:u}}};var f=c.Hover={Mouseover:function(t,s){if(k.discoverable||k.zoom==="Hover"){var v=t.fromElement||t.relatedTarget,u=t.toElement||t.target;if(v&&u&&(v.isMathJax!=u.isMathJax||d.getJaxFor(v)!==d.getJaxFor(u))){var r=this.getJaxFromMath(s);if(r.hover){f.ReHover(r)}else{f.HoverTimer(r,s)}return n.False(t)}}},Mouseout:function(t,s){if(k.discoverable||k.zoom==="Hover"){var v=t.fromElement||t.relatedTarget,u=t.toElement||t.target;if(v&&u&&(v.isMathJax!=u.isMathJax||d.getJaxFor(v)!==d.getJaxFor(u))){var r=this.getJaxFromMath(s);if(r.hover){f.UnHover(r)}else{f.ClearHoverTimer()}return n.False(t)}}},Mousemove:function(t,s){if(k.discoverable||k.zoom==="Hover"){var r=this.getJaxFromMath(s);if(r.hover){return}if(f.lastX==t.clientX&&f.lastY==t.clientY){return}f.lastX=t.clientX;f.lastY=t.clientY;f.HoverTimer(r,s);return n.False(t)}},HoverTimer:function(r,s){this.ClearHoverTimer();this.hoverTimer=setTimeout(g(["Hover",this,r,s]),p.hover)},ClearHoverTimer:function(){if(this.hoverTimer){clearTimeout(this.hoverTimer);delete this.hoverTimer}},Hover:function(r,v){if(i.MathZoom&&i.MathZoom.Hover({},v)){return}var u=b[r.outputJax],w=u.getHoverSpan(r,v),z=u.getHoverBBox(r,w,v),x=(u.config.showMathMenu!=null?u:d).config.showMathMenu;var B=p.frame.x,A=p.frame.y,y=p.frame.bwidth;if(c.msieBorderWidthBug){y=0}r.hover={opacity:0,id:r.inputID+"-Hover"};var s=h.Element("span",{id:r.hover.id,isMathJax:true,style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{className:"MathJax_Hover_Frame",isMathJax:true,style:{display:"inline-block",position:"absolute",top:this.Px(-z.h-A-y-(z.y||0)),left:this.Px(-B-y+(z.x||0)),width:this.Px(z.w+2*B),height:this.Px(z.h+z.d+2*A),opacity:0,filter:"alpha(opacity=0)"}}]]);var t=h.Element("span",{isMathJax:true,id:r.hover.id+"Menu",style:{display:"inline-block","z-index":1,width:0,height:0,position:"relative"}},[["img",{className:"MathJax_Hover_Arrow",isMathJax:true,math:v,src:p.button.src,onclick:this.HoverMenu,jax:u.id,style:{left:this.Px(z.w+B+y+(z.x||0)+p.button.x),top:this.Px(-z.h-A-y-(z.y||0)-p.button.y),opacity:0,filter:"alpha(opacity=0)"}}]]);if(z.width){s.style.width=t.style.width=z.width;s.style.marginRight=t.style.marginRight="-"+z.width;s.firstChild.style.width=z.width;t.firstChild.style.left="";t.firstChild.style.right=this.Px(p.button.wx)}w.parentNode.insertBefore(s,w);if(x){w.parentNode.insertBefore(t,w)}if(w.style){w.style.position="relative"}this.ReHover(r)},ReHover:function(r){if(r.hover.remove){clearTimeout(r.hover.remove)}r.hover.remove=setTimeout(g(["UnHover",this,r]),p.fadeoutDelay);this.HoverFadeTimer(r,p.fadeinInc)},UnHover:function(r){if(!r.hover.nofade){this.HoverFadeTimer(r,-p.fadeoutInc,p.fadeoutStart)}},HoverFade:function(r){delete r.hover.timer;r.hover.opacity=Math.max(0,Math.min(1,r.hover.opacity+r.hover.inc));r.hover.opacity=Math.floor(1000*r.hover.opacity)/1000;var t=document.getElementById(r.hover.id),s=document.getElementById(r.hover.id+"Menu");t.firstChild.style.opacity=r.hover.opacity;t.firstChild.style.filter="alpha(opacity="+Math.floor(100*r.hover.opacity)+")";if(s){s.firstChild.style.opacity=r.hover.opacity;s.firstChild.style.filter=t.style.filter}if(r.hover.opacity===1){return}if(r.hover.opacity>0){this.HoverFadeTimer(r,r.hover.inc);return}t.parentNode.removeChild(t);if(s){s.parentNode.removeChild(s)}if(r.hover.remove){clearTimeout(r.hover.remove)}delete r.hover},HoverFadeTimer:function(r,t,s){r.hover.inc=t;if(!r.hover.timer){r.hover.timer=setTimeout(g(["HoverFade",this,r]),(s||p.fadeDelay))}},HoverMenu:function(r){if(!r){r=window.event}return b[this.jax].ContextMenu(r,this.math,true)},ClearHover:function(r){if(r.hover.remove){clearTimeout(r.hover.remove)}if(r.hover.timer){clearTimeout(r.hover.timer)}f.ClearHoverTimer();delete r.hover},Px:function(r){if(Math.abs(r)<0.006){return"0px"}return r.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var r=new Image();r.src=p.button.src}}};var a=c.Touch={last:0,delay:500,start:function(s){var r=new Date().getTime();var t=(r-a.last<a.delay&&a.up);a.last=r;a.up=false;if(t){a.timeout=setTimeout(a.menu,a.delay,s,this);s.preventDefault()}},end:function(s){var r=new Date().getTime();a.up=(r-a.last<a.delay);if(a.timeout){clearTimeout(a.timeout);delete a.timeout;a.last=0;a.up=false;s.preventDefault();return n.Handler((s.touches[0]||s.touch),"DblClick",this)}},menu:function(s,r){delete a.timeout;a.last=0;a.up=false;return n.Handler((s.touches[0]||s.touch),"ContextMenu",r)}};if(d.Browser.isMobile){var o=p.styles[".MathJax_Hover_Arrow"];o.width="25px";o.height="18px";p.button.x=-6}d.Browser.Select({MSIE:function(r){var t=(document.documentMode||0);var s=r.versionAtLeast("8.0");c.msieBorderWidthBug=(document.compatMode==="BackCompat");c.msieEventBug=r.isIE9;c.msieAlignBug=(!s||t<8);if(t<9){n.LEFTBUTTON=1}},Safari:function(r){c.safariContextMenuBug=true},Opera:function(r){c.operaPositionBug=true},Konqueror:function(r){c.noContextMenuBug=true}});c.topImg=(c.msieAlignBug?h.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):h.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(c.operaPositionBug){c.topImg.style.border="1px solid"}c.config=p=d.CombineConfig("MathEvents",p);var e=function(){var r=p.styles[".MathJax_Hover_Frame"];r.border=p.frame.bwidth+"px solid "+p.frame.bcolor+" ! important";r["box-shadow"]=r["-webkit-box-shadow"]=r["-moz-box-shadow"]=r["-khtml-box-shadow"]="0px 0px "+p.frame.hwidth+" "+p.frame.hcolor};g.Queue(d.Register.StartupHook("End Config",{}),[e],["getImages",f],["Styles",l,p.styles],["Post",d.Startup.signal,"MathEvents Ready"],["loadComplete",l,"[MathJax]/extensions/MathEvents.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.Callback,MathJax.Localization,MathJax.OutputJax,MathJax.InputJax);
(function(a,d,f,c,j){var k="2.5.0";var i=a.CombineConfig("MathZoom",{styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"font-weight":"normal","font-style":"normal","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","box-shadow":"5px 5px 15px #AAAAAA","-webkit-box-shadow":"5px 5px 15px #AAAAAA","-moz-box-shadow":"5px 5px 15px #AAAAAA","-khtml-box-shadow":"5px 5px 15px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_ZoomOverlay":{position:"absolute",left:0,top:0,"z-index":300,display:"inline-block",width:"100%",height:"100%",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"},"#MathJax_ZoomFrame":{position:"relative",display:"inline-block",height:0,width:0},"#MathJax_ZoomEventTrap":{position:"absolute",left:0,top:0,"z-index":302,display:"inline-block",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"}}});var e,b,g;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){g=MathJax.Extension.MathEvents.Event;e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var h=MathJax.Extension.MathZoom={version:k,settings:a.config.menuSettings,scrollSize:18,HandleEvent:function(n,l,m){if(h.settings.CTRL&&!n.ctrlKey){return true}if(h.settings.ALT&&!n.altKey){return true}if(h.settings.CMD&&!n.metaKey){return true}if(h.settings.Shift&&!n.shiftKey){return true}if(!h[l]){return true}return h[l](n,m)},Click:function(m,l){if(this.settings.zoom==="Click"){return this.Zoom(m,l)}},DblClick:function(m,l){if(this.settings.zoom==="Double-Click"||this.settings.zoom==="DoubleClick"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(o,u){this.Remove();b.ClearHoverTimer();g.ClearSelection();var s=MathJax.OutputJax[u.jaxID];var p=s.getJaxFromMath(u);if(p.hover){b.UnHover(p)}var q=this.findContainer(u);var l=Math.floor(0.85*q.clientWidth),t=Math.max(document.body.clientHeight,document.documentElement.clientHeight);if(this.getOverflow(q)!=="visible"){t=Math.min(q.clientHeight,t)}t=Math.floor(0.85*t);var n=d.Element("span",{id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var z=n.lastChild,w=z.firstChild,r=n.firstChild;u.parentNode.insertBefore(n,u);u.parentNode.insertBefore(u,n);if(w.addEventListener){w.addEventListener("mousedown",this.Remove,true)}var m=z.offsetWidth||z.clientWidth;l-=m;t-=m;z.style.maxWidth=l+"px";z.style.maxHeight=t+"px";if(this.msieTrapEventBug){var y=d.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});n.insertBefore(y,z)}if(this.msieZIndexBug){var v=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});n.style.position="relative";n.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];n=v}var x=s.Zoom(p,w,u,l,t);if(this.msiePositionBug){if(this.msieSizeBug){z.style.height=x.zH+"px";z.style.width=x.zW+"px"}if(z.offsetHeight>t){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m<l&&z.offsetHeight-m<t){z.style.overflow="visible"}this.Position(z,x);if(this.msieTrapEventBug){y.style.height=z.clientHeight+"px";y.style.width=z.clientWidth+"px";y.style.left=(parseFloat(z.style.left)+z.clientLeft)+"px";y.style.top=(parseFloat(z.style.top)+z.clientTop)+"px"}z.style.visibility="";if(this.settings.zoom==="Hover"){r.onmouseover=this.Remove}if(window.addEventListener){addEventListener("resize",this.Resize,false)}else{if(window.attachEvent){attachEvent("onresize",this.Resize)}else{this.onresize=window.onresize;window.onresize=this.Resize}}a.signal.Post(["math zoomed",p]);return e(o)},Position:function(p,r){p.style.display="none";var q=this.Resize(),m=q.x,s=q.y,l=r.mW;p.style.display="";var o=-l-Math.floor((p.offsetWidth-l)/2),n=r.Y;p.style.left=Math.max(o,10-m)+"px";p.style.top=Math.max(n,10-s)+"px";if(!h.msiePositionBug){h.SetWH()}},Resize:function(m){if(h.onresize){h.onresize(m)}var q=document.getElementById("MathJax_ZoomFrame"),l=document.getElementById("MathJax_ZoomOverlay");var o=h.getXY(q),n=h.findContainer(q);if(h.getOverflow(n)!=="visible"){l.scroll_parent=n;var p=h.getXY(n);o.x-=p.x;o.y-=p.y;p=h.getBorder(n);o.x-=p.x;o.y-=p.y}l.style.left=(-o.x)+"px";l.style.top=(-o.y)+"px";if(h.msiePositionBug){setTimeout(h.SetWH,0)}else{h.SetWH()}return o},SetWH:function(){var l=document.getElementById("MathJax_ZoomOverlay");if(!l){return}l.style.display="none";var m=l.scroll_parent||document.documentElement||document.body;l.style.width=m.scrollWidth+"px";l.style.height=Math.max(m.clientHeight,m.scrollHeight)+"px";l.style.display=""},findContainer:function(l){l=l.parentNode;while(l.parentNode&&l!==document.body&&h.getOverflow(l)==="visible"){l=l.parentNode}return l},getOverflow:(window.getComputedStyle?function(l){return getComputedStyle(l).overflow}:function(l){return(l.currentStyle||{overflow:"visible"}).overflow}),getBorder:function(o){var m={thin:1,medium:2,thick:3};var n=(window.getComputedStyle?getComputedStyle(o):(o.currentStyle||{borderLeftWidth:0,borderTopWidth:0}));var l=n.borderLeftWidth,p=n.borderTopWidth;if(m[l]){l=m[l]}else{l=parseInt(l)}if(m[p]){p=m[p]}else{p=parseInt(p)}return{x:l,y:p}},getXY:function(o){var l=0,n=0,m;m=o;while(m.offsetParent){l+=m.offsetLeft;m=m.offsetParent}if(h.operaPositionBug){o.style.border="1px solid"}m=o;while(m.offsetParent){n+=m.offsetTop;m=m.offsetParent}if(h.operaPositionBug){o.style.border=""}return{x:l,y:n}},Remove:function(n){var p=document.getElementById("MathJax_ZoomFrame");if(p){var o=MathJax.OutputJax[p.previousSibling.jaxID];var l=o.getJaxFromMath(p.previousSibling);a.signal.Post(["math unzoomed",l]);p.parentNode.removeChild(p);p=document.getElementById("MathJax_ZoomTracker");if(p){p.parentNode.removeChild(p)}if(h.operaRefreshBug){var m=d.addElement(document.body,"div",{style:{position:"fixed",left:0,top:0,width:"100%",height:"100%",backgroundColor:"white",opacity:0},id:"MathJax_OperaDiv"});document.body.removeChild(m)}if(window.removeEventListener){removeEventListener("resize",h.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",h.Resize)}else{window.onresize=h.onresize;delete h.onresize}}}return e(n)}};a.Browser.Select({MSIE:function(l){var n=(document.documentMode||0);var m=(n>=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML);
(function(c,g,k,f,b){var q="2.5.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:q,signal:j};var o=function(r){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",r]].concat([].slice.call(arguments,1)))};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var p=c.CombineConfig("MathMenu",{delay:150,closeImg:k.urlRev(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(n?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:q,items:[],posted:false,title:null,margin:5,Init:function(r){this.items=[].slice.call(arguments,0)},With:function(r){if(r){c.Insert(this,r)}return this},Post:function(s,C,A){if(!s){s=window.event}var r=document.getElementById("MathJax_MenuFrame");if(!r){r=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax]);a.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var t=g.Element("div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"});if(!A){MathJax.Localization.setCSS(t)}for(var v=0,u=this.items.length;v<u;v++){this.items[v].Create(t)}if(a.isMobile){g.addElement(t,"span",{className:"MathJax_Menu_Close",menu:C,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:p.closeImg,style:{width:"100%",height:"100%"}}]])}r.appendChild(t);this.posted=true;t.style.width=(t.offsetWidth+2)+"px";var B=s.pageX,z=s.pageY;if(!B&&!z){B=s.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;z=s.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!C){if(B+t.offsetWidth>document.body.offsetWidth-this.margin){B=document.body.offsetWidth-t.offsetWidth-this.margin}if(a.isMobile){B=Math.max(5,B-Math.floor(t.offsetWidth/2));z-=20}a.skipUp=s.isContextMenu}else{var w="left",D=C.offsetWidth;B=(a.isMobile?30:D-2);z=0;while(C&&C!==r){B+=C.offsetLeft;z+=C.offsetTop;C=C.parentNode}if(!a.isMobile){if((a.isRTL&&B-D-t.offsetWidth>this.margin)||(!a.isRTL&&B+t.offsetWidth>document.body.offsetWidth-this.margin)){w="right";B=Math.max(this.margin,B-D-t.offsetWidth+6)}}if(!n){t.style["borderRadiusTop"+w]=0;t.style["WebkitBorderRadiusTop"+w]=0;t.style["MozBorderRadiusTop"+w]=0;t.style["KhtmlBorderRadiusTop"+w]=0}}t.style.left=B+"px";t.style.top=z+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(s)},Remove:function(r,s){j.Post(["unpost",a.jax]);var t=document.getElementById("MathJax_MenuFrame");if(t){t.parentNode.removeChild(t);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(r)},Find:function(r){return this.FindN(1,r,[].slice.call(arguments,1))},FindId:function(r){return this.FindN(0,r,[].slice.call(arguments,1))},FindN:function(v,s,u){for(var t=0,r=this.items.length;t<r;t++){if(this.items[t].name[v]===s){if(u.length){if(!this.items[t].menu){return null}return this.items[t].menu.FindN(v,u[0],u.slice(1))}return this.items[t]}}return null},IndexOf:function(r){return this.IndexOfN(1,r)},IndexOfId:function(r){return this.IndexOfN(0,r)},IndexOfN:function(u,s){for(var t=0,r=this.items.length;t<r;t++){if(this.items[t].name[u]===s){return t}}return null}},{config:p,div:null,Close:function(r){return a.Event(r,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(r){return a.Event(r,this,"Remove")},Mouseover:function(r){return a.Event(r,this,"Mouseover")},Mouseout:function(r){return a.Event(r,this,"Mouseout")},Mousedown:function(r){return a.Event(r,this,"Mousedown")},Mouseup:function(r){return a.Event(r,this,"Mouseup")},Touchstart:function(r){return a.Event(r,this,"Touchstart")},Touchend:function(r){return a.Event(r,this,"Touchend")},Event:function(t,v,r,u){if(a.skipMouseover&&r==="Mouseover"&&!u){return h(t)}if(a.skipUp){if(r.match(/Mouseup|Touchend/)){delete a.skipUp;return h(t)}if(r==="Touchstart"||(r==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!t){t=window.event}var s=v.menuItem;if(s&&s[r]){return s[r](t,v)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(s){var t=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:s,onmousedown:this.Remove}]]);var r=t.firstChild;if(a.msieBackgroundBug){r.style.backgroundColor="white";r.style.filter="alpha(opacity=0)"}if(a.msieFixedPositionBug){t.width=t.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{r.style.position="fixed"}return t},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var r=document.getElementById("MathJax_MenuFrame");if(r){r=r.firstChild;r.style.width=r.style.height="1px";r.style.width=document.body.scrollWidth+"px";r.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var r=new Image();r.src=p.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(s){if(!this.hidden){var r={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){r.className+=" MathJax_MenuDisabled"}g.addElement(s,"div",r,this.Label(r,s))}},Name:function(){return o(this.name[0],this.name[1])},Mouseover:function(v,x){if(!this.disabled){this.Activate(x)}if(!this.menu||!this.menu.posted){var w=document.getElementById("MathJax_MenuFrame").childNodes,s=x.parentNode.childNodes;for(var t=0,r=s.length;t<r;t++){var u=s[t].menuItem;if(u&&u.menu&&u.menu.posted){u.Deactivate(s[t])}}r=w.length-1;while(r>=0&&x.parentNode.menuItem!==w[r].menuItem){w[r].menuItem.posted=false;w[r].parentNode.removeChild(w[r]);r--}if(this.Timer&&!a.isMobile){this.Timer(v,x)}}},Mouseout:function(r,s){if(!this.menu||!this.menu.posted){this.Deactivate(s)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(r,s){return this.Remove(r,s)},Touchstart:function(r,s){return this.TouchEvent(r,s,"Mousedown")},Touchend:function(r,s){return this.TouchEvent(r,s,"Mouseup")},TouchEvent:function(s,t,r){if(this!==m.lastItem){if(m.lastMenu){a.Event(s,m.lastMenu,"Mouseout")}a.Event(s,t,"Mouseover",true);m.lastItem=this;m.lastMenu=t}if(this.nativeTouch){return null}a.Event(s,t,r);return false},Remove:function(r,s){s=s.parentNode.menuItem;return s.Remove(r,s)},Activate:function(r){this.Deactivate(r);r.className+=" MathJax_MenuActive"},Deactivate:function(r){r.className=r.className.replace(/ MathJax_MenuActive/,"")},With:function(r){if(r){c.Insert(this,r)}return this},isRTL:function(){return a.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(r,t,s){if(!(r instanceof Array)){r=[r,r]}this.name=r;this.action=t;this.With(s)},Label:function(r,s){return[this.Name()]},Mouseup:function(r,s){if(!this.disabled){this.Remove(r,s);j.Post(["command",this]);this.action.call(this,r)}return h(r)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(n&&!c.Browser.isSafari?"\u25B6":"\u25B8"),markerRTL:(n&&!c.Browser.isSafari?"\u25B0":"\u25C2"),Init:function(r,t){if(!(r instanceof Array)){r=[r,r]}this.name=r;var s=1;if(!(t instanceof a.ITEM)){this.With(t),s++}this.menu=a.apply(a,[].slice.call(arguments,s))},Label:function(r,s){this.menu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(r,s){if(this.timer){clearTimeout(this.timer)}r={clientX:r.clientX,clientY:r.clientY};this.timer=setTimeout(f(["Mouseup",this,r,s]),p.delay)},Touchend:function(s,u){var t=this.menu.posted;var r=this.SUPER(arguments).Touchend.apply(this,arguments);if(t){this.Deactivate(u);delete m.lastItem;delete m.lastMenu}return r},Mouseup:function(s,u){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(s,u,this.ltr)}else{var t=document.getElementById("MathJax_MenuFrame").childNodes,r=t.length-1;while(r>=0){var v=t[r];v.menuItem.posted=false;v.parentNode.removeChild(v);if(v.menuItem===this.menu){break}r--}}}return h(s)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(n?"\u25CF":"\u2713"),Init:function(s,r,t){if(!(s instanceof Array)){s=[s,s]}this.name=s;this.variable=r;this.With(t);if(this.value==null){this.value=this.name[0]}},Label:function(s,t){var r={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(p.settings[this.variable]!==this.value){r={style:{display:"none"}}}return[["span",r,[this.marker]]," "+this.Name()]},Mouseup:function(u,v){if(!this.disabled){var w=v.parentNode.childNodes;for(var s=0,r=w.length;s<r;s++){var t=w[s].menuItem;if(t&&t.variable===this.variable){w[s].firstChild.style.display="none"}}v.firstChild.display="";p.settings[this.variable]=this.value;a.cookie[this.variable]=p.settings[this.variable];a.saveCookie();j.Post(["radio button",this])}this.Remove(u,v);if(this.action&&!this.disabled){this.action.call(a,this)}return h(u)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(s,r,t){if(!(s instanceof Array)){s=[s,s]}this.name=s;this.variable=r;this.With(t)},Label:function(s,t){var r={className:"MathJax_MenuCheck"+this.rtlClass()};if(!p.settings[this.variable]){r={style:{display:"none"}}}return[["span",r,[this.marker]]," "+this.Name()]},Mouseup:function(r,s){if(!this.disabled){s.firstChild.display=(p.settings[this.variable]?"none":"");p.settings[this.variable]=!p.settings[this.variable];a.cookie[this.variable]=p.settings[this.variable];a.saveCookie();j.Post(["checkbox",this])}this.Remove(r,s);if(this.action&&!this.disabled){this.action.call(a,this)}return h(r)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(r,s){if(!(r instanceof Array)){r=[r,r]}this.name=r;this.With(s)},Label:function(r,s){delete r.onmouseover,delete r.onmouseout;delete r.onmousedown;r.className+=" MathJax_MenuLabel";return[this.Name()]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(r,s){delete r.onmouseover,delete r.onmouseout;delete r.onmousedown;r.className+=" MathJax_MenuRule";return null}});a.About=function(){var t=b["HTML-CSS"]||{};var s=(t.imgFonts?"image":(t.fontInUse?(t.webFonts?"web":"local")+" "+t.fontInUse:(b.SVG?"web SVG":"generic")))+" fonts";var x=(!t.webFonts||t.imgFonts?null:t.allowWebFonts.replace(/otf/,"woff or otf")+" fonts");var r=["MathJax.js v"+MathJax.fileversion,["br"]];r.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(r,MathJax.InputJax,["InputJax","%1 Input Jax v%2"]);a.About.GetJax(r,MathJax.OutputJax,["OutputJax","%1 Output Jax v%2"]);a.About.GetJax(r,MathJax.ElementJax,["ElementJax","%1 Element Jax v%2"]);r.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(r,MathJax.Extension,["Extension","%1 Extension v%2"],true);r.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[c.Browser+" v"+c.Browser.version+(x?" \u2014 "+o(x.replace(/ /g,""),x):"")]]);a.About.div=a.Background(a.About);var v=g.addElement(a.About.div,"div",{id:"MathJax_About"},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],o(s.replace(/ /g,""),"using "+s),["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","max-height":"20em",overflow:"auto","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},r],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]],["img",{src:p.closeImg,style:{width:"21px",height:"21px",position:"absolute",top:".2em",right:".2em"},onclick:a.About.Remove}]]);MathJax.Localization.setCSS(v);var w=(document.documentElement||{});var u=window.innerHeight||w.clientHeight||w.scrollHeight||0;if(a.prototype.msieAboutBug){v.style.width="20em";v.style.position="absolute";v.style.left=Math.floor((document.documentElement.scrollWidth-v.offsetWidth)/2)+"px";v.style.top=(Math.floor((u-v.offsetHeight)/3)+document.body.scrollTop)+"px"}else{v.style.marginLeft=Math.floor(-v.offsetWidth/2)+"px";v.style.top=Math.floor((u-v.offsetHeight)/3)+"px"}};a.About.Remove=function(r){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(s,x,v,u){var w=[];for(var y in x){if(x.hasOwnProperty(y)&&x[y]){if((u&&x[y].version)||(x[y].isa&&x[y].isa(x))){w.push(o(v[0],v[1],(x[y].id||y),x[y].version))}}}w.sort();for(var t=0,r=w.length;t<r;t++){s.push(w[t],["br"])}return s};a.Help=function(){k.Require("[MathJax]/extensions/HelpDialog.js",function(){MathJax.Extension.Help.Dialog()})};a.ShowSource=function(v){if(!v){v=window.event}var u={screenX:v.screenX,screenY:v.screenY};if(!a.jax){return}if(this.format==="MathML"){var s=MathJax.ElementJax.mml;if(s&&typeof(s.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML("",a.jax),v)}catch(t){if(!t.restart){throw t}f.After([this,a.ShowSource,u],t.restart)}}else{if(!k.loadingToMathML){k.loadingToMathML=true;a.ShowSource.Window(v);f.Queue(k.Require("[MathJax]/extensions/toMathML.js"),function(){delete k.loadingToMathML;if(!s.mbase.prototype.toMathML){s.mbase.prototype.toMathML=function(){}}},[this,a.ShowSource,u]);return}}}else{if(this.format==="Error"){a.ShowSource.Text(a.jax.errorText,v)}else{if(p.semanticsAnnotations[this.format]){var r=a.jax.root.getAnnotation(this.format);if(r.data[0]){a.ShowSource.Text(r.data[0].toString())}}else{if(a.jax.originalText==null){alert(o("NoOriginalForm","No original form available"));return}a.ShowSource.Text(a.jax.originalText,v)}}}};a.ShowSource.Window=function(s){if(!a.ShowSource.w){var t=[],r=p.windowSettings;for(var u in r){if(r.hasOwnProperty(u)){t.push(u+"="+r[u])}}a.ShowSource.w=window.open("","_blank",t.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(v,t){var r=a.ShowSource.Window(t);delete a.ShowSource.w;v=v.replace(/^\s*/,"").replace(/\s*$/,"");v=v.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");var u=o("EqSource","MathJax Equation Source");if(a.isMobile){r.document.open();r.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>"+u+"</title></head><body style='font-size:85%'>");r.document.write("<pre>"+v+"</pre>");r.document.write("<hr><input type='button' value='"+o("Close","Close")+"' onclick='window.close()' />");r.document.write("</body></html>");r.document.close()}else{r.document.open();r.document.write("<html><head><title>"+u+"</title></head><body style='font-size:85%'>");r.document.write("<table><tr><td><pre>"+v+"</pre></td></tr></table>");r.document.write("</body></html>");r.document.close();var s=r.document.body.firstChild;setTimeout(function(){var A=(r.outerHeight-r.innerHeight)||30,z=(r.outerWidth-r.innerWidth)||30,w,D;z=Math.max(100,Math.min(Math.floor(0.5*screen.width),s.offsetWidth+z+25));A=Math.max(40,Math.min(Math.floor(0.5*screen.height),s.offsetHeight+A+25));if(a.prototype.msieHeightBug){A+=35}r.resizeTo(z,A);var C;try{C=t.screenX}catch(B){}if(t&&C!=null){w=Math.max(0,Math.min(t.screenX-Math.floor(z/2),screen.width-z-20));D=Math.max(0,Math.min(t.screenY-Math.floor(A/2),screen.height-A-20));r.moveTo(w,D)}},50)}};a.Scale=function(){var s=b["HTML-CSS"],r=b.NativeMML,v=b.SVG;var u=(s||r||v||{config:{scale:100}}).config.scale;var t=prompt(o("ScaleMath","Scale all mathematics (compared to surrounding text) by"),u+"%");if(t){if(t.match(/^\s*\d+(\.\d*)?\s*%?\s*$/)){t=parseFloat(t);if(t){if(t!==u){if(s){s.config.scale=t}if(r){r.config.scale=t}if(v){v.config.scale=t}a.cookie.scale=t;a.saveCookie();c.Rerender()}}else{alert(o("NonZeroScale","The scale should not be zero"))}}else{alert(o("PercentScale","The scale should be a percentage (e.g., 120%%)"))}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var s=c.outputJax["jax/mml"];if(s[0]!==p.settings.renderer){var v=c.Browser,u,r=a.Renderer.Messages,t;switch(p.settings.renderer){case"NativeMML":if(!p.settings.warnedMML){if(v.isChrome&&v.version.substr(0,3)!=="24."){u=r.MML.WebKit}else{if(v.isSafari&&!v.versionAtLeast("5.0")){u=r.MML.WebKit}else{if(v.isMSIE){if(!v.hasMathPlayer){u=r.MML.MSIE}}else{u=r.MML[v]}}}t="warnedMML"}break;case"SVG":if(!p.settings.warnedSVG){if(v.isMSIE&&!e){u=r.SVG.MSIE}}break}if(u){u=o(u[0],u[1]);u+="\n\n";u+=o("SwitchAnyway","Switch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)");a.cookie.renderer=s[0].id;a.saveCookie();if(!confirm(u)){a.cookie.renderer=p.settings.renderer=g.Cookie.Get("menu").renderer;a.saveCookie();return}if(t){a.cookie.warned=p.settings.warned=true}a.cookie.renderer=p.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,p.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:["WebkitNativeMMLWarning","Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable."],MSIE:["MSIENativeMMLWarning","Internet Explorer requires the MathPlayer plugin in order to process MathML output."],Opera:["OperaNativeMMLWarning","Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly."],Safari:["SafariNativeMMLWarning","Your browser's native MathML does not implement all the features used by MathJax, so some expressions may not render properly."],Firefox:["FirefoxNativeMMLWarning","Your browser's native MathML does not implement all the features used by MathJax, so some expressions may not render properly."]},SVG:{MSIE:["MSIESVGWarning","SVG is not implemented in Internet Explorer prior to IE9 or when it is emulating IE8 or below. Switching to SVG output will cause the mathematics to not display properly."]}};a.Font=function(){var r=b["HTML-CSS"];if(!r){return}document.location.reload()};a.Locale=function(){MathJax.Localization.setLocale(p.settings.locale);MathJax.Hub.Queue(["Reprocess",MathJax.Hub])};a.LoadLocale=function(){var r=prompt(o("LoadURL","Load translation data from this URL:"));if(r){if(!r.match(/\.js$/)){alert(o("BadURL","The URL should be for a javascript file that defines MathJax translation data.  Javascript file names should end with '.js'"))}k.Require(r,function(s){if(s!=k.STATUS.OK){alert(o("BadData","Failed to load translation data from %1",r))}})}};a.MPEvents=function(t){var s=p.settings.discoverable,r=a.MPEvents.Messages;if(!e){if(p.settings.mpMouse&&!confirm(o.apply(o,r.IE8warning))){delete a.cookie.mpContext;delete p.settings.mpContext;delete a.cookie.mpMouse;delete p.settings.mpMouse;a.saveCookie();return}p.settings.mpContext=p.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=p.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!s&&t.name[1]==="Menu Events"&&p.settings.mpContext){alert(o.apply(o,r.IE9warning))}}};a.MPEvents.Messages={IE8warning:["IE8warning","This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?"],IE9warning:["IE9warning","The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead."]};c.Browser.Select({MSIE:function(r){var s=(document.compatMode==="BackCompat");var t=r.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(s||!t),msieAboutBug:s,msieHeightBug:((document.documentMode||0)<9)});if(e){delete p.styles["#MathJax_About"].filter;delete p.styles[".MathJax_Menu"].filter}},Firefox:function(r){a.skipMouseover=r.isMobile&&r.versionAtLeast("6.0");a.skipMousedown=r.isMobile}});a.isMobile=c.Browser.isMobile;a.noContextMenu=c.Browser.noContextMenu;a.CreateLocaleMenu=function(){if(!a.menu){return}var w=a.menu.Find("Language").menu,t=w.items;var s=[],y=MathJax.Localization.strings;for(var x in y){if(y.hasOwnProperty(x)){s.push(x)}}s=s.sort();w.items=[];for(var u=0,r=s.length;u<r;u++){var v=y[s[u]].menuTitle;if(v){v+=" ("+s[u]+")"}else{v=s[u]}w.items.push(m.RADIO([s[u],v],"locale",{action:a.Locale}))}w.items.push(t[t.length-2],t[t.length-1])};a.CreateAnnotationMenu=function(){if(!a.menu){return}var t=a.menu.Find("Show Math As","Annotation").menu;var s=p.semanticsAnnotations;for(var r in s){if(s.hasOwnProperty(r)){t.items.push(m.COMMAND([r,r],a.ShowSource,{hidden:true,nativeTouch:true,format:r}))}}};c.Register.StartupHook("End Config",function(){p.settings=c.config.menuSettings;if(typeof(p.settings.showRenderer)!=="undefined"){p.showRenderer=p.settings.showRenderer}if(typeof(p.settings.showFontMenu)!=="undefined"){p.showFontMenu=p.settings.showFontMenu}if(typeof(p.settings.showContext)!=="undefined"){p.showContext=p.settings.showContext}a.getCookie();a.menu=a(m.SUBMENU(["Show","Show Math As"],m.COMMAND(["MathMLcode","MathML Code"],a.ShowSource,{nativeTouch:true,format:"MathML"}),m.COMMAND(["Original","Original Form"],a.ShowSource,{nativeTouch:true}),m.SUBMENU(["Annotation","Annotation"],{disabled:true}),m.RULE(),m.CHECKBOX(["texHints","Show TeX hints in MathML"],"texHints"),m.CHECKBOX(["semantics","Add original form as annotation"],"semantics")),m.RULE(),m.SUBMENU(["Settings","Math Settings"],m.SUBMENU(["ZoomTrigger","Zoom Trigger"],m.RADIO(["Hover","Hover"],"zoom",{action:a.Zoom}),m.RADIO(["Click","Click"],"zoom",{action:a.Zoom}),m.RADIO(["DoubleClick","Double-Click"],"zoom",{action:a.Zoom}),m.RADIO(["NoZoom","No Zoom"],"zoom",{value:"None"}),m.RULE(),m.LABEL(["TriggerRequires","Trigger Requires:"]),m.CHECKBOX((c.Browser.isMac?["Option","Option"]:["Alt","Alt"]),"ALT"),m.CHECKBOX(["Command","Command"],"CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX(["Control","Control"],"CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX(["Shift","Shift"],"Shift")),m.SUBMENU(["ZoomFactor","Zoom Factor"],m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU(["Renderer","Math Renderer"],{hidden:!p.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("Fast HTML","renderer",{action:a.Renderer,value:"CommonHTML"}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer}),m.RULE(),m.CHECKBOX("Fast Preview","CHTMLpreview")),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!p.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL(["MPHandles","Let MathPlayer Handle:"]),m.CHECKBOX(["MenuEvents","Menu Events"],"mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX(["MouseEvents","Mouse Events"],"mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX(["MenuAndMouse","Mouse and Menu Events"],"mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU(["FontPrefs","Font Preference"],{hidden:!p.showFontMenu},m.LABEL(["ForHTMLCSS","For HTML-CSS:"]),m.RADIO(["Auto","Auto"],"font",{action:a.Font}),m.RULE(),m.RADIO(["TeXLocal","TeX (local)"],"font",{action:a.Font}),m.RADIO(["TeXWeb","TeX (web)"],"font",{action:a.Font}),m.RADIO(["TeXImage","TeX (image)"],"font",{action:a.Font}),m.RULE(),m.RADIO(["STIXLocal","STIX (local)"],"font",{action:a.Font}),m.RADIO(["STIXWeb","STIX (web)"],"font",{action:a.Font}),m.RULE(),m.RADIO(["AsanaMathWeb","Asana Math (web)"],"font",{action:a.Font}),m.RADIO(["GyrePagellaWeb","Gyre Pagella (web)"],"font",{action:a.Font}),m.RADIO(["GyreTermesWeb","Gyre Termes (web)"],"font",{action:a.Font}),m.RADIO(["LatinModernWeb","Latin Modern (web)"],"font",{action:a.Font}),m.RADIO(["NeoEulerWeb","Neo Euler (web)"],"font",{action:a.Font})),m.SUBMENU(["ContextMenu","Contextual Menu"],{hidden:!p.showContext},m.RADIO("MathJax","context"),m.RADIO(["Browser","Browser"],"context")),m.COMMAND(["Scale","Scale All Math ..."],a.Scale),m.RULE().With({hidden:!p.showDiscoverable,name:["","discover_rule"]}),m.CHECKBOX(["Discoverable","Highlight on Hover"],"discoverable",{hidden:!p.showDiscoverable})),m.SUBMENU(["Locale","Language"],{hidden:!p.showLocale,ltr:true},m.RADIO("en","locale",{action:a.Locale}),m.RULE().With({hidden:!p.showLocaleURL,name:["","localURL_rule"]}),m.COMMAND(["LoadLocale","Load from URL ..."],a.LoadLocale,{hidden:!p.showLocaleURL})),m.RULE(),m.COMMAND(["About","About MathJax"],a.About),m.COMMAND(["Help","MathJax Help"],a.Help));if(a.isMobile){(function(){var s=p.settings;var r=a.menu.Find("Math Settings","Zoom Trigger").menu;r.items[0].disabled=r.items[1].disabled=true;if(s.zoom==="Hover"||s.zoom=="Click"){s.zoom="None"}r.items=r.items.slice(0,4);if(navigator.appVersion.match(/[ (]Android[) ]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}a.CreateLocaleMenu();a.CreateAnnotationMenu()});a.showRenderer=function(r){a.cookie.showRenderer=p.showRenderer=r;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!r};a.showMathPlayer=function(r){a.cookie.showMathPlayer=p.showMathPlayer=r;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!r};a.showFontMenu=function(r){a.cookie.showFontMenu=p.showFontMenu=r;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!r};a.showContext=function(r){a.cookie.showContext=p.showContext=r;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!r};a.showDiscoverable=function(r){a.cookie.showDiscoverable=p.showDiscoverable=r;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!r;a.menu.Find("Math Settings","discover_rule").hidden=!r};a.showLocale=function(r){a.cookie.showLocale=p.showLocale=r;a.saveCookie();a.menu.Find("Language").hidden=!r};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){if(!MathJax.OutputJax["HTML-CSS"].config.imageFont){a.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=true}});f.Queue(c.Register.StartupHook("End Config",{}),["getImages",a],["Styles",k,p.styles],["Post",c.Startup.signal,"MathMenu Ready"],["loadComplete",k,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.CallBack,MathJax.OutputJax);
MathJax.ElementJax.mml=MathJax.ElementJax({mimeType:"jax/mml"},{id:"mml",version:"2.5.1",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.attr&&this.root.attr.mode){if(!this.root.display&&this.root.attr.mode==="display"){this.root.display="block";this.root.attrNames.push("display")}delete this.root.attr.mode;for(var b=0,a=this.root.attrNames.length;b<a;b++){if(this.root.attrNames[b]==="mode"){this.root.attrNames.splice(b,1);break}}}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",UPDIAGONALARROW:"updiagonalarrow",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",PHASORANGLE:"phasorangle",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributes:{displaystyle:1,scriptlevel:1,open:1,close:1,form:1,actiontype:1,fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":1,href:true,style:true},copyAttributeNames:["displaystyle","scriptlevel","open","close","form","actiontype","fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],nocopyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true,xmlns:true},Error:function(d,e){var c=this.merror(d),b=MathJax.Localization.fontDirection(),a=MathJax.Localization.fontFamily();if(e){c=c.With(e)}if(b||a){c=this.mstyle(c);if(b){c.dir=b}if(a){c.style.fontFamily="font-family: "+a}}return c}});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true,notParent:true}))}this.Append.apply(this,arguments)},With:function(e){for(var f in e){if(e.hasOwnProperty(f)){this[f]=e[f]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var f=0,e=arguments.length;f<e;f++){this.SetData(this.data.length,arguments[f])}}},SetData:function(e,f){if(f!=null){if(!(f instanceof a.mbase)){f=(this.isToken||this.isChars?a.chars(f):a.mtext(f))}f.parent=this;f.setInherit(this.inheritFromMe?this:this.inherit)}this.data[e]=f},Parent:function(){var e=this.parent;while(e&&e.notParent){e=e.parent}return e},Get:function(f,k,l){if(!l){if(this[f]!=null){return this[f]}if(this.attr&&this.attr[f]!=null){return this.attr[f]}}var g=this.Parent();if(g&&g["adjustChild_"+f]!=null){return(g["adjustChild_"+f])(this.childPosition(),k)}var j=this.inherit;var e=j;while(j){var i=j[f];if(i==null&&j.attr){i=j.attr[f]}if(i!=null&&j.noInheritAttribute&&!j.noInheritAttribute[f]){var h=j.noInherit[this.type];if(!(h&&h[f])){return i}}e=j;j=j.inherit}if(!k){if(this.defaults[f]===a.AUTO){return this.autoDefault(f)}if(this.defaults[f]!==a.INHERIT&&this.defaults[f]!=null){return this.defaults[f]}if(e){return e.defaults[f]}}return null},hasValue:function(e){return(this.Get(e,true)!=null)},getValues:function(){var f={};for(var g=0,e=arguments.length;g<e;g++){f[arguments[g]]=this.Get(arguments[g])}return f},adjustChild_scriptlevel:function(f,e){return this.Get("scriptlevel",e)},adjustChild_displaystyle:function(f,e){return this.Get("displaystyle",e)},adjustChild_texprimestyle:function(f,e){return this.Get("texprimestyle",e)},childPosition:function(){var h=this,g=h.parent;while(g.notParent){h=g;g=h.parent}for(var f=0,e=g.data.length;f<e;f++){if(g.data[f]===h){return f}}return null},setInherit:function(g){if(g!==this.inherit&&this.inherit==null){this.inherit=g;for(var f=0,e=this.data.length;f<e;f++){if(this.data[f]&&this.data[f].setInherit){this.data[f].setInherit(g)}}}},setTeXclass:function(e){this.getPrevClass(e);return(typeof(this.texClass)!=="undefined"?this:e)},getPrevClass:function(e){if(e){this.prevClass=e.Get("texClass");this.prevLevel=e.Get("scriptlevel")}},updateTeXclass:function(e){if(e){this.prevClass=e.prevClass;delete e.prevClass;this.prevLevel=e.prevLevel;delete e.prevLevel;this.texClass=e.Get("texClass")}},texSpacing:function(){var f=(this.prevClass!=null?this.prevClass:a.TEXCLASS.NONE);var e=(this.Get("texClass")||a.TEXCLASS.ORD);if(f===a.TEXCLASS.NONE||e===a.TEXCLASS.NONE){return""}if(f===a.TEXCLASS.VCENTER){f=a.TEXCLASS.ORD}if(e===a.TEXCLASS.VCENTER){e=a.TEXCLASS.ORD}var g=this.TEXSPACE[f][e];if(this.prevLevel>0&&this.Get("scriptlevel")>0&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var f=0,e=this.data.length;f<e;f++){if(this.data[f]&&this.data[f].hasNewline()){return true}}return false},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"},getAnnotation:function(){return null}},{childrenSpacelike:function(){for(var f=0,e=this.data.length;f<e;f++){if(!this.data[f].isSpacelike()){return false}}return true},childEmbellished:function(){return(this.data[0]&&this.data[0].isEmbellished())},childCore:function(){return this.data[0]},childCoreMO:function(){return(this.data[0]?this.data[0].CoreMO():null)},setChildTeXclass:function(e){if(this.data[0]){e=this.data[0].setTeXclass(e);this.updateTeXclass(this.data[0])}return e},setBaseTeXclasses:function(g){this.getPrevClass(g);this.texClass=null;if(this.data[0]){if(this.isEmbellished()||this.data[0].isa(a.mi)){g=this.data[0].setTeXclass(g);this.updateTeXclass(this.Core())}else{this.data[0].setTeXclass();g=this}}else{g=this}for(var f=1,e=this.data.length;f<e;f++){if(this.data[f]){this.data[f].setTeXclass()}}return g},setSeparateTeXclasses:function(g){this.getPrevClass(g);for(var f=0,e=this.data.length;f<e;f++){if(this.data[f]){this.data[f].setTeXclass()}}if(this.isEmbellished()){this.updateTeXclass(this.Core())}return this}});a.mi=a.mbase.Subclass({type:"mi",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.AUTO,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT},autoDefault:function(f){if(f==="mathvariant"){var e=(this.data[0]||"").toString();return(e.length===1||(e.length===2&&e.charCodeAt(0)>=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h<e;h++){var j=this.OPTABLE[f[h]][k];if(j){l=this.makeDef(j);break}}if(!l){l=this.CheckRange(k)}if(!l&&n){l={}}else{if(!l){l=MathJax.Hub.Insert({},this.defaultDef)}if(this.parent){this.def=l}else{l=MathJax.Hub.Insert({},l)}l.form=f[0]}}this.useMMLspacing&=~(this.SPACE_ATTR[g]||0);if(l[g]!=null){return l[g]}else{if(!n){return this.defaultDef[g]}}return""},CheckRange:function(j){var k=j.charCodeAt(0);if(k>=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g<e&&this.RANGES[g][0]<=k;g++){if(k<=this.RANGES[g][1]){if(this.RANGES[g][3]){var f=a.optableDir+"/"+this.RANGES[g][3]+".js";this.RANGES[g][3]=null;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(f))}var h=a.TEXCLASSNAMES[this.RANGES[g][2]];h=this.OPTABLE.infix[j]=a.mo.OPTYPES[h==="BIN"?"BIN3":h];return this.makeDef(h)}}return null},makeDef:function(f){if(f[2]==null){f[2]=this.defaultDef.texClass}if(!f[3]){f[3]={}}var e=MathJax.Hub.Insert({},f[3]);e.lspace=this.SPACE[f[0]];e.rspace=this.SPACE[f[1]];e.texClass=f[2];if(e.texClass===a.TEXCLASS.REL&&(this.movablelimits||this.data.join("").match(/^[a-z]+$/i))){e.texClass=a.TEXCLASS.OP}return e},getForm:function(){var e=this,g=this.parent,f=this.Parent();while(f&&f.isEmbellished()){e=g;g=f.parent;f=f.Parent()}if(g&&g.type==="mrow"&&g.NonSpaceLength()!==1){if(g.FirstNonSpace()===e){return a.FORM.PREFIX}if(g.LastNonSpace()===e){return a.FORM.POSTFIX}}return a.FORM.INFIX},isEmbellished:function(){return true},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)},CoreParent:function(){var e=this;while(e&&e.isEmbellished()&&e.CoreMO()===this&&!e.isa(a.math)){e=e.Parent()}return e},CoreText:function(e){if(!e){return""}if(e.isEmbellished()){return e.CoreMO().data.join("")}while((((e.isa(a.mrow)||e.isa(a.TeXAtom)||e.isa(a.mstyle)||e.isa(a.mphantom))&&e.data.length===1)||e.isa(a.munderover))&&e.data[0]){e=e.data[0]}if(!e.isToken){return""}else{return e.data.join("")}},remapChars:{"*":"\u2217",'"':"\u2033","\u00B0":"\u2218","\u00B2":"2","\u00B3":"3","\u00B4":"\u2032","\u00B9":"1"},remap:function(f,e){f=f.replace(/-/g,"\u2212");if(e){f=f.replace(/'/g,"\u2032").replace(/`/g,"\u2035");if(f.length===1){f=e[f]||f}}return f},setTeXclass:function(f){var e=this.getValues("form","lspace","rspace","fence");if(this.useMMLspacing){this.texClass=a.TEXCLASS.NONE;return this}if(e.fence&&!this.texClass){if(e.form===a.FORM.PREFIX){this.texClass=a.TEXCLASS.OPEN}if(e.form===a.FORM.POSTFIX){this.texClass=a.TEXCLASS.CLOSE}}this.texClass=this.Get("texClass");if(this.data.join("")==="\u2061"){if(f){f.texClass=a.TEXCLASS.OP;f.fnOP=true}this.texClass=this.prevClass=a.TEXCLASS.NONE;return f}return this.adjustTeXclass(f)},adjustTeXclass:function(e){if(this.texClass===a.TEXCLASS.NONE){return e}if(e){if(e.autoOP&&(this.texClass===a.TEXCLASS.BIN||this.texClass===a.TEXCLASS.REL)){e.texClass=a.TEXCLASS.ORD}this.prevClass=e.texClass||a.TEXCLASS.ORD;this.prevLevel=e.Get("scriptlevel")}else{this.prevClass=a.TEXCLASS.NONE}if(this.texClass===a.TEXCLASS.BIN&&(this.prevClass===a.TEXCLASS.NONE||this.prevClass===a.TEXCLASS.BIN||this.prevClass===a.TEXCLASS.OP||this.prevClass===a.TEXCLASS.REL||this.prevClass===a.TEXCLASS.OPEN||this.prevClass===a.TEXCLASS.PUNCT)){this.texClass=a.TEXCLASS.ORD}else{if(this.prevClass===a.TEXCLASS.BIN&&(this.texClass===a.TEXCLASS.REL||this.texClass===a.TEXCLASS.CLOSE||this.texClass===a.TEXCLASS.PUNCT)){e.texClass=this.prevClass=a.TEXCLASS.ORD}}return this}});a.mtext=a.mbase.Subclass({type:"mtext",isToken:true,isSpacelike:function(){return true},texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mspace=a.mbase.Subclass({type:"mspace",isToken:true,isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"0em",height:"0ex",depth:"0ex",linebreak:a.LINEBREAK.AUTO},hasDimAttr:function(){return(this.hasValue("width")||this.hasValue("height")||this.hasValue("depth"))},hasNewline:function(){return(!this.hasDimAttr()&&this.Get("linebreak")===a.LINEBREAK.NEWLINE)}});a.ms=a.mbase.Subclass({type:"ms",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,lquote:'"',rquote:'"'}});a.mglyph=a.mbase.Subclass({type:"mglyph",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,alt:"",src:"",width:a.AUTO,height:a.AUTO,valign:"0em"}});a.mrow=a.mbase.Subclass({type:"mrow",isSpacelike:a.mbase.childrenSpacelike,inferred:false,notParent:false,isEmbellished:function(){var f=false;for(var g=0,e=this.data.length;g<e;g++){if(this.data[g]==null){continue}if(this.data[g].isEmbellished()){if(f){return false}f=true;this.core=g}else{if(!this.data[g].isSpacelike()){return false}}}return f},NonSpaceLength:function(){var g=0;for(var f=0,e=this.data.length;f<e;f++){if(this.data[f]&&!this.data[f].isSpacelike()){g++}}return g},FirstNonSpace:function(){for(var f=0,e=this.data.length;f<e;f++){if(this.data[f]&&!this.data[f].isSpacelike()){return this.data[f]}}return null},LastNonSpace:function(){for(var e=this.data.length-1;e>=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f<e;f++){if(this.data[f]){g=this.data[f].setTeXclass(g)}}if(!this.hasOwnProperty("texClass")){this.texClass=a.TEXCLASS.INNER}return this}else{for(f=0;f<e;f++){if(this.data[f]){g=this.data[f].setTeXclass(g)}}if(this.data[0]){this.updateTeXclass(this.data[0])}return g}},getAnnotation:function(e){if(this.data.length!=1){return null}return this.data[0].getAnnotation(e)}});a.mfrac=a.mbase.Subclass({type:"mfrac",num:0,den:1,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,linethickness:a.LINETHICKNESS.MEDIUM,numalign:a.ALIGN.CENTER,denomalign:a.ALIGN.CENTER,bevelled:false},adjustChild_displaystyle:function(e){return false},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(!this.Get("displaystyle")||e>0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){delete this.scriptlevel;var e=this.Get("scriptlevel");this.scriptlevel=f;f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}));this.data.open.useMMLspacing&=~this.data.open.SPACE_ATTR.form}if(f.separators!==""){while(f.separators.length<this.data.length){f.separators+=f.separators.charAt(f.separators.length-1)}for(var g=1,e=this.data.length;g<e;g++){if(this.data[g]){this.SetData("sep"+g,a.mo(f.separators.charAt(g-1)).With({separator:true}))}}}if(f.close!==""){this.SetData("close",a.mo(f.close).With({fence:true,form:a.FORM.POSTFIX,texClass:a.TEXCLASS.CLOSE}));this.data.close.useMMLspacing&=~this.data.close.SPACE_ATTR.form}},texClass:a.TEXCLASS.OPEN,setTeXclass:function(g){this.addFakeNodes();this.getPrevClass(g);if(this.data.open){g=this.data.open.setTeXclass(g)}if(this.data[0]){g=this.data[0].setTeXclass(g)}for(var f=1,e=this.data.length;f<e;f++){if(this.data["sep"+f]){g=this.data["sep"+f].setTeXclass(g)}if(this.data[f]){g=this.data[f].setTeXclass(g)}}if(this.data.close){g=this.data.close.setTeXclass(g)}this.updateTeXclass(this.data.open);this.texClass=a.TEXCLASS.INNER;return g}});a.menclose=a.mbase.Subclass({type:"menclose",inferRow:true,linebreakContainer:true,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,notation:a.NOTATION.LONGDIV,texClass:a.TEXCLASS.ORD},setTeXclass:a.mbase.setSeparateTeXclasses});a.msubsup=a.mbase.Subclass({type:"msubsup",base:0,sub:1,sup:2,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,subscriptshift:"",superscriptshift:"",texClass:a.AUTO},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}return 0},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f<e;f++){if(!((arguments[f] instanceof a.mtr)||(arguments[f] instanceof a.mlabeledtr))){arguments[f]=a.mtr(arguments[f])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtr=a.mbase.Subclass({type:"mtr",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{rowalign:true,columnalign:true,groupalign:true},mtable:{rowalign:true,columnalign:true,groupalign:true}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f<e;f++){if(!(arguments[f] instanceof a.mtd)){arguments[f]=a.mtd(arguments[f])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtd=a.mbase.Subclass({type:"mtd",inferRow:true,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowspan:1,columnspan:1,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},setTeXclass:a.mbase.setSeparateTeXclasses});a.maligngroup=a.mbase.Subclass({type:"malign",isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{groupalign:true},mtable:{groupalign:true}}});a.malignmark=a.mbase.Subclass({type:"malignmark",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,edge:a.SIDE.LEFT},isSpacelike:function(){return true}});a.mlabeledtr=a.mtr.Subclass({type:"mlabeledtr"});a.maction=a.mbase.Subclass({type:"maction",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,actiontype:a.ACTIONTYPE.TOGGLE,selection:1},selected:function(){return this.data[this.Get("selection")-1]||a.NULL},isEmbellished:function(){return this.selected().isEmbellished()},isSpacelike:function(){return this.selected().isSpacelike()},Core:function(){return this.selected().Core()},CoreMO:function(){return this.selected().CoreMO()},setTeXclass:function(e){if(this.Get("actiontype")===a.ACTIONTYPE.TOOLTIP&&this.data[1]){this.data[1].setTeXclass()}return this.selected().setTeXclass(e)}});a.semantics=a.mbase.Subclass({type:"semantics",notParent:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{definitionURL:null,encoding:null},setTeXclass:a.mbase.setChildTeXclass,getAnnotation:function(g){var l=MathJax.Hub.config.MathMenu.semanticsAnnotations[g];if(l){for(var h=0,e=this.data.length;h<e;h++){var k=this.data[h].Get("encoding");if(k){for(var f=0,o=l.length;f<o;f++){if(l[f]===k){return this.data[h]}}}}}return null}});a.annotation=a.mbase.Subclass({type:"annotation",isChars:true,linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a["annotation-xml"]=a.mbase.Subclass({type:"annotation-xml",linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a.math=a.mstyle.Subclass({type:"math",defaults:{mathvariant:a.VARIANT.NORMAL,mathsize:a.SIZE.NORMAL,mathcolor:"",mathbackground:a.COLOR.TRANSPARENT,dir:"ltr",scriptlevel:0,displaystyle:a.AUTO,display:"inline",maxwidth:"",overflow:a.OVERFLOW.LINEBREAK,altimg:"","altimg-width":"","altimg-height":"","altimg-valign":"",alttext:"",cdgroup:"",scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8px",infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,lineleading:"1ex",indentshift:"auto",indentalign:a.INDENTALIGN.AUTO,indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,decimalseparator:".",texprimestyle:false},autoDefault:function(e){if(e==="displaystyle"){return this.Get("display")==="block"}return""},linebreakContainer:true,setTeXclass:a.mbase.setChildTeXclass,getAnnotation:function(e){if(this.data.length!=1){return null}return this.data[0].getAnnotation(e)}});a.chars=a.mbase.Subclass({type:"chars",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){return this.data.join("")},toString:function(){return this.data.join("")}});a.entity=a.mbase.Subclass({type:"entity",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){if(this.data[0].substr(0,2)==="#x"){return parseInt(this.data[0].substr(2),16)}else{if(this.data[0].substr(0,1)==="#"){return parseInt(this.data[0].substr(1))}else{return 0}}},toString:function(){var e=this.value();if(e<=65535){return String.fromCharCode(e)}e-=65536;return String.fromCharCode((e>>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f<e;f++){var g=this.Import(arguments[f]);this.data.push(g);this.div.appendChild(g)}},Import:function(j){if(document.importNode){return document.importNode(j,true)}var f,g,e;if(j.nodeType===1){f=document.createElement(j.nodeName);for(g=0,e=j.attributes.length;g<e;g++){var h=j.attributes[g];if(h.specified&&h.nodeValue!=null&&h.nodeValue!=""){f.setAttribute(h.nodeName,h.nodeValue)}if(h.nodeName==="style"){f.style.cssText=h.nodeValue}}if(j.className){f.className=j.className}}else{if(j.nodeType===3||j.nodeType===4){f=document.createTextNode(j.nodeValue)}else{if(j.nodeType===8){f=document.createComment(j.nodeValue)}else{return document.createTextNode("")}}}for(g=0,e=j.childNodes.length;g<e;g++){f.appendChild(this.Import(j.childNodes[g]))}return f},value:function(){return this.div},toString:function(){return this.div.innerHTML}});a.TeXAtom=a.mbase.Subclass({type:"texatom",inferRow:true,notParent:true,texClass:a.TEXCLASS.ORD,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,isEmbellished:a.mbase.childEmbellished,setTeXclass:function(e){this.data[0].setTeXclass();return this.adjustTeXclass(e)},adjustTeXclass:a.mo.prototype.adjustTeXclass});a.NULL=a.mbase().With({type:"null"});var b=a.TEXCLASS;var d={ORD:[0,0,b.ORD],ORD11:[1,1,b.ORD],ORD21:[2,1,b.ORD],ORD02:[0,2,b.ORD],ORD55:[5,5,b.ORD],OP:[1,2,b.OP,{largeop:true,movablelimits:true,symmetric:true}],OPFIXED:[1,2,b.OP,{largeop:true,movablelimits:true}],INTEGRAL:[0,1,b.OP,{largeop:true,symmetric:true}],INTEGRAL2:[1,2,b.OP,{largeop:true,symmetric:true}],BIN3:[3,3,b.BIN],BIN4:[4,4,b.BIN],BIN01:[0,1,b.BIN],BIN5:[5,5,b.BIN],TALLBIN:[4,4,b.BIN,{stretchy:true}],BINOP:[4,4,b.BIN,{largeop:true,movablelimits:true}],REL:[5,5,b.REL],REL1:[1,1,b.REL,{stretchy:true}],REL4:[4,4,b.REL],RELSTRETCH:[5,5,b.REL,{stretchy:true}],RELACCENT:[5,5,b.REL,{accent:true}],WIDEREL:[5,5,b.REL,{accent:true,stretchy:true}],OPEN:[0,0,b.OPEN,{fence:true,stretchy:true,symmetric:true}],CLOSE:[0,0,b.CLOSE,{fence:true,stretchy:true,symmetric:true}],INNER:[0,0,b.INNER],PUNCT:[0,3,b.PUNCT],ACCENT:[0,0,b.ORD,{accent:true}],WIDEACCENT:[0,0,b.ORD,{accent:true,stretchy:true}]};a.mo.Augment({SPACE:["0em","0.1111em","0.1667em","0.2222em","0.2667em","0.3333em"],RANGES:[[32,127,b.REL,"BasicLatin"],[160,255,b.ORD,"Latin1Supplement"],[256,383,b.ORD],[384,591,b.ORD],[688,767,b.ORD,"SpacingModLetters"],[768,879,b.ORD,"CombDiacritMarks"],[880,1023,b.ORD,"GreekAndCoptic"],[7680,7935,b.ORD],[8192,8303,b.PUNCT,"GeneralPunctuation"],[8304,8351,b.ORD],[8352,8399,b.ORD],[8400,8447,b.ORD,"CombDiactForSymbols"],[8448,8527,b.ORD,"LetterlikeSymbols"],[8528,8591,b.ORD],[8592,8703,b.REL,"Arrows"],[8704,8959,b.BIN,"MathOperators"],[8960,9215,b.ORD,"MiscTechnical"],[9312,9471,b.ORD],[9472,9631,b.ORD],[9632,9727,b.ORD,"GeometricShapes"],[9984,10175,b.ORD,"Dingbats"],[10176,10223,b.ORD,"MiscMathSymbolsA"],[10224,10239,b.REL,"SupplementalArrowsA"],[10496,10623,b.REL,"SupplementalArrowsB"],[10624,10751,b.ORD,"MiscMathSymbolsB"],[10752,11007,b.BIN,"SuppMathOperators"],[11008,11263,b.ORD,"MiscSymbolsAndArrows"],[119808,120831,b.ORD]],OPTABLE:{prefix:{"\u2200":d.ORD21,"\u2202":d.ORD21,"\u2203":d.ORD21,"\u2207":d.ORD21,"\u220F":d.OP,"\u2210":d.OP,"\u2211":d.OP,"\u2212":d.BIN01,"\u2213":d.BIN01,"\u221A":[1,1,b.ORD,{stretchy:true}],"\u2220":d.ORD,"\u222B":d.INTEGRAL,"\u222E":d.INTEGRAL,"\u22C0":d.OP,"\u22C1":d.OP,"\u22C2":d.OP,"\u22C3":d.OP,"\u2308":d.OPEN,"\u230A":d.OPEN,"\u27E8":d.OPEN,"\u27EE":d.OPEN,"\u2A00":d.OP,"\u2A01":d.OP,"\u2A02":d.OP,"\u2A04":d.OP,"\u2A06":d.OP,"\u00AC":d.ORD21,"\u00B1":d.BIN01,"(":d.OPEN,"+":d.BIN01,"-":d.BIN01,"[":d.OPEN,"{":d.OPEN,"|":d.OPEN},postfix:{"!":[1,0,b.CLOSE],"&":d.ORD,"\u2032":d.ORD02,"\u203E":d.WIDEACCENT,"\u2309":d.CLOSE,"\u230B":d.CLOSE,"\u23DE":d.WIDEACCENT,"\u23DF":d.WIDEACCENT,"\u266D":d.ORD02,"\u266E":d.ORD02,"\u266F":d.ORD02,"\u27E9":d.CLOSE,"\u27EF":d.CLOSE,"\u02C6":d.WIDEACCENT,"\u02C7":d.WIDEACCENT,"\u02C9":d.WIDEACCENT,"\u02CA":d.ACCENT,"\u02CB":d.ACCENT,"\u02D8":d.ACCENT,"\u02D9":d.ACCENT,"\u02DC":d.WIDEACCENT,"\u0302":d.WIDEACCENT,"\u00A8":d.ACCENT,"\u00AF":d.WIDEACCENT,")":d.CLOSE,"]":d.CLOSE,"^":d.WIDEACCENT,_:d.WIDEACCENT,"`":d.ACCENT,"|":d.CLOSE,"}":d.CLOSE,"~":d.WIDEACCENT},infix:{"":d.ORD,"%":[3,3,b.ORD],"\u2022":d.BIN4,"\u2026":d.INNER,"\u2044":d.TALLBIN,"\u2061":d.ORD,"\u2062":d.ORD,"\u2063":[0,0,b.ORD,{linebreakstyle:"after",separator:true}],"\u2064":d.ORD,"\u2190":d.WIDEREL,"\u2191":d.RELSTRETCH,"\u2192":d.WIDEREL,"\u2193":d.RELSTRETCH,"\u2194":d.WIDEREL,"\u2195":d.RELSTRETCH,"\u2196":d.RELSTRETCH,"\u2197":d.RELSTRETCH,"\u2198":d.RELSTRETCH,"\u2199":d.RELSTRETCH,"\u21A6":d.WIDEREL,"\u21A9":d.WIDEREL,"\u21AA":d.WIDEREL,"\u21BC":d.WIDEREL,"\u21BD":d.WIDEREL,"\u21C0":d.WIDEREL,"\u21C1":d.WIDEREL,"\u21CC":d.WIDEREL,"\u21D0":d.WIDEREL,"\u21D1":d.RELSTRETCH,"\u21D2":d.WIDEREL,"\u21D3":d.RELSTRETCH,"\u21D4":d.WIDEREL,"\u21D5":d.RELSTRETCH,"\u2208":d.REL,"\u2209":d.REL,"\u220B":d.REL,"\u2212":d.BIN4,"\u2213":d.BIN4,"\u2215":d.TALLBIN,"\u2216":d.BIN4,"\u2217":d.BIN4,"\u2218":d.BIN4,"\u2219":d.BIN4,"\u221D":d.REL,"\u2223":d.REL,"\u2225":d.REL,"\u2227":d.BIN4,"\u2228":d.BIN4,"\u2229":d.BIN4,"\u222A":d.BIN4,"\u223C":d.REL,"\u2240":d.BIN4,"\u2243":d.REL,"\u2245":d.REL,"\u2248":d.REL,"\u224D":d.REL,"\u2250":d.REL,"\u2260":d.REL,"\u2261":d.REL,"\u2264":d.REL,"\u2265":d.REL,"\u226A":d.REL,"\u226B":d.REL,"\u227A":d.REL,"\u227B":d.REL,"\u2282":d.REL,"\u2283":d.REL,"\u2286":d.REL,"\u2287":d.REL,"\u228E":d.BIN4,"\u2291":d.REL,"\u2292":d.REL,"\u2293":d.BIN4,"\u2294":d.BIN4,"\u2295":d.BIN4,"\u2296":d.BIN4,"\u2297":d.BIN4,"\u2298":d.BIN4,"\u2299":d.BIN4,"\u22A2":d.REL,"\u22A3":d.REL,"\u22A4":d.ORD55,"\u22A5":d.REL,"\u22A8":d.REL,"\u22C4":d.BIN4,"\u22C5":d.BIN4,"\u22C6":d.BIN4,"\u22C8":d.REL,"\u22EE":d.ORD55,"\u22EF":d.INNER,"\u22F1":[5,5,b.INNER],"\u25B3":d.BIN4,"\u25B5":d.BIN4,"\u25B9":d.BIN4,"\u25BD":d.BIN4,"\u25BF":d.BIN4,"\u25C3":d.BIN4,"\u2758":d.REL,"\u27F5":d.WIDEREL,"\u27F6":d.WIDEREL,"\u27F7":d.WIDEREL,"\u27F8":d.WIDEREL,"\u27F9":d.WIDEREL,"\u27FA":d.WIDEREL,"\u27FC":d.WIDEREL,"\u2A2F":d.BIN4,"\u2A3F":d.BIN4,"\u2AAF":d.REL,"\u2AB0":d.REL,"\u00B1":d.BIN4,"\u00B7":d.BIN4,"\u00D7":d.BIN4,"\u00F7":d.BIN4,"*":d.BIN3,"+":d.BIN4,",":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"-":d.BIN4,".":[3,3,b.ORD],"/":d.ORD11,":":[1,2,b.REL],";":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"<":d.REL,"=":d.REL,">":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js");
MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.5.0";var a=MathJax.ElementJax.mml;SETTINGS=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[],h=(this.isToken?"":k+(g?"":"  "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken&&!this.isChars){j.push(h+"<mrow />")}}}if(this.isToken||this.isChars){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var h=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var g=(this.attrNames||a.copyAttributeNames),f=a.skipAttributes,k=a.copyAttributes;var d=[];if(this.type==="math"&&(!this.attr||!this.attr.xmlns)){d.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var j in h){if(!f[j]&&!k[j]&&h.hasOwnProperty(j)){if(this[j]!=null&&this[j]!==h[j]){if(this.Get(j,null,1)!==this[j]){d.push(j+'="'+this.toMathMLattribute(this[j])+'"')}}}}}for(var e=0,c=g.length;e<c;e++){if(k[g[e]]===1&&!h.hasOwnProperty(g[e])){continue}value=(this.attr||{})[g[e]];if(value==null){value=this[g[e]]}if(value!=null){d.push(g[e]+'="'+this.toMathMLquote(value)+'"')}}this.toMathMLclass(d);if(d.length){return" "+d.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)&&SETTINGS.texHints){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return(RegExp.$2||"")+((1/18)*RegExp.$3).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(f){f=String(f).split("");for(var g=0,d=f.length;g<d;g++){var k=f[g].charCodeAt(0);if(k<=55295||57344<=k){if(k>126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[f[g]];if(j){f[g]=j}}}else{if(g+1<d){var h=f[g+1].charCodeAt(0);var e=(((k-55296)<<10)+(h-56320)+65536);f[g]="&#x"+e.toString(16).toUpperCase()+";";f[g+1]="";g++}else{f[g]=""}}}return f.join("")}});a.math.Augment({toMathML:function(c,d){var f;if(c==null){c=""}if(d&&d.originalText&&SETTINGS.semantics){f=MathJax.InputJax[d.inputJax].annotationEncoding}var l=(this.data[0]&&this.data[0].data.length>1);var o=this.type,j=this.toMathMLattributes();var h=[],n=c+(f?"  "+(l?"  ":""):"")+"  ";for(var g=0,e=this.data.length;g<e;g++){if(this.data[g]){h.push(this.data[g].toMathML(n))}else{h.push(n+"<mrow />")}}if(h.length===0||(h.length===1&&h[0]==="")){if(!f){return"<"+o+j+" />"}h.push(n+"<mrow />")}if(f){if(l){h.unshift(c+"    <mrow>");h.push(c+"    </mrow>")}h.unshift(c+"  <semantics>");var k=d.originalText.replace(/[&<>]/g,function(i){return{">":"&gt;","<":"&lt;","&":"&amp;"}[i]});h.push(c+'    <annotation encoding="'+f+'">'+k+"</annotation>");h.push(c+"  </semantics>")}return c+"<"+o+j+">\n"+h.join("\n")+"\n"+c+"</"+o+">"}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+"  "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+"  "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();if(!c&&this.data[0].data.length===1){return d.substr(2)+this.data[0].toMathML(d)}return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+"  ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js");
(function(ac){var g;var X=MathJax.Object.Subclass({firstChild:null,lastChild:null,Init:function(){this.childNodes=[]},appendChild:function(i){if(i.parent){i.parent.removeChild(i)}if(this.lastChild){this.lastChild.nextSibling=i}if(!this.firstChild){this.firstChild=i}this.childNodes.push(i);i.parent=this;this.lastChild=i;return i},removeChild:function(af){for(var ae=0,ad=this.childNodes.length;ae<ad;ae++){if(this.childNodes[ae]===af){break}}if(ae===ad){return}this.childNodes.splice(ae,1);if(af===this.firstChild){this.firstChild=af.nextSibling}if(af===this.lastChild){if(!this.childNodes.length){this.lastChild=null}else{this.lastChild=this.childNodes[this.childNodes.length-1]}}if(ae){this.childNodes[ae-1].nextSibling=af.nextSibling}af.nextSibling=af.parent=null;return af},replaceChild:function(ag,ae){for(var af=0,ad=this.childNodes.length;af<ad;af++){if(this.childNodes[af]===ae){break}}if(af){this.childNodes[af-1].nextSibling=ag}else{this.firstChild=ag}if(af>=ad-1){this.lastChild=ag}this.childNodes[af]=ag;ag.nextSibling=ae.nextSibling;ae.nextSibling=ae.parent=null;return ae},hasChildNodes:function(i){return(this.childNodes.length>0)},toString:function(){return"{"+this.childNodes.join("")+"}"}});var x=function(){g=MathJax.ElementJax.mml;var i=g.mbase.prototype.Init;g.mbase.Augment({firstChild:null,lastChild:null,nodeValue:null,nextSibling:null,Init:function(){var ad=i.apply(this,arguments)||this;ad.childNodes=ad.data;ad.nodeName=ad.type;return ad},appendChild:function(ag){if(ag.parent){ag.parent.removeChild(ag)}var ae=arguments;if(ag.isa(X)){ae=ag.childNodes;ag.data=ag.childNodes=[];ag.firstChild=ag.lastChild=null}for(var af=0,ad=ae.length;af<ad;af++){ag=ae[af];if(this.lastChild){this.lastChild.nextSibling=ag}if(!this.firstChild){this.firstChild=ag}this.Append(ag);this.lastChild=ag}return ag},removeChild:function(af){for(var ae=0,ad=this.childNodes.length;ae<ad;ae++){if(this.childNodes[ae]===af){break}}if(ae===ad){return}this.childNodes.splice(ae,1);if(af===this.firstChild){this.firstChild=af.nextSibling}if(af===this.lastChild){if(!this.childNodes.length){this.lastChild=null}else{this.lastChild=this.childNodes[this.childNodes.length-1]}}if(ae){this.childNodes[ae-1].nextSibling=af.nextSibling}af.nextSibling=af.parent=null;return af},replaceChild:function(ag,ae){for(var af=0,ad=this.childNodes.length;af<ad;af++){if(this.childNodes[af]===ae){break}}if(af){this.childNodes[af-1].nextSibling=ag}else{this.firstChild=ag}if(af>=ad-1){this.lastChild=ag}this.SetData(af,ag);ag.nextSibling=ae.nextSibling;ae.nextSibling=ae.parent=null;return ae},hasChildNodes:function(ad){return(this.childNodes.length>0)},setAttribute:function(ad,ae){this[ad]=ae}})};var Q={};var e={getElementById:true,createElementNS:function(ad,i){var ae=g[i]();if(i==="mo"&&ac.config.useMathMLspacing){ae.useMMLspacing=128}return ae},createTextNode:function(i){return g.chars(i).With({nodeValue:i})},createDocumentFragment:function(){return X()}};var J={appName:"MathJax"};var Z;var C="blue";var aa="serif";var p=true;var v=true;var d=".";var f=true;var m=(J.appName.slice(0,9)=="Microsoft");function E(i){if(m){return e.createElement(i)}else{return e.createElementNS("http://www.w3.org/1999/xhtml",i)}}var W="http://www.w3.org/1998/Math/MathML";function P(i){if(m){return e.createElement("m:"+i)}else{return e.createElementNS(W,i)}}function O(i,ae){var ad;if(m){ad=e.createElement("m:"+i)}else{ad=e.createElementNS(W,i)}if(ae){ad.appendChild(ae)}return ad}function u(i,ad){z=z.concat([{input:i,tag:"mo",output:ad,tex:null,ttype:V}]);z.sort(T);for(Z=0;Z<z.length;Z++){S[Z]=z[Z].input}}var D=["\uD835\uDC9C","\u212C","\uD835\uDC9E","\uD835\uDC9F","\u2130","\u2131","\uD835\uDCA2","\u210B","\u2110","\uD835\uDCA5","\uD835\uDCA6","\u2112","\u2133","\uD835\uDCA9","\uD835\uDCAA","\uD835\uDCAB","\uD835\uDCAC","\u211B","\uD835\uDCAE","\uD835\uDCAF","\uD835\uDCB0","\uD835\uDCB1","\uD835\uDCB2","\uD835\uDCB3","\uD835\uDCB4","\uD835\uDCB5","\uD835\uDCB6","\uD835\uDCB7","\uD835\uDCB8","\uD835\uDCB9","\u212F","\uD835\uDCBB","\u210A","\uD835\uDCBD","\uD835\uDCBE","\uD835\uDCBF","\uD835\uDCC0","\uD835\uDCC1","\uD835\uDCC2","\uD835\uDCC3","\u2134","\uD835\uDCC5","\uD835\uDCC6","\uD835\uDCC7","\uD835\uDCC8","\uD835\uDCC9","\uD835\uDCCA","\uD835\uDCCB","\uD835\uDCCC","\uD835\uDCCD","\uD835\uDCCE","\uD835\uDCCF"];var H=["\uD835\uDD04","\uD835\uDD05","\u212D","\uD835\uDD07","\uD835\uDD08","\uD835\uDD09","\uD835\uDD0A","\u210C","\u2111","\uD835\uDD0D","\uD835\uDD0E","\uD835\uDD0F","\uD835\uDD10","\uD835\uDD11","\uD835\uDD12","\uD835\uDD13","\uD835\uDD14","\u211C","\uD835\uDD16","\uD835\uDD17","\uD835\uDD18","\uD835\uDD19","\uD835\uDD1A","\uD835\uDD1B","\uD835\uDD1C","\u2128","\uD835\uDD1E","\uD835\uDD1F","\uD835\uDD20","\uD835\uDD21","\uD835\uDD22","\uD835\uDD23","\uD835\uDD24","\uD835\uDD25","\uD835\uDD26","\uD835\uDD27","\uD835\uDD28","\uD835\uDD29","\uD835\uDD2A","\uD835\uDD2B","\uD835\uDD2C","\uD835\uDD2D","\uD835\uDD2E","\uD835\uDD2F","\uD835\uDD30","\uD835\uDD31","\uD835\uDD32","\uD835\uDD33","\uD835\uDD34","\uD835\uDD35","\uD835\uDD36","\uD835\uDD37"];var w=["\uD835\uDD38","\uD835\uDD39","\u2102","\uD835\uDD3B","\uD835\uDD3C","\uD835\uDD3D","\uD835\uDD3E","\u210D","\uD835\uDD40","\uD835\uDD41","\uD835\uDD42","\uD835\uDD43","\uD835\uDD44","\u2115","\uD835\uDD46","\u2119","\u211A","\u211D","\uD835\uDD4A","\uD835\uDD4B","\uD835\uDD4C","\uD835\uDD4D","\uD835\uDD4E","\uD835\uDD4F","\uD835\uDD50","\u2124","\uD835\uDD52","\uD835\uDD53","\uD835\uDD54","\uD835\uDD55","\uD835\uDD56","\uD835\uDD57","\uD835\uDD58","\uD835\uDD59","\uD835\uDD5A","\uD835\uDD5B","\uD835\uDD5C","\uD835\uDD5D","\uD835\uDD5E","\uD835\uDD5F","\uD835\uDD60","\uD835\uDD61","\uD835\uDD62","\uD835\uDD63","\uD835\uDD64","\uD835\uDD65","\uD835\uDD66","\uD835\uDD67","\uD835\uDD68","\uD835\uDD69","\uD835\uDD6A","\uD835\uDD6B"];var c=0,A=1,U=2,j=3,b=4,h=5,a=6,L=7,V=8,n=9,Y=10,K=15;var l={input:'"',tag:"mtext",output:"mbox",tex:null,ttype:Y};var z=[{input:"alpha",tag:"mi",output:"\u03B1",tex:null,ttype:c},{input:"beta",tag:"mi",output:"\u03B2",tex:null,ttype:c},{input:"chi",tag:"mi",output:"\u03C7",tex:null,ttype:c},{input:"delta",tag:"mi",output:"\u03B4",tex:null,ttype:c},{input:"Delta",tag:"mo",output:"\u0394",tex:null,ttype:c},{input:"epsi",tag:"mi",output:"\u03B5",tex:"epsilon",ttype:c},{input:"varepsilon",tag:"mi",output:"\u025B",tex:null,ttype:c},{input:"eta",tag:"mi",output:"\u03B7",tex:null,ttype:c},{input:"gamma",tag:"mi",output:"\u03B3",tex:null,ttype:c},{input:"Gamma",tag:"mo",output:"\u0393",tex:null,ttype:c},{input:"iota",tag:"mi",output:"\u03B9",tex:null,ttype:c},{input:"kappa",tag:"mi",output:"\u03BA",tex:null,ttype:c},{input:"lambda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lambda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"lamda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lamda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"mu",tag:"mi",output:"\u03BC",tex:null,ttype:c},{input:"nu",tag:"mi",output:"\u03BD",tex:null,ttype:c},{input:"omega",tag:"mi",output:"\u03C9",tex:null,ttype:c},{input:"Omega",tag:"mo",output:"\u03A9",tex:null,ttype:c},{input:"phi",tag:"mi",output:f?"\u03D5":"\u03C6",tex:null,ttype:c},{input:"varphi",tag:"mi",output:f?"\u03C6":"\u03D5",tex:null,ttype:c},{input:"Phi",tag:"mo",output:"\u03A6",tex:null,ttype:c},{input:"pi",tag:"mi",output:"\u03C0",tex:null,ttype:c},{input:"Pi",tag:"mo",output:"\u03A0",tex:null,ttype:c},{input:"psi",tag:"mi",output:"\u03C8",tex:null,ttype:c},{input:"Psi",tag:"mi",output:"\u03A8",tex:null,ttype:c},{input:"rho",tag:"mi",output:"\u03C1",tex:null,ttype:c},{input:"sigma",tag:"mi",output:"\u03C3",tex:null,ttype:c},{input:"Sigma",tag:"mo",output:"\u03A3",tex:null,ttype:c},{input:"tau",tag:"mi",output:"\u03C4",tex:null,ttype:c},{input:"theta",tag:"mi",output:"\u03B8",tex:null,ttype:c},{input:"vartheta",tag:"mi",output:"\u03D1",tex:null,ttype:c},{input:"Theta",tag:"mo",output:"\u0398",tex:null,ttype:c},{input:"upsilon",tag:"mi",output:"\u03C5",tex:null,ttype:c},{input:"xi",tag:"mi",output:"\u03BE",tex:null,ttype:c},{input:"Xi",tag:"mo",output:"\u039E",tex:null,ttype:c},{input:"zeta",tag:"mi",output:"\u03B6",tex:null,ttype:c},{input:"*",tag:"mo",output:"\u22C5",tex:"cdot",ttype:c},{input:"**",tag:"mo",output:"\u2217",tex:"ast",ttype:c},{input:"***",tag:"mo",output:"\u22C6",tex:"star",ttype:c},{input:"//",tag:"mo",output:"/",tex:null,ttype:c},{input:"\\\\",tag:"mo",output:"\\",tex:"backslash",ttype:c},{input:"setminus",tag:"mo",output:"\\",tex:null,ttype:c},{input:"xx",tag:"mo",output:"\u00D7",tex:"times",ttype:c},{input:"-:",tag:"mo",output:"\u00F7",tex:"div",ttype:c},{input:"divide",tag:"mo",output:"-:",tex:null,ttype:V},{input:"@",tag:"mo",output:"\u2218",tex:"circ",ttype:c},{input:"o+",tag:"mo",output:"\u2295",tex:"oplus",ttype:c},{input:"ox",tag:"mo",output:"\u2297",tex:"otimes",ttype:c},{input:"o.",tag:"mo",output:"\u2299",tex:"odot",ttype:c},{input:"sum",tag:"mo",output:"\u2211",tex:null,ttype:L},{input:"prod",tag:"mo",output:"\u220F",tex:null,ttype:L},{input:"^^",tag:"mo",output:"\u2227",tex:"wedge",ttype:c},{input:"^^^",tag:"mo",output:"\u22C0",tex:"bigwedge",ttype:L},{input:"vv",tag:"mo",output:"\u2228",tex:"vee",ttype:c},{input:"vvv",tag:"mo",output:"\u22C1",tex:"bigvee",ttype:L},{input:"nn",tag:"mo",output:"\u2229",tex:"cap",ttype:c},{input:"nnn",tag:"mo",output:"\u22C2",tex:"bigcap",ttype:L},{input:"uu",tag:"mo",output:"\u222A",tex:"cup",ttype:c},{input:"uuu",tag:"mo",output:"\u22C3",tex:"bigcup",ttype:L},{input:"!=",tag:"mo",output:"\u2260",tex:"ne",ttype:c},{input:":=",tag:"mo",output:":=",tex:null,ttype:c},{input:"lt",tag:"mo",output:"<",tex:null,ttype:c},{input:"<=",tag:"mo",output:"\u2264",tex:"le",ttype:c},{input:"lt=",tag:"mo",output:"\u2264",tex:"leq",ttype:c},{input:"gt",tag:"mo",output:">",tex:null,ttype:c},{input:">=",tag:"mo",output:"\u2265",tex:"ge",ttype:c},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:c},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:c},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:c},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:c},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:c},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:c},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:c},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:c},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:c},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:c},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:c},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:c},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:c},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:c},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:c},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:c},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:c},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:c},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:c},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:c},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:c},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:c},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:c},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:c},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:c},{input:"(",tag:"mo",output:"(",tex:null,ttype:b},{input:")",tag:"mo",output:")",tex:null,ttype:h},{input:"[",tag:"mo",output:"[",tex:null,ttype:b},{input:"]",tag:"mo",output:"]",tex:null,ttype:h},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:h},{input:"|",tag:"mo",output:"|",tex:null,ttype:n},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:h},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:h},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:h,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:c},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:V},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:V},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:V},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:V},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:c},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:c},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:c},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:c},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:c},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:c},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:c},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:c},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:c},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:c},{input:"/_\\",tag:"mo",output:"\u25B3",tex:"triangle",ttype:c},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:c},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:A,acc:true},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:c},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:c},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:c},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:c},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:c},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:c},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:c},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:c},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:c},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:c},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:c},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:c},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:c},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:c},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:c},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:c},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:c},{input:"f",tag:"mi",output:"f",tex:null,ttype:A,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:A,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:L},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:L},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:A,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:A,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:A,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:A,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:A,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:A,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:A,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:A,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:A,func:true},{input:"arcsin",tag:"mo",output:"arcsin",tex:null,ttype:A,func:true},{input:"arccos",tag:"mo",output:"arccos",tex:null,ttype:A,func:true},{input:"arctan",tag:"mo",output:"arctan",tex:null,ttype:A,func:true},{input:"coth",tag:"mo",output:"coth",tex:null,ttype:A,func:true},{input:"sech",tag:"mo",output:"sech",tex:null,ttype:A,func:true},{input:"csch",tag:"mo",output:"csch",tex:null,ttype:A,func:true},{input:"exp",tag:"mo",output:"exp",tex:null,ttype:A,func:true},{input:"abs",tag:"mo",output:"abs",tex:null,ttype:A,rewriteleftright:["|","|"]},{input:"norm",tag:"mo",output:"norm",tex:null,ttype:A,rewriteleftright:["\u2225","\u2225"]},{input:"floor",tag:"mo",output:"floor",tex:null,ttype:A,rewriteleftright:["\u230A","\u230B"]},{input:"ceil",tag:"mo",output:"ceil",tex:null,ttype:A,rewriteleftright:["\u2308","\u2309"]},{input:"log",tag:"mo",output:"log",tex:null,ttype:A,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:A,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:A,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:c},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:c},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:A,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:A,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:c},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:c},{input:"min",tag:"mo",output:"min",tex:null,ttype:L},{input:"max",tag:"mo",output:"max",tex:null,ttype:L},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:c},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:c},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:c},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:c},{input:">->",tag:"mo",output:"\u21A3",tex:"rightarrowtail",ttype:c},{input:"->>",tag:"mo",output:"\u21A0",tex:"twoheadrightarrow",ttype:c},{input:">->>",tag:"mo",output:"\u2916",tex:"twoheadrightarrowtail",ttype:c},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:c},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:c},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:c},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:c},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:c},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:c},{input:"sqrt",tag:"msqrt",output:"sqrt",tex:null,ttype:A},{input:"root",tag:"mroot",output:"root",tex:null,ttype:U},{input:"frac",tag:"mfrac",output:"/",tex:null,ttype:U},{input:"/",tag:"mfrac",output:"/",tex:null,ttype:j},{input:"stackrel",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"_",tag:"msub",output:"_",tex:null,ttype:j},{input:"^",tag:"msup",output:"^",tex:null,ttype:j},{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:A,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:A,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:A,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:A,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:A,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:A,acc:true},{input:"ubrace",tag:"munder",output:"\u23DF",tex:"underbrace",ttype:K,acc:true},{input:"obrace",tag:"mover",output:"\u23DE",tex:"overbrace",ttype:K,acc:true},{input:"text",tag:"mtext",output:"text",tex:null,ttype:Y},{input:"mbox",tag:"mtext",output:"mbox",tex:null,ttype:Y},{input:"color",tag:"mstyle",ttype:U},{input:"cancel",tag:"menclose",output:"cancel",tex:null,ttype:A},l,{input:"bb",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"bb",tex:null,ttype:A},{input:"mathbf",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"mathbf",tex:null,ttype:A},{input:"sf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"sf",tex:null,ttype:A},{input:"mathsf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"mathsf",tex:null,ttype:A},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:A,codes:w},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:A,codes:w},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:A,codes:D},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:A,codes:D},{input:"tt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"tt",tex:null,ttype:A},{input:"mathtt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"mathtt",tex:null,ttype:A},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:A,codes:H},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:A,codes:H}];function T(ad,i){if(ad.input>i.input){return 1}else{return -1}}var S=[];function o(){var ae=[],ad;for(ad=0;ad<z.length;ad++){if(z[ad].tex){ae[ae.length]={input:z[ad].tex,tag:z[ad].tag,output:z[ad].output,ttype:z[ad].ttype,acc:(z[ad].acc||false)}}}z=z.concat(ae);B()}function B(){var ad;z.sort(T);for(ad=0;ad<z.length;ad++){S[ad]=z[ad].input}}function I(i,ad){z=z.concat([{input:i,tag:"mo",output:ad,tex:null,ttype:V}]);B()}function q(af,ag){var ad;if(af.charAt(ag)=="\\"&&af.charAt(ag+1)!="\\"&&af.charAt(ag+1)!=" "){ad=af.slice(ag+1)}else{ad=af.slice(ag)}for(var ae=0;ae<ad.length&&ad.charCodeAt(ae)<=32;ae=ae+1){}return ad.slice(ae)}function N(ae,ah,ai){if(ai==0){var ag,ad;ai=-1;ag=ae.length;while(ai+1<ag){ad=(ai+ag)>>1;if(ae[ad]<ah){ai=ad}else{ag=ad}}return ag}else{for(var af=ai;af<ae.length&&ae[af]<ah;af++){}}return af}function k(aj){var ad=0;var ae=0;var ag;var am;var al;var ah="";var ai=true;for(var af=1;af<=aj.length&&ai;af++){am=aj.slice(0,af);ae=ad;ad=N(S,am,ae);if(ad<S.length&&aj.slice(0,S[ad].length)==S[ad]){ah=S[ad];ag=ad;af=ah.length}ai=ad<S.length&&aj.slice(0,S[ad].length)>=S[ad]}s=y;if(ah!=""){y=z[ag].ttype;return z[ag]}y=c;ad=1;am=aj.slice(0,1);var ak=true;while("0"<=am&&am<="9"&&ad<=aj.length){am=aj.slice(ad,ad+1);ad++}if(am==d){am=aj.slice(ad,ad+1);if("0"<=am&&am<="9"){ak=false;ad++;while("0"<=am&&am<="9"&&ad<=aj.length){am=aj.slice(ad,ad+1);ad++}}}if((ak&&ad>1)||ad>2){am=aj.slice(0,ad-1);al="mn"}else{ad=2;am=aj.slice(0,1);al=(("A">am||am>"Z")&&("a">am||am>"z")?"mo":"mi")}if(am=="-"&&s==j){y=j;return{input:am,tag:al,output:am,ttype:A,func:true}}return{input:am,tag:al,output:am,ttype:c}}function R(ad){var i;if(!ad.hasChildNodes()){return}if(ad.firstChild.hasChildNodes()&&(ad.nodeName=="mrow"||ad.nodeName=="M:MROW")){i=ad.firstChild.firstChild.nodeValue;if(i=="("||i=="["||i=="{"){ad.removeChild(ad.firstChild)}}if(ad.lastChild.hasChildNodes()&&(ad.nodeName=="mrow"||ad.nodeName=="M:MROW")){i=ad.lastChild.firstChild.nodeValue;if(i==")"||i=="]"||i=="}"){ad.removeChild(ad.lastChild)}}}var F,s,y;function G(aj){var af,ae,am,ah,al,ai=e.createDocumentFragment();aj=q(aj,0);af=k(aj);if(af==null||af.ttype==h&&F>0){return[null,aj]}if(af.ttype==V){aj=af.output+q(aj,af.input.length);af=k(aj)}switch(af.ttype){case L:case c:aj=q(aj,af.input.length);return[O(af.tag,e.createTextNode(af.output)),aj];case b:F++;aj=q(aj,af.input.length);am=r(aj,true);F--;if(typeof af.invisible=="boolean"&&af.invisible){ae=O("mrow",am[0])}else{ae=O("mo",e.createTextNode(af.output));ae=O("mrow",ae);ae.appendChild(am[0])}return[ae,am[1]];case Y:if(af!=l){aj=q(aj,af.input.length)}if(aj.charAt(0)=="{"){ah=aj.indexOf("}")}else{if(aj.charAt(0)=="("){ah=aj.indexOf(")")}else{if(aj.charAt(0)=="["){ah=aj.indexOf("]")}else{if(af==l){ah=aj.slice(1).indexOf('"')+1}else{ah=0}}}}if(ah==-1){ah=aj.length}al=aj.slice(1,ah);if(al.charAt(0)==" "){ae=O("mspace");ae.setAttribute("width","1ex");ai.appendChild(ae)}ai.appendChild(O(af.tag,e.createTextNode(al)));if(al.charAt(al.length-1)==" "){ae=O("mspace");ae.setAttribute("width","1ex");ai.appendChild(ae)}aj=q(aj,ah+1);return[O("mrow",ai),aj];case K:case A:aj=q(aj,af.input.length);am=G(aj);if(am[0]==null){return[O(af.tag,e.createTextNode(af.output)),aj]}if(typeof af.func=="boolean"&&af.func){al=aj.charAt(0);if(al=="^"||al=="_"||al=="/"||al=="|"||al==","||(af.input.length==1&&af.input.match(/\w/)&&al!="(")){return[O(af.tag,e.createTextNode(af.output)),aj]}else{ae=O("mrow",O(af.tag,e.createTextNode(af.output)));ae.appendChild(am[0]);return[ae,am[1]]}}R(am[0]);if(af.input=="sqrt"){return[O(af.tag,am[0]),am[1]]}else{if(typeof af.rewriteleftright!="undefined"){ae=O("mrow",O("mo",e.createTextNode(af.rewriteleftright[0])));ae.appendChild(am[0]);ae.appendChild(O("mo",e.createTextNode(af.rewriteleftright[1])));return[ae,am[1]]}else{if(af.input=="cancel"){ae=O(af.tag,am[0]);ae.setAttribute("notation","updiagonalstrike");return[ae,am[1]]}else{if(typeof af.acc=="boolean"&&af.acc){ae=O(af.tag,am[0]);ae.appendChild(O("mo",e.createTextNode(af.output)));return[ae,am[1]]}else{if(!m&&typeof af.codes!="undefined"){for(ah=0;ah<am[0].childNodes.length;ah++){if(am[0].childNodes[ah].nodeName=="mi"||am[0].nodeName=="mi"){al=(am[0].nodeName=="mi"?am[0].firstChild.nodeValue:am[0].childNodes[ah].firstChild.nodeValue);var ak=[];for(var ag=0;ag<al.length;ag++){if(al.charCodeAt(ag)>64&&al.charCodeAt(ag)<91){ak=ak+af.codes[al.charCodeAt(ag)-65]}else{if(al.charCodeAt(ag)>96&&al.charCodeAt(ag)<123){ak=ak+af.codes[al.charCodeAt(ag)-71]}else{ak=ak+al.charAt(ag)}}}if(am[0].nodeName=="mi"){am[0]=O("mo").appendChild(e.createTextNode(ak))}else{am[0].replaceChild(O("mo").appendChild(e.createTextNode(ak)),am[0].childNodes[ah])}}}}ae=O(af.tag,am[0]);ae.setAttribute(af.atname,af.atval);return[ae,am[1]]}}}}case U:aj=q(aj,af.input.length);am=G(aj);if(am[0]==null){return[O("mo",e.createTextNode(af.input)),aj]}R(am[0]);var ad=G(am[1]);if(ad[0]==null){return[O("mo",e.createTextNode(af.input)),aj]}R(ad[0]);if(af.input=="color"){if(aj.charAt(0)=="{"){ah=aj.indexOf("}")}else{if(aj.charAt(0)=="("){ah=aj.indexOf(")")}else{if(aj.charAt(0)=="["){ah=aj.indexOf("]")}}}al=aj.slice(1,ah);ae=O(af.tag,ad[0]);ae.setAttribute("mathcolor",al);return[ae,ad[1]]}if(af.input=="root"||af.input=="stackrel"){ai.appendChild(ad[0])}ai.appendChild(am[0]);if(af.input=="frac"){ai.appendChild(ad[0])}return[O(af.tag,ai),ad[1]];case j:aj=q(aj,af.input.length);return[O("mo",e.createTextNode(af.output)),aj];case a:aj=q(aj,af.input.length);ae=O("mspace");ae.setAttribute("width","1ex");ai.appendChild(ae);ai.appendChild(O(af.tag,e.createTextNode(af.output)));ae=O("mspace");ae.setAttribute("width","1ex");ai.appendChild(ae);return[O("mrow",ai),aj];case n:F++;aj=q(aj,af.input.length);am=r(aj,false);F--;al="";if(am[0].lastChild!=null){al=am[0].lastChild.firstChild.nodeValue}if(al=="|"){ae=O("mo",e.createTextNode(af.output));ae=O("mrow",ae);ae.appendChild(am[0]);return[ae,am[1]]}else{ae=O("mo",e.createTextNode("\u2223"));ae=O("mrow",ae);return[ae,aj]}default:aj=q(aj,af.input.length);return[O(af.tag,e.createTextNode(af.output)),aj]}}function t(ai){var ag,aj,ah,af,i,ae;ai=q(ai,0);aj=k(ai);i=G(ai);af=i[0];ai=i[1];ag=k(ai);if(ag.ttype==j&&ag.input!="/"){ai=q(ai,ag.input.length);i=G(ai);if(i[0]==null){i[0]=O("mo",e.createTextNode("\u25A1"))}else{R(i[0])}ai=i[1];ae=(aj.ttype==L||aj.ttype==K);if(ag.input=="_"){ah=k(ai);if(ah.input=="^"){ai=q(ai,ah.input.length);var ad=G(ai);R(ad[0]);ai=ad[1];af=O((ae?"munderover":"msubsup"),af);af.appendChild(i[0]);af.appendChild(ad[0]);af=O("mrow",af)}else{af=O((ae?"munder":"msub"),af);af.appendChild(i[0])}}else{if(ag.input=="^"&&ae){af=O("mover",af);af.appendChild(i[0])}else{af=O(ag.tag,af);af.appendChild(i[0])}}if(typeof aj.func!="undefined"&&aj.func){ah=k(ai);if(ah.ttype!=j&&ah.ttype!=h){i=t(ai);af=O("mrow",af);af.appendChild(i[0]);ai=i[1]}}}return[af,ai]}function r(al,ak){var ap,am,ah,at,ai=e.createDocumentFragment();do{al=q(al,0);ah=t(al);am=ah[0];al=ah[1];ap=k(al);if(ap.ttype==j&&ap.input=="/"){al=q(al,ap.input.length);ah=t(al);if(ah[0]==null){ah[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ah[0])}al=ah[1];R(am);am=O(ap.tag,am);am.appendChild(ah[0]);ai.appendChild(am);ap=k(al)}else{if(am!=undefined){ai.appendChild(am)}}}while((ap.ttype!=h&&(ap.ttype!=n||ak)||F==0)&&ap!=null&&ap.output!="");if(ap.ttype==h||ap.ttype==n){var au=ai.childNodes.length;if(au>0&&ai.childNodes[au-1].nodeName=="mrow"){var aw=ai.childNodes[au-1].lastChild.firstChild.nodeValue;if(aw==")"||aw=="]"){var ae=ai.childNodes[au-1].firstChild.firstChild.nodeValue;if(ae=="("&&aw==")"&&ap.output!="}"||ae=="["&&aw=="]"){var af=[];var aq=true;var an=ai.childNodes.length;for(at=0;aq&&at<an;at=at+2){af[at]=[];am=ai.childNodes[at];if(aq){aq=am.nodeName=="mrow"&&(at==an-1||am.nextSibling.nodeName=="mo"&&am.nextSibling.firstChild.nodeValue==",")&&am.firstChild.firstChild.nodeValue==ae&&am.lastChild.firstChild.nodeValue==aw}if(aq){for(var ar=0;ar<am.childNodes.length;ar++){if(am.childNodes[ar].firstChild.nodeValue==","){af[at][af[at].length]=ar}}}if(aq&&at>1){aq=af[at].length==af[at-2].length}}aq=aq&&(af.length>1||af[0].length>0);if(aq){var ag,ad,aj,ao,av=e.createDocumentFragment();for(at=0;at<an;at=at+2){ag=e.createDocumentFragment();ad=e.createDocumentFragment();am=ai.firstChild;aj=am.childNodes.length;ao=0;am.removeChild(am.firstChild);for(ar=1;ar<aj-1;ar++){if(typeof af[at][ao]!="undefined"&&ar==af[at][ao]){am.removeChild(am.firstChild);ag.appendChild(O("mtd",ad));ao++}else{ad.appendChild(am.firstChild)}}ag.appendChild(O("mtd",ad));if(ai.childNodes.length>2){ai.removeChild(ai.firstChild);ai.removeChild(ai.firstChild)}av.appendChild(O("mtr",ag))}am=O("mtable",av);if(typeof ap.invisible=="boolean"&&ap.invisible){am.setAttribute("columnalign","left")}ai.replaceChild(am,ai.firstChild)}}}}al=q(al,ap.input.length);if(typeof ap.invisible!="boolean"||!ap.invisible){am=O("mo",e.createTextNode(ap.output));ai.appendChild(am)}}return[ai,al]}function M(ae,ad){var af,i;F=0;ae=ae.replace(/&nbsp;/g,"");ae=ae.replace(/&gt;/g,">");ae=ae.replace(/&lt;/g,"<");ae=ae.replace(/(Sin|Cos|Tan|Arcsin|Arccos|Arctan|Sinh|Cosh|Tanh|Cot|Sec|Csc|Log|Ln|Abs)/g,function(ag){return ag.toLowerCase()});af=r(ae.replace(/^\s+/g,""),false)[0];i=O("mstyle",af);if(C!=""){i.setAttribute("mathcolor",C)}if(aa!=""){i.setAttribute("fontfamily",aa)}if(p){i.setAttribute("displaystyle","true")}i=O("math",i);if(v){i.setAttribute("title",ae.replace(/\s+/g," "))}return i}v=false;aa="";C="";(function(){for(var ae=0,ad=z.length;ae<ad;ae++){if(z[ae].codes){delete z[ae].codes}if(z[ae].func){z[ae].tag="mi"}}})();ac.Augment({AM:{Init:function(){p=ac.config.displaystyle;d=(ac.config.decimal||ac.config.decimalsign);if(!ac.config.fixphi){for(var ae=0,ad=z.length;ae<ad;ae++){if(z[ae].input==="phi"){z[ae].output="\u03C6"}if(z[ae].input==="varphi"){z[ae].output="\u03D5";ae=ad}}}x();o()},Augment:function(i){for(var ad in i){if(i.hasOwnProperty(ad)){switch(ad){case"displaystyle":p=i[ad];break;case"decimal":decimal=i[ad];break;case"parseMath":M=i[ad];break;case"parseExpr":r=i[ad];break;case"parseIexpr":t=i[ad];break;case"parseSexpr":G=i[ad];break;case"removeBrackets":R=i[ad];break;case"getSymbol":k=i[ad];break;case"position":N=i[ad];break;case"removeCharsAndBlanks":q=i[ad];break;case"createMmlNode":O=i[ad];break;case"createElementMathML":P=i[ad];break;case"createElementXHTML":E=i[ad];break;case"initSymbols":o=i[ad];break;case"refreshSymbols":B=i[ad];break;case"compareNames":T=i[ad];break}this[ad]=i[ad]}}},parseMath:M,parseExpr:r,parseIexpr:t,parseSexr:G,removeBrackets:R,getSymbol:k,position:N,removeCharsAndBlanks:q,createMmlNode:O,createElementMathML:P,createElementXHTML:E,initSymbols:o,refreshSymbols:B,compareNames:T,createDocumentFragment:X,document:e,define:I,newcommand:u,symbols:z,names:S,TOKEN:{CONST:c,UNARY:A,BINARY:U,INFIX:j,LEFTBRACKET:b,RIGHTBRACKET:h,SPACE:a,UNDEROVER:L,DEFINITION:V,LEFTRIGHT:n,TEXT:Y,UNARYUNDEROVER:K}}});var ab=[Q,J];ab=null})(MathJax.InputJax.AsciiMath);(function(b){var a;b.Augment({sourceMenuTitle:["AsciiMathInput","AsciiMath Input"],annotationEncoding:"text/x-asciimath",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(c){var d,f=MathJax.HTML.getScript(c);var g={math:f,script:c};var h=this.prefilterHooks.Execute(g);if(h){return h}f=g.math;try{d=this.AM.parseMath(f)}catch(e){if(!e.asciimathError){throw e}d=this.formatError(e,f)}g.math=a(d);this.postfilterHooks.Execute(g);return this.postfilterHooks.Execute(g)||g.math},formatError:function(f,e,c){var d=f.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["AsciiMath Jax - parse error",d,e,c]);return a.Error(d)},Error:function(c){throw MathJax.Hub.Insert(Error(c),{asciimathError:true})},Startup:function(){a=MathJax.ElementJax.mml;this.AM.Init()}});b.loadComplete("jax.js")})(MathJax.InputJax.AsciiMath);
(function(i,b,e,g){var h;var j,a,d;var f="'Times New Roman',Times,STIXGeneral,serif";var m={".MJXc-script":{"font-size":".8em"},".MJXc-right":{"-webkit-transform-origin":"right","-moz-transform-origin":"right","-ms-transform-origin":"right","-o-transform-origin":"right","transform-origin":"right"},".MJXc-bold":{"font-weight":"bold"},".MJXc-italic":{"font-style":"italic"},".MJXc-scr":{"font-family":"MathJax_Script,"+f},".MJXc-frak":{"font-family":"MathJax_Fraktur,"+f},".MJXc-sf":{"font-family":"MathJax_SansSerif,"+f},".MJXc-cal":{"font-family":"MathJax_Caligraphic,"+f},".MJXc-mono":{"font-family":"MathJax_Typewriter,"+f},".MJXc-largeop":{"font-size":"150%"},".MJXc-largeop.MJXc-int":{"vertical-align":"-.2em"},".MJXc-math":{display:"inline-block","line-height":"1.2","text-indent":"0","font-family":f,"white-space":"nowrap","border-collapse":"collapse"},".MJXc-display":{display:"block","text-align":"center",margin:"1em 0"},".MJXc-math span":{display:"inline-block"},".MJXc-box":{display:"block!important","text-align":"center"},".MJXc-box:after":{content:'" "'},".MJXc-rule":{display:"block!important","margin-top":".1em"},".MJXc-char":{display:"block!important"},".MJXc-mo":{margin:"0 .15em"},".MJXc-mfrac":{margin:"0 .125em","vertical-align":".25em"},".MJXc-denom":{display:"inline-table!important",width:"100%"},".MJXc-denom > *":{display:"table-row!important"},".MJXc-surd":{"vertical-align":"top"},".MJXc-surd > *":{display:"block!important"},".MJXc-script-box > * ":{display:"table!important",height:"50%"},".MJXc-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXc-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXc-script-box > * > * > *":{display:"block!important"},".MJXc-mphantom":{visibility:"hidden"},".MJXc-munderover":{display:"inline-table!important"},".MJXc-over":{display:"inline-block!important","text-align":"center"},".MJXc-over > *":{display:"block!important"},".MJXc-munderover > *":{display:"table-row!important"},".MJXc-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXc-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXc-mtr":{display:"table-row!important"},".MJXc-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXc-mtr > .MJXc-mtd:first-child":{"padding-left":0},".MJXc-mtr:first-child > .MJXc-mtd":{"padding-top":0},".MJXc-mlabeledtr":{display:"table-row!important"},".MJXc-mlabeledtr > .MJXc-mtd:first-child":{"padding-left":0},".MJXc-mlabeledtr:first-child > .MJXc-mtd":{"padding-top":0},".MJXc-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXc-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializeCHTML",this])},InitializeCHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;t<q;t++){u=s[t];if(!u.parentNode){continue}r=u.previousSibling;if(r&&String(r.className).match(/^MathJax_CHTML(_Display)?( MathJax_Processing)?$/)){r.parentNode.removeChild(r)}n=u.MathJax.elementJax;if(!n){continue}n.CHTML={display:(n.root.Get("display")==="block")};v=o=e.Element("span",{className:"MathJax_CHTML",id:n.inputID+"-Frame",isMathJax:true,jaxID:this.id,oncontextmenu:j.Menu,onmousedown:j.Mousedown,onmouseover:j.Mouseover,onmouseout:j.Mouseout,onmousemove:j.Mousemove,onclick:j.Click,ondblclick:j.DblClick});if(b.Browser.noContextMenu){v.ontouchstart=a.start;v.ontouchend=a.end}if(n.CHTML.display){o=e.Element("div",{className:"MathJax_CHTML_Display"});o.appendChild(v)}o.className+=" MathJax_Processing";u.parentNode.insertBefore(o,u)}},Translate:function(o,s){if(!o.parentNode){return}var n=o.MathJax.elementJax,r=n.root,p=document.getElementById(n.inputID+"-Frame"),t=(n.CHTML.display?p.parentNode:p);this.initCHTML(r,p);try{r.toCommonHTML(p)}catch(q){if(q.restart){while(p.firstChild){p.removeChild(p.firstChild)}}throw q}t.className=t.className.split(/ /)[0];if(this.hideProcessedMath){t.className+=" MathJax_Processed";if(o.MathJax.preview){n.CHTML.preview=o.MathJax.preview;delete o.MathJax.preview}}},postTranslate:function(s){var o=s.jax[this.id];if(!this.hideProcessedMath){return}for(var q=0,n=o.length;q<n;q++){var p=o[q];if(p&&p.MathJax.elementJax){p.previousSibling.className=p.previousSibling.className.split(/ /)[0];var r=p.MathJax.elementJax.CHTML;if(r.preview){r.preview.innerHTML="";p.MathJax.preview=r.preview;delete r.preview}}}},getJaxFromMath:function(n){if(n.parentNode.className==="MathJax_CHTML_Display"){n=n.parentNode}do{n=n.nextSibling}while(n&&n.nodeName.toLowerCase()!=="script");return b.getJaxFor(n)},getHoverSpan:function(n,o){return n.root.CHTMLspanElement()},getHoverBBox:function(n,o,p){return BBOX},Zoom:function(o,u,s,n,r){u.className="MathJax";this.idPostfix="-zoom";o.root.toCHTML(u,u);this.idPostfix="";u.style.position="absolute";if(!width){s.style.position="absolute"}var t=u.offsetWidth,q=u.offsetHeight,v=s.offsetHeight,p=s.offsetWidth;if(p===0){p=s.parentNode.offsetWidth}u.style.position=s.style.position="";return{Y:-j.getBBox(u).h,mW:p,mH:v,zW:t,zH:q}},initCHTML:function(o,n){},Remove:function(n){var o=document.getElementById(n.inputID+"-Frame");if(o){if(n.CHTML.display){o=o.parentNode}o.parentNode.removeChild(o)}delete n.CHTML},ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},VARIANT:{bold:"MJXc-bold",italic:"MJXc-italic","bold-italic":"MJXc-bold MJXc-italic",script:"MJXc-scr","bold-script":"MJXc-scr MJXc-bold",fraktur:"MJXc-frak","bold-fraktur":"MJXc-frak MJXc-bold",monospace:"MJXc-mono","sans-serif":"MJXc-sf","-tex-caligraphic":"MJXc-cal"},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18,thin:0.08,medium:0.1,thick:0.15,infinity:k},TeX:{x_height:0.430554},pxPerInch:72,em:16,DELIMITERS:{"(":{dir:c},"{":{dir:c,w:0.58},"[":{dir:c},"|":{dir:c,w:0.275},")":{dir:c},"}":{dir:c,w:0.58},"]":{dir:c},"/":{dir:c},"\\":{dir:c},"\u2223":{dir:c,w:0.275},"\u2225":{dir:c,w:0.55},"\u230A":{dir:c,w:0.5},"\u230B":{dir:c,w:0.5},"\u2308":{dir:c,w:0.5},"\u2309":{dir:c,w:0.5},"\u27E8":{dir:c,w:0.5},"\u27E9":{dir:c,w:0.5},"\u2191":{dir:c,w:0.65},"\u2193":{dir:c,w:0.65},"\u21D1":{dir:c,w:0.75},"\u21D3":{dir:c,w:0.75},"\u2195":{dir:c,w:0.65},"\u21D5":{dir:c,w:0.75},"\u27EE":{dir:c,w:0.275},"\u27EF":{dir:c,w:0.275},"\u23B0":{dir:c,w:0.6},"\u23B1":{dir:c,w:0.6}},REMAPACCENT:{"\u20D7":"\u2192","'":"\u02CB","`":"\u02CA",".":"\u02D9","^":"\u02C6","-":"\u02C9","~":"\u02DC","\u00AF":"\u02C9","\u00B0":"\u02DA","\u00B4":"\u02CA","\u0300":"\u02CB","\u0301":"\u02CA","\u0302":"\u02C6","\u0303":"\u02DC","\u0304":"\u02C9","\u0305":"\u02C9","\u0306":"\u02D8","\u0307":"\u02D9","\u0308":"\u00A8","\u030C":"\u02C7"},REMAPACCENTUNDER:{},length2em:function(r,p){if(typeof(r)!=="string"){r=r.toString()}if(r===""){return""}if(r===h.SIZE.NORMAL){return 1}if(r===h.SIZE.BIG){return 2}if(r===h.SIZE.SMALL){return 0.71}if(this.MATHSPACE[r]){return this.MATHSPACE[r]}var o=r.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var n=parseFloat(o[1]||"1"),q=o[2];if(p==null){p=1}if(q==="em"){return n}if(q==="ex"){return n*this.TeX.x_height}if(q==="%"){return n/100*p}if(q==="px"){return n/this.em}if(q==="pt"){return n/10}if(q==="pc"){return n*1.2}if(q==="in"){return n*this.pxPerInch/this.em}if(q==="cm"){return n*this.pxPerInch/this.em/2.54}if(q==="mm"){return n*this.pxPerInch/this.em/25.4}if(q==="mu"){return n/18}return n*p},Em:function(n){if(Math.abs(n)<0.001){return"0em"}return(n.toFixed(3).replace(/\.?0+$/,""))+"em"},arrayEntry:function(n,o){return n[Math.max(0,Math.min(o,n.length-1))]}});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){h=MathJax.ElementJax.mml;h.mbase.Augment({toCommonHTML:function(o,n){return this.CHTMLdefaultSpan(o,n)},CHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.CHTMLcreateSpan(q);this.CHTMLhandleStyle(q);this.CHTMLhandleColor(q);if(this.isToken){this.CHTMLhandleToken(q)}for(var p=0,n=this.data.length;p<n;p++){this.CHTMLaddChild(q,p,o)}return q},CHTMLaddChild:function(p,o,n){var q=this.data[o];if(q){if(n.childSpans){p=e.addElement(p,"span",{className:n.className})}q.toCommonHTML(p);if(!n.noBBox){this.CHTML.w+=q.CHTML.w+q.CHTML.l+q.CHTML.r;if(q.CHTML.h>this.CHTML.h){this.CHTML.h=q.CHTML.h}if(q.CHTML.d>this.CHTML.d){this.CHTML.d=q.CHTML.d}if(q.CHTML.t>this.CHTML.t){this.CHTML.t=q.CHTML.t}if(q.CHTML.b>this.CHTML.b){this.CHTML.b=q.CHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},CHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.CHTMLcanStretch("Vertical",p,s)){var t=this.CHTML,o=r.CHTML,n=o.w;r.CHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},CHTMLcreateSpan:function(n){if(!this.CHTML){this.CHTML={}}this.CHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.CHTMLspanID){this.CHTMLspanID=g.GetID()}var o=(this.id||"MJXc-Span-"+this.CHTMLspanID);return e.addElement(n,"span",{className:"MJXc-"+this.type,id:o})},CHTMLspanElement:function(){if(!this.CHTMLspanID){return null}return document.getElementById(this.id||"MJXc-Span-"+this.CHTMLspanID)},CHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},CHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},CHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},CHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXc-script"}},CHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s<r;s++){p=A.charCodeAt(s);v=A.charAt(s);if(p>=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.CHTML={}}this.CHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},CHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].CHTML){return this.data[o].CHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},CHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.CHTMLcanStretch(q,o,p)}}return false},CHTMLstretchV:function(n,o){},CHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toCommonHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.CHTMLhandleText(n,o)}});h.entity.Augment({toCommonHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.CHTMLhandleText(n,o)}});h.math.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXc-display"}return n}});h.mo.Augment({toCommonHTML:function(o){o=this.CHTMLdefaultSpan(o);this.CHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.CHTML.l=g.length2em(n.lspace);this.CHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.CHTML.l);o.style.marginRight=g.Em(this.CHTML.r)}else{this.CHTML.l=0.15;this.CHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXc-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.CHTML.h*=1.2;this.CHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXc-int"}}return o},CHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.CHTML.acc=-0.52}else{if(s==="\u2192"){this.CHTML.acc=-0.15;this.CHTML.vec=true}}}},CHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.CHTML.h!==o||this.CHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},CHTMLstretchV:function(p,u){var o=this.CHTMLspanElement(),t=this.CHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXc-right MJXc-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.CHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toCommonHTML:function(u){u=this.CHTMLdefaultSpan(u,{childSpans:true,className:"MJXc-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.CHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.CHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.CHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.CHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.CHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.CHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.CHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},CHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.CHTML[o[0].charAt(0)]:(r?this.CHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toCommonHTML:function(q){var n=this.getValues("displaystyle","accent","accentunder","align");if(!n.displaystyle&&this.data[this.base]!=null&&this.data[this.base].CoreMO().Get("movablelimits")){q=h.msubsup.prototype.toCommonHTML.call(this,q);q.className=q.className.replace(/munderover/,"msubsup");return q}q=this.CHTMLdefaultSpan(q,{childSpans:true,className:"",noBBox:true});var p=this.CHTMLbboxFor(this.over),s=this.CHTMLbboxFor(this.under),u=this.CHTMLbboxFor(this.base),o=this.CHTML,r=p.acc;if(this.data[this.over]){q.lastChild.firstChild.style.marginLeft=p.l=q.lastChild.firstChild.style.marginRight=p.r=0;var t=e.Element("span",{},[["span",{className:"MJXc-over"}]]);t.firstChild.appendChild(q.lastChild);if(q.childNodes.length>(this.data[this.under]?1:0)){t.firstChild.appendChild(q.firstChild)}this.data[this.over].CHTMLhandleScriptlevel(t.firstChild.firstChild);if(r!=null){if(p.vec){t.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}r=r-p.d+0.1;if(u.t!=null){r+=u.t-u.h}t.firstChild.firstChild.style.marginBottom=g.Em(r)}if(q.firstChild){q.insertBefore(t,q.firstChild)}else{q.appendChild(t)}}if(this.data[this.under]){q.lastChild.firstChild.style.marginLeft=s.l=q.lastChild.firstChild.marginRight=s.r=0;this.data[this.under].CHTMLhandleScriptlevel(q.lastChild)}o.w=Math.max(0.8*p.w,0.8*s.w,u.w);o.h=0.8*(p.h+p.d+(r||0))+u.h;o.d=u.d+0.8*(s.h+s.d);return q}});h.msubsup.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.CHTML.h-0.4),u=Math.max(0.2,s.CHTML.d+0.1);var t=this.CHTML;if(n&&p){var r=e.Element("span",{className:"MJXc-script-box",style:{height:g.Em(o+n.CHTML.h*0.8+u+p.CHTML.d*0.8),"vertical-align":g.Em(-u-p.CHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.CHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.CHTML.h-0.05))}}]]]]]]);p.CHTMLhandleScriptlevel(r.firstChild);n.CHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.CHTML.h,n.CHTML.h*0.8+o);t.d=Math.max(s.CHTML.d,p.CHTML.d*0.8+u);t.w=s.CHTML.w+Math.max(n.CHTML.w,p.CHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.CHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.CHTML.h,n.CHTML.h*0.8+o);t.d=Math.max(s.CHTML.d,n.CHTML.d*0.8-o);t.w=s.CHTML.w+n.CHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.CHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.CHTML.h,p.CHTML.h*0.8-u);t.d=Math.max(s.CHTML.d,p.CHTML.d*0.8+u);t.w=s.CHTML.w+p.CHTML.w+0.07}}}return q}});h.mfrac.Augment({toCommonHTML:function(r){r=this.CHTMLdefaultSpan(r,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].CHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].CHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXc-box",style:{"margin-top":"-.8em"}},[["span",{className:"MJXc-denom"},[["span",{},[["span",{className:"MJXc-rule"}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.CHTMLbboxFor(0),p=this.CHTMLbboxFor(1),v=this.CHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-0.9);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}return r}});h.msqrt.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});this.CHTMLlayoutRoot(n,n.firstChild);return n},CHTMLlayoutRoot:function(u,n){var v=this.CHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXc-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXc-root"},[["span",{className:"MJXc-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXc-right MJXc-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.CHTML.h=v.h+0.18;this.CHTML.d=v.d;this.CHTML.w=v.w+p;return u}});h.mroot.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});var p=this.CHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.CHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXc-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.CHTML.w+=Math.max(0,p.w*0.8+s);this.CHTML.h=Math.max(this.CHTML.h,p.h*0.8+o);return q},CHTMLlayoutRoot:h.msqrt.prototype.CHTMLlayoutRoot});h.mfenced.Augment({toCommonHTML:function(q){q=this.CHTMLcreateSpan(q);this.CHTMLhandleStyle(q);this.CHTMLhandleColor(q);this.addFakeNodes();this.CHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;p<n;p++){this.CHTMLaddChild(q,"sep"+p,{});this.CHTMLaddChild(q,p,{})}this.CHTMLaddChild(q,"close",{});var o=this.CHTML.h,r=this.CHTML.d;this.CHTMLstretchChild("open",o,r);for(p=0,n=this.data.length;p<n;p++){this.CHTMLstretchChild("sep"+p,o,r);this.CHTMLstretchChild(p,o,r)}this.CHTMLstretchChild("close",o,r);return q}});h.mrow.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q);var p=this.CHTML.h,r=this.CHTML.d;for(var o=0,n=this.data.length;o<n;o++){this.CHTMLstretchChild(o,p,r)}return q}});h.mstyle.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n);this.CHTMLhandleScriptlevel(n);return n}});h.TeXAtom.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n);n.className="MJXc-mrow";return n}});h.mtable.Augment({toCommonHTML:function(E){E=this.CHTMLdefaultSpan(E,{noBBox:true});var r=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","width");var u=MathJax.Hub.SplitList,F,A,D,z;var N=u(r.columnspacing),w=u(r.rowspacing),L=u(r.columnalign),t=u(r.rowalign);for(F=0,A=N.length;F<A;F++){N[F]=g.length2em(N[F])}for(F=0,A=w.length;F<A;F++){w[F]=g.length2em(w[F])}var K=e.Element("span");while(E.firstChild){K.appendChild(E.firstChild)}E.appendChild(K);var y=0,s=0;for(F=0,A=this.data.length;F<A;F++){var v=this.data[F];if(v){var J=g.arrayEntry(w,F-1),C=g.arrayEntry(t,F);var x=v.CHTML,q=v.CHTMLspanElement();q.style.verticalAlign=C;var B=(v.type==="mlabeledtr"?1:0);for(D=0,z=v.data.length;D<z-B;D++){var p=v.data[D+B];if(p){var M=g.arrayEntry(N,D-1),G=g.arrayEntry(L,D);var I=p.CHTMLspanElement();if(D){x.w+=M;I.style.paddingLeft=g.Em(M)}if(F){I.style.paddingTop=g.Em(J)}I.style.textAlign=G}}y+=x.h+x.d;if(F){y+=J}if(x.w>s){s=x.w}}}var o=this.CHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({CHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.CHTMLcreateSpan(q);this.CHTMLhandleStyle(q);this.CHTMLhandleColor(q);if(this.isToken){this.CHTMLhandleToken(q)}for(var p=1,n=this.data.length;p<n;p++){this.CHTMLaddChild(q,p,o)}return q}});h.semantics.Augment({toCommonHTML:function(n){n=this.CHTMLcreateSpan(n);if(this.data[0]){this.data[0].toCommonHTML(n);MathJax.Hub.Insert(this.data[0].CHTML||{},this.CHTML)}return n}});h.annotation.Augment({toCommonHTML:function(n){}});h["annotation-xml"].Augment({toCommonHTML:function(n){}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",g,"jax.js"]),0)})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){i.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.CommonHTML);
(function(a,e,d){var b=a.config.menuSettings;var c=MathJax.Extension["CHTML-preview"]={version:"2.5.2",config:a.CombineConfig("CHTML-preview",{Chunks:{EqnChunk:10000,EqnChunkFactor:1,EqnChunkDelay:0},color:"inherit!important",updateTime:30,updateDelay:6,messageStyle:"none",disabled:d.isMSIE&&!d.versionAtLeast("8.0")}),Config:function(){a.Config({"HTML-CSS":this.config.Chunks,SVG:this.config.Chunks});MathJax.Ajax.Styles({".MathJax_Preview .MJXc-math":{color:this.config.color}});var k,h,i,f,j;var g=this.config;if(!g.disabled&&b.CHTMLpreview==null){a.Config({menuSettings:{CHTMLpreview:true}})}a.Register.MessageHook("Begin Math Output",function(){if(!f&&b.CHTMLpreview&&b.renderer!=="CommonHTML"){k=a.processUpdateTime;h=a.processUpdateDelay;i=a.config.messageStyle;a.processUpdateTime=g.updateTime;a.processUpdateDelay=g.updateDelay;a.Config({messageStyle:g.messageStyle});MathJax.Message.Clear(0,0);j=true}});a.Register.MessageHook("End Math Output",function(){if(!f&&j){a.processUpdateTime=k;a.processUpdateDelay=h;a.Config({messageStyle:i});f=true}})},Preview:function(f){if(!b.CHTMLpreview||b.renderer==="CommonHTML"){return}var g=f.script.MathJax.preview||f.script.previousSibling;if(!g||g.className!==MathJax.Hub.config.preRemoveClass){g=e.Element("span",{className:MathJax.Hub.config.preRemoveClass});f.script.parentNode.insertBefore(g,f.script);f.script.MathJax.preview=g}g.innerHTML="";g.style.color="inherit";return this.postFilter(g,f)},postFilter:function(h,g){if(!g.math.root.toCommonHTML){var f=MathJax.Callback.Queue();f.Push(["Require",MathJax.Ajax,"[MathJax]/jax/output/CommonHTML/config.js"],["Require",MathJax.Ajax,"[MathJax]/jax/output/CommonHTML/jax.js"]);a.RestartAfter(f.Push({}))}g.math.root.toCommonHTML(h)},Register:function(f){a.Register.StartupHook(f+" Jax Require",function(){var g=MathJax.InputJax[f];g.postfilterHooks.Add(["Preview",MathJax.Extension["CHTML-preview"]],50)})}};c.Register("TeX");c.Register("MathML");c.Register("AsciiMath");a.Register.StartupHook("End Config",["Config",c]);a.Startup.signal.Post("CHTML-preview Ready")})(MathJax.Hub,MathJax.HTML,MathJax.Hub.Browser);MathJax.Ajax.loadComplete("[MathJax]/extensions/CHTML-preview.js");
MathJax.Ajax.loadComplete("[MathJax]/config/AM_HTMLorMML.js");