xiaoben-as2-php/compressed/js/mathjax/config/TeX-AMS_HTML-full.js

/*
 *  /MathJax/config/TeX-AMS_HTML-full.js
 *  
 *  Copyright (c) 2010-2013 The MathJax Consortium
 *
 *  Part of the MathJax library.
 *  See http://www.mathjax.org for details.
 * 
 *  Licensed under the Apache License, Version 2.0;
 *  you may not use this file except in compliance with the License.
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 */MathJax.Ajax.Preloading("[MathJax]/jax/input/TeX/config.js","[MathJax]/jax/output/HTML-CSS/config.js","[MathJax]/extensions/tex2jax.js","[MathJax]/extensions/MathEvents.js","[MathJax]/extensions/MathZoom.js","[MathJax]/extensions/MathMenu.js","[MathJax]/jax/element/mml/jax.js","[MathJax]/extensions/toMathML.js","[MathJax]/extensions/TeX/noErrors.js","[MathJax]/extensions/TeX/noUndefined.js","[MathJax]/jax/input/TeX/jax.js","[MathJax]/extensions/TeX/AMSmath.js","[MathJax]/extensions/TeX/AMSsymbols.js","[MathJax]/jax/output/HTML-CSS/jax.js","[MathJax]/jax/output/HTML-CSS/autoload/mtable.js");MathJax.Hub.Config({"v1.0-compatible":!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(c){return c},formatTag:function(c){return"("+c+")"},formatID:function(c){return"mjx-eqn-"+String(c).replace(/[:"'<>&]/g,"")},formatURL:function(c){return"#"+escape(c)},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(c,g){var b=c.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:!0,minBrowserTranslate:function(d){var g=c.getJaxFor(d),m=["[Math]"],l=document.createElement("span",{className:"MathJax_Preview"});"TeX"===g.inputJax&&(g.root.Get("displaystyle")?(m=b.displayMathDelimiters,m=[m[0]+g.originalText+m[1]],b.multilineDisplay&&(m=m[0].split(/\n/))):(m=b.inlineMathDelimiters,m=[m[0]+g.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+m[1]]));for(var g=0,n=m.length;g<n;g++)l.appendChild(document.createTextNode(m[g])),g<n-1&&l.appendChild(document.createElement("br"));d.parentNode.insertBefore(l,d)}},c.config["HTML-CSS"]||{});"0.0"===c.Browser.version||c.Browser.versionAtLeast(b.minBrowserVersion[c.Browser]||0)||(g.Translate=b.minBrowserTranslate,c.Config({showProcessingMessages:!1}),MathJax.Message.Set(["MathJaxNotSupported","Your browser does not support 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c=[],g=[],b,d,q=this.config;this.match={};b=0;for(d=q.inlineMath.length;b<d;b++)c.push(this.patternQuote(q.inlineMath[b][0])),this.match[q.inlineMath[b][0]]={mode:"",end:q.inlineMath[b][1],pattern:this.endPattern(q.inlineMath[b][1])};b=0;for(d=q.displayMath.length;b<d;b++)c.push(this.patternQuote(q.displayMath[b][0])),this.match[q.displayMath[b][0]]={mode:"; mode\x3ddisplay",end:q.displayMath[b][1],pattern:this.endPattern(q.displayMath[b][1])};c.length&&g.push(c.sort(this.sortLength).join("|"));q.processEnvironments&&g.push("\\\\begin\\{([^}]*)\\}");q.processEscapes&&g.push("\\\\*\\\\\\$");q.processRefs&&g.push("\\\\(eq)?ref\\{[^}]*\\}");this.start=new RegExp(g.join("|"),"g");this.skipTags=new RegExp("^("+q.skipTags.join("|")+")$","i");c=[];MathJax.Hub.config.preRemoveClass&&c.push(MathJax.Hub.config.preRemoveClass);q.ignoreClass&&c.push(q.ignoreClass);this.ignoreClass=c.length?new RegExp("(^| )("+c.join("|")+")( |$)"):/^$/;this.processClass=new RegExp("(^| )("+q.processClass+")( 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g,b;this.search={start:!0};for(this.pattern=this.start;c;){for(this.pattern.lastIndex=0;c&&"#text"===c.nodeName.toLowerCase()&&(g=this.pattern.exec(c.nodeValue));)c=this.search.start?this.startMatch(g,c):this.endMatch(g,c);this.search.matched&&(c=this.encloseMath(c));if(c){do b=c,c=c.nextSibling;while(c&&("br"===c.nodeName.toLowerCase()||"#comment"===c.nodeName.toLowerCase()));if(!c||"#text"!==c.nodeName)return this.search.close?this.prevEndMatch():b}}return c},startMatch:function(c,g){var b=this.match[c[0]];if(null!=b)this.search={end:b.end,mode:b.mode,pcount:0,open:g,olen:c[0].length,opos:this.pattern.lastIndex-c[0].length},this.switchPattern(b.pattern);else if("\\begin"===c[0].substr(0,6))this.search={end:"\\end{"+c[1]+"}",mode:"; mode\x3ddisplay",pcount:0,open:g,olen:0,opos:this.pattern.lastIndex-c[0].length,isBeginEnd:!0},this.switchPattern(this.endPattern(this.search.end));else{if("\\ref"===c[0].substr(0,4)||"\\eqref"===c[0].substr(0,6))return 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c},switchPattern:function(c){c.lastIndex=this.pattern.lastIndex;this.pattern=c;this.search.start=c===this.start},encloseMath:function(c){c=this.search;var g=c.close,b,d;(g=c.cpos===g.length?g.nextSibling:g.splitText(c.cpos))||(b=g=MathJax.HTML.addText(c.close.parentNode,""));c.close=g;for(d=c.opos?c.open.splitText(c.opos):c.open;d.nextSibling&&d.nextSibling!==g;)d.nodeValue=null!==d.nextSibling.nodeValue?"#comment"===d.nextSibling.nodeName?d.nodeValue+d.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1"):d.nodeValue+d.nextSibling.nodeValue:this.msieNewlineBug?d.nodeValue+("br"===d.nextSibling.nodeName.toLowerCase()?"\n":" "):d.nodeValue+" ",d.parentNode.removeChild(d.nextSibling);g=d.nodeValue.substr(c.olen,d.nodeValue.length-c.olen-c.clen);d.parentNode.removeChild(d);"none"!==this.config.preview&&this.createPreview(c.mode,g);d=this.createMathTag(c.mode,g);this.search={};this.pattern.lastIndex=0;b&&b.parentNode.removeChild(b);return d},insertNode:function(c){var g=this.search;g.close.parentNode.insertBefore(c,g.close)},createPreview:function(c,g){var b=this.config.preview;"none"!==b&&("TeX"===b&&(b=[this.filterPreview(g)]),b&&(b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b),this.insertNode(b)))},createMathTag:function(c,g){var b=document.createElement("script");b.type="math/tex"+c;MathJax.HTML.setScript(b,g);this.insertNode(b);return b},filterPreview:function(c){return c},msieNewlineBug:MathJax.Hub.Browser.isMSIE&&9>document.documentMode};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js");(function(c,g,b,d,q,m,l){var n=MathJax.Extension,p=n.MathEvents={version:"2.2"},a=c.config.menuSettings,e={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(m.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"}}},k=p.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",Mousedown:function(a){return k.Handler(a,"Mousedown",this)},Mouseup:function(a){return k.Handler(a,"Mouseup",this)},Mousemove:function(a){return k.Handler(a,"Mousemove",this)},Mouseover:function(a){return k.Handler(a,"Mouseover",this)},Mouseout:function(a){return k.Handler(a,"Mouseout",this)},Click:function(a){return k.Handler(a,"Click",this)},DblClick:function(a){return k.Handler(a,"DblClick",this)},Menu:function(a){return k.Handler(a,"ContextMenu",this)},Handler:function(a,e,d){if(b.loadingMathMenu)return k.False(a);var f=m[d.jaxID];a||(a=window.event);a.isContextMenu="ContextMenu"===e;if(f[e])return f[e](a,d);if(n.MathZoom)return n.MathZoom.HandleEvent(a,e,d)},False:function(a){a||(a=window.event);a&&(a.preventDefault&&a.preventDefault(),a.stopPropagation&&a.stopPropagation(),a.cancelBubble=!0,a.returnValue=!1);return!1},ContextMenu:function(e,f,h){var g=m[f.jaxID],n=g.getJaxFromMath(f);if((null!=g.config.showMathMenu?g:c).config.showMathMenu&&("MathJax"===a.context||h)){p.msieEventBug&&(e=window.event||e);k.ClearSelection();u.ClearHoverTimer();n.hover&&(n.hover.remove&&(clearTimeout(n.hover.remove),delete 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f=m[d.jaxID],b=(null!=f.config.showMathMenu?f:c).config.showMathMenu;if(b){b=(null!=f.config.showMathMenuMSIE?f:c).config.showMathMenuMSIE;if("MathJax"===a.context&&!a.mpContext&&b){if(!p.noContextMenuBug||e.button!==k.RIGHTBUTTON)return}else if(!e[k.MENUKEY]||e.button!==k.LEFTBUTTON)return;return f.ContextMenu(e,d,!0)}},ClearSelection:function(){p.safariContextMenuBug&&setTimeout("window.getSelection().empty()",0);document.selection&&setTimeout("document.selection.empty()",0)},getBBox:function(a){a.appendChild(p.topImg);var e=p.topImg.offsetTop,k=a.offsetHeight-e,d=a.offsetWidth;a.removeChild(p.topImg);return{w:d,h:e,d:k}}},u=p.Hover={Mouseover:function(e,d){if(a.discoverable||"Hover"===a.zoom){var f=e.fromElement||e.relatedTarget,b=e.toElement||e.target;if(f&&b&&(f.isMathJax!=b.isMathJax||c.getJaxFor(f)!==c.getJaxFor(b)))return f=this.getJaxFromMath(d),f.hover?u.ReHover(f):u.HoverTimer(f,d),k.False(e)}},Mouseout:function(e,d){if(a.discoverable||"Hover"===a.zoom){var f=e.fromElement||e.relatedTarget,b=e.toElement||e.target;if(f&&b&&(f.isMathJax!=b.isMathJax||c.getJaxFor(f)!==c.getJaxFor(b)))return f=this.getJaxFromMath(d),f.hover?u.UnHover(f):u.ClearHoverTimer(),k.False(e)}},Mousemove:function(e,f){if(a.discoverable||"Hover"===a.zoom){var d=this.getJaxFromMath(f);if(!d.hover&&(u.lastX!=e.clientX||u.lastY!=e.clientY))return u.lastX=e.clientX,u.lastY=e.clientY,u.HoverTimer(d,f),k.False(e)}},HoverTimer:function(a,k){this.ClearHoverTimer();this.hoverTimer=setTimeout(d(["Hover",this,a,k]),e.hover)},ClearHoverTimer:function(){this.hoverTimer&&(clearTimeout(this.hoverTimer),delete this.hoverTimer)},Hover:function(a,k){if(!n.MathZoom||!n.MathZoom.Hover({},k)){var f=m[a.outputJax],d=f.getHoverSpan(a,k),b=f.getHoverBBox(a,d,k),h=(null!=f.config.showMathMenu?f:c).config.showMathMenu,u=e.frame.x,q=e.frame.y,l=e.frame.bwidth;p.msieBorderWidthBug&&(l=0);a.hover={opacity:0,id:a.inputID+"-Hover"};var B=g.Element("span",{id:a.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(-b.h-q-l-(b.y||0)),left:this.Px(-u-l+(b.x||0)),width:this.Px(b.w+2*u),height:this.Px(b.h+b.d+2*q),opacity:0,filter:"alpha(opacity\x3d0)"}}]]),f=g.Element("span",{isMathJax:!0,id:a.hover.id+"Menu",style:{display:"inline-block","z-index":1,width:0,height:0,position:"relative"}},[["img",{className:"MathJax_Hover_Arrow",isMathJax:!0,math:k,src:e.button.src,onclick:this.HoverMenu,jax:f.id,style:{left:this.Px(b.w+u+l+(b.x||0)+e.button.x),top:this.Px(-b.h-q-l-(b.y||0)-e.button.y),opacity:0,filter:"alpha(opacity\x3d0)"}}]]);b.width&&(B.style.width=f.style.width=b.width,B.style.marginRight=f.style.marginRight="-"+b.width,B.firstChild.style.width=b.width,f.firstChild.style.left="",f.firstChild.style.right=this.Px(e.button.wx));d.parentNode.insertBefore(B,d);h&&d.parentNode.insertBefore(f,d);d.style&&(d.style.position="relative");this.ReHover(a)}},ReHover:function(a){a.hover.remove&&clearTimeout(a.hover.remove);a.hover.remove=setTimeout(d(["UnHover",this,a]),e.fadeoutDelay);this.HoverFadeTimer(a,e.fadeinInc)},UnHover:function(a){a.hover.nofade||this.HoverFadeTimer(a,-e.fadeoutInc,e.fadeoutStart)},HoverFade:function(a){delete 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e=document.documentMode||0,f=a.versionAtLeast("8.0");p.msieBorderWidthBug="BackCompat"===document.compatMode;p.msieEventBug=a.isIE9;p.msieAlignBug=!f||8>e;9>e&&(k.LEFTBUTTON=1)},Safari:function(a){p.safariContextMenuBug=!0},Opera:function(a){p.operaPositionBug=!0},Konqueror:function(a){p.noContextMenuBug=!0}});p.topImg=p.msieAlignBug?g.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):g.Element("span",{style:{width:0,height:0,display:"inline-block"}});p.operaPositionBug&&(p.topImg.style.border="1px solid");p.config=e=c.CombineConfig("MathEvents",e);d.Queue(c.Register.StartupHook("End Config",{}),[function(){var a=e.styles[".MathJax_Hover_Frame"];a.border=e.frame.bwidth+"px solid "+e.frame.bcolor+" ! important";a["box-shadow"]=a["-webkit-box-shadow"]=a["-moz-box-shadow"]=a["-khtml-box-shadow"]="0px 0px "+e.frame.hwidth+" "+e.frame.hcolor}],["getImages",u],["Styles",b,e.styles],["Post",c.Startup.signal,"MathEvents 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a.settings.CTRL&&!e.ctrlKey||a.settings.ALT&&!e.altKey||a.settings.CMD&&!e.metaKey||a.settings.Shift&&!e.shiftKey||!a[k]?!0:a[k](e,d)},Click:function(a,k){if("Click"===this.settings.zoom)return this.Zoom(a,k)},DblClick:function(a,k){if("Double-Click"===this.settings.zoom)return this.Zoom(a,k)},Hover:function(a,k){return"Hover"===this.settings.zoom?(this.Zoom(a,k),!0):!1},Zoom:function(a,k){this.Remove();n.ClearHoverTimer();p.ClearSelection();var d=MathJax.OutputJax[k.jaxID],f=d.getJaxFromMath(k);f.hover&&n.UnHover(f);var b=Math.floor(.85*document.body.clientWidth),r=Math.floor(.85*Math.max(document.body.clientHeight,document.documentElement.clientHeight)),w=g.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":b+"px","max-height":r+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]),v=w.lastChild,t=v.firstChild,q=w.firstChild;k.parentNode.insertBefore(w,k);k.parentNode.insertBefore(k,w);t.addEventListener&&t.addEventListener("mousedown",this.Remove,!0);if(this.msieTrapEventBug){var x=g.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});w.insertBefore(x,v)}this.msieZIndexBug&&(g.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}}),w.style.position="relative",w.style.zIndex=m.styles["#MathJax_ZoomOverlay"]["z-index"]);d=d.Zoom(f,t,k,b,r);this.msiePositionBug&&(this.msieSizeBug&&(v.style.height=d.zH+"px",v.style.width=d.zW+"px"),v.offsetHeight>r&&(v.style.height=r+"px",v.style.width=d.zW+this.scrollSize+"px"),v.offsetWidth>b&&(v.style.width=b+"px",v.style.height=d.zH+this.scrollSize+"px"));this.operaPositionBug&&(v.style.width=Math.min(b,d.zW)+"px");v.offsetWidth&&v.offsetWidth<b&&v.offsetHeight<r&&(v.style.overflow="visible");this.Position(v,d);this.msieTrapEventBug&&(x.style.height=v.clientHeight+"px",x.style.width=v.clientWidth+"px",x.style.left=parseFloat(v.style.left)+v.clientLeft+"px",x.style.top=parseFloat(v.style.top)+v.clientTop+"px");v.style.visibility="";"Hover"===this.settings.zoom&&(q.onmouseover=this.Remove);window.addEventListener?addEventListener("resize",this.Resize,!1):window.attachEvent?attachEvent("onresize",this.Resize):(this.onresize=window.onresize,window.onresize=this.Resize);c.signal.Post(["math 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k=a.scroll_parent||document.documentElement||document.body;a.style.width=k.scrollWidth+"px";a.style.height=Math.max(k.clientHeight,k.scrollHeight)+"px"},getOverflow:window.getComputedStyle?function(a){return getComputedStyle(a).overflow}:function(a){return(a.currentStyle||{overflow:"visible"}).overflow},getBorder:function(a){var k={thin:1,medium:2,thick:3},d=window.getComputedStyle?getComputedStyle(a):a.currentStyle||{borderLeftWidth:0,borderTopWidth:0};a=d.borderLeftWidth;d=d.borderTopWidth;a=k[a]?k[a]:parseInt(a);d=k[d]?k[d]:parseInt(d);return{x:a,y:d}},getXY:function(e){var k=0,d=0,f;for(f=e;f.offsetParent;)k+=f.offsetLeft,f=f.offsetParent;a.operaPositionBug&&(e.style.border="1px solid");for(f=e;f.offsetParent;)d+=f.offsetTop,f=f.offsetParent;a.operaPositionBug&&(e.style.border="");return{x:k,y:d}},Remove:function(e){var k=document.getElementById("MathJax_ZoomFrame");if(k){var d=MathJax.OutputJax[k.previousSibling.jaxID].getJaxFromMath(k.previousSibling);c.signal.Post(["math 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m.styles["#MathJax_Zoom"].filter},Opera:function(e){a.operaPositionBug=!0;a.operaRefreshBug=!0}});a.topImg=a.msieInlineBlockAlignBug?g.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):g.Element("span",{style:{width:0,height:0,display:"inline-block"}});if(a.operaPositionBug||a.msieTopBug)a.topImg.style.border="1px solid";MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",b,m.styles],["Post",c.Startup.signal,"MathZoom Ready"],["loadComplete",b,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML);(function(c,g,b,d,q){var m=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:"2.2",signal:m};var l=function(a){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",a]].concat([].slice.call(arguments,1)))},n=c.Browser.isPC,p=c.Browser.isMSIE,a=8<(document.documentMode||0),e=n?null:"5px",k=c.CombineConfig("MathMenu",{delay:150,closeImg:b.fileURL(q.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 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q="left",p=e.offsetWidth,b=h.isMobile?30:p-2,c=0;e&&e!==d;)b+=e.offsetLeft,c+=e.offsetTop,e=e.parentNode;b+f.offsetWidth>document.body.offsetWidth-this.margin&&!h.isMobile&&(q="right",b=Math.max(this.margin,b-p-f.offsetWidth+6));n||(f.style["borderRadiusTop"+q]=0,f.style["WebkitBorderRadiusTop"+q]=0,f.style["MozBorderRadiusTop"+q]=0,f.style["KhtmlBorderRadiusTop"+q]=0)}else b+f.offsetWidth>document.body.offsetWidth-this.margin&&(b=document.body.offsetWidth-f.offsetWidth-this.margin),h.isMobile&&(b=Math.max(5,b-Math.floor(f.offsetWidth/2)),c-=20),h.skipUp=a.isContextMenu;f.style.left=b+"px";f.style.top=c+"px";document.selection&&document.selection.empty&&document.selection.empty();return u(a)},Remove:function(a,e){m.Post(["unpost",h.jax]);var k=document.getElementById("MathJax_MenuFrame");k&&(k.parentNode.removeChild(k),this.msieFixedPositionBug&&detachEvent("onresize",h.Resize));h.jax.hover&&(delete h.jax.hover.nofade,f.UnHover(h.jax));return u(a)},Find:function(a){return this.FindN(1,a,[].slice.call(arguments,1))},FindId:function(a){return this.FindN(0,a,[].slice.call(arguments,1))},FindN:function(a,e,k){for(var d=0,f=this.items.length;d<f;d++)if(this.items[d].name[a]===e){if(k.length){if(!this.items[d].menu)break;return this.items[d].menu.FindN(a,k[0],k.slice(1))}return this.items[d]}return null},IndexOf:function(a){return this.IndexOfN(1,a)},IndexOfId:function(a){return this.IndexOfN(0,a)},IndexOfN:function(a,e){for(var k=0,d=this.items.length;k<d;k++)if(this.items[k].name[a]===e)return k;return null}},{config:k,div:null,Close:function(a){return h.Event(a,this.menu||this.parentNode,this.menu?"Touchend":"Remove")},Remove:function(a){return h.Event(a,this,"Remove")},Mouseover:function(a){return h.Event(a,this,"Mouseover")},Mouseout:function(a){return h.Event(a,this,"Mouseout")},Mousedown:function(a){return h.Event(a,this,"Mousedown")},Mouseup:function(a){return h.Event(a,this,"Mouseup")},Touchstart:function(a){return h.Event(a,this,"Touchstart")},Touchend:function(a){return h.Event(a,this,"Touchend")},Event:function(a,e,k,d){if(h.skipMouseover&&"Mouseover"===k&&!d)return u(a);if(h.skipUp){if(k.match(/Mouseup|Touchend/))return delete h.skipUp,u(a);("Touchstart"===k||"Mousedown"===k&&!h.skipMousedown)&&delete h.skipUp}a||(a=window.event);return(d=e.menuItem)&&d[k]?d[k](a,e):null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(a){a=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:a,onmousedown:this.Remove}]]);var e=a.firstChild;h.msieBackgroundBug&&(e.style.backgroundColor="white",e.style.filter="alpha(opacity\x3d0)");h.msieFixedPositionBug?(a.width=a.height=0,this.Resize(),attachEvent("onresize",this.Resize)):e.style.position="fixed";return a},Resize:function(){setTimeout(h.SetWH,0)},SetWH:function(){var a=document.getElementById("MathJax_MenuFrame");a&&(a=a.firstChild,a.style.width=a.style.height="1px",a.style.width=document.body.scrollWidth+"px",a.style.height=document.body.scrollHeight+"px")},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){h.isMobile&&((new Image).src=k.closeImg)}}),r=h.ITEM=MathJax.Object.Subclass({name:"",Create:function(a){if(!this.hidden){var e={onmouseover:h.Mouseover,onmouseout:h.Mouseout,onmouseup:h.Mouseup,onmousedown:h.Mousedown,ondragstart:u,onselectstart:u,onselectend:u,ontouchstart:h.Touchstart,ontouchend:h.Touchend,className:"MathJax_MenuItem",menuItem:this};this.disabled&&(e.className+=" MathJax_MenuDisabled");g.addElement(a,"div",e,this.Label(e,a))}},Name:function(){return l(this.name[0],this.name[1])},Mouseover:function(a,e){this.disabled||this.Activate(e);if(!this.menu||!this.menu.posted){for(var k=document.getElementById("MathJax_MenuFrame").childNodes,d=e.parentNode.childNodes,f=0,b=d.length;f<b;f++){var c=d[f].menuItem;c&&c.menu&&c.menu.posted&&c.Deactivate(d[f])}for(b=k.length-1;0<=b&&e.parentNode.menuItem!==k[b].menuItem;)k[b].menuItem.posted=!1,k[b].parentNode.removeChild(k[b]),b--;this.Timer&&!h.isMobile&&this.Timer(a,e)}},Mouseout:function(a,e){this.menu&&this.menu.posted||this.Deactivate(e);this.timer&&(clearTimeout(this.timer),delete this.timer)},Mouseup:function(a,e){return this.Remove(a,e)},Touchstart:function(a,e){return this.TouchEvent(a,e,"Mousedown")},Touchend:function(a,e){return this.TouchEvent(a,e,"Mouseup")},TouchEvent:function(a,e,k){this!==r.lastItem&&(r.lastMenu&&h.Event(a,r.lastMenu,"Mouseout"),h.Event(a,e,"Mouseover",!0),r.lastItem=this,r.lastMenu=e);if(this.nativeTouch)return null;h.Event(a,e,k);return!1},Remove:function(a,e){e=e.parentNode.menuItem;return e.Remove(a,e)},Activate:function(a){this.Deactivate(a);a.className+=" 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d={className:"MathJax_MenuRadioCheck"};k.settings[this.variable]!==this.value&&(d={style:{display:"none"}});return[["span",d,[this.marker]]," "+this.Name()]},Mouseup:function(a,e){if(!this.disabled){for(var d=e.parentNode.childNodes,f=0,b=d.length;f<b;f++){var c=d[f].menuItem;c&&c.variable===this.variable&&(d[f].firstChild.style.display="none")}e.firstChild.display="";k.settings[this.variable]=this.value;h.cookie[this.variable]=k.settings[this.variable];h.saveCookie();m.Post(["radio button",this])}this.Remove(a,e);this.action&&!this.disabled&&this.action.call(h,this);return u(a)}});h.ITEM.CHECKBOX=h.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(a,e,k){a instanceof Array||(a=[a,a]);this.name=a;this.variable=e;this.With(k)},Label:function(a,e){var d={className:"MathJax_MenuCheck"};k.settings[this.variable]||(d={style:{display:"none"}});return[["span",d,[this.marker]]," 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e)e.hasOwnProperty(b)&&e[b]&&(d&&e[b].version||e[b].isa&&e[b].isa(e))&&f.push(l(k[0],k[1],e[b].id||b,e[b].version));f.sort();e=0;for(k=f.length;e<k;e++)a.push(f[e],["br"]);return a};h.Help=function(){b.Require("[MathJax]/extensions/HelpDialog.js",function(){MathJax.Extension.Help.Dialog()})};h.ShowSource=function(a){a||(a=window.event);var e={screenX:a.screenX,screenY:a.screenY};if(h.jax)if("MathML"===this.format){var k=MathJax.ElementJax.mml;if(k&&"undefined"!==typeof k.mbase.prototype.toMathML)try{h.ShowSource.Text(h.jax.root.toMathML(),a)}catch(f){if(!f.restart)throw f;d.After([this,h.ShowSource,e],f.restart)}else b.loadingToMathML||(b.loadingToMathML=!0,h.ShowSource.Window(a),d.Queue(b.Require("[MathJax]/extensions/toMathML.js"),function(){delete b.loadingToMathML;k.mbase.prototype.toMathML||(k.mbase.prototype.toMathML=function(){})},[this,h.ShowSource,e]))}else"Error"===this.format?h.ShowSource.Text(h.jax.errorText,a):null==h.jax.originalText?alert(l("NoOriginalForm","No original form available")):h.ShowSource.Text(h.jax.originalText,a)};h.ShowSource.Window=function(a){if(!h.ShowSource.w){a=[];var e=k.windowSettings,d;for(d in e)e.hasOwnProperty(d)&&a.push(d+"\x3d"+e[d]);h.ShowSource.w=window.open("","_blank",a.join(","))}return h.ShowSource.w};h.ShowSource.Text=function(a,e){var k=h.ShowSource.Window(e);delete h.ShowSource.w;a=a.replace(/^\s*/,"").replace(/\s*$/,"");a=a.replace(/&/g,"\x26amp;").replace(/</g,"\x26lt;").replace(/>/g,"\x26gt;");var d=l("EqSource","MathJax Equation Source");if(h.isMobile)k.document.open(),k.document.write("\x3chtml\x3e\x3chead\x3e\x3cmeta name\x3d'viewport' content\x3d'width\x3ddevice-width, initial-scale\x3d1.0' /\x3e\x3ctitle\x3e"+d+"\x3c/title\x3e\x3c/head\x3e\x3cbody style\x3d'font-size:85%'\x3e"),k.document.write("\x3cpre\x3e"+a+"\x3c/pre\x3e"),k.document.write("\x3chr\x3e\x3cinput type\x3d'button' value\x3d'"+l("Close","Close")+"' onclick\x3d'window.close()' 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a=q["HTML-CSS"],e=q.NativeMML,k=q.SVG,d=(a||e||k||{config:{scale:100}}).config.scale,f=prompt(l("ScaleMath","Scale all mathematics (compared to surrounding text) by"),d+"%");f&&(f.match(/^\s*\d+(\.\d*)?\s*%?\s*$/)?(f=parseFloat(f))?f!==d&&(a&&(a.config.scale=f),e&&(e.config.scale=f),k&&(k.config.scale=f),h.cookie.scale=f,h.saveCookie(),c.Reprocess()):alert(l("NonZeroScale","The scale should not be zero")):alert(l("PercentScale","The scale should be a percentage (e.g., 120%%)")))};h.Zoom=function(){MathJax.Extension.MathZoom||b.Require("[MathJax]/extensions/MathZoom.js")};h.Renderer=function(){var e=c.outputJax["jax/mml"];if(e[0]!==k.settings.renderer){var d=c.Browser,f,b=h.Renderer.Messages,u;switch(k.settings.renderer){case "NativeMML":k.settings.warnedMML||(d.isChrome&&"24."!==d.version.substr(0,3)?f=b.MML.WebKit:d.isSafari&&!d.versionAtLeast("5.0")?f=b.MML.WebKit:d.isMSIE?d.hasMathPlayer||(f=b.MML.MSIE):f=b.MML[d],u="warnedMML");break;case "SVG":k.settings.warnedSVG||!d.isMSIE||a||(f=b.SVG.MSIE)}if(f){f=l(f[0],f[1]);f=f+"\n\n"+l("SwitchAnyway","Switch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)");h.cookie.renderer=e[0].id;h.saveCookie();if(!confirm(f)){h.cookie.renderer=k.settings.renderer=g.Cookie.Get("menu").renderer;h.saveCookie();return}u&&(h.cookie.warned=k.settings.warned=!0);h.cookie.renderer=k.settings.renderer;h.saveCookie()}c.Queue(["setRenderer",c,k.settings.renderer,"jax/mml"],["Rerender",c])}};h.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. 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Javascript file names should end with '.js'")),b.Require(a,function(e){e!=b.STATUS.OK&&alert(l("BadData","Failed to load translation data from %1",a))}))};h.MPEvents=function(e){var d=k.settings.discoverable,f=h.MPEvents.Messages;a?!d&&"Menu Events"===e.name[1]&&k.settings.mpContext&&alert(l.apply(l,f.IE9warning)):k.settings.mpMouse&&!confirm(l.apply(l,f.IE8warning))?(delete h.cookie.mpContext,delete k.settings.mpContext,delete h.cookie.mpMouse,delete k.settings.mpMouse,h.saveCookie()):(k.settings.mpContext=k.settings.mpMouse,h.cookie.mpContext=h.cookie.mpMouse=k.settings.mpMouse,h.saveCookie(),MathJax.Hub.Queue(["Rerender",MathJax.Hub]))};h.MPEvents.Messages={IE8warning:["IE8warning","This will disable the MathJax menu and zoom features, but you can Alt-Click on an expression to obtain the MathJax menu instead.\n\nReally change the MathPlayer settings?"],IE9warning:["IE9warning","The MathJax contextual menu will be disabled, but you can Alt-Click on an expression to obtain the MathJax menu instead."]};c.Browser.Select({MSIE:function(e){var d="BackCompat"===document.compatMode;e=e.versionAtLeast("8.0")&&7<document.documentMode;h.Augment({margin:20,msieBackgroundBug:9>document.documentMode,msieFixedPositionBug:d||!e,msieAboutBug:d});a&&(delete k.styles["#MathJax_About"].filter,delete k.styles[".MathJax_Menu"].filter)},Firefox:function(a){h.skipMouseover=a.isMobile&&a.versionAtLeast("6.0");h.skipMousedown=a.isMobile}});h.isMobile=c.Browser.isMobile;h.noContextMenu=c.Browser.noContextMenu;h.CreateLocaleMenu=function(){if(h.menu){var a=h.menu.Find("Language").menu,e=a.items,k=[],d=MathJax.Localization.strings,f;for(f in d)d.hasOwnProperty(f)&&k.push(f);k=k.sort();a.items=[];f=0;for(var b=k.length;f<b;f++){var c=d[k[f]].menuTitle,c=c?c+(" ("+k[f]+")"):k[f];a.items.push(r.RADIO([k[f],c],"locale",{action:h.Locale}))}a.items.push(e[e.length-2],e[e.length-1])}};c.Register.StartupHook("End Config",function(){k.settings=c.config.menuSettings;"undefined"!==typeof 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Events"],"mpMouse",{action:h.MPEvents,hidden:!a}),r.CHECKBOX(["MenuAndMouse","Mouse and Menu Events"],"mpMouse",{action:h.MPEvents,hidden:a})),r.SUBMENU(["FontPrefs","Font Preference"],{hidden:!k.showFontMenu},r.LABEL(["ForHTMLCSS","For HTML-CSS:"]),r.RADIO(["Auto","Auto"],"font",{action:h.Font}),r.RULE(),r.RADIO(["TeXLocal","TeX (local)"],"font",{action:h.Font}),r.RADIO(["TeXWeb","TeX (web)"],"font",{action:h.Font}),r.RADIO(["TeXImage","TeX (image)"],"font",{action:h.Font}),r.RULE(),r.RADIO(["STIXlocal","STIX (local)"],"font",{action:h.Font})),r.SUBMENU(["ContextMenu","Contextual Menu"],{hidden:!k.showContext},r.RADIO("MathJax","context"),r.RADIO(["Browser","Browser"],"context")),r.COMMAND(["Scale","Scale All Math ..."],h.Scale),r.RULE().With({hidden:!k.showDiscoverable,name:["","discover_rule"]}),r.CHECKBOX(["Discoverable","Highlight on Hover"],"discoverable",{hidden:!k.showDiscoverable})),r.SUBMENU(["Locale","Language"],{hidden:!k.showLocale},r.RADIO("en","locale",{action:h.Locale}),r.RULE().With({hidden:!k.showLocaleURL,name:["","localURL_rule"]}),r.COMMAND(["LoadLocale","Load from URL ..."],h.LoadLocale,{hidden:!k.showLocaleURL})),r.RULE(),r.COMMAND(["About","About MathJax"],h.About),r.COMMAND(["Help","MathJax Help"],h.Help));if(h.isMobile){var e=k.settings,d=h.menu.Find("Math Settings","Zoom Trigger").menu;d.items[0].disabled=d.items[1].disabled=!0;if("Hover"===e.zoom||"Click"==e.zoom)e.zoom="None";d.items=d.items.slice(0,4);navigator.appVersion.match(/[ (]Android[) ]/)&&h.ITEM.SUBMENU.Augment({marker:"\u00bb"})}h.CreateLocaleMenu()});h.showRenderer=function(a){h.cookie.showRenderer=k.showRenderer=a;h.saveCookie();h.menu.Find("Math Settings","Math Renderer").hidden=!a};h.showMathPlayer=function(a){h.cookie.showMathPlayer=k.showMathPlayer=a;h.saveCookie();h.menu.Find("Math Settings","MathPlayer").hidden=!a};h.showFontMenu=function(a){h.cookie.showFontMenu=k.showFontMenu=a;h.saveCookie();h.menu.Find("Math Settings","Font Preference").hidden=!a};h.showContext=function(a){h.cookie.showContext=k.showContext=a;h.saveCookie();h.menu.Find("Math Settings","Contextual Menu").hidden=!a};h.showDiscoverable=function(a){h.cookie.showDiscoverable=k.showDiscoverable=a;h.saveCookie();h.menu.Find("Math Settings","Highlight on Hover").hidden=!a;h.menu.Find("Math Settings","discover_rule").hidden=!a};h.showLocale=function(a){h.cookie.showLocale=k.showLocale=a;h.saveCookie();h.menu.Find("Language").hidden=!a};MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){MathJax.OutputJax["HTML-CSS"].config.imageFont||(h.menu.Find("Math Settings","Font Preference","TeX (image)").disabled=!0)});d.Queue(c.Register.StartupHook("End Config",{}),["getImages",h],["Styles",b,k.styles],["Post",c.Startup.signal,"MathMenu 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"+g.join(" "):""},toMathMLclass:function(g){var b=[];this["class"]&&b.push(this["class"]);if(this.isa(c.TeXAtom)&&SETTINGS.texHints){var d="ORD OP BIN REL OPEN CLOSE PUNCT INNER VCENTER".split(" ")[this.texClass];d&&b.push("MJX-TeXAtom-"+d)}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&&g.unshift('class\x3d"'+b.join(" ")+'"')},toMathMLattribute:function(c){return"string"===typeof c&&c.replace(/ /g,"").match(/^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/)?RegExp.$2+(1/18*RegExp.$3).toFixed(3).replace(/\.?0+$/,"")+"em":this.toMathMLvariants[c]?this.toMathMLvariants[c]:this.toMathMLquote(c)},toMathMLvariants:{"-tex-caligraphic":c.VARIANT.SCRIPT,"-tex-caligraphic-bold":c.VARIANT.BOLDSCRIPT,"-tex-oldstyle":c.VARIANT.NORMAL,"-tex-oldstyle-bold":c.VARIANT.BOLD,"-tex-mathit":c.VARIANT.ITALIC},toMathMLquote:function(c){c=String(c).split("");for(var b=0,d=c.length;b<d;b++){var q=c[b].charCodeAt(0);if(55295>=q||57344<=q)32>q||126<q?c[b]="\x26#x"+q.toString(16).toUpperCase()+";":(q={"\x26":"\x26amp;","\x3c":"\x26lt;","\x3e":"\x26gt;",'"':"\x26quot;"}[c[b]])&&(c[b]=q);else if(b+1<d){var m=c[b+1].charCodeAt(0);c[b]="\x26#x"+((q-55296<<10)+(m-56320)+65536).toString(16).toUpperCase()+";";c[b+1]="";b++}else c[b]=""}return c.join("")}});c.msubsup.Augment({toMathML:function(c){var b=this.type;null==this.data[this.sup]&&(b="msub");null==this.data[this.sub]&&(b="msup");var d=this.toMathMLattributes();delete this.data[0].inferred;for(var q=[],m=0,l=this.data.length;m<l;m++)this.data[m]&&q.push(this.data[m].toMathML(c+"  "));return c+"\x3c"+b+d+"\x3e\n"+q.join("\n")+"\n"+c+"\x3c/"+b+"\x3e"}});c.munderover.Augment({toMathML:function(c){var b=this.type;null==this.data[this.under]&&(b="mover");null==this.data[this.over]&&(b="munder");var d=this.toMathMLattributes();delete this.data[0].inferred;for(var q=[],m=0,l=this.data.length;m<l;m++)this.data[m]&&q.push(this.data[m].toMathML(c+"  "));return c+"\x3c"+b+d+"\x3e\n"+q.join("\n")+"\n"+c+"\x3c/"+b+"\x3e"}});c.TeXAtom.Augment({toMathML:function(c){var b=this.toMathMLattributes();return b||1!==this.data[0].data.length?c+"\x3cmrow"+b+"\x3e\n"+this.data[0].toMathML(c+"  ")+"\n"+c+"\x3c/mrow\x3e":c.substr(2)+this.data[0].toMathML(c)}});c.chars.Augment({toMathML:function(c){return(c||"")+this.toMathMLquote(this.toString())}});c.entity.Augment({toMathML:function(c){return(c||"")+"\x26"+this.data[0]+";\x3c!-- "+this.toString()+" --\x3e"}});c.xml.Augment({toMathML:function(c){return(c||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){c.TeXmathchoice.Augment({toMathML:function(c){return this.Core().toMathML(c)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js");(function(c,g){var b=c.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};c.Register.StartupHook("TeX Jax Ready",function(){var d=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(g,m,l,n){if(b.disabled)return d.apply(this,arguments);var p=g.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",p,m,l,n]);var p=b.inlineDelimiters,a=l||b.multiLine;l||(m=p[0]+m+p[1]);m=a?m.replace(/ /g,"\u00a0"):m.replace(/\n/g," ");return MathJax.ElementJax.mml.merror(m).With({isError:!0,multiLine:a})}})});c.Register.StartupHook("HTML-CSS Jax Config",function(){c.Config({"HTML-CSS":{styles:{".MathJax .noError":c.Insert({"vertical-align":c.Browser.isMSIE&&b.multiLine?"-2px":""},b.style)}}})});c.Register.StartupHook("HTML-CSS Jax Ready",function(){var b=MathJax.ElementJax.mml,c=MathJax.OutputJax["HTML-CSS"],g=b.math.prototype.toHTML,l=b.merror.prototype.toHTML;b.math.Augment({toHTML:function(b,c){var a=this.data[0];a&&a.data[0]&&a.data[0].isError?(b.style.fontSize="",b=this.HTMLcreateSpan(b),b.bbox=a.data[0].toHTML(b).bbox):b=g.call(this,b,c);return b}});b.merror.Augment({toHTML:function(b){if(!this.isError)return l.call(this,b);b=this.HTMLcreateSpan(b);b.className="noError";this.multiLine&&(b.style.display="inline-block");for(var d=this.data[0].data[0].data.join("").split(/\n/),a=0,e=d.length;a<e;a++)c.addText(b,d[a]),a!==e-1&&c.addElement(b,"br",{isMathJax:!0});d=c.getHD(b.parentNode);a=c.getW(b.parentNode);if(1<e){var e=(d.h+d.d)/2,k=c.TeX.x_height/2;b.parentNode.style.verticalAlign=c.Em(d.d+(k-e));d.h=k+e;d.d=e-k}b.bbox={h:d.h,d:d.d,w:a,lw:0,rw:a};return b}})});c.Register.StartupHook("SVG Jax Config",function(){c.Config({SVG:{styles:{".MathJax_SVG .noError":c.Insert({"vertical-align":c.Browser.isMSIE&&b.multiLine?"-2px":""},b.style)}}})});c.Register.StartupHook("SVG Jax Ready",function(){var b=MathJax.ElementJax.mml,c=b.math.prototype.toSVG,m=b.merror.prototype.toSVG;b.math.Augment({toSVG:function(b,d){var g=this.data[0];return b=g&&g.data[0]&&g.data[0].isError?g.data[0].toSVG(b):c.call(this,b,d)}});b.merror.Augment({toSVG:function(b){if(!this.isError||"math"!==this.Parent().type)return m.call(this,b);b=g.addElement(b,"span",{className:"noError",isMathJax:!0});this.multiLine&&(b.style.display="inline-block");for(var c=this.data[0].data[0].data.join("").split(/\n/),d=0,a=c.length;d<a;d++)g.addText(b,c[d]),d!==a-1&&g.addElement(b,"br",{isMathJax:!0});1<a&&(c=b.offsetHeight/2,b.style.verticalAlign=-c+c/a+"px");return b}})});c.Register.StartupHook("NativeMML Jax Ready",function(){var b=MathJax.ElementJax.mml,c=MathJax.Extension["TeX/noErrors"].config,g=b.math.prototype.toNativeMML,l=b.merror.prototype.toNativeMML;b.math.Augment({toNativeMML:function(b){var c=this.data[0];return b=c&&c.data[0]&&c.data[0].isError?c.data[0].toNativeMML(b):g.call(this,b)}});b.merror.Augment({toNativeMML:function(b){if(!this.isError)return l.call(this,b);b=b.appendChild(document.createElement("span"));for(var d=this.data[0].data[0].data.join("").split(/\n/),a=0,e=d.length;a<e;a++)b.appendChild(document.createTextNode(d[a])),a!==e-1&&b.appendChild(document.createElement("br"));this.multiLine&&(b.style.display="inline-block",1<e&&(b.style.verticalAlign="middle"));for(var k in c.style)c.style.hasOwnProperty(k)&&(d=k.replace(/-./g,function(a){return a.charAt(1).toUpperCase()}),b.style[d]=c.style[k]);return b}})});c.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 c=MathJax.Extension["TeX/noUndefined"].config,g=MathJax.ElementJax.mml,b=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(c.disabled)return b.apply(this,arguments);MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(g.mtext(d).With(c.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js");(function(c,g,b){var d,q=function(a){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",a]].concat([].slice.call(arguments,1)))},m=MathJax.Object.Subclass({Init:function(a,e){this.global={isInner:e};this.data=[l.start(this.global)];a&&(this.data[0].env=a);this.env=this.data[0].env},Push:function(){var a,e,k,b;a=0;for(e=arguments.length;a<e;a++)if(k=arguments[a],k instanceof d.mbase&&(k=l.mml(k)),k.global=this.global,b=this.data.length?this.Top().checkItem(k):!0,b instanceof Array)this.Pop(),this.Push.apply(this,b);else if(b instanceof l)this.Pop(),this.Push(b);else if(b)if(this.data.push(k),k.env){for(var f in this.env)this.env.hasOwnProperty(f)&&(k.env[f]=this.env[f]);this.env=k.env}else k.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 e=this.Top();return a?e.data[e.data.length-1]:e.Pop()},toString:function(){return"stack[\n  "+this.data.join("\n  ")+"\n]"}}),l=m.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,e){null==a&&(a=!0);return 1!==this.data.length||e?d.mrow.apply(d,this.data).With(a?{inferred:!0}:{}):this.data[0]},checkItem:function(a){"over"===a.type&&this.isOpen&&(a.num=this.mmlData(!1),this.data=[]);if("cell"===a.type&&this.isOpen){if(a.linebreak)return!1;c.Error(["Misplaced","Misplaced %1",a.name])}a.isClose&&this[a.type+"Error"]&&c.Error(this[a.type+"Error"]);if(!a.isNotStack)return!0;this.Push(a.data[0]);return!1},With:function(a){for(var e in a)a.hasOwnProperty(e)&&(this[e]=a[e]);return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});l.start=l.Subclass({type:"start",isOpen:!0,Init:function(a){this.SUPER(arguments).Init.call(this);this.global=a},checkItem:function(a){return"stop"===a.type?l.mml(this.mmlData()):this.SUPER(arguments).checkItem.call(this,a)}});l.stop=l.Subclass({type:"stop",isClose:!0});l.open=l.Subclass({type:"open",isOpen:!0,stopError:["ExtraOpenMissingClose","Extra open brace or missing close brace"],checkItem:function(a){if("close"===a.type){var e=this.mmlData();return l.mml(d.TeXAtom(e))}return this.SUPER(arguments).checkItem.call(this,a)}});l.close=l.Subclass({type:"close",isClose:!0});l.prime=l.Subclass({type:"prime",checkItem:function(a){if("msubsup"!==this.data[0].type)return[d.msup(this.data[0],this.data[1]),a];this.data[0].SetData(this.data[0].sup,this.data[1]);return[this.data[0],a]}});l.subsup=l.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(a){if("open"===a.type||"left"===a.type)return!0;if("mml"===a.type)return this.primes&&(2!==this.position?this.data[0].SetData(2,this.primes):a.data[0]=d.mrow(this.primes.With({variantForm:!0}),a.data[0])),this.data[0].SetData(this.position,a.data[0]),l.mml(this.data[0]);this.SUPER(arguments).checkItem.call(this,a)&&c.Error(this[["","subError","supError"][this.position]])},Pop:function(){}});l.over=l.Subclass({type:"over",isClose:!0,name:"\\over",checkItem:function(a,e){"over"===a.type&&c.Error(["AmbiguousUseOf","Ambiguous use of %1",a.name]);if(a.isClose){var k=d.mfrac(this.num,this.mmlData(!1));null!=this.thickness&&(k.linethickness=this.thickness);if(this.open||this.close)k.texClass=d.TEXCLASS.INNER,k.texWithDelims=!0,k=c.fenced(this.open,k,this.close);return[l.mml(k),a]}return this.SUPER(arguments).checkItem.call(this,a)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});l.left=l.Subclass({type:"left",isOpen:!0,delim:"(",stopError:["ExtraLeftMissingRight","Extra \\left or missing \\right"],checkItem:function(a){return"right"===a.type?l.mml(c.fenced(this.delim,this.mmlData(),a.delim)):this.SUPER(arguments).checkItem.call(this,a)}});l.right=l.Subclass({type:"right",isClose:!0,delim:")"});l.begin=l.Subclass({type:"begin",isOpen:!0,checkItem:function(a){if("end"===a.type)return a.name!==this.name&&c.Error(["EnvBadEnd","\\begin{%1} ended with \\end{%2}",this.name,a.name]),this.end?this.parse[this.end].call(this.parse,this,this.data):l.mml(this.mmlData());"stop"===a.type&&c.Error(["EnvMissingEnd","Missing \\end{%1}",this.name]);return this.SUPER(arguments).checkItem.call(this,a)}});l.end=l.Subclass({type:"end",isClose:!0});l.style=l.Subclass({type:"style",checkItem:function(a){if(!a.isClose)return this.SUPER(arguments).checkItem.call(this,a);var e=d.mstyle.apply(d,this.data).With(this.styles);return[l.mml(e),a]}});l.position=l.Subclass({type:"position",checkItem:function(a){a.isClose&&c.Error(["MissingBoxFor","Missing box for %1",name]);if(a.isNotStack){var e=a.mmlData();switch(this.move){case "vertical":return e=d.mpadded(e).With({height:this.dh,depth:this.dd,voffset:this.dh}),[l.mml(e)];case "horizontal":return[l.mml(this.left),a,l.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,a)}});l.array=l.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(a){if(a.isClose&&"over"!==a.type){if(a.isEntry)return this.EndEntry(),this.clearEnv(),!1;if(a.isCR)return this.EndEntry(),this.EndRow(),this.clearEnv(),!1;this.EndTable();this.clearEnv();var e=d.mtable.apply(d,this.table).With(this.arraydef);4===this.frame.length?e.frame=this.frame.dashed?"dashed":"solid":this.frame.length&&(e.hasFrame=!0,this.arraydef.rowlines&&(this.arraydef.rowlines=this.arraydef.rowlines.replace(/none( none)+$/,"none")),e=d.menclose(e).With({notation:this.frame.join(" 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e,k;if("open"===a.type||"left"===a.type)return!0;if("mml"===a.type&&a.data[0].type.match(/^(mo|mi|mtext)$/)&&(e=a.data[0],k=e.data.join(""),1===k.length&&!e.movesupsub))return(k=l.not.remap[k.charCodeAt(0)])?e.SetData(0,d.chars(String.fromCharCode(k))):e.Append(d.chars("\u0338")),a;e=d.mpadded(d.mtext("\u29f8")).With({width:0});e=d.TeXAtom(e).With({texClass:d.TEXCLASS.REL});return[e,a]}});l.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};l.dots=l.Subclass({type:"dots",checkItem:function(a){if("open"===a.type||"left"===a.type)return!0;var e=this.ldots;if("mml"===a.type&&a.data[0].isEmbellished()){var k=a.data[0].CoreMO().Get("texClass");if(k===d.TEXCLASS.BIN||k===d.TEXCLASS.REL)e=this.cdots}return[e,a]}});var n={Add:function(a,e,k){e||(e=this);for(var b in a)a.hasOwnProperty(b)&&("object"!==typeof a[b]||a[b]instanceof Array||"object"!==typeof e[b]&&"function"!==typeof e[b]?e[b]&&e[b].isUser&&k||(e[b]=a[b]):this.Add(a[b],e[b],a[b],k));return e}},p=MathJax.Object.Subclass({Init:function(a,e){this.string=a;this.macroCount=this.i=0;var k;if(e){k={};for(var b in e)e.hasOwnProperty(b)&&(k[b]=e[b])}this.stack=c.Stack(k,!!e);this.Parse();this.Push(l.stop())},Parse:function(){for(var a,e;this.i<this.string.length;)if(a=this.string.charAt(this.i++),e=a.charCodeAt(0),55296<=e&&56320>e&&(a+=this.string.charAt(this.i++)),n.special[a])this[n.special[a]](a);else 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e=this.string.slice(this.i-1).match(n.number);e?(a=d.mn(e[0].replace(/[{}]/g,"")),this.i+=e[0].length-1):a=d.mo(d.chars(a));this.stack.env.font&&(a.mathvariant=this.stack.env.font);this.Push(this.mmlToken(a))},Open:function(a){this.Push(l.open())},Close:function(a){this.Push(l.close())},Tilde:function(a){this.Push(d.mtext(d.chars("\u00a0")))},Space:function(a){},Superscript:function(a){this.GetNext().match(/\d/)&&(this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1));var e,b;e=this.stack.Top();"prime"===e.type?(a=e.data[0],b=e.data[1],this.stack.Pop()):(a=this.stack.Prev())||(a=d.mi(""));a.isEmbellishedWrapper&&(a=a.data[0].data[0]);if("msubsup"===a.type)a.data[a.sup]&&c.Error(["DoubleExponent","Double exponent: use braces to clarify"]),e=a.sup;else if(a.movesupsub){if("munderover"!==a.type||a.data[a.over])a.movablelimits&&a.isa(d.mi)&&(a=this.mi2mo(a)),a=d.munderover(a,null,null).With({movesupsub:!0});e=a.over}else 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e=this.GetBrackets(a);a=this.GetArgument(a);"\\frac"===a&&(a+="{"+this.GetArgument(a)+"}{"+this.GetArgument(a)+"}");a=c.Parse(a,this.stack.env).mml();a=e?d.mroot(a,this.parseRoot(e)):d.msqrt.apply(d,a.array());this.Push(a)},Root:function(a){var e=this.GetUpTo(a,"\\of");a=this.ParseArg(a);this.Push(d.mroot(a,this.parseRoot(e)))},parseRoot:function(a){var e=this.stack.env,b=e.inRoot;e.inRoot=!0;var u=c.Parse(a,e);a=u.mml();u=u.stack.global;if(u.leftRoot||u.upRoot)a=d.mpadded(a),u.leftRoot&&(a.width=u.leftRoot),u.upRoot&&(a.voffset=u.upRoot,a.height=u.upRoot);e.inRoot=b;return a},MoveRoot:function(a,e){this.stack.env.inRoot||c.Error(["MisplacedMoveRoot","%1 can appear only within a root",a]);this.stack.global[e]&&c.Error(["MultipleMoveRoot","Multiple use of %1",a]);var b=this.GetArgument(a);b.match(/-?[0-9]+/)||c.Error(["IntegerArg","The argument to %1 must be an integer",a]);b=b/15+"em";"-"!==b.substr(0,1)&&(b="+"+b);this.stack.global[e]=b},Accent:function(a,e,b){a=this.ParseArg(a);var c={accent:!0};this.stack.env.font&&(c.mathvariant=this.stack.env.font);e=this.mmlToken(d.mo(d.entity("#x"+e)).With(c));e.stretchy=b?!0:!1;this.Push(d.TeXAtom(d.munderover(a,null,e).With({accent:!0})))},UnderOver:function(a,e,b){var c={o:"over",u:"under"}[a.charAt(1)];a=this.ParseArg(a);a.Get("movablelimits")&&(a.movablelimits=!1);a=d.munderover(a,null,null);b&&(a.movesupsub=!0);a.data[a[c]]=this.mmlToken(d.mo(d.entity("#x"+e)).With({stretchy:!0,accent:"under"==c}));this.Push(a)},Overset:function(a){var e=this.ParseArg(a);a=this.ParseArg(a);this.Push(d.mover(a,e))},Underset:function(a){var e=this.ParseArg(a);a=this.ParseArg(a);this.Push(d.munder(a,e))},TeXAtom:function(a,e){var b={texClass:e};if(e==d.TEXCLASS.OP){b.movesupsub=b.movablelimits=!0;var u=this.GetArgument(a),f=u.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);f?(b.mathvariant=d.VARIANT.NORMAL,b=l.fn(this.mmlToken(d.mi(f[1]).With(b)))):b=l.fn(d.TeXAtom(c.Parse(u,this.stack.env).mml()).With(b))}else 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e},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(d.mpadded(d.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(a,e,b){a=d.mphantom(this.ParseArg(a));if(e||b)a=d.mpadded(a),b&&(a.height=a.depth=0),e&&(a.width=0);this.Push(d.TeXAtom(a))},Smash:function(a){var e=this.trimSpaces(this.GetBrackets(a,""));a=d.mpadded(this.ParseArg(a));switch(e){case "b":a.depth=0;break;case "t":a.height=0;break;default:a.height=a.depth=0}this.Push(d.TeXAtom(a))},Lap:function(a){var e=d.mpadded(this.ParseArg(a)).With({width:0});"\\llap"===a&&(e.lspace="-1 width");this.Push(d.TeXAtom(e))},RaiseLower:function(a){var e=this.GetDimen(a),b=l.position().With({name:a,move:"vertical"});"-"===e.charAt(0)&&(e=e.slice(1),a={raise:"\\lower",lower:"\\raise"}[a.substr(1)]);"\\lower"===a?(b.dh="-"+e,b.dd="+"+e):(b.dh="+"+e,b.dd="-"+e);this.Push(b)},MoveLeftRight:function(a){var e=this.GetDimen(a),b="-"===e.charAt(0)?e.slice(1):"-"+e;if("\\moveleft"===a)var c=e,e=b,b=c;this.Push(l.position().With({name:a,move:"horizontal",left:d.mspace().With({width:e,mathsize:d.SIZE.NORMAL}),right:d.mspace().With({width:b,mathsize:d.SIZE.NORMAL})}))},Hskip:function(a){this.Push(d.mspace().With({width:this.GetDimen(a),mathsize:d.SIZE.NORMAL}))},Rule:function(a,e){var b=this.GetDimen(a),c=this.GetDimen(a),f=this.GetDimen(a),h={width:b,height:c,depth:f};"blank"!==e?(parseFloat(b)&&parseFloat(c)+parseFloat(f)&&(h.mathbackground=this.stack.env.color||"black"),b=d.mpadded(d.mrow()).With(h)):b=d.mspace().With(h);this.Push(b)},MakeBig:function(a,e,b){b*=n.p_height;b=String(b).replace(/(\.\d\d\d).+/,"$1")+"em";a=this.GetDelimiter(a);this.Push(d.TeXAtom(d.mo(a).With({minsize:b,maxsize:b,fence:!0,stretchy:!0,symmetric:!0})).With({texClass:e}))},BuildRel:function(a){var e=this.ParseUpTo(a,"\\over");a=this.ParseArg(a);this.Push(d.TeXAtom(d.munderover(a,null,e)).With({mclass:d.TEXCLASS.REL}))},HBox:function(a,e){this.Push.apply(this,this.InternalMath(this.GetArgument(a),e))},FBox:function(a){this.Push(d.menclose.apply(d,this.InternalMath(this.GetArgument(a))).With({notation:"box"}))},Not:function(a){this.Push(l.not())},Dots:function(a){this.Push(l.dots().With({ldots:this.mmlToken(d.mo(d.entity("#x2026")).With({stretchy:!1})),cdots:this.mmlToken(d.mo(d.entity("#x22EF")).With({stretchy:!1}))}))},Require:function(a){a=this.GetArgument(a).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");this.Extension(null,a)},Extension:function(a,e,k){e=c.extensionDir+"/"+e;e.match(/\.js$/)||(e+=".js");b.loaded[b.fileURL(e)]||(null!=a&&delete n[k||"macros"][a.replace(/^\\/,"")],g.RestartAfter(b.Require(e)))},Macro:function(a,e,b,d){if(b){var f=[];if(null!=d){var h=this.GetBrackets(a);f.push(null==h?d:h)}for(d=f.length;d<b;d++)f.push(this.GetArgument(a));e=this.SubstituteArgs(f,e)}this.string=this.AddArgs(e,this.string.slice(this.i));this.i=0;++this.macroCount>c.config.MAXMACROS&&c.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])},Matrix:function(a,e,b,d,f,h,g,n){var p=this.GetNext();""===p&&c.Error(["MissingArgFor","Missing argument for %1",a]);"{"===p?this.i++:(this.string=p+"}"+this.string.slice(this.i+1),this.i=0);a=l.array().With({requireClose:!0,arraydef:{rowspacing:h||"4pt",columnspacing:f||"1em"}});n&&(a.isCases=!0);if(e||b)a.open=e,a.close=b;"D"===g&&(a.arraydef.displaystyle=!0);null!=d&&(a.arraydef.columnalign=d);this.Push(a)},Entry:function(a){this.Push(l.cell().With({isEntry:!0,name:a}));if(this.stack.Top().isCases){var e=this.string,b=0;a=this.i;for(var d=e.length;a<d;){var f=e.charAt(a);"{"===f?(b++,a++):"}"===f?0===b?d=0:(b--,a++):"\x26"===f&&0===b?c.Error(["ExtraAlignTab","Extra alignment tab in \\cases text"]):"\\"===f?e.substr(a).match(/^((\\cr)[^a-zA-Z]|\\\\)/)?d=0:a+=2:a++}e=e.substr(this.i,a-this.i);e.match(/^\s*\\text[^a-zA-Z]/)||(this.Push.apply(this,this.InternalMath(e)),this.i=a)}},Cr:function(a){this.Push(l.cell().With({isCR:!0,name:a}))},CrLaTeX:function(a){var e;"["===this.string.charAt(this.i)&&(e=this.GetBrackets(a,"").replace(/ /g,""))&&!e.match(/^((-?(\.\d+|\d+(\.\d*)?))(pt|em|ex|mu|mm|cm|in|pc))$/)&&c.Error(["BracketMustBeDimension","Bracket argument to %1 must be a dimension",a]);this.Push(l.cell().With({isCR:!0,name:a,linebreak:!0}));a=this.stack.Top();if(a.isa(l.array)){if(e&&a.arraydef.rowspacing){var b=a.arraydef.rowspacing.split(/ 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a=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=a.offsetWidth/5;this.hiddenDiv.removeChild(a);this.startMarker=this.createStrut(this.Element("span"),10,!0);this.endMarker=this.addText(this.Element("span"),"x").parentNode;this.HDspan=this.Element("span");this.operaHeightBug&&this.createStrut(this.HDspan,0);if(this.msieInlineBlockAlignBug){this.HDimg=this.addElement(this.HDspan,"img",{style:{height:"0px",width:"1px"}});try{this.HDimg.src="about:blank"}catch(e){}}else this.HDimg=this.createStrut(this.HDspan,0);this.EmExSpan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["span",{className:"MathJax_ExBox"}],["span",{className:"MathJax"},[["span",{className:"MathJax_EmBox"}]]]]);this.linebreakSpan=this.Element("span",null,[["hr",{style:{width:"100%",size:1,padding:0,border:0,margin:0}}]]);return c.Styles(this.config.styles,["InitializeHTML",this])},removeSTIXfonts:function(a){for(var e=0,b=a.length;e<b;e++)"STIX"===a[e]&&(a.splice(e,1),b--,e--);"STIX"===this.config.preferredFont&&(this.config.preferredFont=a[0])},PreloadWebFonts:function(){if(b.allowWebFonts&&b.config.preloadWebFonts)for(var a=0,e=b.config.preloadWebFonts.length;a<e;a++){var c=b.FONTDATA.FONTS[b.config.preloadWebFonts[a]];c.available||b.Font.testFont(c)}},InitializeHTML:function(){this.PreloadWebFonts();document.body.appendChild(this.EmExSpan);document.body.appendChild(this.linebreakSpan);this.defaultEx=this.EmExSpan.firstChild.offsetHeight/60;this.defaultEm=this.EmExSpan.lastChild.firstChild.offsetHeight/60;this.defaultWidth=this.linebreakSpan.firstChild.offsetWidth;document.body.removeChild(this.linebreakSpan);document.body.removeChild(this.EmExSpan)},preTranslate:function(a){var e=a.jax[this.id],b,c=e.length,d,h,r,w,v,t,m=!1,x=this.config.linebreaks.automatic,q=this.config.linebreaks.width;x?((m=null!=q.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/))?q=q.replace(/\s*container\s*/,""):t=this.defaultWidth,""===q&&(q="100%")):t=1E5;for(b=0;b<c;b++)if(d=e[b],d.parentNode&&((h=d.previousSibling)&&String(h.className).match(/^MathJax(_Display)?( MathJax_Processing)?$/)&&h.parentNode.removeChild(h),h=d.MathJax.elementJax))h.HTMLCSS={display:"block"===h.root.Get("display")},r=w=this.Element("span",{className:"MathJax",id:h.inputID+"-Frame",isMathJax:!0,jaxID:this.id,oncontextmenu:l.Menu,onmousedown:l.Mousedown,onmouseover:l.Mouseover,onmouseout:l.Mouseout,onmousemove:l.Mousemove,onclick:l.Click,ondblclick:l.DblClick}),g.Browser.noContextMenu&&(r.ontouchstart=n.start,r.ontouchend=n.end),h.HTMLCSS.display?(w=this.Element("div",{className:"MathJax_Display"}),w.appendChild(r)):this.msieDisappearingBug&&(r.style.display="inline-block"),w.setAttribute("role","textbox"),w.setAttribute("aria-readonly","true"),w.className+=" MathJax_Processing",d.parentNode.insertBefore(w,d),d.parentNode.insertBefore(this.EmExSpan.cloneNode(!0),d),m&&w.parentNode.insertBefore(this.linebreakSpan.cloneNode(!0),w);for(b=0;b<c;b++)if(d=e[b],d.parentNode&&(v=d.previousSibling,w=v.previousSibling,h=d.MathJax.elementJax)){d=v.firstChild.offsetHeight/60;v=v.lastChild.firstChild.offsetHeight/60;m&&(t=w.previousSibling.firstChild.offsetWidth);if(0===d||"NaN"===d)this.hiddenDiv.appendChild(w),h.HTMLCSS.isHidden=!0,d=this.defaultEx,v=this.defaultEm,m&&(t=this.defaultWidth);w=Math.floor(Math.max(this.config.minScaleAdjust/100,d/this.TeX.x_height/v)*this.config.scale);h.HTMLCSS.scale=w/100;h.HTMLCSS.fontSize=w+"%";h.HTMLCSS.em=h.HTMLCSS.outerEm=v;this.em=v*w/100;h.HTMLCSS.ex=d;h.HTMLCSS.lineWidth=x?this.length2em(q,1,t/this.em):1E6}for(b=0;b<c;b++)if(d=e[b],d.parentNode&&(v=e[b].previousSibling,h=e[b].MathJax.elementJax))m&&(r=v.previousSibling,h.HTMLCSS.isHidden||(r=r.previousSibling),r.parentNode.removeChild(r)),v.parentNode.removeChild(v);a.HTMLCSSeqn=a.HTMLCSSlast=0;a.HTMLCSSi=-1;a.HTMLCSSchunk=this.config.EqnChunk;a.HTMLCSSdelay=!1},Translate:function(a,e){if(a.parentNode){e.HTMLCSSdelay&&(e.HTMLCSSdelay=!1,g.RestartAfter(MathJax.Callback.Delay(this.config.EqnChunkDelay)));var b=a.MathJax.elementJax,c=b.root,f=document.getElementById(b.inputID+"-Frame"),h=b.HTMLCSS.display?f.parentNode:f;this.em=d.mbase.prototype.em=b.HTMLCSS.em*b.HTMLCSS.scale;this.outerEm=b.HTMLCSS.em;this.scale=b.HTMLCSS.scale;this.linebreakWidth=b.HTMLCSS.lineWidth;f.style.fontSize=b.HTMLCSS.fontSize;this.initImg(f);this.initHTML(c,f);c.setTeXclass();try{c.toHTML(f,h)}catch(r){if(r.restart)for(;f.firstChild;)f.removeChild(f.firstChild);throw r;}b.HTMLCSS.isHidden&&a.parentNode.insertBefore(h,a);h.className=h.className.split(/ /)[0];this.hideProcessedMath&&(h.className+=" MathJax_Processed",a.MathJax.preview&&(b.HTMLCSS.preview=a.MathJax.preview,delete a.MathJax.preview),e.HTMLCSSeqn+=e.i-e.HTMLCSSi,e.HTMLCSSi=e.i,e.HTMLCSSeqn>=e.HTMLCSSlast+e.HTMLCSSchunk&&(this.postTranslate(e),e.HTMLCSSchunk=Math.floor(e.HTMLCSSchunk*this.config.EqnChunkFactor),e.HTMLCSSdelay=!0))}},postTranslate:function(a){var e=a.jax[this.id];if(this.hideProcessedMath){for(var b=a.HTMLCSSlast,c=a.HTMLCSSeqn;b<c;b++){var d=e[b];if(d&&d.MathJax.elementJax){d.previousSibling.className=d.previousSibling.className.split(/ /)[0];var h=d.MathJax.elementJax.HTMLCSS;h.preview&&(h.preview.innerHTML="",d.MathJax.preview=h.preview,delete h.preview)}}this.forceReflow&&(e=(document.styleSheets||[])[0]||{},e.disabled=!0,e.disabled=!1);a.HTMLCSSlast=a.HTMLCSSeqn}},getJaxFromMath:function(a){"MathJax_Display"===a.parentNode.className&&(a=a.parentNode);do a=a.nextSibling;while(a&&"script"!==a.nodeName.toLowerCase());return g.getJaxFor(a)},getHoverSpan:function(a,e){return a.root.HTMLspanElement()},getHoverBBox:function(a,e,b){e=e.bbox;a=a.HTMLCSS.outerEm;a={w:e.w*a,h:e.h*a,d:e.d*a};e.width&&(a.width=e.width);return a},Zoom:function(a,e,c,g,f){e.className="MathJax";e.style.fontSize=a.HTMLCSS.fontSize;f=e.appendChild(this.EmExSpan.cloneNode(!0));var h=f.lastChild.firstChild.offsetHeight/60;this.em=d.mbase.prototype.em=h;this.outerEm=h/a.HTMLCSS.scale;f.parentNode.removeChild(f);this.idPostfix="-zoom";a.root.toHTML(e,e);this.idPostfix="";if(f=a.root.HTMLspanElement().bbox.width){e.style.width=Math.floor(g-1.5*b.em)+"px";e.style.display="inline-block";for(a=document.getElementById((a.root.id||"MathJax-Span-"+a.root.spanID)+"-zoom").firstChild;a&&a.style.width!==f;)a=a.nextSibling;a&&(a.style.width="100%")}e.style.position="absolute";f||(c.style.position="absolute");a=e.offsetWidth;g=e.offsetHeight;f=c.offsetHeight;h=c.offsetWidth;0===h&&(h=c.parentNode.offsetWidth);e.style.position=c.style.position="";return{Y:-l.getBBox(e).h,mW:h,mH:f,zW:a,zH:g}},initImg:function(a){},initHTML:function(a,e){},initFont:function(a){var e=b.FONTDATA.FONTS,d=b.config.availableFonts;if(d&&d.length&&b.Font.testFont(e[a]))return e[a].available=!0,null;if(!this.allowWebFonts)return null;e[a].isWebFont=!0;b.FontFaceBug&&(e[a].family=a,b.msieFontCSSBug&&(e[a].family+="-Web"));return c.Styles({"@font-face":this.Font.fontFace(a)})},Remove:function(a){var e=document.getElementById(a.inputID+"-Frame");e&&(a.HTMLCSS.display&&(e=e.parentNode),e.parentNode.removeChild(e));delete a.HTMLCSS},getHD:function(a){var e=a.style.position;a.style.position="absolute";this.HDimg.style.height="0px";a.appendChild(this.HDspan);var b={h:a.offsetHeight};this.HDimg.style.height=b.h+"px";b.d=a.offsetHeight-b.h;b.h-=b.d;b.h/=this.em;b.d/=this.em;a.removeChild(this.HDspan);a.style.position=e;return b},getW:function(a){var e,b;e=(a.bbox||{}).w;var c=a;if(a.bbox&&a.bbox.exactW)return e;if(a.bbox&&0<=e&&!this.initialSkipBug||this.negativeBBoxes||!a.firstChild)e=a.offsetWidth,b=a.parentNode.offsetHeight;else if(a.bbox&&0>e&&this.msieNegativeBBoxBug)e=-a.offsetWidth,b=a.parentNode.offsetHeight;else{if(this.initialSkipBug){var d=a.style.position;a.style.position="absolute";c=this.startMarker;a.insertBefore(c,a.firstChild)}a.appendChild(this.endMarker);e=this.endMarker.offsetLeft-c.offsetLeft;a.removeChild(this.endMarker);this.initialSkipBug&&(a.removeChild(c),a.style.position=d)}null!=b&&(a.parentNode.HH=b/this.em);return e/this.em},Measured:function(a,e){var b=a.bbox;if(null==b.width&&b.w&&!b.isMultiline){var c=this.getW(a);b.rw+=c-b.w;b.w=c;b.exactW=!0}e||(e=a.parentNode);e.bbox||(e.bbox=b);return a},Remeasured:function(a,e){e.bbox=this.Measured(a,e).bbox},MeasureSpans:function(a){var e=[],b,c,d,h,g;c=0;for(d=a.length;c<d;c++)if(b=a[c])h=b.bbox,g=this.parentNode(b),h.exactW||h.width||0===h.w||h.isMultiline?g.bbox||(g.bbox=h):this.negativeBBoxes||!b.firstChild||0<=h.w&&!this.initialSkipBug||0>h.w&&this.msieNegativeBBoxBug?e.push([b]):this.initialSkipBug?(h=this.startMarker.cloneNode(!0),g=this.endMarker.cloneNode(!0),b.insertBefore(h,b.firstChild),b.appendChild(g),e.push([b,h,g,b.style.position]),b.style.position="absolute"):(g=this.endMarker.cloneNode(!0),b.appendChild(g),e.push([b,null,g]));c=0;for(d=e.length;c<d;c++)b=e[c][0],h=b.bbox,g=this.parentNode(b),0<=h.w&&!this.initialSkipBug||this.negativeBBoxes||!b.firstChild?(a=b.offsetWidth,g.HH=g.offsetHeight/this.em):0>h.w&&this.msieNegativeBBoxBug?(a=-b.offsetWidth,g.HH=g.offsetHeight/this.em):a=e[c][2].offsetLeft-((e[c][1]||{}).offsetLeft||0),a/=this.em,h.rw+=a-h.w,h.w=a,h.exactW=!0,g.bbox||(g.bbox=h);c=0;for(d=e.length;c<d;c++)b=e[c],b[1]&&(b[1].parentNode.removeChild(b[1]),b[0].style.position=b[3]),b[2]&&b[2].parentNode.removeChild(b[2])},Em:function(a){return 6E-4>Math.abs(a)?"0em":a.toFixed(3).replace(/\.?0+$/,"")+"em"},EmRounded:function(a){a=(Math.round(a*b.em)+.05)/b.em;return 6E-4>Math.abs(a)?"0em":a.toFixed(3).replace(/\.?0+$/,"")+"em"},unEm:function(a){return parseFloat(a)},Px:function(a){a*=this.em;return(0>a?"-":"")+Math.abs(a).toFixed(1).replace(/\.?0+$/,"")+"px"},unPx:function(a){return parseFloat(a)/this.em},Percent:function(a){return(100*a).toFixed(1).replace(/\.?0+$/,"")+"%"},length2em:function(a,e,c){"string"!==typeof a&&(a=a.toString());if(""===a)return"";if(a===d.SIZE.NORMAL)return 1;if(a===d.SIZE.BIG)return 2;if(a===d.SIZE.SMALL)return.71;if("infinity"===a)return b.BIGDIMEN;var g=this.FONTDATA.TeX_factor;if(a.match(/mathspace$/))return b.MATHSPACE[a]*g;var f=a.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);a=parseFloat(f[1]||"1");f=f[2];null==c&&(c=1);null==e&&(e=1);return"em"===f?a*g:"ex"===f?a*b.TeX.x_height*g:"%"===f?a/100*c:"px"===f?a/b.em:"pt"===f?a/10*g:"pc"===f?1.2*a*g:"in"===f?a*this.pxPerInch/b.em:"cm"===f?a*this.pxPerInch/b.em/2.54:"mm"===f?a*this.pxPerInch/b.em/25.4:"mu"===f?a/18*g*e:a*g*c},thickness2em:function(a,e){var c=b.TeX.rule_thickness;return a===d.LINETHICKNESS.MEDIUM?c:a===d.LINETHICKNESS.THIN?.67*c:a===d.LINETHICKNESS.THICK?1.67*c:this.length2em(a,e,c)},getPadding:function(a){var b={top:0,right:0,bottom:0,left:0},c=!1,d;for(d in b)if(b.hasOwnProperty(d)){var f=a.style["padding"+d.charAt(0).toUpperCase()+d.substr(1)];f&&(b[d]=this.length2em(f),c=!0)}return c?b:!1},getBorders:function(a){var b={top:0,right:0,bottom:0,left:0},c={},d=!1,f;for(f in b)if(b.hasOwnProperty(f)){var h="border"+f.charAt(0).toUpperCase()+f.substr(1);a.style[h+"Style"]&&(d=!0,b[f]=this.length2em(a.style[h+"Width"]),c[h]=[a.style[h+"Width"],a.style[h+"Style"],a.style[h+"Color"]].join(" "))}b.css=c;return d?b:!1},setBorders:function(a,b){if(b)for(var c in b.css)b.css.hasOwnProperty(c)&&(a.style[c]=b.css[c])},createStrut:function(a,b,c){b=this.Element("span",{isMathJax:!0,style:{display:"inline-block",overflow:"hidden",height:b+"px",width:"1px",marginRight:"-1px"}});c?a.insertBefore(b,a.firstChild):a.appendChild(b);return b},createBlank:function(a,b,c){b=this.Element("span",{isMathJax:!0,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(b)}});c?a.insertBefore(b,a.firstChild):a.appendChild(b);return b},createShift:function(a,b,c){b=this.Element("span",{style:{marginLeft:this.Em(b)},isMathJax:!0});c?a.insertBefore(b,a.firstChild):a.appendChild(b);return b},createSpace:function(a,e,c,g,f,h){e<-c&&(c=-e);var r=this.Em(e+c),l=this.Em(-c);this.msieInlineBlockAlignBug&&(l=this.Em(b.getHD(a.parentNode).d-c));a.isBox||h?(h=null==a.scale?1:a.scale,a.bbox={exactW:!0,h:e*h,d:c*h,w:g*h,rw:g*h,lw:0},a.style.height=r,a.style.verticalAlign=l,a.HH=(e+c)*h):a=this.addElement(a,"span",{style:{height:r,verticalAlign:l},isMathJax:!0});0<=g?(a.style.width=this.Em(g),a.style.display="inline-block",a.style.overflow="hidden"):(this.msieNegativeSpaceBug&&(a.style.height=""),a.style.marginLeft=this.Em(g),b.safariNegativeSpaceBug&&a.parentNode.firstChild==a&&this.createBlank(a,0,!0));f&&f!==d.COLOR.TRANSPARENT&&(a.style.backgroundColor=f,a.style.position="relative");return a},createRule:function(a,e,c,d,f){e<-c&&(c=-e);var h=b.TeX.min_rule_thickness,g=1;0<d&&d*this.em<h&&(d=h/this.em);0<e+c&&(e+c)*this.em<h&&(g=1/(e+c)*(h/this.em),e*=g,c*=g);f=f?"solid "+f:"solid";f=this.Em(d)+" "+f;h=1===g?this.Em(e+c):h+"px";g=this.Em(-c);f=this.addElement(a,"span",{style:{borderLeft:f,display:"inline-block",overflow:"hidden",width:0,height:h,verticalAlign:g},bbox:{h:e,d:c,w:d,rw:d,lw:0,exactW:!0},noAdjust:!0,HH:e+c,isMathJax:!0});0<d&&0==f.offsetWidth&&(f.style.width=this.Em(d));if(a.isBox||"mspace"==a.className)a.bbox=f.bbox,a.HH=e+c;return f},createFrame:function(a,b,c,d,f,h){b<-c&&(c=-b);var g=2*f;this.msieFrameSizeBug&&(d<g&&(d=g),b+c<g&&(b=g-c));this.msieBorderWidthBug&&(g=0);var l=this.Em(b+c-g),v=this.Em(-c-f),g=this.Em(d-g);f=this.Em(f)+" "+h;a=this.addElement(a,"span",{style:{border:f,display:"inline-block",overflow:"hidden",width:g,height:l},bbox:{h:b,d:c,w:d,rw:d,lw:0,exactW:!0},noAdjust:!0,HH:b+c,isMathJax:!0});v&&(a.style.verticalAlign=v);return a},parentNode:function(a){a=a.parentNode;"a"===a.nodeName.toLowerCase()&&(a=a.parentNode);return a},createStack:function(a,b,c){this.msiePaddingWidthBug&&this.createStrut(a,0);var d=String(c).match(/%$/),f=d||null==c?0:c;a=this.addElement(a,"span",{noAdjust:!0,HH:0,isMathJax:!0,style:{display:"inline-block",position:"relative",width:d?"100%":this.Em(f),height:0}});b||(a.parentNode.bbox=a.bbox={exactW:!0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:f,lw:this.BIGDIMEN,rw:d||null==c?-this.BIGDIMEN:c},d&&(a.bbox.width=c));return a},createBox:function(a,b){var c=this.addElement(a,"span",{style:{position:"absolute"},isBox:!0,isMathJax:!0});null!=b&&(c.style.width=b);return c},addBox:function(a,b){b.style.position="absolute";b.isBox=b.isMathJax=!0;return a.appendChild(b)},placeBox:function(a,e,c,d){a.isMathJax=!0;var f=b.parentNode(a),h=a.bbox,g=f.bbox;this.msiePlaceBoxBug&&this.addText(a,this.NBSP);this.imgSpaceBug&&this.addText(a,this.imgSpace);var l,v=0;l=null!=a.HH?a.HH:h?Math.max(3,h.h+h.d):a.offsetHeight/this.em;a.noAdjust||(l=Math.round((l+1)*this.em)/this.em,this.msieInlineBlockAlignBug?this.addElement(a,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:!0,style:{width:0,height:this.Em(l)}}):(this.addElement(a,"span",{isMathJax:!0,style:{display:"inline-block",width:0,height:this.Em(l)}}),b.chromeHeightBug&&(l-=(a.lastChild.offsetHeight-Math.round(l*this.em))/this.em)));if(h&&(this.initialSkipBug&&(0>h.lw&&(v=h.lw,b.createBlank(a,-v,!0)),h.rw>h.w&&b.createBlank(a,h.rw-h.w+.1)),!this.msieClipRectBug&&!h.noclip&&!d)){d=3/this.em;var t=null==h.H?h.h:h.H,m=l+(null==h.D?h.d:h.D)+d,n=h.lw-3*d,q=1E3;this.initialSkipBug&&0>h.lw&&(n=-3*d);h.isFixed&&(q=h.width-n);a.style.clip="rect("+this.Em(l-t-d)+" "+this.Em(q)+" "+this.Em(m)+" 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Array||(h=[h]);a.fonts!=h&&(a.fonts=h);a.FONTS=[];c=0;for(d=h.length;c<d;c++)f[h[c]]&&(a.FONTS.push(f[h[c]]),f[h[c]].name=h[c])}c=0;for(d=a.FONTS.length;c<d;c++)if(f=a.FONTS[c],"string"===typeof f&&(delete a.FONTS,this.loadFont(f)),f[e])if(5===f[e].length&&(f[e][5]={}),b.allowWebFonts&&!f.available)this.loadWebFont(f);else return f;else this.findBlock(f,e);return this.unknownChar(a,e)},unknownChar:function(a,e){var c=a.defaultFont||{family:b.config.undefinedFamily};a.bold&&(c.weight="bold");a.italic&&(c.style="italic");c[e]||(c[e]=[800,200,500,0,500,{isUnknown:!0}]);g.signal.Post(["HTML-CSS Jax - unknown char",e,a]);return c},findBlock:function(a,b){if(a.Ranges)for(var c=0,d=a.Ranges.length;c<d&&!(b<a.Ranges[c][0]);c++)if(b<=a.Ranges[c][1]){for(var f=a.Ranges[c][2],h=a.Ranges.length-1;0<=h;h--)a.Ranges[h][2]==f&&a.Ranges.splice(h,1);this.loadFont(a.directory+"/"+f+".js")}},loadFont:function(a){var 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d=this.data[0].toHTML(a);null!=c?this.data[0].HTMLstretchV(a,b,c):null!=b&&this.data[0].HTMLstretchH(a,b);a.bbox=d.bbox}this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLstretchH:d.mbase.HTMLstretchH,HTMLstretchV:d.mbase.HTMLstretchV});d.mfrac.Augment({toHTML:function(a){a=this.HTMLcreateSpan(a);var c=b.createStack(a),d=b.createBox(c),g=b.createBox(c);b.MeasureSpans([this.HTMLboxChild(0,d),this.HTMLboxChild(1,g)]);var f=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled"),h=this.HTMLgetScale(),l=f.displaystyle,m=b.TeX.axis_height*h;if(f.bevelled){var f=l?.4:.15,n=Math.max(d.bbox.h+d.bbox.d,g.bbox.h+g.bbox.d)+2*f,c=b.createBox(c);b.createDelimiter(c,47,n);b.placeBox(d,0,(d.bbox.d-d.bbox.h)/2+m+f);b.placeBox(c,d.bbox.w-f/2,(c.bbox.d-c.bbox.h)/2+m);b.placeBox(g,d.bbox.w+c.bbox.w-f,(g.bbox.d-g.bbox.h)/2+m-f)}else{var n=Math.max(d.bbox.w,g.bbox.w),t=b.thickness2em(f.linethickness,h),q,p,A=b.TeX.min_rule_thickness/this.em;l?(q=b.TeX.num1,p=b.TeX.denom1):(q=0===t?b.TeX.num3:b.TeX.num2,p=b.TeX.denom2);q*=h;p*=h;0===t?(h=Math.max((l?7:3)*b.TeX.rule_thickness,2*A),l=q-d.bbox.d-(g.bbox.h-p),l<h&&(q+=(h-l)/2,p+=(h-l)/2)):(h=Math.max((l?2:0)*A+t,t/2+1.5*A),l=q-d.bbox.d-(m+t/2),l<h&&(q+=h-l),l=m-t/2-(g.bbox.h-p),l<h&&(p+=h-l),c=b.createBox(c),b.createRule(c,t,0,n+2*t),b.placeBox(c,0,m-t/2));b.alignBox(d,f.numalign,q);b.alignBox(g,f.denomalign,-p)}this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLcanStretch:function(a){return!1},HTMLhandleSpace:function(a){if(!this.texWithDelims){var c=(this.useMMLspacing?0:b.length2em(this.texSpacing()||0))+.12;a.style.paddingLeft=b.Em(c);a.style.paddingRight=b.Em(.12)}}});d.msqrt.Augment({toHTML:function(a){a=this.HTMLcreateSpan(a);var c=b.createStack(a),d=b.createBox(c),g=b.createBox(c),f=b.createBox(c),h=this.HTMLgetScale(),l=b.TeX.rule_thickness*h,m,n,t;m=this.Get("displaystyle")?b.TeX.x_height*h:l;m=Math.max(l+m/4,1.5*b.TeX.min_rule_thickness/this.em);var q=this.HTMLboxChild(0,d);n=q.bbox.h+q.bbox.d+m+l;b.createDelimiter(f,8730,n,h);b.MeasureSpans([q,f]);t=q.bbox.w;var p=0;if(f.isMultiChar||b.AdjustSurd&&b.imgFonts)f.bbox.w*=.95;f.bbox.h+f.bbox.d>n&&(m=(f.bbox.h+f.bbox.d-(n-l))/2);n=b.FONTDATA.DELIMITERS[b.FONTDATA.RULECHAR];!n||t<n.HW[0][0]*h||.75>h?b.createRule(g,0,l,t):b.createDelimiter(g,b.FONTDATA.RULECHAR,t,h);n=q.bbox.h+m+l;m=n*b.rfuzz;f.isMultiChar&&(m=b.rfuzz);p=this.HTMLaddRoot(c,f,p,f.bbox.h+f.bbox.d-n,h);b.placeBox(f,p,n-f.bbox.h);b.placeBox(g,p+f.bbox.w,n-g.bbox.h+m);b.placeBox(d,p+f.bbox.w,0);this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLaddRoot:function(a,b,c,d,f){return c}});d.mroot.Augment({toHTML:d.msqrt.prototype.toHTML,HTMLaddRoot:function(a,c,d,g,f){a=b.createBox(a);this.data[1]?(d=this.data[1].toHTML(a),d.style.paddingRight=d.style.paddingLeft="",b.Measured(d,a)):a.bbox=this.HTMLzeroBBox();g=this.HTMLrootHeight(c.bbox.h+c.bbox.d,f,a)-g;f=Math.min(a.bbox.w,a.bbox.rw);d=Math.max(f,c.offset);b.placeBox(a,d-f,g);return d-c.offset},HTMLrootHeight:function(a,b,c){return.45*(a-.9*b)+.6*b+Math.max(0,c.bbox.d-.075)}});d.mfenced.Augment({toHTML:function(a){a=this.HTMLcreateSpan(a);this.data.open&&this.data.open.toHTML(a);null!=this.data[0]&&this.data[0].toHTML(a);for(var b=1,c=this.data.length;b<c;b++)this.data[b]&&(this.data["sep"+b]&&this.data["sep"+b].toHTML(a),this.data[b].toHTML(a));this.data.close&&this.data.close.toHTML(a);for(var d=this.HTMLcomputeBBox(a),f=a.bbox.h,g=a.bbox.d,b=0,c=d.length;b<c;b++)d[b].HTMLstretchV(a,f,g);d.length&&this.HTMLcomputeBBox(a,!0);this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLcomputeBBox:function(a,b){var c=a.bbox={},d=[];this.HTMLcheckStretchy(this.data.open,c,d,b);this.HTMLcheckStretchy(this.data[0],c,d,b);for(var f=1,g=this.data.length;f<g;f++)this.data[f]&&(this.HTMLcheckStretchy(this.data["sep"+f],c,d,b),this.HTMLcheckStretchy(this.data[f],c,d,b));this.HTMLcheckStretchy(this.data.close,c,d,b);this.HTMLcleanBBox(c);return d},HTMLcheckStretchy:function(a,b,c,d){a&&(!d&&a.HTMLcanStretch("Vertical")&&(c.push(a),a=a.CoreMO()||a),this.HTMLcombineBBoxes(a,b))}});d.menclose.Augment({toHTML:d.mbase.HTMLautoload});d.maction.Augment({toHTML:d.mbase.HTMLautoload});d.semantics.Augment({toHTML:function(a,b,c){a=this.HTMLcreateSpan(a);if(null!=this.data[0]){var d=this.data[0].toHTML(a);null!=c?this.data[0].HTMLstretchV(a,b,c):null!=b&&this.data[0].HTMLstretchH(a,b);a.bbox=d.bbox}this.HTMLhandleSpace(a);return a},HTMLstretchH:d.mbase.HTMLstretchH,HTMLstretchV:d.mbase.HTMLstretchV});d.munderover.Augment({toHTML:function(a,c,g){var l=this.getValues("displaystyle","accent","accentunder","align");if(!l.displaystyle&&null!=this.data[this.base]&&this.data[this.base].CoreMO().Get("movablelimits"))return d.msubsup.prototype.toHTML.call(this,a);a=this.HTMLcreateSpan(a);var f=this.HTMLgetScale(),h=b.createStack(a),m=[],n=[],q=[],t,p,x;p=0;for(x=this.data.length;p<x;p++)null!=this.data[p]&&(t=m[p]=b.createBox(h),n[p]=this.data[p].toHTML(t),p==this.base?(null!=g?this.data[this.base].HTMLstretchV(t,c,g):null!=c&&this.data[this.base].HTMLstretchH(t,c),q[p]=null==g&&null!=c?!1:this.data[p].HTMLcanStretch("Horizontal")):q[p]=this.data[p].HTMLcanStretch("Horizontal"));b.MeasureSpans(n);h=n=-b.BIGDIMEN;p=0;for(x=this.data.length;p<x;p++)this.data[p]&&(m[p].bbox.w>h&&(h=m[p].bbox.w),!q[p]&&h>n&&(n=h));null==g&&null!=c?n=c:n==-b.BIGDIMEN&&(n=h);p=h=0;for(x=this.data.length;p<x;p++)this.data[p]&&(t=m[p],q[p]&&(t.bbox=this.data[p].HTMLstretchH(t,n).bbox),t.bbox.w>h&&(h=t.bbox.w));c=b.TeX.rule_thickness;g=b.FONTDATA.TeX_factor;var q=m[this.base]||{bbox:this.HTMLzeroBBox()},A,y,C,B=0;q.bbox.ic&&(B=1.3*q.bbox.ic+.05);p=0;for(x=this.data.length;p<x;p++)null!=this.data[p]&&(t=m[p],n=b.TeX.big_op_spacing5*f,(C=p!=this.base&&l[this.ACCENTS[p]])&&t.bbox.w<=1/b.em+1E-4&&(t.bbox.w=t.bbox.rw-t.bbox.lw,t.bbox.noclip=!0,t.bbox.lw&&t.insertBefore(b.createSpace(t.parentNode,0,0,-t.bbox.lw),t.firstChild),b.createBlank(t,0,0,t.bbox.rw+.1)),A={left:0,center:(h-t.bbox.w)/2,right:h-t.bbox.w}[l.align],y=0,p==this.over?(C?(C=Math.max(c*f*g,2.5/this.em),n=0,q.bbox.skew&&(A+=q.bbox.skew)):(C=b.TeX.big_op_spacing1*f*g,y=b.TeX.big_op_spacing3*f*g,C=Math.max(C,y-Math.max(0,t.bbox.d))),C=Math.max(C,1.5/this.em),A+=B/2,y=q.bbox.h+t.bbox.d+C,t.bbox.h+=n):p==this.under&&(C?(C=3*c*f*g,n=0):(C=b.TeX.big_op_spacing2*f*g,y=b.TeX.big_op_spacing4*f*g,C=Math.max(C,y-t.bbox.h)),C=Math.max(C,1.5/this.em),A-=B/2,y=-(q.bbox.d+t.bbox.h+C),t.bbox.d+=n),b.placeBox(t,A,y));this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLstretchH:d.mbase.HTMLstretchH,HTMLstretchV:d.mbase.HTMLstretchV});d.msubsup.Augment({toHTML:function(a,c,d){a=this.HTMLcreateSpan(a);var g=this.HTMLgetScale(),f=this.HTMLgetMu(a),h=b.createStack(a),l,m=[],n=b.createBox(h);this.data[this.base]?(m.push(this.data[this.base].toHTML(n)),null!=d?this.data[this.base].HTMLstretchV(n,c,d):null!=c&&this.data[this.base].HTMLstretchH(n,c)):n.bbox=this.HTMLzeroBBox();c=b.TeX.x_height*g;d=b.TeX.scriptspace*g*.75;var p;this.HTMLnotEmpty(this.data[this.sup])&&(p=b.createBox(h),m.push(this.data[this.sup].toHTML(p)));this.HTMLnotEmpty(this.data[this.sub])&&(l=b.createBox(h),m.push(this.data[this.sub].toHTML(l)));b.MeasureSpans(m);p&&(p.bbox.w+=d,p.bbox.rw=Math.max(p.bbox.w,p.bbox.rw));l&&(l.bbox.w+=d,l.bbox.rw=Math.max(l.bbox.w,l.bbox.rw));b.placeBox(n,0,0);var m=p?this.data[this.sup].HTMLgetScale():l?this.data[this.sub].HTMLgetScale():this.HTMLgetScale(),q=b.TeX.sup_drop*m,h=n.bbox.h-q,x=n.bbox.d+b.TeX.sub_drop*m,m=0;n.bbox.ic&&(n.bbox.w-=n.bbox.ic,m=1.3*n.bbox.ic+.05);!this.data[this.base]||"mi"!==this.data[this.base].type&&"mo"!==this.data[this.base].type||1!==this.data[this.base].data.join("").length||1!==n.bbox.scale||this.data[this.base].Get("largeop")||(h=x=0);d=this.getValues("subscriptshift","superscriptshift");d.subscriptshift=""===d.subscriptshift?0:b.length2em(d.subscriptshift,f);d.superscriptshift=""===d.superscriptshift?0:b.length2em(d.superscriptshift,f);p?l?(x=Math.max(x,b.TeX.sub2*g),g*=b.TeX.rule_thickness,h-p.bbox.d-(l.bbox.h-x)<3*g&&(x=3*g-h+p.bbox.d+l.bbox.h,q=.8*c-(h-p.bbox.d),0<q&&(h+=q,x-=q)),b.placeBox(p,n.bbox.w+m,Math.max(h,d.superscriptshift)),b.placeBox(l,n.bbox.w,-Math.max(x,d.subscriptshift))):(l=this.getValues("displaystyle","texprimestyle"),l=b.TeX[l.displaystyle?"sup1":l.texprimestyle?"sup3":"sup2"],h=Math.max(h,l*g,p.bbox.d+.25*c,d.superscriptshift),b.placeBox(p,n.bbox.w+m,h,p.bbox)):l&&(x=Math.max(x,b.TeX.sub1*g,l.bbox.h-.8*c,d.subscriptshift),b.placeBox(l,n.bbox.w,-x,l.bbox));this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLstretchH:d.mbase.HTMLstretchH,HTMLstretchV:d.mbase.HTMLstretchV});d.mmultiscripts.Augment({toHTML:d.mbase.HTMLautoload});d.mtable.Augment({toHTML:d.mbase.HTMLautoload});d["annotation-xml"].Augment({toHTML:d.mbase.HTMLautoload});d.math.Augment({toHTML:function(a,c){var k=this.Get("alttext");k&&""!==k&&c.setAttribute("aria-label",k);var l=b.addElement(a,"nobr",{isMathJax:!0});a=this.HTMLcreateSpan(l);var k=b.createStack(a),f=b.createBox(k),h;k.style.fontSize=l.parentNode.style.fontSize;l.parentNode.style.fontSize="";null!=this.data[0]&&(b.msieColorBug&&(this.background&&(this.data[0].background=this.background,delete this.background),this.mathbackground&&(this.data[0].mathbackground=this.mathbackground,delete this.mathbackground)),d.mbase.prototype.displayAlign=g.config.displayAlign,d.mbase.prototype.displayIndent=g.config.displayIndent,h=this.data[0].toHTML(f),h.bbox.exactW=!1,h=b.Measured(h,f));b.placeBox(f,0,0);a.style.width=b.Em((Math.round(h.bbox.w*this.em)+.25)/b.outerEm);a.style.display="inline-block";var l=1/b.em,m=b.em/b.outerEm;b.em/=m;a.bbox.h*=m;a.bbox.d*=m;a.bbox.w*=m;a.bbox.lw*=m;a.bbox.rw*=m;h&&null!=h.bbox.width&&(a.style.minWidth=h.bbox.minWidth||a.style.width,a.style.width=k.style.width=h.bbox.width,f.style.width="100%");this.HTMLhandleColor(a);h&&b.createRule(a,(h.bbox.h+l)*m,(h.bbox.d+l)*m,0);this.isMultiline||"block"!==this.Get("display")||null!=a.bbox.width||(k=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift"),k.indentalignfirst!==d.INDENTALIGN.INDENTALIGN&&(k.indentalign=k.indentalignfirst),k.indentalign===d.INDENTALIGN.AUTO&&(k.indentalign=this.displayAlign),c.style.textAlign=k.indentalign,k.indentshiftfirst!==d.INDENTSHIFT.INDENTSHIFT&&(k.indentshift=k.indentshiftfirst),"auto"===k.indentshift&&(k.indentshift=this.displayIndent),k.indentshift&&k.indentalign!==d.INDENTALIGN.CENTER&&(a.style[{left:"marginLeft",right:"marginRight"}[k.indentalign]]=b.Em(b.length2em(k.indentshift))));return a},HTMLspanElement:d.mbase.prototype.HTMLspanElement});d.TeXAtom.Augment({toHTML:function(a){a=this.HTMLcreateSpan(a);if(null!=this.data[0])if(this.texClass===d.TEXCLASS.VCENTER){var c=b.createStack(a),c=b.createBox(c);b.Measured(this.data[0].toHTML(c),c);b.placeBox(c,0,b.TeX.axis_height-(c.bbox.h+c.bbox.d)/2+c.bbox.d)}else a.bbox=this.data[0].toHTML(a).bbox;this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",b,"jax.js"]),0)})});g.Register.StartupHook("End Config",function(){g.Browser.Select({MSIE:function(a){var c=document.documentMode||0,d=a.versionAtLeast("7.0"),g=a.versionAtLeast("8.0")&&7<c,f="BackCompat"===document.compatMode;9>c&&(b.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white",b.config.styles[".MathJax .MathJax_HitBox"].opacity=0,b.config.styles[".MathJax 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Version\/\d/)&&navigator.vendor.match(/Apple/),f=navigator.appVersion.match(/ Android (\d+)\.(\d+)/),f=d&&a.isMobile&&(navigator.platform.match(/iPad|iPod|iPhone/)&&!a.versionAtLeast("5.0")||null!=f&&(2>f[1]||2==f[1]&&2>f[2]));b.Augment({config:{styles:{".MathJax img, .MathJax nobr, .MathJax 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