/*
 *  /MathJax/config/TeX-AMS_HTML.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.Hub.Config({"v1.0-compatible":!1});MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.2.1",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:!0}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js");MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.2",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",mtextFontInherit:!1,EqnChunk:MathJax.Hub.Browser.isMobile?10:50,EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:!1,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\x3d2, OffY\x3d2, Color\x3d'gray', Positive\x3d'true')",padding:"3px 4px","z-index":401}}}});MathJax.Hub.Browser.isMSIE&&9<=document.documentMode&&delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter;MathJax.Hub.config.delayJaxRegistration||MathJax.OutputJax["HTML-CSS"].Register("jax/mml");MathJax.Hub.Register.StartupHook("End Config",[function(a,e){var b=a.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:!0,minBrowserTranslate:function(c){var e=a.getJaxFor(c),n=["[Math]"],f=document.createElement("span",{className:"MathJax_Preview"});"TeX"===e.inputJax&&(e.root.Get("displaystyle")?(n=b.displayMathDelimiters,n=[n[0]+e.originalText+n[1]],b.multilineDisplay&&(n=n[0].split(/\n/))):(n=b.inlineMathDelimiters,n=[n[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+n[1]]));for(var e=0,h=n.length;e<h;e++)f.appendChild(document.createTextNode(n[e])),e<h-1&&f.appendChild(document.createElement("br"));c.parentNode.insertBefore(f,c)}},a.config["HTML-CSS"]||{});"0.0"===a.Browser.version||a.Browser.versionAtLeast(b.minBrowserVersion[a.Browser]||0)||(e.Translate=b.minBrowserTranslate,a.Config({showProcessingMessages:!1}),MathJax.Message.Set(["MathJaxNotSupported","Your browser does not support MathJax"],null,4E3),a.Startup.signal.Post("MathJax not supported"))},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js");MathJax.Extension.tex2jax={version:"2.2",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],balanceBraces:!0,skipTags:"script noscript style textarea pre code".split(" "),ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:!1,processEnvironments:!0,processRefs:!0,preview:"TeX"},PreProcess:function(a){this.configured||(this.config=MathJax.Hub.CombineConfig("tex2jax",this.config),this.config.Augment&&MathJax.Hub.Insert(this,this.config.Augment),"undefined"===typeof this.config.previewTeX||this.config.previewTeX||(this.config.preview="none"),this.configured=!0);"string"===typeof a&&(a=document.getElementById(a));a||(a=document.body);this.createPatterns()&&this.scanElement(a,a.nextSibling)},createPatterns:function(){var a=[],e=[],b,c,m=this.config;this.match={};b=0;for(c=m.inlineMath.length;b<c;b++)a.push(this.patternQuote(m.inlineMath[b][0])),this.match[m.inlineMath[b][0]]={mode:"",end:m.inlineMath[b][1],pattern:this.endPattern(m.inlineMath[b][1])};b=0;for(c=m.displayMath.length;b<c;b++)a.push(this.patternQuote(m.displayMath[b][0])),this.match[m.displayMath[b][0]]={mode:"; mode\x3ddisplay",end:m.displayMath[b][1],pattern:this.endPattern(m.displayMath[b][1])};a.length&&e.push(a.sort(this.sortLength).join("|"));m.processEnvironments&&e.push("\\\\begin\\{([^}]*)\\}");m.processEscapes&&e.push("\\\\*\\\\\\$");m.processRefs&&e.push("\\\\(eq)?ref\\{[^}]*\\}");this.start=new RegExp(e.join("|"),"g");this.skipTags=new RegExp("^("+m.skipTags.join("|")+")$","i");a=[];MathJax.Hub.config.preRemoveClass&&a.push(MathJax.Hub.config.preRemoveClass);m.ignoreClass&&a.push(m.ignoreClass);this.ignoreClass=a.length?new RegExp("(^| )("+a.join("|")+")( |$)"):/^$/;this.processClass=new RegExp("(^| )("+m.processClass+")( |$)");return 0<e.length},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(a,e){return a.length!==e.length?e.length-a.length:a==e?0:a<e?-1:1},scanElement:function(a,e,b){for(var c,m,n;a&&a!=e;)"#text"===a.nodeName.toLowerCase()?b||(a=this.scanText(a)):(c="undefined"===typeof a.className?"":a.className,m="undefined"===typeof a.tagName?"":a.tagName,"string"!==typeof c&&(c=String(c)),n=this.processClass.exec(c),!a.firstChild||c.match(/(^| )MathJax/)||!n&&this.skipTags.exec(m)||(c=(b||this.ignoreClass.exec(c))&&!n,this.scanElement(a.firstChild,e,c))),a&&(a=a.nextSibling)},scanText:function(a){if(""==a.nodeValue.replace(/\s+/,""))return a;var e,b;this.search={start:!0};for(this.pattern=this.start;a;){for(this.pattern.lastIndex=0;a&&"#text"===a.nodeName.toLowerCase()&&(e=this.pattern.exec(a.nodeValue));)a=this.search.start?this.startMatch(e,a):this.endMatch(e,a);this.search.matched&&(a=this.encloseMath(a));if(a){do b=a,a=a.nextSibling;while(a&&("br"===a.nodeName.toLowerCase()||"#comment"===a.nodeName.toLowerCase()));if(!a||"#text"!==a.nodeName)return this.search.close?this.prevEndMatch():b}}return a},startMatch:function(a,e){var b=this.match[a[0]];if(null!=b)this.search={end:b.end,mode:b.mode,pcount:0,open:e,olen:a[0].length,opos:this.pattern.lastIndex-a[0].length},this.switchPattern(b.pattern);else if("\\begin"===a[0].substr(0,6))this.search={end:"\\end{"+a[1]+"}",mode:"; mode\x3ddisplay",pcount:0,open:e,olen:0,opos:this.pattern.lastIndex-a[0].length,isBeginEnd:!0},this.switchPattern(this.endPattern(this.search.end));else{if("\\ref"===a[0].substr(0,4)||"\\eqref"===a[0].substr(0,6))return this.search={mode:"",end:"",open:e,pcount:0,olen:0,opos:this.pattern.lastIndex-a[0].length},this.endMatch([""],e);var b=a[0].substr(0,a[0].length-1),c;0===b.length%2?(c=[b.replace(/\\\\/g,"\\")],b=1):(c=[b.substr(1).replace(/\\\\/g,"\\"),"$"],b=0);c=MathJax.HTML.Element("span",null,c);var m=MathJax.HTML.TextNode(e.nodeValue.substr(0,a.index));e.nodeValue=e.nodeValue.substr(a.index+a[0].length-b);e.parentNode.insertBefore(c,e);e.parentNode.insertBefore(m,c);this.pattern.lastIndex=b}return e},endMatch:function(a,e){var b=this.search;a[0]==b.end?(b.close&&0!==b.pcount||(b.close=e,b.cpos=this.pattern.lastIndex,b.clen=b.isBeginEnd?0:a[0].length),0===b.pcount&&(b.matched=!0,e=this.encloseMath(e),this.switchPattern(this.start))):"{"===a[0]?b.pcount++:"}"===a[0]&&b.pcount&&b.pcount--;return e},prevEndMatch:function(){this.search.matched=!0;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(a){a=this.search;var e=a.close,b,c;(e=a.cpos===e.length?e.nextSibling:e.splitText(a.cpos))||(b=e=MathJax.HTML.addText(a.close.parentNode,""));a.close=e;for(c=a.opos?a.open.splitText(a.opos):a.open;c.nextSibling&&c.nextSibling!==e;)c.nodeValue=null!==c.nextSibling.nodeValue?"#comment"===c.nextSibling.nodeName?c.nodeValue+c.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1"):c.nodeValue+c.nextSibling.nodeValue:this.msieNewlineBug?c.nodeValue+("br"===c.nextSibling.nodeName.toLowerCase()?"\n":" "):c.nodeValue+" ",c.parentNode.removeChild(c.nextSibling);e=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);"none"!==this.config.preview&&this.createPreview(a.mode,e);c=this.createMathTag(a.mode,e);this.search={};this.pattern.lastIndex=0;b&&b.parentNode.removeChild(b);return c},insertNode:function(a){var e=this.search;e.close.parentNode.insertBefore(a,e.close)},createPreview:function(a,e){var b=this.config.preview;"none"!==b&&("TeX"===b&&(b=[this.filterPreview(e)]),b&&(b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b),this.insertNode(b)))},createMathTag:function(a,e){var b=document.createElement("script");b.type="math/tex"+a;MathJax.HTML.setScript(b,e);this.insertNode(b);return b},filterPreview:function(a){return a},msieNewlineBug:MathJax.Hub.Browser.isMSIE&&9>document.documentMode};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js");(function(a,e,b,c,m,n,f){var h=MathJax.Extension,p=h.MathEvents={version:"2.2"},d=a.config.menuSettings,k={hover:500,frame:{x:3.5,y:5,bwidth:1,bcolor:"#A6D",hwidth:"15px",hcolor:"#83A"},button:{x:-4,y:-3,wx:-2,src:b.fileURL(n.imageDir+"/MenuArrow-15.png")},fadeinInc:.2,fadeoutInc:.05,fadeDelay:50,fadeoutStart:400,fadeoutDelay:15E3,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"}}},l=p.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",Mousedown:function(d){return l.Handler(d,"Mousedown",this)},Mouseup:function(d){return l.Handler(d,"Mouseup",this)},Mousemove:function(d){return l.Handler(d,"Mousemove",this)},Mouseover:function(d){return l.Handler(d,"Mouseover",this)},Mouseout:function(d){return l.Handler(d,"Mouseout",this)},Click:function(d){return l.Handler(d,"Click",this)},DblClick:function(d){return l.Handler(d,"DblClick",this)},Menu:function(d){return l.Handler(d,"ContextMenu",this)},Handler:function(d,a,c){if(b.loadingMathMenu)return l.False(d);var k=n[c.jaxID];d||(d=window.event);d.isContextMenu="ContextMenu"===a;if(k[a])return k[a](d,c);if(h.MathZoom)return h.MathZoom.HandleEvent(d,a,c)},False:function(d){d||(d=window.event);d&&(d.preventDefault&&d.preventDefault(),d.stopPropagation&&d.stopPropagation(),d.cancelBubble=!0,d.returnValue=!1);return!1},ContextMenu:function(k,v,e){var h=n[v.jaxID],g=h.getJaxFromMath(v);if((null!=h.config.showMathMenu?h:a).config.showMathMenu&&("MathJax"===d.context||e)){p.msieEventBug&&(k=window.event||k);l.ClearSelection();r.ClearHoverTimer();g.hover&&(g.hover.remove&&(clearTimeout(g.hover.remove),delete g.hover.remove),g.hover.nofade=!0);var t=MathJax.Menu;if(t){if(t.loadingDomain)return l.False(k);h=m.loadDomain("MathMenu");if(!h)return t.jax=g,v=t.menu.Find("Show Math As").menu,v.items[0].name=g.sourceMenuTitle,v.items[0].format=g.sourceMenuFormat||"MathML",v.items[1].name=f[g.inputJax].sourceMenuTitle,t.menu.Find("Math Settings","MathPlayer").hidden=!("NativeMML"===g.outputJax&&a.Browser.hasMathPlayer),t.menu.Post(k);t.loadingDomain=!0;g=function(){delete t.loadingDomain}}else{if(b.loadingMathMenu)return l.False(k);b.loadingMathMenu=!0;h=b.Require("[MathJax]/extensions/MathMenu.js");g=function(){delete b.loadingMathMenu;MathJax.Menu||(MathJax.Menu={})}}c.Queue(h,g,["ContextMenu",l,{pageX:k.pageX,pageY:k.pageY,clientX:k.clientX,clientY:k.clientY},v,e]);return l.False(k)}},AltContextMenu:function(c,k){var b=n[k.jaxID],e=(null!=b.config.showMathMenu?b:a).config.showMathMenu;if(e){e=(null!=b.config.showMathMenuMSIE?b:a).config.showMathMenuMSIE;if("MathJax"===d.context&&!d.mpContext&&e){if(!p.noContextMenuBug||c.button!==l.RIGHTBUTTON)return}else if(!c[l.MENUKEY]||c.button!==l.LEFTBUTTON)return;return b.ContextMenu(c,k,!0)}},ClearSelection:function(){p.safariContextMenuBug&&setTimeout("window.getSelection().empty()",0);document.selection&&setTimeout("document.selection.empty()",0)},getBBox:function(d){d.appendChild(p.topImg);var a=p.topImg.offsetTop,c=d.offsetHeight-a,k=d.offsetWidth;d.removeChild(p.topImg);return{w:k,h:a,d:c}}},r=p.Hover={Mouseover:function(c,k){if(d.discoverable||"Hover"===d.zoom){var b=c.fromElement||c.relatedTarget,e=c.toElement||c.target;if(b&&e&&(b.isMathJax!=e.isMathJax||a.getJaxFor(b)!==a.getJaxFor(e)))return b=this.getJaxFromMath(k),b.hover?r.ReHover(b):r.HoverTimer(b,k),l.False(c)}},Mouseout:function(c,k){if(d.discoverable||"Hover"===d.zoom){var b=c.fromElement||c.relatedTarget,e=c.toElement||c.target;if(b&&e&&(b.isMathJax!=e.isMathJax||a.getJaxFor(b)!==a.getJaxFor(e)))return b=this.getJaxFromMath(k),b.hover?r.UnHover(b):r.ClearHoverTimer(),l.False(c)}},Mousemove:function(a,c){if(d.discoverable||"Hover"===d.zoom){var k=this.getJaxFromMath(c);if(!k.hover&&(r.lastX!=a.clientX||r.lastY!=a.clientY))return r.lastX=a.clientX,r.lastY=a.clientY,r.HoverTimer(k,c),l.False(a)}},HoverTimer:function(d,a){this.ClearHoverTimer();this.hoverTimer=setTimeout(c(["Hover",this,d,a]),k.hover)},ClearHoverTimer:function(){this.hoverTimer&&(clearTimeout(this.hoverTimer),delete this.hoverTimer)},Hover:function(d,c){if(!h.MathZoom||!h.MathZoom.Hover({},c)){var b=n[d.outputJax],l=b.getHoverSpan(d,c),r=b.getHoverBBox(d,l,c),g=(null!=b.config.showMathMenu?b:a).config.showMathMenu,m=k.frame.x,f=k.frame.y,t=k.frame.bwidth;p.msieBorderWidthBug&&(t=0);d.hover={opacity:0,id:d.inputID+"-Hover"};var x=e.Element("span",{id:d.hover.id,isMathJax:!0,style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{className:"MathJax_Hover_Frame",isMathJax:!0,style:{display:"inline-block",position:"absolute",top:this.Px(-r.h-f-t-(r.y||0)),left:this.Px(-m-t+(r.x||0)),width:this.Px(r.w+2*m),height:this.Px(r.h+r.d+2*f),opacity:0,filter:"alpha(opacity\x3d0)"}}]]),b=e.Element("span",{isMathJax:!0,id:d.hover.id+"Menu",style:{display:"inline-block","z-index":1,width:0,height:0,position:"relative"}},[["img",{className:"MathJax_Hover_Arrow",isMathJax:!0,math:c,src:k.button.src,onclick:this.HoverMenu,jax:b.id,style:{left:this.Px(r.w+m+t+(r.x||0)+k.button.x),top:this.Px(-r.h-f-t-(r.y||0)-k.button.y),opacity:0,filter:"alpha(opacity\x3d0)"}}]]);r.width&&(x.style.width=b.style.width=r.width,x.style.marginRight=b.style.marginRight="-"+r.width,x.firstChild.style.width=r.width,b.firstChild.style.left="",b.firstChild.style.right=this.Px(k.button.wx));l.parentNode.insertBefore(x,l);g&&l.parentNode.insertBefore(b,l);l.style&&(l.style.position="relative");this.ReHover(d)}},ReHover:function(d){d.hover.remove&&clearTimeout(d.hover.remove);d.hover.remove=setTimeout(c(["UnHover",this,d]),k.fadeoutDelay);this.HoverFadeTimer(d,k.fadeinInc)},UnHover:function(d){d.hover.nofade||this.HoverFadeTimer(d,-k.fadeoutInc,k.fadeoutStart)},HoverFade:function(d){delete d.hover.timer;d.hover.opacity=Math.max(0,Math.min(1,d.hover.opacity+d.hover.inc));d.hover.opacity=Math.floor(1E3*d.hover.opacity)/1E3;var a=document.getElementById(d.hover.id),c=document.getElementById(d.hover.id+"Menu");a.firstChild.style.opacity=d.hover.opacity;a.firstChild.style.filter="alpha(opacity\x3d"+Math.floor(100*d.hover.opacity)+")";c&&(c.firstChild.style.opacity=d.hover.opacity,c.firstChild.style.filter=a.style.filter);1!==d.hover.opacity&&(0<d.hover.opacity?this.HoverFadeTimer(d,d.hover.inc):(a.parentNode.removeChild(a),c&&c.parentNode.removeChild(c),d.hover.remove&&clearTimeout(d.hover.remove),delete d.hover))},HoverFadeTimer:function(d,a,b){d.hover.inc=a;d.hover.timer||(d.hover.timer=setTimeout(c(["HoverFade",this,d]),b||k.fadeDelay))},HoverMenu:function(d){d||(d=window.event);return n[this.jax].ContextMenu(d,this.math,!0)},ClearHover:function(d){d.hover.remove&&clearTimeout(d.hover.remove);d.hover.timer&&clearTimeout(d.hover.timer);r.ClearHoverTimer();delete d.hover},Px:function(d){return.006>Math.abs(d)?"0px":d.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){(new Image).src=k.button.src}},t=p.Touch={last:0,delay:500,start:function(d){var a=(new Date).getTime(),c=a-t.last<t.delay&&t.up;t.last=a;t.up=!1;c&&(t.timeout=setTimeout(t.menu,t.delay,d,this),d.preventDefault())},end:function(d){var a=(new Date).getTime();t.up=a-t.last<t.delay;if(t.timeout)return clearTimeout(t.timeout),delete t.timeout,t.last=0,t.up=!1,d.preventDefault(),l.Handler(d.touches[0]||d.touch,"DblClick",this)},menu:function(d,a){delete t.timeout;t.last=0;t.up=!1;return l.Handler(d.touches[0]||d.touch,"ContextMenu",a)}};if(a.Browser.isMobile){var g=k.styles[".MathJax_Hover_Arrow"];g.width="25px";g.height="18px";k.button.x=-6}a.Browser.Select({MSIE:function(d){var a=document.documentMode||0,c=d.versionAtLeast("8.0");p.msieBorderWidthBug="BackCompat"===document.compatMode;p.msieEventBug=d.isIE9;p.msieAlignBug=!c||8>a;9>a&&(l.LEFTBUTTON=1)},Safari:function(d){p.safariContextMenuBug=!0},Opera:function(d){p.operaPositionBug=!0},Konqueror:function(d){p.noContextMenuBug=!0}});p.topImg=p.msieAlignBug?e.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):e.Element("span",{style:{width:0,height:0,display:"inline-block"}});p.operaPositionBug&&(p.topImg.style.border="1px solid");p.config=k=a.CombineConfig("MathEvents",k);c.Queue(a.Register.StartupHook("End Config",{}),[function(){var d=k.styles[".MathJax_Hover_Frame"];d.border=k.frame.bwidth+"px solid "+k.frame.bcolor+" ! important";d["box-shadow"]=d["-webkit-box-shadow"]=d["-moz-box-shadow"]=d["-khtml-box-shadow"]="0px 0px "+k.frame.hwidth+" "+k.frame.hcolor}],["getImages",r],["Styles",b,k.styles],["Post",a.Startup.signal,"MathEvents Ready"],["loadComplete",b,"[MathJax]/extensions/MathEvents.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.Callback,MathJax.Localization,MathJax.OutputJax,MathJax.InputJax);(function(a,e,b,c,m){var n=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\x3d2, OffY\x3d2, Color\x3d'gray', Positive\x3d'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\x3d0)"},"#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\x3d0)"}}}),f,h,p;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){p=MathJax.Extension.MathEvents.Event;f=MathJax.Extension.MathEvents.Event.False;h=MathJax.Extension.MathEvents.Hover});var d=MathJax.Extension.MathZoom={version:"2.2",settings:a.config.menuSettings,scrollSize:18,HandleEvent:function(a,c,b){return d.settings.CTRL&&!a.ctrlKey||d.settings.ALT&&!a.altKey||d.settings.CMD&&!a.metaKey||d.settings.Shift&&!a.shiftKey||!d[c]?!0:d[c](a,b)},Click:function(d,a){if("Click"===this.settings.zoom)return this.Zoom(d,a)},DblClick:function(d,a){if("Double-Click"===this.settings.zoom)return this.Zoom(d,a)},Hover:function(d,a){return"Hover"===this.settings.zoom?(this.Zoom(d,a),!0):!1},Zoom:function(d,c){this.Remove();h.ClearHoverTimer();p.ClearSelection();var b=MathJax.OutputJax[c.jaxID],m=b.getJaxFromMath(c);m.hover&&h.UnHover(m);var g=Math.floor(.85*document.body.clientWidth),q=Math.floor(.85*Math.max(document.body.clientHeight,document.documentElement.clientHeight)),v=e.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":g+"px","max-height":q+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]),u=v.lastChild,y=u.firstChild,z=v.firstChild;c.parentNode.insertBefore(v,c);c.parentNode.insertBefore(c,v);y.addEventListener&&y.addEventListener("mousedown",this.Remove,!0);if(this.msieTrapEventBug){var w=e.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});v.insertBefore(w,u)}this.msieZIndexBug&&(e.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}}),v.style.position="relative",v.style.zIndex=n.styles["#MathJax_ZoomOverlay"]["z-index"]);b=b.Zoom(m,y,c,g,q);this.msiePositionBug&&(this.msieSizeBug&&(u.style.height=b.zH+"px",u.style.width=b.zW+"px"),u.offsetHeight>q&&(u.style.height=q+"px",u.style.width=b.zW+this.scrollSize+"px"),u.offsetWidth>g&&(u.style.width=g+"px",u.style.height=b.zH+this.scrollSize+"px"));this.operaPositionBug&&(u.style.width=Math.min(g,b.zW)+"px");u.offsetWidth&&u.offsetWidth<g&&u.offsetHeight<q&&(u.style.overflow="visible");this.Position(u,b);this.msieTrapEventBug&&(w.style.height=u.clientHeight+"px",w.style.width=u.clientWidth+"px",w.style.left=parseFloat(u.style.left)+u.clientLeft+"px",w.style.top=parseFloat(u.style.top)+u.clientTop+"px");u.style.visibility="";"Hover"===this.settings.zoom&&(z.onmouseover=this.Remove);window.addEventListener?addEventListener("resize",this.Resize,!1):window.attachEvent?attachEvent("onresize",this.Resize):(this.onresize=window.onresize,window.onresize=this.Resize);a.signal.Post(["math zoomed",m]);return f(d)},Position:function(a,c){var b=this.Resize(),e=b.y,h=c.mW,m=c.Y;a.style.left=Math.max(-h-Math.floor((a.offsetWidth-h)/2),10-b.x)+"px";a.style.top=Math.max(m,10-e)+"px";d.msiePositionBug||d.SetWH()},Resize:function(a){if(d.onresize)d.onresize(a);var c=document.getElementById("MathJax_ZoomFrame");a=document.getElementById("MathJax_ZoomOverlay");for(var b=d.getXY(c),c=c.parentNode,e=d.getOverflow(c);c.parentNode&&c!==document.body&&"visible"===e;)c=c.parentNode,e=d.getOverflow(c);"visible"!==e&&(a.scroll_parent=c,e=d.getXY(c),b.x-=e.x,b.y-=e.y,e=d.getBorder(c),b.x-=e.x,b.y-=e.y);a.style.left=-b.x+"px";a.style.top=-b.y+"px";d.msiePositionBug?setTimeout(d.SetWH,0):d.SetWH();return b},SetWH:function(){var d=document.getElementById("MathJax_ZoomOverlay");d.style.width=d.style.height="1px";var a=d.scroll_parent||document.documentElement||document.body;d.style.width=a.scrollWidth+"px";d.style.height=Math.max(a.clientHeight,a.scrollHeight)+"px"},getOverflow:window.getComputedStyle?function(d){return getComputedStyle(d).overflow}:function(d){return(d.currentStyle||{overflow:"visible"}).overflow},getBorder:function(d){var a={thin:1,medium:2,thick:3},c=window.getComputedStyle?getComputedStyle(d):d.currentStyle||{borderLeftWidth:0,borderTopWidth:0};d=c.borderLeftWidth;c=c.borderTopWidth;d=a[d]?a[d]:parseInt(d);c=a[c]?a[c]:parseInt(c);return{x:d,y:c}},getXY:function(a){var c=0,b=0,e;for(e=a;e.offsetParent;)c+=e.offsetLeft,e=e.offsetParent;d.operaPositionBug&&(a.style.border="1px solid");for(e=a;e.offsetParent;)b+=e.offsetTop,e=e.offsetParent;d.operaPositionBug&&(a.style.border="");return{x:c,y:b}},Remove:function(c){var b=document.getElementById("MathJax_ZoomFrame");if(b){var h=MathJax.OutputJax[b.previousSibling.jaxID].getJaxFromMath(b.previousSibling);a.signal.Post(["math unzoomed",h]);b.parentNode.removeChild(b);(b=document.getElementById("MathJax_ZoomTracker"))&&b.parentNode.removeChild(b);d.operaRefreshBug&&(b=e.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(b));window.removeEventListener?removeEventListener("resize",d.Resize,!1):window.detachEvent?detachEvent("onresize",d.Resize):(window.onresize=d.onresize,delete d.onresize)}return f(c)}};a.Browser.Select({MSIE:function(a){var c=document.documentMode||0,b=9<=c;d.msiePositionBug=!b;d.msieSizeBug=a.versionAtLeast("7.0")&&(!document.documentMode||7===c||8===c);d.msieZIndexBug=7>=c;d.msieInlineBlockAlignBug=7>=c;d.msieTrapEventBug=!window.addEventListener;"BackCompat"===document.compatMode&&(d.scrollSize=52);b&&delete n.styles["#MathJax_Zoom"].filter},Opera:function(a){d.operaPositionBug=!0;d.operaRefreshBug=!0}});d.topImg=d.msieInlineBlockAlignBug?e.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):e.Element("span",{style:{width:0,height:0,display:"inline-block"}});if(d.operaPositionBug||d.msieTopBug)d.topImg.style.border="1px solid";MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",b,n.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",b,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML);(function(a,e,b,c,m){var n=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:"2.2",signal:n};var f=function(d){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",d]].concat([].slice.call(arguments,1)))},h=a.Browser.isPC,p=a.Browser.isMSIE,d=8<(document.documentMode||0),k=h?null:"5px",l=a.CombineConfig("MathMenu",{delay:150,closeImg:b.fileURL(m.imageDir+"/CloseX-31.png"),showRenderer:!0,showMathPlayer:!0,showFontMenu:!1,showContext:!1,showDiscoverable:!1,showLocale:!0,showLocaleURL:!1,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\x3d2, OffY\x3d2, Color\x3d'gray', Positive\x3d'true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:h?"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":k,"-webkit-border-radius":k,"-moz-border-radius":k,"-khtml-border-radius":k,"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\x3d2, OffY\x3d2, Color\x3d'gray', Positive\x3d'true')"},".MathJax_MenuItem":{padding:h?"2px 2em":"1px 2em",background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":p?"'Arial unicode MS'":null},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":p?"'Arial unicode MS'":null},".MathJax_MenuRadioCheck":{position:"absolute",left:h?"1em":".7em"},".MathJax_MenuLabel":{padding:h?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em","font-style":"italic"},".MathJax_MenuRule":{"border-top":h?"1px solid #CCCCCC":"1px solid #DDDDDD",margin:h?"4px 1px 0px":"4px 3px"},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":h?"Highlight":"#606872",color:h?"HighlightText":"white"},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}}),r,t;a.Register.StartupHook("MathEvents Ready",function(){r=MathJax.Extension.MathEvents.Event.False;t=MathJax.Extension.MathEvents.Hover});var g=MathJax.Menu=MathJax.Object.Subclass({version:"2.2",items:[],posted:!1,title:null,margin:5,Init:function(d){this.items=[].slice.call(arguments,0)},With:function(d){d&&a.Insert(this,d);return this},Post:function(d,a){d||(d=window.event);var c=document.getElementById("MathJax_MenuFrame");c||(c=g.Background(this),delete q.lastItem,delete q.lastMenu,delete g.skipUp,n.Post(["post",g.jax]));var k=e.addElement(c,"div",{onmouseup:g.Mouseup,ondblclick:r,ondragstart:r,onselectstart:r,oncontextmenu:r,menuItem:this,className:"MathJax_Menu"});MathJax.Localization.setCSS(k);for(var b=0,m=this.items.length;b<m;b++)this.items[b].Create(k);g.isMobile&&e.addElement(k,"span",{className:"MathJax_Menu_Close",menu:a,ontouchstart:g.Close,ontouchend:r,onmousedown:g.Close,onmouseup:r},[["img",{src:l.closeImg,style:{width:"100%",height:"100%"}}]]);this.posted=!0;k.style.width=k.offsetWidth+2+"px";b=d.pageX;m=d.pageY;b||m||(b=d.clientX+document.body.scrollLeft+document.documentElement.scrollLeft,m=d.clientY+document.body.scrollTop+document.documentElement.scrollTop);if(a){for(var f="left",p=a.offsetWidth,b=g.isMobile?30:p-2,m=0;a&&a!==c;)b+=a.offsetLeft,m+=a.offsetTop,a=a.parentNode;b+k.offsetWidth>document.body.offsetWidth-this.margin&&!g.isMobile&&(f="right",b=Math.max(this.margin,b-p-k.offsetWidth+6));h||(k.style["borderRadiusTop"+f]=0,k.style["WebkitBorderRadiusTop"+f]=0,k.style["MozBorderRadiusTop"+f]=0,k.style["KhtmlBorderRadiusTop"+f]=0)}else b+k.offsetWidth>document.body.offsetWidth-this.margin&&(b=document.body.offsetWidth-k.offsetWidth-this.margin),g.isMobile&&(b=Math.max(5,b-Math.floor(k.offsetWidth/2)),m-=20),g.skipUp=d.isContextMenu;k.style.left=b+"px";k.style.top=m+"px";document.selection&&document.selection.empty&&document.selection.empty();return r(d)},Remove:function(d,a){n.Post(["unpost",g.jax]);var c=document.getElementById("MathJax_MenuFrame");c&&(c.parentNode.removeChild(c),this.msieFixedPositionBug&&detachEvent("onresize",g.Resize));g.jax.hover&&(delete g.jax.hover.nofade,t.UnHover(g.jax));return r(d)},Find:function(d){return this.FindN(1,d,[].slice.call(arguments,1))},FindId:function(d){return this.FindN(0,d,[].slice.call(arguments,1))},FindN:function(d,a,c){for(var k=0,b=this.items.length;k<b;k++)if(this.items[k].name[d]===a){if(c.length){if(!this.items[k].menu)break;return this.items[k].menu.FindN(d,c[0],c.slice(1))}return this.items[k]}return null},IndexOf:function(d){return this.IndexOfN(1,d)},IndexOfId:function(d){return this.IndexOfN(0,d)},IndexOfN:function(d,a){for(var c=0,k=this.items.length;c<k;c++)if(this.items[c].name[d]===a)return c;return null}},{config:l,div:null,Close:function(d){return g.Event(d,this.menu||this.parentNode,this.menu?"Touchend":"Remove")},Remove:function(d){return g.Event(d,this,"Remove")},Mouseover:function(d){return g.Event(d,this,"Mouseover")},Mouseout:function(d){return g.Event(d,this,"Mouseout")},Mousedown:function(d){return g.Event(d,this,"Mousedown")},Mouseup:function(d){return g.Event(d,this,"Mouseup")},Touchstart:function(d){return g.Event(d,this,"Touchstart")},Touchend:function(d){return g.Event(d,this,"Touchend")},Event:function(d,a,c,k){if(g.skipMouseover&&"Mouseover"===c&&!k)return r(d);if(g.skipUp){if(c.match(/Mouseup|Touchend/))return delete g.skipUp,r(d);("Touchstart"===c||"Mousedown"===c&&!g.skipMousedown)&&delete g.skipUp}d||(d=window.event);return(k=a.menuItem)&&k[c]?k[c](d,a):null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(d){d=e.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:d,onmousedown:this.Remove}]]);var a=d.firstChild;g.msieBackgroundBug&&(a.style.backgroundColor="white",a.style.filter="alpha(opacity\x3d0)");g.msieFixedPositionBug?(d.width=d.height=0,this.Resize(),attachEvent("onresize",this.Resize)):a.style.position="fixed";return d},Resize:function(){setTimeout(g.SetWH,0)},SetWH:function(){var d=document.getElementById("MathJax_MenuFrame");d&&(d=d.firstChild,d.style.width=d.style.height="1px",d.style.width=document.body.scrollWidth+"px",d.style.height=document.body.scrollHeight+"px")},saveCookie:function(){e.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=e.Cookie.Get("menu")},getImages:function(){g.isMobile&&((new Image).src=l.closeImg)}}),q=g.ITEM=MathJax.Object.Subclass({name:"",Create:function(d){if(!this.hidden){var a={onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmouseup:g.Mouseup,onmousedown:g.Mousedown,ondragstart:r,onselectstart:r,onselectend:r,ontouchstart:g.Touchstart,ontouchend:g.Touchend,className:"MathJax_MenuItem",menuItem:this};this.disabled&&(a.className+=" MathJax_MenuDisabled");e.addElement(d,"div",a,this.Label(a,d))}},Name:function(){return f(this.name[0],this.name[1])},Mouseover:function(d,a){this.disabled||this.Activate(a);if(!this.menu||!this.menu.posted){for(var c=document.getElementById("MathJax_MenuFrame").childNodes,k=a.parentNode.childNodes,b=0,l=k.length;b<l;b++){var e=k[b].menuItem;e&&e.menu&&e.menu.posted&&e.Deactivate(k[b])}for(l=c.length-1;0<=l&&a.parentNode.menuItem!==c[l].menuItem;)c[l].menuItem.posted=!1,c[l].parentNode.removeChild(c[l]),l--;this.Timer&&!g.isMobile&&this.Timer(d,a)}},Mouseout:function(d,a){this.menu&&this.menu.posted||this.Deactivate(a);this.timer&&(clearTimeout(this.timer),delete this.timer)},Mouseup:function(d,a){return this.Remove(d,a)},Touchstart:function(d,a){return this.TouchEvent(d,a,"Mousedown")},Touchend:function(d,a){return this.TouchEvent(d,a,"Mouseup")},TouchEvent:function(d,a,c){this!==q.lastItem&&(q.lastMenu&&g.Event(d,q.lastMenu,"Mouseout"),g.Event(d,a,"Mouseover",!0),q.lastItem=this,q.lastMenu=a);if(this.nativeTouch)return null;g.Event(d,a,c);return!1},Remove:function(d,a){a=a.parentNode.menuItem;return a.Remove(d,a)},Activate:function(d){this.Deactivate(d);d.className+=" MathJax_MenuActive"},Deactivate:function(d){d.className=d.className.replace(/ MathJax_MenuActive/,"")},With:function(d){d&&a.Insert(this,d);return this}});g.ITEM.COMMAND=g.ITEM.Subclass({action:function(){},Init:function(d,a,c){d instanceof Array||(d=[d,d]);this.name=d;this.action=a;this.With(c)},Label:function(d,a){return[this.Name()]},Mouseup:function(d,a){this.disabled||(this.Remove(d,a),n.Post(["command",this]),this.action.call(this,d));return r(d)}});g.ITEM.SUBMENU=g.ITEM.Subclass({menu:null,marker:h&&!a.Browser.isSafari?"\u25b6":"\u25b8",Init:function(d,a){d instanceof Array||(d=[d,d]);this.name=d;var c=1;a instanceof g.ITEM||(this.With(a),c++);this.menu=g.apply(g,[].slice.call(arguments,c))},Label:function(d,a){this.menu.posted=!1;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(d,a){this.timer&&clearTimeout(this.timer);d={clientX:d.clientX,clientY:d.clientY};this.timer=setTimeout(c(["Mouseup",this,d,a]),l.delay)},Touchend:function(d,a){var c=this.menu.posted,k=this.SUPER(arguments).Touchend.apply(this,arguments);c&&(this.Deactivate(a),delete q.lastItem,delete q.lastMenu);return k},Mouseup:function(d,a){if(!this.disabled)if(this.menu.posted)for(var c=document.getElementById("MathJax_MenuFrame").childNodes,k=c.length-1;0<=k;){var b=c[k];b.menuItem.posted=!1;b.parentNode.removeChild(b);if(b.menuItem===this.menu)break;k--}else this.timer&&(clearTimeout(this.timer),delete this.timer),this.menu.Post(d,a);return r(d)}});g.ITEM.RADIO=g.ITEM.Subclass({variable:null,marker:h?"\u25cf":"\u2713",Init:function(d,a,c){d instanceof Array||(d=[d,d]);this.name=d;this.variable=a;this.With(c);null==this.value&&(this.value=this.name[0])},Label:function(d,a){var c={className:"MathJax_MenuRadioCheck"};l.settings[this.variable]!==this.value&&(c={style:{display:"none"}});return[["span",c,[this.marker]]," "+this.Name()]},Mouseup:function(d,a){if(!this.disabled){for(var c=a.parentNode.childNodes,k=0,b=c.length;k<b;k++){var e=c[k].menuItem;e&&e.variable===this.variable&&(c[k].firstChild.style.display="none")}a.firstChild.display="";l.settings[this.variable]=this.value;g.cookie[this.variable]=l.settings[this.variable];g.saveCookie();n.Post(["radio button",this])}this.Remove(d,a);this.action&&!this.disabled&&this.action.call(g,this);return r(d)}});g.ITEM.CHECKBOX=g.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(d,a,c){d instanceof Array||(d=[d,d]);this.name=d;this.variable=a;this.With(c)},Label:function(d,a){var c={className:"MathJax_MenuCheck"};l.settings[this.variable]||(c={style:{display:"none"}});return[["span",c,[this.marker]]," "+this.Name()]},Mouseup:function(d,a){this.disabled||(a.firstChild.display=l.settings[this.variable]?"none":"",l.settings[this.variable]=!l.settings[this.variable],g.cookie[this.variable]=l.settings[this.variable],g.saveCookie(),n.Post(["checkbox",this]));this.Remove(d,a);this.action&&!this.disabled&&this.action.call(g,this);return r(d)}});g.ITEM.LABEL=g.ITEM.Subclass({Init:function(d,a){d instanceof Array||(d=[d,d]);this.name=d;this.With(a)},Label:function(d,a){delete d.onmouseover;delete d.onmouseout;delete d.onmousedown;d.className+=" MathJax_MenuLabel";return[this.Name()]}});g.ITEM.RULE=g.ITEM.Subclass({Label:function(d,a){delete d.onmouseover;delete d.onmouseout;delete d.onmousedown;d.className+=" MathJax_MenuRule";return null}});g.About=function(){var d=m["HTML-CSS"]||{},c=(d.imgFonts?"image":d.fontInUse?(d.webFonts?"web":"local")+" "+d.fontInUse:m.SVG?"web SVG":"generic")+" fonts",d=!d.webFonts||d.imgFonts?null:d.allowWebFonts.replace(/otf/,"woff or otf")+" fonts",k=["MathJax.js v"+MathJax.fileversion,["br"]];k.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);g.About.GetJax(k,MathJax.InputJax,["InputJax","%1 Input Jax v%2"]);g.About.GetJax(k,MathJax.OutputJax,["OutputJax","%1 Output Jax v%2"]);g.About.GetJax(k,MathJax.ElementJax,["ElementJax","%1 Element Jax v%2"]);k.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);g.About.GetJax(k,MathJax.Extension,["Extension","%1 Extension v%2"],!0);k.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[a.Browser+" v"+a.Browser.version+(d?" \u2014 "+f(d.replace(/ /g,""),d):"")]]);g.About.div=g.Background(g.About);c=e.addElement(g.About.div,"div",{id:"MathJax_About"},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],f(c.replace(/ /g,""),"using "+c),["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"}},k],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]],["img",{src:l.closeImg,style:{width:"21px",height:"21px",position:"absolute",top:".2em",right:".2em"},onclick:g.About.Remove}]]);MathJax.Localization.setCSS(c);d=document.documentElement||{};d=window.innerHeight||d.clientHeight||d.scrollHeight||0;g.prototype.msieAboutBug?(c.style.width="20em",c.style.position="absolute",c.style.left=Math.floor((document.documentElement.scrollWidth-c.offsetWidth)/2)+"px",c.style.top=Math.floor((d-c.offsetHeight)/3)+document.body.scrollTop+"px"):(c.style.marginLeft=Math.floor(-c.offsetWidth/2)+"px",c.style.top=Math.floor((d-c.offsetHeight)/3)+"px")};g.About.Remove=function(d){g.About.div&&(document.body.removeChild(g.About.div),delete g.About.div)};g.About.GetJax=function(d,a,c,k){var b=[],l;for(l in a)a.hasOwnProperty(l)&&a[l]&&(k&&a[l].version||a[l].isa&&a[l].isa(a))&&b.push(f(c[0],c[1],a[l].id||l,a[l].version));b.sort();a=0;for(c=b.length;a<c;a++)d.push(b[a],["br"]);return d};g.Help=function(){b.Require("[MathJax]/extensions/HelpDialog.js",function(){MathJax.Extension.Help.Dialog()})};g.ShowSource=function(d){d||(d=window.event);var a={screenX:d.screenX,screenY:d.screenY};if(g.jax)if("MathML"===this.format){var k=MathJax.ElementJax.mml;if(k&&"undefined"!==typeof k.mbase.prototype.toMathML)try{g.ShowSource.Text(g.jax.root.toMathML(),d)}catch(l){if(!l.restart)throw l;c.After([this,g.ShowSource,a],l.restart)}else b.loadingToMathML||(b.loadingToMathML=!0,g.ShowSource.Window(d),c.Queue(b.Require("[MathJax]/extensions/toMathML.js"),function(){delete b.loadingToMathML;k.mbase.prototype.toMathML||(k.mbase.prototype.toMathML=function(){})},[this,g.ShowSource,a]))}else"Error"===this.format?g.ShowSource.Text(g.jax.errorText,d):null==g.jax.originalText?alert(f("NoOriginalForm","No original form available")):g.ShowSource.Text(g.jax.originalText,d)};g.ShowSource.Window=function(d){if(!g.ShowSource.w){d=[];var a=l.windowSettings,c;for(c in a)a.hasOwnProperty(c)&&d.push(c+"\x3d"+a[c]);g.ShowSource.w=window.open("","_blank",d.join(","))}return g.ShowSource.w};g.ShowSource.Text=function(d,a){var c=g.ShowSource.Window(a);delete g.ShowSource.w;d=d.replace(/^\s*/,"").replace(/\s*$/,"");d=d.replace(/&/g,"\x26amp;").replace(/</g,"\x26lt;").replace(/>/g,"\x26gt;");var k=f("EqSource","MathJax Equation Source");if(g.isMobile)c.document.open(),c.document.write("\x3chtml\x3e\x3chead\x3e\x3cmeta name\x3d'viewport' content\x3d'width\x3ddevice-width, initial-scale\x3d1.0' /\x3e\x3ctitle\x3e"+k+"\x3c/title\x3e\x3c/head\x3e\x3cbody style\x3d'font-size:85%'\x3e"),c.document.write("\x3cpre\x3e"+d+"\x3c/pre\x3e"),c.document.write("\x3chr\x3e\x3cinput type\x3d'button' value\x3d'"+f("Close","Close")+"' onclick\x3d'window.close()' /\x3e"),c.document.write("\x3c/body\x3e\x3c/html\x3e"),c.document.close();else{c.document.open();c.document.write("\x3chtml\x3e\x3chead\x3e\x3ctitle\x3e"+k+"\x3c/title\x3e\x3c/head\x3e\x3cbody style\x3d'font-size:85%'\x3e");c.document.write("\x3ctable\x3e\x3ctr\x3e\x3ctd\x3e\x3cpre\x3e"+d+"\x3c/pre\x3e\x3c/td\x3e\x3c/tr\x3e\x3c/table\x3e");c.document.write("\x3c/body\x3e\x3c/html\x3e");c.document.close();var b=c.document.body.firstChild;setTimeout(function(){var d=c.outerHeight-c.innerHeight||30,k=c.outerWidth-c.innerWidth||30,k=Math.max(100,Math.min(Math.floor(.5*screen.width),b.offsetWidth+k+25)),d=Math.max(40,Math.min(Math.floor(.5*screen.height),b.offsetHeight+d+25));c.resizeTo(k,d);a&&null!=a.screenX&&(k=Math.max(0,Math.min(a.screenX-Math.floor(k/2),screen.width-k-20)),d=Math.max(0,Math.min(a.screenY-Math.floor(d/2),screen.height-d-20)),c.moveTo(k,d))},50)}};g.Scale=function(){var d=m["HTML-CSS"],c=m.NativeMML,k=m.SVG,b=(d||c||k||{config:{scale:100}}).config.scale,l=prompt(f("ScaleMath","Scale all mathematics (compared to surrounding text) by"),b+"%");l&&(l.match(/^\s*\d+(\.\d*)?\s*%?\s*$/)?(l=parseFloat(l))?l!==b&&(d&&(d.config.scale=l),c&&(c.config.scale=l),k&&(k.config.scale=l),g.cookie.scale=l,g.saveCookie(),a.Reprocess()):alert(f("NonZeroScale","The scale should not be zero")):alert(f("PercentScale","The scale should be a percentage (e.g., 120%%)")))};g.Zoom=function(){MathJax.Extension.MathZoom||b.Require("[MathJax]/extensions/MathZoom.js")};g.Renderer=function(){var c=a.outputJax["jax/mml"];if(c[0]!==l.settings.renderer){var k=a.Browser,b,h=g.Renderer.Messages,m;switch(l.settings.renderer){case "NativeMML":l.settings.warnedMML||(k.isChrome&&"24."!==k.version.substr(0,3)?b=h.MML.WebKit:k.isSafari&&!k.versionAtLeast("5.0")?b=h.MML.WebKit:k.isMSIE?k.hasMathPlayer||(b=h.MML.MSIE):b=h.MML[k],m="warnedMML");break;case "SVG":l.settings.warnedSVG||!k.isMSIE||d||(b=h.SVG.MSIE)}if(b){b=f(b[0],b[1]);b=b+"\n\n"+f("SwitchAnyway","Switch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)");g.cookie.renderer=c[0].id;g.saveCookie();if(!confirm(b)){g.cookie.renderer=l.settings.renderer=e.Cookie.Get("menu").renderer;g.saveCookie();return}m&&(g.cookie.warned=l.settings.warned=!0);g.cookie.renderer=l.settings.renderer;g.saveCookie()}a.Queue(["setRenderer",a,l.settings.renderer,"jax/mml"],["Rerender",a])}};g.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."]}};g.Font=function(){m["HTML-CSS"]&&document.location.reload()};g.Locale=function(){MathJax.Localization.setLocale(l.settings.locale);MathJax.Hub.Queue(["Reprocess",MathJax.Hub])};g.LoadLocale=function(){var d=prompt(f("LoadURL","Load translation data from this URL:"));d&&(d.match(/\.js$/)||alert(f("BadURL","The URL should be for a javascript file that defines MathJax translation data.  Javascript file names should end with '.js'")),b.Require(d,function(a){a!=b.STATUS.OK&&alert(f("BadData","Failed to load translation data from %1",d))}))};g.MPEvents=function(a){var c=l.settings.discoverable,k=g.MPEvents.Messages;d?!c&&"Menu Events"===a.name[1]&&l.settings.mpContext&&alert(f.apply(f,k.IE9warning)):l.settings.mpMouse&&!confirm(f.apply(f,k.IE8warning))?(delete g.cookie.mpContext,delete l.settings.mpContext,delete g.cookie.mpMouse,delete l.settings.mpMouse,g.saveCookie()):(l.settings.mpContext=l.settings.mpMouse,g.cookie.mpContext=g.cookie.mpMouse=l.settings.mpMouse,g.saveCookie(),MathJax.Hub.Queue(["Rerender",MathJax.Hub]))};g.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."]};a.Browser.Select({MSIE:function(a){var c="BackCompat"===document.compatMode;a=a.versionAtLeast("8.0")&&7<document.documentMode;g.Augment({margin:20,msieBackgroundBug:9>document.documentMode,msieFixedPositionBug:c||!a,msieAboutBug:c});d&&(delete l.styles["#MathJax_About"].filter,delete l.styles[".MathJax_Menu"].filter)},Firefox:function(d){g.skipMouseover=d.isMobile&&d.versionAtLeast("6.0");g.skipMousedown=d.isMobile}});g.isMobile=a.Browser.isMobile;g.noContextMenu=a.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(g.menu){var d=g.menu.Find("Language").menu,a=d.items,c=[],k=MathJax.Localization.strings,b;for(b in k)k.hasOwnProperty(b)&&c.push(b);c=c.sort();d.items=[];b=0;for(var l=c.length;b<l;b++){var e=k[c[b]].menuTitle,e=e?e+(" ("+c[b]+")"):c[b];d.items.push(q.RADIO([c[b],e],"locale",{action:g.Locale}))}d.items.push(a[a.length-2],a[a.length-1])}};a.Register.StartupHook("End Config",function(){l.settings=a.config.menuSettings;"undefined"!==typeof l.settings.showRenderer&&(l.showRenderer=l.settings.showRenderer);"undefined"!==typeof l.settings.showFontMenu&&(l.showFontMenu=l.settings.showFontMenu);"undefined"!==typeof l.settings.showContext&&(l.showContext=l.settings.showContext);g.getCookie();g.menu=g(q.SUBMENU(["Show","Show Math As"],q.COMMAND(["MathMLcode","MathML Code"],g.ShowSource,{nativeTouch:!0,format:"MathML"}),q.COMMAND(["Original","Original Form"],g.ShowSource,{nativeTouch:!0}),q.RULE(),q.CHECKBOX(["texHints","Show TeX hints in MathML"],"texHints")),q.RULE(),q.SUBMENU(["Settings","Math Settings"],q.SUBMENU(["ZoomTrigger","Zoom Trigger"],q.RADIO(["Hover","Hover"],"zoom",{action:g.Zoom}),q.RADIO(["Click","Click"],"zoom",{action:g.Zoom}),q.RADIO(["DoubleClick","Double-Click"],"zoom",{action:g.Zoom}),q.RADIO(["NoZoom","No Zoom"],"zoom",{value:"None"}),q.RULE(),q.LABEL(["TriggerRequires","Trigger Requires:"]),q.CHECKBOX(a.Browser.isMac?["Option","Option"]:["Alt","Alt"],"ALT"),q.CHECKBOX(["Command","Command"],"CMD",{hidden:!a.Browser.isMac}),q.CHECKBOX(["Control","Control"],"CTRL",{hidden:a.Browser.isMac}),q.CHECKBOX(["Shift","Shift"],"Shift")),q.SUBMENU(["ZoomFactor","Zoom Factor"],q.RADIO("125%","zscale"),q.RADIO("133%","zscale"),q.RADIO("150%","zscale"),q.RADIO("175%","zscale"),q.RADIO("200%","zscale"),q.RADIO("250%","zscale"),q.RADIO("300%","zscale"),q.RADIO("400%","zscale")),q.RULE(),q.SUBMENU(["Renderer","Math Renderer"],{hidden:!l.showRenderer},q.RADIO("HTML-CSS","renderer",{action:g.Renderer}),q.RADIO("MathML","renderer",{action:g.Renderer,value:"NativeMML"}),q.RADIO("SVG","renderer",{action:g.Renderer})),q.SUBMENU("MathPlayer",{hidden:!a.Browser.isMSIE||!l.showMathPlayer,disabled:!a.Browser.hasMathPlayer},q.LABEL(["MPHandles","Let MathPlayer Handle:"]),q.CHECKBOX(["MenuEvents","Menu Events"],"mpContext",{action:g.MPEvents,hidden:!d}),q.CHECKBOX(["MouseEvents","Mouse Events"],"mpMouse",{action:g.MPEvents,hidden:!d}),q.CHECKBOX(["MenuAndMouse","Mouse and Menu Events"],"mpMouse",{action:g.MPEvents,hidden:d})),q.SUBMENU(["FontPrefs","Font Preference"],{hidden:!l.showFontMenu},q.LABEL(["ForHTMLCSS","For HTML-CSS:"]),q.RADIO(["Auto","Auto"],"font",{action:g.Font}),q.RULE(),q.RADIO(["TeXLocal","TeX (local)"],"font",{action:g.Font}),q.RADIO(["TeXWeb","TeX (web)"],"font",{action:g.Font}),q.RADIO(["TeXImage","TeX (image)"],"font",{action:g.Font}),q.RULE(),q.RADIO(["STIXlocal","STIX (local)"],"font",{action:g.Font})),q.SUBMENU(["ContextMenu","Contextual Menu"],{hidden:!l.showContext},q.RADIO("MathJax","context"),q.RADIO(["Browser","Browser"],"context")),q.COMMAND(["Scale","Scale All Math ..."],g.Scale),q.RULE().With({hidden:!l.showDiscoverable,name:["","discover_rule"]}),q.CHECKBOX(["Discoverable","Highlight on Hover"],"discoverable",{hidden:!l.showDiscoverable})),q.SUBMENU(["Locale","Language"],{hidden:!l.showLocale},q.RADIO("en","locale",{action:g.Locale}),q.RULE().With({hidden:!l.showLocaleURL,name:["","localURL_rule"]}),q.COMMAND(["LoadLocale","Load from URL ..."],g.LoadLocale,{hidden:!l.showLocaleURL})),q.RULE(),q.COMMAND(["About","About MathJax"],g.About),q.COMMAND(["Help","MathJax Help"],g.Help));if(g.isMobile){var c=l.settings,k=g.menu.Find("Math Settings","Zoom Trigger").menu;k.items[0].disabled=k.items[1].disabled=!0;if("Hover"===c.zoom||"Click"==c.zoom)c.zoom="None";k.items=k.items.slice(0,4);navigator.appVersion.match(/[ (]Android[) ]/)&&g.ITEM.SUBMENU.Augment({marker:"\u00bb"})}g.CreateLocaleMenu()});g.showRenderer=function(d){g.cookie.showRenderer=l.showRenderer=d;g.saveCookie();g.menu.Find("Math Settings","Math Renderer").hidden=!d};g.showMathPlayer=function(d){g.cookie.showMathPlayer=l.showMathPlayer=d;g.saveCookie();g.menu.Find("Math Settings","MathPlayer").hidden=!d};g.showFontMenu=function(d){g.cookie.showFontMenu=l.showFontMenu=d;g.saveCookie();g.menu.Find("Math Settings","Font Preference").hidden=!d};g.showContext=function(d){g.cookie.showContext=l.showContext=d;g.saveCookie();g.menu.Find("Math Settings","Contextual Menu").hidden=!d};g.showDiscoverable=function(d){g.cookie.showDiscoverable=l.showDiscoverable=d;g.saveCookie();g.menu.Find("Math Settings","Highlight on Hover").hidden=!d;g.menu.Find("Math Settings","discover_rule").hidden=!d};g.showLocale=function(d){g.cookie.showLocale=l.showLocale=d;g.saveCookie();g.menu.Find("Language").hidden=!d};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){MathJax.OutputJax["HTML-CSS"].config.imageFont||(g.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=!0)});c.Queue(a.Register.StartupHook("End Config",{}),["getImages",g],["Styles",b,l.styles],["Post",a.Startup.signal,"MathMenu Ready"],["loadComplete",b,"[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:"2.2",directory:MathJax.ElementJax.directory+"/mml",extensionDir:MathJax.ElementJax.extensionDir+"/mml",optableDir:MathJax.ElementJax.directory+"/mml/optable"});MathJax.ElementJax.mml.Augment({Init:function(){this.root=1===arguments.length&&"math"===arguments[0].type?arguments[0]:MathJax.ElementJax.mml.math.apply(this,arguments);if(this.root.attr&&this.root.attr.mode){this.root.display||"display"!==this.root.attr.mode||(this.root.display="block",this.root.attrNames.push("display"));delete this.root.attr.mode;for(var a=0,e=this.root.attrNames.length;a<e;a++)if("mode"===this.root.attrNames[a]){this.root.attrNames.splice(a,1);break}}}},{INHERIT:"_inherit_",AUTO:"_auto_",SIZE:{INFINITY:"infinity",SMALL:"small",NORMAL:"normal",BIG:"big"},COLOR:{TRANSPARENT:"transparent"},VARIANT:{NORMAL:"normal",BOLD:"bold",ITALIC:"italic",BOLDITALIC:"bold-italic",DOUBLESTRUCK:"double-struck",FRAKTUR:"fraktur",BOLDFRAKTUR:"bold-fraktur",SCRIPT:"script",BOLDSCRIPT:"bold-script",SANSSERIF:"sans-serif",BOLDSANSSERIF:"bold-sans-serif",SANSSERIFITALIC:"sans-serif-italic",SANSSERIFBOLDITALIC:"sans-serif-bold-italic",MONOSPACE:"monospace",INITIAL:"inital",TAILED:"tailed",LOOPED:"looped",STRETCHED:"stretched",CALIGRAPHIC:"-tex-caligraphic",OLDSTYLE:"-tex-oldstyle"},FORM:{PREFIX:"prefix",INFIX:"infix",POSTFIX:"postfix"},LINEBREAK:{AUTO:"auto",NEWLINE:"newline",NOBREAK:"nobreak",GOODBREAK:"goodbreak",BADBREAK:"badbreak"},LINEBREAKSTYLE:{BEFORE:"before",AFTER:"after",DUPLICATE:"duplicate",INFIXLINBREAKSTYLE:"infixlinebreakstyle"},INDENTALIGN:{LEFT:"left",CENTER:"center",RIGHT:"right",AUTO:"auto",ID:"id",INDENTALIGN:"indentalign"},INDENTSHIFT:{INDENTSHIFT:"indentshift"},LINETHICKNESS:{THIN:"thin",MEDIUM:"medium",THICK:"thick"},NOTATION:{LONGDIV:"longdiv",ACTUARIAL:"actuarial",RADICAL:"radical",BOX:"box",ROUNDEDBOX:"roundedbox",CIRCLE:"circle",LEFT:"left",RIGHT:"right",TOP:"top",BOTTOM:"bottom",UPDIAGONALSTRIKE:"updiagonalstrike",DOWNDIAGONALSTRIKE:"downdiagonalstrike",VERTICALSTRIKE:"verticalstrike",HORIZONTALSTRIKE:"horizontalstrike",MADRUWB:"madruwb"},ALIGN:{TOP:"top",BOTTOM:"bottom",CENTER:"center",BASELINE:"baseline",AXIS:"axis",LEFT:"left",RIGHT:"right"},LINES:{NONE:"none",SOLID:"solid",DASHED:"dashed"},SIDE:{LEFT:"left",RIGHT:"right",LEFTOVERLAP:"leftoverlap",RIGHTOVERLAP:"rightoverlap"},WIDTH:{AUTO:"auto",FIT:"fit"},ACTIONTYPE:{TOGGLE:"toggle",STATUSLINE:"statusline",TOOLTIP:"tooltip",INPUT:"input"},LENGTH:{VERYVERYTHINMATHSPACE:"veryverythinmathspace",VERYTHINMATHSPACE:"verythinmathspace",THINMATHSPACE:"thinmathspace",MEDIUMMATHSPACE:"mediummathspace",THICKMATHSPACE:"thickmathspace",VERYTHICKMATHSPACE:"verythickmathspace",VERYVERYTHICKMATHSPACE:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE:"negativeverythinmathspace",NEGATIVETHINMATHSPACE:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE:"negativemediummathspace",NEGATIVETHICKMATHSPACE:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE:"negativeveryverythickmathspace"},OVERFLOW:{LINBREAK:"linebreak",SCROLL:"scroll",ELIDE:"elide",TRUNCATE:"truncate",SCALE:"scale"},UNIT:{EM:"em",EX:"ex",PX:"px",IN:"in",CM:"cm",MM:"mm",PT:"pt",PC:"pc"},TEXCLASS:{ORD:0,OP:1,BIN:2,REL:3,OPEN:4,CLOSE:5,PUNCT:6,INNER:7,VCENTER:8,NONE:-1},TEXCLASSNAMES:"ORD OP BIN REL OPEN CLOSE PUNCT INNER VCENTER".split(" "),copyAttributes:{fontfamily:!0,fontsize:!0,fontweight:!0,fontstyle:!0,color:!0,background:!0,id:!0,"class":!0,href:!0,style:!0},skipAttributes:{texClass:!0,useHeight:!0,texprimestyle:!0},copyAttributeNames:"fontfamily fontsize fontweight fontstyle color background id class href style".split(" ")});(function(a){a.mbase=MathJax.Object.Subclass({type:"base",isToken:!1,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT},noInherit:{},noInheritAttribute:{texClass:!0},linebreakContainer:!1,Init:function(){this.data=[];!this.inferRow||1===arguments.length&&arguments[0].inferred||this.Append(a.mrow().With({inferred:!0,notParent:!0}));this.Append.apply(this,arguments)},With:function(a){for(var b in a)a.hasOwnProperty(b)&&(this[b]=a[b]);return this},Append:function(){if(this.inferRow&&this.data.length)this.data[0].Append.apply(this.data[0],arguments);else for(var a=0,b=arguments.length;a<b;a++)this.SetData(this.data.length,arguments[a])},SetData:function(c,b){null!=b&&(b instanceof a.mbase||(b=this.isToken?a.chars(b):a.mtext(b)),b.parent=this,b.setInherit(this.inheritFromMe?this:this.inherit));this.data[c]=b},Parent:function(){for(var a=this.parent;a&&a.notParent;)a=a.parent;return a},Get:function(c,b){if(null!=this[c])return this[c];if(this.attr&&null!=this.attr[c])return this.attr[c];var e=this.Parent();if(e&&null!=e["adjustChild_"+c])return e["adjustChild_"+c](this.childPosition(),b);for(var f=e=this.inherit;e;){f=e[c];null==f&&e.attr&&(f=e.attr[c]);if(null!=f&&e.noInheritAttribute&&!e.noInheritAttribute[c]){var h=e.noInherit[this.type];if(!h||!h[c])return f}f=e;e=e.inherit}if(!b){if(this.defaults[c]===a.AUTO)return this.autoDefault(c);if(this.defaults[c]!==a.INHERIT&&null!=this.defaults[c])return this.defaults[c];if(f)return f.defaults[c]}return null},hasValue:function(a){return null!=this.Get(a,!0)},getValues:function(){for(var a={},b=0,e=arguments.length;b<e;b++)a[arguments[b]]=this.Get(arguments[b]);return a},adjustChild_scriptlevel:function(a,b){return this.Get("scriptlevel",b)},adjustChild_displaystyle:function(a,b){return this.Get("displaystyle",b)},adjustChild_texprimestyle:function(a,b){return this.Get("texprimestyle",b)},childPosition:function(){for(var a=this,b=a.parent;b.notParent;)a=b,b=a.parent;for(var e=0,f=b.data.length;e<f;e++)if(b.data[e]===a)return e;return null},setInherit:function(a){if(a!==this.inherit&&null==this.inherit){this.inherit=a;for(var b=0,e=this.data.length;b<e;b++)this.data[b]&&this.data[b].setInherit&&this.data[b].setInherit(a)}},setTeXclass:function(a){this.getPrevClass(a);return"undefined"!==typeof this.texClass?this:a},getPrevClass:function(a){a&&(this.prevClass=a.Get("texClass"),this.prevLevel=a.Get("scriptlevel"))},updateTeXclass:function(a){a&&(this.prevClass=a.prevClass,delete a.prevClass,this.prevLevel=a.prevLevel,delete a.prevLevel,this.texClass=a.Get("texClass"))},texSpacing:function(){var c=null!=this.prevClass?this.prevClass:a.TEXCLASS.NONE,b=this.Get("texClass")||a.TEXCLASS.ORD;if(c===a.TEXCLASS.NONE||b===a.TEXCLASS.NONE)return"";c===a.TEXCLASS.VCENTER&&(c=a.TEXCLASS.ORD);b===a.TEXCLASS.VCENTER&&(b=a.TEXCLASS.ORD);c=this.TEXSPACE[c][b];return 0<this.prevLevel&&0<this.Get("scriptlevel")&&0<=c?"":this.TEXSPACELENGTH[Math.abs(c)]},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(a){return""},isSpacelike:function(){return!1},isEmbellished:function(){return!1},Core:function(){return this},CoreMO:function(){return this},hasNewline:function(){if(this.isEmbellished())return this.CoreMO().hasNewline();if(this.isToken||this.linebreakContainer)return!1;for(var a=0,b=this.data.length;a<b;a++)if(this.data[a]&&this.data[a].hasNewline())return!0;return!1},array:function(){return this.inferred?this.data:[this]},toString:function(){return this.type+"("+this.data.join(",")+")"}},{childrenSpacelike:function(){for(var a=0,b=this.data.length;a<b;a++)if(!this.data[a].isSpacelike())return!1;return!0},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(a){this.data[0]&&(a=this.data[0].setTeXclass(a),this.updateTeXclass(this.data[0]));return a},setBaseTeXclasses:function(c){this.getPrevClass(c);this.texClass=null;this.data[0]?this.isEmbellished()||this.data[0].isa(a.mi)?(c=this.data[0].setTeXclass(c),this.updateTeXclass(this.Core())):(this.data[0].setTeXclass(),c=this):c=this;for(var b=1,e=this.data.length;b<e;b++)this.data[b]&&this.data[b].setTeXclass();return c},setSeparateTeXclasses:function(a){this.getPrevClass(a);a=0;for(var b=this.data.length;a<b;a++)this.data[a]&&this.data[a].setTeXclass();this.isEmbellished()&&this.updateTeXclass(this.Core());return this}});a.mi=a.mbase.Subclass({type:"mi",isToken:!0,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.AUTO,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT},autoDefault:function(c){return"mathvariant"===c?(c=(this.data[0]||"").toString(),1===c.length||2===c.length&&55296<=c.charCodeAt(0)&&56320>c.charCodeAt(0)?a.VARIANT.ITALIC:a.VARIANT.NORMAL):""},setTeXclass:function(c){this.getPrevClass(c);c=this.data.join("");1<c.length&&c.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD&&(this.texClass=a.TEXCLASS.OP,this.autoOP=!0);return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:!0,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:!0,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:!1,separator:!1,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:!1,symmetric:!0,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:!1,movablelimits:!1,accent:!1,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(c,b){var e=this.def;if(!e){if("form"===c)return this.useMMLspacing&=~this.SPACE_ATTR.form,this.getForm();for(var f=this.data.join(""),h=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX],p=0,d=h.length;p<d;p++){var k=this.OPTABLE[h[p]][f];if(k){e=this.makeDef(k);break}}e||(e=this.CheckRange(f));!e&&b?e={}:(e||(e=MathJax.Hub.Insert({},this.defaultDef)),e.form=h[0],this.def=e)}this.useMMLspacing&=~(this.SPACE_ATTR[c]||0);return null!=e[c]?e[c]:b?"":this.defaultDef[c]},CheckRange:function(c){var b=c.charCodeAt(0);55296<=b&&56320>b&&(b=(b-55296<<10)+(c.charCodeAt(1)-56320)+65536);for(var e=0,f=this.RANGES.length;e<f&&this.RANGES[e][0]<=b;e++)if(b<=this.RANGES[e][1])return this.RANGES[e][3]&&(b=a.optableDir+"/"+this.RANGES[e][3]+".js",this.RANGES[e][3]=null,MathJax.Hub.RestartAfter(MathJax.Ajax.Require(b))),e=a.TEXCLASSNAMES[this.RANGES[e][2]],e=this.OPTABLE.infix[c]=a.mo.OPTYPES["BIN"===e?"BIN3":e],this.makeDef(e);return null},makeDef:function(c){null==c[2]&&(c[2]=this.defaultDef.texClass);c[3]||(c[3]={});var b=MathJax.Hub.Insert({},c[3]);b.lspace=this.SPACE[c[0]];b.rspace=this.SPACE[c[1]];b.texClass=c[2];b.texClass===a.TEXCLASS.REL&&(this.movablelimits||this.data.join("").match(/^[a-z]+$/i))&&(b.texClass=a.TEXCLASS.OP);return b},getForm:function(){for(var c=this,b=this.parent,e=this.Parent();e&&e.isEmbellished();)c=b,b=e.parent,e=e.Parent();if(b&&"mrow"===b.type&&1!==b.NonSpaceLength()){if(b.FirstNonSpace()===c)return a.FORM.PREFIX;if(b.LastNonSpace()===c)return a.FORM.POSTFIX}return a.FORM.INFIX},isEmbellished:function(){return!0},hasNewline:function(){return this.Get("linebreak")===a.LINEBREAK.NEWLINE},setTeXclass:function(c){this.getValues("lspace","rspace");if(this.useMMLspacing)return this.texClass=a.TEXCLASS.NONE,this;this.texClass=this.Get("texClass");return"\u2061"===this.data.join("")?(c&&(c.texClass=a.TEXCLASS.OP),this.texClass=this.prevClass=a.TEXCLASS.NONE,c):this.adjustTeXclass(c)},adjustTeXclass:function(c){if(this.texClass===a.TEXCLASS.NONE)return c;c?(!c.autoOP||this.texClass!==a.TEXCLASS.BIN&&this.texClass!==a.TEXCLASS.REL||(c.texClass=a.TEXCLASS.ORD),this.prevClass=c.texClass||a.TEXCLASS.ORD,this.prevLevel=c.Get("scriptlevel")):this.prevClass=a.TEXCLASS.NONE;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.prevClass!==a.TEXCLASS.BIN||this.texClass!==a.TEXCLASS.REL&&this.texClass!==a.TEXCLASS.CLOSE&&this.texClass!==a.TEXCLASS.PUNCT||(c.texClass=this.prevClass=a.TEXCLASS.ORD):this.texClass=a.TEXCLASS.ORD;return this}});a.mtext=a.mbase.Subclass({type:"mtext",isToken:!0,isSpacelike:function(){return!0},texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT}});a.mspace=a.mbase.Subclass({type:"mspace",isToken:!0,isSpacelike:function(){return!0},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:!0,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,lquote:'"',rquote:'"'}});a.mglyph=a.mbase.Subclass({type:"mglyph",isToken:!0,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:!1,notParent:!1,isEmbellished:function(){for(var a=!1,b=0,e=this.data.length;b<e;b++)if(null!=this.data[b])if(this.data[b].isEmbellished()){if(a)return!1;a=!0;this.core=b}else if(!this.data[b].isSpacelike())return!1;return a},NonSpaceLength:function(){for(var a=0,b=0,e=this.data.length;b<e;b++)this.data[b]&&!this.data[b].isSpacelike()&&a++;return a},FirstNonSpace:function(){for(var a=0,b=this.data.length;a<b;a++)if(this.data[a]&&!this.data[a].isSpacelike())return this.data[a];return null},LastNonSpace:function(){for(var a=this.data.length-1;0<=a;a--)if(this.data[0]&&!this.data[a].isSpacelike())return this.data[a];return null},Core:function(){return this.isEmbellished()&&"undefined"!==typeof this.core?this.data[this.core]:this},CoreMO:function(){return this.isEmbellished()&&"undefined"!==typeof this.core?this.data[this.core].CoreMO():this},toString:function(){return this.inferred?"["+this.data.join(",")+"]":this.SUPER(arguments).toString.call(this)},setTeXclass:function(a){for(var b=0,e=this.data.length;b<e;b++)this.data[b]&&(a=this.data[b].setTeXclass(a));this.data[0]&&this.updateTeXclass(this.data[0]);return a}});a.mfrac=a.mbase.Subclass({type:"mfrac",num:0,den:1,linebreakContainer:!0,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:!1},adjustChild_displaystyle:function(a){return!1},adjustChild_scriptlevel:function(a){a=this.Get("scriptlevel");(!this.Get("displaystyle")||0<a)&&a++;return a},adjustChild_texprimestyle:function(a){return a==this.den?!0:this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:!0,linebreakContainer:!0,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(a){return!0}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:!0,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(a){return 1===a?!1:this.Get("displaystyle")},adjustChild_scriptlevel:function(a){var b=this.Get("scriptlevel");1===a&&(b+=2);return b},adjustChild_texprimestyle:function(a){return 0===a?!0: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:!0,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(.5),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(a){a=this.scriptlevel;if(null==a)a=this.Get("scriptlevel");else if(String(a).match(/^ *[-+]/)){delete this.scriptlevel;var b=this.Get("scriptlevel");this.scriptlevel=a;a=b+parseInt(a)}return a},inheritFromMe:!0,noInherit:{mpadded:{width:!0,height:!0,depth:!0,lspace:!0,voffset:!0},mtable:{width:!0,height:!0,depth:!0,align:!0}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:!0,linebreakContainer:!0,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:!0,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:!0,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(c){this.getPrevClass(c);var b=this.getValues("open","close","separators");b.open=b.open.replace(/[ \t\n\r]/g,"");b.close=b.close.replace(/[ \t\n\r]/g,"");b.separators=b.separators.replace(/[ \t\n\r]/g,"");""!==b.open&&(this.SetData("open",a.mo(b.open).With({stretchy:!0,texClass:a.TEXCLASS.OPEN})),c=this.data.open.setTeXclass(c));if(""!==b.separators)for(;b.separators.length<this.data.length;)b.separators+=b.separators.charAt(b.separators.length-1);this.data[0]&&(c=this.data[0].setTeXclass(c));for(var e=1,f=this.data.length;e<f;e++)this.data[e]&&(""!==b.separators&&(this.SetData("sep"+e,a.mo(b.separators.charAt(e-1))),c=this.data["sep"+e].setTeXclass(c)),c=this.data[e].setTeXclass(c));""!==b.close&&(this.SetData("close",a.mo(b.close).With({stretchy:!0,texClass:a.TEXCLASS.CLOSE})),c=this.data.close.setTeXclass(c));this.updateTeXclass(this.data.open);return c}});a.menclose=a.mbase.Subclass({type:"menclose",inferRow:!0,linebreakContainer:!0,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(c){return"texClass"===c?this.isEmbellished()?this.CoreMO().Get(c):a.TEXCLASS.ORD:0},adjustChild_displaystyle:function(a){return 0<a?!1:this.Get("displaystyle")},adjustChild_scriptlevel:function(a){var b=this.Get("scriptlevel");0<a&&b++;return b},adjustChild_texprimestyle:function(a){return a===this.sub?!0: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(a){return 1===a%2?!0: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:!0,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(c){return"texClass"===c?this.isEmbellished()?this.CoreMO().Get(c):a.TEXCLASS.ORD:"accent"===c&&this.data[this.over]?this.data[this.over].CoreMO().Get("accent"):"accentunder"===c&&this.data[this.under]?this.data[this.under].CoreMO().Get("accent"):!1},adjustChild_displaystyle:function(a){return 0<a?!1:this.Get("displaystyle")},adjustChild_scriptlevel:function(a){var b=this.Get("scriptlevel"),e=this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits");a!=this.under||!e&&this.Get("accentunder")||b++;a!=this.over||!e&&this.Get("accent")||b++;return b},adjustChild_texprimestyle:function(a){return a===this.base&&this.data[this.over]?!0: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:!0,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:!1,equalcolumns:!1,displaystyle:!1,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:!0,noInherit:{mover:{align:!0},munder:{align:!0},munderover:{align:!0},mtable:{align:!0,rowalign:!0,columnalign:!0,groupalign:!0,alignmentscope:!0,columnwidth:!0,width:!0,rowspacing:!0,columnspacing:!0,rowlines:!0,columnlines:!0,frame:!0,framespacing:!0,equalrows:!0,equalcolumns:!0,side:!0,minlabelspacing:!0,texClass:!0,useHeight:1}},linebreakContainer:!0,Append:function(){for(var c=0,b=arguments.length;c<b;c++)arguments[c]instanceof a.mtr||arguments[c]instanceof a.mlabeledtr||(arguments[c]=a.mtd(arguments[c]));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:!0,noInherit:{mrow:{rowalign:!0,columnalign:!0,groupalign:!0},mtable:{rowalign:!0,columnalign:!0,groupalign:!0}},linebreakContainer:!0,Append:function(){for(var c=0,b=arguments.length;c<b;c++)arguments[c]instanceof a.mtd||(arguments[c]=a.mtd(arguments[c]));this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtd=a.mbase.Subclass({type:"mtd",inferRow:!0,linebreakContainer:!0,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!0},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:!0,noInherit:{mrow:{groupalign:!0},mtable:{groupalign:!0}}});a.malignmark=a.mbase.Subclass({type:"malignmark",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,edge:a.SIDE.LEFT},isSpacelike:function(){return!0}});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(c){this.Get("actiontype")===a.ACTIONTYPE.TOOLTIP&&this.data[1]&&this.data[1].setTeXclass();return this.selected().setTeXclass(c)}});a.semantics=a.mbase.Subclass({type:"semantics",notParent:!0,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{definitionURL:null,encoding:null},setTeXclass:a.mbase.setChildTeXclass});a.annotation=a.mbase.Subclass({type:"annotation",isToken:!0,linebreakContainer:!0,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a["annotation-xml"]=a.mbase.Subclass({type:"annotation-xml",linebreakContainer:!0,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a.math=a.mstyle.Subclass({type:"math",defaults:{mathvariant:a.VARIANT.NORMAL,mathsize:a.SIZE.NORMAL,mathcolor:"",mathbackground:a.COLOR.TRANSPARENT,scriptlevel:0,displaystyle:a.AUTO,display:"inline",maxwidth:"",overflow:a.OVERFLOW.LINEBREAK,altimg:"","altimg-width":"","altimg-height":"","altimg-valign":"",alttext:"",cdgroup:"",scriptsizemultiplier:Math.sqrt(.5),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:!1},autoDefault:function(a){return"displaystyle"===a?"block"===this.Get("display"):""},linebreakContainer:!0,setTeXclass:a.mbase.setChildTeXclass});a.chars=a.mbase.Subclass({type:"chars",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){return this.data.join("")},toString:function(){return this.data.join("")}});a.entity=a.mbase.Subclass({type:"entity",Append:function(){this.data.push.apply(this.data,arguments)},value:function(){return"#x"===this.data[0].substr(0,2)?parseInt(this.data[0].substr(2),16):"#"===this.data[0].substr(0,1)?parseInt(this.data[0].substr(1)):0},toString:function(){var a=this.value();if(65535>=a)return String.fromCharCode(a);a-=65536;return String.fromCharCode((a>>10)+55296)+String.fromCharCode((a&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 a=0,b=arguments.length;a<b;a++){var e=this.Import(arguments[a]);this.data.push(e);this.div.appendChild(e)}},Import:function(a){if(document.importNode)return document.importNode(a,!0);var b,e,f;if(1===a.nodeType){b=document.createElement(a.nodeName);e=0;for(f=a.attributes.length;e<f;e++){var h=a.attributes[e];h.specified&&null!=h.nodeValue&&""!=h.nodeValue&&b.setAttribute(h.nodeName,h.nodeValue);"style"===h.nodeName&&(b.style.cssText=h.nodeValue)}a.className&&(b.className=a.className)}else if(3===a.nodeType||4===a.nodeType)b=document.createTextNode(a.nodeValue);else if(8===a.nodeType)b=document.createComment(a.nodeValue);else return document.createTextNode("");e=0;for(f=a.childNodes.length;e<f;e++)b.appendChild(this.Import(a.childNodes[e]));return b},value:function(){return this.div},toString:function(){return this.div.innerHTML}});a.TeXAtom=a.mbase.Subclass({type:"texatom",inferRow:!0,notParent:!0,texClass:a.TEXCLASS.ORD,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,isEmbellished:a.mbase.childEmbellished,setTeXclass:function(a){this.data[0].setTeXclass();return this.adjustTeXclass(a)},adjustTeXclass:a.mo.prototype.adjustTeXclass});a.NULL=a.mbase().With({type:"null"});var e=a.TEXCLASS,b={ORD:[0,0,e.ORD],ORD11:[1,1,e.ORD],ORD21:[2,1,e.ORD],ORD02:[0,2,e.ORD],ORD55:[5,5,e.ORD],OP:[1,2,e.OP,{largeop:!0,movablelimits:!0,symmetric:!0}],OPFIXED:[1,2,e.OP,{largeop:!0,movablelimits:!0}],INTEGRAL:[0,1,e.OP,{largeop:!0,symmetric:!0}],INTEGRAL2:[1,2,e.OP,{largeop:!0,symmetric:!0}],BIN3:[3,3,e.BIN],BIN4:[4,4,e.BIN],BIN01:[0,1,e.BIN],BIN5:[5,5,e.BIN],TALLBIN:[4,4,e.BIN,{stretchy:!0}],BINOP:[4,4,e.BIN,{largeop:!0,movablelimits:!0}],REL:[5,5,e.REL],REL1:[1,1,e.REL,{stretchy:!0}],REL4:[4,4,e.REL],RELSTRETCH:[5,5,e.REL,{stretchy:!0}],RELACCENT:[5,5,e.REL,{accent:!0}],WIDEREL:[5,5,e.REL,{accent:!0,stretchy:!0}],OPEN:[0,0,e.OPEN,{fence:!0,stretchy:!0,symmetric:!0}],CLOSE:[0,0,e.CLOSE,{fence:!0,stretchy:!0,symmetric:!0}],INNER:[0,0,e.INNER],PUNCT:[0,3,e.PUNCT],ACCENT:[0,0,e.ORD,{accent:!0}],WIDEACCENT:[0,0,e.ORD,{accent:!0,stretchy:!0}]};a.mo.Augment({SPACE:"0em 0.1111em 0.1667em 0.2222em 0.2667em 0.3333em".split(" "),RANGES:[[32,127,e.REL,"BasicLatin"],[160,255,e.ORD,"Latin1Supplement"],[256,383,e.ORD],[384,591,e.ORD],[688,767,e.ORD,"SpacingModLetters"],[768,879,e.ORD,"CombDiacritMarks"],[880,1023,e.ORD,"GreekAndCoptic"],[7680,7935,e.ORD],[8192,8303,e.PUNCT,"GeneralPunctuation"],[8304,8351,e.ORD],[8352,8399,e.ORD],[8400,8447,e.ORD,"CombDiactForSymbols"],[8448,8527,e.ORD,"LetterlikeSymbols"],[8528,8591,e.ORD],[8592,8703,e.REL,"Arrows"],[8704,8959,e.BIN,"MathOperators"],[8960,9215,e.ORD,"MiscTechnical"],[9312,9471,e.ORD],[9472,9631,e.ORD],[9632,9727,e.ORD,"GeometricShapes"],[9984,10175,e.ORD,"Dingbats"],[10176,10223,e.ORD,"MiscMathSymbolsA"],[10224,10239,e.REL,"SupplementalArrowsA"],[10496,10623,e.REL,"SupplementalArrowsB"],[10624,10751,e.ORD,"MiscMathSymbolsB"],[10752,11007,e.BIN,"SuppMathOperators"],[11008,11263,e.ORD,"MiscSymbolsAndArrows"],[119808,120831,e.ORD]],OPTABLE:{prefix:{"\u2200":b.ORD21,"\u2202":b.ORD21,"\u2203":b.ORD21,"\u2207":b.ORD21,"\u220f":b.OP,"\u2210":b.OP,"\u2211":b.OP,"\u2212":b.BIN01,"\u2213":b.BIN01,"\u221a":[1,1,e.ORD,{stretchy:!0}],"\u2220":b.ORD,"\u222b":b.INTEGRAL,"\u222e":b.INTEGRAL,"\u22c0":b.OP,"\u22c1":b.OP,"\u22c2":b.OP,"\u22c3":b.OP,"\u2308":b.OPEN,"\u230a":b.OPEN,"\u27e8":b.OPEN,"\u27ee":b.OPEN,"\u2a00":b.OP,"\u2a01":b.OP,"\u2a02":b.OP,"\u2a04":b.OP,"\u2a06":b.OP,"\u00ac":b.ORD21,"\u00b1":b.BIN01,"(":b.OPEN,"+":b.BIN01,"-":b.BIN01,"[":b.OPEN,"{":b.OPEN,"|":b.OPEN},postfix:{"!":[1,0,e.CLOSE],"\x26":b.ORD,"\u2032":b.ORD02,"\u203e":b.WIDEACCENT,"\u2309":b.CLOSE,"\u230b":b.CLOSE,"\u23de":b.WIDEACCENT,"\u23df":b.WIDEACCENT,"\u266d":b.ORD02,"\u266e":b.ORD02,"\u266f":b.ORD02,"\u27e9":b.CLOSE,"\u27ef":b.CLOSE,"\u02c6":b.WIDEACCENT,"\u02c7":b.WIDEACCENT,"\u02c9":b.WIDEACCENT,"\u02ca":b.ACCENT,"\u02cb":b.ACCENT,"\u02d8":b.ACCENT,"\u02d9":b.ACCENT,"\u02dc":b.WIDEACCENT,"\u0302":b.WIDEACCENT,"\u00a8":b.ACCENT,"\u00af":b.WIDEACCENT,")":b.CLOSE,"]":b.CLOSE,"^":b.WIDEACCENT,_:b.WIDEACCENT,"`":b.ACCENT,"|":b.CLOSE,"}":b.CLOSE,"~":b.WIDEACCENT},infix:{"":b.ORD,"%":[3,3,e.ORD],"\u2022":b.BIN4,"\u2026":b.INNER,"\u2044":b.TALLBIN,"\u2061":b.ORD,"\u2062":b.ORD,"\u2063":[0,0,e.ORD,{linebreakstyle:"after",separator:!0}],"\u2064":b.ORD,"\u2190":b.WIDEREL,"\u2191":b.RELSTRETCH,"\u2192":b.WIDEREL,"\u2193":b.RELSTRETCH,"\u2194":b.WIDEREL,"\u2195":b.RELSTRETCH,"\u2196":b.RELSTRETCH,"\u2197":b.RELSTRETCH,"\u2198":b.RELSTRETCH,"\u2199":b.RELSTRETCH,"\u21a6":b.WIDEREL,"\u21a9":b.WIDEREL,"\u21aa":b.WIDEREL,"\u21bc":b.WIDEREL,"\u21bd":b.WIDEREL,"\u21c0":b.WIDEREL,"\u21c1":b.WIDEREL,"\u21cc":b.WIDEREL,"\u21d0":b.WIDEREL,"\u21d1":b.RELSTRETCH,"\u21d2":b.WIDEREL,"\u21d3":b.RELSTRETCH,"\u21d4":b.WIDEREL,"\u21d5":b.RELSTRETCH,"\u2208":b.REL,"\u2209":b.REL,"\u220b":b.REL,"\u2212":b.BIN4,"\u2213":b.BIN4,"\u2215":b.TALLBIN,"\u2216":b.BIN4,"\u2217":b.BIN4,"\u2218":b.BIN4,"\u2219":b.BIN4,"\u221d":b.REL,"\u2223":b.REL,"\u2225":b.REL,"\u2227":b.BIN4,"\u2228":b.BIN4,"\u2229":b.BIN4,"\u222a":b.BIN4,"\u223c":b.REL,"\u2240":b.BIN4,"\u2243":b.REL,"\u2245":b.REL,"\u2248":b.REL,"\u224d":b.REL,"\u2250":b.REL,"\u2260":b.REL,"\u2261":b.REL,"\u2264":b.REL,"\u2265":b.REL,"\u226a":b.REL,"\u226b":b.REL,"\u227a":b.REL,"\u227b":b.REL,"\u2282":b.REL,"\u2283":b.REL,"\u2286":b.REL,"\u2287":b.REL,"\u228e":b.BIN4,"\u2291":b.REL,"\u2292":b.REL,"\u2293":b.BIN4,"\u2294":b.BIN4,"\u2295":b.BIN4,"\u2296":b.BIN4,"\u2297":b.BIN4,"\u2298":b.BIN4,"\u2299":b.BIN4,"\u22a2":b.REL,"\u22a3":b.REL,"\u22a4":b.ORD55,"\u22a5":b.REL,"\u22a8":b.REL,"\u22c4":b.BIN4,"\u22c5":b.BIN4,"\u22c6":b.BIN4,"\u22c8":b.REL,"\u22ee":b.ORD55,"\u22ef":b.INNER,"\u22f1":[5,5,e.INNER],"\u25b3":b.BIN4,"\u25b5":b.BIN4,"\u25b9":b.BIN4,"\u25bd":b.BIN4,"\u25bf":b.BIN4,"\u25c3":b.BIN4,"\u2758":b.REL,"\u27f5":b.WIDEREL,"\u27f6":b.WIDEREL,"\u27f7":b.WIDEREL,"\u27f8":b.WIDEREL,"\u27f9":b.WIDEREL,"\u27fa":b.WIDEREL,"\u27fc":b.WIDEREL,"\u2a2f":b.BIN4,"\u2a3f":b.BIN4,"\u2aaf":b.REL,"\u2ab0":b.REL,"\u00b1":b.BIN4,"\u00b7":b.BIN4,"\u00d7":b.BIN4,"\u00f7":b.BIN4,"*":b.BIN3,"+":b.BIN4,",":[0,3,e.PUNCT,{linebreakstyle:"after",separator:!0}],"-":b.BIN4,".":[3,3,e.ORD],"/":b.ORD11,":":[1,2,e.REL],";":[0,3,e.PUNCT,{linebreakstyle:"after",separator:!0}],"\x3c":b.REL,"\x3d":b.REL,"\x3e":b.REL,"?":[1,1,e.CLOSE],"\\":b.ORD,"^":b.ORD11,_:b.ORD11,"|":[2,2,e.ORD,{fence:!0,stretchy:!0,symmetric:!0}],"#":b.ORD,$:b.ORD,".":[0,3,e.PUNCT,{separator:!0}],"\u02b9":b.ORD,"\u0300":b.ACCENT,"\u0301":b.ACCENT,"\u0303":b.WIDEACCENT,"\u0304":b.ACCENT,"\u0306":b.ACCENT,"\u0307":b.ACCENT,"\u0308":b.ACCENT,"\u030c":b.ACCENT,"\u0332":b.WIDEACCENT,"\u0338":b.REL4,"\u2015":[0,0,e.ORD,{stretchy:!0}],"\u2017":[0,0,e.ORD,{stretchy:!0}],"\u2020":b.BIN3,"\u2021":b.BIN3,"\u20d7":b.ACCENT,"\u2111":b.ORD,"\u2113":b.ORD,"\u2118":b.ORD,"\u211c":b.ORD,"\u2205":b.ORD,"\u221e":b.ORD,"\u2305":b.BIN3,"\u2306":b.BIN3,"\u2322":b.REL4,"\u2323":b.REL4,"\u2329":b.OPEN,"\u232a":b.CLOSE,"\u23aa":b.ORD,"\u23af":[0,0,e.ORD,{stretchy:!0}],"\u23b0":b.OPEN,"\u23b1":b.CLOSE,"\u2500":b.ORD,"\u25ef":b.BIN3,"\u2660":b.ORD,"\u2661":b.ORD,"\u2662":b.ORD,"\u2663":b.ORD,"\u3008":b.OPEN,"\u3009":b.CLOSE,"\ufe37":b.WIDEACCENT,"\ufe38":b.WIDEACCENT}}},{OPTYPES:b});a.mo.prototype.OPTABLE.infix["^"]=b.WIDEREL;a.mo.prototype.OPTABLE.infix._=b.WIDEREL})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js");MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var a=MathJax.ElementJax.mml;SETTINGS=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(a){var b=this.inferred&&this.parent.inferRow;null==a&&(a="");var c=this.type,m=this.toMathMLattributes();if("mspace"===c)return a+"\x3c"+c+m+" /\x3e";for(var n=[],f=this.isToken?"":a+(b?"":"  "),h=0,p=this.data.length;h<p;h++)this.data[h]?n.push(this.data[h].toMathML(f)):this.isToken||n.push(f+"\x3cmrow /\x3e");return this.isToken?a+"\x3c"+c+m+"\x3e"+n.join("")+"\x3c/"+c+"\x3e":b?n.join("\n"):0===n.length||1===n.length&&""===n[0]?a+"\x3c"+c+m+" /\x3e":a+"\x3c"+c+m+"\x3e\n"+n.join("\n")+"\n"+a+"\x3c/"+c+"\x3e"},toMathMLattributes:function(){var e=[],b=this.defaults,c=this.attrNames||a.copyAttributeNames,m=a.skipAttributes;"math"!==this.type||this.attr&&this.attr.xmlns||e.push('xmlns\x3d"http://www.w3.org/1998/Math/MathML"');if(!this.attrNames){"mstyle"===this.type&&(b=a.math.prototype.defaults);for(var n in b)if(!m[n]&&b.hasOwnProperty(n)){var f="open"===n||"close"===n;if(null!=this[n]&&(f||this[n]!==b[n])){var h=this[n];delete this[n];(f||this.Get(n)!==h)&&e.push(n+'\x3d"'+this.toMathMLattribute(h)+'"');this[n]=h}}}b=0;for(m=c.length;b<m;b++)"class"!==c[b]&&(h=(this.attr||{})[c[b]],null==h&&(h=this[c[b]]),null!=h&&e.push(c[b]+'\x3d"'+this.toMathMLquote(h)+'"'));this.toMathMLclass(e);return e.length?" "+e.join(" "):""},toMathMLclass:function(e){var b=[];this["class"]&&b.push(this["class"]);if(this.isa(a.TeXAtom)&&SETTINGS.texHints){var c="ORD OP BIN REL OPEN CLOSE PUNCT INNER VCENTER".split(" ")[this.texClass];c&&b.push("MJX-TeXAtom-"+c)}this.mathvariant&&this.toMathMLvariants[this.mathvariant]&&b.push("MJX"+this.mathvariant);this.arrow&&b.push("MJX-arrow");this.variantForm&&b.push("MJX-variant");b.length&&e.unshift('class\x3d"'+b.join(" ")+'"')},toMathMLattribute:function(a){return"string"===typeof a&&a.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)?RegExp.$2+(1/18*RegExp.$3).toFixed(3).replace(/\.?0+$/,"")+"em":this.toMathMLvariants[a]?this.toMathMLvariants[a]:this.toMathMLquote(a)},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(a){a=String(a).split("");for(var b=0,c=a.length;b<c;b++){var m=a[b].charCodeAt(0);if(55295>=m||57344<=m)32>m||126<m?a[b]="\x26#x"+m.toString(16).toUpperCase()+";":(m={"\x26":"\x26amp;","\x3c":"\x26lt;","\x3e":"\x26gt;",'"':"\x26quot;"}[a[b]])&&(a[b]=m);else if(b+1<c){var n=a[b+1].charCodeAt(0);a[b]="\x26#x"+((m-55296<<10)+(n-56320)+65536).toString(16).toUpperCase()+";";a[b+1]="";b++}else a[b]=""}return a.join("")}});a.msubsup.Augment({toMathML:function(a){var b=this.type;null==this.data[this.sup]&&(b="msub");null==this.data[this.sub]&&(b="msup");var c=this.toMathMLattributes();delete this.data[0].inferred;for(var m=[],n=0,f=this.data.length;n<f;n++)this.data[n]&&m.push(this.data[n].toMathML(a+"  "));return a+"\x3c"+b+c+"\x3e\n"+m.join("\n")+"\n"+a+"\x3c/"+b+"\x3e"}});a.munderover.Augment({toMathML:function(a){var b=this.type;null==this.data[this.under]&&(b="mover");null==this.data[this.over]&&(b="munder");var c=this.toMathMLattributes();delete this.data[0].inferred;for(var m=[],n=0,f=this.data.length;n<f;n++)this.data[n]&&m.push(this.data[n].toMathML(a+"  "));return a+"\x3c"+b+c+"\x3e\n"+m.join("\n")+"\n"+a+"\x3c/"+b+"\x3e"}});a.TeXAtom.Augment({toMathML:function(a){var b=this.toMathMLattributes();return b||1!==this.data[0].data.length?a+"\x3cmrow"+b+"\x3e\n"+this.data[0].toMathML(a+"  ")+"\n"+a+"\x3c/mrow\x3e":a.substr(2)+this.data[0].toMathML(a)}});a.chars.Augment({toMathML:function(a){return(a||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(a){return(a||"")+"\x26"+this.data[0]+";\x3c!-- "+this.toString()+" --\x3e"}});a.xml.Augment({toMathML:function(a){return(a||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(a){return this.Core().toMathML(a)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js");(function(a,e){var b=a.CombineConfig("TeX.noErrors",{disabled:!1,multiLine:!0,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});MathJax.Extension["TeX/noErrors"]={version:"2.2",config:b};a.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(e,n,f,h){if(b.disabled)return c.apply(this,arguments);var p=e.message.replace(/\n.*/,"");a.signal.Post(["TeX Jax - parse error",p,n,f,h]);var p=b.inlineDelimiters,d=f||b.multiLine;f||(n=p[0]+n+p[1]);n=d?n.replace(/ /g,"\u00a0"):n.replace(/\n/g," ");return MathJax.ElementJax.mml.merror(n).With({isError:!0,multiLine:d})}})});a.Register.StartupHook("HTML-CSS Jax Config",function(){a.Config({"HTML-CSS":{styles:{".MathJax .noError":a.Insert({"vertical-align":a.Browser.isMSIE&&b.multiLine?"-2px":""},b.style)}}})});a.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"],e=a.math.prototype.toHTML,f=a.merror.prototype.toHTML;a.math.Augment({toHTML:function(a,b){var d=this.data[0];d&&d.data[0]&&d.data[0].isError?(a.style.fontSize="",a=this.HTMLcreateSpan(a),a.bbox=d.data[0].toHTML(a).bbox):a=e.call(this,a,b);return a}});a.merror.Augment({toHTML:function(a){if(!this.isError)return f.call(this,a);a=this.HTMLcreateSpan(a);a.className="noError";this.multiLine&&(a.style.display="inline-block");for(var c=this.data[0].data[0].data.join("").split(/\n/),d=0,k=c.length;d<k;d++)b.addText(a,c[d]),d!==k-1&&b.addElement(a,"br",{isMathJax:!0});c=b.getHD(a.parentNode);d=b.getW(a.parentNode);if(1<k){var k=(c.h+c.d)/2,l=b.TeX.x_height/2;a.parentNode.style.verticalAlign=b.Em(c.d+(l-k));c.h=l+k;c.d=k-l}a.bbox={h:c.h,d:c.d,w:d,lw:0,rw:d};return a}})});a.Register.StartupHook("SVG Jax Config",function(){a.Config({SVG:{styles:{".MathJax_SVG .noError":a.Insert({"vertical-align":a.Browser.isMSIE&&b.multiLine?"-2px":""},b.style)}}})});a.Register.StartupHook("SVG Jax Ready",function(){var a=MathJax.ElementJax.mml,b=a.math.prototype.toSVG,n=a.merror.prototype.toSVG;a.math.Augment({toSVG:function(a,c){var e=this.data[0];return a=e&&e.data[0]&&e.data[0].isError?e.data[0].toSVG(a):b.call(this,a,c)}});a.merror.Augment({toSVG:function(a){if(!this.isError||"math"!==this.Parent().type)return n.call(this,a);a=e.addElement(a,"span",{className:"noError",isMathJax:!0});this.multiLine&&(a.style.display="inline-block");for(var b=this.data[0].data[0].data.join("").split(/\n/),c=0,d=b.length;c<d;c++)e.addText(a,b[c]),c!==d-1&&e.addElement(a,"br",{isMathJax:!0});1<d&&(b=a.offsetHeight/2,a.style.verticalAlign=-b+b/d+"px");return a}})});a.Register.StartupHook("NativeMML Jax Ready",function(){var a=MathJax.ElementJax.mml,b=MathJax.Extension["TeX/noErrors"].config,e=a.math.prototype.toNativeMML,f=a.merror.prototype.toNativeMML;a.math.Augment({toNativeMML:function(a){var b=this.data[0];return a=b&&b.data[0]&&b.data[0].isError?b.data[0].toNativeMML(a):e.call(this,a)}});a.merror.Augment({toNativeMML:function(a){if(!this.isError)return f.call(this,a);a=a.appendChild(document.createElement("span"));for(var c=this.data[0].data[0].data.join("").split(/\n/),d=0,k=c.length;d<k;d++)a.appendChild(document.createTextNode(c[d])),d!==k-1&&a.appendChild(document.createElement("br"));this.multiLine&&(a.style.display="inline-block",1<k&&(a.style.verticalAlign="middle"));for(var e in b.style)b.style.hasOwnProperty(e)&&(c=e.replace(/-./g,function(d){return d.charAt(1).toUpperCase()}),a.style[c]=b.style[e]);return a}})});a.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js");MathJax.Extension["TeX/noUndefined"]={version:"2.2",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:!1,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var a=MathJax.Extension["TeX/noUndefined"].config,e=MathJax.ElementJax.mml,b=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(c){if(a.disabled)return b.apply(this,arguments);MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",c]);this.Push(e.mtext(c).With(a.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js");(function(a,e,b){var c,m=function(d){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",d]].concat([].slice.call(arguments,1)))},n=MathJax.Object.Subclass({Init:function(d,a){this.global={isInner:a};this.data=[f.start(this.global)];d&&(this.data[0].env=d);this.env=this.data[0].env},Push:function(){var d,a,b,e;d=0;for(a=arguments.length;d<a;d++)if(b=arguments[d],b instanceof c.mbase&&(b=f.mml(b)),b.global=this.global,e=this.data.length?this.Top().checkItem(b):!0,e instanceof Array)this.Pop(),this.Push.apply(this,e);else if(e instanceof f)this.Pop(),this.Push(e);else if(e)if(this.data.push(b),b.env){for(var h in this.env)this.env.hasOwnProperty(h)&&(b.env[h]=this.env[h]);this.env=b.env}else b.env=this.env},Pop:function(){var a=this.data.pop();a.isOpen||delete a.env;this.env=this.data.length?this.Top().env:{};return a},Top:function(a){null==a&&(a=1);return this.data.length<a?null:this.data[this.data.length-a]},Prev:function(a){var b=this.Top();return a?b.data[b.data.length-1]:b.Pop()},toString:function(){return"stack[\n  "+this.data.join("\n  ")+"\n]"}}),f=n.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(){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(a,b){null==a&&(a=!0);return 1!==this.data.length||b?c.mrow.apply(c,this.data).With(a?{inferred:!0}:{}):this.data[0]},checkItem:function(d){"over"===d.type&&this.isOpen&&(d.num=this.mmlData(!1),this.data=[]);if("cell"===d.type&&this.isOpen){if(d.linebreak)return!1;a.Error(["Misplaced","Misplaced %1",d.name])}d.isClose&&this[d.type+"Error"]&&a.Error(this[d.type+"Error"]);if(!d.isNotStack)return!0;this.Push(d.data[0]);return!1},With:function(a){for(var b in a)a.hasOwnProperty(b)&&(this[b]=a[b]);return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});f.start=f.Subclass({type:"start",isOpen:!0,Init:function(a){this.SUPER(arguments).Init.call(this);this.global=a},checkItem:function(a){return"stop"===a.type?f.mml(this.mmlData()):this.SUPER(arguments).checkItem.call(this,a)}});f.stop=f.Subclass({type:"stop",isClose:!0});f.open=f.Subclass({type:"open",isOpen:!0,stopError:["ExtraOpenMissingClose","Extra open brace or missing close brace"],checkItem:function(a){if("close"===a.type){var b=this.mmlData();return f.mml(c.TeXAtom(b))}return this.SUPER(arguments).checkItem.call(this,a)}});f.close=f.Subclass({type:"close",isClose:!0});f.prime=f.Subclass({type:"prime",checkItem:function(a){if("msubsup"!==this.data[0].type)return[c.msup(this.data[0],this.data[1]),a];this.data[0].SetData(this.data[0].sup,this.data[1]);return[this.data[0],a]}});f.subsup=f.Subclass({type:"subsup",stopError:["MissingScript","Missing superscript or subscript argument"],supError:["MissingOpenForSup","Missing open brace for superscript"],subError:["MissingOpenForSup","Missing open brace for subscript"],checkItem:function(d){if("open"===d.type||"left"===d.type)return!0;if("mml"===d.type)return this.primes&&(2!==this.position?this.data[0].SetData(2,this.primes):d.data[0]=c.mrow(this.primes.With({variantForm:!0}),d.data[0])),this.data[0].SetData(this.position,d.data[0]),f.mml(this.data[0]);this.SUPER(arguments).checkItem.call(this,d)&&a.Error(this[["","subError","supError"][this.position]])},Pop:function(){}});f.over=f.Subclass({type:"over",isClose:!0,name:"\\over",checkItem:function(d,b){"over"===d.type&&a.Error(["AmbiguousUseOf","Ambiguous use of %1",d.name]);if(d.isClose){var e=c.mfrac(this.num,this.mmlData(!1));null!=this.thickness&&(e.linethickness=this.thickness);if(this.open||this.close)e.texClass=c.TEXCLASS.INNER,e.texWithDelims=!0,e=a.fenced(this.open,e,this.close);return[f.mml(e),d]}return this.SUPER(arguments).checkItem.call(this,d)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});f.left=f.Subclass({type:"left",isOpen:!0,delim:"(",stopError:["ExtraLeftMissingRight","Extra \\left or missing \\right"],checkItem:function(d){return"right"===d.type?f.mml(a.fenced(this.delim,this.mmlData(),d.delim)):this.SUPER(arguments).checkItem.call(this,d)}});f.right=f.Subclass({type:"right",isClose:!0,delim:")"});f.begin=f.Subclass({type:"begin",isOpen:!0,checkItem:function(d){if("end"===d.type)return d.name!==this.name&&a.Error(["EnvBadEnd","\\begin{%1} ended with \\end{%2}",this.name,d.name]),this.end?this.parse[this.end].call(this.parse,this,this.data):f.mml(this.mmlData());"stop"===d.type&&a.Error(["EnvMissingEnd","Missing \\end{%1}",this.name]);return this.SUPER(arguments).checkItem.call(this,d)}});f.end=f.Subclass({type:"end",isClose:!0});f.style=f.Subclass({type:"style",checkItem:function(a){if(!a.isClose)return this.SUPER(arguments).checkItem.call(this,a);var b=c.mstyle.apply(c,this.data).With(this.styles);return[f.mml(b),a]}});f.position=f.Subclass({type:"position",checkItem:function(d){d.isClose&&a.Error(["MissingBoxFor","Missing box for %1",name]);if(d.isNotStack){var b=d.mmlData();switch(this.move){case "vertical":return b=c.mpadded(b).With({height:this.dh,depth:this.dd,voffset:this.dh}),[f.mml(b)];case "horizontal":return[f.mml(this.left),d,f.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,d)}});f.array=f.Subclass({type:"array",isOpen:!0,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.frame=[];this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(d){if(d.isClose&&"over"!==d.type){if(d.isEntry)return this.EndEntry(),this.clearEnv(),!1;if(d.isCR)return this.EndEntry(),this.EndRow(),this.clearEnv(),!1;this.EndTable();this.clearEnv();var b=c.mtable.apply(c,this.table).With(this.arraydef);4===this.frame.length?b.frame=this.frame.dashed?"dashed":"solid":this.frame.length&&(b.hasFrame=!0,this.arraydef.rowlines&&(this.arraydef.rowlines=this.arraydef.rowlines.replace(/none( none)+$/,"none")),b=c.menclose(b).With({notation:this.frame.join(" "),isFrame:!0}),"none"!=(this.arraydef.columnlines||"none")||"none"!=(this.arraydef.rowlines||"none"))&&(b.padding=0);if(this.open||this.close)b=a.fenced(this.open,b,this.close);b=f.mml(b);if(this.requireClose){if("close"===d.type)return b;a.Error(["MissingCloseBrace","Missing close brace"])}return[b,d]}return this.SUPER(arguments).checkItem.call(this,d)},EndEntry:function(){this.row.push(c.mtd.apply(c,this.data));this.data=[]},EndRow:function(){this.table.push(c.mtr.apply(c,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length)this.EndEntry(),this.EndRow();this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var a=this.arraydef.rowlines.split(/ /);a.length===this.table.length?(this.frame.push("bottom"),a.pop(),this.arraydef.rowlines=a.join(" ")):a.length<this.table.length-1&&(this.arraydef.rowlines+=" none")}if(this.rowspacing){for(a=this.arraydef.rowspacing.split(/ /);a.length<this.table.length;)a.push(this.rowspacing+"em");this.arraydef.rowspacing=a.join(" ")}},clearEnv:function(){for(var a in this.env)this.env.hasOwnProperty(a)&&delete this.env[a]}});f.cell=f.Subclass({type:"cell",isClose:!0});f.mml=f.Subclass({type:"mml",isNotStack:!0,Add:function(){this.data.push.apply(this.data,arguments);return this}});f.fn=f.Subclass({type:"fn",checkItem:function(a){if(this.data[0]){if("mml"!==a.type||!a.data[0]||a.data[0].isa(c.mspace))return[this.data[0],a];var b=a.data[0];b.isEmbellished()&&(b=b.CoreMO());return[0,0,1,1,0,1,1,0,0,0][b.Get("texClass")]?[this.data[0],a]:[this.data[0],c.mo(c.entity("#x2061")).With({texClass:c.TEXCLASS.NONE}),a]}return this.SUPER(arguments).checkItem.apply(this,arguments)}});f.not=f.Subclass({type:"not",checkItem:function(a){var b,e;if("open"===a.type||"left"===a.type)return!0;if("mml"===a.type&&a.data[0].type.match(/^(mo|mi|mtext)$/)&&(b=a.data[0],e=b.data.join(""),1===e.length&&!b.movesupsub))return(e=f.not.remap[e.charCodeAt(0)])?b.SetData(0,c.chars(String.fromCharCode(e))):b.Append(c.chars("\u0338")),a;b=c.mpadded(c.mtext("\u29f8")).With({width:0});b=c.TeXAtom(b).With({texClass:c.TEXCLASS.REL});return[b,a]}});f.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};f.dots=f.Subclass({type:"dots",checkItem:function(a){if("open"===a.type||"left"===a.type)return!0;var b=this.ldots;if("mml"===a.type&&a.data[0].isEmbellished()){var e=a.data[0].CoreMO().Get("texClass");if(e===c.TEXCLASS.BIN||e===c.TEXCLASS.REL)b=this.cdots}return[b,a]}});var h={Add:function(a,b,c){b||(b=this);for(var e in a)a.hasOwnProperty(e)&&("object"!==typeof a[e]||a[e]instanceof Array||"object"!==typeof b[e]&&"function"!==typeof b[e]?b[e]&&b[e].isUser&&c||(b[e]=a[e]):this.Add(a[e],b[e],a[e],c));return b}},p=MathJax.Object.Subclass({Init:function(d,b){this.string=d;this.macroCount=this.i=0;var c;if(b){c={};for(var e in b)b.hasOwnProperty(e)&&(c[e]=b[e])}this.stack=a.Stack(c,!!b);this.Parse();this.Push(f.stop())},Parse:function(){for(var a,b;this.i<this.string.length;)if(a=this.string.charAt(this.i++),b=a.charCodeAt(0),55296<=b&&56320>b&&(a+=this.string.charAt(this.i++)),h.special[a])this[h.special[a]](a);else h.letter.test(a)?this.Variable(a):h.digit.test(a)?this.Number(a):this.Other(a)},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){return"mml"!==this.stack.Top().type?null:this.stack.Top().data[0]},mmlToken:function(a){return a},ControlSequence:function(a){var b=this.GetCS(),c=this.csFindMacro(b);if(c){c instanceof Array||(c=[c]);var e=c[0];e instanceof Function||(e=this[e]);e.apply(this,[a+b].concat(c.slice(1)))}else h.mathchar0mi[b]?this.csMathchar0mi(b,h.mathchar0mi[b]):h.mathchar0mo[b]?this.csMathchar0mo(b,h.mathchar0mo[b]):h.mathchar7[b]?this.csMathchar7(b,h.mathchar7[b]):null!=h.delimiter["\\"+b]?this.csDelimiter(b,h.delimiter["\\"+b]):this.csUndefined(a+b)},csFindMacro:function(a){return h.macros[a]},csMathchar0mi:function(a,b){var e={mathvariant:c.VARIANT.ITALIC};b instanceof Array&&(e=b[1],b=b[0]);this.Push(this.mmlToken(c.mi(c.entity("#x"+b)).With(e)))},csMathchar0mo:function(a,b){var e={stretchy:!1};b instanceof Array&&(e=b[1],e.stretchy=!1,b=b[0]);this.Push(this.mmlToken(c.mo(c.entity("#x"+b)).With(e)))},csMathchar7:function(a,b){var e={mathvariant:c.VARIANT.NORMAL};b instanceof Array&&(e=b[1],b=b[0]);this.stack.env.font&&(e.mathvariant=this.stack.env.font);this.Push(this.mmlToken(c.mi(c.entity("#x"+b)).With(e)))},csDelimiter:function(a,b){var e={};b instanceof Array&&(e=b[1],b=b[0]);b=4===b.length?c.entity("#x"+b):c.chars(b);this.Push(this.mmlToken(c.mo(b).With({fence:!1,stretchy:!1}).With(e)))},csUndefined:function(d){a.Error(["UndefinedControlSequence","Undefined control sequence %1",d])},Variable:function(a){var b={};this.stack.env.font&&(b.mathvariant=this.stack.env.font);this.Push(this.mmlToken(c.mi(c.chars(a)).With(b)))},Number:function(a){var b=this.string.slice(this.i-1).match(h.number);b?(a=c.mn(b[0].replace(/[{}]/g,"")),this.i+=b[0].length-1):a=c.mo(c.chars(a));this.stack.env.font&&(a.mathvariant=this.stack.env.font);this.Push(this.mmlToken(a))},Open:function(a){this.Push(f.open())},Close:function(a){this.Push(f.close())},Tilde:function(a){this.Push(c.mtext(c.chars("\u00a0")))},Space:function(a){},Superscript:function(d){this.GetNext().match(/\d/)&&(this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1));var b,e;b=this.stack.Top();"prime"===b.type?(d=b.data[0],e=b.data[1],this.stack.Pop()):(d=this.stack.Prev())||(d=c.mi(""));d.isEmbellishedWrapper&&(d=d.data[0].data[0]);if("msubsup"===d.type)d.data[d.sup]&&a.Error(["DoubleExponent","Double exponent: use braces to clarify"]),b=d.sup;else if(d.movesupsub){if("munderover"!==d.type||d.data[d.over])d.movablelimits&&d.isa(c.mi)&&(d=this.mi2mo(d)),d=c.munderover(d,null,null).With({movesupsub:!0});b=d.over}else d=c.msubsup(d,null,null),b=d.sup;this.Push(f.subsup(d).With({position:b,primes:e}))},Subscript:function(d){this.GetNext().match(/\d/)&&(this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1));var b,e;b=this.stack.Top();"prime"===b.type?(d=b.data[0],e=b.data[1],this.stack.Pop()):(d=this.stack.Prev())||(d=c.mi(""));d.isEmbellishedWrapper&&(d=d.data[0].data[0]);if("msubsup"===d.type)d.data[d.sub]&&a.Error(["DoubleSubscripts","Double subscripts: use braces to clarify"]),b=d.sub;else if(d.movesupsub){if("munderover"!==d.type||d.data[d.under])d.movablelimits&&d.isa(c.mi)&&(d=this.mi2mo(d)),d=c.munderover(d,null,null).With({movesupsub:!0});b=d.under}else d=c.msubsup(d,null,null),b=d.sub;this.Push(f.subsup(d).With({position:b,primes:e}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(d){var b=this.stack.Prev();b||(b=c.mi());"msubsup"===b.type&&b.data[b.sup]&&a.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"]);var e="";this.i--;do e+=this.PRIME,this.i++,d=this.GetNext();while("'"===d||d===this.SMARTQUOTE);e=["","\u2032","\u2033","\u2034","\u2057"][e.length]||e;this.Push(f.prime(b,this.mmlToken(c.mo(e))))},mi2mo:function(a){var b=c.mo();b.Append.apply(b,a.data);for(var e in b.defaults)b.defaults.hasOwnProperty(e)&&null!=a[e]&&(b[e]=a[e]);for(e in c.copyAttributes)c.copyAttributes.hasOwnProperty(e)&&null!=a[e]&&(b[e]=a[e]);return b},Comment:function(a){for(;this.i<this.string.length&&"\n"!=this.string.charAt(this.i);)this.i++},Hash:function(d){a.Error(["CantUseHash1","You can't use 'macro parameter character #' in math mode"])},Other:function(a){var b={stretchy:!1};this.stack.env.font&&(b.mathvariant=this.stack.env.font);h.remap[a]?(a=h.remap[a],a instanceof Array&&(b=a[1],a=a[0]),a=c.mo(c.entity("#x"+a)).With(b)):a=c.mo(a).With(b);""==a.autoDefault("texClass",!0)&&(a=c.TeXAtom(a));this.Push(this.mmlToken(a))},SetFont:function(a,b){this.stack.env.font=b},SetStyle:function(a,b,c,e){this.stack.env.style=b;this.stack.env.level=e;this.Push(f.style().With({styles:{displaystyle:c,scriptlevel:e}}))},SetSize:function(a,b){this.stack.env.size=b;this.Push(f.style().With({styles:{mathsize:b+"em"}}))},Color:function(a){var b=this.GetArgument(a),e=this.stack.env.color;this.stack.env.color=b;a=this.ParseArg(a);e?this.stack.env.color:delete this.stack.env.color;this.Push(c.mstyle(a).With({mathcolor:b}))},Spacer:function(a,b){this.Push(c.mspace().With({width:b,mathsize:c.SIZE.NORMAL,scriptlevel:0}))},LeftRight:function(a){this.Push(f[a.substr(1)]().With({delim:this.GetDelimiter(a)}))},Middle:function(d){var b=this.GetDelimiter(d);"left"!==this.stack.Top().type&&a.Error(["MisplacedMiddle","%1 must be within \\left and \\right",d]);this.Push(c.mo(b).With({stretchy:!0}))},NamedFn:function(a,b){b||(b=a.substr(1));var e=c.mi(b).With({texClass:c.TEXCLASS.OP});this.Push(f.fn(this.mmlToken(e)))},NamedOp:function(a,b){b||(b=a.substr(1));b=b.replace(/&thinsp;/,"\u2006");var e=c.mo(b).With({movablelimits:!0,movesupsub:!0,form:c.FORM.PREFIX,texClass:c.TEXCLASS.OP});e.useMMLspacing&=~e.SPACE_ATTR.form;this.Push(this.mmlToken(e))},Limits:function(d,b){var e=this.stack.Prev("nopop");e&&e.texClass===c.TEXCLASS.OP||a.Error(["MisplacedLimits","%1 is allowed only on operators",d]);e.movesupsub=b?!0:!1;e.movablelimits=!1},Over:function(a,b,c){var e=f.over().With({name:a});b||c?(e.open=b,e.close=c):a.match(/withdelims$/)&&(e.open=this.GetDelimiter(a),e.close=this.GetDelimiter(a));if(a.match(/^\\above/))e.thickness=this.GetDimen(a);else if(a.match(/^\\atop/)||b||c)e.thickness=0;this.Push(e)},Frac:function(a){var b=this.ParseArg(a);a=this.ParseArg(a);this.Push(c.mfrac(b,a))},Sqrt:function(d){var b=this.GetBrackets(d);d=this.GetArgument(d);"\\frac"===d&&(d+="{"+this.GetArgument(d)+"}{"+this.GetArgument(d)+"}");d=a.Parse(d,this.stack.env).mml();d=b?c.mroot(d,this.parseRoot(b)):c.msqrt.apply(c,d.array());this.Push(d)},Root:function(a){var b=this.GetUpTo(a,"\\of");a=this.ParseArg(a);this.Push(c.mroot(a,this.parseRoot(b)))},parseRoot:function(d){var b=this.stack.env,e=b.inRoot;b.inRoot=!0;var h=a.Parse(d,b);d=h.mml();h=h.stack.global;if(h.leftRoot||h.upRoot)d=c.mpadded(d),h.leftRoot&&(d.width=h.leftRoot),h.upRoot&&(d.voffset=h.upRoot,d.height=h.upRoot);b.inRoot=e;return d},MoveRoot:function(d,b){this.stack.env.inRoot||a.Error(["MisplacedMoveRoot","%1 can appear only within a root",d]);this.stack.global[b]&&a.Error(["MultipleMoveRoot","Multiple use of %1",d]);var c=this.GetArgument(d);c.match(/-?[0-9]+/)||a.Error(["IntegerArg","The argument to %1 must be an integer",d]);c=c/15+"em";"-"!==c.substr(0,1)&&(c="+"+c);this.stack.global[b]=c},Accent:function(a,b,e){a=this.ParseArg(a);var h={accent:!0};this.stack.env.font&&(h.mathvariant=this.stack.env.font);b=this.mmlToken(c.mo(c.entity("#x"+b)).With(h));b.stretchy=e?!0:!1;this.Push(c.TeXAtom(c.munderover(a,null,b).With({accent:!0})))},UnderOver:function(a,b,e){var h={o:"over",u:"under"}[a.charAt(1)];a=this.ParseArg(a);a.Get("movablelimits")&&(a.movablelimits=!1);a=c.munderover(a,null,null);e&&(a.movesupsub=!0);a.data[a[h]]=this.mmlToken(c.mo(c.entity("#x"+b)).With({stretchy:!0,accent:"under"==h}));this.Push(a)},Overset:function(a){var b=this.ParseArg(a);a=this.ParseArg(a);this.Push(c.mover(a,b))},Underset:function(a){var b=this.ParseArg(a);a=this.ParseArg(a);this.Push(c.munder(a,b))},TeXAtom:function(d,b){var e={texClass:b};if(b==c.TEXCLASS.OP){e.movesupsub=e.movablelimits=!0;var h=this.GetArgument(d),p=h.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);p?(e.mathvariant=c.VARIANT.NORMAL,e=f.fn(this.mmlToken(c.mi(p[1]).With(e)))):e=f.fn(c.TeXAtom(a.Parse(h,this.stack.env).mml()).With(e))}else e=c.TeXAtom(this.ParseArg(d)).With(e);this.Push(e)},MmlToken:function(d){var b=this.GetArgument(d),e=this.GetBrackets(d,"").replace(/^\s+/,"");d=this.GetArgument(d);var h={attrNames:[]},f;for(c[b]&&c[b].prototype.isToken||a.Error(["NotMathMLToken","%1 is not a token element",b]);""!==e;){(f=e.match(/^([a-z]+)\s*=\s*(\'[^']*'|"[^"]*"|[^ ]*)\s*/i))||a.Error("InvalidMathMLAttr","Invalid MathML attribute: %1",e);c[b].prototype.defaults[f[1]]||this.MmlTokenAllow[f[1]]||a.Error(["UnknownAttrForElement","%1 is not a recognized attribute for %2",f[1],b]);var g=this.MmlFilterAttribute(f[1],f[2].replace(/^(['"])(.*)\1$/,"$2"));g&&("true"===g.toLowerCase()?g=!0:"false"===g.toLowerCase()&&(g=!1),h[f[1]]=g,h.attrNames.push(f[1]));e=e.substr(f[0].length)}this.Push(this.mmlToken(c[b](d).With(h)))},MmlFilterAttribute:function(a,b){return b},MmlTokenAllow:{fontfamily:1,fontsize:1,fontweight:1,fontstyle:1,color:1,background:1,id:1,"class":1,href:1,style:1},Strut:function(a){this.Push(c.mpadded(c.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(a,b,e){a=c.mphantom(this.ParseArg(a));if(b||e)a=c.mpadded(a),e&&(a.height=a.depth=0),b&&(a.width=0);this.Push(c.TeXAtom(a))},Smash:function(a){var b=this.trimSpaces(this.GetBrackets(a,""));a=c.mpadded(this.ParseArg(a));switch(b){case "b":a.depth=0;break;case "t":a.height=0;break;default:a.height=a.depth=0}this.Push(c.TeXAtom(a))},Lap:function(a){var b=c.mpadded(this.ParseArg(a)).With({width:0});"\\llap"===a&&(b.lspace="-1 width");this.Push(c.TeXAtom(b))},RaiseLower:function(a){var b=this.GetDimen(a),c=f.position().With({name:a,move:"vertical"});"-"===b.charAt(0)&&(b=b.slice(1),a={raise:"\\lower",lower:"\\raise"}[a.substr(1)]);"\\lower"===a?(c.dh="-"+b,c.dd="+"+b):(c.dh="+"+b,c.dd="-"+b);this.Push(c)},MoveLeftRight:function(a){var b=this.GetDimen(a),e="-"===b.charAt(0)?b.slice(1):"-"+b;if("\\moveleft"===a)var h=b,b=e,e=h;this.Push(f.position().With({name:a,move:"horizontal",left:c.mspace().With({width:b,mathsize:c.SIZE.NORMAL}),right:c.mspace().With({width:e,mathsize:c.SIZE.NORMAL})}))},Hskip:function(a){this.Push(c.mspace().With({width:this.GetDimen(a),mathsize:c.SIZE.NORMAL}))},Rule:function(a,b){var e=this.GetDimen(a),h=this.GetDimen(a),f=this.GetDimen(a),g={width:e,height:h,depth:f};"blank"!==b?(parseFloat(e)&&parseFloat(h)+parseFloat(f)&&(g.mathbackground=this.stack.env.color||"black"),e=c.mpadded(c.mrow()).With(g)):e=c.mspace().With(g);this.Push(e)},MakeBig:function(a,b,e){e*=h.p_height;e=String(e).replace(/(\.\d\d\d).+/,"$1")+"em";a=this.GetDelimiter(a);this.Push(c.TeXAtom(c.mo(a).With({minsize:e,maxsize:e,fence:!0,stretchy:!0,symmetric:!0})).With({texClass:b}))},BuildRel:function(a){var b=this.ParseUpTo(a,"\\over");a=this.ParseArg(a);this.Push(c.TeXAtom(c.munderover(a,null,b)).With({mclass:c.TEXCLASS.REL}))},HBox:function(a,b){this.Push.apply(this,this.InternalMath(this.GetArgument(a),b))},FBox:function(a){this.Push(c.menclose.apply(c,this.InternalMath(this.GetArgument(a))).With({notation:"box"}))},Not:function(a){this.Push(f.not())},Dots:function(a){this.Push(f.dots().With({ldots:this.mmlToken(c.mo(c.entity("#x2026")).With({stretchy:!1})),cdots:this.mmlToken(c.mo(c.entity("#x22EF")).With({stretchy:!1}))}))},Require:function(a){a=this.GetArgument(a).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");this.Extension(null,a)},Extension:function(d,c,l){c=a.extensionDir+"/"+c;c.match(/\.js$/)||(c+=".js");b.loaded[b.fileURL(c)]||(null!=d&&delete h[l||"macros"][d.replace(/^\\/,"")],e.RestartAfter(b.Require(c)))},Macro:function(b,c,e,h){if(e){var f=[];if(null!=h){var g=this.GetBrackets(b);f.push(null==g?h:g)}for(h=f.length;h<e;h++)f.push(this.GetArgument(b));c=this.SubstituteArgs(f,c)}this.string=this.AddArgs(c,this.string.slice(this.i));this.i=0;++this.macroCount>a.config.MAXMACROS&&a.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])},Matrix:function(b,c,e,h,p,g,q,n){var m=this.GetNext();""===m&&a.Error(["MissingArgFor","Missing argument for %1",b]);"{"===m?this.i++:(this.string=m+"}"+this.string.slice(this.i+1),this.i=0);b=f.array().With({requireClose:!0,arraydef:{rowspacing:g||"4pt",columnspacing:p||"1em"}});n&&(b.isCases=!0);if(c||e)b.open=c,b.close=e;"D"===q&&(b.arraydef.displaystyle=!0);null!=h&&(b.arraydef.columnalign=h);this.Push(b)},Entry:function(b){this.Push(f.cell().With({isEntry:!0,name:b}));if(this.stack.Top().isCases){var c=this.string,e=0;b=this.i;for(var h=c.length;b<h;){var p=c.charAt(b);"{"===p?(e++,b++):"}"===p?0===e?h=0:(e--,b++):"\x26"===p&&0===e?a.Error(["ExtraAlignTab","Extra alignment tab in \\cases text"]):"\\"===p?c.substr(b).match(/^((\\cr)[^a-zA-Z]|\\\\)/)?h=0:b+=2:b++}c=c.substr(this.i,b-this.i);c.match(/^\s*\\text[^a-zA-Z]/)||(this.Push.apply(this,this.InternalMath(c)),this.i=b)}},Cr:function(a){this.Push(f.cell().With({isCR:!0,name:a}))},CrLaTeX:function(b){var e;"["===this.string.charAt(this.i)&&(e=this.GetBrackets(b,"").replace(/ /g,""))&&!e.match(/^((-?(\.\d+|\d+(\.\d*)?))(pt|em|ex|mu|mm|cm|in|pc))$/)&&a.Error(["BracketMustBeDimension","Bracket argument to %1 must be a dimension",b]);this.Push(f.cell().With({isCR:!0,name:b,linebreak:!0}));b=this.stack.Top();if(b.isa(f.array)){if(e&&b.arraydef.rowspacing){var h=b.arraydef.rowspacing.split(/ /);b.rowspacing||(b.rowspacing=this.dimen2em(h[0]));for(;h.length<b.table.length;)h.push(this.Em(b.rowspacing));h[b.table.length-1]=this.Em(Math.max(0,b.rowspacing+this.dimen2em(e)));b.arraydef.rowspacing=h.join(" ")}}else e&&this.Push(c.mspace().With({depth:e})),this.Push(c.mo().With({linebreak:c.LINEBREAK.NEWLINE}))},emPerInch:7.2,dimen2em:function(a){var b=a.match(/^(-?(?:\.\d+|\d+(?:\.\d*)?))(pt|em|ex|mu|pc|in|mm|cm)/);a=parseFloat(b[1]||"1");b=b[2];return"em"===b?a:"ex"===b?.43*a:"pt"===b?a/10:"pc"===b?1.2*a:"in"===b?a*this.emPerInch:"cm"===b?a*this.emPerInch/2.54:"mm"===b?a*this.emPerInch/25.4:"mu"===b?a/18:0},Em:function(a){return 6E-4>Math.abs(a)?"0em":a.toFixed(3).replace(/\.?0+$/,"")+"em"},HLine:function(b,c){null==c&&(c="solid");var e=this.stack.Top();e.isa(f.array)&&!e.data.length||a.Error(["Misplaced","Misplaced %1",b]);if(0==e.table.length)e.frame.push("top");else{for(var h=e.arraydef.rowlines?e.arraydef.rowlines.split(/ /):[];h.length<e.table.length;)h.push("none");h[e.table.length-1]=c;e.arraydef.rowlines=h.join(" ")}},Begin:function(b){var c=this.GetArgument(b);c.match(/[^a-z*]/i)&&a.Error(["InvalidEnv","Invalid environment name '%1'",c]);(b=this.envFindName(c))||a.Error(["UnknownEnv","Unknown environment '%1'",c]);++this.macroCount>a.config.MAXMACROS&&a.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"]);b instanceof Array||(b=[b]);c=f.begin().With({name:c,end:b[1],parse:this});b[0]&&this[b[0]]&&(c=this[b[0]].apply(this,[c].concat(b.slice(2))));this.Push(c)},End:function(a){this.Push(f.end().With({name:this.GetArgument(a)}))},envFindName:function(a){return h.environment[a]},Equation:function(a,b){return b},ExtensionEnv:function(a,b){this.Extension(a.name,b,"environment")},Array:function(a,b,c,e,h,g,p,n){e||(e=this.GetArgument("\\begin{"+a.name+"}"));var m=("c"+e).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");e=e.replace(/[^clr]/g,"").split("").join(" ");e=e.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");e=f.array().With({arraydef:{columnalign:e,columnspacing:h||"1em",rowspacing:g||"4pt"}});m.match(/[|:]/)&&(m.charAt(0).match(/[|:]/)&&(e.frame.push("left"),e.frame.dashed=":"===m.charAt(0)),m.charAt(m.length-1).match(/[|:]/)&&e.frame.push("right"),m=m.substr(1,m.length-2),e.arraydef.columnlines=m.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed"));b&&(e.open=this.convertDelimiter(b));c&&(e.close=this.convertDelimiter(c));"D"===p&&(e.arraydef.displaystyle=!0);"S"===p&&(e.arraydef.scriptlevel=1);n&&(e.arraydef.useHeight=!1);this.Push(a);return e},AlignedArray:function(a){var b=this.GetBrackets("\\begin{"+a.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),b)},setArrayAlign:function(a,b){b=this.trimSpaces(b||"");"t"===b?a.arraydef.align="baseline 1":"b"===b?a.arraydef.align="baseline -1":"c"===b?a.arraydef.align="center":b&&(a.arraydef.align=b);return a},convertDelimiter:function(a){a&&(a=h.delimiter[a]);if(null==a)return null;a instanceof Array&&(a=a[0]);4===a.length&&(a=String.fromCharCode(parseInt(a,16)));return a},trimSpaces:function(a){return"string"!=typeof a?a:a.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){for(;this.nextIsSpace();)this.i++;return this.string.charAt(this.i)},GetCS:function(){var a=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(a)return this.i+=a[1].length,a[1];this.i++;return" "},GetArgument:function(b,c){switch(this.GetNext()){case "":return c||a.Error(["MissingArgFor","Missing argument for %1",b]),null;case "}":return c||a.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"]),null;case "\\":return this.i++,"\\"+this.GetCS();case "{":for(var e=++this.i,h=1;this.i<this.string.length;)switch(this.string.charAt(this.i++)){case "\\":this.i++;break;case "{":h++;break;case "}":if(0==h&&a.Error(["ExtraClose","Extra close brace"]),0==--h)return this.string.slice(e,this.i-1)}a.Error(["MissingCloseBrace","Missing close brace"])}return this.string.charAt(this.i++)},GetBrackets:function(b,c){if("["!=this.GetNext())return c;for(var e=++this.i,h=0;this.i<this.string.length;)switch(this.string.charAt(this.i++)){case "{":h++;break;case "\\":this.i++;break;case "}":0>=h--&&a.Error(["ExtraCloseLooking","Extra close brace while looking for %1","']'"]);break;case "]":if(0==h)return this.string.slice(e,this.i-1)}a.Error(["MissingCloseBracket","Couldn't find closing ']' for argument to %1",b])},GetDelimiter:function(b){for(;this.nextIsSpace();)this.i++;var c=this.string.charAt(this.i);if(this.i<this.string.length&&(this.i++,"\\"==c&&(c+=this.GetCS(b)),null!=h.delimiter[c]))return this.convertDelimiter(c);a.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",b])},GetDimen:function(b){var c;this.nextIsSpace()&&this.i++;if("{"==this.string.charAt(this.i)){if(c=this.GetArgument(b),c.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/))return c.replace(/ /g,"")}else if(c=this.string.slice(this.i),c=c.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/))return this.i+=c[0].length,c[1].replace(/ /g,"");a.Error(["MissingDimOrUnits","Missing dimension or its units for %1",b])},GetUpTo:function(b,c){for(;this.nextIsSpace();)this.i++;for(var e=this.i,h,f,g=0;this.i<this.string.length;){h=this.i;f=this.string.charAt(this.i++);switch(f){case "\\":f+=this.GetCS();break;case "{":g++;break;case "}":0==g&&a.Error(["ExtraCloseLooking","Extra close brace while looking for %1",c]),g--}if(0==g&&f==c)return this.string.slice(e,h)}a.Error(["TokenNotFoundForCommand","Couldn't find %1 for %2",c,b])},ParseArg:function(b){return a.Parse(this.GetArgument(b),this.stack.env).mml()},ParseUpTo:function(b,c){return a.Parse(this.GetUpTo(b,c),this.stack.env).mml()},InternalMath:function(b,e){var h={displaystyle:!1};null!=e&&(h.scriptlevel=e);this.stack.env.font&&(h.mathvariant=this.stack.env.font);if(!b.match(/\\?\$|\\\(|\\(eq)?ref\s*\{/))return[this.InternalText(b,h)];for(var f=0,p=0,g,m="",n=[];f<b.length;)g=b.charAt(f++),"$"===g?"$"===m?(n.push(c.TeXAtom(a.Parse(b.slice(p,f-1),{}).mml().With(h))),m="",p=f):""===m&&(p<f-1&&n.push(this.InternalText(b.slice(p,f-1),h)),m="$",p=f):"}"===g&&"}"===m?(n.push(c.TeXAtom(a.Parse(b.slice(p,f),{}).mml().With(h))),m="",p=f):"\\"===g&&(""===m&&b.substr(f).match(/^(eq)?ref\s*\{/)?(p<f-1&&n.push(this.InternalText(b.slice(p,f-1),h)),m="}",p=f-1):(g=b.charAt(f++),"("===g&&""===m?(p<f-2&&n.push(this.InternalText(b.slice(p,f-2),h)),m=")",p=f):")"===g&&")"===m?(n.push(c.TeXAtom(a.Parse(b.slice(p,f-2),{}).mml().With(h))),m="",p=f):"$"===g&&""===m&&(f--,b=b.substr(0,f-1)+b.substr(f))));""!==m&&a.Error(["MathNotTerminated","Math not terminated in text box"]);p<b.length&&n.push(this.InternalText(b.slice(p),h));return n},InternalText:function(a,b){a=a.replace(/^\s+/,"\u00a0").replace(/\s+$/,"\u00a0");return c.mtext(c.chars(a)).With(b)},SubstituteArgs:function(b,c){for(var e="",h="",f,g=0;g<c.length;)f=c.charAt(g++),"\\"===f?e+=f+c.charAt(g++):"#"===f?(f=c.charAt(g++),"#"===f?e+=f:((!f.match(/[1-9]/)||f>b.length)&&a.Error(["IllegalMacroParam","Illegal macro parameter reference"]),h=this.AddArgs(this.AddArgs(h,e),b[f-1]),e="")):e+=f;return this.AddArgs(h,e)},AddArgs:function(b,c){c.match(/^[a-z]/i)&&b.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)&&(b+=" ");b.length+c.length>a.config.MAXBUFFER&&a.Error(["MaxBufferSize","MathJax internal buffer size exceeded; is there a recursive macro call?"]);return b+c}});a.Augment({Stack:n,Parse:p,Definitions:h,Startup:function(){c=MathJax.ElementJax.mml;e.Insert(h,{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","\x26":"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:c.VARIANT.NORMAL}],aleph:["2135",{mathvariant:c.VARIANT.NORMAL}],hbar:["210F",{variantForm:!0}],imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:c.VARIANT.NORMAL}],Re:["211C",{mathvariant:c.VARIANT.NORMAL}],Im:["2111",{mathvariant:c.VARIANT.NORMAL}],partial:["2202",{mathvariant:c.VARIANT.NORMAL}],infty:["221E",{mathvariant:c.VARIANT.NORMAL}],prime:["2032",{mathvariant:c.VARIANT.NORMAL,variantForm:!0}],emptyset:["2205",{mathvariant:c.VARIANT.NORMAL}],nabla:["2207",{mathvariant:c.VARIANT.NORMAL}],top:["22A4",{mathvariant:c.VARIANT.NORMAL}],bot:["22A5",{mathvariant:c.VARIANT.NORMAL}],angle:["2220",{mathvariant:c.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:c.VARIANT.NORMAL}],backslash:["2216",{mathvariant:c.VARIANT.NORMAL,variantForm:!0}],forall:["2200",{mathvariant:c.VARIANT.NORMAL}],exists:["2203",{mathvariant:c.VARIANT.NORMAL}],neg:["00AC",{mathvariant:c.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:c.VARIANT.NORMAL}],flat:["266D",{mathvariant:c.VARIANT.NORMAL}],natural:["266E",{mathvariant:c.VARIANT.NORMAL}],sharp:["266F",{mathvariant:c.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:c.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:c.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:c.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:c.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:c.TEXCLASS.OP,movesupsub:!0}],bigvee:["22C1",{texClass:c.TEXCLASS.OP,movesupsub:!0}],bigwedge:["22C0",{texClass:c.TEXCLASS.OP,movesupsub:!0}],biguplus:["2A04",{texClass:c.TEXCLASS.OP,movesupsub:!0}],bigcap:["22C2",{texClass:c.TEXCLASS.OP,movesupsub:!0}],bigcup:["22C3",{texClass:c.TEXCLASS.OP,movesupsub:!0}],"int":["222B",{texClass:c.TEXCLASS.OP}],intop:["222B",{texClass:c.TEXCLASS.OP,movesupsub:!0,movablelimits:!0}],iint:["222C",{texClass:c.TEXCLASS.OP}],iiint:["222D",{texClass:c.TEXCLASS.OP}],prod:["220F",{texClass:c.TEXCLASS.OP,movesupsub:!0}],sum:["2211",{texClass:c.TEXCLASS.OP,movesupsub:!0}],bigotimes:["2A02",{texClass:c.TEXCLASS.OP,movesupsub:!0}],bigoplus:["2A01",{texClass:c.TEXCLASS.OP,movesupsub:!0}],bigodot:["2A00",{texClass:c.TEXCLASS.OP,movesupsub:!0}],oint:["222E",{texClass:c.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:c.TEXCLASS.OP,movesupsub:!0}],smallint:["222B",{largeop:!1}],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:!1}],oslash:["2298",{largeop:!1}],otimes:["2297",{largeop:!1}],ominus:["2296",{largeop:!1}],oplus:["2295",{largeop:!1}],mp:"2213",pm:"00B1",circ:"2218",bigcirc:"25EF",setminus:["2216",{variantForm:!0}],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:c.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:c.TEXCLASS.PUNCT}],colon:["003A",{texClass:c.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","\x26":"0026",And:"0026"},delimiter:{"(":"(",")":")","[":"[","]":"]","\x3c":"27E8","\x3e":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:c.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:c.TEXCLASS.ORD}],"\\|":["2225",{texClass:c.TEXCLASS.ORD}],"\\vert":["|",{texClass:c.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",!0,0],textstyle:["SetStyle","T",!1,0],scriptstyle:["SetStyle","S",!1,1],scriptscriptstyle:["SetStyle","SS",!1,2],rm:["SetFont",c.VARIANT.NORMAL],mit:["SetFont",c.VARIANT.ITALIC],oldstyle:["SetFont",c.VARIANT.OLDSTYLE],cal:["SetFont",c.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",c.VARIANT.BOLD],bbFont:["SetFont",c.VARIANT.DOUBLESTRUCK],scr:["SetFont",c.VARIANT.SCRIPT],frak:["SetFont",c.VARIANT.FRAKTUR],sf:["SetFont",c.VARIANT.SANSSERIF],tt:["SetFont",c.VARIANT.MONOSPACE],tiny:["SetSize",.5],Tiny:["SetSize",.6],scriptsize:["SetSize",.7],small:["SetSize",.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\x26thinsp;inf"],limsup:["NamedOp","lim\x26thinsp;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",c.LENGTH.THINMATHSPACE],":":["Spacer",c.LENGTH.MEDIUMMATHSPACE],"\x3e":["Spacer",c.LENGTH.MEDIUMMATHSPACE],";":["Spacer",c.LENGTH.THICKMATHSPACE],"!":["Spacer",c.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",c.LENGTH.THINMATHSPACE],negthinspace:["Spacer",c.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",c.TEXCLASS.ORD,.85],Big:["MakeBig",c.TEXCLASS.ORD,1.15],bigg:["MakeBig",c.TEXCLASS.ORD,1.45],Bigg:["MakeBig",c.TEXCLASS.ORD,1.75],bigl:["MakeBig",c.TEXCLASS.OPEN,.85],Bigl:["MakeBig",c.TEXCLASS.OPEN,1.15],biggl:["MakeBig",c.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",c.TEXCLASS.OPEN,1.75],bigr:["MakeBig",c.TEXCLASS.CLOSE,.85],Bigr:["MakeBig",c.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",c.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",c.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",c.TEXCLASS.REL,.85],Bigm:["MakeBig",c.TEXCLASS.REL,1.15],biggm:["MakeBig",c.TEXCLASS.REL,1.45],Biggm:["MakeBig",c.TEXCLASS.REL,1.75],mathord:["TeXAtom",c.TEXCLASS.ORD],mathop:["TeXAtom",c.TEXCLASS.OP],mathopen:["TeXAtom",c.TEXCLASS.OPEN],mathclose:["TeXAtom",c.TEXCLASS.CLOSE],mathbin:["TeXAtom",c.TEXCLASS.BIN],mathrel:["TeXAtom",c.TEXCLASS.REL],mathpunct:["TeXAtom",c.TEXCLASS.PUNCT],mathinner:["TeXAtom",c.TEXCLASS.INNER],vcenter:["TeXAtom",c.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,!0],eqalign:["Matrix",null,null,"right left",c.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",c.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",c.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\mmlToken{mo}{mod}}"],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],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/.85});if(this.config.Macros){var a=this.config.Macros,b;for(b in a)a.hasOwnProperty(b)&&(h.macros[b]="string"===typeof a[b]?["Macro",a[b]]:["Macro"].concat(a[b]),h.macros[b].isUser=!0)}},config:{MAXMACROS:1E4,MAXBUFFER:5120},sourceMenuTitle:["TeXCommands","TeX Commands"],prefilterHooks:MathJax.Callback.Hooks(!0),postfilterHooks:MathJax.Callback.Hooks(!0),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);"none"!==this.config.equationNumbers.autoNumber&&(this.config.extensions||(this.config.extensions=[]),this.config.extensions.push("AMSmath.js"))},Translate:function(b){var e,h=!1,f=MathJax.HTML.getScript(b),p=null!=b.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/),g={math:f,display:p,script:b};this.prefilterHooks.Execute(g);f=g.math;try{e=a.Parse(f).mml()}catch(m){if(!m.texError)throw m;e=this.formatError(m,f,p,b);h=!0}e=e.inferred?c.apply(MathJax.ElementJax,e.data):c(e);p&&(e.root.display="block");h&&(e.texError=!0);g.math=e;this.postfilterHooks.Execute(g);return g.math},prefilterMath:function(a,b,c){return a},postfilterMath:function(a,b,c){this.combineRelations(a.root);return a},formatError:function(a,b,h,f){a=a.message.replace(/\n.*/,"");e.signal.Post(["TeX Jax - parse error",a,b,h,f]);return c.merror(a)},Error:function(a){a instanceof Array&&(a=m.apply(m,a));throw e.Insert(Error(a),{texError:!0});},Macro:function(a,b,c){h.macros[a]=["Macro"].concat([].slice.call(arguments,1));h.macros[a].isUser=!0},fenced:function(a,b,e){var h=c.mrow();h.open=a;h.close=e;a&&h.Append(c.mo(a).With({fence:!0,stretchy:!0,texClass:c.TEXCLASS.OPEN}));"mrow"===b.type?h.Append.apply(h,b.data):h.Append(b);e&&h.Append(c.mo(e).With({fence:!0,stretchy:!0,texClass:c.TEXCLASS.CLOSE}));return h},combineRelations:function(a){var b,e,h,f;b=0;for(e=a.data.length;b<e;b++)if(a.data[b]){if(a.isa(c.mrow))for(;b+1<e&&(h=a.data[b])&&(f=a.data[b+1])&&h.isa(c.mo)&&f.isa(c.mo)&&h.Get("texClass")===c.TEXCLASS.REL&&f.Get("texClass")===c.TEXCLASS.REL;)h.variantForm!=f.variantForm||h.Get("mathvariant")!=f.Get("mathvariant")||h.style!=f.style||h["class"]!=f["class"]||h.id||f.id?(h.rspace=f.lspace="0pt",b++):(h.Append.apply(h,f.data),a.data.splice(b+1,1),e--);a.data[b].isToken||this.combineRelations(a.data[b])}}});a.prefilterHooks.Add(function(b){b.math=a.prefilterMath(b.math,b.display,b.script)});a.postfilterHooks.Add(function(b){b.math=a.postfilterMath(b.math,b.display,b.script)});a.loadComplete("jax.js")})(MathJax.InputJax.TeX,MathJax.Hub,MathJax.Ajax);MathJax.Extension["TeX/AMSmath"]={version:"2.2",number:0,startNumber:0,labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var a=MathJax.ElementJax.mml,e=MathJax.InputJax.TeX,b=MathJax.Extension["TeX/AMSmath"],c=e.Definitions,m=e.Stack.Item,n=e.config.equationNumbers,f=function(a){for(var b=[],c=0,f=a.length;c<f;c++)b[c]=e.Parse.prototype.Em(a[c]);return b.join(" ")};c.Add({mathchar0mo:{iiiint:["2A0C",{texClass:a.TEXCLASS.OP}]},macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",a.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",a.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",!0],substack:["Macro","\\begin{subarray}{c}#1\\end{subarray}",1],injlim:["NamedOp","inj\x26thinsp;lim"],projlim:["NamedOp","proj\x26thinsp;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",a.ALIGN.LEFT],shoveright:["HandleShove",a.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,!0,!0,"rlrlrlrlrlrl",f([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,!1,!0,"rlrlrlrlrlrl",f([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],multline:["Multline",null,!0],"multline*":["Multline",null,!1],split:["AMSarray",null,!1,!1,"rl",f([5/18])],gather:["AMSarray",null,!0,!0,"c"],"gather*":["AMSarray",null,!1,!0,"c"],alignat:["AlignAt",null,!0,!0],"alignat*":["AlignAt",null,!1,!0],alignedat:["AlignAt",null,!1,!1],aligned:["AlignedArray",null,null,null,"rlrlrlrlrlrl",f([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,f([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",f([1/3]),".2em","S",1],equation:["EquationBegin","Equation",!0],"equation*":["EquationBegin","EquationStar",!1],eqnarray:["AMSarray",null,!0,!0,"rcl",a.LENGTH.THICKMATHSPACE,".5em"],"eqnarray*":["AMSarray",null,!1,!0,"rcl",a.LENGTH.THICKMATHSPACE,".5em"]},delimiter:{"\\lvert":["2223",{texClass:a.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:a.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:a.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:a.TEXCLASS.CLOSE}]}},null,!0);e.Parse.Augment({HandleTag:function(b){var c=this.GetStar(),d=this.trimSpaces(this.GetArgument(b)),f=d;c||(d=n.formatTag(d));c=this.stack.global;c.tagID=f;c.notags&&e.Error(["CommandNotAllowedInEnv","%1 not allowed in %2 environment",b,c.notags]);c.tag&&e.Error(["MultipleCommand","Multiple %1",b]);c.tag=a.mtd.apply(a,this.InternalMath(d)).With({id:n.formatID(f)})},HandleNoTag:function(a){this.stack.global.tag&&delete this.stack.global.tag;this.stack.global.notag=!0},HandleLabel:function(a){var c=this.stack.global,d=this.GetArgument(a);""===d||b.refUpdate||(c.label&&e.Error(["MultipleCommand","Multiple %1",a]),c.label=d,(b.labels[d]||b.eqlabels[d])&&e.Error(["MultipleLabel","Label '%1' multiply defined",d]),b.eqlabels[d]="???")},HandleRef:function(c,e){var d=this.GetArgument(c),f=b.labels[d]||b.eqlabels[d];f||(f="??",b.badref=!b.refUpdate);var l=f;e&&(l=n.formatTag(l));n.useLabelIds&&(f=d);this.Push(a.mrow.apply(a,this.InternalMath(l)).With({href:n.formatURL(n.formatID(f)),"class":"MathJax_ref"}))},HandleDeclareOp:function(a){var b=this.GetStar()?"\\limits":"",c=this.trimSpaces(this.GetArgument(a));"\\"==c.charAt(0)&&(c=c.substr(1));a=this.GetArgument(a);a=a.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");e.Definitions.macros[c]=["Macro","\\mathop{\\rm "+a+"}"+b]},HandleOperatorName:function(a){var b=this.GetStar()?"\\limits":"\\nolimits";a=this.trimSpaces(this.GetArgument(a));a=a.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+a+"}"+b+" "+this.string.slice(this.i);this.i=0},HandleShove:function(a,b){var c=this.stack.Top();("multline"!==c.type||c.data.length)&&e.Error(["CommandAtTheBeginingOfLine","%1 must come at the beginning of the line",a]);c.data.shove=b},CFrac:function(b){var c=this.trimSpaces(this.GetBrackets(b,"")),d=this.GetArgument(b),f=this.GetArgument(b),d=a.mfrac(e.Parse("\\strut\\textstyle{"+d+"}",this.stack.env).mml(),e.Parse("\\strut\\textstyle{"+f+"}",this.stack.env).mml()),c={l:a.ALIGN.LEFT,r:a.ALIGN.RIGHT,"":""}[c];null==c&&e.Error(["IllegalAlign","Illegal alignment specified in %1",b]);c&&(d.numalign=d.denomalign=c);this.Push(d)},Genfrac:function(b,c,d,f,l){c=null==c?this.GetDelimiterArg(b):this.convertDelimiter(c);d=null==d?this.GetDelimiterArg(b):this.convertDelimiter(d);null==f&&(f=this.GetArgument(b));null==l&&(l=this.trimSpaces(this.GetArgument(b)));var m=this.ParseArg(b),n=this.ParseArg(b),m=a.mfrac(m,n);""!==f&&(m.linethickness=f);if(c||d)m=e.fenced(c,m,d);""!==l&&(c=["D","T","S","SS"][l],null==c&&e.Error(["BadMathStyleFor","Bad math style for %1",b]),m=a.mstyle(m),"D"===c?(m.displaystyle=!0,m.scriptlevel=0):(m.displaystyle=!1,m.scriptlevel=l-1));this.Push(m)},Multline:function(a,b){this.Push(a);this.checkEqnEnv();return m.multline(b,this.stack).With({arraydef:{displaystyle:!0,rowspacing:".5em",width:e.config.MultLineWidth,columnwidth:"100%",side:e.config.TagSide,minlabelspacing:e.config.TagIndent}})},AMSarray:function(a,b,c,f,l){this.Push(a);c&&this.checkEqnEnv();f=f.replace(/[^clr]/g,"").split("").join(" ");f=f.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return m.AMSarray(a.name,b,c,this.stack).With({arraydef:{displaystyle:!0,rowspacing:".5em",columnalign:f,columnspacing:l||"1em",rowspacing:"3pt",side:e.config.TagSide,minlabelspacing:e.config.TagIndent}})},AlignAt:function(a,b,c){var f,l,m="",n=[];c||(l=this.GetBrackets("\\begin{"+a.name+"}"));f=this.GetArgument("\\begin{"+a.name+"}");for(f.match(/[^0-9]/)&&e.Error(["PositiveIntegerArg","Argument to %1 must me a positive integer","\\begin{"+a.name+"}"]);0<f;)m+="rl",n.push("0em 0em"),f--;n=n.join(" ");if(c)return this.AMSarray(a,b,c,m,n);a=this.Array.call(this,a,null,null,m,n,".5em","D");return this.setArrayAlign(a,l)},EquationBegin:function(a,b){this.checkEqnEnv();this.stack.global.forcetag=b&&"none"!==n.autoNumber;return a},EquationStar:function(a,b){this.stack.global.tagged=!0;return b},checkEqnEnv:function(){this.stack.global.eqnenv&&e.Error(["ErroneousNestingEq","Erroneous nesting of equation structures"]);this.stack.global.eqnenv=!0},MultiIntegral:function(a,b){var c=this.GetNext();if("\\"===c){var e=this.i,c=this.GetArgument(a);this.i=e;"\\limits"===c&&(b="\\idotsint"===a?"\\!\\!\\mathop{\\,\\,"+b+"}":"\\!\\!\\!\\mathop{\\,\\,\\,"+b+"}")}this.string=b+" "+this.string.slice(this.i);this.i=0},xArrow:function(b,c,d,f){d={width:"+"+(d+f)+"mu",lspace:d+"mu"};f=this.GetBrackets(b);b=this.ParseArg(b);c=a.mo(a.chars(String.fromCharCode(c))).With({stretchy:!0,texClass:a.TEXCLASS.REL});c=a.munderover(c);c.SetData(c.over,a.mpadded(b).With(d).With({voffset:".15em"}));f&&(f=e.Parse(f,this.stack.env).mml(),c.SetData(c.under,a.mpadded(f).With(d).With({voffset:"-.24em"})));this.Push(c)},GetDelimiterArg:function(a){var b=this.trimSpaces(this.GetArgument(a));if(""==b)return null;null==c.delimiter[b]&&e.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",a]);return this.convertDelimiter(b)},GetStar:function(){var a="*"===this.GetNext();a&&this.i++;return a}});m.Augment({autoTag:function(){var c=this.global;if(!c.notag){b.number++;c.tagID=n.formatNumber(b.number.toString());var f=e.Parse("\\text{"+n.formatTag(c.tagID)+"}",{}).mml();c.tag=a.mtd(f.With({id:n.formatID(c.tagID)}))}},getTag:function(){var a=this.global,c=a.tag;a.tagged=!0;a.label&&(b.eqlabels[a.label]=a.tagID,n.useLabelIds&&(c.id=n.formatID(a.label)));delete a.tag;delete a.tagID;delete a.label;return c}});m.multline=m.array.Subclass({type:"multline",Init:function(a,b){this.SUPER(arguments).Init.apply(this);this.numbered=a&&"none"!==n.autoNumber;this.save={notag:b.global.notag};b.global.tagged=!a&&!b.global.forcetag},EndEntry:function(){var b=a.mtd.apply(a,this.data);this.data.shove&&(b.columnalign=this.data.shove);this.row.push(b);this.data=[]},EndRow:function(){1!=this.row.length&&e.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 b=this.table.length-1,c,d=-1;this.table[0][0].columnalign||(this.table[0][0].columnalign=a.ALIGN.LEFT);this.table[b][0].columnalign||(this.table[b][0].columnalign=a.ALIGN.RIGHT);!this.global.tag&&this.numbered&&this.autoTag();this.global.tag&&!this.global.notags&&(d="left"===this.arraydef.side?0:this.table.length-1,this.table[d]=[this.getTag()].concat(this.table[d]));c=0;for(b=this.table.length;c<b;c++)this.table[c]=(c===d?a.mlabeledtr:a.mtr).apply(a,this.table[c])}this.global.notag=this.save.notag}});m.AMSarray=m.array.Subclass({type:"AMSarray",Init:function(a,b,c,e){this.SUPER(arguments).Init.apply(this);this.numbered=b&&"none"!==n.autoNumber;this.save={notags:e.global.notags,notag:e.global.notag};e.global.notags=c?null:a;e.global.tagged=!b&&!e.global.forcetag},EndRow:function(){var b=a.mtr;!this.global.tag&&this.numbered&&this.autoTag();this.global.tag&&!this.global.notags&&(this.row=[this.getTag()].concat(this.row),b=a.mlabeledtr);this.numbered&&delete this.global.notag;this.table.push(b.apply(a,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notags=this.save.notags;this.global.notag=this.save.notag}});m.start.Augment({oldCheckItem:m.start.prototype.checkItem,checkItem:function(c){if("stop"===c.type){c=this.mmlData();var f=this.global;!b.display||f.tag||f.tagged||f.isInner||"all"!==n.autoNumber&&!f.forcetag||this.autoTag();if(f.tag){var f=[this.getTag(),a.mtd(c)],d={side:e.config.TagSide,minlabelspacing:e.config.TagIndent,columnalign:c.displayAlign};c.displayAlign===a.INDENTALIGN.LEFT?(d.width="100%",c.displayIndent&&!String(c.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)&&(d.columnwidth=c.displayIndent+" fit",d.columnspacing="0",f=[f[0],a.mtd(),f[1]])):c.displayAlign===a.INDENTALIGN.RIGHT&&(d.width="100%",c.displayIndent&&!String(c.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)&&(d.columnwidth="fit "+c.displayIndent,d.columnspacing="0",f[2]=a.mtd()));c=a.mtable(a.mlabeledtr.apply(a,f)).With(d)}return m.mml(c)}return this.oldCheckItem.call(this,c)}});e.prefilterHooks.Add(function(a){b.display=a.display;b.number=b.startNumber;b.eqlabels={};b.badref=!1;b.refUpdate&&(b.number=a.script.MathJax.startNumber)});e.postfilterHooks.Add(function(a){a.script.MathJax.startNumber=b.startNumber;b.startNumber=b.number;MathJax.Hub.Insert(b.labels,b.eqlabels);b.badref&&!a.math.texError&&b.refs.push(a.script)});MathJax.Hub.Register.MessageHook("Begin Math Input",function(){b.refs=[];b.refUpdate=!1});MathJax.Hub.Register.MessageHook("End Math Input",function(a){if(b.refs.length){b.refUpdate=!0;a=0;for(var c=b.refs.length;a<c;a++)b.refs[a].MathJax.state=MathJax.ElementJax.STATE.UPDATE;return MathJax.Hub.processInput({scripts:b.refs,start:(new Date).getTime(),i:0,j:0,jax:{},jaxIDs:[]})}return null});e.resetEquationNumbers=function(a,c){b.startNumber=a||0;c||(b.labels={})};MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js");MathJax.Extension["TeX/AMSsymbols"]={version:"2.2"};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var a=MathJax.ElementJax.mml;MathJax.InputJax.TeX.Definitions.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:!0}],hslash:"210F",varnothing:["2205",{variantForm:!0}],blacktriangle:"25B4",triangledown:["25BD",{variantForm:!0}],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:!0}],backsimeq:"22CD",thickapprox:["2248",{variantForm:!0}],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:!0}],shortmid:["2223",{variantForm:!0}],smallfrown:["2322",{variantForm:!0}],shortparallel:["2225",{variantForm:!0}],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:!0}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:!0}],ngeqslant:["2A88",{variantForm:!0}],nleqq:["2270",{variantForm:!0}],ngeqq:["2271",{variantForm:!0}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:!0}],gvertneqq:["2269",{variantForm:!0}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:!0}],nsucceq:["22E1",{variantForm:!0}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:!0}],nshortparallel:["2226",{variantForm:!0}],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:!0}],nsupseteqq:["2289",{variantForm:!0}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:!0}],varsupsetneq:["228B",{variantForm:!0}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:!0}],varsupsetneqq:["2ACC",{variantForm:!0}],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:!0}],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,!0);var e=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":e,"\u2323":e,"\u25b3":e,"\ue006":e,"\ue007":e,"\ue00c":e,"\ue00d":e,"\ue00e":e,"\ue00f":e,"\ue010":e,"\ue011":e,"\ue016":e,"\ue017":e,"\ue018":e,"\ue019":e,"\ue01a":e,"\ue01b":e,"\ue04b":e,"\ue04f":e}}});MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js");MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS_HTML.js");