/*
 *  /MathJax/config/TeX-AMS_HTML-full.js
 *  
 *  Copyright (c) 2010-2013 The MathJax Consortium
 *
 *  Part of the MathJax library.
 *  See http://www.mathjax.org for details.
 * 
 *  Licensed under the Apache License, Version 2.0;
 *  you may not use this file except in compliance with the License.
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 */

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

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

MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.3",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/[:"'<>&]/g,"")},formatURL:function(a){return"#"+escape(a)},useLabelIds:true}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js");
MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.3",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:{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_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.Extension.tex2jax={version:"2.3",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],balanceBraces:true,skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c<a;c++){d.push(this.patternQuote(b.inlineMath[c][0]));this.match[b.inlineMath[c][0]]={mode:"",end:b.inlineMath[c][1],pattern:this.endPattern(b.inlineMath[c][1])}}for(c=0,a=b.displayMath.length;c<a;c++){d.push(this.patternQuote(b.displayMath[c][0]));this.match[b.displayMath[c][0]]={mode:"; mode=display",end:b.displayMath[c][1],pattern:this.endPattern(b.displayMath[c][1])}}if(d.length){e.push(d.sort(this.sortLength).join("|"))}if(b.processEnvironments){e.push("\\\\begin\\{([^}]*)\\}")}if(b.processEscapes){e.push("\\\\*\\\\\\$")}if(b.processRefs){e.push("\\\\(eq)?ref\\{[^}]*\\}")}this.start=new RegExp(e.join("|"),"g");this.skipTags=new RegExp("^("+b.skipTags.join("|")+")$","i");var f=[];if(MathJax.Hub.config.preRemoveClass){f.push(MathJax.Hub.config.preRemoveClass)}if(b.ignoreClass){f.push(b.ignoreClass)}this.ignoreClass=(f.length?new RegExp("(^| )("+f.join("|")+")( |$)"):/^$/);this.processClass=new RegExp("(^| )("+b.processClass+")( |$)");return(e.length>0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d<c?-1:1))},scanElement:function(c,b,g){var a,e,d,f;while(c&&c!=b){if(c.nodeName.toLowerCase()==="#text"){if(!g){c=this.scanText(c)}}else{a=(typeof(c.className)==="undefined"?"":c.className);e=(typeof(c.tagName)==="undefined"?"":c.tagName);if(typeof(a)!=="string"){a=String(a)}f=this.processClass.exec(a);if(c.firstChild&&!a.match(/(^| )MathJax/)&&(f||!this.skipTags.exec(e))){d=(g||this.ignoreClass.exec(a))&&!f;this.scanElement(c.firstChild,b,d)}}if(c){c=c.nextSibling}}},scanText:function(b){if(b.nodeValue.replace(/\s+/,"")==""){return b}var a,c;this.search={start:true};this.pattern=this.start;while(b){this.pattern.lastIndex=0;while(b&&b.nodeName.toLowerCase()==="#text"&&(a=this.pattern.exec(b.nodeValue))){if(this.search.start){b=this.startMatch(a,b)}else{b=this.endMatch(a,b)}}if(this.search.matched){b=this.encloseMath(b)}if(b){do{c=b;b=b.nextSibling}while(b&&(b.nodeName.toLowerCase()==="br"||b.nodeName.toLowerCase()==="#comment"));if(!b||b.nodeName!=="#text"){return(this.search.close?this.prevEndMatch():c)}}}return b},startMatch:function(a,b){var f=this.match[a[0]];if(f!=null){this.search={end:f.end,mode:f.mode,pcount:0,open:b,olen:a[0].length,opos:this.pattern.lastIndex-a[0].length};this.switchPattern(f.pattern)}else{if(a[0].substr(0,6)==="\\begin"){this.search={end:"\\end{"+a[1]+"}",mode:"; mode=display",pcount:0,open:b,olen:0,opos:this.pattern.lastIndex-a[0].length,isBeginEnd:true};this.switchPattern(this.endPattern(this.search.end))}else{if(a[0].substr(0,4)==="\\ref"||a[0].substr(0,6)==="\\eqref"){this.search={mode:"",end:"",open:b,pcount:0,olen:0,opos:this.pattern.lastIndex-a[0].length};return this.endMatch([""],b)}else{var d=a[0].substr(0,a[0].length-1),g,c;if(d.length%2===0){c=[d.replace(/\\\\/g,"\\")];g=1}else{c=[d.substr(1).replace(/\\\\/g,"\\"),"$"];g=0}c=MathJax.HTML.Element("span",null,c);var e=MathJax.HTML.TextNode(b.nodeValue.substr(0,a.index));b.nodeValue=b.nodeValue.substr(a.index+a[0].length-g);b.parentNode.insertBefore(c,b);b.parentNode.insertBefore(e,c);this.pattern.lastIndex=g}}}return b},endMatch:function(a,c){var b=this.search;if(a[0]==b.end){if(!b.close||b.pcount===0){b.close=c;b.cpos=this.pattern.lastIndex;b.clen=(b.isBeginEnd?0:a[0].length)}if(b.pcount===0){b.matched=true;c=this.encloseMath(c);this.switchPattern(this.start)}}else{if(a[0]==="{"){b.pcount++}else{if(a[0]==="}"&&b.pcount){b.pcount--}}}return c},prevEndMatch:function(){this.search.matched=true;var a=this.encloseMath(this.search.close);this.switchPattern(this.start);return a},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=(a===this.start)},encloseMath:function(b){var a=this.search,f=a.close,e,c;if(a.cpos===f.length){f=f.nextSibling}else{f=f.splitText(a.cpos)}if(!f){e=f=MathJax.HTML.addText(a.close.parentNode,"")}a.close=f;c=(a.opos?a.open.splitText(a.opos):a.open);while(c.nextSibling&&c.nextSibling!==f){if(c.nextSibling.nodeValue!==null){if(c.nextSibling.nodeName==="#comment"){c.nodeValue+=c.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{c.nodeValue+=c.nextSibling.nodeValue}}else{if(this.msieNewlineBug){c.nodeValue+=(c.nextSibling.nodeName.toLowerCase()==="br"?"\n":" ")}else{c.nodeValue+=" "}}c.parentNode.removeChild(c.nextSibling)}var d=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);if(this.config.preview!=="none"){this.createPreview(a.mode,d)}c=this.createMathTag(a.mode,d);this.search={};this.pattern.lastIndex=0;if(e){e.parentNode.removeChild(e)}return c},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(c,a){var b=this.config.preview;if(b==="none"){return}if(b==="TeX"){b=[this.filterPreview(a)]}if(b){b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b);this.insertNode(b)}},createMathTag:function(c,b){var a=document.createElement("script");a.type="math/tex"+c;MathJax.HTML.setScript(a,b);this.insertNode(a);return a},filterPreview:function(a){return a},msieNewlineBug:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9)};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js");
(function(d,h,l,g,m,b,j){var q="2.3";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.fileURL(b.imageDir+"/MenuArrow-15.png")},fadeinInc:0.2,fadeoutInc:0.05,fadeDelay:50,fadeoutStart:400,fadeoutDelay:15*1000,styles:{".MathJax_Hover_Frame":{"border-radius":".25em","-webkit-border-radius":".25em","-moz-border-radius":".25em","-khtml-border-radius":".25em","box-shadow":"0px 0px 15px #83A","-webkit-box-shadow":"0px 0px 15px #83A","-moz-box-shadow":"0px 0px 15px #83A","-khtml-box-shadow":"0px 0px 15px #83A",border:"1px solid #A6D ! important",display:"inline-block",position:"absolute"},".MathJax_Hover_Arrow":{position:"absolute",width:"15px",height:"11px",cursor:"pointer"}}};var 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()}if(r.stopPropagation){r.stopPropagation()}r.cancelBubble=true;r.returnValue=false}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;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(){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="2.3";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(n,s){this.Remove();b.ClearHoverTimer();g.ClearSelection();var q=MathJax.OutputJax[s.jaxID];var o=q.getJaxFromMath(s);if(o.hover){b.UnHover(o)}var l=Math.floor(0.85*document.body.clientWidth),r=Math.floor(0.85*Math.max(document.body.clientHeight,document.documentElement.clientHeight));var m=d.Element("span",{id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale,"max-width":l+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var x=m.lastChild,u=x.firstChild,p=m.firstChild;s.parentNode.insertBefore(m,s);s.parentNode.insertBefore(s,m);if(u.addEventListener){u.addEventListener("mousedown",this.Remove,true)}if(this.msieTrapEventBug){var w=d.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});m.insertBefore(w,x)}if(this.msieZIndexBug){var t=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});m.style.position="relative";m.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];m=t}var v=q.Zoom(o,u,s,l,r);if(this.msiePositionBug){if(this.msieSizeBug){x.style.height=v.zH+"px";x.style.width=v.zW+"px"}if(x.offsetHeight>r){x.style.height=r+"px";x.style.width=(v.zW+this.scrollSize)+"px"}if(x.offsetWidth>l){x.style.width=l+"px";x.style.height=(v.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){x.style.width=Math.min(l,v.zW)+"px"}if(x.offsetWidth&&x.offsetWidth<l&&x.offsetHeight<r){x.style.overflow="visible"}this.Position(x,v);if(this.msieTrapEventBug){w.style.height=x.clientHeight+"px";w.style.width=x.clientWidth+"px";w.style.left=(parseFloat(x.style.left)+x.clientLeft)+"px";w.style.top=(parseFloat(x.style.top)+x.clientTop)+"px"}x.style.visibility="";if(this.settings.zoom==="Hover"){p.onmouseover=this.Remove}if(window.addEventListener){addEventListener("resize",this.Resize,false)}else{if(window.attachEvent){attachEvent("onresize",this.Resize)}else{this.onresize=window.onresize;window.onresize=this.Resize}}a.signal.Post(["math zoomed",o]);return e(n)},Position:function(p,r){var q=this.Resize(),m=q.x,s=q.y,l=r.mW;var o=-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 r=document.getElementById("MathJax_ZoomFrame"),l=document.getElementById("MathJax_ZoomOverlay");var o=h.getXY(r);var n=r.parentNode,q=h.getOverflow(n);while(n.parentNode&&n!==document.body&&q==="visible"){n=n.parentNode;q=h.getOverflow(n)}if(q!=="visible"){l.scroll_parent=n;var p=h.getXY(n);o.x-=p.x;o.y-=p.y;p=h.getBorder(n);o.x-=p.x;o.y-=p.y}l.style.left=(-o.x)+"px";l.style.top=(-o.y)+"px";if(h.msiePositionBug){setTimeout(h.SetWH,0)}else{h.SetWH()}return o},SetWH:function(){var l=document.getElementById("MathJax_ZoomOverlay");l.style.width=l.style.height="1px";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"},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="2.3";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.fileURL(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_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(n?"1em":".7em")},".MathJax_MenuLabel":{padding:(n?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(n?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(n?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version: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,B){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])}var t=g.addElement(r,"div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"});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:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:p.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;t.style.width=(t.offsetWidth+2)+"px";var A=s.pageX,z=s.pageY;if(!A&&!z){A=s.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;z=s.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+t.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-t.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(t.offsetWidth/2));z-=20}a.skipUp=s.isContextMenu}else{var w="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);z=0;while(B&&B!==r){A+=B.offsetLeft;z+=B.offsetTop;B=B.parentNode}if(A+t.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){w="right";A=Math.max(this.margin,A-C-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=A+"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}});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"),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.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)}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"};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"};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(),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*$/,"");v=v.replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");var u=o("EqSource","MathJax Equation Source");if(a.isMobile){r.document.open();r.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>"+u+"</title></head><body style='font-size:85%'>");r.document.write("<pre>"+v+"</pre>");r.document.write("<hr><input type='button' value='"+o("Close","Close")+"' onclick='window.close()' />");r.document.write("</body></html>");r.document.close()}else{r.document.open();r.document.write("<html><head><title>"+u+"</title></head><body style='font-size:85%'>");r.document.write("<table><tr><td><pre>"+v+"</pre></td></tr></table>");r.document.write("</body></html>");r.document.close();var s=r.document.body.firstChild;setTimeout(function(){var A=(r.outerHeight-r.innerHeight)||30,z=(r.outerWidth-r.innerWidth)||30,w,B;z=Math.max(100,Math.min(Math.floor(0.5*screen.width),s.offsetWidth+z+25));A=Math.max(40,Math.min(Math.floor(0.5*screen.height),s.offsetHeight+A+25));r.resizeTo(z,A);if(t&&t.screenX!=null){w=Math.max(0,Math.min(t.screenX-Math.floor(z/2),screen.width-z-20));B=Math.max(0,Math.min(t.screenY-Math.floor(A/2),screen.height-A-20));r.moveTo(w,B)}},50)}};a.Scale=function(){var s=b["HTML-CSS"],r=b.NativeMML,v=b.SVG;var u=(s||r||v||{config:{scale:100}}).config.scale;var t=prompt(o("ScaleMath","Scale all mathematics (compared to surrounding text) by"),u+"%");if(t){if(t.match(/^\s*\d+(\.\d*)?\s*%?\s*$/)){t=parseFloat(t);if(t){if(t!==u){if(s){s.config.scale=t}if(r){r.config.scale=t}if(v){v.config.scale=t}a.cookie.scale=t;a.saveCookie();c.Reprocess()}}else{alert(o("NonZeroScale","The scale should not be zero"))}}else{alert(o("PercentScale","The scale should be a percentage (e.g., 120%%)"))}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){k.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var s=c.outputJax["jax/mml"];if(s[0]!==p.settings.renderer){var v=c.Browser,u,r=a.Renderer.Messages,t;switch(p.settings.renderer){case"NativeMML":if(!p.settings.warnedMML){if(v.isChrome&&v.version.substr(0,3)!=="24."){u=r.MML.WebKit}else{if(v.isSafari&&!v.versionAtLeast("5.0")){u=r.MML.WebKit}else{if(v.isMSIE){if(!v.hasMathPlayer){u=r.MML.MSIE}}else{u=r.MML[v]}}}t="warnedMML"}break;case"SVG":if(!p.settings.warnedSVG){if(v.isMSIE&&!e){u=r.SVG.MSIE}}break}if(u){u=o(u[0],u[1]);u+="\n\n";u+=o("SwitchAnyway","Switch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)");a.cookie.renderer=s[0].id;a.saveCookie();if(!confirm(u)){a.cookie.renderer=p.settings.renderer=g.Cookie.Get("menu").renderer;a.saveCookie();return}if(t){a.cookie.warned=p.settings.warned=true}a.cookie.renderer=p.settings.renderer;a.saveCookie()}c.Queue(["setRenderer",c,p.settings.renderer,"jax/mml"],["Rerender",c])}};a.Renderer.Messages={MML:{WebKit:["WebkitNativeMMLWarning","Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable."],MSIE:["MSIENativeMMLWarning","Internet Explorer requires the MathPlayer plugin in order to process MathML output."],Opera:["OperaNativeMMLWarning","Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly."],Safari:["SafariNativeMMLWarning","Your browser's native MathML does not implement all the features used by MathJax, so some expressions may not render properly."],Firefox:["FirefoxNativeMMLWarning","Your browser's native MathML does not implement all the features used by MathJax, so some expressions may not render properly."]},SVG:{MSIE:["MSIESVGWarning","SVG is not implemented in Internet Explorer prior to IE9 or when it is emulating IE8 or below. Switching to SVG output will cause the mathematics to not display properly."]}};a.Font=function(){var r=b["HTML-CSS"];if(!r){return}document.location.reload()};a.Locale=function(){MathJax.Localization.setLocale(p.settings.locale);MathJax.Hub.Queue(["Reprocess",MathJax.Hub])};a.LoadLocale=function(){var r=prompt(o("LoadURL","Load translation data from this URL:"));if(r){if(!r.match(/\.js$/)){alert(o("BadURL","The URL should be for a javascript file that defines MathJax translation data.  Javascript file names should end with '.js'"))}k.Require(r,function(s){if(s!=k.STATUS.OK){alert(o("BadData","Failed to load translation data from %1",r))}})}};a.MPEvents=function(t){var s=p.settings.discoverable,r=a.MPEvents.Messages;if(!e){if(p.settings.mpMouse&&!confirm(o.apply(o,r.IE8warning))){delete a.cookie.mpContext;delete p.settings.mpContext;delete a.cookie.mpMouse;delete p.settings.mpMouse;a.saveCookie();return}p.settings.mpContext=p.settings.mpMouse;a.cookie.mpContext=a.cookie.mpMouse=p.settings.mpMouse;a.saveCookie();MathJax.Hub.Queue(["Rerender",MathJax.Hub])}else{if(!s&&t.name[1]==="Menu Events"&&p.settings.mpContext){alert(o.apply(o,r.IE9warning))}}};a.MPEvents.Messages={IE8warning:["IE8warning","This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?"],IE9warning:["IE9warning","The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead."]};c.Browser.Select({MSIE:function(r){var s=(document.compatMode==="BackCompat");var t=r.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:(document.documentMode<9),msieFixedPositionBug:(s||!t),msieAboutBug:s});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.RULE(),m.SUBMENU(["Settings","Math Settings"],m.SUBMENU(["ZoomTrigger","Zoom Trigger"],m.RADIO(["Hover","Hover"],"zoom",{action:a.Zoom}),m.RADIO(["Click","Click"],"zoom",{action:a.Zoom}),m.RADIO(["DoubleClick","Double-Click"],"zoom",{action:a.Zoom}),m.RADIO(["NoZoom","No Zoom"],"zoom",{value:"None"}),m.RULE(),m.LABEL(["TriggerRequires","Trigger Requires:"]),m.CHECKBOX((c.Browser.isMac?["Option","Option"]:["Alt","Alt"]),"ALT"),m.CHECKBOX(["Command","Command"],"CMD",{hidden:!c.Browser.isMac}),m.CHECKBOX(["Control","Control"],"CTRL",{hidden:c.Browser.isMac}),m.CHECKBOX(["Shift","Shift"],"Shift")),m.SUBMENU(["ZoomFactor","Zoom Factor"],m.RADIO("125%","zscale"),m.RADIO("133%","zscale"),m.RADIO("150%","zscale"),m.RADIO("175%","zscale"),m.RADIO("200%","zscale"),m.RADIO("250%","zscale"),m.RADIO("300%","zscale"),m.RADIO("400%","zscale")),m.RULE(),m.SUBMENU(["Renderer","Math Renderer"],{hidden:!p.showRenderer},m.RADIO("HTML-CSS","renderer",{action:a.Renderer}),m.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"}),m.RADIO("SVG","renderer",{action:a.Renderer})),m.SUBMENU("MathPlayer",{hidden:!c.Browser.isMSIE||!p.showMathPlayer,disabled:!c.Browser.hasMathPlayer},m.LABEL(["MPHandles","Let MathPlayer Handle:"]),m.CHECKBOX(["MenuEvents","Menu Events"],"mpContext",{action:a.MPEvents,hidden:!e}),m.CHECKBOX(["MouseEvents","Mouse Events"],"mpMouse",{action:a.MPEvents,hidden:!e}),m.CHECKBOX(["MenuAndMouse","Mouse and Menu Events"],"mpMouse",{action:a.MPEvents,hidden:e})),m.SUBMENU(["FontPrefs","Font Preference"],{hidden:!p.showFontMenu},m.LABEL(["ForHTMLCSS","For HTML-CSS:"]),m.RADIO(["Auto","Auto"],"font",{action:a.Font}),m.RULE(),m.RADIO(["TeXLocal","TeX (local)"],"font",{action:a.Font}),m.RADIO(["TeXWeb","TeX (web)"],"font",{action:a.Font}),m.RADIO(["TeXImage","TeX (image)"],"font",{action:a.Font}),m.RULE(),m.RADIO(["STIXLocal","STIX (local)"],"font",{action:a.Font}),m.RADIO(["STIXWeb","STIX (web)"],"font",{action:a.Font}),m.RULE(),m.RADIO(["AsanaMathWeb","Asana Math (web)"],"font",{action:a.Font}),m.RADIO(["GyrePagellaWeb","Gyre Pagella (web)"],"font",{action:a.Font}),m.RADIO(["GyreTermesWeb","Gyre Termes (web)"],"font",{action:a.Font}),m.RADIO(["LatinModernWeb","Latin Modern (web)"],"font",{action:a.Font}),m.RADIO(["NeoEulerWeb","Neo Euler (web)"],"font",{action:a.Font})),m.SUBMENU(["ContextMenu","Contextual Menu"],{hidden:!p.showContext},m.RADIO("MathJax","context"),m.RADIO(["Browser","Browser"],"context")),m.COMMAND(["Scale","Scale All Math ..."],a.Scale),m.RULE().With({hidden:!p.showDiscoverable,name:["","discover_rule"]}),m.CHECKBOX(["Discoverable","Highlight on Hover"],"discoverable",{hidden:!p.showDiscoverable})),m.SUBMENU(["Locale","Language"],{hidden:!p.showLocale},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:"2.3",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",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},TEXCLASSNAMES:["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"],copyAttributes:{fontfamily:true,fontsize:true,fontweight:true,fontstyle:true,color:true,background:true,id:true,"class":true,href:true,style:true},skipAttributes:{texClass:true,useHeight:true,texprimestyle:true},copyAttributeNames:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],Error:function(d,e){var c=this.merror(d),b=MathJax.Localization.fontDirection(),a=MathJax.Localization.fontFamily();if(e){c=c.With(e)}if(b||a){c=this.mstyle(c);if(b){c.dir=b}if(a){c.style.fontFamily="font-family: "+a}}return c}});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:false,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:true},linebreakContainer:false,Init:function(){this.data=[];if(this.inferRow&&!(arguments.length===1&&arguments[0].inferred)){this.Append(a.mrow().With({inferred:true,notParent:true}))}this.Append.apply(this,arguments)},With:function(d){for(var e in d){if(d.hasOwnProperty(e)){this[e]=d[e]}}return this},Append:function(){if(this.inferRow&&this.data.length){this.data[0].Append.apply(this.data[0],arguments)}else{for(var e=0,d=arguments.length;e<d;e++){this.SetData(this.data.length,arguments[e])}}},SetData:function(d,e){if(e!=null){if(!(e instanceof a.mbase)){e=(this.isToken?a.chars(e):a.mtext(e))}e.parent=this;e.setInherit(this.inheritFromMe?this:this.inherit)}this.data[d]=e},Parent:function(){var d=this.parent;while(d&&d.notParent){d=d.parent}return d},Get:function(e,j){if(this[e]!=null){return this[e]}if(this.attr&&this.attr[e]!=null){return this.attr[e]}var f=this.Parent();if(f&&f["adjustChild_"+e]!=null){return(f["adjustChild_"+e])(this.childPosition(),j)}var i=this.inherit;var d=i;while(i){var h=i[e];if(h==null&&i.attr){h=i.attr[e]}if(h!=null&&i.noInheritAttribute&&!i.noInheritAttribute[e]){var g=i.noInherit[this.type];if(!(g&&g[e])){return h}}d=i;i=i.inherit}if(!j){if(this.defaults[e]===a.AUTO){return this.autoDefault(e)}if(this.defaults[e]!==a.INHERIT&&this.defaults[e]!=null){return this.defaults[e]}if(d){return d.defaults[e]}}return null},hasValue:function(d){return(this.Get(d,true)!=null)},getValues:function(){var e={};for(var f=0,d=arguments.length;f<d;f++){e[arguments[f]]=this.Get(arguments[f])}return e},adjustChild_scriptlevel:function(e,d){return this.Get("scriptlevel",d)},adjustChild_displaystyle:function(e,d){return this.Get("displaystyle",d)},adjustChild_texprimestyle:function(e,d){return this.Get("texprimestyle",d)},childPosition:function(){var g=this,f=g.parent;while(f.notParent){g=f;f=g.parent}for(var e=0,d=f.data.length;e<d;e++){if(f.data[e]===g){return e}}return null},setInherit:function(f){if(f!==this.inherit&&this.inherit==null){this.inherit=f;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].setInherit){this.data[e].setInherit(f)}}}},setTeXclass:function(d){this.getPrevClass(d);return(typeof(this.texClass)!=="undefined"?this:d)},getPrevClass:function(d){if(d){this.prevClass=d.Get("texClass");this.prevLevel=d.Get("scriptlevel")}},updateTeXclass:function(d){if(d){this.prevClass=d.prevClass;delete d.prevClass;this.prevLevel=d.prevLevel;delete d.prevLevel;this.texClass=d.Get("texClass")}},texSpacing:function(){var e=(this.prevClass!=null?this.prevClass:a.TEXCLASS.NONE);var d=(this.Get("texClass")||a.TEXCLASS.ORD);if(e===a.TEXCLASS.NONE||d===a.TEXCLASS.NONE){return""}if(e===a.TEXCLASS.VCENTER){e=a.TEXCLASS.ORD}if(d===a.TEXCLASS.VCENTER){d=a.TEXCLASS.ORD}var f=this.TEXSPACE[e][d];if(this.prevLevel>0&&this.Get("scriptlevel")>0&&f>=0){return""}return this.TEXSPACELENGTH[Math.abs(f)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(d){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished()){return this.CoreMO().hasNewline()}if(this.isToken||this.linebreakContainer){return false}for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&this.data[e].hasNewline()){return true}}return false},array:function(){if(this.inferred){return this.data}else{return[this]}},toString:function(){return this.type+"("+this.data.join(",")+")"},getAnnotation:function(){return null}},{childrenSpacelike:function(){for(var e=0,d=this.data.length;e<d;e++){if(!this.data[e].isSpacelike()){return false}}return true},childEmbellished:function(){return(this.data[0]&&this.data[0].isEmbellished())},childCore:function(){return this.data[0]},childCoreMO:function(){return(this.data[0]?this.data[0].CoreMO():null)},setChildTeXclass:function(d){if(this.data[0]){d=this.data[0].setTeXclass(d);this.updateTeXclass(this.data[0])}return d},setBaseTeXclasses:function(f){this.getPrevClass(f);this.texClass=null;if(this.data[0]){if(this.isEmbellished()||this.data[0].isa(a.mi)){f=this.data[0].setTeXclass(f);this.updateTeXclass(this.Core())}else{this.data[0].setTeXclass();f=this}}else{f=this}for(var e=1,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].setTeXclass()}}return f},setSeparateTeXclasses:function(f){this.getPrevClass(f);for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){this.data[e].setTeXclass()}}if(this.isEmbellished()){this.updateTeXclass(this.Core())}return this}});a.mi=a.mbase.Subclass({type:"mi",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.AUTO,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT},autoDefault:function(e){if(e==="mathvariant"){var d=(this.data[0]||"").toString();return(d.length===1||(d.length===2&&d.charCodeAt(0)>=55296&&d.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(e){this.getPrevClass(e);var d=this.data.join("");if(d.length>1&&d.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:true,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2,form:4},useMMLspacing:7,autoDefault:function(f,l){var k=this.def;if(!k){if(f==="form"){this.useMMLspacing&=~this.SPACE_ATTR.form;return this.getForm()}var j=this.data.join("");var e=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var g=0,d=e.length;g<d;g++){var h=this.OPTABLE[e[g]][j];if(h){k=this.makeDef(h);break}}if(!k){k=this.CheckRange(j)}if(!k&&l){k={}}else{if(!k){k=MathJax.Hub.Insert({},this.defaultDef)}k.form=e[0];this.def=k}}this.useMMLspacing&=~(this.SPACE_ATTR[f]||0);if(k[f]!=null){return k[f]}else{if(!l){return this.defaultDef[f]}}return""},CheckRange:function(h){var j=h.charCodeAt(0);if(j>=55296&&j<56320){j=(((j-55296)<<10)+(h.charCodeAt(1)-56320))+65536}for(var f=0,d=this.RANGES.length;f<d&&this.RANGES[f][0]<=j;f++){if(j<=this.RANGES[f][1]){if(this.RANGES[f][3]){var e=a.optableDir+"/"+this.RANGES[f][3]+".js";this.RANGES[f][3]=null;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(e))}var g=a.TEXCLASSNAMES[this.RANGES[f][2]];g=this.OPTABLE.infix[h]=a.mo.OPTYPES[g==="BIN"?"BIN3":g];return this.makeDef(g)}}return null},makeDef:function(e){if(e[2]==null){e[2]=this.defaultDef.texClass}if(!e[3]){e[3]={}}var d=MathJax.Hub.Insert({},e[3]);d.lspace=this.SPACE[e[0]];d.rspace=this.SPACE[e[1]];d.texClass=e[2];if(d.texClass===a.TEXCLASS.REL&&(this.movablelimits||this.data.join("").match(/^[a-z]+$/i))){d.texClass=a.TEXCLASS.OP}return d},getForm:function(){var d=this,f=this.parent,e=this.Parent();while(e&&e.isEmbellished()){d=f;f=e.parent;e=e.Parent()}if(f&&f.type==="mrow"&&f.NonSpaceLength()!==1){if(f.FirstNonSpace()===d){return a.FORM.PREFIX}if(f.LastNonSpace()===d){return a.FORM.POSTFIX}}return a.FORM.INFIX},isEmbellished:function(){return true},hasNewline:function(){return(this.Get("linebreak")===a.LINEBREAK.NEWLINE)},setTeXclass:function(d){this.getValues("lspace","rspace");if(this.useMMLspacing){this.texClass=a.TEXCLASS.NONE;return this}this.texClass=this.Get("texClass");if(this.data.join("")==="\u2061"){if(d){d.texClass=a.TEXCLASS.OP}this.texClass=this.prevClass=a.TEXCLASS.NONE;return d}return this.adjustTeXclass(d)},adjustTeXclass:function(d){if(this.texClass===a.TEXCLASS.NONE){return d}if(d){if(d.autoOP&&(this.texClass===a.TEXCLASS.BIN||this.texClass===a.TEXCLASS.REL)){d.texClass=a.TEXCLASS.ORD}this.prevClass=d.texClass||a.TEXCLASS.ORD;this.prevLevel=d.Get("scriptlevel")}else{this.prevClass=a.TEXCLASS.NONE}if(this.texClass===a.TEXCLASS.BIN&&(this.prevClass===a.TEXCLASS.NONE||this.prevClass===a.TEXCLASS.BIN||this.prevClass===a.TEXCLASS.OP||this.prevClass===a.TEXCLASS.REL||this.prevClass===a.TEXCLASS.OPEN||this.prevClass===a.TEXCLASS.PUNCT)){this.texClass=a.TEXCLASS.ORD}else{if(this.prevClass===a.TEXCLASS.BIN&&(this.texClass===a.TEXCLASS.REL||this.texClass===a.TEXCLASS.CLOSE||this.texClass===a.TEXCLASS.PUNCT)){d.texClass=this.prevClass=a.TEXCLASS.ORD}}return this}});a.mtext=a.mbase.Subclass({type:"mtext",isToken:true,isSpacelike:function(){return true},texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,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 e=false;for(var f=0,d=this.data.length;f<d;f++){if(this.data[f]==null){continue}if(this.data[f].isEmbellished()){if(e){return false}e=true;this.core=f}else{if(!this.data[f].isSpacelike()){return false}}}return e},NonSpaceLength:function(){var f=0;for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){f++}}return f},FirstNonSpace:function(){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},LastNonSpace:function(){for(var d=this.data.length-1;d>=0;d--){if(this.data[0]&&!this.data[d].isSpacelike()){return this.data[d]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(f){for(var e=0,d=this.data.length;e<d;e++){if(this.data[e]){f=this.data[e].setTeXclass(f)}}if(this.data[0]){this.updateTeXclass(this.data[0])}return f},getAnnotation:function(d){if(this.data.length!=1){return null}return this.data[0].getAnnotation(d)}});a.mfrac=a.mbase.Subclass({type:"mfrac",num:0,den:1,linebreakContainer:true,texClass:a.TEXCLASS.INNER,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,linethickness:a.LINETHICKNESS.MEDIUM,numalign:a.ALIGN.CENTER,denomalign:a.ALIGN.CENTER,bevelled:false},adjustChild_displaystyle:function(d){return false},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(!this.Get("displaystyle")||d>0){d++}return d},adjustChild_texprimestyle:function(d){if(d==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(d){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(d){if(d===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e===1){d+=2}return d},adjustChild_texprimestyle:function(d){if(d===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(f){var e=this.scriptlevel;if(e==null){e=this.Get("scriptlevel")}else{if(String(e).match(/^ *[-+]/)){delete this.scriptlevel;var d=this.Get("scriptlevel");this.scriptlevel=e;e=d+parseInt(e)}}return e},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(g){this.getPrevClass(g);var e=this.getValues("open","close","separators");e.open=e.open.replace(/[ \t\n\r]/g,"");e.close=e.close.replace(/[ \t\n\r]/g,"");e.separators=e.separators.replace(/[ \t\n\r]/g,"");if(e.open!==""){this.SetData("open",a.mo(e.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));g=this.data.open.setTeXclass(g)}if(e.separators!==""){while(e.separators.length<this.data.length){e.separators+=e.separators.charAt(e.separators.length-1)}}if(this.data[0]){g=this.data[0].setTeXclass(g)}for(var f=1,d=this.data.length;f<d;f++){if(this.data[f]){if(e.separators!==""){this.SetData("sep"+f,a.mo(e.separators.charAt(f-1)));g=this.data["sep"+f].setTeXclass(g)}g=this.data[f].setTeXclass(g)}}if(e.close!==""){this.SetData("close",a.mo(e.close).With({stretchy:true,texClass:a.TEXCLASS.CLOSE}));g=this.data.close.setTeXclass(g)}this.updateTeXclass(this.data.open);return g}});a.menclose=a.mbase.Subclass({type:"menclose",inferRow:true,linebreakContainer:true,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,notation:a.NOTATION.LONGDIV,texClass:a.TEXCLASS.ORD},setTeXclass:a.mbase.setSeparateTeXclasses});a.msubsup=a.mbase.Subclass({type:"msubsup",base:0,sub:1,sup:2,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,subscriptshift:"",superscriptshift:"",texClass:a.AUTO},autoDefault:function(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}return 0},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(e){var d=this.Get("scriptlevel");if(e>0){d++}return d},adjustChild_texprimestyle:function(d){if(d===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(d){if(d%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(d){if(d==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(d):a.TEXCLASS.ORD)}if(d==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(d==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(d){if(d>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");var d=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(f==this.under&&(d||!this.Get("accentunder"))){e++}if(f==this.over&&(d||!this.Get("accent"))){e++}return e},adjustChild_texprimestyle:function(d){if(d===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e<d;e++){if(!((arguments[e] instanceof a.mtr)||(arguments[e] instanceof a.mlabeledtr))){arguments[e]=a.mtd(arguments[e])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtr=a.mbase.Subclass({type:"mtr",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{rowalign:true,columnalign:true,groupalign:true},mtable:{rowalign:true,columnalign:true,groupalign:true}},linebreakContainer:true,Append:function(){for(var e=0,d=arguments.length;e<d;e++){if(!(arguments[e] instanceof a.mtd)){arguments[e]=a.mtd(arguments[e])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtd=a.mbase.Subclass({type:"mtd",inferRow:true,linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowspan:1,columnspan:1,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},setTeXclass:a.mbase.setSeparateTeXclasses});a.maligngroup=a.mbase.Subclass({type:"malign",isSpacelike:function(){return true},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:true,noInherit:{mrow:{groupalign:true},mtable:{groupalign:true}}});a.malignmark=a.mbase.Subclass({type:"malignmark",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,edge:a.SIDE.LEFT},isSpacelike:function(){return true}});a.mlabeledtr=a.mtr.Subclass({type:"mlabeledtr"});a.maction=a.mbase.Subclass({type:"maction",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,actiontype:a.ACTIONTYPE.TOGGLE,selection:1},selected:function(){return this.data[this.Get("selection")-1]||a.NULL},isEmbellished:function(){return this.selected().isEmbellished()},isSpacelike:function(){return this.selected().isSpacelike()},Core:function(){return this.selected().Core()},CoreMO:function(){return this.selected().CoreMO()},setTeXclass:function(d){if(this.Get("actiontype")===a.ACTIONTYPE.TOOLTIP&&this.data[1]){this.data[1].setTeXclass()}return this.selected().setTeXclass(d)}});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(f){var k=MathJax.Hub.config.MathMenu.semanticsAnnotations[f];if(k){for(var g=0,d=this.data.length;g<d;g++){var h=this.data[g].Get("encoding");if(h){for(var e=0,l=k.length;e<l;e++){if(k[e]===h){return this.data[g]}}}}}return null}});a.annotation=a.mbase.Subclass({type:"annotation",isToken:true,linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a["annotation-xml"]=a.mbase.Subclass({type:"annotation-xml",linebreakContainer:true,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a.math=a.mstyle.Subclass({type:"math",defaults:{mathvariant:a.VARIANT.NORMAL,mathsize:a.SIZE.NORMAL,mathcolor:"",mathbackground:a.COLOR.TRANSPARENT,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(d){if(d==="displaystyle"){return this.Get("display")==="block"}return""},linebreakContainer:true,setTeXclass:a.mbase.setChildTeXclass,getAnnotation:function(d){if(this.data.length!=1){return null}return this.data[0].getAnnotation(d)}});a.chars=a.mbase.Subclass({type:"chars",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){return this.data.join("")},toString:function(){return this.data.join("")}});a.entity=a.mbase.Subclass({type:"entity",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){if(this.data[0].substr(0,2)==="#x"){return parseInt(this.data[0].substr(2),16)}else{if(this.data[0].substr(0,1)==="#"){return parseInt(this.data[0].substr(1))}else{return 0}}},toString:function(){var d=this.value();if(d<=65535){return String.fromCharCode(d)}d-=65536;return String.fromCharCode((d>>10)+55296)+String.fromCharCode((d&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var e=0,d=arguments.length;e<d;e++){var f=this.Import(arguments[e]);this.data.push(f);this.div.appendChild(f)}},Import:function(h){if(document.importNode){return document.importNode(h,true)}var e,f,d;if(h.nodeType===1){e=document.createElement(h.nodeName);for(f=0,d=h.attributes.length;f<d;f++){var g=h.attributes[f];if(g.specified&&g.nodeValue!=null&&g.nodeValue!=""){e.setAttribute(g.nodeName,g.nodeValue)}if(g.nodeName==="style"){e.style.cssText=g.nodeValue}}if(h.className){e.className=h.className}}else{if(h.nodeType===3||h.nodeType===4){e=document.createTextNode(h.nodeValue)}else{if(h.nodeType===8){e=document.createComment(h.nodeValue)}else{return document.createTextNode("")}}}for(f=0,d=h.childNodes.length;f<d;f++){e.appendChild(this.Import(h.childNodes[f]))}return e},value:function(){return this.div},toString:function(){return this.div.innerHTML}});a.TeXAtom=a.mbase.Subclass({type:"texatom",inferRow:true,notParent:true,texClass:a.TEXCLASS.ORD,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,isEmbellished:a.mbase.childEmbellished,setTeXclass:function(d){this.data[0].setTeXclass();return this.adjustTeXclass(d)},adjustTeXclass:a.mo.prototype.adjustTeXclass});a.NULL=a.mbase().With({type:"null"});var b=a.TEXCLASS;var c={ORD:[0,0,b.ORD],ORD11:[1,1,b.ORD],ORD21:[2,1,b.ORD],ORD02:[0,2,b.ORD],ORD55:[5,5,b.ORD],OP:[1,2,b.OP,{largeop:true,movablelimits:true,symmetric:true}],OPFIXED:[1,2,b.OP,{largeop:true,movablelimits:true}],INTEGRAL:[0,1,b.OP,{largeop:true,symmetric:true}],INTEGRAL2:[1,2,b.OP,{largeop:true,symmetric:true}],BIN3:[3,3,b.BIN],BIN4:[4,4,b.BIN],BIN01:[0,1,b.BIN],BIN5:[5,5,b.BIN],TALLBIN:[4,4,b.BIN,{stretchy:true}],BINOP:[4,4,b.BIN,{largeop:true,movablelimits:true}],REL:[5,5,b.REL],REL1:[1,1,b.REL,{stretchy:true}],REL4:[4,4,b.REL],RELSTRETCH:[5,5,b.REL,{stretchy:true}],RELACCENT:[5,5,b.REL,{accent:true}],WIDEREL:[5,5,b.REL,{accent:true,stretchy:true}],OPEN:[0,0,b.OPEN,{fence:true,stretchy:true,symmetric:true}],CLOSE:[0,0,b.CLOSE,{fence:true,stretchy:true,symmetric:true}],INNER:[0,0,b.INNER],PUNCT:[0,3,b.PUNCT],ACCENT:[0,0,b.ORD,{accent:true}],WIDEACCENT:[0,0,b.ORD,{accent:true,stretchy:true}]};a.mo.Augment({SPACE:["0em","0.1111em","0.1667em","0.2222em","0.2667em","0.3333em"],RANGES:[[32,127,b.REL,"BasicLatin"],[160,255,b.ORD,"Latin1Supplement"],[256,383,b.ORD],[384,591,b.ORD],[688,767,b.ORD,"SpacingModLetters"],[768,879,b.ORD,"CombDiacritMarks"],[880,1023,b.ORD,"GreekAndCoptic"],[7680,7935,b.ORD],[8192,8303,b.PUNCT,"GeneralPunctuation"],[8304,8351,b.ORD],[8352,8399,b.ORD],[8400,8447,b.ORD,"CombDiactForSymbols"],[8448,8527,b.ORD,"LetterlikeSymbols"],[8528,8591,b.ORD],[8592,8703,b.REL,"Arrows"],[8704,8959,b.BIN,"MathOperators"],[8960,9215,b.ORD,"MiscTechnical"],[9312,9471,b.ORD],[9472,9631,b.ORD],[9632,9727,b.ORD,"GeometricShapes"],[9984,10175,b.ORD,"Dingbats"],[10176,10223,b.ORD,"MiscMathSymbolsA"],[10224,10239,b.REL,"SupplementalArrowsA"],[10496,10623,b.REL,"SupplementalArrowsB"],[10624,10751,b.ORD,"MiscMathSymbolsB"],[10752,11007,b.BIN,"SuppMathOperators"],[11008,11263,b.ORD,"MiscSymbolsAndArrows"],[119808,120831,b.ORD]],OPTABLE:{prefix:{"\u2200":c.ORD21,"\u2202":c.ORD21,"\u2203":c.ORD21,"\u2207":c.ORD21,"\u220F":c.OP,"\u2210":c.OP,"\u2211":c.OP,"\u2212":c.BIN01,"\u2213":c.BIN01,"\u221A":[1,1,b.ORD,{stretchy:true}],"\u2220":c.ORD,"\u222B":c.INTEGRAL,"\u222E":c.INTEGRAL,"\u22C0":c.OP,"\u22C1":c.OP,"\u22C2":c.OP,"\u22C3":c.OP,"\u2308":c.OPEN,"\u230A":c.OPEN,"\u27E8":c.OPEN,"\u27EE":c.OPEN,"\u2A00":c.OP,"\u2A01":c.OP,"\u2A02":c.OP,"\u2A04":c.OP,"\u2A06":c.OP,"\u00AC":c.ORD21,"\u00B1":c.BIN01,"(":c.OPEN,"+":c.BIN01,"-":c.BIN01,"[":c.OPEN,"{":c.OPEN,"|":c.OPEN},postfix:{"!":[1,0,b.CLOSE],"&":c.ORD,"\u2032":c.ORD02,"\u203E":c.WIDEACCENT,"\u2309":c.CLOSE,"\u230B":c.CLOSE,"\u23DE":c.WIDEACCENT,"\u23DF":c.WIDEACCENT,"\u266D":c.ORD02,"\u266E":c.ORD02,"\u266F":c.ORD02,"\u27E9":c.CLOSE,"\u27EF":c.CLOSE,"\u02C6":c.WIDEACCENT,"\u02C7":c.WIDEACCENT,"\u02C9":c.WIDEACCENT,"\u02CA":c.ACCENT,"\u02CB":c.ACCENT,"\u02D8":c.ACCENT,"\u02D9":c.ACCENT,"\u02DC":c.WIDEACCENT,"\u0302":c.WIDEACCENT,"\u00A8":c.ACCENT,"\u00AF":c.WIDEACCENT,")":c.CLOSE,"]":c.CLOSE,"^":c.WIDEACCENT,_:c.WIDEACCENT,"`":c.ACCENT,"|":c.CLOSE,"}":c.CLOSE,"~":c.WIDEACCENT},infix:{"":c.ORD,"%":[3,3,b.ORD],"\u2022":c.BIN4,"\u2026":c.INNER,"\u2044":c.TALLBIN,"\u2061":c.ORD,"\u2062":c.ORD,"\u2063":[0,0,b.ORD,{linebreakstyle:"after",separator:true}],"\u2064":c.ORD,"\u2190":c.WIDEREL,"\u2191":c.RELSTRETCH,"\u2192":c.WIDEREL,"\u2193":c.RELSTRETCH,"\u2194":c.WIDEREL,"\u2195":c.RELSTRETCH,"\u2196":c.RELSTRETCH,"\u2197":c.RELSTRETCH,"\u2198":c.RELSTRETCH,"\u2199":c.RELSTRETCH,"\u21A6":c.WIDEREL,"\u21A9":c.WIDEREL,"\u21AA":c.WIDEREL,"\u21BC":c.WIDEREL,"\u21BD":c.WIDEREL,"\u21C0":c.WIDEREL,"\u21C1":c.WIDEREL,"\u21CC":c.WIDEREL,"\u21D0":c.WIDEREL,"\u21D1":c.RELSTRETCH,"\u21D2":c.WIDEREL,"\u21D3":c.RELSTRETCH,"\u21D4":c.WIDEREL,"\u21D5":c.RELSTRETCH,"\u2208":c.REL,"\u2209":c.REL,"\u220B":c.REL,"\u2212":c.BIN4,"\u2213":c.BIN4,"\u2215":c.TALLBIN,"\u2216":c.BIN4,"\u2217":c.BIN4,"\u2218":c.BIN4,"\u2219":c.BIN4,"\u221D":c.REL,"\u2223":c.REL,"\u2225":c.REL,"\u2227":c.BIN4,"\u2228":c.BIN4,"\u2229":c.BIN4,"\u222A":c.BIN4,"\u223C":c.REL,"\u2240":c.BIN4,"\u2243":c.REL,"\u2245":c.REL,"\u2248":c.REL,"\u224D":c.REL,"\u2250":c.REL,"\u2260":c.REL,"\u2261":c.REL,"\u2264":c.REL,"\u2265":c.REL,"\u226A":c.REL,"\u226B":c.REL,"\u227A":c.REL,"\u227B":c.REL,"\u2282":c.REL,"\u2283":c.REL,"\u2286":c.REL,"\u2287":c.REL,"\u228E":c.BIN4,"\u2291":c.REL,"\u2292":c.REL,"\u2293":c.BIN4,"\u2294":c.BIN4,"\u2295":c.BIN4,"\u2296":c.BIN4,"\u2297":c.BIN4,"\u2298":c.BIN4,"\u2299":c.BIN4,"\u22A2":c.REL,"\u22A3":c.REL,"\u22A4":c.ORD55,"\u22A5":c.REL,"\u22A8":c.REL,"\u22C4":c.BIN4,"\u22C5":c.BIN4,"\u22C6":c.BIN4,"\u22C8":c.REL,"\u22EE":c.ORD55,"\u22EF":c.INNER,"\u22F1":[5,5,b.INNER],"\u25B3":c.BIN4,"\u25B5":c.BIN4,"\u25B9":c.BIN4,"\u25BD":c.BIN4,"\u25BF":c.BIN4,"\u25C3":c.BIN4,"\u2758":c.REL,"\u27F5":c.WIDEREL,"\u27F6":c.WIDEREL,"\u27F7":c.WIDEREL,"\u27F8":c.WIDEREL,"\u27F9":c.WIDEREL,"\u27FA":c.WIDEREL,"\u27FC":c.WIDEREL,"\u2A2F":c.BIN4,"\u2A3F":c.BIN4,"\u2AAF":c.REL,"\u2AB0":c.REL,"\u00B1":c.BIN4,"\u00B7":c.BIN4,"\u00D7":c.BIN4,"\u00F7":c.BIN4,"*":c.BIN3,"+":c.BIN4,",":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"-":c.BIN4,".":[3,3,b.ORD],"/":c.ORD11,":":[1,2,b.REL],";":[0,3,b.PUNCT,{linebreakstyle:"after",separator:true}],"<":c.REL,"=":c.REL,">":c.REL,"?":[1,1,b.CLOSE],"\\":c.ORD,"^":c.ORD11,_:c.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":c.ORD,"$":c.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":c.ORD,"\u0300":c.ACCENT,"\u0301":c.ACCENT,"\u0303":c.WIDEACCENT,"\u0304":c.ACCENT,"\u0306":c.ACCENT,"\u0307":c.ACCENT,"\u0308":c.ACCENT,"\u030C":c.ACCENT,"\u0332":c.WIDEACCENT,"\u0338":c.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":c.BIN3,"\u2021":c.BIN3,"\u20D7":c.ACCENT,"\u2111":c.ORD,"\u2113":c.ORD,"\u2118":c.ORD,"\u211C":c.ORD,"\u2205":c.ORD,"\u221E":c.ORD,"\u2305":c.BIN3,"\u2306":c.BIN3,"\u2322":c.REL4,"\u2323":c.REL4,"\u2329":c.OPEN,"\u232A":c.CLOSE,"\u23AA":c.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":c.OPEN,"\u23B1":c.CLOSE,"\u2500":c.ORD,"\u25EF":c.BIN3,"\u2660":c.ORD,"\u2661":c.ORD,"\u2662":c.ORD,"\u2663":c.ORD,"\u3008":c.OPEN,"\u3009":c.CLOSE,"\uFE37":c.WIDEACCENT,"\uFE38":c.WIDEACCENT}}},{OPTYPES:c});a.mo.prototype.OPTABLE.infix["^"]=c.WIDEREL;a.mo.prototype.OPTABLE.infix._=c.WIDEREL})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js");
MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b="2.3";var a=MathJax.ElementJax.mml;SETTINGS=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(k){var g=(this.inferred&&this.parent.inferRow);if(k==null){k=""}var e=this.type,d=this.toMathMLattributes();if(e==="mspace"){return k+"<"+e+d+" />"}var j=[];var h=(this.isToken?"":k+(g?"":"  "));for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){j.push(this.data[f].toMathML(h))}else{if(!this.isToken){j.push(h+"<mrow />")}}}if(this.isToken){return k+"<"+e+d+">"+j.join("")+"</"+e+">"}if(g){return j.join("\n")}if(j.length===0||(j.length===1&&j[0]==="")){return k+"<"+e+d+" />"}return k+"<"+e+d+">\n"+j.join("\n")+"\n"+k+"</"+e+">"},toMathMLattributes:function(){var j=[],g=this.defaults;var c=(this.attrNames||a.copyAttributeNames),l=a.skipAttributes;if(this.type==="math"&&(!this.attr||!this.attr.xmlns)){j.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){if(this.type==="mstyle"){g=a.math.prototype.defaults}for(var d in g){if(!l[d]&&g.hasOwnProperty(d)){var e=(d==="open"||d==="close");if(this[d]!=null&&(e||this[d]!==g[d])){var k=this[d];delete this[d];if(e||this.Get(d)!==k){j.push(d+'="'+this.toMathMLattribute(k)+'"')}this[d]=k}}}}for(var h=0,f=c.length;h<f;h++){if(c[h]==="class"){continue}k=(this.attr||{})[c[h]];if(k==null){k=this[c[h]]}if(k!=null){j.push(c[h]+'="'+this.toMathMLquote(k)+'"')}}this.toMathMLclass(j);if(j.length){return" "+j.join(" ")}else{return""}},toMathMLclass:function(c){var e=[];if(this["class"]){e.push(this["class"])}if(this.isa(a.TeXAtom)&&SETTINGS.texHints){var d=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(d){e.push("MJX-TeXAtom-"+d)}}if(this.mathvariant&&this.toMathMLvariants[this.mathvariant]){e.push("MJX"+this.mathvariant)}if(this.variantForm){e.push("MJX-variant")}if(e.length){c.unshift('class="'+e.join(" ")+'"')}},toMathMLattribute:function(c){if(typeof(c)==="string"&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)){return RegExp.$2+((1/18)*RegExp.$3).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.toMathMLvariants[c]){return this.toMathMLvariants[c]}}return this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":a.VARIANT.SCRIPT,"-tex-caligraphic-bold":a.VARIANT.BOLDSCRIPT,"-tex-oldstyle":a.VARIANT.NORMAL,"-tex-oldstyle-bold":a.VARIANT.BOLD,"-tex-mathit":a.VARIANT.ITALIC},toMathMLquote:function(f){f=String(f).split("");for(var g=0,d=f.length;g<d;g++){var k=f[g].charCodeAt(0);if(k<=55295||57344<=k){if(k<32||k>126){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&amp;","<":"&lt;",">":"&gt;",'"':"&quot;"}[f[g]];if(j){f[g]=j}}}else{if(g+1<d){var h=f[g+1].charCodeAt(0);var e=(((k-55296)<<10)+(h-56320)+65536);f[g]="&#x"+e.toString(16).toUpperCase()+";";f[g+1]="";g++}else{f[g]=""}}}return f.join("")}});a.msubsup.Augment({toMathML:function(h){var e=this.type;if(this.data[this.sup]==null){e="msub"}if(this.data[this.sub]==null){e="msup"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+"  "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.munderover.Augment({toMathML:function(h){var e=this.type;if(this.data[this.under]==null){e="mover"}if(this.data[this.over]==null){e="munder"}var d=this.toMathMLattributes();delete this.data[0].inferred;var g=[];for(var f=0,c=this.data.length;f<c;f++){if(this.data[f]){g.push(this.data[f].toMathML(h+"  "))}}return h+"<"+e+d+">\n"+g.join("\n")+"\n"+h+"</"+e+">"}});a.TeXAtom.Augment({toMathML:function(d){var c=this.toMathMLattributes();if(!c&&this.data[0].data.length===1){return d.substr(2)+this.data[0].toMathML(d)}return d+"<mrow"+c+">\n"+this.data[0].toMathML(d+"  ")+"\n"+d+"</mrow>"}});a.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(c){return(c||"")+"&"+this.data[0]+";<!-- "+this.toString()+" -->"}});a.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js");
(function(b,e){var d="2.3";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Config",function(){b.Config({"HTML-CSS":{styles:{".MathJax .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.call(this,j,k)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.call(this,p)}p=this.HTMLcreateSpan(p);p.className="noError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var o=0,l=r.length;o<l;o++){h.addText(p,r[o]);if(o!==l-1){h.addElement(p,"br",{isMathJax:true})}}var q=h.getHD(p.parentNode),k=h.getW(p.parentNode);if(l>1){var n=(q.h+q.d)/2,j=h.TeX.x_height/2;p.parentNode.style.verticalAlign=h.Em(q.d+(j-n));q.h=j+n;q.d=n-j}p.bbox={h:q.h,d:q.d,w:k,lw:0,rw:k};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.call(this,i,j)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.call(this,n)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l<j;l++){e.addText(n,o[l]);if(l!==j-1){e.addElement(n,"br",{isMathJax:true})}}if(j>1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.call(this,j)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.call(this,n)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l<k;l++){n.appendChild(document.createTextNode(o[l]));if(l!==k-1){n.appendChild(document.createElement("br"))}}if(this.multiLine){n.style.display="inline-block";if(k>1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js");
MathJax.Extension["TeX/noUndefined"]={version:"2.3",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js");
(function(d,c,i){var h,g="\u00A0";var j=function(l){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",l]].concat([].slice.call(arguments,1)))};var e=MathJax.Object.Subclass({Init:function(m,l){this.global={isInner:l};this.data=[b.start(this.global)];if(m){this.data[0].env=m}this.env=this.data[0].env},Push:function(){var n,l,o,p;for(n=0,l=arguments.length;n<l;n++){o=arguments[n];if(o instanceof h.mbase){o=b.mml(o)}o.global=this.global;p=(this.data.length?this.Top().checkItem(o):true);if(p instanceof Array){this.Pop();this.Push.apply(this,p)}else{if(p instanceof b){this.Pop();this.Push(p)}else{if(p){this.data.push(o);if(o.env){for(var q in this.env){if(this.env.hasOwnProperty(q)){o.env[q]=this.env[q]}}this.env=o.env}else{o.env=this.env}}}}}},Pop:function(){var l=this.data.pop();if(!l.isOpen){delete l.env}this.env=(this.data.length?this.Top().env:{});return l},Top:function(l){if(l==null){l=1}if(this.data.length<l){return null}return this.data[this.data.length-l]},Prev:function(l){var m=this.Top();if(l){return m.data[m.data.length-1]}else{return m.Pop()}},toString:function(){return"stack[\n  "+this.data.join("\n  ")+"\n]"}});var b=e.Item=MathJax.Object.Subclass({type:"base",endError:["ExtraOpenMissingClose","Extra open brace or missing close brace"],closeError:["ExtraCloseMissingOpen","Extra close brace or missing open brace"],rightError:["MissingLeftExtraRight","Missing \\left or extra \\right"],Init:function(){if(this.isOpen){this.env={}}this.data=[];this.Push.apply(this,arguments)},Push:function(){this.data.push.apply(this.data,arguments)},Pop:function(){return this.data.pop()},mmlData:function(l,m){if(l==null){l=true}if(this.data.length===1&&!m){return this.data[0]}return h.mrow.apply(h,this.data).With((l?{inferred:true}:{}))},checkItem:function(l){if(l.type==="over"&&this.isOpen){l.num=this.mmlData(false);this.data=[]}if(l.type==="cell"&&this.isOpen){if(l.linebreak){return false}d.Error(["Misplaced","Misplaced %1",l.name])}if(l.isClose&&this[l.type+"Error"]){d.Error(this[l.type+"Error"])}if(!l.isNotStack){return true}this.Push(l.data[0]);return false},With:function(l){for(var m in l){if(l.hasOwnProperty(m)){this[m]=l[m]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:true,Init:function(l){this.SUPER(arguments).Init.call(this);this.global=l},checkItem:function(l){if(l.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,l)}});b.stop=b.Subclass({type:"stop",isClose:true});b.open=b.Subclass({type:"open",isOpen:true,stopError:["ExtraOpenMissingClose","Extra open brace or missing close brace"],checkItem:function(m){if(m.type==="close"){var l=this.mmlData();return b.mml(h.TeXAtom(l))}return this.SUPER(arguments).checkItem.call(this,m)}});b.close=b.Subclass({type:"close",isClose:true});b.prime=b.Subclass({type:"prime",checkItem:function(l){if(this.data[0].type!=="msubsup"){return[h.msup(this.data[0],this.data[1]),l]}this.data[0].SetData(this.data[0].sup,this.data[1]);return[this.data[0],l]}});b.subsup=b.Subclass({type:"subsup",stopError:["MissingScript","Missing superscript or subscript argument"],supError:["MissingOpenForSup","Missing open brace for superscript"],subError:["MissingOpenForSub","Missing open brace for subscript"],checkItem:function(l){if(l.type==="open"||l.type==="left"){return true}if(l.type==="mml"){if(this.primes){if(this.position!==2){this.data[0].SetData(2,this.primes)}else{l.data[0]=h.mrow(this.primes.With({variantForm:true}),l.data[0])}}this.data[0].SetData(this.position,l.data[0]);return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,l)){d.Error(this[["","subError","supError"][this.position]])}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:true,name:"\\over",checkItem:function(n,l){if(n.type==="over"){d.Error(["AmbiguousUseOf","Ambiguous use of %1",n.name])}if(n.isClose){var m=h.mfrac(this.num,this.mmlData(false));if(this.thickness!=null){m.linethickness=this.thickness}if(this.open||this.close){m.texClass=h.TEXCLASS.INNER;m.texWithDelims=true;m=d.fenced(this.open,m,this.close)}return[b.mml(m),n]}return this.SUPER(arguments).checkItem.call(this,n)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:true,delim:"(",stopError:["ExtraLeftMissingRight","Extra \\left or missing \\right"],checkItem:function(l){if(l.type==="right"){return b.mml(d.fenced(this.delim,this.mmlData(),l.delim))}return this.SUPER(arguments).checkItem.call(this,l)}});b.right=b.Subclass({type:"right",isClose:true,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:true,checkItem:function(l){if(l.type==="end"){if(l.name!==this.name){d.Error(["EnvBadEnd","\\begin{%1} ended with \\end{%2}",this.name,l.name])}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(l.type==="stop"){d.Error(["EnvMissingEnd","Missing \\end{%1}",this.name])}return this.SUPER(arguments).checkItem.call(this,l)}});b.end=b.Subclass({type:"end",isClose:true});b.style=b.Subclass({type:"style",checkItem:function(m){if(!m.isClose){return this.SUPER(arguments).checkItem.call(this,m)}var l=h.mstyle.apply(h,this.data).With(this.styles);return[b.mml(l),m]}});b.position=b.Subclass({type:"position",checkItem:function(m){if(m.isClose){d.Error(["MissingBoxFor","Missing box for %1",this.name])}if(m.isNotStack){var l=m.mmlData();switch(this.move){case"vertical":l=h.mpadded(l).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(l)];case"horizontal":return[b.mml(this.left),m,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,m)}});b.array=b.Subclass({type:"array",isOpen:true,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.frame=[];this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(m){if(m.isClose&&m.type!=="over"){if(m.isEntry){this.EndEntry();this.clearEnv();return false}if(m.isCR){this.EndEntry();this.EndRow();this.clearEnv();return false}this.EndTable();this.clearEnv();var l=h.mtable.apply(h,this.table).With(this.arraydef);if(this.frame.length===4){l.frame=(this.frame.dashed?"dashed":"solid")}else{if(this.frame.length){l.hasFrame=true;if(this.arraydef.rowlines){this.arraydef.rowlines=this.arraydef.rowlines.replace(/none( none)+$/,"none")}l=h.menclose(l).With({notation:this.frame.join(" "),isFrame:true});if((this.arraydef.columnlines||"none")!="none"||(this.arraydef.rowlines||"none")!="none"){l.padding=0}}}if(this.open||this.close){l=d.fenced(this.open,l,this.close)}l=b.mml(l);if(this.requireClose){if(m.type==="close"){return l}d.Error(["MissingCloseBrace","Missing close brace"])}return[l,m]}return this.SUPER(arguments).checkItem.call(this,m)},EndEntry:function(){this.row.push(h.mtd.apply(h,this.data));this.data=[]},EndRow:function(){this.table.push(h.mtr.apply(h,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var l=this.arraydef.rowlines.split(/ /);if(l.length===this.table.length){this.frame.push("bottom");l.pop();this.arraydef.rowlines=l.join(" ")}else{if(l.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}if(this.rowspacing){var m=this.arraydef.rowspacing.split(/ /);while(m.length<this.table.length){m.push(this.rowspacing+"em")}this.arraydef.rowspacing=m.join(" ")}},clearEnv:function(){for(var l in this.env){if(this.env.hasOwnProperty(l)){delete this.env[l]}}}});b.cell=b.Subclass({type:"cell",isClose:true});b.mml=b.Subclass({type:"mml",isNotStack:true,Add:function(){this.data.push.apply(this.data,arguments);return this}});b.fn=b.Subclass({type:"fn",checkItem:function(m){if(this.data[0]){if(m.type!=="mml"||!m.data[0]){return[this.data[0],m]}if(m.data[0].isa(h.mspace)){return[this.data[0],m]}var l=m.data[0];if(l.isEmbellished()){l=l.CoreMO()}if([0,0,1,1,0,1,1,0,0,0][l.Get("texClass")]){return[this.data[0],m]}return[this.data[0],h.mo(h.entity("#x2061")).With({texClass:h.TEXCLASS.NONE}),m]}return this.SUPER(arguments).checkItem.apply(this,arguments)}});b.not=b.Subclass({type:"not",checkItem:function(m){var l,n;if(m.type==="open"||m.type==="left"){return true}if(m.type==="mml"&&m.data[0].type.match(/^(mo|mi|mtext)$/)){l=m.data[0],n=l.data.join("");if(n.length===1&&!l.movesupsub){n=b.not.remap[n.charCodeAt(0)];if(n){l.SetData(0,h.chars(String.fromCharCode(n)))}else{l.Append(h.chars("\u0338"))}return m}}l=h.mpadded(h.mtext("\u29F8")).With({width:0});l=h.TeXAtom(l).With({texClass:h.TEXCLASS.REL});return[l,m]}});b.not.remap={8592:8602,8594:8603,8596:8622,8656:8653,8658:8655,8660:8654,8712:8713,8715:8716,8739:8740,8741:8742,8764:8769,126:8769,8771:8772,8773:8775,8776:8777,8781:8813,61:8800,8801:8802,60:8814,62:8815,8804:8816,8805:8817,8818:8820,8819:8821,8822:8824,8823:8825,8826:8832,8827:8833,8834:8836,8835:8837,8838:8840,8839:8841,8866:8876,8872:8877,8873:8878,8875:8879,8828:8928,8829:8929,8849:8930,8850:8931,8882:8938,8883:8939,8884:8940,8885:8941,8707:8708};b.dots=b.Subclass({type:"dots",checkItem:function(m){if(m.type==="open"||m.type==="left"){return true}var n=this.ldots;if(m.type==="mml"&&m.data[0].isEmbellished()){var l=m.data[0].CoreMO().Get("texClass");if(l===h.TEXCLASS.BIN||l===h.TEXCLASS.REL){n=this.cdots}}return[n,m]}});var f={Add:function(l,o,n){if(!o){o=this}for(var m in l){if(l.hasOwnProperty(m)){if(typeof l[m]==="object"&&!(l[m] instanceof Array)&&(typeof o[m]==="object"||typeof o[m]==="function")){this.Add(l[m],o[m],l[m],n)}else{if(!o[m]||!o[m].isUser||!n){o[m]=l[m]}}}}return o}};var k=function(){h=MathJax.ElementJax.mml;c.Insert(f,{letter:/[a-z]/i,digit:/[0-9.]/,number:/^(?:[0-9]+(?:\{,\}[0-9]{3})*(?:\.[0-9]*)*|\.[0-9]+)/,special:{"\\":"ControlSequence","{":"Open","}":"Close","~":"Tilde","^":"Superscript",_:"Subscript"," ":"Space","\t":"Space","\r":"Space","\n":"Space","'":"Prime","%":"Comment","&":"Entry","#":"Hash","\u2019":"Prime"},remap:{"-":"2212","*":"2217","`":"2018"},mathchar0mi:{alpha:"03B1",beta:"03B2",gamma:"03B3",delta:"03B4",epsilon:"03F5",zeta:"03B6",eta:"03B7",theta:"03B8",iota:"03B9",kappa:"03BA",lambda:"03BB",mu:"03BC",nu:"03BD",xi:"03BE",omicron:"03BF",pi:"03C0",rho:"03C1",sigma:"03C3",tau:"03C4",upsilon:"03C5",phi:"03D5",chi:"03C7",psi:"03C8",omega:"03C9",varepsilon:"03B5",vartheta:"03D1",varpi:"03D6",varrho:"03F1",varsigma:"03C2",varphi:"03C6",S:["00A7",{mathvariant:h.VARIANT.NORMAL}],aleph:["2135",{mathvariant:h.VARIANT.NORMAL}],hbar:["210F",{variantForm:true}],imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:h.VARIANT.NORMAL}],Re:["211C",{mathvariant:h.VARIANT.NORMAL}],Im:["2111",{mathvariant:h.VARIANT.NORMAL}],partial:["2202",{mathvariant:h.VARIANT.NORMAL}],infty:["221E",{mathvariant:h.VARIANT.NORMAL}],prime:["2032",{mathvariant:h.VARIANT.NORMAL,variantForm:true}],emptyset:["2205",{mathvariant:h.VARIANT.NORMAL}],nabla:["2207",{mathvariant:h.VARIANT.NORMAL}],top:["22A4",{mathvariant:h.VARIANT.NORMAL}],bot:["22A5",{mathvariant:h.VARIANT.NORMAL}],angle:["2220",{mathvariant:h.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:h.VARIANT.NORMAL}],backslash:["2216",{mathvariant:h.VARIANT.NORMAL,variantForm:true}],forall:["2200",{mathvariant:h.VARIANT.NORMAL}],exists:["2203",{mathvariant:h.VARIANT.NORMAL}],neg:["00AC",{mathvariant:h.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:h.VARIANT.NORMAL}],flat:["266D",{mathvariant:h.VARIANT.NORMAL}],natural:["266E",{mathvariant:h.VARIANT.NORMAL}],sharp:["266F",{mathvariant:h.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:h.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:h.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:h.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:h.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:h.TEXCLASS.OP,movesupsub:true}],bigvee:["22C1",{texClass:h.TEXCLASS.OP,movesupsub:true}],bigwedge:["22C0",{texClass:h.TEXCLASS.OP,movesupsub:true}],biguplus:["2A04",{texClass:h.TEXCLASS.OP,movesupsub:true}],bigcap:["22C2",{texClass:h.TEXCLASS.OP,movesupsub:true}],bigcup:["22C3",{texClass:h.TEXCLASS.OP,movesupsub:true}],"int":["222B",{texClass:h.TEXCLASS.OP}],intop:["222B",{texClass:h.TEXCLASS.OP,movesupsub:true,movablelimits:true}],iint:["222C",{texClass:h.TEXCLASS.OP}],iiint:["222D",{texClass:h.TEXCLASS.OP}],prod:["220F",{texClass:h.TEXCLASS.OP,movesupsub:true}],sum:["2211",{texClass:h.TEXCLASS.OP,movesupsub:true}],bigotimes:["2A02",{texClass:h.TEXCLASS.OP,movesupsub:true}],bigoplus:["2A01",{texClass:h.TEXCLASS.OP,movesupsub:true}],bigodot:["2A00",{texClass:h.TEXCLASS.OP,movesupsub:true}],oint:["222E",{texClass:h.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:h.TEXCLASS.OP,movesupsub:true}],smallint:["222B",{largeop:false}],triangleleft:"25C3",triangleright:"25B9",bigtriangleup:"25B3",bigtriangledown:"25BD",wedge:"2227",land:"2227",vee:"2228",lor:"2228",cap:"2229",cup:"222A",ddagger:"2021",dagger:"2020",sqcap:"2293",sqcup:"2294",uplus:"228E",amalg:"2A3F",diamond:"22C4",bullet:"2219",wr:"2240",div:"00F7",odot:["2299",{largeop:false}],oslash:["2298",{largeop:false}],otimes:["2297",{largeop:false}],ominus:["2296",{largeop:false}],oplus:["2295",{largeop:false}],mp:"2213",pm:"00B1",circ:"2218",bigcirc:"25EF",setminus:["2216",{variantForm:true}],cdot:"22C5",ast:"2217",times:"00D7",star:"22C6",propto:"221D",sqsubseteq:"2291",sqsupseteq:"2292",parallel:"2225",mid:"2223",dashv:"22A3",vdash:"22A2",leq:"2264",le:"2264",geq:"2265",ge:"2265",lt:"003C",gt:"003E",succ:"227B",prec:"227A",approx:"2248",succeq:"2AB0",preceq:"2AAF",supset:"2283",subset:"2282",supseteq:"2287",subseteq:"2286","in":"2208",ni:"220B",notin:"2209",owns:"220B",gg:"226B",ll:"226A",sim:"223C",simeq:"2243",perp:"22A5",equiv:"2261",asymp:"224D",smile:"2323",frown:"2322",ne:"2260",neq:"2260",cong:"2245",doteq:"2250",bowtie:"22C8",models:"22A8",notChar:"29F8",Leftrightarrow:"21D4",Leftarrow:"21D0",Rightarrow:"21D2",leftrightarrow:"2194",leftarrow:"2190",gets:"2190",rightarrow:"2192",to:"2192",mapsto:"21A6",leftharpoonup:"21BC",leftharpoondown:"21BD",rightharpoonup:"21C0",rightharpoondown:"21C1",nearrow:"2197",searrow:"2198",nwarrow:"2196",swarrow:"2199",rightleftharpoons:"21CC",hookrightarrow:"21AA",hookleftarrow:"21A9",longleftarrow:"27F5",Longleftarrow:"27F8",longrightarrow:"27F6",Longrightarrow:"27F9",Longleftrightarrow:"27FA",longleftrightarrow:"27F7",longmapsto:"27FC",ldots:"2026",cdots:"22EF",vdots:"22EE",ddots:"22F1",dotsc:"2026",dotsb:"22EF",dotsm:"22EF",dotsi:"22EF",dotso:"2026",ldotp:["002E",{texClass:h.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:h.TEXCLASS.PUNCT}],colon:["003A",{texClass:h.TEXCLASS.PUNCT}]},mathchar7:{Gamma:"0393",Delta:"0394",Theta:"0398",Lambda:"039B",Xi:"039E",Pi:"03A0",Sigma:"03A3",Upsilon:"03A5",Phi:"03A6",Psi:"03A8",Omega:"03A9",_:"005F","#":"0023","$":"0024","%":"0025","&":"0026",And:"0026"},delimiter:{"(":"(",")":")","[":"[","]":"]","<":"27E8",">":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:h.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:h.TEXCLASS.ORD}],"\\|":["2225",{texClass:h.TEXCLASS.ORD}],"\\vert":["|",{texClass:h.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",h.VARIANT.NORMAL],mit:["SetFont",h.VARIANT.ITALIC],oldstyle:["SetFont",h.VARIANT.OLDSTYLE],cal:["SetFont",h.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",h.VARIANT.BOLD],bbFont:["SetFont",h.VARIANT.DOUBLESTRUCK],scr:["SetFont",h.VARIANT.SCRIPT],frak:["SetFont",h.VARIANT.FRAKTUR],sf:["SetFont",h.VARIANT.SANSSERIF],tt:["SetFont",h.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim&thinsp;inf"],limsup:["NamedOp","lim&thinsp;sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",h.LENGTH.THINMATHSPACE],":":["Spacer",h.LENGTH.MEDIUMMATHSPACE],">":["Spacer",h.LENGTH.MEDIUMMATHSPACE],";":["Spacer",h.LENGTH.THICKMATHSPACE],"!":["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",h.LENGTH.THINMATHSPACE],negthinspace:["Spacer",h.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",h.TEXCLASS.ORD,0.85],Big:["MakeBig",h.TEXCLASS.ORD,1.15],bigg:["MakeBig",h.TEXCLASS.ORD,1.45],Bigg:["MakeBig",h.TEXCLASS.ORD,1.75],bigl:["MakeBig",h.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",h.TEXCLASS.OPEN,1.15],biggl:["MakeBig",h.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",h.TEXCLASS.OPEN,1.75],bigr:["MakeBig",h.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",h.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",h.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",h.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",h.TEXCLASS.REL,0.85],Bigm:["MakeBig",h.TEXCLASS.REL,1.15],biggm:["MakeBig",h.TEXCLASS.REL,1.45],Biggm:["MakeBig",h.TEXCLASS.REL,1.75],mathord:["TeXAtom",h.TEXCLASS.ORD],mathop:["TeXAtom",h.TEXCLASS.OP],mathopen:["TeXAtom",h.TEXCLASS.OPEN],mathclose:["TeXAtom",h.TEXCLASS.CLOSE],mathbin:["TeXAtom",h.TEXCLASS.BIN],mathrel:["TeXAtom",h.TEXCLASS.REL],mathpunct:["TeXAtom",h.TEXCLASS.PUNCT],mathinner:["TeXAtom",h.TEXCLASS.INNER],vcenter:["TeXAtom",h.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","00B4"],grave:["Accent","0060"],ddot:["Accent","00A8"],tilde:["Accent","007E"],bar:["Accent","00AF"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","005E"],vec:["Accent","2192"],dot:["Accent","02D9"],widetilde:["Accent","007E",1],widehat:["Accent","005E",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",h.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",h.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".2em","T"],equation:[null,"Equation"],"equation*":[null,"Equation"],eqnarray:["ExtensionEnv",null,"AMSmath"],"eqnarray*":["ExtensionEnv",null,"AMSmath"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var l=this.config.Macros;for(var m in l){if(l.hasOwnProperty(m)){if(typeof(l[m])==="string"){f.macros[m]=["Macro",l[m]]}else{f.macros[m]=["Macro"].concat(l[m])}f.macros[m].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(m,n){this.string=m;this.i=0;this.macroCount=0;var l;if(n){l={};for(var o in n){if(n.hasOwnProperty(o)){l[o]=n[o]}}}this.stack=d.Stack(l,!!n);this.Parse();this.Push(b.stop())},Parse:function(){var m,l;while(this.i<this.string.length){m=this.string.charAt(this.i++);l=m.charCodeAt(0);if(l>=55296&&l<56320){m+=this.string.charAt(this.i++)}if(f.special[m]){this[f.special[m]](m)}else{if(f.letter.test(m)){this.Variable(m)}else{if(f.digit.test(m)){this.Number(m)}else{this.Other(m)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(l){return l},ControlSequence:function(o){var l=this.GetCS(),n=this.csFindMacro(l);if(n){if(!(n instanceof Array)){n=[n]}var m=n[0];if(!(m instanceof Function)){m=this[m]}m.apply(this,[o+l].concat(n.slice(1)))}else{if(f.mathchar0mi[l]){this.csMathchar0mi(l,f.mathchar0mi[l])}else{if(f.mathchar0mo[l]){this.csMathchar0mo(l,f.mathchar0mo[l])}else{if(f.mathchar7[l]){this.csMathchar7(l,f.mathchar7[l])}else{if(f.delimiter["\\"+l]!=null){this.csDelimiter(l,f.delimiter["\\"+l])}else{this.csUndefined(o+l)}}}}}},csFindMacro:function(l){return f.macros[l]},csMathchar0mi:function(l,n){var m={mathvariant:h.VARIANT.ITALIC};if(n instanceof Array){m=n[1];n=n[0]}this.Push(this.mmlToken(h.mi(h.entity("#x"+n)).With(m)))},csMathchar0mo:function(l,n){var m={stretchy:false};if(n instanceof Array){m=n[1];m.stretchy=false;n=n[0]}this.Push(this.mmlToken(h.mo(h.entity("#x"+n)).With(m)))},csMathchar7:function(l,n){var m={mathvariant:h.VARIANT.NORMAL};if(n instanceof Array){m=n[1];n=n[0]}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.entity("#x"+n)).With(m)))},csDelimiter:function(l,n){var m={};if(n instanceof Array){m=n[1];n=n[0]}if(n.length===4){n=h.entity("#x"+n)}else{n=h.chars(n)}this.Push(this.mmlToken(h.mo(n).With({fence:false,stretchy:false}).With(m)))},csUndefined:function(l){d.Error(["UndefinedControlSequence","Undefined control sequence %1",l])},Variable:function(m){var l={};if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(h.mi(h.chars(m)).With(l)))},Number:function(o){var l,m=this.string.slice(this.i-1).match(f.number);if(m){l=h.mn(m[0].replace(/[{}]/g,""));this.i+=m[0].length-1}else{l=h.mo(h.chars(o))}if(this.stack.env.font){l.mathvariant=this.stack.env.font}this.Push(this.mmlToken(l))},Open:function(l){this.Push(b.open())},Close:function(l){this.Push(b.close())},Tilde:function(l){this.Push(h.mtext(h.chars(g)))},Space:function(l){},Superscript:function(p){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var l,o,m,n=this.stack.Top();if(n.type==="prime"){m=n.data[0];o=n.data[1];this.stack.Pop()}else{m=this.stack.Prev();if(!m){m=h.mi("")}}if(m.isEmbellishedWrapper){m=m.data[0].data[0]}if(m.type==="msubsup"){if(m.data[m.sup]){d.Error(["DoubleExponent","Double exponent: use braces to clarify"])}l=m.sup}else{if(m.movesupsub){if(m.type!=="munderover"||m.data[m.over]){if(m.movablelimits&&m.isa(h.mi)){m=this.mi2mo(m)}m=h.munderover(m,null,null).With({movesupsub:true})}l=m.over}else{m=h.msubsup(m,null,null);l=m.sup}}this.Push(b.subsup(m).With({position:l,primes:o}))},Subscript:function(p){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var l,o,m,n=this.stack.Top();if(n.type==="prime"){m=n.data[0];o=n.data[1];this.stack.Pop()}else{m=this.stack.Prev();if(!m){m=h.mi("")}}if(m.isEmbellishedWrapper){m=m.data[0].data[0]}if(m.type==="msubsup"){if(m.data[m.sub]){d.Error(["DoubleSubscripts","Double subscripts: use braces to clarify"])}l=m.sub}else{if(m.movesupsub){if(m.type!=="munderover"||m.data[m.under]){if(m.movablelimits&&m.isa(h.mi)){m=this.mi2mo(m)}m=h.munderover(m,null,null).With({movesupsub:true})}l=m.under}else{m=h.msubsup(m,null,null);l=m.sub}}this.Push(b.subsup(m).With({position:l,primes:o}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(n){var m=this.stack.Prev();if(!m){m=h.mi()}if(m.type==="msubsup"&&m.data[m.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var l="";this.i--;do{l+=this.PRIME;this.i++,n=this.GetNext()}while(n==="'"||n===this.SMARTQUOTE);l=["","\u2032","\u2033","\u2034","\u2057"][l.length]||l;this.Push(b.prime(m,this.mmlToken(h.mo(l))))},mi2mo:function(l){var m=h.mo();m.Append.apply(m,l.data);var n;for(n in m.defaults){if(m.defaults.hasOwnProperty(n)&&l[n]!=null){m[n]=l[n]}}for(n in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(n)&&l[n]!=null){m[n]=l[n]}}return m},Comment:function(l){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(l){d.Error(["CantUseHash1","You can't use 'macro parameter character #' in math mode"])},Other:function(n){var m={stretchy:false},l;if(this.stack.env.font){m.mathvariant=this.stack.env.font}if(f.remap[n]){n=f.remap[n];if(n instanceof Array){m=n[1];n=n[0]}l=h.mo(h.entity("#x"+n)).With(m)}else{l=h.mo(n).With(m)}if(l.autoDefault("texClass",true)==""){l=h.TeXAtom(l)}this.Push(this.mmlToken(l))},SetFont:function(m,l){this.stack.env.font=l},SetStyle:function(m,l,n,o){this.stack.env.style=l;this.stack.env.level=o;this.Push(b.style().With({styles:{displaystyle:n,scriptlevel:o}}))},SetSize:function(l,m){this.stack.env.size=m;this.Push(b.style().With({styles:{mathsize:m+"em"}}))},Color:function(n){var m=this.GetArgument(n);var l=this.stack.env.color;this.stack.env.color=m;var o=this.ParseArg(n);if(l){this.stack.env.color}else{delete this.stack.env.color}this.Push(h.mstyle(o).With({mathcolor:m}))},Spacer:function(l,m){this.Push(h.mspace().With({width:m,mathsize:h.SIZE.NORMAL,scriptlevel:0}))},LeftRight:function(l){this.Push(b[l.substr(1)]().With({delim:this.GetDelimiter(l)}))},Middle:function(l){var m=this.GetDelimiter(l);if(this.stack.Top().type!=="left"){d.Error(["MisplacedMiddle","%1 must be within \\left and \\right",l])}this.Push(h.mo(m).With({stretchy:true}))},NamedFn:function(m,n){if(!n){n=m.substr(1)}var l=h.mi(n).With({texClass:h.TEXCLASS.OP});this.Push(b.fn(this.mmlToken(l)))},NamedOp:function(m,n){if(!n){n=m.substr(1)}n=n.replace(/&thinsp;/,"\u2006");var l=h.mo(n).With({movablelimits:true,movesupsub:true,form:h.FORM.PREFIX,texClass:h.TEXCLASS.OP});l.useMMLspacing&=~l.SPACE_ATTR.form;this.Push(this.mmlToken(l))},Limits:function(m,l){var n=this.stack.Prev("nopop");if(!n||n.texClass!==h.TEXCLASS.OP){d.Error(["MisplacedLimits","%1 is allowed only on operators",m])}n.movesupsub=(l?true:false);n.movablelimits=false},Over:function(n,m,o){var l=b.over().With({name:n});if(m||o){l.open=m;l.close=o}else{if(n.match(/withdelims$/)){l.open=this.GetDelimiter(n);l.close=this.GetDelimiter(n)}}if(n.match(/^\\above/)){l.thickness=this.GetDimen(n)}else{if(n.match(/^\\atop/)||m||o){l.thickness=0}}this.Push(l)},Frac:function(m){var l=this.ParseArg(m);var n=this.ParseArg(m);this.Push(h.mfrac(l,n))},Sqrt:function(o){var p=this.GetBrackets(o),l=this.GetArgument(o);if(l==="\\frac"){l+="{"+this.GetArgument(l)+"}{"+this.GetArgument(l)+"}"}var m=d.Parse(l,this.stack.env).mml();if(!p){m=h.msqrt.apply(h,m.array())}else{m=h.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(m){var o=this.GetUpTo(m,"\\of");var l=this.ParseArg(m);this.Push(h.mroot(l,this.parseRoot(o)))},parseRoot:function(q){var m=this.stack.env,l=m.inRoot;m.inRoot=true;var p=d.Parse(q,m);q=p.mml();var o=p.stack.global;if(o.leftRoot||o.upRoot){q=h.mpadded(q);if(o.leftRoot){q.width=o.leftRoot}if(o.upRoot){q.voffset=o.upRoot;q.height=o.upRoot}}m.inRoot=l;return q},MoveRoot:function(l,o){if(!this.stack.env.inRoot){d.Error(["MisplacedMoveRoot","%1 can appear only within a root",l])}if(this.stack.global[o]){d.Error(["MultipleMoveRoot","Multiple use of %1",l])}var m=this.GetArgument(l);if(!m.match(/-?[0-9]+/)){d.Error(["IntegerArg","The argument to %1 must be an integer",l])}m=(m/15)+"em";if(m.substr(0,1)!=="-"){m="+"+m}this.stack.global[o]=m},Accent:function(n,l,q){var p=this.ParseArg(n);var o={accent:true};if(this.stack.env.font){o.mathvariant=this.stack.env.font}var m=this.mmlToken(h.mo(h.entity("#x"+l)).With(o));m.stretchy=(q?true:false);this.Push(h.TeXAtom(h.munderover(p,null,m).With({accent:true})))},UnderOver:function(n,q,l){var p={o:"over",u:"under"}[n.charAt(1)];var o=this.ParseArg(n);if(o.Get("movablelimits")){o.movablelimits=false}var m=h.munderover(o,null,null);if(l){m.movesupsub=true}m.data[m[p]]=this.mmlToken(h.mo(h.entity("#x"+q)).With({stretchy:true,accent:(p=="under")}));this.Push(m)},Overset:function(l){var n=this.ParseArg(l),m=this.ParseArg(l);this.Push(h.mover(m,n))},Underset:function(l){var n=this.ParseArg(l),m=this.ParseArg(l);this.Push(h.munder(m,n))},TeXAtom:function(o,q){var p={texClass:q},n;if(q==h.TEXCLASS.OP){p.movesupsub=p.movablelimits=true;var l=this.GetArgument(o);var m=l.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(m){p.mathvariant=h.VARIANT.NORMAL;n=b.fn(this.mmlToken(h.mi(m[1]).With(p)))}else{n=b.fn(h.TeXAtom(d.Parse(l,this.stack.env).mml()).With(p))}}else{n=h.TeXAtom(this.ParseArg(o)).With(p)}this.Push(n)},MmlToken:function(n){var o=this.GetArgument(n),l=this.GetBrackets(n,"").replace(/^\s+/,""),r=this.GetArgument(n),q={attrNames:[]},m;if(!h[o]||!h[o].prototype.isToken){d.Error(["NotMathMLToken","%1 is not a token element",o])}while(l!==""){m=l.match(/^([a-z]+)\s*=\s*(\'[^']*'|"[^"]*"|[^ ]*)\s*/i);if(!m){d.Error(["InvalidMathMLAttr","Invalid MathML attribute: %1",l])}if(!h[o].prototype.defaults[m[1]]&&!this.MmlTokenAllow[m[1]]){d.Error(["UnknownAttrForElement","%1 is not a recognized attribute for %2",m[1],o])}var p=this.MmlFilterAttribute(m[1],m[2].replace(/^(['"])(.*)\1$/,"$2"));if(p){if(p.toLowerCase()==="true"){p=true}else{if(p.toLowerCase()==="false"){p=false}}q[m[1]]=p;q.attrNames.push(m[1])}l=l.substr(m[0].length)}this.Push(this.mmlToken(h[o](r).With(q)))},MmlFilterAttribute:function(l,m){return m},MmlTokenAllow:{fontfamily:1,fontsize:1,fontweight:1,fontstyle:1,color:1,background:1,id:1,"class":1,href:1,style:1},Strut:function(l){this.Push(h.mpadded(h.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(m,l,n){var o=h.mphantom(this.ParseArg(m));if(l||n){o=h.mpadded(o);if(n){o.height=o.depth=0}if(l){o.width=0}}this.Push(h.TeXAtom(o))},Smash:function(n){var m=this.trimSpaces(this.GetBrackets(n,""));var l=h.mpadded(this.ParseArg(n));switch(m){case"b":l.depth=0;break;case"t":l.height=0;break;default:l.height=l.depth=0}this.Push(h.TeXAtom(l))},Lap:function(m){var l=h.mpadded(this.ParseArg(m)).With({width:0});if(m==="\\llap"){l.lspace="-1 width"}this.Push(h.TeXAtom(l))},RaiseLower:function(l){var m=this.GetDimen(l);var n=b.position().With({name:l,move:"vertical"});if(m.charAt(0)==="-"){m=m.slice(1);l={raise:"\\lower",lower:"\\raise"}[l.substr(1)]}if(l==="\\lower"){n.dh="-"+m;n.dd="+"+m}else{n.dh="+"+m;n.dd="-"+m}this.Push(n)},MoveLeftRight:function(l){var o=this.GetDimen(l);var n=(o.charAt(0)==="-"?o.slice(1):"-"+o);if(l==="\\moveleft"){var m=o;o=n;n=m}this.Push(b.position().With({name:l,move:"horizontal",left:h.mspace().With({width:o,mathsize:h.SIZE.NORMAL}),right:h.mspace().With({width:n,mathsize:h.SIZE.NORMAL})}))},Hskip:function(l){this.Push(h.mspace().With({width:this.GetDimen(l),mathsize:h.SIZE.NORMAL}))},Rule:function(n,p){var l=this.GetDimen(n),o=this.GetDimen(n),r=this.GetDimen(n);var m,q={width:l,height:o,depth:r};if(p!=="blank"){if(parseFloat(l)&&parseFloat(o)+parseFloat(r)){q.mathbackground=(this.stack.env.color||"black")}m=h.mpadded(h.mrow()).With(q)}else{m=h.mspace().With(q)}this.Push(m)},MakeBig:function(l,o,m){m*=f.p_height;m=String(m).replace(/(\.\d\d\d).+/,"$1")+"em";var n=this.GetDelimiter(l);this.Push(h.TeXAtom(h.mo(n).With({minsize:m,maxsize:m,fence:true,stretchy:true,symmetric:true})).With({texClass:o}))},BuildRel:function(l){var m=this.ParseUpTo(l,"\\over");var n=this.ParseArg(l);this.Push(h.TeXAtom(h.munderover(n,null,m)).With({mclass:h.TEXCLASS.REL}))},HBox:function(l,m){this.Push.apply(this,this.InternalMath(this.GetArgument(l),m))},FBox:function(l){this.Push(h.menclose.apply(h,this.InternalMath(this.GetArgument(l))).With({notation:"box"}))},Not:function(l){this.Push(b.not())},Dots:function(l){this.Push(b.dots().With({ldots:this.mmlToken(h.mo(h.entity("#x2026")).With({stretchy:false})),cdots:this.mmlToken(h.mo(h.entity("#x22EF")).With({stretchy:false}))}))},Require:function(l){var m=this.GetArgument(l).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");this.Extension(null,m)},Extension:function(l,m,n){if(l&&!typeof(l)==="string"){l=l.name}m=d.extensionDir+"/"+m;if(!m.match(/\.js$/)){m+=".js"}if(!i.loaded[i.fileURL(m)]){if(l!=null){delete f[n||"macros"][l.replace(/^\\/,"")]}c.RestartAfter(i.Require(m))}},Macro:function(n,q,p,r){if(p){var m=[];if(r!=null){var l=this.GetBrackets(n);m.push(l==null?r:l)}for(var o=m.length;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(m,o,t,q,s,n,l,u){var r=this.GetNext();if(r===""){d.Error(["MissingArgFor","Missing argument for %1",m])}if(r==="{"){this.i++}else{this.string=r+"}"+this.string.slice(this.i+1);this.i=0}var p=b.array().With({requireClose:true,arraydef:{rowspacing:(n||"4pt"),columnspacing:(s||"1em")}});if(u){p.isCases=true}if(o||t){p.open=o;p.close=t}if(l==="D"){p.arraydef.displaystyle=true}if(q!=null){p.arraydef.columnalign=q}this.Push(p)},Entry:function(o){this.Push(b.cell().With({isEntry:true,name:o}));if(this.stack.Top().isCases){var n=this.string;var r=0,p=this.i,l=n.length;while(p<l){var s=n.charAt(p);if(s==="{"){r++;p++}else{if(s==="}"){if(r===0){l=0}else{r--;p++}}else{if(s==="&"&&r===0){d.Error(["ExtraAlignTab","Extra alignment tab in \\cases text"])}else{if(s==="\\"){if(n.substr(p).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){l=0}else{p+=2}}else{p++}}}}}var q=n.substr(this.i,p-this.i);if(!q.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(q));this.i=p}}},Cr:function(l){this.Push(b.cell().With({isCR:true,name:l}))},CrLaTeX:function(l){var p;if(this.string.charAt(this.i)==="["){p=this.GetBrackets(l,"").replace(/ /g,"");if(p&&!p.match(/^((-?(\.\d+|\d+(\.\d*)?))(pt|em|ex|mu|mm|cm|in|pc))$/)){d.Error(["BracketMustBeDimension","Bracket argument to %1 must be a dimension",l])}}this.Push(b.cell().With({isCR:true,name:l,linebreak:true}));var o=this.stack.Top();if(o.isa(b.array)){if(p&&o.arraydef.rowspacing){var m=o.arraydef.rowspacing.split(/ /);if(!o.rowspacing){o.rowspacing=this.dimen2em(m[0])}while(m.length<o.table.length){m.push(this.Em(o.rowspacing))}m[o.table.length-1]=this.Em(Math.max(0,o.rowspacing+this.dimen2em(p)));o.arraydef.rowspacing=m.join(" ")}}else{if(p){this.Push(h.mspace().With({depth:p}))}this.Push(h.mo().With({linebreak:h.LINEBREAK.NEWLINE}))}},emPerInch:7.2,dimen2em:function(p){var n=p.match(/^(-?(?:\.\d+|\d+(?:\.\d*)?))(pt|em|ex|mu|pc|in|mm|cm)/);var l=parseFloat(n[1]||"1"),o=n[2];if(o==="em"){return l}if(o==="ex"){return l*0.43}if(o==="pt"){return l/10}if(o==="pc"){return l*1.2}if(o==="in"){return l*this.emPerInch}if(o==="cm"){return l*this.emPerInch/2.54}if(o==="mm"){return l*this.emPerInch/25.4}if(o==="mu"){return l/18}return 0},Em:function(l){if(Math.abs(l)<0.0006){return"0em"}return l.toFixed(3).replace(/\.?0+$/,"")+"em"},HLine:function(m,n){if(n==null){n="solid"}var o=this.stack.Top();if(!o.isa(b.array)||o.data.length){d.Error(["Misplaced","Misplaced %1",m])}if(o.table.length==0){o.frame.push("top")}else{var l=(o.arraydef.rowlines?o.arraydef.rowlines.split(/ /):[]);while(l.length<o.table.length){l.push("none")}l[o.table.length-1]=n;o.arraydef.rowlines=l.join(" ")}},Begin:function(m){var n=this.GetArgument(m);if(n.match(/[^a-z*]/i)){d.Error(["InvalidEnv","Invalid environment name '%1'",n])}var o=this.envFindName(n);if(!o){d.Error(["UnknownEnv","Unknown environment '%1'",n])}if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(!(o instanceof Array)){o=[o]}var l=b.begin().With({name:n,end:o[1],parse:this});if(o[0]&&this[o[0]]){l=this[o[0]].apply(this,[l].concat(o.slice(2)))}this.Push(l)},End:function(l){this.Push(b.end().With({name:this.GetArgument(l)}))},envFindName:function(l){return f.environment[l]},Equation:function(l,m){return m},ExtensionEnv:function(m,l){this.Extension(m.name,l,"environment")},Array:function(m,o,t,r,s,n,l,p){if(!r){r=this.GetArgument("\\begin{"+m.name+"}")}var u=("c"+r).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");r=r.replace(/[^clr]/g,"").split("").join(" ");r=r.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var q=b.array().With({arraydef:{columnalign:r,columnspacing:(s||"1em"),rowspacing:(n||"4pt")}});if(u.match(/[|:]/)){if(u.charAt(0).match(/[|:]/)){q.frame.push("left");q.frame.dashed=u.charAt(0)===":"}if(u.charAt(u.length-1).match(/[|:]/)){q.frame.push("right")}u=u.substr(1,u.length-2);q.arraydef.columnlines=u.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(o){q.open=this.convertDelimiter(o)}if(t){q.close=this.convertDelimiter(t)}if(l==="D"){q.arraydef.displaystyle=true}else{if(l){q.arraydef.displaystyle=false}}if(l==="S"){q.arraydef.scriptlevel=1}if(p){q.arraydef.useHeight=false}this.Push(m);return q},AlignedArray:function(l){var m=this.GetBrackets("\\begin{"+l.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),m)},setArrayAlign:function(m,l){l=this.trimSpaces(l||"");if(l==="t"){m.arraydef.align="baseline 1"}else{if(l==="b"){m.arraydef.align="baseline -1"}else{if(l==="c"){m.arraydef.align="center"}else{if(l){m.arraydef.align=l}}}}return m},convertDelimiter:function(l){if(l){l=f.delimiter[l]}if(l==null){return null}if(l instanceof Array){l=l[0]}if(l.length===4){l=String.fromCharCode(parseInt(l,16))}return l},trimSpaces:function(l){if(typeof(l)!="string"){return l}return l.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var l=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(l){this.i+=l[1].length;return l[1]}else{this.i++;return" "}},GetArgument:function(m,n){switch(this.GetNext()){case"":if(!n){d.Error(["MissingArgFor","Missing argument for %1",m])}return null;case"}":if(!n){d.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"])}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var l=++this.i,o=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":o++;break;case"}":if(--o==0){return this.string.slice(l,this.i-1)}break}}d.Error(["MissingCloseBrace","Missing close brace"]);break}return this.string.charAt(this.i++)},GetBrackets:function(m,o){if(this.GetNext()!="["){return o}var l=++this.i,n=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":n++;break;case"\\":this.i++;break;case"}":if(n--<=0){d.Error(["ExtraCloseLooking","Extra close brace while looking for %1","']'"])}break;case"]":if(n==0){return this.string.slice(l,this.i-1)}break}}d.Error(["MissingCloseBracket","Couldn't find closing ']' for argument to %1",m])},GetDelimiter:function(l){while(this.nextIsSpace()){this.i++}var m=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(m=="\\"){m+=this.GetCS(l)}if(f.delimiter[m]!=null){return this.convertDelimiter(m)}}d.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",l])},GetDimen:function(m){var n;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){n=this.GetArgument(m);if(n.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return n.replace(/ /g,"")}}else{n=this.string.slice(this.i);var l=n.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(l){this.i+=l[0].length;return l[1].replace(/ /g,"")}}d.Error(["MissingDimOrUnits","Missing dimension or its units for %1",m])},GetUpTo:function(n,o){while(this.nextIsSpace()){this.i++}var m=this.i,l,q,p=0;while(this.i<this.string.length){l=this.i;q=this.string.charAt(this.i++);switch(q){case"\\":q+=this.GetCS();break;case"{":p++;break;case"}":if(p==0){d.Error(["ExtraCloseLooking","Extra close brace while looking for %1",o])}p--;break}if(p==0&&q==o){return this.string.slice(m,l)}}d.Error(["TokenNotFoundForCommand","Couldn't find %1 for %2",o,n])},ParseArg:function(l){return d.Parse(this.GetArgument(l),this.stack.env).mml()},ParseUpTo:function(l,m){return d.Parse(this.GetUpTo(l,m),this.stack.env).mml()},InternalMath:function(q,s){var p={displaystyle:false};if(s!=null){p.scriptlevel=s}if(this.stack.env.font){p.mathvariant=this.stack.env.font}if(!q.match(/\\?\$|\\\(|\\(eq)?ref\s*\{/)){return[this.InternalText(q,p)]}var o=0,l=0,r,n="";var m=[];while(o<q.length){r=q.charAt(o++);if(r==="$"){if(n==="$"){m.push(h.TeXAtom(d.Parse(q.slice(l,o-1),{}).mml().With(p)));n="";l=o}else{if(n===""){if(l<o-1){m.push(this.InternalText(q.slice(l,o-1),p))}n="$";l=o}}}else{if(r==="}"&&n==="}"){m.push(h.TeXAtom(d.Parse(q.slice(l,o),{}).mml().With(p)));n="";l=o}else{if(r==="\\"){if(n===""&&q.substr(o).match(/^(eq)?ref\s*\{/)){if(l<o-1){m.push(this.InternalText(q.slice(l,o-1),p))}n="}";l=o-1}else{r=q.charAt(o++);if(r==="("&&n===""){if(l<o-2){m.push(this.InternalText(q.slice(l,o-2),p))}n=")";l=o}else{if(r===")"&&n===")"){m.push(h.TeXAtom(d.Parse(q.slice(l,o-2),{}).mml().With(p)));n="";l=o}else{if(r==="$"&&n===""){o--;q=q.substr(0,o-1)+q.substr(o)}}}}}}}}if(n!==""){d.Error(["MathNotTerminated","Math not terminated in text box"])}if(l<q.length){m.push(this.InternalText(q.slice(l),p))}return m},InternalText:function(m,l){m=m.replace(/^\s+/,g).replace(/\s+$/,g);return h.mtext(h.chars(m)).With(l)},SubstituteArgs:function(m,l){var p="";var o="";var q;var n=0;while(n<l.length){q=l.charAt(n++);if(q==="\\"){p+=q+l.charAt(n++)}else{if(q==="#"){q=l.charAt(n++);if(q==="#"){p+=q}else{if(!q.match(/[1-9]/)||q>m.length){d.Error(["IllegalMacroParam","Illegal macro parameter reference"])}o=this.AddArgs(this.AddArgs(o,p),m[q-1]);p=""}}else{p+=q}}}return this.AddArgs(o,p)},AddArgs:function(m,l){if(l.match(/^[a-z]/i)&&m.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){m+=" "}if(m.length+l.length>d.config.MAXBUFFER){d.Error(["MaxBufferSize","MathJax internal buffer size exceeded; is there a recursive macro call?"])}return m+l}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:k,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:["TeXCommands","TeX Commands"],prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(l){var m,n=false,p=MathJax.HTML.getScript(l);var r=(l.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var q={math:p,display:r,script:l};this.prefilterHooks.Execute(q);p=q.math;try{m=d.Parse(p).mml()}catch(o){if(!o.texError){throw o}m=this.formatError(o,p,r,l);n=true}if(m.inferred){m=h.apply(MathJax.ElementJax,m.data)}else{m=h(m)}if(r){m.root.display="block"}if(n){m.texError=true}q.math=m;this.postfilterHooks.Execute(q);return q.math},prefilterMath:function(m,n,l){return m},postfilterMath:function(m,n,l){this.combineRelations(m.root);return m},formatError:function(o,n,p,l){var m=o.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",m,n,p,l]);return h.Error(m)},Error:function(l){if(l instanceof Array){l=j.apply(j,l)}throw c.Insert(Error(l),{texError:true})},Macro:function(l,m,n){f.macros[l]=["Macro"].concat([].slice.call(arguments,1));f.macros[l].isUser=true},fenced:function(n,m,o){var l=h.mrow();l.open=n;l.close=o;if(n){l.Append(h.mo(n).With({fence:true,stretchy:true,texClass:h.TEXCLASS.OPEN}))}if(m.type==="mrow"){l.Append.apply(l,m.data)}else{l.Append(m)}if(o){l.Append(h.mo(o).With({fence:true,stretchy:true,texClass:h.TEXCLASS.CLOSE}))}return l},combineRelations:function(p){var q,l,o,n;for(q=0,l=p.data.length;q<l;q++){if(p.data[q]){if(p.isa(h.mrow)){while(q+1<l&&(o=p.data[q])&&(n=p.data[q+1])&&o.isa(h.mo)&&n.isa(h.mo)&&o.Get("texClass")===h.TEXCLASS.REL&&n.Get("texClass")===h.TEXCLASS.REL){if(o.variantForm==n.variantForm&&o.Get("mathvariant")==n.Get("mathvariant")&&o.style==n.style&&o["class"]==n["class"]&&!o.id&&!n.id){o.Append.apply(o,n.data);p.data.splice(q+1,1);l--}else{o.rspace=n.lspace="0pt";q++}}}if(!p.data[q].isToken){this.combineRelations(p.data[q])}}}}});d.prefilterHooks.Add(function(l){l.math=d.prefilterMath(l.math,l.display,l.script)});d.postfilterHooks.Add(function(l){l.math=d.postfilterMath(l.math,l.display,l.script)});d.loadComplete("jax.js")})(MathJax.InputJax.TeX,MathJax.Hub,MathJax.Ajax);
MathJax.Extension["TeX/AMSmath"]={version:"2.3",number:0,startNumber:0,labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,g=MathJax.InputJax.TeX,f=MathJax.Extension["TeX/AMSmath"];var d=g.Definitions,e=g.Stack.Item,a=g.config.equationNumbers;var c=function(j){var l=[];for(var k=0,h=j.length;k<h;k++){l[k]=g.Parse.prototype.Em(j[k])}return l.join(" ")};d.Add({mathchar0mo:{iiiint:["2A0C",{texClass:b.TEXCLASS.OP}]},macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",b.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",b.LENGTH.NEGATIVETHICKMATHSPACE],idotsint:["MultiIntegral","\\int\\cdots\\int"],dddot:["Accent","20DB"],ddddot:["Accent","20DC"],sideset:["Macro","\\mathop{\\mathop{\\rlap{\\phantom{#3}}}\\nolimits#1\\!\\mathop{#3}\\nolimits#2}",3],boxed:["Macro","\\fbox{$\\displaystyle{#1}$}",1],tag:"HandleTag",notag:"HandleNoTag",label:"HandleLabel",ref:"HandleRef",eqref:["HandleRef",true],substack:["Macro","\\begin{subarray}{c}#1\\end{subarray}",1],injlim:["NamedOp","inj&thinsp;lim"],projlim:["NamedOp","proj&thinsp;lim"],varliminf:["Macro","\\mathop{\\underline{\\mmlToken{mi}{lim}}}"],varlimsup:["Macro","\\mathop{\\overline{\\mmlToken{mi}{lim}}}"],varinjlim:["Macro","\\mathop{\\underrightarrow{\\mmlToken{mi}{lim}\\Rule{-1pt}{0pt}{1pt}}\\Rule{0pt}{0pt}{.45em}}"],varprojlim:["Macro","\\mathop{\\underleftarrow{\\mmlToken{mi}{lim}\\Rule{-1pt}{0pt}{1pt}}\\Rule{0pt}{0pt}{.45em}}"],DeclareMathOperator:"HandleDeclareOp",operatorname:"HandleOperatorName",genfrac:"Genfrac",frac:["Genfrac","","","",""],tfrac:["Genfrac","","","",1],dfrac:["Genfrac","","","",0],binom:["Genfrac","(",")","0em",""],tbinom:["Genfrac","(",")","0em",1],dbinom:["Genfrac","(",")","0em",0],cfrac:"CFrac",shoveleft:["HandleShove",b.ALIGN.LEFT],shoveright:["HandleShove",b.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",c([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",c([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],multline:["Multline",null,true],"multline*":["Multline",null,false],split:["AMSarray",null,false,false,"rl",c([5/18])],gather:["AMSarray",null,true,true,"c"],"gather*":["AMSarray",null,false,true,"c"],alignat:["AlignAt",null,true,true],"alignat*":["AlignAt",null,false,true],alignedat:["AlignAt",null,false,false],aligned:["AlignedArray",null,null,null,"rlrlrlrlrlrl",c([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18]),".5em","D"],gathered:["AlignedArray",null,null,null,"c",null,".5em","D"],subarray:["Array",null,null,null,null,c([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",c([1/3]),".2em","S",1],equation:["EquationBegin","Equation",true],"equation*":["EquationBegin","EquationStar",false],eqnarray:["AMSarray",null,true,true,"rcl",b.LENGTH.THICKMATHSPACE,".5em"],"eqnarray*":["AMSarray",null,false,true,"rcl",b.LENGTH.THICKMATHSPACE,".5em"]},delimiter:{"\\lvert":["2223",{texClass:b.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:b.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:b.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:b.TEXCLASS.CLOSE}]}},null,true);g.Parse.Augment({HandleTag:function(j){var l=this.GetStar();var i=this.trimSpaces(this.GetArgument(j)),h=i;if(!l){i=a.formatTag(i)}var k=this.stack.global;k.tagID=h;if(k.notags){g.Error(["CommandNotAllowedInEnv","%1 not allowed in %2 environment",j,k.notags])}if(k.tag){g.Error(["MultipleCommand","Multiple %1",j])}k.tag=b.mtd.apply(b,this.InternalMath(i)).With({id:a.formatID(h)})},HandleNoTag:function(h){if(this.stack.global.tag){delete this.stack.global.tag}this.stack.global.notag=true},HandleLabel:function(i){var j=this.stack.global,h=this.GetArgument(i);if(h===""){return}if(!f.refUpdate){if(j.label){g.Error(["MultipleCommand","Multiple %1",i])}j.label=h;if(f.labels[h]||f.eqlabels[h]){g.Error(["MultipleLabel","Label '%1' multiply defined",h])}f.eqlabels[h]="???"}},HandleRef:function(j,l){var i=this.GetArgument(j);var k=f.labels[i]||f.eqlabels[i];if(!k){k="??";f.badref=!f.refUpdate}var h=k;if(l){h=a.formatTag(h)}if(a.useLabelIds){k=i}this.Push(b.mrow.apply(b,this.InternalMath(h)).With({href:a.formatURL(a.formatID(k)),"class":"MathJax_ref"}))},HandleDeclareOp:function(i){var h=(this.GetStar()?"\\limits":"");var j=this.trimSpaces(this.GetArgument(i));if(j.charAt(0)=="\\"){j=j.substr(1)}var k=this.GetArgument(i);k=k.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");g.Definitions.macros[j]=["Macro","\\mathop{\\rm "+k+"}"+h]},HandleOperatorName:function(i){var h=(this.GetStar()?"\\limits":"\\nolimits");var j=this.trimSpaces(this.GetArgument(i));j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+j+"}"+h+" "+this.string.slice(this.i);this.i=0},HandleShove:function(i,h){var j=this.stack.Top();if(j.type!=="multline"||j.data.length){g.Error(["CommandAtTheBeginingOfLine","%1 must come at the beginning of the line",i])}j.data.shove=h},CFrac:function(k){var h=this.trimSpaces(this.GetBrackets(k,"")),j=this.GetArgument(k),l=this.GetArgument(k);var i=b.mfrac(g.Parse("\\strut\\textstyle{"+j+"}",this.stack.env).mml(),g.Parse("\\strut\\textstyle{"+l+"}",this.stack.env).mml());h=({l:b.ALIGN.LEFT,r:b.ALIGN.RIGHT,"":""})[h];if(h==null){g.Error(["IllegalAlign","Illegal alignment specified in %1",k])}if(h){i.numalign=i.denomalign=h}this.Push(i)},Genfrac:function(i,k,p,m,h){if(k==null){k=this.GetDelimiterArg(i)}else{k=this.convertDelimiter(k)}if(p==null){p=this.GetDelimiterArg(i)}else{p=this.convertDelimiter(p)}if(m==null){m=this.GetArgument(i)}if(h==null){h=this.trimSpaces(this.GetArgument(i))}var l=this.ParseArg(i);var o=this.ParseArg(i);var j=b.mfrac(l,o);if(m!==""){j.linethickness=m}if(k||p){j=g.fenced(k,j,p)}if(h!==""){var n=(["D","T","S","SS"])[h];if(n==null){g.Error(["BadMathStyleFor","Bad math style for %1",i])}j=b.mstyle(j);if(n==="D"){j.displaystyle=true;j.scriptlevel=0}else{j.displaystyle=false;j.scriptlevel=h-1}}this.Push(j)},Multline:function(i,h){this.Push(i);this.checkEqnEnv();return e.multline(h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",width:g.config.MultLineWidth,columnwidth:"100%",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AMSarray:function(j,i,h,l,k){this.Push(j);if(h){this.checkEqnEnv()}l=l.replace(/[^clr]/g,"").split("").join(" ");l=l.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return e.AMSarray(j.name,i,h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:l,columnspacing:(k||"1em"),rowspacing:"3pt",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AlignAt:function(k,i,h){var p,j,o="",m=[];if(!h){j=this.GetBrackets("\\begin{"+k.name+"}")}p=this.GetArgument("\\begin{"+k.name+"}");if(p.match(/[^0-9]/)){g.Error(["PositiveIntegerArg","Argument to %1 must me a positive integer","\\begin{"+k.name+"}"])}while(p>0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error(["ErroneousNestingEq","Erroneous nesting of equation structures"])}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i)},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]==null){g.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",h])}return this.convertDelimiter(i)},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h.With({id:a.formatID(i.tagID)}))}},getTag:function(){var i=this.global,h=i.tag;i.tagged=true;if(i.label){f.eqlabels[i.label]=i.tagID;if(a.useLabelIds){h.id=a.formatID(i.label)}}delete i.tag;delete i.tagID;delete i.label;return h}});e.multline=e.array.Subclass({type:"multline",Init:function(i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(i&&a.autoNumber!=="none");this.save={notag:h.global.notag};h.global.tagged=!i&&!h.global.forcetag},EndEntry:function(){var h=b.mtd.apply(b,this.data);if(this.data.shove){h.columnalign=this.data.shove}this.row.push(h);this.data=[]},EndRow:function(){if(this.row.length!=1){g.Error(["MultlineRowsOneCol","The rows within the %1 environment must have exactly one column","multline"])}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var j=this.table.length-1,l,k=-1;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=b.ALIGN.LEFT}if(!this.table[j][0].columnalign){this.table[j][0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){k=(this.arraydef.side==="left"?0:this.table.length-1);this.table[k]=[this.getTag()].concat(this.table[k])}for(l=0,j=this.table.length;l<j;l++){var h=(l===k?b.mlabeledtr:b.mtr);this.table[l]=h.apply(b,this.table[l])}}this.global.notag=this.save.notag}});e.AMSarray=e.array.Subclass({type:"AMSarray",Init:function(k,j,i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(j&&a.autoNumber!=="none");this.save={notags:h.global.notags,notag:h.global.notag};h.global.notags=(i?null:k);h.global.tagged=!j&&!h.global.forcetag},EndRow:function(){var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.row=[this.getTag()].concat(this.row);h=b.mlabeledtr}if(this.numbered){delete this.global.notag}this.table.push(h.apply(b,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notags=this.save.notags;this.global.notag=this.save.notag}});e.start.Augment({oldCheckItem:e.start.prototype.checkItem,checkItem:function(j){if(j.type==="stop"){var h=this.mmlData(),i=this.global;if(f.display&&!i.tag&&!i.tagged&&!i.isInner&&(a.autoNumber==="all"||i.forcetag)){this.autoTag()}if(i.tag){var l=[this.getTag(),b.mtd(h)];var k={side:g.config.TagSide,minlabelspacing:g.config.TagIndent,columnalign:h.displayAlign};if(h.displayAlign===b.INDENTALIGN.LEFT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth=h.displayIndent+" fit";k.columnspacing="0";l=[l[0],b.mtd(),l[1]]}}else{if(h.displayAlign===b.INDENTALIGN.RIGHT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth="fit "+h.displayIndent;k.columnspacing="0";l[2]=b.mtd()}}}h=b.mtable(b.mlabeledtr.apply(b,l)).With(k)}return e.mml(h)}return this.oldCheckItem.call(this,j)}});g.prefilterHooks.Add(function(h){f.display=h.display;f.number=f.startNumber;f.eqlabels={};f.badref=false;if(f.refUpdate){f.number=h.script.MathJax.startNumber}});g.postfilterHooks.Add(function(h){h.script.MathJax.startNumber=f.startNumber;f.startNumber=f.number;MathJax.Hub.Insert(f.labels,f.eqlabels);if(f.badref&&!h.math.texError){f.refs.push(h.script)}});MathJax.Hub.Register.MessageHook("Begin Math Input",function(){f.refs=[];f.refUpdate=false});MathJax.Hub.Register.MessageHook("End Math Input",function(k){if(f.refs.length){f.refUpdate=true;for(var j=0,h=f.refs.length;j<h;j++){f.refs[j].MathJax.state=MathJax.ElementJax.STATE.UPDATE}return MathJax.Hub.processInput({scripts:f.refs,start:new Date().getTime(),i:0,j:0,jax:{},jaxIDs:[]})}return null});g.resetEquationNumbers=function(i,h){f.startNumber=(i||0);if(!h){f.labels={}}};MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js");
MathJax.Extension["TeX/AMSsymbols"]={version:"2.3"};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var a=MathJax.ElementJax.mml,b=MathJax.InputJax.TeX.Definitions;b.Add({mathchar0mi:{digamma:"03DD",varkappa:"03F0",varGamma:["0393",{mathvariant:a.VARIANT.ITALIC}],varDelta:["0394",{mathvariant:a.VARIANT.ITALIC}],varTheta:["0398",{mathvariant:a.VARIANT.ITALIC}],varLambda:["039B",{mathvariant:a.VARIANT.ITALIC}],varXi:["039E",{mathvariant:a.VARIANT.ITALIC}],varPi:["03A0",{mathvariant:a.VARIANT.ITALIC}],varSigma:["03A3",{mathvariant:a.VARIANT.ITALIC}],varUpsilon:["03A5",{mathvariant:a.VARIANT.ITALIC}],varPhi:["03A6",{mathvariant:a.VARIANT.ITALIC}],varPsi:["03A8",{mathvariant:a.VARIANT.ITALIC}],varOmega:["03A9",{mathvariant:a.VARIANT.ITALIC}],beth:"2136",gimel:"2137",daleth:"2138",backprime:["2035",{variantForm:true}],hslash:"210F",varnothing:["2205",{variantForm:true}],blacktriangle:"25B4",triangledown:["25BD",{variantForm:true}],blacktriangledown:"25BE",square:"25FB",Box:"25FB",blacksquare:"25FC",lozenge:"25CA",Diamond:"25CA",blacklozenge:"29EB",circledS:["24C8",{mathvariant:a.VARIANT.NORMAL}],bigstar:"2605",sphericalangle:"2222",measuredangle:"2221",nexists:"2204",complement:"2201",mho:"2127",eth:["00F0",{mathvariant:a.VARIANT.NORMAL}],Finv:"2132",diagup:"2571",Game:"2141",diagdown:"2572",Bbbk:["006B",{mathvariant:a.VARIANT.DOUBLESTRUCK}],yen:"00A5",circledR:"00AE",checkmark:"2713",maltese:"2720"},mathchar0mo:{dotplus:"2214",ltimes:"22C9",smallsetminus:"2216",rtimes:"22CA",Cap:"22D2",doublecap:"22D2",leftthreetimes:"22CB",Cup:"22D3",doublecup:"22D3",rightthreetimes:"22CC",barwedge:"22BC",curlywedge:"22CF",veebar:"22BB",curlyvee:"22CE",doublebarwedge:"2A5E",boxminus:"229F",circleddash:"229D",boxtimes:"22A0",circledast:"229B",boxdot:"22A1",circledcirc:"229A",boxplus:"229E",centerdot:"22C5",divideontimes:"22C7",intercal:"22BA",leqq:"2266",geqq:"2267",leqslant:"2A7D",geqslant:"2A7E",eqslantless:"2A95",eqslantgtr:"2A96",lesssim:"2272",gtrsim:"2273",lessapprox:"2A85",gtrapprox:"2A86",approxeq:"224A",lessdot:"22D6",gtrdot:"22D7",lll:"22D8",llless:"22D8",ggg:"22D9",gggtr:"22D9",lessgtr:"2276",gtrless:"2277",lesseqgtr:"22DA",gtreqless:"22DB",lesseqqgtr:"2A8B",gtreqqless:"2A8C",doteqdot:"2251",Doteq:"2251",eqcirc:"2256",risingdotseq:"2253",circeq:"2257",fallingdotseq:"2252",triangleq:"225C",backsim:"223D",thicksim:["223C",{variantForm:true}],backsimeq:"22CD",thickapprox:["2248",{variantForm:true}],subseteqq:"2AC5",supseteqq:"2AC6",Subset:"22D0",Supset:"22D1",sqsubset:"228F",sqsupset:"2290",preccurlyeq:"227C",succcurlyeq:"227D",curlyeqprec:"22DE",curlyeqsucc:"22DF",precsim:"227E",succsim:"227F",precapprox:"2AB7",succapprox:"2AB8",vartriangleleft:"22B2",lhd:"22B2",vartriangleright:"22B3",rhd:"22B3",trianglelefteq:"22B4",unlhd:"22B4",trianglerighteq:"22B5",unrhd:"22B5",vDash:"22A8",Vdash:"22A9",Vvdash:"22AA",smallsmile:["2323",{variantForm:true}],shortmid:["2223",{variantForm:true}],smallfrown:["2322",{variantForm:true}],shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C2",blacktriangleright:"25B8",therefore:"2234",because:"2235",eqsim:"2242",vartriangle:["25B3",{variantForm:true}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:true}],ngeqslant:["2A88",{variantForm:true}],nleqq:["2270",{variantForm:true}],ngeqq:["2271",{variantForm:true}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:true}],gvertneqq:["2269",{variantForm:true}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:true}],nsucceq:["22E1",{variantForm:true}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:true}],nshortparallel:["2226",{variantForm:true}],nmid:"2224",nparallel:"2226",nvdash:"22AC",nvDash:"22AD",nVdash:"22AE",nVDash:"22AF",ntriangleleft:"22EA",ntriangleright:"22EB",ntrianglelefteq:"22EC",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigarrow:"21DD",leadsto:"21DD",dashrightarrow:"21E2",dashleftarrow:"21E0",nleftarrow:"219A",nrightarrow:"219B",nLeftarrow:"21CD",nRightarrow:"21CF",nleftrightarrow:"21AE",nLeftrightarrow:"21CE"},delimiter:{"\\ulcorner":"231C","\\urcorner":"231D","\\llcorner":"231E","\\lrcorner":"231F"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}},null,true);var c=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":c,"\u2323":c,"\u25B3":c,"\uE006":c,"\uE007":c,"\uE00C":c,"\uE00D":c,"\uE00E":c,"\uE00F":c,"\uE010":c,"\uE011":c,"\uE016":c,"\uE017":c,"\uE018":c,"\uE019":c,"\uE01A":c,"\uE01B":c,"\uE04B":c,"\uE04F":c}}});MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js");
(function(h,b,d){var g,i=b.Browser.isMobile;var e=function(){var k=[].slice.call(arguments,0);k[0][0]=["HTML-CSS",k[0][0]];return MathJax.Message.Set.apply(MathJax.Message,k)};var f=MathJax.Object.Subclass({timeout:(i?15:8)*1000,FontInfo:{STIX:{family:"STIXSizeOneSym",testString:"() {} []"},TeX:{family:"MathJax_Size1",testString:"() {} []"},"STIX-Web":{family:"STIXWeb_Size1",testString:"() {} []"},"Asana-Math":{family:"AsanaMath_Size1",testString:"() {} []"},"Gyre-Pagella":{family:"GyrePagella_Size1",testString:"() {} []"},"Gyre-Termes":{family:"GyreTermes_Size1",testString:"() {} []"},"Latin-Modern":{family:"LatinModern_Size1",testString:"() {} []"},"Neo-Euler":{family:"NeoEuler_Size1",testString:"() {} []"}},comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,whiteSpace:"nowrap",textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal",fontSizeAdjust:"none"}},[""]);this.text=this.div.firstChild},findFont:function(o,l){if(l&&this.testCollection(l)){return l}for(var n=0,k=o.length;n<k;n++){if(o[n]===l){continue}if(this.testCollection(o[n])){return o[n]}}return null},testCollection:function(k){return this.testFont(this.FontInfo[k])},testFont:function(n){if(n.isWebFont&&d.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(n.weight||"normal");this.div.style.fontStyle=(n.style||"normal")}var l=this.getComparisonWidths(n.testString,n.noStyleChar);if(l){this.div.style.fontFamily="'"+n.family+"',"+this.comparisonFont[0];if(this.div.offsetWidth==l[0]){this.div.style.fontFamily="'"+n.family+"',"+this.comparisonFont[l[2]];if(this.div.offsetWidth==l[1]){return false}}if(this.div.offsetWidth!=l[3]||this.div.offsetHeight!=l[4]){if(n.noStyleChar||!d.FONTDATA||!d.FONTDATA.hasStyleChar){return true}for(var o=0,k=this.testSize.length;o<k;o++){if(this.testStyleChar(n,this.testSize[o])){return true}}}}return false},styleChar:"\uEFFD",versionChar:"\uEFFE",compChar:"\uEFFF",testStyleChar:function(m,p){var s=3+(m.weight?2:0)+(m.style?4:0);var l="",o=0;var r=this.div.style.fontSize;this.div.style.fontSize=p;if(d.msieItalicWidthBug&&m.style==="italic"){this.text.nodeValue=l=this.compChar;o=this.div.offsetWidth}if(d.safariTextNodeBug){this.div.innerHTML=this.compChar+l}else{this.text.nodeValue=this.compChar+l}var k=this.div.offsetWidth-o;if(d.safariTextNodeBug){this.div.innerHTML=this.styleChar+l}else{this.text.nodeValue=this.styleChar+l}var q=Math.floor((this.div.offsetWidth-o)/k+0.5);if(q===s){if(d.safariTextNodeBug){this.div.innerHTML=this.versionChar+l}else{this.text.nodeValue=this.versionChar+l}m.version=Math.floor((this.div.offsetWidth-o)/k+1.5)/2}this.div.style.fontSize=r;return(q===s)},getComparisonWidths:function(p,n){if(d.FONTDATA&&d.FONTDATA.hasStyleChar&&!n){p+=this.styleChar+" "+this.compChar}if(d.safariTextNodeBug){this.div.innerHTML=p}else{this.text.nodeValue=p}this.div.style.fontFamily=this.comparisonFont[0];var l=this.div.offsetWidth;this.div.style.fontFamily=d.webFontDefault;var r=this.div.offsetWidth,o=this.div.offsetHeight;for(var q=1,k=this.comparisonFont.length;q<k;q++){this.div.style.fontFamily=this.comparisonFont[q];if(this.div.offsetWidth!=l){return[l,this.div.offsetWidth,q,r,o]}}return null},loadWebFont:function(l){b.Startup.signal.Post("HTML-CSS Jax - Web-Font "+d.fontInUse+"/"+l.directory);var o=e(["LoadWebFont","Loading web-font %1",d.fontInUse+"/"+l.directory]);var k=MathJax.Callback({});var m=MathJax.Callback(["loadComplete",this,l,o,k]);h.timer.start(h,[this.checkWebFont,l,m],0,this.timeout);return k},loadComplete:function(m,p,l,k){MathJax.Message.Clear(p);if(k===h.STATUS.OK){this.webFontLoaded=true;l();return}this.loadError(m);if(b.Browser.isFirefox&&d.allowWebFonts){var o=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){o+=":"+document.location.port}o+="/";if(h.fileURL(d.webfontDir).substr(0,o.length)!==o){this.firefoxFontError(m)}}if(!this.webFontLoaded){d.loadWebFontError(m,l)}else{l()}},loadError:function(k){e(["CantLoadWebFont","Can't load web font %1",d.fontInUse+"/"+k.directory],null,2000);b.Startup.signal.Post(["HTML-CSS Jax - web font error",d.fontInUse+"/"+k.directory,k])},firefoxFontError:function(k){e(["FirefoxCantLoadWebFont","Firefox can't load web fonts from a remote host"],null,3000);b.Startup.signal.Post("HTML-CSS Jax - Firefox web fonts on remote host error")},checkWebFont:function(k,l,m){if(k.time(m)){return}if(d.Font.testFont(l)){m(k.STATUS.OK)}else{setTimeout(k,k.delay)}},fontFace:function(m){var n=d.allowWebFonts;var p=d.FONTDATA.FONTS[m];if(d.msieFontCSSBug&&!p.family.match(/-Web$/)){p.family+="-Web"}var l=h.fileURL(d.webfontDir+"/"+n);var k=m.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!k.match(/-/)){k+="-Regular"}if(n==="svg"){k+=".svg#"+k}else{k+="."+n}var o={"font-family":p.family,src:"url('"+l+"/"+k+"')"};if(n==="otf"){o.src+=" format('opentype')";l=h.fileURL(d.webfontDir+"/woff");o.src="url('"+l+"/"+k.replace(/otf$/,"woff")+"') format('woff'), "+o.src}else{if(n!=="eot"){o.src+=" format('"+n+"')"}}if(!(d.FontFaceBug&&p.isWebFont)){if(m.match(/-bold/)){o["font-weight"]="bold"}if(m.match(/-italic/)){o["font-style"]="italic"}}return o}});var j,a,c;d.Augment({config:{styles:{".MathJax":{display:"inline","font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none",direction:"ltr",border:0,padding:0,margin:0},".MathJax_Display":{position:"relative",display:"block",width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0 !important",padding:"0 !important",margin:"0 !important","vertical-align":"0 !important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},".MathJax nobr":{"white-space":"nowrap ! important"},".MathJax img":{display:"inline ! important","float":"none ! important"},".MathJax *":{transition:"none","-webkit-transition":"none","-moz-transition":"none","-ms-transition":"none","-o-transition":"none"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax_Processed":{display:"none!important"},".MathJax_ExBox":{display:"block",overflow:"hidden",width:"1px",height:"60ex"},".MathJax .MathJax_EmBox":{display:"block",overflow:"hidden",width:"1px",height:"60em"},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity=0)"},".MathJax .MathJax_HitBox *":{filter:"none",opacity:1,background:"transparent"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",opacity:1,background:"transparent"},"@font-face":{"font-family":"MathJax_Blank",src:"url('about:blank')"}}},settings:b.config.menuSettings,hideProcessedMath:true,Font:null,webFontDefault:"MathJax_Blank",allowWebFonts:"otf",maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.Font=f();this.SUPER(arguments).Config.call(this);var l=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(l.scale){this.config.scale=l.scale}if(l.font&&l.font!=="Auto"){if(l.font==="TeXLocal"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(l.font==="TeXWeb"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(l.font==="TeXimage"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}else{if(l.font==="STIXlocal"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="STIX-Web"}else{if(l.font==="STIXWeb"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="STIX-Web"}else{if(l.font==="AsanaMathWeb"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="Asana-Math"}else{if(l.font==="GyrePagellaWeb"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="Gyre-Pagella"}else{if(l.font==="GyreTermesWeb"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="Gyre-Termes"}else{if(l.font==="LatinModernWeb"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="Latin-Modern"}else{if(l.font==="NeoEulerWeb"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="Neo-Euler"}}}}}}}}}}}var k=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!k&&this.allowWebFonts){k=this.config.webFont;if(k){this.webFonts=true}}if(!k&&this.config.imageFont){k=this.config.imageFont;this.imgFonts=true}if(k){this.fontInUse=k;this.fontDir+="/"+k;this.webfontDir+="/"+k;this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");b.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{e(["CantFindFontUsing","Can't find a valid font using %1","["+this.config.availableFonts.join(", ")+"]"],null,3000);this.fontInUse="generic";this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]},"-generic-variant":{fonts:[]},"-largeOp":{fonts:[]},"-smallOp":{fonts:[]}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}};b.Startup.signal.Post("HTML-CSS Jax - no valid font")}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;this.hiddenDiv=this.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=this.addElement(this.hiddenDiv,"div",{id:"MathJax_Hidden"});var l=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=l.offsetWidth/5;this.hiddenDiv.removeChild(l);this.startMarker=this.createStrut(this.Element("span"),10,true);this.endMarker=this.addText(this.Element("span"),"x").parentNode;this.HDspan=this.Element("span");if(this.operaHeightBug){this.createStrut(this.HDspan,0)}if(this.msieInlineBlockAlignBug){this.HDimg=this.addElement(this.HDspan,"img",{style:{height:"0px",width:"1px"}});try{this.HDimg.src="about:blank"}catch(k){}}else{this.HDimg=this.createStrut(this.HDspan,0)}this.EmExSpan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["span",{className:"MathJax_ExBox"}],["span",{className:"MathJax"},[["span",{className:"MathJax_EmBox"}]]]]);this.linebreakSpan=this.Element("span",null,[["hr",{style:{width:"100%",size:1,padding:0,border:0,margin:0}}]]);return h.Styles(this.config.styles,["InitializeHTML",this])},removeSTIXfonts:function(n){for(var l=0,k=n.length;l<k;l++){if(n[l]==="STIX"){n.splice(l,1);k--;l--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=n[0]}},PreloadWebFonts:function(){if(!d.allowWebFonts||!d.config.preloadWebFonts){return}for(var l=0,k=d.config.preloadWebFonts.length;l<k;l++){var n=d.FONTDATA.FONTS[d.config.preloadWebFonts[l]];if(!n.available){d.Font.testFont(n)}}},InitializeHTML:function(){this.PreloadWebFonts();document.body.appendChild(this.EmExSpan);document.body.appendChild(this.linebreakSpan);this.defaultEx=this.EmExSpan.firstChild.offsetHeight/60;this.defaultEm=this.EmExSpan.lastChild.firstChild.offsetHeight/60;this.defaultWidth=this.linebreakSpan.firstChild.offsetWidth;document.body.removeChild(this.linebreakSpan);document.body.removeChild(this.EmExSpan)},preTranslate:function(o){var u=o.jax[this.id],v,r=u.length,z,t,A,n,y,l,x,q,s,k,w=false,B=this.config.linebreaks.automatic,p=this.config.linebreaks.width;if(B){w=(p.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)!=null);if(w){p=p.replace(/\s*container\s*/,"")}else{k=this.defaultWidth}if(p===""){p="100%"}}else{k=100000}for(v=0;v<r;v++){z=u[v];if(!z.parentNode){continue}t=z.previousSibling;if(t&&String(t.className).match(/^MathJax(_Display)?( MathJax_Processing)?$/)){t.parentNode.removeChild(t)}l=z.MathJax.elementJax;if(!l){continue}l.HTMLCSS={display:(l.root.Get("display")==="block")};A=n=this.Element("span",{className:"MathJax",id:l.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){A.ontouchstart=a.start;A.ontouchend=a.end}if(l.HTMLCSS.display){n=this.Element("div",{className:"MathJax_Display"});n.appendChild(A)}else{if(this.msieDisappearingBug){A.style.display="inline-block"}}n.setAttribute("role","textbox");n.setAttribute("aria-readonly","true");n.className+=" MathJax_Processing";z.parentNode.insertBefore(n,z);z.parentNode.insertBefore(this.EmExSpan.cloneNode(true),z);if(w){n.parentNode.insertBefore(this.linebreakSpan.cloneNode(true),n)}}for(v=0;v<r;v++){z=u[v];if(!z.parentNode){continue}y=z.previousSibling;n=y.previousSibling;l=z.MathJax.elementJax;if(!l){continue}x=y.firstChild.offsetHeight/60;q=y.lastChild.firstChild.offsetHeight/60;if(w){k=n.previousSibling.firstChild.offsetWidth}if(x===0||x==="NaN"){this.hiddenDiv.appendChild(n);l.HTMLCSS.isHidden=true;x=this.defaultEx;q=this.defaultEm;if(w){k=this.defaultWidth}}s=(this.config.matchFontHeight?x/this.TeX.x_height/q:1);s=Math.floor(Math.max(this.config.minScaleAdjust/100,s)*this.config.scale);l.HTMLCSS.scale=s/100;l.HTMLCSS.fontSize=s+"%";l.HTMLCSS.em=l.HTMLCSS.outerEm=q;this.em=q*s/100;l.HTMLCSS.ex=x;l.HTMLCSS.lineWidth=(B?this.length2em(p,1,k/this.em):1000000)}for(v=0;v<r;v++){z=u[v];if(!z.parentNode){continue}y=u[v].previousSibling;l=u[v].MathJax.elementJax;if(!l){continue}if(w){A=y.previousSibling;if(!l.HTMLCSS.isHidden){A=A.previousSibling}A.parentNode.removeChild(A)}y.parentNode.removeChild(y)}o.HTMLCSSeqn=o.HTMLCSSlast=0;o.HTMLCSSi=-1;o.HTMLCSSchunk=this.config.EqnChunk;o.HTMLCSSdelay=false},Translate:function(l,p){if(!l.parentNode){return}if(p.HTMLCSSdelay){p.HTMLCSSdelay=false;b.RestartAfter(MathJax.Callback.Delay(this.config.EqnChunkDelay))}var k=l.MathJax.elementJax,o=k.root,m=document.getElementById(k.inputID+"-Frame"),q=(k.HTMLCSS.display?m.parentNode:m);this.em=g.mbase.prototype.em=k.HTMLCSS.em*k.HTMLCSS.scale;this.outerEm=k.HTMLCSS.em;this.scale=k.HTMLCSS.scale;this.linebreakWidth=k.HTMLCSS.lineWidth;if(this.scale!==1){m.style.fontSize=k.HTMLCSS.fontSize}this.initImg(m);this.initHTML(o,m);o.setTeXclass();try{o.toHTML(m,q)}catch(n){if(n.restart){while(m.firstChild){m.removeChild(m.firstChild)}}throw n}if(k.HTMLCSS.isHidden){l.parentNode.insertBefore(q,l)}q.className=q.className.split(/ /)[0];if(this.hideProcessedMath){q.className+=" MathJax_Processed";if(l.MathJax.preview){k.HTMLCSS.preview=l.MathJax.preview;delete l.MathJax.preview}p.HTMLCSSeqn+=(p.i-p.HTMLCSSi);p.HTMLCSSi=p.i;if(p.HTMLCSSeqn>=p.HTMLCSSlast+p.HTMLCSSchunk){this.postTranslate(p,true);p.HTMLCSSchunk=Math.floor(p.HTMLCSSchunk*this.config.EqnChunkFactor);p.HTMLCSSdelay=true}}},postTranslate:function(s,o){var l=s.jax[this.id];if(!this.hideProcessedMath){return}for(var q=s.HTMLCSSlast,k=s.HTMLCSSeqn;q<k;q++){var n=l[q];if(n&&n.MathJax.elementJax){n.previousSibling.className=n.previousSibling.className.split(/ /)[0];var r=n.MathJax.elementJax.HTMLCSS;if(r.preview){r.preview.innerHTML="";n.MathJax.preview=r.preview;delete r.preview}}}if(this.forceReflow){var p=(document.styleSheets||[])[0]||{};p.disabled=true;p.disabled=false}s.HTMLCSSlast=s.HTMLCSSeqn},getJaxFromMath:function(k){if(k.parentNode.className==="MathJax_Display"){k=k.parentNode}do{k=k.nextSibling}while(k&&k.nodeName.toLowerCase()!=="script");return b.getJaxFor(k)},getHoverSpan:function(k,l){return k.root.HTMLspanElement()},getHoverBBox:function(k,n,o){var p=n.bbox,m=k.HTMLCSS.outerEm;var l={w:p.w*m,h:p.h*m,d:p.d*m};if(p.width){l.width=p.width}return l},Zoom:function(l,v,u,k,s){v.className="MathJax";v.style.fontSize=l.HTMLCSS.fontSize;var x=v.appendChild(this.EmExSpan.cloneNode(true));var o=x.lastChild.firstChild.offsetHeight/60;this.em=g.mbase.prototype.em=o;this.outerEm=o/l.HTMLCSS.scale;x.parentNode.removeChild(x);this.idPostfix="-zoom";l.root.toHTML(v,v);this.idPostfix="";var n=l.root.HTMLspanElement().bbox.width;if(n){v.style.width=Math.floor(k-1.5*d.em)+"px";v.style.display="inline-block";var m=(l.root.id||"MathJax-Span-"+l.root.spanID)+"-zoom";var p=document.getElementById(m).firstChild;while(p&&p.style.width!==n){p=p.nextSibling}if(p){p.style.width="100%"}}v.style.position="absolute";if(!n){u.style.position="absolute"}var t=v.offsetWidth,r=v.offsetHeight,w=u.offsetHeight,q=u.offsetWidth;if(q===0){q=u.parentNode.offsetWidth}v.style.position=u.style.position="";return{Y:-j.getBBox(v).h,mW:q,mH:w,zW:t,zH:r}},initImg:function(k){},initHTML:function(l,k){},initFont:function(k){var m=d.FONTDATA.FONTS,l=d.config.availableFonts;if(l&&l.length&&d.Font.testFont(m[k])){m[k].available=true;return null}if(!this.allowWebFonts){return null}m[k].isWebFont=true;if(d.FontFaceBug){m[k].family=k;if(d.msieFontCSSBug){m[k].family+="-Web"}}return h.Styles({"@font-face":this.Font.fontFace(k)})},Remove:function(k){var l=document.getElementById(k.inputID+"-Frame");if(l){if(k.HTMLCSS.display){l=l.parentNode}l.parentNode.removeChild(l)}delete k.HTMLCSS},getHD:function(l){var k=l.style.position;l.style.position="absolute";this.HDimg.style.height="0px";l.appendChild(this.HDspan);var m={h:l.offsetHeight};this.HDimg.style.height=m.h+"px";m.d=l.offsetHeight-m.h;m.h-=m.d;m.h/=this.em;m.d/=this.em;l.removeChild(this.HDspan);l.style.position=k;return m},getW:function(o){var l,n,m=(o.bbox||{}).w,p=o;if(o.bbox&&o.bbox.exactW){return m}if((o.bbox&&m>=0&&!this.initialSkipBug)||this.negativeBBoxes||!o.firstChild){l=o.offsetWidth;n=o.parentNode.offsetHeight}else{if(o.bbox&&m<0&&this.msieNegativeBBoxBug){l=-o.offsetWidth,n=o.parentNode.offsetHeight}else{if(this.initialSkipBug){var k=o.style.position;o.style.position="absolute";p=this.startMarker;o.insertBefore(p,o.firstChild)}o.appendChild(this.endMarker);l=this.endMarker.offsetLeft-p.offsetLeft;o.removeChild(this.endMarker);if(this.initialSkipBug){o.removeChild(p);o.style.position=k}}}if(n!=null){o.parentNode.HH=n/this.em}return l/this.em},Measured:function(m,l){var n=m.bbox;if(n.width==null&&n.w&&!n.isMultiline){var k=this.getW(m);n.rw+=k-n.w;n.w=k;n.exactW=true}if(!l){l=m.parentNode}if(!l.bbox){l.bbox=n}return m},Remeasured:function(l,k){k.bbox=this.Measured(l,k).bbox},MeasureSpans:function(o){var r=[],t,q,n,u,k,p,l,s;for(q=0,n=o.length;q<n;q++){t=o[q];if(!t){continue}u=t.bbox;s=this.parentNode(t);if(u.exactW||u.width||u.w===0||u.isMultiline){if(!s.bbox){s.bbox=u}continue}if(this.negativeBBoxes||!t.firstChild||(u.w>=0&&!this.initialSkipBug)||(u.w<0&&this.msieNegativeBBoxBug)){r.push([t])}else{if(this.initialSkipBug){k=this.startMarker.cloneNode(true);p=this.endMarker.cloneNode(true);t.insertBefore(k,t.firstChild);t.appendChild(p);r.push([t,k,p,t.style.position]);t.style.position="absolute"}else{p=this.endMarker.cloneNode(true);t.appendChild(p);r.push([t,null,p])}}}for(q=0,n=r.length;q<n;q++){t=r[q][0];u=t.bbox;s=this.parentNode(t);if((u.w>=0&&!this.initialSkipBug)||this.negativeBBoxes||!t.firstChild){l=t.offsetWidth;s.HH=s.offsetHeight/this.em}else{if(u.w<0&&this.msieNegativeBBoxBug){l=-t.offsetWidth,s.HH=s.offsetHeight/this.em}else{l=r[q][2].offsetLeft-((r[q][1]||{}).offsetLeft||0)}}l/=this.em;u.rw+=l-u.w;u.w=l;u.exactW=true;if(!s.bbox){s.bbox=u}}for(q=0,n=r.length;q<n;q++){t=r[q];if(t[1]){t[1].parentNode.removeChild(t[1]),t[0].style.position=t[3]}if(t[2]){t[2].parentNode.removeChild(t[2])}}},Em:function(k){if(Math.abs(k)<0.0006){return"0em"}return k.toFixed(3).replace(/\.?0+$/,"")+"em"},EmRounded:function(k){k=(Math.round(k*d.em)+0.05)/d.em;if(Math.abs(k)<0.0006){return"0em"}return k.toFixed(3).replace(/\.?0+$/,"")+"em"},unEm:function(k){return parseFloat(k)},Px:function(k){k*=this.em;var l=(k<0?"-":"");return l+Math.abs(k).toFixed(1).replace(/\.?0+$/,"")+"px"},unPx:function(k){return parseFloat(k)/this.em},Percent:function(k){return(100*k).toFixed(1).replace(/\.?0+$/,"")+"%"},length2em:function(r,l,p){if(typeof(r)!=="string"){r=r.toString()}if(r===""){return""}if(r===g.SIZE.NORMAL){return 1}if(r===g.SIZE.BIG){return 2}if(r===g.SIZE.SMALL){return 0.71}if(r==="infinity"){return d.BIGDIMEN}var o=this.FONTDATA.TeX_factor;if(r.match(/mathspace$/)){return d.MATHSPACE[r]*o}var n=r.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var k=parseFloat(n[1]||"1"),q=n[2];if(p==null){p=1}if(l==null){l=1}if(q==="em"){return k*o}if(q==="ex"){return k*d.TeX.x_height*o}if(q==="%"){return k/100*p}if(q==="px"){return k/d.em}if(q==="pt"){return k/10*o}if(q==="pc"){return k*1.2*o}if(q==="in"){return k*this.pxPerInch/d.em}if(q==="cm"){return k*this.pxPerInch/d.em/2.54}if(q==="mm"){return k*this.pxPerInch/d.em/25.4}if(q==="mu"){return k/18*o*l}return k*o*p},thickness2em:function(l,k){var m=d.TeX.rule_thickness;if(l===g.LINETHICKNESS.MEDIUM){return m}if(l===g.LINETHICKNESS.THIN){return 0.67*m}if(l===g.LINETHICKNESS.THICK){return 1.67*m}return this.length2em(l,k,m)},getPadding:function(l){var n={top:0,right:0,bottom:0,left:0},k=false;for(var o in n){if(n.hasOwnProperty(o)){var m=l.style["padding"+o.charAt(0).toUpperCase()+o.substr(1)];if(m){n[o]=this.length2em(m);k=true}}}return(k?n:false)},getBorders:function(p){var m={top:0,right:0,bottom:0,left:0},n={},l=false;for(var q in m){if(m.hasOwnProperty(q)){var k="border"+q.charAt(0).toUpperCase()+q.substr(1);var o=p.style[k+"Style"];if(o){l=true;m[q]=this.length2em(p.style[k+"Width"]);n[k]=[p.style[k+"Width"],p.style[k+"Style"],p.style[k+"Color"]].join(" ")}}}m.css=n;return(l?m:false)},setBorders:function(k,l){if(l){for(var m in l.css){if(l.css.hasOwnProperty(m)){k.style[m]=l.css[m]}}}},createStrut:function(m,l,n){var k=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:l+"px",width:"1px",marginRight:"-1px"}});if(n){m.insertBefore(k,m.firstChild)}else{m.appendChild(k)}return k},createBlank:function(l,k,m){var n=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(k)}});if(m){l.insertBefore(n,l.firstChild)}else{l.appendChild(n)}return n},createShift:function(l,k,n){var m=this.Element("span",{style:{marginLeft:this.Em(k)},isMathJax:true});if(n){l.insertBefore(m,l.firstChild)}else{l.appendChild(m)}return m},createSpace:function(p,n,o,q,m,s){if(n<-o){o=-n}var r=this.Em(n+o),k=this.Em(-o);if(this.msieInlineBlockAlignBug){k=this.Em(d.getHD(p.parentNode).d-o)}if(p.isBox||s){var l=(p.scale==null?1:p.scale);p.bbox={exactW:true,h:n*l,d:o*l,w:q*l,rw:q*l,lw:0};p.style.height=r;p.style.verticalAlign=k;p.HH=(n+o)*l}else{p=this.addElement(p,"span",{style:{height:r,verticalAlign:k},isMathJax:true})}if(q>=0){p.style.width=this.Em(q);p.style.display="inline-block";p.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){p.style.height=""}p.style.marginLeft=this.Em(q);if(d.safariNegativeSpaceBug&&p.parentNode.firstChild==p){this.createBlank(p,0,true)}}if(m&&m!==g.COLOR.TRANSPARENT){p.style.backgroundColor=m;p.style.position="relative"}return p},createRule:function(r,n,p,s,l){if(n<-p){p=-n}var m=d.TeX.min_rule_thickness,o=1;if(s>0&&s*this.em<m){s=m/this.em}if(n+p>0&&(n+p)*this.em<m){o=1/(n+p)*(m/this.em);n*=o;p*=o}if(!l){l="solid"}else{l="solid "+l}l=this.Em(s)+" "+l;var t=(o===1?this.Em(n+p):m+"px"),k=this.Em(-p);var q=this.addElement(r,"span",{style:{borderLeft:l,display:"inline-block",overflow:"hidden",width:0,height:t,verticalAlign:k},bbox:{h:n,d:p,w:s,rw:s,lw:0,exactW:true},noAdjust:true,HH:n+p,isMathJax:true});if(s>0&&q.offsetWidth==0){q.style.width=this.Em(s)}if(r.isBox||r.className=="mspace"){r.bbox=q.bbox,r.HH=n+p}return q},createFrame:function(s,q,r,u,x,l){if(q<-r){r=-q}var p=2*x;if(this.msieFrameSizeBug){if(u<p){u=p}if(q+r<p){q=p-r}}if(this.msieBorderWidthBug){p=0}var v=this.Em(q+r-p),k=this.Em(-r-x),o=this.Em(u-p);var m=this.Em(x)+" "+l;var n=this.addElement(s,"span",{style:{border:m,display:"inline-block",overflow:"hidden",width:o,height:v},bbox:{h:q,d:r,w:u,rw:u,lw:0,exactW:true},noAdjust:true,HH:q+r,isMathJax:true});if(k){n.style.verticalAlign=k}return n},parentNode:function(l){var k=l.parentNode;if(k.nodeName.toLowerCase()==="a"){k=k.parentNode}return k},createStack:function(m,o,l){if(this.msiePaddingWidthBug){this.createStrut(m,0)}var n=String(l).match(/%$/);var k=(!n&&l!=null?l:0);m=this.addElement(m,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(n?"100%":this.Em(k)),height:0}});if(!o){m.parentNode.bbox=m.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:k,lw:this.BIGDIMEN,rw:(!n&&l!=null?l:-this.BIGDIMEN)};if(n){m.bbox.width=l}}return m},createBox:function(l,k){var m=this.addElement(l,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(k!=null){m.style.width=k}return m},addBox:function(k,l){l.style.position="absolute";l.isBox=l.isMathJax=true;return k.appendChild(l)},placeBox:function(u,s,q,o){u.isMathJax=true;var v=d.parentNode(u),C=u.bbox,z=v.bbox;if(this.msiePlaceBoxBug){this.addText(u,this.NBSP)}if(this.imgSpaceBug){this.addText(u,this.imgSpace)}var w,F=0;if(u.HH!=null){w=u.HH}else{if(C){w=Math.max(3,C.h+C.d)}else{w=u.offsetHeight/this.em}}if(!u.noAdjust){w+=1;w=Math.round(w*this.em)/this.em;if(this.msieInlineBlockAlignBug){this.addElement(u,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(w)}})}else{this.addElement(u,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(w)}});if(d.chromeHeightBug){w-=(u.lastChild.offsetHeight-Math.round(w*this.em))/this.em}}}if(C){if(this.initialSkipBug){if(C.lw<0){F=C.lw;d.createBlank(u,-F,true)}if(C.rw>C.w){d.createBlank(u,C.rw-C.w+0.1)}}if(!this.msieClipRectBug&&!C.noclip&&!o){var B=3/this.em;var A=(C.H==null?C.h:C.H),m=(C.D==null?C.d:C.D);var E=w-A-B,p=w+m+B,n=C.lw-3*B,k=1000;if(this.initialSkipBug&&C.lw<0){n=-3*B}if(C.isFixed){k=C.width-n}u.style.clip="rect("+this.Em(E)+" "+this.Em(k)+" "+this.Em(p)+" "+this.Em(n)+")"}}u.style.top=this.Em(-q-w);u.style.left=this.Em(s+F);if(C&&z){if(C.H!=null&&(z.H==null||C.H+q>z.H)){z.H=C.H+q}if(C.D!=null&&(z.D==null||C.D-q>z.D)){z.D=C.D-q}if(C.h+q>z.h){z.h=C.h+q}if(C.d-q>z.d){z.d=C.d-q}if(z.H!=null&&z.H<=z.h){delete z.H}if(z.D!=null&&z.D<=z.d){delete z.D}if(C.w+s>z.w){z.w=C.w+s;if(z.width==null){v.style.width=this.Em(z.w)}}if(C.rw+s>z.rw){z.rw=C.rw+s}if(C.lw+s<z.lw){z.lw=C.lw+s}if(C.width!=null&&!C.isFixed){if(z.width==null){v.style.width=z.width="100%";if(C.minWidth){v.style.minWidth=z.minWidth=C.minWidth}}u.style.width=C.width}}},alignBox:function(n,t,s){this.placeBox(n,0,s);var p=n.bbox;if(p.isMultiline){return}var m=p.width!=null&&!p.isFixed;var o=0,q=-p.w/2,k="50%";if(this.initialSkipBug){o=p.w-p.rw-0.1;q+=p.lw}if(this.msieMarginScaleBug){q=(q*this.em)+"px"}else{q=this.Em(q)}if(m){q="";k=(50-parseFloat(p.width)/2)+"%"}b.Insert(n.style,({right:{left:"",right:this.Em(o)},center:{left:k,marginLeft:q}})[t])},setStackWidth:function(l,k){if(typeof(k)==="number"){l.style.width=this.Em(Math.max(0,k));var m=l.bbox;if(m){m.w=k;m.exactW=true}m=l.parentNode.bbox;if(m){m.w=k;m.exactW=true}}else{l.style.width=l.parentNode.style.width="100%";if(l.bbox){l.bbox.width=k}if(l.parentNode.bbox){l.parentNode.bbox.width=k}}},createDelimiter:function(u,k,n,q,o){if(!k){u.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};u.bbox.rw=u.bbox.w;this.createSpace(u,u.bbox.h,u.bbox.d,u.bbox.w);return}if(!q){q=1}if(!(n instanceof Array)){n=[n,n]}var t=n[1];n=n[0];var l={alias:k};while(l.alias){k=l.alias;l=this.FONTDATA.DELIMITERS[k];if(!l){l={HW:[0,this.FONTDATA.VARIANT[g.VARIANT.NORMAL]]}}}if(l.load){b.RestartAfter(h.Require(this.fontDir+"/fontdata-"+l.load+".js"))}for(var s=0,p=l.HW.length;s<p;s++){if(l.HW[s][0]*q>=n-0.01||(s==p-1&&!l.stretch)){if(l.HW[s][2]){q*=l.HW[s][2]}if(l.HW[s][3]){k=l.HW[s][3]}var r=this.addElement(u,"span");this.createChar(r,[k,l.HW[s][1]],q,o);u.bbox=r.bbox;u.offset=0.65*u.bbox.w;u.scale=q;return}}if(l.stretch){this["extendDelimiter"+l.dir](u,t,l.stretch,q,o)}},extendDelimiterV:function(A,t,E,F,w){var o=this.createStack(A,true);var v=this.createBox(o),u=this.createBox(o);this.createChar(v,(E.top||E.ext),F,w);this.createChar(u,(E.bot||E.ext),F,w);var m={bbox:{w:0,lw:0,rw:0}},D=m,p;var B=v.bbox.h+v.bbox.d+u.bbox.h+u.bbox.d;var r=-v.bbox.h;this.placeBox(v,0,r,true);r-=v.bbox.d;if(E.mid){D=this.createBox(o);this.createChar(D,E.mid,F,w);B+=D.bbox.h+D.bbox.d}if(E.min&&t<B*E.min){t=B*E.min}if(t>B){m=this.Element("span");this.createChar(m,E.ext,F,w);var C=m.bbox.h+m.bbox.d,l=C-0.05,x,q,z=(E.mid?2:1);q=x=Math.min(Math.ceil((t-B)/(z*l)),this.maxStretchyParts);if(!E.fullExtenders){l=(t-B)/(z*x)}var s=(x/(x+1))*(C-l);l=C-s;r+=s+l-m.bbox.h;while(z-->0){while(x-->0){if(!this.msieCloneNodeBug){p=m.cloneNode(true)}else{p=this.Element("span");this.createChar(p,E.ext,F,w)}p.bbox=m.bbox;r-=l;this.placeBox(this.addBox(o,p),0,r,true)}r+=s-m.bbox.d;if(E.mid&&z){this.placeBox(D,0,r-D.bbox.h,true);x=q;r+=-(D.bbox.h+D.bbox.d)+s+l-m.bbox.h}}}else{r+=(B-t)/2;if(E.mid){this.placeBox(D,0,r-D.bbox.h,true);r+=-(D.bbox.h+D.bbox.d)}r+=(B-t)/2}this.placeBox(u,0,r-u.bbox.h,true);r-=u.bbox.h+u.bbox.d;A.bbox={w:Math.max(v.bbox.w,m.bbox.w,u.bbox.w,D.bbox.w),lw:Math.min(v.bbox.lw,m.bbox.lw,u.bbox.lw,D.bbox.lw),rw:Math.max(v.bbox.rw,m.bbox.rw,u.bbox.rw,D.bbox.rw),h:0,d:-r,exactW:true};A.scale=F;A.offset=0.55*A.bbox.w;A.isMultiChar=true;this.setStackWidth(o,A.bbox.w)},extendDelimiterH:function(B,o,E,G,y){var r=this.createStack(B,true);var p=this.createBox(r),C=this.createBox(r);this.createChar(p,(E.left||E.rep),G,y);this.createChar(C,(E.right||E.rep),G,y);var l=this.Element("span");this.createChar(l,E.rep,G,y);var D={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},m;this.placeBox(p,-p.bbox.lw,0,true);var u=(p.bbox.rw-p.bbox.lw)+(C.bbox.rw-C.bbox.lw)-0.05,t=p.bbox.rw-p.bbox.lw-0.025,v;if(E.mid){D=this.createBox(r);this.createChar(D,E.mid,G,y);u+=D.bbox.w}if(E.min&&o<u*E.min){o=u*E.min}if(o>u){var F=l.bbox.rw-l.bbox.lw,q=F-0.05,z,s,A=(E.mid?2:1);s=z=Math.min(Math.ceil((o-u)/(A*q)),this.maxStretchyParts);if(!E.fillExtenders){q=(o-u)/(A*z)}v=(z/(z+1))*(F-q);q=F-v;t-=l.bbox.lw+v;while(A-->0){while(z-->0){if(!this.cloneNodeBug){m=l.cloneNode(true)}else{m=this.Element("span");this.createChar(m,E.rep,G,y)}m.bbox=l.bbox;this.placeBox(this.addBox(r,m),t,0,true);t+=q}if(E.mid&&A){this.placeBox(D,t,0,true);t+=D.bbox.w-v;z=s}}}else{t-=(u-o)/2;if(E.mid){this.placeBox(D,t,0,true);t+=D.bbox.w}t-=(u-o)/2}this.placeBox(C,t,0,true);B.bbox={w:t+C.bbox.rw,lw:0,rw:t+C.bbox.rw,H:Math.max(p.bbox.h,l.bbox.h,C.bbox.h,D.bbox.h),D:Math.max(p.bbox.d,l.bbox.d,C.bbox.d,D.bbox.d),h:l.bbox.h,d:l.bbox.d,exactW:true};B.scale=G;B.isMultiChar=true;this.setStackWidth(r,B.bbox.w)},createChar:function(s,p,n,k){s.isMathJax=true;var r=s,t="",o={fonts:[p[1]],noRemap:true};if(k&&k===g.VARIANT.BOLD){o.fonts=[p[1]+"-bold",p[1]]}if(typeof(p[1])!=="string"){o=p[1]}if(p[0] instanceof Array){for(var q=0,l=p[0].length;q<l;q++){t+=String.fromCharCode(p[0][q])}}else{t=String.fromCharCode(p[0])}if(p[4]){n*=p[4]}if(n!==1||p[3]){r=this.addElement(s,"span",{style:{fontSize:this.Percent(n)},scale:n,isMathJax:true});this.handleVariant(r,o,t);s.bbox=r.bbox}else{this.handleVariant(s,o,t)}if(p[2]){s.style.marginLeft=this.Em(p[2])}if(p[3]){s.firstChild.style.verticalAlign=this.Em(p[3]);s.bbox.h+=p[3];if(s.bbox.h<0){s.bbox.h=0}}if(p[5]){s.bbox.h+=p[5]}if(p[6]){s.bbox.d+=p[6]}if(this.AccentBug&&s.bbox.w===0){r.firstChild.nodeValue+=this.NBSP}},positionDelimiter:function(l,k){k-=l.bbox.h;l.bbox.d-=k;l.bbox.h+=k;if(k){if(this.safariVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&l.isMultiChar)){if(l.firstChild.style.display===""&&l.style.top!==""){l=l.firstChild;k-=d.unEm(l.style.top)}l.style.position="relative";l.style.top=this.Em(-k)}else{l.style.verticalAlign=this.Em(k);if(d.ffVerticalAlignBug){d.createRule(l.parentNode,l.bbox.h,0,0)}}}},handleVariant:function(A,p,s){var z="",x,C,t,D,k=A,l=!!A.style.fontFamily;if(s.length===0){return}if(!A.bbox){A.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!p){p=this.FONTDATA.VARIANT[g.VARIANT.NORMAL]}D=p;for(var B=0,y=s.length;B<y;B++){p=D;x=s.charCodeAt(B);C=s.charAt(B);if(x>=55296&&x<56319){B++;x=(((x-55296)<<10)+(s.charCodeAt(B)-56320))+65536;if(this.FONTDATA.RemapPlane1){var E=this.FONTDATA.RemapPlane1(x,p);x=E.n;p=E.variant}}else{var u,r,v=this.FONTDATA.RANGES;for(u=0,r=v.length;u<r;u++){if(v[u].name==="alpha"&&p.noLowerCase){continue}var q=p["offset"+v[u].offset];if(q&&x>=v[u].low&&x<=v[u].high){if(v[u].remap&&v[u].remap[x]){x=q+v[u].remap[x]}else{x=x-v[u].low+q;if(v[u].add){x+=v[u].add}}if(p["variant"+v[u].offset]){p=this.FONTDATA.VARIANT[p["variant"+v[u].offset]]}break}}}if(p.remap&&p.remap[x]){if(p.remap[x] instanceof Array){var o=p.remap[x];x=o[0];p=this.FONTDATA.VARIANT[o[1]]}else{if(typeof(p.remap[x])==="string"){s=p.remap[x]+s.substr(B+1);B=0;y=s.length;x=s.charCodeAt(0)}else{x=p.remap[x];if(p.remap.variant){p=this.FONTDATA.VARIANT[p.remap.variant]}}}}if(this.FONTDATA.REMAP[x]&&!p.noRemap){x=this.FONTDATA.REMAP[x];if(x instanceof Array){p=this.FONTDATA.VARIANT[x[1]];x=x[0]}if(typeof(x)==="string"){s=x+s.substr(B+1);B=0;y=s.length;x=x.charCodeAt(0)}}t=this.lookupChar(p,x);C=t[x];if(l||(!this.checkFont(t,k.style)&&!C[5].img)){if(z.length){this.addText(k,z);z=""}var w=!!k.style.fontFamily||!!A.style.fontStyle||!!A.style.fontWeight||!t.directory||l;l=false;if(k!==A){w=!this.checkFont(t,A.style);k=A}if(w){k=this.addElement(A,"span",{isMathJax:true,subSpan:true})}this.handleFont(k,t,k!==A)}z=this.handleChar(k,t,C,x,z);if(!(C[5]||{}).space){if(C[0]/1000>A.bbox.h){A.bbox.h=C[0]/1000}if(C[1]/1000>A.bbox.d){A.bbox.d=C[1]/1000}}if(A.bbox.w+C[3]/1000<A.bbox.lw){A.bbox.lw=A.bbox.w+C[3]/1000}if(A.bbox.w+C[4]/1000>A.bbox.rw){A.bbox.rw=A.bbox.w+C[4]/1000}A.bbox.w+=C[2]/1000}if(z.length){this.addText(k,z)}if(A.scale&&A.scale!==1){A.bbox.h*=A.scale;A.bbox.d*=A.scale;A.bbox.w*=A.scale;A.bbox.lw*=A.scale;A.bbox.rw*=A.scale}if(s.length==1&&t.skew&&t.skew[x]){A.bbox.skew=t.skew[x]}},checkFont:function(k,l){var m=(l.fontWeight||"normal");if(m.match(/^\d+$/)){m=(parseInt(m)>=600?"bold":"normal")}return(k.family.replace(/'/g,"")===l.fontFamily.replace(/'/g,"")&&(k.style||"normal")===(l.fontStyle||"normal")&&(k.weight||"normal")===m)},handleFont:function(m,k,o){m.style.fontFamily=k.family;if(!k.directory){m.style.fontSize=Math.floor(100/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&k.isWebFont)){var l=k.style||"normal",n=k.weight||"normal";if(l!=="normal"||o){m.style.fontStyle=l}if(n!=="normal"||o){m.style.fontWeight=n}}},handleChar:function(l,k,s,r,q){var p=s[5];if(p.space){if(q.length){this.addText(l,q)}d.createShift(l,s[2]/1000);return""}if(p.img){return this.handleImg(l,k,s,r,q)}if(p.isUnknown&&this.FONTDATA.DELIMITERS[r]){if(q.length){this.addText(l,q)}var o=l.scale;d.createDelimiter(l,r,0,1,k);if(this.FONTDATA.DELIMITERS[r].dir==="V"){l.style.verticalAlign=this.Em(l.bbox.d);l.bbox.h+=l.bbox.d;l.bbox.d=0}l.scale=o;s[0]=l.bbox.h*1000;s[1]=l.bbox.d*1000;s[2]=l.bbox.w*1000;s[3]=l.bbox.lw*1000;s[4]=l.bbox.rw*1000;return""}if(p.c==null){if(r<=65535){p.c=String.fromCharCode(r)}else{var m=r-65536;p.c=String.fromCharCode((m>>10)+55296)+String.fromCharCode((m&1023)+56320)}}if(p.rfix){this.addText(l,q+p.c);d.createShift(l,p.rfix/1000);return""}if(s[2]||!this.msieAccentBug||q.length){return q+p.c}d.createShift(l,s[3]/1000);d.createShift(l,(s[4]-s[3])/1000);this.addText(l,p.c);d.createShift(l,-s[4]/1000);return""},handleImg:function(l,k,p,o,m){return m},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o<k;o++){if(r[q[o]]){p.FONTS.push(r[q[o]]);r[q[o]].name=q[o]}}}for(o=0,k=p.FONTS.length;o<k;o++){var l=p.FONTS[o];if(typeof(l)==="string"){delete p.FONTS;this.loadFont(l)}if(l[s]){if(l[s].length===5){l[s][5]={}}if(d.allowWebFonts&&!l.available){this.loadWebFont(l)}else{return l}}else{this.findBlock(l,s)}}return this.unknownChar(p,s)},unknownChar:function(k,m){var l=(k.defaultFont||{family:d.config.undefinedFamily});if(k.bold){l.weight="bold"}if(k.italic){l.style="italic"}if(!l[m]){l[m]=[800,200,500,0,500,{isUnknown:true}]}b.signal.Post(["HTML-CSS Jax - unknown char",m,k]);return l},findBlock:function(l,q){if(l.Ranges){for(var p=0,k=l.Ranges.length;p<k;p++){if(q<l.Ranges[p][0]){return}if(q<=l.Ranges[p][1]){var o=l.Ranges[p][2];for(var n=l.Ranges.length-1;n>=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(l){var k=MathJax.Callback.Queue();k.Push(["Require",h,this.fontDir+"/"+l]);if(this.imgFonts){if(!MathJax.isPacked){l=l.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}k.Push(["Require",h,this.webfontDir+"/png/"+l])}b.RestartAfter(k.Push({}))},loadWebFont:function(k){k.available=k.isWebFont=true;if(d.FontFaceBug){k.family=k.name;if(d.msieFontCSSBug){k.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(k))},loadWebFontError:function(l,k){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");l.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");e(["WebFontNotAvailable","Web-Fonts not available -- using image fonts instead"],null,3000);h.Require(this.directory+"/imageFonts.js",k)}else{this.allowWebFonts=false;k()}},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:10000000,ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},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},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.1,min_rule_thickness:1.25},NBSP:"\u00A0",rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){g=MathJax.ElementJax.mml;g.mbase.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);if(this.type!="mrow"){o=this.HTMLhandleSize(o)}for(var l=0,k=this.data.length;l<k;l++){if(this.data[l]){this.data[l].toHTML(o)}}var q=this.HTMLcomputeBBox(o);var n=o.bbox.h,p=o.bbox.d;for(l=0,k=q.length;l<k;l++){q[l].HTMLstretchV(o,n,p)}if(q.length){this.HTMLcomputeBBox(o,true)}if(this.HTMLlineBreaks(o)){o=this.HTMLmultiline(o)}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLlineBreaks:function(){return false},HTMLmultiline:function(){g.mbase.HTMLautoloadFile("multiline")},HTMLcomputeBBox:function(q,p,o,k){if(o==null){o=0}if(k==null){k=this.data.length}var n=q.bbox={exactW:true},r=[];while(o<k){var l=this.data[o];if(!l){continue}if(!p&&l.HTMLcanStretch("Vertical")){r.push(l);l=(l.CoreMO()||l)}this.HTMLcombineBBoxes(l,n);o++}this.HTMLcleanBBox(n);return r},HTMLcombineBBoxes:function(k,l){if(l.w==null){this.HTMLemptyBBox(l)}var n=(k.bbox?k:k.HTMLspanElement());if(!n||!n.bbox){return}var m=n.bbox;if(m.d>l.d){l.d=m.d}if(m.h>l.h){l.h=m.h}if(m.D!=null&&m.D>l.D){l.D=m.D}if(m.H!=null&&m.H>l.H){l.H=m.H}if(n.style.paddingLeft){l.w+=d.unEm(n.style.paddingLeft)*(n.scale||1)}if(l.w+m.lw<l.lw){l.lw=l.w+m.lw}if(l.w+m.rw>l.rw){l.rw=l.w+m.rw}l.w+=m.w;if(n.style.paddingRight){l.w+=d.unEm(n.style.paddingRight)*(n.scale||1)}if(m.width){l.width=m.width;l.minWidth=m.minWidth}if(m.ic){l.ic=m.ic}else{delete l.ic}if(l.exactW&&!m.exactW){delete l.exactW}},HTMLemptyBBox:function(k){k.h=k.d=k.H=k.D=k.rw=-d.BIGDIMEN;k.w=0;k.lw=d.BIGDIMEN;return k},HTMLcleanBBox:function(k){if(k.h===this.BIGDIMEN){k.h=k.d=k.H=k.D=k.w=k.rw=k.lw=0}if(k.D<=k.d){delete k.D}if(k.H<=k.h){delete k.H}},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(l){if(this.isEmbellished()){var k=this.Core();if(k&&k!==this){return k.HTMLcanStretch(l)}}return false},HTMLstretchH:function(l,k){return this.HTMLspanElement()},HTMLstretchV:function(l,k,m){return this.HTMLspanElement()},HTMLnotEmpty:function(k){while(k){if((k.type!=="mrow"&&k.type!=="texatom")||k.data.length>1){return true}k=k.data[0]}return false},HTMLmeasureChild:function(l,k){if(this.data[l]){d.Measured(this.data[l].toHTML(k),k)}else{k.bbox=this.HTMLzeroBBox()}},HTMLboxChild:function(l,k){if(!this.data[l]){this.SetData(l,g.mrow())}return this.data[l].toHTML(k)},HTMLcreateSpan:function(k){if(this.spanID){var l=this.HTMLspanElement();if(l&&(l.parentNode===k||(l.parentNode||{}).parentNode===k)){while(l.firstChild){l.removeChild(l.firstChild)}l.bbox=this.HTMLzeroBBox();l.scale=1;l.isMultChar=l.HH=null;l.style.cssText="";return l}}if(this.href){k=d.addElement(k,"a",{href:this.href,isMathJax:true})}k=d.addElement(k,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){k.style.display="inline-block"}if(this["class"]){k.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}k.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;k.bbox=this.HTMLzeroBBox();this.styles={};if(this.style){k.style.cssText=this.style;if(k.style.fontSize){this.mathsize=k.style.fontSize;k.style.fontSize=""}this.styles={border:d.getBorders(k),padding:d.getPadding(k)};if(this.styles.border){k.style.border=""}if(this.styles.padding){k.style.padding=""}}if(this.href){k.parentNode.bbox=k.bbox}return k},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+d.idPostfix)},HTMLhandleVariant:function(l,k,m){d.handleVariant(l,k,m)},HTMLhandleSize:function(k){if(!k.scale){k.scale=this.HTMLgetScale();if(k.scale!==1){k.style.fontSize=d.Percent(k.scale)}}return k},HTMLhandleDir:function(l){var k=this.Get("dir",true);if(k){l.dir=k}return l},HTMLhandleColor:function(w){var y=this.getValues("mathcolor","color");if(this.mathbackground){y.mathbackground=this.mathbackground}if(this.background){y.background=this.background}if(this.style&&w.style.backgroundColor){y.mathbackground=w.style.backgroundColor;w.style.backgroundColor="transparent"}var t=(this.styles||{}).border,v=(this.styles||{}).padding;if(y.color&&!this.mathcolor){y.mathcolor=y.color}if(y.background&&!this.mathbackground){y.mathbackground=y.background}if(y.mathcolor){w.style.color=y.mathcolor}if((y.mathbackground&&y.mathbackground!==g.COLOR.TRANSPARENT)||t||v){var A=w.bbox,z=(A.exact?0:1/d.em),u=0,s=0,m=w.style.paddingLeft,q=w.style.paddingRight;if(this.isToken){u=A.lw;s=A.rw-A.w}if(m!==""){u+=d.unEm(m)*(w.scale||1)}if(q!==""){s-=d.unEm(q)*(w.scale||1)}var l=(d.PaddingWidthBug||A.keepPadding||A.exactW?0:s-u);var o=Math.max(0,d.getW(w)+l);var x=A.h+A.d,k=-A.d,r=0,p=0;if(o>0){o+=2*z;u-=z}if(x>0){x+=2*z;k-=z}s=-o-u;if(t){s-=t.right;k-=t.bottom;r+=t.left;p+=t.right;A.h+=t.top;A.d+=t.bottom;A.w+=t.left+t.right;A.lw-=t.left;A.rw+=t.right}if(v){x+=v.top+v.bottom;o+=v.left+v.right;s-=v.right;k-=v.bottom;r+=v.left;p+=v.right;A.h+=v.top;A.d+=v.bottom;A.w+=v.left+v.right;A.lw-=v.left;A.rw+=v.right}if(p){w.style.paddingRight=d.Em(p)}var n=d.Element("span",{id:"MathJax-Color-"+this.spanID+d.idPostfix,isMathJax:true,style:{display:"inline-block",backgroundColor:y.mathbackground,width:d.Em(o),height:d.Em(x),verticalAlign:d.Em(k),marginLeft:d.Em(u),marginRight:d.Em(s)}});d.setBorders(n,t);if(A.width){n.style.width=A.width;n.style.marginRight="-"+A.width}if(d.msieInlineBlockAlignBug){n.style.position="relative";n.style.width=n.style.height=0;n.style.verticalAlign=n.style.marginLeft=n.style.marginRight="";n.style.border=n.style.padding="";if(t&&d.msieBorderWidthBug){x+=t.top+t.bottom;o+=t.left+t.right}n.style.width=d.Em(r+z);d.placeBox(d.addElement(n,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:(y.mathbackground||"transparent"),width:d.Em(o),height:d.Em(x)}}),u,A.h+z);d.setBorders(n.firstChild,t)}w.parentNode.insertBefore(n,w);if(d.msieColorPositionBug){w.style.position="relative"}return n}return null},HTMLremoveColor:function(){var k=document.getElementById("MathJax-Color-"+this.spanID+d.idPostfix);if(k){k.parentNode.removeChild(k)}},HTMLhandleSpace:function(o){if(this.useMMLspacing){if(this.type!=="mo"){return}var m=this.getValues("scriptlevel","lspace","rspace");if(m.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var l=this.HTMLgetMu(o);m.lspace=Math.max(0,d.length2em(m.lspace,l));m.rspace=Math.max(0,d.length2em(m.rspace,l));var k=this,n=this.Parent();while(n&&n.isEmbellished()&&n.Core()===k){k=n;n=n.Parent();o=k.HTMLspanElement()}if(m.lspace){o.style.paddingLeft=d.Em(m.lspace)}if(m.rspace){o.style.paddingRight=d.Em(m.rspace)}}}else{var p=this.texSpacing();if(p!==""){p=d.length2em(p,this.HTMLgetScale())/(o.scale||1);if(o.style.paddingLeft){p+=d.unEm(o.style.paddingLeft)}o.style.paddingLeft=d.Em(p)}}},HTMLgetScale:function(){var m=1,k=this.getValues("mathsize","scriptlevel","fontsize");if(this.style){var l=this.HTMLspanElement();if(l.style.fontSize!=""){k.fontsize=l.style.fontSize}}if(k.fontsize&&!this.mathsize){k.mathsize=k.fontsize}if(k.scriptlevel!==0){if(k.scriptlevel>2){k.scriptlevel=2}m=Math.pow(this.Get("scriptsizemultiplier"),k.scriptlevel);k.scriptminsize=d.length2em(this.Get("scriptminsize"));if(m<k.scriptminsize){m=k.scriptminsize}}if(this.isToken){m*=d.length2em(k.mathsize)}return m},HTMLgetMu:function(m){var k=1,l=this.getValues("scriptlevel","scriptsizemultiplier");if(m.scale&&m.scale!==1){k=1/m.scale}if(l.scriptlevel!==0){if(l.scriptlevel>2){l.scriptlevel=2}k=Math.sqrt(Math.pow(l.scriptsizemultiplier,l.scriptlevel))}return k},HTMLgetVariant:function(){var k=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");k.hasVariant=this.Get("mathvariant",true);if(!k.hasVariant){k.family=k.fontfamily;k.weight=k.fontweight;k.style=k.fontstyle}if(this.style){var m=this.HTMLspanElement();if(!k.family&&m.style.fontFamily){k.family=m.style.fontFamily}if(!k.weight&&m.style.fontWeight){k.weight=m.style.fontWeight}if(!k.style&&m.style.fontStyle){k.style=m.style.fontStyle}}if(k.weight&&k.weight.match(/^\d+$/)){k.weight=(parseInt(k.weight)>600?"bold":"normal")}var l=k.mathvariant;if(this.variantForm){l="-"+d.fontInUse+"-variant"}if(k.family&&!k.hasVariant){if(!k.weight&&k.mathvariant.match(/bold/)){k.weight="bold"}if(!k.style&&k.mathvariant.match(/italic/)){k.style="italic"}return{FONTS:[],fonts:[],noRemap:true,defaultFont:{family:k.family,style:k.style,weight:k.weight}}}if(k.weight==="bold"){l={normal:g.VARIANT.BOLD,italic:g.VARIANT.BOLDITALIC,fraktur:g.VARIANT.BOLDFRAKTUR,script:g.VARIANT.BOLDSCRIPT,"sans-serif":g.VARIANT.BOLDSANSSERIF,"sans-serif-italic":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.weight==="normal"){l={bold:g.VARIANT.normal,"bold-italic":g.VARIANT.ITALIC,"bold-fraktur":g.VARIANT.FRAKTUR,"bold-script":g.VARIANT.SCRIPT,"bold-sans-serif":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.SANSSERIFITALIC}[l]||l}}if(k.style==="italic"){l={normal:g.VARIANT.ITALIC,bold:g.VARIANT.BOLDITALIC,"sans-serif":g.VARIANT.SANSSERIFITALIC,"bold-sans-serif":g.VARIANT.SANSSERIFBOLDITALIC}[l]||l}else{if(k.style==="normal"){l={italic:g.VARIANT.NORMAL,"bold-italic":g.VARIANT.BOLD,"sans-serif-italic":g.VARIANT.SANSSERIF,"sans-serif-bold-italic":g.VARIANT.BOLDSANSSERIF}[l]||l}}if(!(l in d.FONTDATA.VARIANT)){l="normal"}return d.FONTDATA.VARIANT[l]}},{HTMLautoload:function(){var k=d.autoloadDir+"/"+this.type+".js";b.RestartAfter(h.Require(k))},HTMLautoloadFile:function(k){var l=d.autoloadDir+"/"+k+".js";b.RestartAfter(h.Require(l))},HTMLstretchH:function(l,k){this.HTMLremoveColor();return this.toHTML(l,k)},HTMLstretchV:function(l,k,m){this.HTMLremoveColor();return this.toHTML(l,k,m)}});g.chars.Augment({toHTML:function(n,m,l,o){var r=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(100/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.entity.Augment({toHTML:function(n,m,l,o){var r=this.toString().replace(/[\u2061-\u2064]/g,"");if(l){r=l(r,o)}if(m.fontInherit){var q=Math.floor(100/d.scale+0.5)+"%";d.addElement(n,"span",{style:{"font-size":q}},[r]);if(m.bold){n.lastChild.style.fontWeight="bold"}if(m.italic){n.lastChild.style.fontStyle="italic"}var p=d.getHD(n),k=d.getW(n);n.bbox={h:p.h,d:p.d,w:k,lw:0,rw:k,exactW:true}}else{this.HTMLhandleVariant(n,m,r)}}});g.mi.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;l<k;l++){if(this.data[l]){this.data[l].toHTML(o,n)}}if(!o.bbox){o.bbox=this.HTMLzeroBBox()}var q=this.data.join(""),p=o.bbox;if(p.skew&&q.length!==1){delete p.skew}if(p.rw>p.w&&q.length===1&&!n.noIC){p.ic=p.rw-p.w;d.createBlank(o,p.ic);p.w=p.rw}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.mn.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));o.bbox=null;var n=this.HTMLgetVariant();for(var l=0,k=this.data.length;l<k;l++){if(this.data[l]){this.data[l].toHTML(o,n)}}if(!o.bbox){o.bbox=this.HTMLzeroBBox()}if(this.data.join("").length!==1){delete o.bbox.skew}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.mo.Augment({toHTML:function(u){u=this.HTMLhandleSize(this.HTMLcreateSpan(u));if(this.data.length==0){return u}else{u.bbox=null}var x=this.data.join("");var q=this.HTMLgetVariant();var w=this.getValues("largeop","displaystyle");if(w.largeop){q=d.FONTDATA.VARIANT[w.displaystyle?"-largeOp":"-smallOp"]}var v=this.CoreParent(),o=(v&&v.isa(g.msubsup)&&this!==v.data[v.base]),l=(o?this.HTMLremapChars:null);if(x.length===1&&v&&v.isa(g.munderover)&&this.CoreText(v.data[v.base]).length===1){var s=v.data[v.over],t=v.data[v.under];if(s&&this===s.CoreMO()&&v.Get("accent")){l=d.FONTDATA.REMAPACCENT}else{if(t&&this===t.CoreMO()&&v.Get("accentunder")){l=d.FONTDATA.REMAPACCENTUNDER}}}if(o&&x.match(/['`"\u00B4\u2032-\u2037\u2057]/)){q=d.FONTDATA.VARIANT["-"+d.fontInUse+"-variant"]}for(var r=0,n=this.data.length;r<n;r++){if(this.data[r]){this.data[r].toHTML(u,q,this.HTMLremap,l)}}if(!u.bbox){u.bbox=this.HTMLzeroBBox()}if(x.length!==1){delete u.bbox.skew}if(d.AccentBug&&u.bbox.w===0&&x.length===1&&u.firstChild){u.firstChild.nodeValue+=d.NBSP;d.createSpace(u,0,0,-u.offsetWidth/d.em)}if(w.largeop){var k=(u.bbox.h-u.bbox.d)/2-d.TeX.axis_height*u.scale;if(d.safariVerticalAlignBug&&u.lastChild.nodeName==="IMG"){u.lastChild.style.verticalAlign=d.Em(d.unEm(u.lastChild.style.verticalAlign||0)/d.em-k/u.scale)}else{if(d.konquerorVerticalAlignBug&&u.lastChild.nodeName==="IMG"){u.style.position="relative";u.lastChild.style.position="relative";u.lastChild.style.top=d.Em(k/u.scale)}else{u.style.verticalAlign=d.Em(-k/u.scale)}}u.bbox.h-=k;u.bbox.d+=k;if(u.bbox.rw>u.bbox.w){u.bbox.ic=u.bbox.rw-u.bbox.w;d.createBlank(u,u.bbox.ic);u.bbox.w=u.bbox.rw}}this.HTMLhandleSpace(u);this.HTMLhandleColor(u);this.HTMLhandleDir(u);return u},CoreParent:function(){var k=this;while(k&&k.isEmbellished()&&k.CoreMO()===this&&!k.isa(g.math)){k=k.Parent()}return k},CoreText:function(k){if(!k){return""}if(k.isEmbellished()){return k.CoreMO().data.join("")}while((k.isa(g.mrow)||k.isa(g.TeXAtom)||k.isa(g.mstyle)||k.isa(g.mphantom))&&k.data.length===1&&k.data[0]){k=k.data[0]}if(!k.isToken){return""}else{return k.data.join("")}},HTMLremapChars:{"*":"\u2217",'"':"\u2033","\u00B0":"\u2218","\u00B2":"2","\u00B3":"3","\u00B4":"\u2032","\u00B9":"1"},HTMLremap:function(l,k){l=l.replace(/-/g,"\u2212");if(k){l=l.replace(/'/g,"\u2032").replace(/`/g,"\u2035");if(l.length===1){l=k[l]||l}}return l},HTMLcanStretch:function(n){if(!this.Get("stretchy")){return false}var o=this.data.join("");if(o.length>1){return false}var l=this.CoreParent();if(l&&l.isa(g.munderover)&&this.CoreText(l.data[l.base]).length===1){var m=l.data[l.over],k=l.data[l.under];if(m&&this===m.CoreMO()&&l.Get("accent")){o=d.FONTDATA.REMAPACCENT[o]||o}else{if(k&&this===k.CoreMO()&&l.Get("accentunder")){o=d.FONTDATA.REMAPACCENTUNDER[o]||o}}}o=d.FONTDATA.DELIMITERS[o.charCodeAt(0)];return(o&&o.dir==n.substr(0,1))},HTMLstretchV:function(m,n,o){this.HTMLremoveColor();var r=this.getValues("symmetric","maxsize","minsize");var p=this.HTMLspanElement(),s=this.HTMLgetMu(p),q;var k=d.TeX.axis_height,l=p.scale;if(r.symmetric){q=2*Math.max(n-k,o+k)}else{q=n+o}r.maxsize=d.length2em(r.maxsize,s,p.bbox.h+p.bbox.d);r.minsize=d.length2em(r.minsize,s,p.bbox.h+p.bbox.d);q=Math.max(r.minsize,Math.min(r.maxsize,q));p=this.HTMLcreateSpan(m);d.createDelimiter(p,this.data.join("").charCodeAt(0),q,l);if(r.symmetric){q=(p.bbox.h+p.bbox.d)/2+k}else{q=(p.bbox.h+p.bbox.d)*n/(n+o)}d.positionDelimiter(p,q);this.HTMLhandleSpace(p);this.HTMLhandleColor(p);return p},HTMLstretchH:function(o,k){this.HTMLremoveColor();var m=this.getValues("maxsize","minsize","mathvariant","fontweight");if((m.fontweight==="bold"||parseInt(m.fontweight)>=600)&&!this.Get("mathvariant",true)){m.mathvariant=g.VARIANT.BOLD}var n=this.HTMLspanElement(),l=this.HTMLgetMu(n),p=n.scale;m.maxsize=d.length2em(m.maxsize,l,n.bbox.w);m.minsize=d.length2em(m.minsize,l,n.bbox.w);k=Math.max(m.minsize,Math.min(m.maxsize,k));n=this.HTMLcreateSpan(o);d.createDelimiter(n,this.data.join("").charCodeAt(0),k,p,m.mathvariant);this.HTMLhandleSpace(n);this.HTMLhandleColor(n);return n}});g.mtext.Augment({toHTML:function(o){o=this.HTMLhandleSize(this.HTMLcreateSpan(o));var n=this.HTMLgetVariant();if(d.config.mtextFontInherit||this.Parent().type==="merror"){n={bold:n.bold,italic:n.italic,fontInherit:true}}for(var l=0,k=this.data.length;l<k;l++){if(this.data[l]){this.data[l].toHTML(o,n)}}if(!o.bbox){o.bbox=this.HTMLzeroBBox()}if(this.data.join("").length!==1){delete o.bbox.skew}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.merror.Augment({toHTML:function(l){var n=MathJax.HTML.addElement(l,"span",{style:{display:"inline-block"}});l=this.SUPER(arguments).toHTML.call(this,n);var m=d.getHD(n),k=d.getW(n);n.bbox={h:m.h,d:m.d,w:k,lw:0,rw:k,exactW:true};n.id=l.id;l.id=null;return n}});g.ms.Augment({toHTML:g.mbase.HTMLautoload});g.mglyph.Augment({toHTML:g.mbase.HTMLautoload});g.mspace.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);var m=this.getValues("height","depth","width");var l=this.HTMLgetMu(o);m.mathbackground=this.mathbackground;if(this.background&&!this.mathbackground){m.mathbackground=this.background}var n=d.length2em(m.height,l),p=d.length2em(m.depth,l),k=d.length2em(m.width,l);d.createSpace(o,n,p,k,m.mathbackground,true);return o}});g.mphantom.Augment({toHTML:function(o,l,q){o=this.HTMLcreateSpan(o);if(this.data[0]!=null){var p=this.data[0].toHTML(o);if(q!=null){d.Remeasured(this.data[0].HTMLstretchV(o,l,q),o)}else{if(l!=null){d.Remeasured(this.data[0].HTMLstretchH(o,l),o)}else{p=d.Measured(p,o)}}o.bbox={w:p.bbox.w,h:p.bbox.h,d:p.bbox.d,lw:0,rw:0,exactW:true};for(var n=0,k=o.childNodes.length;n<k;n++){o.childNodes[n].style.visibility="hidden"}}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mpadded.Augment({toHTML:function(s,m,k){s=this.HTMLcreateSpan(s);if(this.data[0]!=null){var q=d.createStack(s,true);var n=d.createBox(q);var l=this.data[0].toHTML(n);if(k!=null){d.Remeasured(this.data[0].HTMLstretchV(n,m,k),n)}else{if(m!=null){d.Remeasured(this.data[0].HTMLstretchH(n,m),n)}else{d.Measured(l,n)}}var t=this.getValues("height","depth","width","lspace","voffset"),r=0,p=0,u=this.HTMLgetMu(s);if(t.lspace){r=this.HTMLlength2em(n,t.lspace,u)}if(t.voffset){p=this.HTMLlength2em(n,t.voffset,u)}d.placeBox(n,r,p);s.bbox={h:n.bbox.h,d:n.bbox.d,w:n.bbox.w,exactW:true,lw:Math.min(0,n.bbox.lw+r),rw:Math.max(n.bbox.w,n.bbox.rw+r),H:Math.max((n.bbox.H==null?-d.BIGDIMEN:n.bbox.H),n.bbox.h+p),D:Math.max((n.bbox.D==null?-d.BIGDIMEN:n.bbox.D),n.bbox.d-p)};if(t.height!==""){s.bbox.h=this.HTMLlength2em(n,t.height,u,"h",0)}if(t.depth!==""){s.bbox.d=this.HTMLlength2em(n,t.depth,u,"d",0)}if(t.width!==""){s.bbox.w=this.HTMLlength2em(n,t.width,u,"w",0)}if(s.bbox.H<=s.bbox.h){delete s.bbox.H}if(s.bbox.D<=s.bbox.d){delete s.bbox.D}var o=/^\s*(\d+(\.\d*)?|\.\d+)\s*(pt|em|ex|mu|px|pc|in|mm|cm)\s*$/;s.bbox.exact=!!((this.data[0]&&this.data[0].data.length==0)||o.exec(t.height)||o.exec(t.width)||o.exec(t.depth));d.setStackWidth(q,s.bbox.w)}this.HTMLhandleSpace(s);this.HTMLhandleColor(s);return s},HTMLlength2em:function(q,r,l,s,k){if(k==null){k=-d.BIGDIMEN}var o=String(r).match(/width|height|depth/);var p=(o?q.bbox[o[0].charAt(0)]:(s?q.bbox[s]:0));var n=d.length2em(r,l,p);if(s&&String(r).match(/^\s*[-+]/)){return Math.max(k,q.bbox[s]+n)}else{return n}},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mrow.Augment({HTMLlineBreaks:function(k){if(!this.parent.linebreakContainer){return false}return(d.config.linebreaks.automatic&&k.bbox.w>d.linebreakWidth)||this.hasNewline()},HTMLstretchH:function(m,k){this.HTMLremoveColor();var l=this.HTMLspanElement();this.data[this.core].HTMLstretchH(l,k);this.HTMLcomputeBBox(l,true);this.HTMLhandleColor(l);return l},HTMLstretchV:function(m,l,n){this.HTMLremoveColor();var k=this.HTMLspanElement();this.data[this.core].HTMLstretchV(k,l,n);this.HTMLcomputeBBox(k,true);this.HTMLhandleColor(k);return k}});g.mstyle.Augment({toHTML:function(l,k,m){l=this.HTMLcreateSpan(l);if(this.data[0]!=null){var n=this.data[0].toHTML(l);if(m!=null){this.data[0].HTMLstretchV(l,k,m)}else{if(k!=null){this.data[0].HTMLstretchH(l,k)}}l.bbox=n.bbox}this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mfrac.Augment({toHTML:function(D){D=this.HTMLcreateSpan(D);var m=d.createStack(D);var r=d.createBox(m),o=d.createBox(m);d.MeasureSpans([this.HTMLboxChild(0,r),this.HTMLboxChild(1,o)]);var k=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled");var I=this.HTMLgetScale(),C=k.displaystyle;var G=d.TeX.axis_height*I;if(k.bevelled){var F=(C?0.4:0.15);var s=Math.max(r.bbox.h+r.bbox.d,o.bbox.h+o.bbox.d)+2*F;var E=d.createBox(m);d.createDelimiter(E,47,s);d.placeBox(r,0,(r.bbox.d-r.bbox.h)/2+G+F);d.placeBox(E,r.bbox.w-F/2,(E.bbox.d-E.bbox.h)/2+G);d.placeBox(o,r.bbox.w+E.bbox.w-F,(o.bbox.d-o.bbox.h)/2+G-F)}else{var l=Math.max(r.bbox.w,o.bbox.w);var y=d.thickness2em(k.linethickness,I),A,z,x,w;var B=d.TeX.min_rule_thickness/this.em;if(C){x=d.TeX.num1;w=d.TeX.denom1}else{x=(y===0?d.TeX.num3:d.TeX.num2);w=d.TeX.denom2}x*=I;w*=I;if(y===0){A=Math.max((C?7:3)*d.TeX.rule_thickness,2*B);z=(x-r.bbox.d)-(o.bbox.h-w);if(z<A){x+=(A-z)/2;w+=(A-z)/2}}else{A=Math.max((C?2:0)*B+y,y/2+1.5*B);z=(x-r.bbox.d)-(G+y/2);if(z<A){x+=A-z}z=(G-y/2)-(o.bbox.h-w);if(z<A){w+=A-z}var n=d.createBox(m);d.createRule(n,y,0,l+2*y);d.placeBox(n,0,G-y/2)}d.alignBox(r,k.numalign,x);d.alignBox(o,k.denomalign,-w)}this.HTMLhandleSpace(D);this.HTMLhandleColor(D);return D},HTMLcanStretch:function(k){return false},HTMLhandleSpace:function(k){if(!this.texWithDelims){var l=(this.useMMLspacing?0:d.length2em(this.texSpacing()||0))+0.12;k.style.paddingLeft=d.Em(l);k.style.paddingRight=d.Em(0.12)}}});g.msqrt.Augment({toHTML:function(w){w=this.HTMLcreateSpan(w);var z=d.createStack(w);var n=d.createBox(z),u=d.createBox(z),s=d.createBox(z);var r=this.HTMLgetScale();var A=d.TeX.rule_thickness*r,m,l,y,o;if(this.Get("displaystyle")){m=d.TeX.x_height*r}else{m=A}l=Math.max(A+m/4,1.5*d.TeX.min_rule_thickness/this.em);var k=this.HTMLboxChild(0,n);y=k.bbox.h+k.bbox.d+l+A;d.createDelimiter(s,8730,y,r);d.MeasureSpans([k,s]);o=k.bbox.w;var v=0;if(s.isMultiChar||(d.AdjustSurd&&d.imgFonts)){s.bbox.w*=0.95}if(s.bbox.h+s.bbox.d>y){l=((s.bbox.h+s.bbox.d)-(y-A))/2}var B=d.FONTDATA.DELIMITERS[d.FONTDATA.RULECHAR];if(!B||o<B.HW[0][0]*r||r<0.75){d.createRule(u,0,A,o)}else{d.createDelimiter(u,d.FONTDATA.RULECHAR,o,r)}y=k.bbox.h+l+A;l=y*d.rfuzz;if(s.isMultiChar){l=d.rfuzz}v=this.HTMLaddRoot(z,s,v,s.bbox.h+s.bbox.d-y,r);d.placeBox(s,v,y-s.bbox.h);d.placeBox(u,v+s.bbox.w,y-u.bbox.h+l);d.placeBox(n,v+s.bbox.w,0);this.HTMLhandleSpace(w);this.HTMLhandleColor(w);return w},HTMLaddRoot:function(m,l,k,o,n){return k}});g.mroot.Augment({toHTML:g.msqrt.prototype.toHTML,HTMLaddRoot:function(s,l,q,o,k){var m=d.createBox(s);if(this.data[1]){var p=this.data[1].toHTML(m);p.style.paddingRight=p.style.paddingLeft="";d.Measured(p,m)}else{m.bbox=this.HTMLzeroBBox()}var n=this.HTMLrootHeight(l.bbox.h+l.bbox.d,k,m)-o;var r=Math.min(m.bbox.w,m.bbox.rw);q=Math.max(r,l.offset);d.placeBox(m,q-r,n);return q-l.offset},HTMLrootHeight:function(m,l,k){return 0.45*(m-0.9*l)+0.6*l+Math.max(0,k.bbox.d-0.075)}});g.mfenced.Augment({toHTML:function(o){o=this.HTMLcreateSpan(o);if(this.data.open){this.data.open.toHTML(o)}if(this.data[0]!=null){this.data[0].toHTML(o)}for(var l=1,k=this.data.length;l<k;l++){if(this.data[l]){if(this.data["sep"+l]){this.data["sep"+l].toHTML(o)}this.data[l].toHTML(o)}}if(this.data.close){this.data.close.toHTML(o)}var q=this.HTMLcomputeBBox(o);var n=o.bbox.h,p=o.bbox.d;for(l=0,k=q.length;l<k;l++){q[l].HTMLstretchV(o,n,p)}if(q.length){this.HTMLcomputeBBox(o,true)}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);return o},HTMLcomputeBBox:function(p,o){var l=p.bbox={},q=[];this.HTMLcheckStretchy(this.data.open,l,q,o);this.HTMLcheckStretchy(this.data[0],l,q,o);for(var n=1,k=this.data.length;n<k;n++){if(this.data[n]){this.HTMLcheckStretchy(this.data["sep"+n],l,q,o);this.HTMLcheckStretchy(this.data[n],l,q,o)}}this.HTMLcheckStretchy(this.data.close,l,q,o);this.HTMLcleanBBox(l);return q},HTMLcheckStretchy:function(k,l,n,m){if(k){if(!m&&k.HTMLcanStretch("Vertical")){n.push(k);k=(k.CoreMO()||k)}this.HTMLcombineBBoxes(k,l)}}});g.menclose.Augment({toHTML:g.mbase.HTMLautoload});g.maction.Augment({toHTML:g.mbase.HTMLautoload});g.semantics.Augment({toHTML:function(l,k,m){l=this.HTMLcreateSpan(l);if(this.data[0]!=null){var n=this.data[0].toHTML(l);if(m!=null){this.data[0].HTMLstretchV(l,k,m)}else{if(k!=null){this.data[0].HTMLstretchH(l,k)}}l.bbox=n.bbox}this.HTMLhandleSpace(l);return l},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.munderover.Augment({toHTML:function(L,H,F){var l=this.getValues("displaystyle","accent","accentunder","align");if(!l.displaystyle&&this.data[this.base]!=null&&this.data[this.base].CoreMO().Get("movablelimits")){return g.msubsup.prototype.toHTML.call(this,L)}L=this.HTMLcreateSpan(L);var P=this.HTMLgetScale();var q=d.createStack(L);var r=[],o=[],N=[],w,M,I;for(M=0,I=this.data.length;M<I;M++){if(this.data[M]!=null){w=r[M]=d.createBox(q);o[M]=this.data[M].toHTML(w);if(M==this.base){if(F!=null){this.data[this.base].HTMLstretchV(w,H,F)}else{if(H!=null){this.data[this.base].HTMLstretchH(w,H)}}N[M]=(F==null&&H!=null?false:this.data[M].HTMLcanStretch("Horizontal"))}else{N[M]=this.data[M].HTMLcanStretch("Horizontal")}}}d.MeasureSpans(o);var n=-d.BIGDIMEN,K=n;for(M=0,I=this.data.length;M<I;M++){if(this.data[M]){if(r[M].bbox.w>K){K=r[M].bbox.w}if(!N[M]&&K>n){n=K}}}if(F==null&&H!=null){n=H}else{if(n==-d.BIGDIMEN){n=K}}for(M=K=0,I=this.data.length;M<I;M++){if(this.data[M]){w=r[M];if(N[M]){w.bbox=this.data[M].HTMLstretchH(w,n).bbox}if(w.bbox.w>K){K=w.bbox.w}}}var E=d.TeX.rule_thickness,G=d.FONTDATA.TeX_factor;var p=r[this.base]||{bbox:this.HTMLzeroBBox()};var v,s,A,z,u,C,J,O=0;if(p.bbox.ic){O=1.3*p.bbox.ic+0.05}for(M=0,I=this.data.length;M<I;M++){if(this.data[M]!=null){w=r[M];u=d.TeX.big_op_spacing5*P;var B=(M!=this.base&&l[this.ACCENTS[M]]);if(B&&w.bbox.w<=1/d.em+0.0001){w.bbox.w=w.bbox.rw-w.bbox.lw;w.bbox.noclip=true;if(w.bbox.lw){w.insertBefore(d.createSpace(w.parentNode,0,0,-w.bbox.lw),w.firstChild)}d.createBlank(w,0,0,w.bbox.rw+0.1)}C={left:0,center:(K-w.bbox.w)/2,right:K-w.bbox.w}[l.align];v=C;s=0;if(M==this.over){if(B){J=Math.max(E*P*G,2.5/this.em);u=0;if(p.bbox.skew){v+=p.bbox.skew}}else{A=d.TeX.big_op_spacing1*P*G;z=d.TeX.big_op_spacing3*P*G;J=Math.max(A,z-Math.max(0,w.bbox.d))}J=Math.max(J,1.5/this.em);v+=O/2;s=p.bbox.h+w.bbox.d+J;w.bbox.h+=u}else{if(M==this.under){if(B){J=3*E*P*G;u=0}else{A=d.TeX.big_op_spacing2*P*G;z=d.TeX.big_op_spacing4*P*G;J=Math.max(A,z-w.bbox.h)}J=Math.max(J,1.5/this.em);v-=O/2;s=-(p.bbox.d+w.bbox.h+J);w.bbox.d+=u}}d.placeBox(w,v,s)}}this.HTMLhandleSpace(L);this.HTMLhandleColor(L);return L},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.msubsup.Augment({toHTML:function(K,I,C){K=this.HTMLcreateSpan(K);var N=this.HTMLgetScale(),H=this.HTMLgetMu(K);var w=d.createStack(K),l,n=[];var o=d.createBox(w);if(this.data[this.base]){n.push(this.data[this.base].toHTML(o));if(C!=null){this.data[this.base].HTMLstretchV(o,I,C)}else{if(I!=null){this.data[this.base].HTMLstretchH(o,I)}}}else{o.bbox=this.HTMLzeroBBox()}var L=d.TeX.x_height*N,B=d.TeX.scriptspace*N*0.75;var k,x;if(this.HTMLnotEmpty(this.data[this.sup])){k=d.createBox(w);n.push(this.data[this.sup].toHTML(k))}if(this.HTMLnotEmpty(this.data[this.sub])){x=d.createBox(w);n.push(this.data[this.sub].toHTML(x))}d.MeasureSpans(n);if(k){k.bbox.w+=B;k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw)}if(x){x.bbox.w+=B;x.bbox.rw=Math.max(x.bbox.w,x.bbox.rw)}d.placeBox(o,0,0);var m;if(k){m=this.data[this.sup].HTMLgetScale()}else{if(x){m=this.data[this.sub].HTMLgetScale()}else{m=this.HTMLgetScale()}}var F=d.TeX.sup_drop*m,E=d.TeX.sub_drop*m;var z=o.bbox.h-F,y=o.bbox.d+E,M=0,G;if(o.bbox.ic){o.bbox.w-=o.bbox.ic;M=1.3*o.bbox.ic+0.05}if(this.data[this.base]&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&o.bbox.scale===1&&!this.data[this.base].Get("largeop")){z=y=0}}var J=this.getValues("subscriptshift","superscriptshift");J.subscriptshift=(J.subscriptshift===""?0:d.length2em(J.subscriptshift,H));J.superscriptshift=(J.superscriptshift===""?0:d.length2em(J.superscriptshift,H));if(!k){if(x){y=Math.max(y,d.TeX.sub1*N,x.bbox.h-(4/5)*L,J.subscriptshift);d.placeBox(x,o.bbox.w,-y,x.bbox)}}else{if(!x){l=this.getValues("displaystyle","texprimestyle");G=d.TeX[(l.displaystyle?"sup1":(l.texprimestyle?"sup3":"sup2"))];z=Math.max(z,G*N,k.bbox.d+(1/4)*L,J.superscriptshift);d.placeBox(k,o.bbox.w+M,z,k.bbox)}else{y=Math.max(y,d.TeX.sub2*N);var A=d.TeX.rule_thickness*N;if((z-k.bbox.d)-(x.bbox.h-y)<3*A){y=3*A-z+k.bbox.d+x.bbox.h;F=(4/5)*L-(z-k.bbox.d);if(F>0){z+=F;y-=F}}d.placeBox(k,o.bbox.w+M,Math.max(z,J.superscriptshift));d.placeBox(x,o.bbox.w,-Math.max(y,J.subscriptshift))}}this.HTMLhandleSpace(K);this.HTMLhandleColor(K);return K},HTMLstretchH:g.mbase.HTMLstretchH,HTMLstretchV:g.mbase.HTMLstretchV});g.mmultiscripts.Augment({toHTML:g.mbase.HTMLautoload});g.mtable.Augment({toHTML:g.mbase.HTMLautoload});g["annotation-xml"].Augment({toHTML:g.mbase.HTMLautoload});g.math.Augment({toHTML:function(u,l){var r=this.Get("alttext");if(r&&r!==""){l.setAttribute("aria-label",r)}var m=d.addElement(u,"nobr",{isMathJax:true});u=this.HTMLcreateSpan(m);var s=d.createStack(u),n=d.createBox(s),t;s.style.fontSize=m.parentNode.style.fontSize;m.parentNode.style.fontSize="";if(this.data[0]!=null){if(d.msieColorBug){if(this.background){this.data[0].background=this.background;delete this.background}if(this.mathbackground){this.data[0].mathbackground=this.mathbackground;delete this.mathbackground}}g.mbase.prototype.displayAlign=b.config.displayAlign;g.mbase.prototype.displayIndent=b.config.displayIndent;var o=this.data[0].toHTML(n);o.bbox.exactW=false;t=d.Measured(o,n)}d.placeBox(n,0,0);u.style.width=d.Em((Math.round(t.bbox.w*this.em)+0.25)/d.outerEm);u.style.display="inline-block";var k=1/d.em,q=d.em/d.outerEm;d.em/=q;u.bbox.h*=q;u.bbox.d*=q;u.bbox.w*=q;u.bbox.lw*=q;u.bbox.rw*=q;if(t&&t.bbox.width!=null){u.style.minWidth=(t.bbox.minWidth||u.style.width);u.style.width=s.style.width=t.bbox.width;n.style.width="100%"}this.HTMLhandleColor(u);if(t){d.createRule(u,(t.bbox.h+k)*q,(t.bbox.d+k)*q,0)}if(!this.isMultiline&&this.Get("display")==="block"&&u.bbox.width==null){var v=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(v.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){v.indentalign=v.indentalignfirst}if(v.indentalign===g.INDENTALIGN.AUTO){v.indentalign=this.displayAlign}l.style.textAlign=v.indentalign;if(v.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){v.indentshift=v.indentshiftfirst}if(v.indentshift==="auto"){v.indentshift=this.displayIndent}if(v.indentshift&&v.indentalign!==g.INDENTALIGN.CENTER){u.style[{left:"marginLeft",right:"marginRight"}[v.indentalign]]=d.Em(d.length2em(v.indentshift))}}return u},HTMLspanElement:g.mbase.prototype.HTMLspanElement});g.TeXAtom.Augment({toHTML:function(l){l=this.HTMLcreateSpan(l);if(this.data[0]!=null){if(this.texClass===g.TEXCLASS.VCENTER){var k=d.createStack(l);var m=d.createBox(k);d.Measured(this.data[0].toHTML(m),m);d.placeBox(m,0,d.TeX.axis_height-(m.bbox.h+m.bbox.d)/2+m.bbox.d)}else{l.bbox=this.data[0].toHTML(l).bbox}}this.HTMLhandleSpace(l);this.HTMLhandleColor(l);return l}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(k){var o=(document.documentMode||0);var n=k.versionAtLeast("7.0");var m=k.versionAtLeast("8.0")&&o>7;var l=(document.compatMode==="BackCompat");if(o<9){d.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white";d.config.styles[".MathJax .MathJax_HitBox"].opacity=0;d.config.styles[".MathJax .MathJax_HitBox"].filter="alpha(opacity=0)"}d.Augment({PaddingWidthBug:true,msieAccentBug:true,msieColorBug:true,msieColorPositionBug:true,msieRelativeWidthBug:l,msieDisappearingBug:(o>=8),msieMarginScaleBug:(o<8),msiePaddingWidthBug:true,msieBorderWidthBug:l,msieFrameSizeBug:(o<=8),msieInlineBlockAlignBug:(!m||l),msiePlaceBoxBug:(m&&!l),msieClipRectBug:!m,msieNegativeSpaceBug:l,cloneNodeBug:(m&&k.version==="8.0"),initialSkipBug:(o<8),msieNegativeBBoxBug:(o>=8),msieIE6:!n,msieItalicWidthBug:true,FontFaceBug:true,msieFontCSSBug:k.isIE9,allowWebFonts:(o>=9?"woff":"eot")})},Firefox:function(l){var m=false;if(l.versionAtLeast("3.5")){var k=String(document.location).replace(/[^\/]*$/,"");if(document.location.protocol!=="file:"||b.config.root.match(/^https?:\/\//)||(b.config.root+"/").substr(0,k.length)===k){m="otf"}}d.Augment({ffVerticalAlignBug:true,AccentBug:true,allowWebFonts:m})},Safari:function(p){var n=p.versionAtLeast("3.0");var m=p.versionAtLeast("3.1");var k=navigator.appVersion.match(/ Safari\/\d/)&&navigator.appVersion.match(/ Version\/\d/)&&navigator.vendor.match(/Apple/);var l=(navigator.appVersion.match(/ Android (\d+)\.(\d+)/));var q=(m&&p.isMobile&&((navigator.platform.match(/iPad|iPod|iPhone/)&&!p.versionAtLeast("5.0"))||(l!=null&&(l[1]<2||(l[1]==2&&l[2]<2)))));d.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax a":{"max-width":"5000em","max-height":"5000em"}}},rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariVerticalAlignBug:!m,safariTextNodeBug:!n,forceReflow:true,allowWebFonts:(m&&!q?"otf":false)});if(k){d.Augment({webFontDefault:(p.isMobile?"sans-serif":"serif")})}if(p.isPC){d.Augment({adjustAvailableFonts:d.removeSTIXfonts,checkWebFontsTwice:true})}if(q){var o=b.config["HTML-CSS"];if(o){o.availableFonts=[];o.preferredFont=null}else{b.config["HTML-CSS"]={availableFonts:[],preferredFont:null}}}},Chrome:function(k){d.Augment({Em:d.EmRounded,cloneNodeBug:true,rfuzz:0.011,AccentBug:true,AdjustSurd:true,negativeBBoxes:true,safariNegativeSpaceBug:true,safariWebFontSerif:[""],forceReflow:true,allowWebFonts:(k.versionAtLeast("4.0")?"otf":"svg")})},Opera:function(k){k.isMini=(navigator.appVersion.match("Opera Mini")!=null);d.config.styles[".MathJax .merror"]["vertical-align"]=null;d.config.styles[".MathJax span"]["z-index"]=0;d.Augment({operaHeightBug:true,operaVerticalAlignBug:true,operaFontSizeBug:k.versionAtLeast("10.61"),initialSkipBug:true,FontFaceBug:true,PaddingWidthBug:true,allowWebFonts:(k.versionAtLeast("10.0")&&!k.isMini?"otf":false),adjustAvailableFonts:d.removeSTIXfonts})},Konqueror:function(k){d.Augment({konquerorVerticalAlignBug:true})}})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){h.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.OutputJax["HTML-CSS"]);
MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="2.3";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a.mtable.Augment({toHTML:function(t){t=this.HTMLcreateSpan(t);if(this.data.length===0){return t}var K=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");var aJ=K.width.match(/%$/);var ay=b.createStack(t);var aG=this.HTMLgetScale(),aA=this.HTMLgetMu(t),aB=-1;var aq=[],au=[],ak=[],aw=[],av=[],af,ae,ap=-1,ad,ao,Z,aF,R,aC,aO=[];var al=b.FONTDATA.baselineskip*aG*K.useHeight,aT,I=b.FONTDATA.lineH*aG,O=b.FONTDATA.lineD*aG;for(af=0,ad=this.data.length;af<ad;af++){aF=this.data[af];Z=(aF.type==="mlabeledtr"?aB:0);aw[af]=[];aq[af]=au[af]=0;for(ae=Z,ao=aF.data.length+Z;ae<ao;ae++){if(ak[ae]==null){if(ae>ap){ap=ae}av[ae]=b.createStack(b.createBox(ay));ak[ae]=-b.BIGDIMEN}aw[af][ae]=b.createBox(av[ae]);aO.push(aF.data[ae-Z].toHTML(aw[af][ae]))}}b.MeasureSpans(aO);for(af=0,ad=this.data.length;af<ad;af++){aF=this.data[af];Z=(aF.type==="mlabeledtr"?aB:0);for(ae=Z,ao=aF.data.length+Z;ae<ao;ae++){R=aF.data[ae-Z];if(R.isMultiline){aw[af][ae].style.width="100%"}if(R.isEmbellished()){aC=R.CoreMO();var aS=aC.Get("minsize",true);if(aS){var aL=aC.HTMLspanElement().bbox;if(aC.HTMLcanStretch("Vertical")){aT=aL.h+aL.d;if(aT){aS=b.length2em(aS,aA,aT);if(aS*aL.h/aT>aq[af]){aq[af]=aS*aL.h/aT}if(aS*aL.d/aT>au[af]){au[af]=aS*aL.d/aT}}}else{if(aC.HTMLcanStretch("Horizontal")){aS=b.length2em(aS,aA,aL.w);if(aS>ak[ae]){ak[ae]=aS}}}}}if(aw[af][ae].bbox.h>aq[af]){aq[af]=aw[af][ae].bbox.h}if(aw[af][ae].bbox.d>au[af]){au[af]=aw[af][ae].bbox.d}if(aw[af][ae].bbox.w>ak[ae]){ak[ae]=aw[af][ae].bbox.w}}}if(aq[0]+au[0]){aq[0]=Math.max(aq[0],I)}if(aq[aw.length-1]+au[aw.length-1]){au[aw.length-1]=Math.max(au[aw.length-1],O)}var aE=MathJax.Hub.SplitList;var az=aE(K.columnspacing),aQ=aE(K.rowspacing),e=aE(K.columnalign),E=aE(K.rowalign),d=aE(K.columnlines),z=aE(K.rowlines),aM=aE(K.columnwidth),V=[];for(af=0,ad=az.length;af<ad;af++){az[af]=b.length2em(az[af],aA)}for(af=0,ad=aQ.length;af<ad;af++){aQ[af]=b.length2em(aQ[af],aA)}while(az.length<ap){az.push(az[az.length-1])}while(e.length<=ap){e.push(e[e.length-1])}while(d.length<ap){d.push(d[d.length-1])}while(aM.length<=ap){aM.push(aM[aM.length-1])}while(aQ.length<aw.length){aQ.push(aQ[aQ.length-1])}while(E.length<=aw.length){E.push(E[E.length-1])}while(z.length<aw.length){z.push(z[z.length-1])}if(av[aB]){e[aB]=(K.side.substr(0,1)==="l"?"left":"right");az[aB]=-ak[aB]}for(af=0,ad=aw.length;af<ad;af++){aF=this.data[af];V[af]=[];if(aF.rowalign){E[af]=aF.rowalign}if(aF.columnalign){V[af]=aE(aF.columnalign);while(V[af].length<=ap){V[af].push(V[af][V[af].length-1])}}}if(K.equalrows){var aD=Math.max.apply(Math,aq),X=Math.max.apply(Math,au);for(af=0,ad=aw.length;af<ad;af++){Z=((aD+X)-(aq[af]+au[af]))/2;aq[af]+=Z;au[af]+=Z}}aT=aq[0]+au[aw.length-1];for(af=0,ad=aw.length-1;af<ad;af++){aT+=Math.max((aq[af]+au[af]?al:0),au[af]+aq[af+1]+aQ[af])}var aI=0,aH=0,aV,g=aT;if(K.frame!=="none"||(K.columnlines+K.rowlines).match(/solid|dashed/)){var w=aE(K.framespacing);if(w.length!=2){w=aE(this.defaults.framespacing)}aI=b.length2em(w[0],aA);aH=b.length2em(w[1],aA);g=aT+2*aH}var aj,aU,ab="";if(typeof(K.align)!=="string"){K.align=String(K.align)}if(K.align.match(/(top|bottom|center|baseline|axis)( +(-?\d+))?/)){ab=RegExp.$3;K.align=RegExp.$1}else{K.align=this.defaults.align}if(ab!==""){ab=parseInt(ab);if(ab<0){ab=aw.length+1+ab}if(ab<1){ab=1}else{if(ab>aw.length){ab=aw.length}}aj=0;aU=-(aT+aH)+aq[0];for(af=0,ad=ab-1;af<ad;af++){var N=Math.max((aq[af]+au[af]?al:0),au[af]+aq[af+1]+aQ[af]);aj+=N;aU+=N}}else{aj=({top:-(aq[0]+aH),bottom:aT+aH-aq[0],center:aT/2-aq[0],baseline:aT/2-aq[0],axis:aT/2+b.TeX.axis_height*aG-aq[0]})[K.align];aU=({top:-(aT+2*aH),bottom:0,center:-(aT/2+aH),baseline:-(aT/2+aH),axis:b.TeX.axis_height*aG-aT/2-aH})[K.align]}var ac,ag=0,B=0,L=0,aa=0,ah=0,an=[],at=[],S=1;if(K.equalcolumns&&K.width!=="auto"){if(aJ){ac=(100/(ap+1)).toFixed(2).replace(/\.?0+$/,"")+"%";for(af=0,ad=Math.min(ap+1,aM.length);af<ad;af++){aM[af]=ac}ac=0;ag=1;ah=ap+1;for(af=0,ad=Math.min(ap+1,az.length);af<ad;af++){ac+=az[af]}}else{ac=b.length2em(K.width,aA);for(af=0,ad=Math.min(ap+1,az.length);af<ad;af++){ac-=az[af]}ac/=ap+1;for(af=0,ad=Math.min(ap+1,aM.length);af<ad;af++){ak[af]=ac}}}else{for(af=0,ad=Math.min(ap+1,aM.length);af<ad;af++){if(aM[af]==="auto"){B+=ak[af]}else{if(aM[af]==="fit"){at[ah]=af;ah++;B+=ak[af]}else{if(aM[af].match(/%$/)){an[aa]=af;aa++;L+=ak[af];ag+=b.length2em(aM[af],aA,1)}else{ak[af]=b.length2em(aM[af],aA);B+=ak[af]}}}}if(aJ){ac=0;for(af=0,ad=Math.min(ap,az.length);af<ad;af++){ac+=az[af]}if(ag>0.98){S=0.98/ag;ag=0.98}}else{if(K.width==="auto"){if(ag>0.98){S=L/(B+L);ac=B+L}else{ac=B/(1-ag)}}else{ac=b.length2em(K.width,aA);for(af=0,ad=Math.min(ap+1,az.length);af<ad;af++){ac-=az[af]}}for(af=0,ad=an.length;af<ad;af++){ak[an[af]]=b.length2em(aM[an[af]],aA,ac*S);B+=ak[an[af]]}if(Math.abs(ac-B)>0.01){if(ah&&ac>B){ac=(ac-B)/ah;for(af=0,ad=at.length;af<ad;af++){ak[at[af]]+=ac}}else{ac=ac/B;for(ae=0;ae<=ap;ae++){ak[ae]*=ac}}}if(K.equalcolumns){var Q=Math.max.apply(Math,ak);for(ae=0;ae<=ap;ae++){ak[ae]=Q}}}}var T=aj,o,r,aR;Z=(av[aB]?aB:0);for(ae=Z;ae<=ap;ae++){for(af=0,ad=aw.length;af<ad;af++){if(aw[af][ae]){Z=(this.data[af].type==="mlabeledtr"?aB:0);R=this.data[af].data[ae-Z];if(R.HTMLcanStretch("Horizontal")){aw[af][ae].bbox=R.HTMLstretchH(av[ae],ak[ae]).bbox}else{if(R.HTMLcanStretch("Vertical")){aC=R.CoreMO();var aK=aC.symmetric;aC.symmetric=false;aw[af][ae].bbox=R.HTMLstretchV(av[ae],aq[af],au[af]).bbox;aw[af][ae].HH=null;aC.symmetric=aK}}aR=R.rowalign||this.data[af].rowalign||E[af];o=({top:aq[af]-aw[af][ae].bbox.h,bottom:aw[af][ae].bbox.d-au[af],center:((aq[af]-au[af])-(aw[af][ae].bbox.h-aw[af][ae].bbox.d))/2,baseline:0,axis:0})[aR]||0;aR=(R.columnalign||V[af][ae]||e[ae]);b.alignBox(aw[af][ae],aR,T+o)}if(af<aw.length-1){T-=Math.max((aq[af]+au[af]?al:0),au[af]+aq[af+1]+aQ[af])}}T=aj}if(aJ){var G=b.createBox(ay);G.style.left=G.style.top=0;G.style.right=b.Em(ac+2*aI);G.style.display="inline-block";G.style.height="0px";if(b.msieRelativeWidthBug){G=b.createBox(G);G.style.position="relative";G.style.height="1em";G.style.width="100%";G.bbox=ay.bbox}var aP=0,aW=aI,k,l;if(ah){k=100*(1-ag)/ah,l=B/ah}else{k=100*(1-ag)/(ap+1);l=B/(ap+1)}for(ae=0;ae<=ap;ae++){b.placeBox(av[ae].parentNode,0,0);av[ae].style.position="relative";av[ae].style.left=b.Em(aW);av[ae].style.width="100%";av[ae].parentNode.parentNode.removeChild(av[ae].parentNode);var am=b.createBox(G);b.addBox(am,av[ae]);av[ae]=am;var h=am.style;h.display="inline-block";h.left=aP+"%";if(aM[ae].match(/%$/)){var u=parseFloat(aM[ae])*S;if(ah===0){h.width=(k+u)+"%";aP+=k+u;am=b.createBox(am);b.addBox(am,av[ae].firstChild);am.style.left=0;am.style.right=b.Em(l);aW-=l}else{h.width=u+"%";aP+=u}}else{if(aM[ae]==="fit"||ah===0){h.width=k+"%";am=b.createBox(am);b.addBox(am,av[ae].firstChild);am.style.left=0;am.style.right=b.Em(l-ak[ae]);aW+=ak[ae]-l;aP+=k}else{h.width=b.Em(ak[ae]);aW+=ak[ae]}}if(b.msieRelativeWidthBug){b.addText(am.firstChild,b.NBSP);am.firstChild.style.position="relative"}aW+=az[ae];if(d[ae]!=="none"&&ae<ap&&ae!==aB){r=b.createBox(G);r.style.left=aP+"%";r=b.createRule(r,g,0,1.25/b.em);r.style.position="absolute";r.bbox={h:g,d:0,w:0,rw:1.25/b.em,lw:0};r.parentNode.bbox=ay.bbox;b.placeBox(r,aW-az[ae]/2,aU,true);r.style.borderStyle=d[ae]}}}else{var U=aI;for(ae=0;ae<=ap;ae++){if(!av[ae].bbox.width){b.setStackWidth(av[ae],ak[ae])}if(aM[ae]!=="auto"&&aM[ae]!=="fit"){av[ae].bbox.width=ak[ae];av[ae].bbox.isFixed=true}b.placeBox(av[ae].parentNode,U,0);U+=ak[ae]+az[ae];if(d[ae]!=="none"&&ae<ap&&ae!==aB){r=b.createRule(ay,g,0,1.25/b.em);b.addBox(ay,r);r.bbox={h:g,d:0,w:0,rw:1.25/b.em,lw:0};b.placeBox(r,U-az[ae]/2,aU,true);r.style.borderStyle=d[ae]}}}ay.bbox.d=-aU;ay.bbox.h=g+aU;b.setStackWidth(ay,ay.bbox.w+aI);aV=ay.bbox.w;var ai;if(K.frame!=="none"){ai=b.createFrame(ay,g,0,aV,1.25/b.em,K.frame);b.addBox(ay,ai);b.placeBox(ai,0,aU,true);if(aJ){ai.style.width="100%"}}T=aj;for(af=0,ad=aw.length-1;af<ad;af++){o=Math.max(al,au[af]+aq[af+1]+aQ[af]);if(z[af]!=="none"){r=b.createRule(ay,1.25/b.em,0,aV);b.addBox(ay,r);r.bbox={h:1.25/b.em,d:0,w:aV,rw:aV,lw:0};b.placeBox(r,0,T-au[af]-(o-au[af]-aq[af+1])/2,true);if(z[af]==="dashed"||aJ){r.style.borderTop=r.style.height+" "+z[af];r.style.height=0;r.style.width=r.style.borderLeftWidth;r.style.borderLeft="";if(aJ){r.style.width="100%"}}}T-=o}if(aJ){t.bbox.width=K.width;ay.style.width="100%"}if(av[aB]){var ax=ay.bbox.w,q;var ar=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(ar.indentalignfirst!==a.INDENTALIGN.INDENTALIGN){ar.indentalign=ar.indentalignfirst}if(ar.indentalign===a.INDENTALIGN.AUTO){ar.indentalign=this.displayAlign}if(ar.indentshiftfirst!==a.INDENTSHIFT.INDENTSHIFT){ar.indentshift=ar.indentshiftfirst}if(ar.indentshift==="auto"){ar.indentshift=this.displayIndent}var aN=b.createStack(t,false,"100%");b.addBox(aN,ay);b.alignBox(ay,ar.indentalign,0);if(ar.indentshift&&ar.indentalign!==a.INDENTALIGN.CENTER){q=b.length2em(ar.indentshift,aA);ax+=q;ay.style[ar.indentalign]=b.Em(q)}av[aB].parentNode.parentNode.removeChild(av[aB].parentNode);b.addBox(aN,av[aB]);b.alignBox(av[aB],e[aB],0);if(b.msieRelativeWidthBug){ay.style.top=av[aB].style.top=""}if(aJ){ay.style.width=K.width;t.bbox.width="100%"}q=b.length2em(K.minlabelspacing,aA);av[aB].style.marginRight=av[aB].style.marginLeft=b.Em(q);if(ar.indentalign===a.INDENTALIGN.CENTER){ax+=4*q+2*av[aB].bbox.w}else{if(ar.indentalign!==e[aB]){ax+=2*q+av[aB].bbox.w}}t.style.minWidth=t.bbox.minWidth=aN.style.minWidth=aN.bbox.minWidth=b.Em(ax)}if(!aJ){this.HTMLhandleSpace(t)}var v=this.HTMLhandleColor(t);if(v&&aJ){if(!ai){ai=b.createFrame(ay,g,0,aV,0,"none");b.addBox(ay,ai);b.placeBox(ai,0,aU,true);ai.style.width="100%"}ai.style.backgroundColor=v.style.backgroundColor;ai.parentNode.insertBefore(ai,ai.parentNode.firstChild);v.parentNode.removeChild(v)}return t},HTMLhandleSpace:function(d){d.bbox.keepPadding=true;d.bbox.exact=true;if(!this.hasFrame&&d.bbox.width==null){d.style.paddingLeft=d.style.paddingRight=b.Em(1/6)}this.SUPER(arguments).HTMLhandleSpace.call(this,d)}});a.mtd.Augment({toHTML:function(e,d,g){e=this.HTMLcreateSpan(e);if(this.data[0]){var f=this.data[0].toHTML(e);if(g!=null){f=this.data[0].HTMLstretchV(e,d,g)}else{if(d!=null){f=this.data[0].HTMLstretchH(e,d)}}e.bbox=f.bbox}this.HTMLhandleSpace(e);this.HTMLhandleColor(e);return e},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV});MathJax.Hub.Startup.signal.Post("HTML-CSS mtable Ready");MathJax.Ajax.loadComplete(b.autoloadDir+"/mtable.js")});
MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS_HTML-full.js");