| 12345678910111213 |
- /*
- * /MathJax/config/MML_HTMLorMML-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.Hub.Config({delayJaxRegistration:!0});MathJax.Ajax.Preloading("[MathJax]/jax/input/MathML/config.js","[MathJax]/jax/output/HTML-CSS/config.js","[MathJax]/jax/output/NativeMML/config.js","[MathJax]/config/MMLorHTML.js","[MathJax]/extensions/mml2jax.js","[MathJax]/extensions/MathEvents.js","[MathJax]/extensions/MathZoom.js","[MathJax]/extensions/MathMenu.js","[MathJax]/jax/element/mml/jax.js","[MathJax]/extensions/toMathML.js","[MathJax]/jax/input/MathML/jax.js","[MathJax]/jax/output/NativeMML/jax.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.MathML=MathJax.InputJax({id:"MathML",version:"2.2",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:!1}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.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,f){var b=c.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:!0,minBrowserTranslate:function(k){var p=c.getJaxFor(k),f=["[Math]"],m=document.createElement("span",{className:"MathJax_Preview"});"TeX"===p.inputJax&&(p.root.Get("displaystyle")?(f=b.displayMathDelimiters,f=[f[0]+p.originalText+f[1]],b.multilineDisplay&&(f=f[0].split(/\n/))):(f=b.inlineMathDelimiters,f=[f[0]+p.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+f[1]]));for(var p=0,q=f.length;p<q;p++)m.appendChild(document.createTextNode(f[p])),p<q-1&&m.appendChild(document.createElement("br"));k.parentNode.insertBefore(m,k)}},c.config["HTML-CSS"]||{});"0.0"===c.Browser.version||c.Browser.versionAtLeast(b.minBrowserVersion[c.Browser]||0)||(f.Translate=b.minBrowserTranslate,c.Config({showProcessingMessages:!1}),MathJax.Message.Set(["MathJaxNotSupported","Your browser does not support MathJax"],null,4E3),c.Startup.signal.Post("MathJax not supported"))},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js");MathJax.OutputJax.NativeMML=MathJax.OutputJax({id:"NativeMML",version:"2.2",directory:MathJax.OutputJax.directory+"/NativeMML",extensionDir:MathJax.OutputJax.extensionDir+"/NativeMML",config:{scale:100,minScaleAdjust:50,styles:{"DIV.MathJax_MathML":{"text-align":"center",margin:".75em 0px"}}}});MathJax.Hub.config.delayJaxRegistration||MathJax.OutputJax.NativeMML.Register("jax/mml");MathJax.OutputJax.NativeMML.loadComplete("config.js");(function(c,f){var b=MathJax.Hub.CombineConfig("MMLorHTML",{prefer:{MSIE:"MML",Firefox:"HTML",Opera:"HTML",Chrome:"HTML",Safari:"HTML",other:"HTML"}}),k={Firefox:3,Opera:9.52,MSIE:6,Chrome:.3,Safari:2,Konqueror:4},p="0.0"===f.version||f.versionAtLeast(k[f]||0),l=f.isFirefox&&f.versionAtLeast("1.5")||f.isMSIE&&f.hasMathPlayer||f.isSafari&&f.versionAtLeast("5.0")||f.isOpera&&f.versionAtLeast("9.52");c.Register.StartupHook("End Config",function(){var k=b.prefer&&"object"===typeof b.prefer?b.prefer[MathJax.Hub.Browser]||b.prefer.other||"HTML":b.prefer;p||l?!l||"MML"!==k&&p?(MathJax.OutputJax["HTML-CSS"]?MathJax.OutputJax["HTML-CSS"].Register("jax/mml"):c.config.jax.unshift("output/HTML-CSS"),c.Startup.signal.Post("HTML-CSS output selected")):(MathJax.OutputJax.NativeMML?MathJax.OutputJax.NativeMML.Register("jax/mml"):c.config.jax.unshift("output/NativeMML"),c.Startup.signal.Post("NativeMML output selected")):(c.PreProcess.disabled=!0,c.prepareScripts.disabled=!0,MathJax.Message.Set(["MathJaxNotSupported","Your browser does not support MathJax"],null,4E3),c.Startup.signal.Post("MathJax not supported"))})})(MathJax.Hub,MathJax.Hub.Browser);MathJax.Ajax.loadComplete("[MathJax]/config/MMLorHTML.js");MathJax.Extension.mml2jax={version:"2.2",config:{preview:"alttext"},MMLnamespace:"http://www.w3.org/1998/Math/MathML",PreProcess:function(c){this.configured||(this.config=MathJax.Hub.CombineConfig("mml2jax",this.config),this.config.Augment&&MathJax.Hub.Insert(this,this.config.Augment),this.InitBrowser(),this.configured=!0);"string"===typeof c&&(c=document.getElementById(c));c||(c=document.body);this.ProcessMathArray(c.getElementsByTagName("math"));c.getElementsByTagNameNS&&this.ProcessMathArray(c.getElementsByTagNameNS(this.MMLnamespace,"math"));var f,b;if("undefined"!==typeof document.namespaces)try{for(f=0,b=document.namespaces.length;f<b;f++){var k=document.namespaces[f];k.urn===this.MMLnamespace&&this.ProcessMathArray(c.getElementsByTagName(k.name+":math"))}}catch(l){}else if(k=document.getElementsByTagName("html")[0])for(f=0,b=k.attributes.length;f<b;f++){var p=k.attributes[f];"xmlns:"===p.nodeName.substr(0,6)&&p.nodeValue===this.MMLnamespace&&this.ProcessMathArray(c.getElementsByTagName(p.nodeName.substr(6)+":math"))}},ProcessMathArray:function(c){var f;if(c.length)if(this.MathTagBug)for(f=c.length-1;0<=f;f--)"MATH"===c[f].nodeName?this.ProcessMathFlattened(c[f]):this.ProcessMath(c[f]);else for(f=c.length-1;0<=f;f--)this.ProcessMath(c[f])},ProcessMath:function(c){var f=c.parentNode,b=document.createElement("script");b.type="math/mml";f.insertBefore(b,c);if(this.AttributeBug){var k=this.OuterHTML(c);this.CleanupHTML&&(k=k.replace(/<\?import .*?>/i,"").replace(/<\?xml:namespace .*?\/>/i,""),k=k.replace(/ /g,"\x26#xA0;"));MathJax.HTML.setScript(b,k);f.removeChild(c)}else f=MathJax.HTML.Element("span"),f.appendChild(c),MathJax.HTML.setScript(b,f.innerHTML);"none"!==this.config.preview&&this.createPreview(c,b)},ProcessMathFlattened:function(c){var f=c.parentNode,b=document.createElement("script");b.type="math/mml";f.insertBefore(b,c);for(var f="",k,p=c;c&&"/MATH"!==c.nodeName;)k=c,c=c.nextSibling,f+=this.NodeHTML(k),k.parentNode.removeChild(k);c&&"/MATH"===c.nodeName&&c.parentNode.removeChild(c);b.text=f+"\x3c/math\x3e";"none"!==this.config.preview&&this.createPreview(p,b)},NodeHTML:function(c){var f,b,k;if("#text"===c.nodeName)f=this.quoteHTML(c.nodeValue);else if("#comment"===c.nodeName)f="\x3c!--"+c.nodeValue+"--\x3e";else{f="\x3c"+c.nodeName.toLowerCase();b=0;for(k=c.attributes.length;b<k;b++){var p=c.attributes[b];if(p.specified){f+=" "+p.nodeName.toLowerCase().replace(/xmlns:xmlns/,"xmlns")+"\x3d";var l=p.nodeValue;null==l&&"style"===p.nodeName&&c.style&&(l=c.style.cssText);f+='"'+this.quoteHTML(l)+'"'}}f+="\x3e";if(null!=c.outerHTML&&c.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){b=0;for(k=c.childNodes.length;b<k;b++)f+=this.OuterHTML(c.childNodes[b]);f+="\x3c/"+c.nodeName.toLowerCase()+"\x3e"}}return f},OuterHTML:function(c){if("#"===c.nodeName.charAt(0))return this.NodeHTML(c);if(!this.AttributeBug)return c.outerHTML;for(var f=this.NodeHTML(c),b=0,k=c.childNodes.length;b<k;b++)f+=this.OuterHTML(c.childNodes[b]);return f+="\x3c/"+c.nodeName.toLowerCase()+"\x3e"},quoteHTML:function(c){null==c&&(c="");return c.replace(/&/g,"\x26#x26;").replace(/</g,"\x26lt;").replace(/>/g,"\x26gt;").replace(/\"/g,"\x26quot;")},createPreview:function(c,f){var b=this.config.preview;"none"!==b&&("alttext"===b&&(b=c.getAttribute("alttext"),b=null!=b?[this.filterPreview(b)]:null),b&&(b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b),f.parentNode.insertBefore(b,f)))},filterPreview:function(c){return c},InitBrowser:function(){var c=MathJax.HTML.Element("span",{id:"\x3c",className:"mathjax",innerHTML:"\x3cmath\x3e\x3cmi\x3ex\x3c/mi\x3e\x3cmspace /\x3e\x3c/math\x3e"}),f=c.outerHTML||"";this.AttributeBug=""!==f&&!(f.match(/id="<"/)&&f.match(/class="mathjax"/)&&f.match(/<\/math>/));this.MathTagBug=1<c.childNodes.length;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js");(function(c,f,b,k,p,l,m){var q=MathJax.Extension,n=q.MathEvents={version:"2.2"},a=c.config.menuSettings,h={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(l.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"}}},d=n.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",Mousedown:function(a){return d.Handler(a,"Mousedown",this)},Mouseup:function(a){return d.Handler(a,"Mouseup",this)},Mousemove:function(a){return d.Handler(a,"Mousemove",this)},Mouseover:function(a){return d.Handler(a,"Mouseover",this)},Mouseout:function(a){return d.Handler(a,"Mouseout",this)},Click:function(a){return d.Handler(a,"Click",this)},DblClick:function(a){return d.Handler(a,"DblClick",this)},Menu:function(a){return d.Handler(a,"ContextMenu",this)},Handler:function(a,h,g){if(b.loadingMathMenu)return d.False(a);var e=l[g.jaxID];a||(a=window.event);a.isContextMenu="ContextMenu"===h;if(e[h])return e[h](a,g);if(q.MathZoom)return q.MathZoom.HandleEvent(a,h,g)},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(h,g,e){var f=l[g.jaxID],r=f.getJaxFromMath(g);if((null!=f.config.showMathMenu?f:c).config.showMathMenu&&("MathJax"===a.context||e)){n.msieEventBug&&(h=window.event||h);d.ClearSelection();u.ClearHoverTimer();r.hover&&(r.hover.remove&&(clearTimeout(r.hover.remove),delete r.hover.remove),r.hover.nofade=!0);var B=MathJax.Menu;if(B){if(B.loadingDomain)return d.False(h);f=p.loadDomain("MathMenu");if(!f)return B.jax=r,g=B.menu.Find("Show Math As").menu,g.items[0].name=r.sourceMenuTitle,g.items[0].format=r.sourceMenuFormat||"MathML",g.items[1].name=m[r.inputJax].sourceMenuTitle,B.menu.Find("Math Settings","MathPlayer").hidden=!("NativeMML"===r.outputJax&&c.Browser.hasMathPlayer),B.menu.Post(h);B.loadingDomain=!0;r=function(){delete B.loadingDomain}}else{if(b.loadingMathMenu)return d.False(h);b.loadingMathMenu=!0;f=b.Require("[MathJax]/extensions/MathMenu.js");r=function(){delete b.loadingMathMenu;MathJax.Menu||(MathJax.Menu={})}}k.Queue(f,r,["ContextMenu",d,{pageX:h.pageX,pageY:h.pageY,clientX:h.clientX,clientY:h.clientY},g,e]);return d.False(h)}},AltContextMenu:function(h,g){var e=l[g.jaxID],b=(null!=e.config.showMathMenu?e:c).config.showMathMenu;if(b){b=(null!=e.config.showMathMenuMSIE?e:c).config.showMathMenuMSIE;if("MathJax"===a.context&&!a.mpContext&&b){if(!n.noContextMenuBug||h.button!==d.RIGHTBUTTON)return}else if(!h[d.MENUKEY]||h.button!==d.LEFTBUTTON)return;return e.ContextMenu(h,g,!0)}},ClearSelection:function(){n.safariContextMenuBug&&setTimeout("window.getSelection().empty()",0);document.selection&&setTimeout("document.selection.empty()",0)},getBBox:function(a){a.appendChild(n.topImg);var h=n.topImg.offsetTop,d=a.offsetHeight-h,g=a.offsetWidth;a.removeChild(n.topImg);return{w:g,h:h,d:d}}},u=n.Hover={Mouseover:function(h,g){if(a.discoverable||"Hover"===a.zoom){var e=h.fromElement||h.relatedTarget,b=h.toElement||h.target;if(e&&b&&(e.isMathJax!=b.isMathJax||c.getJaxFor(e)!==c.getJaxFor(b)))return e=this.getJaxFromMath(g),e.hover?u.ReHover(e):u.HoverTimer(e,g),d.False(h)}},Mouseout:function(h,g){if(a.discoverable||"Hover"===a.zoom){var e=h.fromElement||h.relatedTarget,b=h.toElement||h.target;if(e&&b&&(e.isMathJax!=b.isMathJax||c.getJaxFor(e)!==c.getJaxFor(b)))return e=this.getJaxFromMath(g),e.hover?u.UnHover(e):u.ClearHoverTimer(),d.False(h)}},Mousemove:function(h,g){if(a.discoverable||"Hover"===a.zoom){var e=this.getJaxFromMath(g);if(!e.hover&&(u.lastX!=h.clientX||u.lastY!=h.clientY))return u.lastX=h.clientX,u.lastY=h.clientY,u.HoverTimer(e,g),d.False(h)}},HoverTimer:function(a,d){this.ClearHoverTimer();this.hoverTimer=setTimeout(k(["Hover",this,a,d]),h.hover)},ClearHoverTimer:function(){this.hoverTimer&&(clearTimeout(this.hoverTimer),delete this.hoverTimer)},Hover:function(a,d){if(!q.MathZoom||!q.MathZoom.Hover({},d)){var g=l[a.outputJax],e=g.getHoverSpan(a,d),b=g.getHoverBBox(a,e,d),u=(null!=g.config.showMathMenu?g:c).config.showMathMenu,k=h.frame.x,p=h.frame.y,m=h.frame.bwidth;n.msieBorderWidthBug&&(m=0);a.hover={opacity:0,id:a.inputID+"-Hover"};var y=f.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-p-m-(b.y||0)),left:this.Px(-k-m+(b.x||0)),width:this.Px(b.w+2*k),height:this.Px(b.h+b.d+2*p),opacity:0,filter:"alpha(opacity\x3d0)"}}]]),g=f.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:d,src:h.button.src,onclick:this.HoverMenu,jax:g.id,style:{left:this.Px(b.w+k+m+(b.x||0)+h.button.x),top:this.Px(-b.h-p-m-(b.y||0)-h.button.y),opacity:0,filter:"alpha(opacity\x3d0)"}}]]);b.width&&(y.style.width=g.style.width=b.width,y.style.marginRight=g.style.marginRight="-"+b.width,y.firstChild.style.width=b.width,g.firstChild.style.left="",g.firstChild.style.right=this.Px(h.button.wx));e.parentNode.insertBefore(y,e);u&&e.parentNode.insertBefore(g,e);e.style&&(e.style.position="relative");this.ReHover(a)}},ReHover:function(a){a.hover.remove&&clearTimeout(a.hover.remove);a.hover.remove=setTimeout(k(["UnHover",this,a]),h.fadeoutDelay);this.HoverFadeTimer(a,h.fadeinInc)},UnHover:function(a){a.hover.nofade||this.HoverFadeTimer(a,-h.fadeoutInc,h.fadeoutStart)},HoverFade:function(a){delete a.hover.timer;a.hover.opacity=Math.max(0,Math.min(1,a.hover.opacity+a.hover.inc));a.hover.opacity=Math.floor(1E3*a.hover.opacity)/1E3;var h=document.getElementById(a.hover.id),d=document.getElementById(a.hover.id+"Menu");h.firstChild.style.opacity=a.hover.opacity;h.firstChild.style.filter="alpha(opacity\x3d"+Math.floor(100*a.hover.opacity)+")";d&&(d.firstChild.style.opacity=a.hover.opacity,d.firstChild.style.filter=h.style.filter);1!==a.hover.opacity&&(0<a.hover.opacity?this.HoverFadeTimer(a,a.hover.inc):(h.parentNode.removeChild(h),d&&d.parentNode.removeChild(d),a.hover.remove&&clearTimeout(a.hover.remove),delete a.hover))},HoverFadeTimer:function(a,d,g){a.hover.inc=d;a.hover.timer||(a.hover.timer=setTimeout(k(["HoverFade",this,a]),g||h.fadeDelay))},HoverMenu:function(a){a||(a=window.event);return l[this.jax].ContextMenu(a,this.math,!0)},ClearHover:function(a){a.hover.remove&&clearTimeout(a.hover.remove);a.hover.timer&&clearTimeout(a.hover.timer);u.ClearHoverTimer();delete a.hover},Px:function(a){return.006>Math.abs(a)?"0px":a.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){(new Image).src=h.button.src}},e=n.Touch={last:0,delay:500,start:function(a){var h=(new Date).getTime(),d=h-e.last<e.delay&&e.up;e.last=h;e.up=!1;d&&(e.timeout=setTimeout(e.menu,e.delay,a,this),a.preventDefault())},end:function(a){var h=(new Date).getTime();e.up=h-e.last<e.delay;if(e.timeout)return clearTimeout(e.timeout),delete e.timeout,e.last=0,e.up=!1,a.preventDefault(),d.Handler(a.touches[0]||a.touch,"DblClick",this)},menu:function(a,h){delete e.timeout;e.last=0;e.up=!1;return d.Handler(a.touches[0]||a.touch,"ContextMenu",h)}};if(c.Browser.isMobile){var g=h.styles[".MathJax_Hover_Arrow"];g.width="25px";g.height="18px";h.button.x=-6}c.Browser.Select({MSIE:function(a){var h=document.documentMode||0,g=a.versionAtLeast("8.0");n.msieBorderWidthBug="BackCompat"===document.compatMode;n.msieEventBug=a.isIE9;n.msieAlignBug=!g||8>h;9>h&&(d.LEFTBUTTON=1)},Safari:function(a){n.safariContextMenuBug=!0},Opera:function(a){n.operaPositionBug=!0},Konqueror:function(a){n.noContextMenuBug=!0}});n.topImg=n.msieAlignBug?f.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):f.Element("span",{style:{width:0,height:0,display:"inline-block"}});n.operaPositionBug&&(n.topImg.style.border="1px solid");n.config=h=c.CombineConfig("MathEvents",h);k.Queue(c.Register.StartupHook("End Config",{}),[function(){var a=h.styles[".MathJax_Hover_Frame"];a.border=h.frame.bwidth+"px solid "+h.frame.bcolor+" ! important";a["box-shadow"]=a["-webkit-box-shadow"]=a["-moz-box-shadow"]=a["-khtml-box-shadow"]="0px 0px "+h.frame.hwidth+" "+h.frame.hcolor}],["getImages",u],["Styles",b,h.styles],["Post",c.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(c,f,b,k,p){var l=c.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)"}}}),m,q,n;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event;m=MathJax.Extension.MathEvents.Event.False;q=MathJax.Extension.MathEvents.Hover});var a=MathJax.Extension.MathZoom={version:"2.2",settings:c.config.menuSettings,scrollSize:18,HandleEvent:function(h,d,b){return a.settings.CTRL&&!h.ctrlKey||a.settings.ALT&&!h.altKey||a.settings.CMD&&!h.metaKey||a.settings.Shift&&!h.shiftKey||!a[d]?!0:a[d](h,b)},Click:function(a,d){if("Click"===this.settings.zoom)return this.Zoom(a,d)},DblClick:function(a,d){if("Double-Click"===this.settings.zoom)return this.Zoom(a,d)},Hover:function(a,d){return"Hover"===this.settings.zoom?(this.Zoom(a,d),!0):!1},Zoom:function(a,d){this.Remove();q.ClearHoverTimer();n.ClearSelection();var b=MathJax.OutputJax[d.jaxID],e=b.getJaxFromMath(d);e.hover&&q.UnHover(e);var g=Math.floor(.85*document.body.clientWidth),t=Math.floor(.85*Math.max(document.body.clientHeight,document.documentElement.clientHeight)),v=f.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":t+"px"}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]),k=v.lastChild,p=k.firstChild,r=v.firstChild;d.parentNode.insertBefore(v,d);d.parentNode.insertBefore(d,v);p.addEventListener&&p.addEventListener("mousedown",this.Remove,!0);if(this.msieTrapEventBug){var B=f.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});v.insertBefore(B,k)}this.msieZIndexBug&&(f.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=l.styles["#MathJax_ZoomOverlay"]["z-index"]);b=b.Zoom(e,p,d,g,t);this.msiePositionBug&&(this.msieSizeBug&&(k.style.height=b.zH+"px",k.style.width=b.zW+"px"),k.offsetHeight>t&&(k.style.height=t+"px",k.style.width=b.zW+this.scrollSize+"px"),k.offsetWidth>g&&(k.style.width=g+"px",k.style.height=b.zH+this.scrollSize+"px"));this.operaPositionBug&&(k.style.width=Math.min(g,b.zW)+"px");k.offsetWidth&&k.offsetWidth<g&&k.offsetHeight<t&&(k.style.overflow="visible");this.Position(k,b);this.msieTrapEventBug&&(B.style.height=k.clientHeight+"px",B.style.width=k.clientWidth+"px",B.style.left=parseFloat(k.style.left)+k.clientLeft+"px",B.style.top=parseFloat(k.style.top)+k.clientTop+"px");k.style.visibility="";"Hover"===this.settings.zoom&&(r.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 zoomed",e]);return m(a)},Position:function(h,d){var b=this.Resize(),e=b.y,g=d.mW,c=d.Y;h.style.left=Math.max(-g-Math.floor((h.offsetWidth-g)/2),10-b.x)+"px";h.style.top=Math.max(c,10-e)+"px";a.msiePositionBug||a.SetWH()},Resize:function(h){if(a.onresize)a.onresize(h);var d=document.getElementById("MathJax_ZoomFrame");h=document.getElementById("MathJax_ZoomOverlay");for(var b=a.getXY(d),d=d.parentNode,e=a.getOverflow(d);d.parentNode&&d!==document.body&&"visible"===e;)d=d.parentNode,e=a.getOverflow(d);"visible"!==e&&(h.scroll_parent=d,e=a.getXY(d),b.x-=e.x,b.y-=e.y,e=a.getBorder(d),b.x-=e.x,b.y-=e.y);h.style.left=-b.x+"px";h.style.top=-b.y+"px";a.msiePositionBug?setTimeout(a.SetWH,0):a.SetWH();return b},SetWH:function(){var a=document.getElementById("MathJax_ZoomOverlay");a.style.width=a.style.height="1px";var d=a.scroll_parent||document.documentElement||document.body;a.style.width=d.scrollWidth+"px";a.style.height=Math.max(d.clientHeight,d.scrollHeight)+"px"},getOverflow:window.getComputedStyle?function(a){return getComputedStyle(a).overflow}:function(a){return(a.currentStyle||{overflow:"visible"}).overflow},getBorder:function(a){var d={thin:1,medium:2,thick:3},b=window.getComputedStyle?getComputedStyle(a):a.currentStyle||{borderLeftWidth:0,borderTopWidth:0};a=b.borderLeftWidth;b=b.borderTopWidth;a=d[a]?d[a]:parseInt(a);b=d[b]?d[b]:parseInt(b);return{x:a,y:b}},getXY:function(h){var d=0,b=0,e;for(e=h;e.offsetParent;)d+=e.offsetLeft,e=e.offsetParent;a.operaPositionBug&&(h.style.border="1px solid");for(e=h;e.offsetParent;)b+=e.offsetTop,e=e.offsetParent;a.operaPositionBug&&(h.style.border="");return{x:d,y:b}},Remove:function(h){var d=document.getElementById("MathJax_ZoomFrame");if(d){var b=MathJax.OutputJax[d.previousSibling.jaxID].getJaxFromMath(d.previousSibling);c.signal.Post(["math unzoomed",b]);d.parentNode.removeChild(d);(d=document.getElementById("MathJax_ZoomTracker"))&&d.parentNode.removeChild(d);a.operaRefreshBug&&(d=f.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(d));window.removeEventListener?removeEventListener("resize",a.Resize,!1):window.detachEvent?detachEvent("onresize",a.Resize):(window.onresize=a.onresize,delete a.onresize)}return m(h)}};c.Browser.Select({MSIE:function(h){var d=document.documentMode||0,b=9<=d;a.msiePositionBug=!b;a.msieSizeBug=h.versionAtLeast("7.0")&&(!document.documentMode||7===d||8===d);a.msieZIndexBug=7>=d;a.msieInlineBlockAlignBug=7>=d;a.msieTrapEventBug=!window.addEventListener;"BackCompat"===document.compatMode&&(a.scrollSize=52);b&&delete l.styles["#MathJax_Zoom"].filter},Opera:function(h){a.operaPositionBug=!0;a.operaRefreshBug=!0}});a.topImg=a.msieInlineBlockAlignBug?f.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):f.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,l.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,f,b,k,p){var l=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:"2.2",signal:l};var m=function(a){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",a]].concat([].slice.call(arguments,1)))},q=c.Browser.isPC,n=c.Browser.isMSIE,a=8<(document.documentMode||0),h=q?null:"5px",d=c.CombineConfig("MathMenu",{delay:150,closeImg:b.fileURL(p.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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t.lastItem,delete t.lastMenu,delete g.skipUp,l.Post(["post",g.jax]));var e=f.addElement(b,"div",{onmouseup:g.Mouseup,ondblclick:u,ondragstart:u,onselectstart:u,oncontextmenu:u,menuItem:this,className:"MathJax_Menu"});MathJax.Localization.setCSS(e);for(var c=0,k=this.items.length;c<k;c++)this.items[c].Create(e);g.isMobile&&f.addElement(e,"span",{className:"MathJax_Menu_Close",menu:h,ontouchstart:g.Close,ontouchend:u,onmousedown:g.Close,onmouseup:u},[["img",{src:d.closeImg,style:{width:"100%",height:"100%"}}]]);this.posted=!0;e.style.width=e.offsetWidth+2+"px";c=a.pageX;k=a.pageY;c||k||(c=a.clientX+document.body.scrollLeft+document.documentElement.scrollLeft,k=a.clientY+document.body.scrollTop+document.documentElement.scrollTop);if(h){for(var p="left",m=h.offsetWidth,c=g.isMobile?30:m-2,k=0;h&&h!==b;)c+=h.offsetLeft,k+=h.offsetTop,h=h.parentNode;c+e.offsetWidth>document.body.offsetWidth-this.margin&&!g.isMobile&&(p="right",c=Math.max(this.margin,c-m-e.offsetWidth+6));q||(e.style["borderRadiusTop"+p]=0,e.style["WebkitBorderRadiusTop"+p]=0,e.style["MozBorderRadiusTop"+p]=0,e.style["KhtmlBorderRadiusTop"+p]=0)}else c+e.offsetWidth>document.body.offsetWidth-this.margin&&(c=document.body.offsetWidth-e.offsetWidth-this.margin),g.isMobile&&(c=Math.max(5,c-Math.floor(e.offsetWidth/2)),k-=20),g.skipUp=a.isContextMenu;e.style.left=c+"px";e.style.top=k+"px";document.selection&&document.selection.empty&&document.selection.empty();return u(a)},Remove:function(a,h){l.Post(["unpost",g.jax]);var d=document.getElementById("MathJax_MenuFrame");d&&(d.parentNode.removeChild(d),this.msieFixedPositionBug&&detachEvent("onresize",g.Resize));g.jax.hover&&(delete g.jax.hover.nofade,e.UnHover(g.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,h,d){for(var g=0,b=this.items.length;g<b;g++)if(this.items[g].name[a]===h){if(d.length){if(!this.items[g].menu)break;return this.items[g].menu.FindN(a,d[0],d.slice(1))}return this.items[g]}return null},IndexOf:function(a){return this.IndexOfN(1,a)},IndexOfId:function(a){return this.IndexOfN(0,a)},IndexOfN:function(a,h){for(var d=0,g=this.items.length;d<g;d++)if(this.items[d].name[a]===h)return d;return null}},{config:d,div:null,Close:function(a){return g.Event(a,this.menu||this.parentNode,this.menu?"Touchend":"Remove")},Remove:function(a){return g.Event(a,this,"Remove")},Mouseover:function(a){return g.Event(a,this,"Mouseover")},Mouseout:function(a){return g.Event(a,this,"Mouseout")},Mousedown:function(a){return g.Event(a,this,"Mousedown")},Mouseup:function(a){return g.Event(a,this,"Mouseup")},Touchstart:function(a){return g.Event(a,this,"Touchstart")},Touchend:function(a){return g.Event(a,this,"Touchend")},Event:function(a,h,d,b){if(g.skipMouseover&&"Mouseover"===d&&!b)return u(a);if(g.skipUp){if(d.match(/Mouseup|Touchend/))return delete g.skipUp,u(a);("Touchstart"===d||"Mousedown"===d&&!g.skipMousedown)&&delete g.skipUp}a||(a=window.event);return(b=h.menuItem)&&b[d]?b[d](a,h):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=f.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:a,onmousedown:this.Remove}]]);var h=a.firstChild;g.msieBackgroundBug&&(h.style.backgroundColor="white",h.style.filter="alpha(opacity\x3d0)");g.msieFixedPositionBug?(a.width=a.height=0,this.Resize(),attachEvent("onresize",this.Resize)):h.style.position="fixed";return a},Resize:function(){setTimeout(g.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(){f.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=f.Cookie.Get("menu")},getImages:function(){g.isMobile&&((new Image).src=d.closeImg)}}),t=g.ITEM=MathJax.Object.Subclass({name:"",Create:function(a){if(!this.hidden){var h={onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmouseup:g.Mouseup,onmousedown:g.Mousedown,ondragstart:u,onselectstart:u,onselectend:u,ontouchstart:g.Touchstart,ontouchend:g.Touchend,className:"MathJax_MenuItem",menuItem:this};this.disabled&&(h.className+=" MathJax_MenuDisabled");f.addElement(a,"div",h,this.Label(h,a))}},Name:function(){return m(this.name[0],this.name[1])},Mouseover:function(a,h){this.disabled||this.Activate(h);if(!this.menu||!this.menu.posted){for(var d=document.getElementById("MathJax_MenuFrame").childNodes,b=h.parentNode.childNodes,e=0,c=b.length;e<c;e++){var k=b[e].menuItem;k&&k.menu&&k.menu.posted&&k.Deactivate(b[e])}for(c=d.length-1;0<=c&&h.parentNode.menuItem!==d[c].menuItem;)d[c].menuItem.posted=!1,d[c].parentNode.removeChild(d[c]),c--;this.Timer&&!g.isMobile&&this.Timer(a,h)}},Mouseout:function(a,h){this.menu&&this.menu.posted||this.Deactivate(h);this.timer&&(clearTimeout(this.timer),delete this.timer)},Mouseup:function(a,h){return this.Remove(a,h)},Touchstart:function(a,h){return this.TouchEvent(a,h,"Mousedown")},Touchend:function(a,h){return this.TouchEvent(a,h,"Mouseup")},TouchEvent:function(a,h,d){this!==t.lastItem&&(t.lastMenu&&g.Event(a,t.lastMenu,"Mouseout"),g.Event(a,h,"Mouseover",!0),t.lastItem=this,t.lastMenu=h);if(this.nativeTouch)return null;g.Event(a,h,d);return!1},Remove:function(a,h){h=h.parentNode.menuItem;return h.Remove(a,h)},Activate:function(a){this.Deactivate(a);a.className+=" 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g={className:"MathJax_MenuRadioCheck"};d.settings[this.variable]!==this.value&&(g={style:{display:"none"}});return[["span",g,[this.marker]]," "+this.Name()]},Mouseup:function(a,h){if(!this.disabled){for(var b=h.parentNode.childNodes,e=0,c=b.length;e<c;e++){var k=b[e].menuItem;k&&k.variable===this.variable&&(b[e].firstChild.style.display="none")}h.firstChild.display="";d.settings[this.variable]=this.value;g.cookie[this.variable]=d.settings[this.variable];g.saveCookie();l.Post(["radio button",this])}this.Remove(a,h);this.action&&!this.disabled&&this.action.call(g,this);return u(a)}});g.ITEM.CHECKBOX=g.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(a,h,d){a instanceof Array||(a=[a,a]);this.name=a;this.variable=h;this.With(d)},Label:function(a,h){var g={className:"MathJax_MenuCheck"};d.settings[this.variable]||(g={style:{display:"none"}});return[["span",g,[this.marker]]," 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form available")):g.ShowSource.Text(g.jax.originalText,a)};g.ShowSource.Window=function(a){if(!g.ShowSource.w){a=[];var h=d.windowSettings,b;for(b in h)h.hasOwnProperty(b)&&a.push(b+"\x3d"+h[b]);g.ShowSource.w=window.open("","_blank",a.join(","))}return g.ShowSource.w};g.ShowSource.Text=function(a,h){var d=g.ShowSource.Window(h);delete g.ShowSource.w;a=a.replace(/^\s*/,"").replace(/\s*$/,"");a=a.replace(/&/g,"\x26amp;").replace(/</g,"\x26lt;").replace(/>/g,"\x26gt;");var b=m("EqSource","MathJax Equation Source");if(g.isMobile)d.document.open(),d.document.write("\x3chtml\x3e\x3chead\x3e\x3cmeta name\x3d'viewport' content\x3d'width\x3ddevice-width, initial-scale\x3d1.0' /\x3e\x3ctitle\x3e"+b+"\x3c/title\x3e\x3c/head\x3e\x3cbody style\x3d'font-size:85%'\x3e"),d.document.write("\x3cpre\x3e"+a+"\x3c/pre\x3e"),d.document.write("\x3chr\x3e\x3cinput type\x3d'button' value\x3d'"+m("Close","Close")+"' onclick\x3d'window.close()' 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a=p["HTML-CSS"],h=p.NativeMML,d=p.SVG,b=(a||h||d||{config:{scale:100}}).config.scale,e=prompt(m("ScaleMath","Scale all mathematics (compared to surrounding text) by"),b+"%");e&&(e.match(/^\s*\d+(\.\d*)?\s*%?\s*$/)?(e=parseFloat(e))?e!==b&&(a&&(a.config.scale=e),h&&(h.config.scale=e),d&&(d.config.scale=e),g.cookie.scale=e,g.saveCookie(),c.Reprocess()):alert(m("NonZeroScale","The scale should not be zero")):alert(m("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 h=c.outputJax["jax/mml"];if(h[0]!==d.settings.renderer){var b=c.Browser,e,k=g.Renderer.Messages,u;switch(d.settings.renderer){case "NativeMML":d.settings.warnedMML||(b.isChrome&&"24."!==b.version.substr(0,3)?e=k.MML.WebKit:b.isSafari&&!b.versionAtLeast("5.0")?e=k.MML.WebKit:b.isMSIE?b.hasMathPlayer||(e=k.MML.MSIE):e=k.MML[b],u="warnedMML");break;case "SVG":d.settings.warnedSVG||!b.isMSIE||a||(e=k.SVG.MSIE)}if(e){e=m(e[0],e[1]);e=e+"\n\n"+m("SwitchAnyway","Switch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)");g.cookie.renderer=h[0].id;g.saveCookie();if(!confirm(e)){g.cookie.renderer=d.settings.renderer=f.Cookie.Get("menu").renderer;g.saveCookie();return}u&&(g.cookie.warned=d.settings.warned=!0);g.cookie.renderer=d.settings.renderer;g.saveCookie()}c.Queue(["setRenderer",c,d.settings.renderer,"jax/mml"],["Rerender",c])}};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. 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Javascript file names should end with '.js'")),b.Require(a,function(h){h!=b.STATUS.OK&&alert(m("BadData","Failed to load translation data from %1",a))}))};g.MPEvents=function(h){var b=d.settings.discoverable,e=g.MPEvents.Messages;a?!b&&"Menu Events"===h.name[1]&&d.settings.mpContext&&alert(m.apply(m,e.IE9warning)):d.settings.mpMouse&&!confirm(m.apply(m,e.IE8warning))?(delete g.cookie.mpContext,delete d.settings.mpContext,delete g.cookie.mpMouse,delete d.settings.mpMouse,g.saveCookie()):(d.settings.mpContext=d.settings.mpMouse,g.cookie.mpContext=g.cookie.mpMouse=d.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."]};c.Browser.Select({MSIE:function(h){var b="BackCompat"===document.compatMode;h=h.versionAtLeast("8.0")&&7<document.documentMode;g.Augment({margin:20,msieBackgroundBug:9>document.documentMode,msieFixedPositionBug:b||!h,msieAboutBug:b});a&&(delete d.styles["#MathJax_About"].filter,delete d.styles[".MathJax_Menu"].filter)},Firefox:function(a){g.skipMouseover=a.isMobile&&a.versionAtLeast("6.0");g.skipMousedown=a.isMobile}});g.isMobile=c.Browser.isMobile;g.noContextMenu=c.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(g.menu){var a=g.menu.Find("Language").menu,h=a.items,d=[],b=MathJax.Localization.strings,e;for(e in b)b.hasOwnProperty(e)&&d.push(e);d=d.sort();a.items=[];e=0;for(var c=d.length;e<c;e++){var k=b[d[e]].menuTitle,k=k?k+(" ("+d[e]+")"):d[e];a.items.push(t.RADIO([d[e],k],"locale",{action:g.Locale}))}a.items.push(h[h.length-2],h[h.length-1])}};c.Register.StartupHook("End Config",function(){d.settings=c.config.menuSettings;"undefined"!==typeof 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Events"],"mpMouse",{action:g.MPEvents,hidden:!a}),t.CHECKBOX(["MenuAndMouse","Mouse and Menu Events"],"mpMouse",{action:g.MPEvents,hidden:a})),t.SUBMENU(["FontPrefs","Font Preference"],{hidden:!d.showFontMenu},t.LABEL(["ForHTMLCSS","For HTML-CSS:"]),t.RADIO(["Auto","Auto"],"font",{action:g.Font}),t.RULE(),t.RADIO(["TeXLocal","TeX (local)"],"font",{action:g.Font}),t.RADIO(["TeXWeb","TeX (web)"],"font",{action:g.Font}),t.RADIO(["TeXImage","TeX (image)"],"font",{action:g.Font}),t.RULE(),t.RADIO(["STIXlocal","STIX (local)"],"font",{action:g.Font})),t.SUBMENU(["ContextMenu","Contextual Menu"],{hidden:!d.showContext},t.RADIO("MathJax","context"),t.RADIO(["Browser","Browser"],"context")),t.COMMAND(["Scale","Scale All Math ..."],g.Scale),t.RULE().With({hidden:!d.showDiscoverable,name:["","discover_rule"]}),t.CHECKBOX(["Discoverable","Highlight on Hover"],"discoverable",{hidden:!d.showDiscoverable})),t.SUBMENU(["Locale","Language"],{hidden:!d.showLocale},t.RADIO("en","locale",{action:g.Locale}),t.RULE().With({hidden:!d.showLocaleURL,name:["","localURL_rule"]}),t.COMMAND(["LoadLocale","Load from URL ..."],g.LoadLocale,{hidden:!d.showLocaleURL})),t.RULE(),t.COMMAND(["About","About MathJax"],g.About),t.COMMAND(["Help","MathJax Help"],g.Help));if(g.isMobile){var h=d.settings,b=g.menu.Find("Math Settings","Zoom Trigger").menu;b.items[0].disabled=b.items[1].disabled=!0;if("Hover"===h.zoom||"Click"==h.zoom)h.zoom="None";b.items=b.items.slice(0,4);navigator.appVersion.match(/[ (]Android[) ]/)&&g.ITEM.SUBMENU.Augment({marker:"\u00bb"})}g.CreateLocaleMenu()});g.showRenderer=function(a){g.cookie.showRenderer=d.showRenderer=a;g.saveCookie();g.menu.Find("Math Settings","Math Renderer").hidden=!a};g.showMathPlayer=function(a){g.cookie.showMathPlayer=d.showMathPlayer=a;g.saveCookie();g.menu.Find("Math Settings","MathPlayer").hidden=!a};g.showFontMenu=function(a){g.cookie.showFontMenu=d.showFontMenu=a;g.saveCookie();g.menu.Find("Math Settings","Font Preference").hidden=!a};g.showContext=function(a){g.cookie.showContext=d.showContext=a;g.saveCookie();g.menu.Find("Math Settings","Contextual Menu").hidden=!a};g.showDiscoverable=function(a){g.cookie.showDiscoverable=d.showDiscoverable=a;g.saveCookie();g.menu.Find("Math Settings","Highlight on Hover").hidden=!a;g.menu.Find("Math Settings","discover_rule").hidden=!a};g.showLocale=function(a){g.cookie.showLocale=d.showLocale=a;g.saveCookie();g.menu.Find("Language").hidden=!a};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)});k.Queue(c.Register.StartupHook("End Config",{}),["getImages",g],["Styles",b,d.styles],["Post",c.Startup.signal,"MathMenu 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"+f.join(" "):""},toMathMLclass:function(f){var b=[];this["class"]&&b.push(this["class"]);if(this.isa(c.TeXAtom)&&SETTINGS.texHints){var k="ORD OP BIN REL OPEN CLOSE PUNCT INNER VCENTER".split(" ")[this.texClass];k&&b.push("MJX-TeXAtom-"+k)}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&&f.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,k=c.length;b<k;b++){var p=c[b].charCodeAt(0);if(55295>=p||57344<=p)32>p||126<p?c[b]="\x26#x"+p.toString(16).toUpperCase()+";":(p={"\x26":"\x26amp;","\x3c":"\x26lt;","\x3e":"\x26gt;",'"':"\x26quot;"}[c[b]])&&(c[b]=p);else if(b+1<k){var l=c[b+1].charCodeAt(0);c[b]="\x26#x"+((p-55296<<10)+(l-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 k=this.toMathMLattributes();delete this.data[0].inferred;for(var p=[],l=0,m=this.data.length;l<m;l++)this.data[l]&&p.push(this.data[l].toMathML(c+" "));return c+"\x3c"+b+k+"\x3e\n"+p.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 k=this.toMathMLattributes();delete this.data[0].inferred;for(var p=[],l=0,m=this.data.length;l<m;l++)this.data[l]&&p.push(this.data[l].toMathML(c+" "));return c+"\x3c"+b+k+"\x3e\n"+p.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,f){var b,k=function(b){return MathJax.Localization._.apply(MathJax.Localization,[["MathML",b]].concat([].slice.call(arguments,1)))};c.Parse=MathJax.Object.Subclass({Init:function(b){this.Parse(b)},Parse:function(b){"string"!==typeof b?b=b.parentNode:(b=c.ParseXML(this.preProcessMath.call(this,b)),null==b&&c.Error(["ErrorParsingMathML","Error parsing MathML"]));var f=b.getElementsByTagName("parsererror")[0];f&&c.Error(["ParsingError","Error parsing MathML: %1",f.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,"")]);1!==b.childNodes.length&&c.Error(["MathMLSingleElement","MathML must be formed by a single element"]);"html"===b.firstChild.nodeName.toLowerCase()&&(f=b.getElementsByTagName("h1")[0])&&"XML parsing error"===f.textContent&&f.nextSibling&&c.Error(["ParsingError","Error parsing MathML: %1",String(f.nextSibling.nodeValue).replace(/fatal parsing error: /,"")]);"math"!==b.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")&&c.Error(["MathMLRootElement","MathML must be formed by a \x3cmath\x3e element, not %1","\x3c"+b.firstChild.nodeName+"\x3e"]);this.mml=this.MakeMML(b.firstChild)},MakeMML:function(f){var l=String(f.getAttribute("class")||""),m;m=f.nodeName.toLowerCase().replace(/^[a-z]+:/,"");if(l=l.match(/(^| )MJX-TeXAtom-([^ ]*)/))m=this.TeXAtom(l[2]);else if(b[m]&&b[m].isa&&b[m].isa(b.mbase))m=b[m]();else return MathJax.Hub.signal.Post(["MathML Jax - unknown node type",m]),b.merror(k("UnknownNodeType","Unknown node type: %1",m));this.AddAttributes(m,f);this.CheckClass(m,m["class"]);this.AddChildren(m,f);c.config.useMathMLspacing&&(m.useMMLspacing=8);return m},TeXAtom:function(c){c=b.TeXAtom().With({texClass:b.TEXCLASS[c]});c.texClass===b.TEXCLASS.OP&&(c.movesupsub=c.movablelimits=!0);return c},CheckClass:function(b,c){c=(c||"").split(/ /);for(var f=[],k=0,n=c.length;k<n;k++)"MJX-"===c[k].substr(0,4)?"MJX-arrow"===c[k]?b.arrow=!0:"MJX-variant"===c[k]?(b.variantForm=!0,MathJax.Extension["TeX/AMSsymbols"]||MathJax.Hub.RestartAfter(MathJax.Ajax.Require("[MathJax]/extensions/TeX/AMSsymbols.js"))):"MJX-TeXAtom"!==c[k].substr(0,11)&&(b.mathvariant=c[k].substr(3),"-tex-caligraphic-bold"===b.mathvariant||"-tex-oldstyle-bold"===b.mathvariant)&&(MathJax.Extension["TeX/boldsymbol"]||MathJax.Hub.RestartAfter(MathJax.Ajax.Require("[MathJax]/extensions/TeX/boldsymbol.js"))):f.push(c[k]);f.length?b["class"]=f.join(" "):delete b["class"]},AddAttributes:function(c,f){c.attr={};c.attrNames=[];for(var k=0,q=f.attributes.length;k<q;k++){var n=f.attributes[k].name;"xlink:href"==n&&(n="href");if(!n.match(/:/)&&!n.match(/^_moz-math-((column|row)(align|line)|font-style)$/)){var a=f.attributes[k].value,a=this.filterAttribute(n,a);null!=a&&("true"===a.toLowerCase()?a=!0:"false"===a.toLowerCase()&&(a=!1),null!=c.defaults[n]||b.copyAttributes[n]?c[n]=a:c.attr[n]=a,c.attrNames.push(n))}}},filterAttribute:function(b,c){return c},AddChildren:function(f,k){for(var m=0,q=k.childNodes.length;m<q;m++){var n=k.childNodes[m];"#comment"!==n.nodeName&&("#text"===n.nodeName?f.isToken&&!f.mmlSelfClosing?(n=n.nodeValue.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity),f.Append(b.chars(this.trimSpace(n)))):n.nodeValue.match(/\S/)&&c.Error(["UnexpectedTextNode","Unexpected text node: %1","'"+n.nodeValue+"'"]):"annotation-xml"===f.type?f.Append(b.xml(n)):(n=this.MakeMML(n),f.Append(n),n.mmlSelfClosing&&n.data.length&&(f.Append.apply(f,n.data),n.data=[])))}"mrow"===f.type&&2<=f.data.length&&(m=f.data[0],q=f.data[f.data.length-1],"mo"===m.type&&m.Get("fence")&&"mo"===q.type&&q.Get("fence")&&(m.data[0]&&(f.open=m.data.join("")),q.data[0]&&(f.close=q.data.join(""))))},preProcessMath:function(b){b.match(/^<[a-z]+:/i)&&!b.match(/^<[^<>]* xmlns:/)&&(b=b.replace(/^<([a-z]+)(:math)/i,'\x3c$1$2 xmlns:$1\x3d"http://www.w3.org/1998/Math/MathML"'));var c=b.match(/^(<math( ('.*?'|".*?"|[^>])+)>)/i);c&&c[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)&&(b=c[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+b.substr(c[0].length));b.match(/^<math/i)&&!b.match(/^<[^<>]* xmlns=/)&&(b=b.replace(/^<(math)/i,'\x3cmath xmlns\x3d"http://www.w3.org/1998/Math/MathML"'));b=b.replace(/^\s*(?:\/\/)?<!(--)?\[CDATA\[((.|\n)*)(\/\/)?\]\]\1>\s*$/,"$2");return b.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(b){return b.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/ +/g," ")},replaceEntity:function(b,f){if(f.match(/^(lt|amp|quot)$/))return b;if(c.Parse.Entity[f])return c.Parse.Entity[f];var k=f.charAt(0).toLowerCase(),q=f.match(/^[a-zA-Z](fr|scr|opf)$/);q&&(k=q[1]);c.Parse.loaded[k]||(c.Parse.loaded[k]=!0,MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+"/"+k+".js")));return b}},{loaded:[]});c.Augment({sourceMenuTitle:["OriginalMathML","Original MathML"],prefilterHooks:MathJax.Callback.Hooks(!0),postfilterHooks:MathJax.Callback.Hooks(!0),Translate:function(k){this.ParseXML||(this.ParseXML=this.createParser());var l,m,q={script:k};k.firstChild&&"math"===k.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")?q.math=k.firstChild:(m=MathJax.HTML.getScript(k),f.isMSIE&&(m=m.replace(/( )+$/,"")),q.math=m);this.prefilterHooks.Execute(q);m=q.math;try{l=c.Parse(m).mml}catch(n){if(!n.mathmlError)throw n;l=this.formatError(n,m,k)}q.math=b(l);this.postfilterHooks.Execute(q);return q.math},prefilterMath:function(b,c){return b},prefilterMathML:function(b,c){return b},formatError:function(c,f,k){c=c.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",c,f,k]);return b.merror(c)},Error:function(b){b instanceof Array&&(b=k.apply(k,b));throw MathJax.Hub.Insert(Error(b),{mathmlError:!0});},parseDOM:function(b){return this.parser.parseFromString(b,"text/xml")},parseMS:function(b){return this.parser.loadXML(b)?this.parser:null},parseDIV:function(b){this.div.innerHTML=b.replace(/<([a-z]+)([^>]*)\/>/g,"\x3c$1$2\x3e\x3c/$1\x3e");return this.div},parseError:function(b){return null},createMSParser:function(){for(var b=null,c="MSXML2.DOMDocument.6.0 MSXML2.DOMDocument.5.0 MSXML2.DOMDocument.4.0 MSXML2.DOMDocument.3.0 MSXML2.DOMDocument.2.0 Microsoft.XMLDOM".split(" "),f=0,k=c.length;f<k&&!b;f++)try{b=new ActiveXObject(c[f])}catch(n){}return b},createParser:function(){if(window.DOMParser)return this.parser=new DOMParser,this.parseDOM;if(window.ActiveXObject){this.parser=this.createMSParser();if(!this.parser)return MathJax.Localization.Try(this.parserCreationError),this.parseError;this.parser.async=!1;return this.parseMS}this.div=MathJax.Hub.Insert(document.createElement("div"),{style:{visibility:"hidden",overflow:"hidden",height:"1px",position:"absolute",top:0}});document.body.firstChild?document.body.insertBefore(this.div,document.body.firstChild):document.body.appendChild(this.div);return this.parseDIV},parserCreationError:function(){alert(k("CantCreateXMLParser","MathJax can't create an XML parser for MathML. Check that\nthe 'Script ActiveX controls marked safe for scripting' security\nsetting is enabled (use the Internet Options item in the Tools\nmenu, and select the Security panel, then press the Custom Level\nbutton to check this).\n\nMathML equations will not be able to be processed by MathJax."))},Startup:function(){b=MathJax.ElementJax.mml;b.mspace.Augment({mmlSelfClosing:!0});b.none.Augment({mmlSelfClosing:!0});b.mprescripts.Augment({mmlSelfClosing:!0})}});c.prefilterHooks.Add(function(b){b.math="string"===typeof b.math?c.prefilterMath(b.math,b.script):c.prefilterMathML(b.math,b.script)});c.Parse.Entity={ApplyFunction:"\u2061",Backslash:"\u2216",Because:"\u2235",Breve:"\u02d8",Cap:"\u22d2",CenterDot:"\u00b7",CircleDot:"\u2299",CircleMinus:"\u2296",CirclePlus:"\u2295",CircleTimes:"\u2297",Congruent:"\u2261",ContourIntegral:"\u222e",Coproduct:"\u2210",Cross:"\u2a2f",Cup:"\u22d3",CupCap:"\u224d",Dagger:"\u2021",Del:"\u2207",Delta:"\u0394",Diamond:"\u22c4",DifferentialD:"\u2146",DotEqual:"\u2250",DoubleDot:"\u00a8",DoubleRightTee:"\u22a8",DoubleVerticalBar:"\u2225",DownArrow:"\u2193",DownLeftVector:"\u21bd",DownRightVector:"\u21c1",DownTee:"\u22a4",Downarrow:"\u21d3",Element:"\u2208",EqualTilde:"\u2242",Equilibrium:"\u21cc",Exists:"\u2203",ExponentialE:"\u2147",FilledVerySmallSquare:"\u25aa",ForAll:"\u2200",Gamma:"\u0393",Gg:"\u22d9",GreaterEqual:"\u2265",GreaterEqualLess:"\u22db",GreaterFullEqual:"\u2267",GreaterLess:"\u2277",GreaterSlantEqual:"\u2a7e",GreaterTilde:"\u2273",Hacek:"\u02c7",Hat:"^",HumpDownHump:"\u224e",HumpEqual:"\u224f",Im:"\u2111",ImaginaryI:"\u2148",Integral:"\u222b",Intersection:"\u22c2",InvisibleComma:"\u2063",InvisibleTimes:"\u2062",Lambda:"\u039b",Larr:"\u219e",LeftAngleBracket:"\u27e8",LeftArrow:"\u2190",LeftArrowRightArrow:"\u21c6",LeftCeiling:"\u2308",LeftDownVector:"\u21c3",LeftFloor:"\u230a",LeftRightArrow:"\u2194",LeftTee:"\u22a3",LeftTriangle:"\u22b2",LeftTriangleEqual:"\u22b4",LeftUpVector:"\u21bf",LeftVector:"\u21bc",Leftarrow:"\u21d0",Leftrightarrow:"\u21d4",LessEqualGreater:"\u22da",LessFullEqual:"\u2266",LessGreater:"\u2276",LessSlantEqual:"\u2a7d",LessTilde:"\u2272",Ll:"\u22d8",Lleftarrow:"\u21da",LongLeftArrow:"\u27f5",LongLeftRightArrow:"\u27f7",LongRightArrow:"\u27f6",Longleftarrow:"\u27f8",Longleftrightarrow:"\u27fa",Longrightarrow:"\u27f9",Lsh:"\u21b0",MinusPlus:"\u2213",NestedGreaterGreater:"\u226b",NestedLessLess:"\u226a",NotDoubleVerticalBar:"\u2226",NotElement:"\u2209",NotEqual:"\u2260",NotExists:"\u2204",NotGreater:"\u226f",NotGreaterEqual:"\u2271",NotLeftTriangle:"\u22ea",NotLeftTriangleEqual:"\u22ec",NotLess:"\u226e",NotLessEqual:"\u2270",NotPrecedes:"\u2280",NotPrecedesSlantEqual:"\u22e0",NotRightTriangle:"\u22eb",NotRightTriangleEqual:"\u22ed",NotSubsetEqual:"\u2288",NotSucceeds:"\u2281",NotSucceedsSlantEqual:"\u22e1",NotSupersetEqual:"\u2289",NotTilde:"\u2241",NotVerticalBar:"\u2224",Omega:"\u03a9",OverBar:"\u203e",OverBrace:"\u23de",PartialD:"\u2202",Phi:"\u03a6",Pi:"\u03a0",PlusMinus:"\u00b1",Precedes:"\u227a",PrecedesEqual:"\u2aaf",PrecedesSlantEqual:"\u227c",PrecedesTilde:"\u227e",Product:"\u220f",Proportional:"\u221d",Psi:"\u03a8",Rarr:"\u21a0",Re:"\u211c",ReverseEquilibrium:"\u21cb",RightAngleBracket:"\u27e9",RightArrow:"\u2192",RightArrowLeftArrow:"\u21c4",RightCeiling:"\u2309",RightDownVector:"\u21c2",RightFloor:"\u230b",RightTee:"\u22a2",RightTeeArrow:"\u21a6",RightTriangle:"\u22b3",RightTriangleEqual:"\u22b5",RightUpVector:"\u21be",RightVector:"\u21c0",Rightarrow:"\u21d2",Rrightarrow:"\u21db",Rsh:"\u21b1",Sigma:"\u03a3",SmallCircle:"\u2218",Sqrt:"\u221a",Square:"\u25a1",SquareIntersection:"\u2293",SquareSubset:"\u228f",SquareSubsetEqual:"\u2291",SquareSuperset:"\u2290",SquareSupersetEqual:"\u2292",SquareUnion:"\u2294",Star:"\u22c6",Subset:"\u22d0",SubsetEqual:"\u2286",Succeeds:"\u227b",SucceedsEqual:"\u2ab0",SucceedsSlantEqual:"\u227d",SucceedsTilde:"\u227f",SuchThat:"\u220b",Sum:"\u2211",Superset:"\u2283",SupersetEqual:"\u2287",Supset:"\u22d1",Therefore:"\u2234",Theta:"\u0398",Tilde:"\u223c",TildeEqual:"\u2243",TildeFullEqual:"\u2245",TildeTilde:"\u2248",UnderBar:"_",UnderBrace:"\u23df",Union:"\u22c3",UnionPlus:"\u228e",UpArrow:"\u2191",UpDownArrow:"\u2195",UpTee:"\u22a5",Uparrow:"\u21d1",Updownarrow:"\u21d5",Upsilon:"\u03a5",Vdash:"\u22a9",Vee:"\u22c1",VerticalBar:"\u2223",VerticalTilde:"\u2240",Vvdash:"\u22aa",Wedge:"\u22c0",Xi:"\u039e",acute:"\u00b4",aleph:"\u2135",alpha:"\u03b1",amalg:"\u2a3f",and:"\u2227",ang:"\u2220",angmsd:"\u2221",angsph:"\u2222",ape:"\u224a",backprime:"\u2035",backsim:"\u223d",backsimeq:"\u22cd",beta:"\u03b2",beth:"\u2136",between:"\u226c",bigcirc:"\u25ef",bigodot:"\u2a00",bigoplus:"\u2a01",bigotimes:"\u2a02",bigsqcup:"\u2a06",bigstar:"\u2605",bigtriangledown:"\u25bd",bigtriangleup:"\u25b3",biguplus:"\u2a04",blacklozenge:"\u29eb",blacktriangle:"\u25b4",blacktriangledown:"\u25be",blacktriangleleft:"\u25c2",bowtie:"\u22c8",boxdl:"\u2510",boxdr:"\u250c",boxminus:"\u229f",boxplus:"\u229e",boxtimes:"\u22a0",boxul:"\u2518",boxur:"\u2514",bsol:"\\",bull:"\u2022",cap:"\u2229",check:"\u2713",chi:"\u03c7",circ:"\u02c6",circeq:"\u2257",circlearrowleft:"\u21ba",circlearrowright:"\u21bb",circledR:"\u00ae",circledS:"\u24c8",circledast:"\u229b",circledcirc:"\u229a",circleddash:"\u229d",clubs:"\u2663",colon:":",comp:"\u2201",ctdot:"\u22ef",cuepr:"\u22de",cuesc:"\u22df",cularr:"\u21b6",cup:"\u222a",curarr:"\u21b7",curlyvee:"\u22ce",curlywedge:"\u22cf",dagger:"\u2020",daleth:"\u2138",ddarr:"\u21ca",deg:"\u00b0",delta:"\u03b4",digamma:"\u03dd",div:"\u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p,l=f.Browser.isMSIE,m,q,n,a;f.Register.StartupHook("MathZoom Ready",function(){a=MathJax.Extension.MathZoom});var h=function(a,b){var h=k.Element("span");a="padding"+a;b&&(h.style.cssText=b.getAttribute("style")||"",""===h.style.padding&&""===(h.style[a]||"")&&(h.style[a]="0px",b.setAttribute("style",h.style.cssText)))},d=function(a,b,h){if(a){var d=k.Element("span");d.style.cssText=a.getAttribute("style")||"";if(""===d.style.padding){b={paddingLeft:h,paddingTop:b,paddingRight:"0px",paddingBottom:"0px"};for(var c in b)b.hasOwnProperty(c)&&""===(d.style[c]||"")&&(d.style[c]=b[c])}a.setAttribute("style",d.style.cssText)}};c.Augment({config:{styles:{".MathJax_MathML":{"font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none",direction:"ltr",border:0,padding:0,margin:0},"span.MathJax_MathML":{display:"inline"},"div.MathJax_MathML":{display:"block"},".MathJax_mmlExBox":{display:"block",overflow:"hidden",height:"1px",width:"60ex",padding:0,border:0,margin:0}}},settings:f.config.menuSettings,ex:1,Config:function(){this.SUPER(arguments).Config.call(this);this.settings.scale&&(this.config.scale=this.settings.scale);if("center"!==f.config.displayAlign){var a=f.config.displayAlign,b={"text-align":a+"!important"};b["margin-"+a]=f.config.displayIndent+"!important";f.Insert(this.config.styles,{"div.MathJax_MathML":b,"div.MathJax_MathML math":{"text-align":a},"div.MathJax_MathContainer \x3e span":{"text-align":a+"!important"}})}this.require||(this.require=[]);this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){m=MathJax.Extension.MathEvents.Event;q=MathJax.Extension.MathEvents.Touch;n=MathJax.Extension.MathEvents.Hover;this.ContextMenu=m.ContextMenu;this.Mousedown=m.AltContextMenu;this.Mouseover=n.Mouseover;this.Mouseout=n.Mouseout;this.Mousemove=n.Mousemove;l||(this.EmExSpan=k.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["div",{className:"MathJax_mmlExBox"}],["span",{className:"MathJax_MathML"}]]),p.math(p.mspace().With({width:"60ex"})).toNativeMML(this.EmExSpan.lastChild));return b.Styles(this.config.styles)},InitializeMML:function(){this.initialized=!0;if(l)try{if(!f.Browser.mpNamespace){var a=document.createElement("object");a.id="mathplayer";a.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(a);document.namespaces.add("m","http://www.w3.org/1998/Math/MathML");f.Browser.mpNamespace=!0}f.Browser.mpImported||(document.namespaces.m.doImport("#mathplayer"),f.Browser.mpImported=!0)}catch(b){alert(MathJax.Localization._(["MathML","MathPlayer"],"MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics."))}else document.body.appendChild(this.EmExSpan),this.defaultEx=this.EmExSpan.firstChild.offsetWidth/60,this.defaultMEx=this.EmExSpan.lastChild.offsetWidth/60,document.body.removeChild(this.EmExSpan)},preTranslate:function(a){a=a.jax[this.id];var b,h=a.length,d,c,f;for(b=0;b<h;b++)if(d=a[b],d.parentNode&&(this.initialized||this.InitializeMML(),(c=d.previousSibling)&&"MathJax_MathML"===c.className&&c.parentNode.removeChild(c),c=d.MathJax.elementJax))f=c.root,c.NativeMML={},f="block"===f.Get("display")?"div":"span",c=k.Element(f,{className:"MathJax_MathML",id:c.inputID+"-Frame"},[["span",{className:"MathJax_MathContainer",isMathJax:!0,jaxID:this.id,style:{position:"relative",display:"inline-block","white-space":"nowrap"}},[["span",{isMathJax:!0,style:{display:"inline-block"}}]]]]),d.parentNode.insertBefore(c,d),l||d.parentNode.insertBefore(this.EmExSpan.cloneNode(!0),d);for(b=0;b<h;b++)if(d=a[b],d.parentNode&&(c=d.MathJax.elementJax)){if(l)f=100;else{f=d.previousSibling;d=f.firstChild.offsetWidth/60;f=f.lastChild.offsetWidth/60;if(0===d||"NaN"===d)d=this.defaultEx,f=this.defaultMEx;f=(1<f?d/f:1)*this.config.scale;f=Math.floor(Math.max(this.config.minScaleAdjust/100,f));c.NativeMML.ex=d}c.NativeMML.fontSize=f+"%"}if(!l)for(b=0;b<h;b++)d=a[b],d.parentNode&&d.MathJax.elementJax&&(f=a[b].previousSibling,f.parentNode.removeChild(f))},Translate:function(a){if(a.parentNode){a=a.MathJax.elementJax;var b=a.root,h=document.getElementById(a.inputID+"-Frame"),d=h.firstChild,c=d.firstChild;h.style.fontSize=a.NativeMML.fontSize;this.ex=a.NativeMML.ex||this.defaultEx;try{b.toNativeMML(c)}catch(k){if(k.restart)for(;c.firstChild;)c.removeChild(c.firstChild);throw k;}if(l)if(d.addEventListener)for(var H in this.MSIE9events)this.MSIE9events.hasOwnProperty(H)&&d.addEventListener(H,this.MSIE9event,!0);else!(null!=this.config.showMathMenuMSIE?this:f).config.showMathMenuMSIE||this.settings.mpContext||this.settings.mpMouse?(d.style.position="",c.firstChild.onmousedown=this.MSIEaltMenu):this.MSIEoverlay(d);else 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h=this.getHoverBBox(null,b,{});k.addElement(a,"span",{style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{isMathJax:!0,className:"MathJax_MathPlayer_Overlay",style:{display:"inline-block",position:"absolute",left:n.Px(-h.w),top:n.Px(-h.h-(h.y||0)-1),width:n.Px(h.w),height:n.Px(h.h+h.d),cursor:"pointer","background-color":"white",filter:"alpha(opacity\x3d0)"}}]]);f.Insert(a,{msieMath:b,onmousedown:this.MSIEevent,oncontextmenu:this.MSIEevent,onclick:this.MSIEevent,onmouseup:this.MSIEevent,onmousemove:this.MSIEevent,ondblclick:this.MSIEevent,onmouseover:this.MSIEevent,onmouseout:this.MSIEevent})},MSIEevents:{mousedown:"Mousedown",contextmenu:"ContextMenu",click:"Click",mouseup:"Mouseup",mousemove:"Mousemove",dblclick:"DblClick",mouseover:"Mouseover",mouseout:"Mouseout"},MSIEevent:function(){var b=window.event,h=c.MSIEevents[b.type];if(c[h]&&!1===c[h](b,this)||a&&!1===a.HandleEvent(b,h,this))return!1;"MathJax_MathPlayer_Overlay"===b.srcElement.className&&this.msieMath.fireEvent&&("ContextMenu"!==h&&"Mouseover"!==h&&"Mouseout"!==h||this.msieMath.fireEvent("on"+b.type,b));return m.False(b)},MSIEaltMenu:function(){for(var a=this.parentNode.parentNode;!a.jaxID;)a=a.parentNode;m.AltContextMenu(window.event,a)},MSIE9events:{contextmenu:"Menu",click:"Click",dblclick:"DblClick",mouseup:"False",mouseover:"Mouseover",mouseout:"Mouseout"},MSIE9event:function(a){return"contextmenu"===a.type&&c.settings.mpContext||"mouseup"===a.type&&c.settings.mpMouse?!0:"click"===a.type&&c.settings.mpContext?m.AltContextMenu(a,this):m[c.MSIE9events[a.type]].call(this,a)},getJaxFromMath:function(a){a=a.parentNode;do a=a.nextSibling;while(a&&"script"!==a.nodeName.toLowerCase());return f.getJaxFor(a)},getHoverSpan:function(a,b){return b.firstChild},getHoverBBox:function(a,b,h){return m.getBBox(b.parentNode)},Zoom:function(a,b,h,d,f){a.root.toNativeMML(b);this.msieIE8HeightBug&&(b.style.position="absolute");a=h.offsetWidth||h.scrollWidth;h=h.offsetHeight||h.scrollHeight;d=b.offsetWidth;f=b.offsetHeight;if(c.widthBug){var k=b.firstChild.firstChild.scrollWidth;k>d&&(d=k,b.style.width=d+"px")}this.msieIE8HeightBug&&(b.style.position="");return{Y:-m.getBBox(b.parentNode).h,mW:a,mH:h,zW:d,zH:f}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em"}});f.Register.StartupHook("mml Jax Ready",function(){p=MathJax.ElementJax.mml;p.mbase.Augment({toNativeMML:function(a){var b=this.NativeMMLelement(this.type);this.NativeMMLattributes(b);for(var h=0,d=this.data.length;h<d;h++)this.data[h]?this.data[h].toNativeMML(b):b.appendChild(this.NativeMMLelement("mrow"));a.appendChild(b)},NativeMMLattributes:function(a){var b=this.defaults,h=this.attrNames||p.copyAttributeNames,d=p.skipAttributes;if(!this.attrNames){"mstyle"===this.type&&(b=p.math.prototype.defaults);for(var c in b)!d[c]&&b.hasOwnProperty(c)&&null!=this[c]&&a.setAttribute(c,this.NativeMMLattribute(this[c]))}b=0;for(d=h.length;b<d;b++)c=(this.attr||{})[h[b]],null==c&&(c=this[h[b]]),null!=c&&a.setAttribute(h[b],this.NativeMMLattribute(c));this.NativeMMLclass(a)},NativeMMLclass:function(a){var b=[];this["class"]&&b.push(this["class"]);if(this.isa(p.TeXAtom)){var h="ORD OP BIN REL OPEN CLOSE PUNCT INNER VCENTER".split(" ")[this.texClass];h&&b.push("MJX-TeXAtom-"+h)}this.mathvariant&&this.NativeMMLvariants[this.mathvariant]&&b.push("MJX"+this.mathvariant);this.arrow&&b.push("MJX-arrow");this.variantForm&&b.push("MJX-variant");b.length&&a.setAttribute("class",b.join(" 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d=this.NativeMMLelement("mfenced");this.NativeMMLattributes(d);b=0;h=this.data.length;this.open&&(d.setAttribute("open",this.open),b++);this.close&&(d.setAttribute("close",this.close),h--);var e=d;1<h-b+1&&(e=this.NativeMMLelement("mrow"),a.appendChild(d),a=d);for(;b<h;b++)this.data[b]?this.data[b].toNativeMML(e):e.appendChild(this.NativeMMLelement("mrow"));a.appendChild(e)}else this.SUPER(arguments).toNativeMML.call(this,a)}});p.msubsup.Augment({toNativeMML:function(a){var b=this.type;null==this.data[this.sup]&&(b="msub");null==this.data[this.sub]&&(b="msup");b=this.NativeMMLelement(b);this.NativeMMLattributes(b);delete this.data[0].inferred;for(var h=0,d=this.data.length;h<d;h++)this.data[h]&&this.data[h].toNativeMML(b);a.appendChild(b)}});p.munderover.Augment({toNativeMML:function(a){var b=this.type;null==this.data[this.under]&&(b="mover");null==this.data[this.over]&&(b="munder");b=this.NativeMMLelement(b);this.NativeMMLattributes(b);delete this.data[0].inferred;for(var h=0,d=this.data.length;h<d;h++)this.data[h]&&this.data[h].toNativeMML(b);a.appendChild(b)}});if(!l){var a=MathJax.Hub.SplitList;p.mtable.Augment({toNativeMML:function(b){var h,d;if(c.tableSpacingBug){h=this.getValues("rowspacing","columnspacing");this.nMMLtopPadding=a("0px "+h.rowspacing);this.nMMLleftPadding=a("0px "+h.columnspacing);var e=this.nMMLtopPadding,k=e.length;h=0;for(d=this.data.length;h<d;h++)this.data[h]&&(this.data[h].nMMLtopPadding=e[h<k?h:k-1])}if(c.tableLabelBug)for(h=0,d=this.data.length;h<d;h++)if(this.data[h]&&this.data[h].isa(p.mlabeledtr)){var r=f.config.displayAlign.charAt(0),l=this.Get("side").charAt(0);this.nMMLhasLabels=!0;this.nMMLlaMatch=r===l;this.nMMLforceWidth="c"===r||!!(this.width||"").match("%");break}this.width&&this.ffTableWidthBug&&(h=(this.style||"").replace(/;\s*$/,"").split(";"),""===h[0]&&h.shift(),h.push("width:"+this.width),this.style=h.join(";"));this.SUPER(arguments).toNativeMML.call(this,b);if(this.nMMLhasLabels){h=b.firstChild;if(this.nMMLforceWidth||"r"!==l)if(r=("l"!==r?1:0)+("l"===l?1:0)){var l={columnalign:"left",columnwidth:"auto",columnspacing:"0px",columnlines:"none"},m;for(m in l)l.hasOwnProperty(m)&&this[m]&&(d=[l[m],l[m]].slice(2-r).join(" ")+" ",h.setAttribute(m,d+h.getAttribute(m)))}!this.nMMLforceWidth&&this.nMMLlaMatch||h.setAttribute("width","100%")}}});p.mtr.Augment({toNativeMML:function(a){this.SUPER(arguments).toNativeMML.call(this,a);var b=a.lastChild;if(c.tableSpacingBug)for(var e=this.parent.nMMLleftPadding,u=e.length,k=b.firstChild,r=0;k;k=k.nextSibling,r++)d(k,this.nMMLtopPadding,e[r<u?r:u-1]);if(c.tableLabelBug&&(e=this.parent.nMMLforceWidth,u=this.parent.Get("side").charAt(0),k=f.config.displayAlign.charAt(0),this.parent.nMMLhasLabels&&b.firstChild)){if(e||"r"!==u)h("Left",b.firstChild),"l"!==k&&b.insertBefore(this.NativeMMLelement("mtd"),b.firstChild).setAttribute("style","padding:0"),"l"===u&&b.insertBefore(this.NativeMMLelement("mtd"),b.firstChild).setAttribute("style","padding:0");(e||"l"!==u)&&h("Right",b.lastChild)}}});p.mlabeledtr.Augment({toNativeMML:function(a){var b=this.NativeMMLelement("mtr");this.NativeMMLattributes(b);for(var e=1,u=this.data.length;e<u;e++)this.data[e]?this.data[e].toNativeMML(b):b.appendChild(this.NativeMMLelement("mtd"));if(c.tableSpacingBug)for(var u=this.parent.nMMLleftPadding,k=u.length,e=0,r=b.firstChild;r;r=r.nextSibling,e++)d(r,this.nMMLtopPadding,u[e<k?e:k-1]);if(c.tableLabelBug){var e=this.parent.Get("side").charAt(0),u=f.config.displayAlign.charAt(0),l=f.config.displayIndent;this.data[0].toNativeMML(b);r=k=b.lastChild;e===u?(k.setAttribute("style","width:"+l),k.setAttribute("columnalign",f.config.displayAlign)):(r=this.NativeMMLelement("mpadded"),r.setAttribute("style","width:0"),r.setAttribute("width","0px"),r.appendChild(k.firstChild),k.appendChild(r));h("",k);b.removeChild(k);var l=100,m=this.parent.nMMLforceWidth;(this.parent.width||"").match(/%/)&&(l-=parseFloat(this.parent.width));var p=l;if(m||"r"!==e)h("Left",b.firstChild),"l"!==u&&("c"===u&&(p/=2),l-=p,b.insertBefore(this.NativeMMLelement("mtd"),b.firstChild).setAttribute("style","padding:0;width:"+p+"%")),"l"===e&&b.insertBefore(k,b.firstChild);if(m||"l"!==e)h("Right",b.lastChild),"r"!==u&&b.appendChild(this.NativeMMLelement("mtd")).setAttribute("style","padding:0;width:"+l+"%"),"r"===e&&(e!==u&&r.setAttribute("lspace","-1width"),b.appendChild(k))}a.appendChild(b)}});p.mtd.Augment({toNativeMML:function(a){a=a.appendChild(this.NativeMMLelement(this.type));this.NativeMMLattributes(a);c.widthBug&&(a=a.appendChild(this.NativeMMLelement("mrow")));for(var b=0,h=this.data.length;b<h;b++)this.data[b]?this.data[b].toNativeMML(a):a.appendChild(this.NativeMMLelement("mrow"))}});p.mspace.Augment({toNativeMML:function(a){this.SUPER(arguments).toNativeMML.call(this,a);if(c.spaceWidthBug&&this.width){var b=a.lastChild,h=b.getAttribute("width"),d=b.getAttribute("style")||"";""!=d&&(d+=";");b.setAttribute("style",d+"width:"+h)}}});var b=MathJax.Ajax.fileURL(MathJax.OutputJax.fontDir+"/HTML-CSS/TeX/otf");c.Augment({config:{styles:{'[mathvariant\x3d"double-struck"]':{"font-family":"MathJax_AMS, MathJax_AMS-WEB"},'[mathvariant\x3d"script"]':{"font-family":"MathJax_Script, MathJax_Script-WEB"},'[mathvariant\x3d"fraktur"]':{"font-family":"MathJax_Fraktur, MathJax_Fraktur-WEB"},'[mathvariant\x3d"bold-script"]':{"font-family":"MathJax_Script, MathJax_Caligraphic-WEB","font-weight":"bold"},'[mathvariant\x3d"bold-fraktur"]':{"font-family":"MathJax_Fraktur, 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d=0,e=this.data.length;d<e;d++)this.data[d]?this.data[d].toNativeMML(b):b.appendChild(this.NativeMMLelement("mrow"));d=(this.data[0]||[]).data[0]||{};if(d.nMMLhasLabels){if(d.nMMLforceWidth||!d.nMMLlaMatch)b.setAttribute("style","width:100%"),a.style.width=a.parentNode.style.width="100%";d.nMMLlaMatch&&"div"===a.parentNode.parentNode.nodeName.toLowerCase()&&a.parentNode.parentNode.style.setProperty("margin-"+f.config.displayAlign,"0px","important")}a.appendChild(h);c.widthBug&&!d.nMMLforceWidth&&d.nMMLlaMatch&&(a.style.width=(h.firstChild.scrollWidth/c.ex).toFixed(3)+"ex")}});p.mfenced.Augment({toNativeMML:function(a){if(c.mfencedBug){var b=f.Browser.isOpera,h,d,e,u=this.getValues("open","close","separators");u.open=u.open.replace(/^\s+/,"").replace(/\s+$/,"");u.close=u.close.replace(/^\s+/,"").replace(/\s+$/,"");u.separators=u.separators.replace(/\s+/g,"").split("");if(0==u.separators.length)u.separators=null;else 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c=this.div.offsetWidth,e=this.div.offsetHeight,g=1,f=this.comparisonFont.length;g<f;g++)if(this.div.style.fontFamily=this.comparisonFont[g],this.div.offsetWidth!=d)return[d,this.div.offsetWidth,g,c,e];return null},loadWebFont:function(a){f.Startup.signal.Post("HTML-CSS Jax - Web-Font "+b.fontInUse+"/"+a.directory);var h=p(["LoadWebFont","Loading web-font %1",b.fontInUse+"/"+a.directory]),d=MathJax.Callback({}),h=MathJax.Callback(["loadComplete",this,a,h,d]);c.timer.start(c,[this.checkWebFont,a,h],0,this.timeout);return d},loadComplete:function(a,h,d,u){MathJax.Message.Clear(h);u===c.STATUS.OK?(this.webFontLoaded=!0,d()):(this.loadError(a),f.Browser.isFirefox&&b.allowWebFonts&&(h=document.location.protocol+"//"+document.location.hostname,""!=document.location.port&&(h+=":"+document.location.port),h+="/",c.fileURL(b.webfontDir).substr(0,h.length)!==h&&this.firefoxFontError(a)),this.webFontLoaded?d():b.loadWebFontError(a,d))},loadError:function(a){p(["CantLoadWebFont","Can't load web font 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format('"+h+"')");b.FontFaceBug&&d.isWebFont||(a.match(/-bold/)&&(g["font-weight"]="bold"),a.match(/-italic/)&&(g["font-style"]="italic"));return g}}),m,q,n;b.Augment({config:{styles:{".MathJax":{display:"inline","font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none",direction:"ltr",border:0,padding:0,margin:0},".MathJax_Display":{position:"relative",display:"block",width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0 !important",padding:"0 !important",margin:"0 !important","vertical-align":"0 !important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},".MathJax nobr":{"white-space":"nowrap ! important"},".MathJax img":{display:"inline ! important","float":"none ! important"},".MathJax *":{transition:"none","-webkit-transition":"none","-moz-transition":"none","-ms-transition":"none","-o-transition":"none"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax_Processed":{display:"none!important"},".MathJax_ExBox":{display:"block",overflow:"hidden",width:"1px",height:"60ex"},".MathJax .MathJax_EmBox":{display:"block",overflow:"hidden",width:"1px",height:"60em"},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity\x3d0)"},".MathJax .MathJax_HitBox *":{filter:"none",opacity:1,background:"transparent"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",opacity:1,background:"transparent"},"@font-face":{"font-family":"MathJax_Blank",src:"url('about:blank')"}}},settings:f.config.menuSettings,hideProcessedMath:!0,Font:null,webFontDefault:"MathJax_Blank",allowWebFonts:"otf",maxStretchyParts:1E3,Config:function(){this.require||(this.require=[]);this.Font=l();this.SUPER(arguments).Config.call(this);var a=this.settings;this.adjustAvailableFonts&&this.adjustAvailableFonts(this.config.availableFonts);a.scale&&(this.config.scale=a.scale);a.font&&"Auto"!==a.font&&("TeX (local)"===a.font?(this.config.availableFonts=["TeX"],this.config.preferredFont=this.config.webFont="TeX"):"STIX (local)"===a.font?(this.config.availableFonts=["STIX"],this.config.preferredFont="STIX",this.config.webFont="TeX"):"TeX (web)"===a.font?(this.config.availableFonts=[],this.config.preferredFont="",this.config.webFont="TeX"):"TeX (image)"===a.font&&(this.config.availableFonts=[],this.config.preferredFont=this.config.webFont=""));a=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);!a&&this.allowWebFonts&&(a=this.config.webFont)&&(this.webFonts=!0);!a&&this.config.imageFont&&(a=this.config.imageFont,this.imgFonts=!0);a?(this.fontInUse=a,this.fontDir+="/"+a,this.webfontDir+="/"+a,this.require.push(this.fontDir+"/fontdata.js"),this.imgFonts&&(this.require.push(this.directory+"/imageFonts.js"),f.Startup.signal.Post("HTML-CSS Jax - using image fonts"))):(p(["CantFindFontUsing","Can't find a valid font using %1","["+this.config.availableFonts.join(", 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font"));this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){m=MathJax.Extension.MathEvents.Event;q=MathJax.Extension.MathEvents.Touch;n=MathJax.Extension.MathEvents.Hover;this.ContextMenu=m.ContextMenu;this.Mousedown=m.AltContextMenu;this.Mouseover=n.Mouseover;this.Mouseout=n.Mouseout;this.Mousemove=n.Mousemove;this.hiddenDiv=this.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});document.body.firstChild?document.body.insertBefore(this.hiddenDiv,document.body.firstChild):document.body.appendChild(this.hiddenDiv);this.hiddenDiv=this.addElement(this.hiddenDiv,"div",{id:"MathJax_Hidden"});var 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(b){}}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 b=0,d=a.length;b<d;b++)"STIX"===a[b]&&(a.splice(b,1),d--,b--);"STIX"===this.config.preferredFont&&(this.config.preferredFont=a[0])},PreloadWebFonts:function(){if(b.allowWebFonts&&b.config.preloadWebFonts)for(var a=0,h=b.config.preloadWebFonts.length;a<h;a++){var d=b.FONTDATA.FONTS[b.config.preloadWebFonts[a]];d.available||b.Font.testFont(d)}},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 b=a.jax[this.id],d,c=b.length,e,g,k,v,l,A,r=!1,p=this.config.linebreaks.automatic,n=this.config.linebreaks.width;p?((r=null!=n.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/))?n=n.replace(/\s*container\s*/,""):A=this.defaultWidth,""===n&&(n="100%")):A=1E5;for(d=0;d<c;d++)if(e=b[d],e.parentNode&&((g=e.previousSibling)&&String(g.className).match(/^MathJax(_Display)?( MathJax_Processing)?$/)&&g.parentNode.removeChild(g),g=e.MathJax.elementJax))g.HTMLCSS={display:"block"===g.root.Get("display")},k=v=this.Element("span",{className:"MathJax",id:g.inputID+"-Frame",isMathJax:!0,jaxID:this.id,oncontextmenu:m.Menu,onmousedown:m.Mousedown,onmouseover:m.Mouseover,onmouseout:m.Mouseout,onmousemove:m.Mousemove,onclick:m.Click,ondblclick:m.DblClick}),f.Browser.noContextMenu&&(k.ontouchstart=q.start,k.ontouchend=q.end),g.HTMLCSS.display?(v=this.Element("div",{className:"MathJax_Display"}),v.appendChild(k)):this.msieDisappearingBug&&(k.style.display="inline-block"),v.setAttribute("role","textbox"),v.setAttribute("aria-readonly","true"),v.className+=" MathJax_Processing",e.parentNode.insertBefore(v,e),e.parentNode.insertBefore(this.EmExSpan.cloneNode(!0),e),r&&v.parentNode.insertBefore(this.linebreakSpan.cloneNode(!0),v);for(d=0;d<c;d++)if(e=b[d],e.parentNode&&(l=e.previousSibling,v=l.previousSibling,g=e.MathJax.elementJax)){e=l.firstChild.offsetHeight/60;l=l.lastChild.firstChild.offsetHeight/60;r&&(A=v.previousSibling.firstChild.offsetWidth);if(0===e||"NaN"===e)this.hiddenDiv.appendChild(v),g.HTMLCSS.isHidden=!0,e=this.defaultEx,l=this.defaultEm,r&&(A=this.defaultWidth);v=Math.floor(Math.max(this.config.minScaleAdjust/100,e/this.TeX.x_height/l)*this.config.scale);g.HTMLCSS.scale=v/100;g.HTMLCSS.fontSize=v+"%";g.HTMLCSS.em=g.HTMLCSS.outerEm=l;this.em=l*v/100;g.HTMLCSS.ex=e;g.HTMLCSS.lineWidth=p?this.length2em(n,1,A/this.em):1E6}for(d=0;d<c;d++)if(e=b[d],e.parentNode&&(l=b[d].previousSibling,g=b[d].MathJax.elementJax))r&&(k=l.previousSibling,g.HTMLCSS.isHidden||(k=k.previousSibling),k.parentNode.removeChild(k)),l.parentNode.removeChild(l);a.HTMLCSSeqn=a.HTMLCSSlast=0;a.HTMLCSSi=-1;a.HTMLCSSchunk=this.config.EqnChunk;a.HTMLCSSdelay=!1},Translate:function(a,b){if(a.parentNode){b.HTMLCSSdelay&&(b.HTMLCSSdelay=!1,f.RestartAfter(MathJax.Callback.Delay(this.config.EqnChunkDelay)));var d=a.MathJax.elementJax,c=d.root,e=document.getElementById(d.inputID+"-Frame"),g=d.HTMLCSS.display?e.parentNode:e;this.em=k.mbase.prototype.em=d.HTMLCSS.em*d.HTMLCSS.scale;this.outerEm=d.HTMLCSS.em;this.scale=d.HTMLCSS.scale;this.linebreakWidth=d.HTMLCSS.lineWidth;e.style.fontSize=d.HTMLCSS.fontSize;this.initImg(e);this.initHTML(c,e);c.setTeXclass();try{c.toHTML(e,g)}catch(t){if(t.restart)for(;e.firstChild;)e.removeChild(e.firstChild);throw t;}d.HTMLCSS.isHidden&&a.parentNode.insertBefore(g,a);g.className=g.className.split(/ /)[0];this.hideProcessedMath&&(g.className+=" MathJax_Processed",a.MathJax.preview&&(d.HTMLCSS.preview=a.MathJax.preview,delete a.MathJax.preview),b.HTMLCSSeqn+=b.i-b.HTMLCSSi,b.HTMLCSSi=b.i,b.HTMLCSSeqn>=b.HTMLCSSlast+b.HTMLCSSchunk&&(this.postTranslate(b),b.HTMLCSSchunk=Math.floor(b.HTMLCSSchunk*this.config.EqnChunkFactor),b.HTMLCSSdelay=!0))}},postTranslate:function(a){var b=a.jax[this.id];if(this.hideProcessedMath){for(var d=a.HTMLCSSlast,c=a.HTMLCSSeqn;d<c;d++){var e=b[d];if(e&&e.MathJax.elementJax){e.previousSibling.className=e.previousSibling.className.split(/ /)[0];var g=e.MathJax.elementJax.HTMLCSS;g.preview&&(g.preview.innerHTML="",e.MathJax.preview=g.preview,delete g.preview)}}this.forceReflow&&(b=(document.styleSheets||[])[0]||{},b.disabled=!0,b.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 f.getJaxFor(a)},getHoverSpan:function(a,b){return a.root.HTMLspanElement()},getHoverBBox:function(a,b,d){b=b.bbox;a=a.HTMLCSS.outerEm;a={w:b.w*a,h:b.h*a,d:b.d*a};b.width&&(a.width=b.width);return a},Zoom:function(a,h,d,c,e){h.className="MathJax";h.style.fontSize=a.HTMLCSS.fontSize;e=h.appendChild(this.EmExSpan.cloneNode(!0));var g=e.lastChild.firstChild.offsetHeight/60;this.em=k.mbase.prototype.em=g;this.outerEm=g/a.HTMLCSS.scale;e.parentNode.removeChild(e);this.idPostfix="-zoom";a.root.toHTML(h,h);this.idPostfix="";if(e=a.root.HTMLspanElement().bbox.width){h.style.width=Math.floor(c-1.5*b.em)+"px";h.style.display="inline-block";for(a=document.getElementById((a.root.id||"MathJax-Span-"+a.root.spanID)+"-zoom").firstChild;a&&a.style.width!==e;)a=a.nextSibling;a&&(a.style.width="100%")}h.style.position="absolute";e||(d.style.position="absolute");a=h.offsetWidth;c=h.offsetHeight;e=d.offsetHeight;g=d.offsetWidth;0===g&&(g=d.parentNode.offsetWidth);h.style.position=d.style.position="";return{Y:-m.getBBox(h).h,mW:g,mH:e,zW:a,zH:c}},initImg:function(a){},initHTML:function(a,b){},initFont:function(a){var h=b.FONTDATA.FONTS,d=b.config.availableFonts;if(d&&d.length&&b.Font.testFont(h[a]))return h[a].available=!0,null;if(!this.allowWebFonts)return null;h[a].isWebFont=!0;b.FontFaceBug&&(h[a].family=a,b.msieFontCSSBug&&(h[a].family+="-Web"));return c.Styles({"@font-face":this.Font.fontFace(a)})},Remove:function(a){var b=document.getElementById(a.inputID+"-Frame");b&&(a.HTMLCSS.display&&(b=b.parentNode),b.parentNode.removeChild(b));delete a.HTMLCSS},getHD:function(a){var b=a.style.position;a.style.position="absolute";this.HDimg.style.height="0px";a.appendChild(this.HDspan);var d={h:a.offsetHeight};this.HDimg.style.height=d.h+"px";d.d=a.offsetHeight-d.h;d.h-=d.d;d.h/=this.em;d.d/=this.em;a.removeChild(this.HDspan);a.style.position=b;return d},getW:function(a){var b,d;b=(a.bbox||{}).w;var c=a;if(a.bbox&&a.bbox.exactW)return b;if(a.bbox&&0<=b&&!this.initialSkipBug||this.negativeBBoxes||!a.firstChild)b=a.offsetWidth,d=a.parentNode.offsetHeight;else if(a.bbox&&0>b&&this.msieNegativeBBoxBug)b=-a.offsetWidth,d=a.parentNode.offsetHeight;else{if(this.initialSkipBug){var e=a.style.position;a.style.position="absolute";c=this.startMarker;a.insertBefore(c,a.firstChild)}a.appendChild(this.endMarker);b=this.endMarker.offsetLeft-c.offsetLeft;a.removeChild(this.endMarker);this.initialSkipBug&&(a.removeChild(c),a.style.position=e)}null!=d&&(a.parentNode.HH=d/this.em);return b/this.em},Measured:function(a,b){var d=a.bbox;if(null==d.width&&d.w&&!d.isMultiline){var c=this.getW(a);d.rw+=c-d.w;d.w=c;d.exactW=!0}b||(b=a.parentNode);b.bbox||(b.bbox=d);return a},Remeasured:function(a,b){b.bbox=this.Measured(a,b).bbox},MeasureSpans:function(a){var b=[],d,c,e,g,f;c=0;for(e=a.length;c<e;c++)if(d=a[c])g=d.bbox,f=this.parentNode(d),g.exactW||g.width||0===g.w||g.isMultiline?f.bbox||(f.bbox=g):this.negativeBBoxes||!d.firstChild||0<=g.w&&!this.initialSkipBug||0>g.w&&this.msieNegativeBBoxBug?b.push([d]):this.initialSkipBug?(g=this.startMarker.cloneNode(!0),f=this.endMarker.cloneNode(!0),d.insertBefore(g,d.firstChild),d.appendChild(f),b.push([d,g,f,d.style.position]),d.style.position="absolute"):(f=this.endMarker.cloneNode(!0),d.appendChild(f),b.push([d,null,f]));c=0;for(e=b.length;c<e;c++)d=b[c][0],g=d.bbox,f=this.parentNode(d),0<=g.w&&!this.initialSkipBug||this.negativeBBoxes||!d.firstChild?(a=d.offsetWidth,f.HH=f.offsetHeight/this.em):0>g.w&&this.msieNegativeBBoxBug?(a=-d.offsetWidth,f.HH=f.offsetHeight/this.em):a=b[c][2].offsetLeft-((b[c][1]||{}).offsetLeft||0),a/=this.em,g.rw+=a-g.w,g.w=a,g.exactW=!0,f.bbox||(f.bbox=g);c=0;for(e=b.length;c<e;c++)d=b[c],d[1]&&(d[1].parentNode.removeChild(d[1]),d[0].style.position=d[3]),d[2]&&d[2].parentNode.removeChild(d[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,h,d){"string"!==typeof a&&(a=a.toString());if(""===a)return"";if(a===k.SIZE.NORMAL)return 1;if(a===k.SIZE.BIG)return 2;if(a===k.SIZE.SMALL)return.71;if("infinity"===a)return b.BIGDIMEN;var c=this.FONTDATA.TeX_factor;if(a.match(/mathspace$/))return b.MATHSPACE[a]*c;var e=a.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);a=parseFloat(e[1]||"1");e=e[2];null==d&&(d=1);null==h&&(h=1);return"em"===e?a*c:"ex"===e?a*b.TeX.x_height*c:"%"===e?a/100*d:"px"===e?a/b.em:"pt"===e?a/10*c:"pc"===e?1.2*a*c:"in"===e?a*this.pxPerInch/b.em:"cm"===e?a*this.pxPerInch/b.em/2.54:"mm"===e?a*this.pxPerInch/b.em/25.4:"mu"===e?a/18*c*h:a*c*d},thickness2em:function(a,h){var d=b.TeX.rule_thickness;return a===k.LINETHICKNESS.MEDIUM?d:a===k.LINETHICKNESS.THIN?.67*d:a===k.LINETHICKNESS.THICK?1.67*d:this.length2em(a,h,d)},getPadding:function(a){var b={top:0,right:0,bottom:0,left:0},d=!1,c;for(c in b)if(b.hasOwnProperty(c)){var e=a.style["padding"+c.charAt(0).toUpperCase()+c.substr(1)];e&&(b[c]=this.length2em(e),d=!0)}return d?b:!1},getBorders:function(a){var b={top:0,right:0,bottom:0,left:0},d={},c=!1,e;for(e in b)if(b.hasOwnProperty(e)){var g="border"+e.charAt(0).toUpperCase()+e.substr(1);a.style[g+"Style"]&&(c=!0,b[e]=this.length2em(a.style[g+"Width"]),d[g]=[a.style[g+"Width"],a.style[g+"Style"],a.style[g+"Color"]].join(" "))}b.css=d;return c?b:!1},setBorders:function(a,b){if(b)for(var d in b.css)b.css.hasOwnProperty(d)&&(a.style[d]=b.css[d])},createStrut:function(a,b,d){b=this.Element("span",{isMathJax:!0,style:{display:"inline-block",overflow:"hidden",height:b+"px",width:"1px",marginRight:"-1px"}});d?a.insertBefore(b,a.firstChild):a.appendChild(b);return b},createBlank:function(a,b,d){b=this.Element("span",{isMathJax:!0,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(b)}});d?a.insertBefore(b,a.firstChild):a.appendChild(b);return b},createShift:function(a,b,d){b=this.Element("span",{style:{marginLeft:this.Em(b)},isMathJax:!0});d?a.insertBefore(b,a.firstChild):a.appendChild(b);return b},createSpace:function(a,h,d,c,e,g){h<-d&&(d=-h);var f=this.Em(h+d),v=this.Em(-d);this.msieInlineBlockAlignBug&&(v=this.Em(b.getHD(a.parentNode).d-d));a.isBox||g?(g=null==a.scale?1:a.scale,a.bbox={exactW:!0,h:h*g,d:d*g,w:c*g,rw:c*g,lw:0},a.style.height=f,a.style.verticalAlign=v,a.HH=(h+d)*g):a=this.addElement(a,"span",{style:{height:f,verticalAlign:v},isMathJax:!0});0<=c?(a.style.width=this.Em(c),a.style.display="inline-block",a.style.overflow="hidden"):(this.msieNegativeSpaceBug&&(a.style.height=""),a.style.marginLeft=this.Em(c),b.safariNegativeSpaceBug&&a.parentNode.firstChild==a&&this.createBlank(a,0,!0));e&&e!==k.COLOR.TRANSPARENT&&(a.style.backgroundColor=e,a.style.position="relative");return a},createRule:function(a,h,d,c,e){h<-d&&(d=-h);var g=b.TeX.min_rule_thickness,f=1;0<c&&c*this.em<g&&(c=g/this.em);0<h+d&&(h+d)*this.em<g&&(f=1/(h+d)*(g/this.em),h*=f,d*=f);e=e?"solid "+e:"solid";e=this.Em(c)+" "+e;g=1===f?this.Em(h+d):g+"px";f=this.Em(-d);e=this.addElement(a,"span",{style:{borderLeft:e,display:"inline-block",overflow:"hidden",width:0,height:g,verticalAlign:f},bbox:{h:h,d:d,w:c,rw:c,lw:0,exactW:!0},noAdjust:!0,HH:h+d,isMathJax:!0});0<c&&0==e.offsetWidth&&(e.style.width=this.Em(c));if(a.isBox||"mspace"==a.className)a.bbox=e.bbox,a.HH=h+d;return e},createFrame:function(a,b,d,c,e,g){b<-d&&(d=-b);var f=2*e;this.msieFrameSizeBug&&(c<f&&(c=f),b+d<f&&(b=f-d));this.msieBorderWidthBug&&(f=0);var k=this.Em(b+d-f),l=this.Em(-d-e),f=this.Em(c-f);e=this.Em(e)+" "+g;a=this.addElement(a,"span",{style:{border:e,display:"inline-block",overflow:"hidden",width:f,height:k},bbox:{h:b,d:d,w:c,rw:c,lw:0,exactW:!0},noAdjust:!0,HH:b+d,isMathJax:!0});l&&(a.style.verticalAlign=l);return a},parentNode:function(a){a=a.parentNode;"a"===a.nodeName.toLowerCase()&&(a=a.parentNode);return a},createStack:function(a,b,d){this.msiePaddingWidthBug&&this.createStrut(a,0);var c=String(d).match(/%$/),e=c||null==d?0:d;a=this.addElement(a,"span",{noAdjust:!0,HH:0,isMathJax:!0,style:{display:"inline-block",position:"relative",width:c?"100%":this.Em(e),height:0}});b||(a.parentNode.bbox=a.bbox={exactW:!0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:e,lw:this.BIGDIMEN,rw:c||null==d?-this.BIGDIMEN:d},c&&(a.bbox.width=d));return a},createBox:function(a,b){var d=this.addElement(a,"span",{style:{position:"absolute"},isBox:!0,isMathJax:!0});null!=b&&(d.style.width=b);return d},addBox:function(a,b){b.style.position="absolute";b.isBox=b.isMathJax=!0;return a.appendChild(b)},placeBox:function(a,h,d,c){a.isMathJax=!0;var e=b.parentNode(a),g=a.bbox,f=e.bbox;this.msiePlaceBoxBug&&this.addText(a,this.NBSP);this.imgSpaceBug&&this.addText(a,this.imgSpace);var k,l=0;k=null!=a.HH?a.HH:g?Math.max(3,g.h+g.d):a.offsetHeight/this.em;a.noAdjust||(k=Math.round((k+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(k)}}):(this.addElement(a,"span",{isMathJax:!0,style:{display:"inline-block",width:0,height:this.Em(k)}}),b.chromeHeightBug&&(k-=(a.lastChild.offsetHeight-Math.round(k*this.em))/this.em)));if(g&&(this.initialSkipBug&&(0>g.lw&&(l=g.lw,b.createBlank(a,-l,!0)),g.rw>g.w&&b.createBlank(a,g.rw-g.w+.1)),!this.msieClipRectBug&&!g.noclip&&!c)){c=3/this.em;var m=null==g.H?g.h:g.H,r=k+(null==g.D?g.d:g.D)+c,p=g.lw-3*c,n=1E3;this.initialSkipBug&&0>g.lw&&(p=-3*c);g.isFixed&&(n=g.width-p);a.style.clip="rect("+this.Em(k-m-c)+" "+this.Em(n)+" "+this.Em(r)+" 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d=a.bbox;d&&(d.w=b,d.exactW=!0);if(d=a.parentNode.bbox)d.w=b,d.exactW=!0}else a.style.width=a.parentNode.style.width="100%",a.bbox&&(a.bbox.width=b),a.parentNode.bbox&&(a.parentNode.bbox.width=b)},createDelimiter:function(a,b,d,u,e){if(b){u||(u=1);d instanceof Array||(d=[d,d]);var g=d[1];d=d[0];for(var t={alias:b};t.alias;)b=t.alias,(t=this.FONTDATA.DELIMITERS[b])||(t={HW:[0,this.FONTDATA.VARIANT[k.VARIANT.NORMAL]]});t.load&&f.RestartAfter(c.Require(this.fontDir+"/fontdata-"+t.load+".js"));for(var l=0,m=t.HW.length;l<m;l++)if(t.HW[l][0]*u>=d-.01||l==m-1&&!t.stretch){t.HW[l][2]&&(u*=t.HW[l][2]);t.HW[l][3]&&(b=t.HW[l][3]);d=this.addElement(a,"span");this.createChar(d,[b,t.HW[l][1]],u,e);a.bbox=d.bbox;a.offset=.65*a.bbox.w;a.scale=u;return}if(t.stretch)this["extendDelimiter"+t.dir](a,g,t.stretch,u,e)}else a.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0},a.bbox.rw=a.bbox.w,this.createSpace(a,a.bbox.h,a.bbox.d,a.bbox.w)},extendDelimiterV:function(a,b,d,c,e){var g=this.createStack(a,!0),f=this.createBox(g),k=this.createBox(g);this.createChar(f,d.top||d.ext,c,e);this.createChar(k,d.bot||d.ext,c,e);var l={bbox:{w:0,lw:0,rw:0}},m=l,r,p=f.bbox.h+f.bbox.d+k.bbox.h+k.bbox.d,n=-f.bbox.h;this.placeBox(f,0,n,!0);n-=f.bbox.d;d.mid&&(m=this.createBox(g),this.createChar(m,d.mid,c,e),p+=m.bbox.h+m.bbox.d);d.min&&b<p*d.min&&(b=p*d.min);if(b>p){l=this.Element("span");this.createChar(l,d.ext,c,e);r=l.bbox.h+l.bbox.d;var q=r-.05,z,y,D=d.mid?2:1;y=z=Math.min(Math.ceil((b-p)/(D*q)),this.maxStretchyParts);d.fullExtenders||(q=(b-p)/(D*z));b=z/(z+1)*(r-q);q=r-b;for(n+=b+q-l.bbox.h;0<D--;){for(;0<z--;)this.msieCloneNodeBug?(r=this.Element("span"),this.createChar(r,d.ext,c,e)):r=l.cloneNode(!0),r.bbox=l.bbox,n-=q,this.placeBox(this.addBox(g,r),0,n,!0);n+=b-l.bbox.d;d.mid&&D&&(this.placeBox(m,0,n-m.bbox.h,!0),z=y,n+=-(m.bbox.h+m.bbox.d)+b+q-l.bbox.h)}}else n+=(p-b)/2,d.mid&&(this.placeBox(m,0,n-m.bbox.h,!0),n+=-(m.bbox.h+m.bbox.d)),n+=(p-b)/2;this.placeBox(k,0,n-k.bbox.h,!0);n-=k.bbox.h+k.bbox.d;a.bbox={w:Math.max(f.bbox.w,l.bbox.w,k.bbox.w,m.bbox.w),lw:Math.min(f.bbox.lw,l.bbox.lw,k.bbox.lw,m.bbox.lw),rw:Math.max(f.bbox.rw,l.bbox.rw,k.bbox.rw,m.bbox.rw),h:0,d:-n,exactW:!0};a.scale=c;a.offset=.55*a.bbox.w;a.isMultiChar=!0;this.setStackWidth(g,a.bbox.w)},extendDelimiterH:function(a,b,d,c,e){var g=this.createStack(a,!0),f=this.createBox(g),k=this.createBox(g);this.createChar(f,d.left||d.rep,c,e);this.createChar(k,d.right||d.rep,c,e);var l=this.Element("span");this.createChar(l,d.rep,c,e);var m={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},r;this.placeBox(f,-f.bbox.lw,0,!0);var p=f.bbox.rw-f.bbox.lw+(k.bbox.rw-k.bbox.lw)-.05,n=f.bbox.rw-f.bbox.lw-.025;d.mid&&(m=this.createBox(g),this.createChar(m,d.mid,c,e),p+=m.bbox.w);d.min&&b<p*d.min&&(b=p*d.min);if(b>p){r=l.bbox.rw-l.bbox.lw;var q=r-.05,z,y,D=d.mid?2:1;y=z=Math.min(Math.ceil((b-p)/(D*q)),this.maxStretchyParts);d.fillExtenders||(q=(b-p)/(D*z));b=z/(z+1)*(r-q);q=r-b;for(n-=l.bbox.lw+b;0<D--;){for(;0<z--;)this.cloneNodeBug?(r=this.Element("span"),this.createChar(r,d.rep,c,e)):r=l.cloneNode(!0),r.bbox=l.bbox,this.placeBox(this.addBox(g,r),n,0,!0),n+=q;d.mid&&D&&(this.placeBox(m,n,0,!0),n+=m.bbox.w-b,z=y)}}else n-=(p-b)/2,d.mid&&(this.placeBox(m,n,0,!0),n+=m.bbox.w),n-=(p-b)/2;this.placeBox(k,n,0,!0);a.bbox={w:n+k.bbox.rw,lw:0,rw:n+k.bbox.rw,H:Math.max(f.bbox.h,l.bbox.h,k.bbox.h,m.bbox.h),D:Math.max(f.bbox.d,l.bbox.d,k.bbox.d,m.bbox.d),h:l.bbox.h,d:l.bbox.d,exactW:!0};a.scale=c;a.isMultiChar=!0;this.setStackWidth(g,a.bbox.w)},createChar:function(a,b,d,c){a.isMathJax=!0;var e=a,g="",f={fonts:[b[1]],noRemap:!0};c&&c===k.VARIANT.BOLD&&(f.fonts=[b[1]+"-bold",b[1]]);"string"!==typeof b[1]&&(f=b[1]);if(b[0]instanceof Array){c=0;for(var l=b[0].length;c<l;c++)g+=String.fromCharCode(b[0][c])}else g=String.fromCharCode(b[0]);b[4]&&(d*=b[4]);1!==d||b[3]?(e=this.addElement(a,"span",{style:{fontSize:this.Percent(d)},scale:d,isMathJax:!0}),this.handleVariant(e,f,g),a.bbox=e.bbox):this.handleVariant(a,f,g);b[2]&&(a.style.marginLeft=this.Em(b[2]));b[3]&&(a.firstChild.style.verticalAlign=this.Em(b[3]),a.bbox.h+=b[3],0>a.bbox.h&&(a.bbox.h=0));b[5]&&(a.bbox.h+=b[5]);b[6]&&(a.bbox.d+=b[6]);this.AccentBug&&0===a.bbox.w&&(e.firstChild.nodeValue+=this.NBSP)},positionDelimiter:function(a,c){c-=a.bbox.h;a.bbox.d-=c;a.bbox.h+=c;c&&(this.safariVerticalAlignBug||this.konquerorVerticalAlignBug||this.operaVerticalAlignBug&&a.isMultiChar?(""===a.firstChild.style.display&&""!==a.style.top&&(a=a.firstChild,c-=b.unEm(a.style.top)),a.style.position="relative",a.style.top=this.Em(-c)):(a.style.verticalAlign=this.Em(c),b.ffVerticalAlignBug&&b.createRule(a.parentNode,a.bbox.h,0,0)))},handleVariant:function(a,b,d){var c="",e,g,f,l=a,m=!!a.style.fontFamily;if(0!==d.length){a.bbox||(a.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN});b||(b=this.FONTDATA.VARIANT[k.VARIANT.NORMAL]);f=b;for(var p=0,r=d.length;p<r;p++){b=f;e=d.charCodeAt(p);d.charAt(p);if(55296<=e&&56319>e)p++,e=(e-55296<<10)+(d.charCodeAt(p)-56320)+65536,this.FONTDATA.RemapPlane1&&(b=this.FONTDATA.RemapPlane1(e,b),e=b.n,b=b.variant);else{var n,q=this.FONTDATA.RANGES;g=0;for(n=q.length;g<n;g++)if("alpha"!==q[g].name||!b.noLowerCase){var w=b["offset"+q[g].offset];if(w&&e>=q[g].low&&e<=q[g].high){q[g].remap&&q[g].remap[e]?e=w+q[g].remap[e]:(e=e-q[g].low+w,q[g].add&&(e+=q[g].add));b["variant"+q[g].offset]&&(b=this.FONTDATA.VARIANT[b["variant"+q[g].offset]]);break}}}b.remap&&b.remap[e]&&(b.remap[e]instanceof Array?(b=b.remap[e],e=b[0],b=this.FONTDATA.VARIANT[b[1]]):"string"===typeof b.remap[e]?(d=b.remap[e]+d.substr(p+1),p=0,r=d.length,e=d.charCodeAt(0)):(e=b.remap[e],b.remap.variant&&(b=this.FONTDATA.VARIANT[b.remap.variant])));this.FONTDATA.REMAP[e]&&!b.noRemap&&(e=this.FONTDATA.REMAP[e],e instanceof Array&&(b=this.FONTDATA.VARIANT[e[1]],e=e[0]),"string"===typeof e&&(d=e+d.substr(p+1),p=0,r=d.length,e=e.charCodeAt(0)));g=this.lookupChar(b,e);b=g[e];if(m||!this.checkFont(g,l.style)&&!b[5].img)c.length&&(this.addText(l,c),c=""),n=!!l.style.fontFamily||!!a.style.fontStyle||!!a.style.fontWeight||!g.directory||m,m=!1,l!==a&&(n=!this.checkFont(g,a.style),l=a),n&&(l=this.addElement(a,"span",{isMathJax:!0,subSpan:!0})),this.handleFont(l,g,l!==a);c=this.handleChar(l,g,b,e,c);(b[5]||{}).space||(b[0]/1E3>a.bbox.h&&(a.bbox.h=b[0]/1E3),b[1]/1E3>a.bbox.d&&(a.bbox.d=b[1]/1E3));a.bbox.w+b[3]/1E3<a.bbox.lw&&(a.bbox.lw=a.bbox.w+b[3]/1E3);a.bbox.w+b[4]/1E3>a.bbox.rw&&(a.bbox.rw=a.bbox.w+b[4]/1E3);a.bbox.w+=b[2]/1E3}c.length&&this.addText(l,c);a.scale&&1!==a.scale&&(a.bbox.h*=a.scale,a.bbox.d*=a.scale,a.bbox.w*=a.scale,a.bbox.lw*=a.scale,a.bbox.rw*=a.scale);1==d.length&&g.skew&&g.skew[e]&&(a.bbox.skew=g.skew[e])}},checkFont:function(a,b){var d=b.fontWeight||"normal";d.match(/^\d+$/)&&(d=600<=parseInt(d)?"bold":"normal");return a.family.replace(/'/g,"")===b.fontFamily.replace(/'/g,"")&&(a.style||"normal")===(b.fontStyle||"normal")&&(a.weight||"normal")===d},handleFont:function(a,c,d){a.style.fontFamily=c.family;c.directory||(a.style.fontSize=Math.floor(100/b.scale+.5)+"%");if(!b.FontFaceBug||!c.isWebFont){var f=c.style||"normal";c=c.weight||"normal";if("normal"!==f||d)a.style.fontStyle=f;if("normal"!==c||d)a.style.fontWeight=c}},handleChar:function(a,c,d,f,e){var g=d[5];if(g.space)return e.length&&this.addText(a,e),b.createShift(a,d[2]/1E3),"";if(g.img)return this.handleImg(a,c,d,f,e);if(g.isUnknown&&this.FONTDATA.DELIMITERS[f])return e.length&&this.addText(a,e),e=a.scale,b.createDelimiter(a,f,0,1,c),"V"===this.FONTDATA.DELIMITERS[f].dir&&(a.style.verticalAlign=this.Em(a.bbox.d),a.bbox.h+=a.bbox.d,a.bbox.d=0),a.scale=e,d[0]=1E3*a.bbox.h,d[1]=1E3*a.bbox.d,d[2]=1E3*a.bbox.w,d[3]=1E3*a.bbox.lw,d[4]=1E3*a.bbox.rw,"";null==g.c&&(65535>=f?g.c=String.fromCharCode(f):(c=f-65536,g.c=String.fromCharCode((c>>10)+55296)+String.fromCharCode((c&1023)+56320)));if(g.rfix)return this.addText(a,e+g.c),b.createShift(a,g.rfix/1E3),"";if(d[2]||!this.msieAccentBug||e.length)return e+g.c;b.createShift(a,d[3]/1E3);b.createShift(a,(d[4]-d[3])/1E3);this.addText(a,g.c);b.createShift(a,-d[4]/1E3);return""},handleImg:function(a,b,c,f,e){return e},lookupChar:function(a,c){var d,f;if(!a.FONTS){var e=this.FONTDATA.FONTS,g=a.fonts||this.FONTDATA.VARIANT.normal.fonts;g instanceof Array||(g=[g]);a.fonts!=g&&(a.fonts=g);a.FONTS=[];d=0;for(f=g.length;d<f;d++)e[g[d]]&&(a.FONTS.push(e[g[d]]),e[g[d]].name=g[d])}d=0;for(f=a.FONTS.length;d<f;d++)if(e=a.FONTS[d],"string"===typeof e&&(delete a.FONTS,this.loadFont(e)),e[c])if(5===e[c].length&&(e[c][5]={}),b.allowWebFonts&&!e.available)this.loadWebFont(e);else return e;else this.findBlock(e,c);return this.unknownChar(a,c)},unknownChar:function(a,c){var d=a.defaultFont||{family:b.config.undefinedFamily};a.bold&&(d.weight="bold");a.italic&&(d.style="italic");d[c]||(d[c]=[800,200,500,0,500,{isUnknown:!0}]);f.signal.Post(["HTML-CSS Jax - unknown char",c,a]);return d},findBlock:function(a,b){if(a.Ranges)for(var c=0,f=a.Ranges.length;c<f&&!(b<a.Ranges[c][0]);c++)if(b<=a.Ranges[c][1]){for(var e=a.Ranges[c][2],g=a.Ranges.length-1;0<=g;g--)a.Ranges[g][2]==e&&a.Ranges.splice(g,1);this.loadFont(a.directory+"/"+e+".js")}},loadFont:function(a){var h=MathJax.Callback.Queue();h.Push(["Require",c,this.fontDir+"/"+a]);this.imgFonts&&(MathJax.isPacked||(a=a.replace(/\/([^\/]*)$/,b.imgPacked+"/$1")),h.Push(["Require",c,this.webfontDir+"/png/"+a]));f.RestartAfter(h.Push({}))},loadWebFont:function(a){a.available=a.isWebFont=!0;b.FontFaceBug&&(a.family=a.name,b.msieFontCSSBug&&(a.family+="-Web"));f.RestartAfter(this.Font.loadWebFont(a))},loadWebFontError:function(a,b){f.Startup.signal.Post("HTML-CSS Jax - disable web fonts");a.isWebFont=!1;this.config.imageFont&&this.config.imageFont===this.fontInUse?(this.imgFonts=!0,f.Startup.signal.Post("HTML-CSS Jax - switch to image fonts"),f.Startup.signal.Post("HTML-CSS Jax - using image fonts"),p(["WebFontNotAvailable","Web-Fonts not available -- using image fonts instead"],null,3E3),c.Require(this.directory+"/imageFonts.js",b)):(this.allowWebFonts=!1,b())},Element:MathJax.HTML.Element,addElement:MathJax.HTML.addElement,TextNode:MathJax.HTML.TextNode,addText:MathJax.HTML.addText,ucMatch:MathJax.HTML.ucMatch,BIGDIMEN:1E7,ID:0,idPostfix:"",GetID:function(){this.ID++;return 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g=d=0,k=this.HTMLgetMu(a);c.lspace&&(d=this.HTMLlength2em(e,c.lspace,k));c.voffset&&(g=this.HTMLlength2em(e,c.voffset,k));b.placeBox(e,d,g);a.bbox={h:e.bbox.h,d:e.bbox.d,w:e.bbox.w,exactW:!0,lw:Math.min(0,e.bbox.lw+d),rw:Math.max(e.bbox.w,e.bbox.rw+d),H:Math.max(null==e.bbox.H?-b.BIGDIMEN:e.bbox.H,e.bbox.h+g),D:Math.max(null==e.bbox.D?-b.BIGDIMEN:e.bbox.D,e.bbox.d-g)};""!==c.height&&(a.bbox.h=this.HTMLlength2em(e,c.height,k,"h",0));""!==c.depth&&(a.bbox.d=this.HTMLlength2em(e,c.depth,k,"d",0));""!==c.width&&(a.bbox.w=this.HTMLlength2em(e,c.width,k,"w",0));a.bbox.H<=a.bbox.h&&delete a.bbox.H;a.bbox.D<=a.bbox.d&&delete a.bbox.D;e=/^\s*(\d+(\.\d*)?|\.\d+)\s*(pt|em|ex|mu|px|pc|in|mm|cm)\s*$/;a.bbox.exact=!!(this.data[0]&&0==this.data[0].data.length||e.exec(c.height)||e.exec(c.width)||e.exec(c.depth));b.setStackWidth(f,a.bbox.w)}this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLlength2em:function(a,c,d,f,e){null==e&&(e=-b.BIGDIMEN);var 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f=this.data[0].toHTML(a);null!=c?this.data[0].HTMLstretchV(a,b,c):null!=b&&this.data[0].HTMLstretchH(a,b);a.bbox=f.bbox}this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLstretchH:k.mbase.HTMLstretchH,HTMLstretchV:k.mbase.HTMLstretchV});k.mfrac.Augment({toHTML:function(a){a=this.HTMLcreateSpan(a);var c=b.createStack(a),d=b.createBox(c),f=b.createBox(c);b.MeasureSpans([this.HTMLboxChild(0,d),this.HTMLboxChild(1,f)]);var e=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled"),g=this.HTMLgetScale(),k=e.displaystyle,l=b.TeX.axis_height*g;if(e.bevelled){var e=k?.4:.15,m=Math.max(d.bbox.h+d.bbox.d,f.bbox.h+f.bbox.d)+2*e,c=b.createBox(c);b.createDelimiter(c,47,m);b.placeBox(d,0,(d.bbox.d-d.bbox.h)/2+l+e);b.placeBox(c,d.bbox.w-e/2,(c.bbox.d-c.bbox.h)/2+l);b.placeBox(f,d.bbox.w+c.bbox.w-e,(f.bbox.d-f.bbox.h)/2+l-e)}else{var m=Math.max(d.bbox.w,f.bbox.w),p=b.thickness2em(e.linethickness,g),n,q,C=b.TeX.min_rule_thickness/this.em;k?(n=b.TeX.num1,q=b.TeX.denom1):(n=0===p?b.TeX.num3:b.TeX.num2,q=b.TeX.denom2);n*=g;q*=g;0===p?(g=Math.max((k?7:3)*b.TeX.rule_thickness,2*C),k=n-d.bbox.d-(f.bbox.h-q),k<g&&(n+=(g-k)/2,q+=(g-k)/2)):(g=Math.max((k?2:0)*C+p,p/2+1.5*C),k=n-d.bbox.d-(l+p/2),k<g&&(n+=g-k),k=l-p/2-(f.bbox.h-q),k<g&&(q+=g-k),c=b.createBox(c),b.createRule(c,p,0,m+2*p),b.placeBox(c,0,l-p/2));b.alignBox(d,e.numalign,n);b.alignBox(f,e.denomalign,-q)}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)}}});k.msqrt.Augment({toHTML:function(a){a=this.HTMLcreateSpan(a);var c=b.createStack(a),d=b.createBox(c),f=b.createBox(c),e=b.createBox(c),g=this.HTMLgetScale(),k=b.TeX.rule_thickness*g,l,m,p;l=this.Get("displaystyle")?b.TeX.x_height*g:k;l=Math.max(k+l/4,1.5*b.TeX.min_rule_thickness/this.em);var n=this.HTMLboxChild(0,d);m=n.bbox.h+n.bbox.d+l+k;b.createDelimiter(e,8730,m,g);b.MeasureSpans([n,e]);p=n.bbox.w;var q=0;if(e.isMultiChar||b.AdjustSurd&&b.imgFonts)e.bbox.w*=.95;e.bbox.h+e.bbox.d>m&&(l=(e.bbox.h+e.bbox.d-(m-k))/2);m=b.FONTDATA.DELIMITERS[b.FONTDATA.RULECHAR];!m||p<m.HW[0][0]*g||.75>g?b.createRule(f,0,k,p):b.createDelimiter(f,b.FONTDATA.RULECHAR,p,g);m=n.bbox.h+l+k;l=m*b.rfuzz;e.isMultiChar&&(l=b.rfuzz);q=this.HTMLaddRoot(c,e,q,e.bbox.h+e.bbox.d-m,g);b.placeBox(e,q,m-e.bbox.h);b.placeBox(f,q+e.bbox.w,m-f.bbox.h+l);b.placeBox(d,q+e.bbox.w,0);this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLaddRoot:function(a,b,c,f,e){return c}});k.mroot.Augment({toHTML:k.msqrt.prototype.toHTML,HTMLaddRoot:function(a,c,d,f,e){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();f=this.HTMLrootHeight(c.bbox.h+c.bbox.d,e,a)-f;e=Math.min(a.bbox.w,a.bbox.rw);d=Math.max(e,c.offset);b.placeBox(a,d-e,f);return d-c.offset},HTMLrootHeight:function(a,b,c){return.45*(a-.9*b)+.6*b+Math.max(0,c.bbox.d-.075)}});k.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 f=this.HTMLcomputeBBox(a),e=a.bbox.h,g=a.bbox.d,b=0,c=f.length;b<c;b++)f[b].HTMLstretchV(a,e,g);f.length&&this.HTMLcomputeBBox(a,!0);this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLcomputeBBox:function(a,b){var c=a.bbox={},f=[];this.HTMLcheckStretchy(this.data.open,c,f,b);this.HTMLcheckStretchy(this.data[0],c,f,b);for(var e=1,g=this.data.length;e<g;e++)this.data[e]&&(this.HTMLcheckStretchy(this.data["sep"+e],c,f,b),this.HTMLcheckStretchy(this.data[e],c,f,b));this.HTMLcheckStretchy(this.data.close,c,f,b);this.HTMLcleanBBox(c);return f},HTMLcheckStretchy:function(a,b,c,f){a&&(!f&&a.HTMLcanStretch("Vertical")&&(c.push(a),a=a.CoreMO()||a),this.HTMLcombineBBoxes(a,b))}});k.menclose.Augment({toHTML:k.mbase.HTMLautoload});k.maction.Augment({toHTML:k.mbase.HTMLautoload});k.semantics.Augment({toHTML:function(a,b,c){a=this.HTMLcreateSpan(a);if(null!=this.data[0]){var f=this.data[0].toHTML(a);null!=c?this.data[0].HTMLstretchV(a,b,c):null!=b&&this.data[0].HTMLstretchH(a,b);a.bbox=f.bbox}this.HTMLhandleSpace(a);return a},HTMLstretchH:k.mbase.HTMLstretchH,HTMLstretchV:k.mbase.HTMLstretchV});k.munderover.Augment({toHTML:function(a,c,d){var f=this.getValues("displaystyle","accent","accentunder","align");if(!f.displaystyle&&null!=this.data[this.base]&&this.data[this.base].CoreMO().Get("movablelimits"))return k.msubsup.prototype.toHTML.call(this,a);a=this.HTMLcreateSpan(a);var e=this.HTMLgetScale(),g=b.createStack(a),l=[],m=[],p=[],n,r,q;r=0;for(q=this.data.length;r<q;r++)null!=this.data[r]&&(n=l[r]=b.createBox(g),m[r]=this.data[r].toHTML(n),r==this.base?(null!=d?this.data[this.base].HTMLstretchV(n,c,d):null!=c&&this.data[this.base].HTMLstretchH(n,c),p[r]=null==d&&null!=c?!1:this.data[r].HTMLcanStretch("Horizontal")):p[r]=this.data[r].HTMLcanStretch("Horizontal"));b.MeasureSpans(m);g=m=-b.BIGDIMEN;r=0;for(q=this.data.length;r<q;r++)this.data[r]&&(l[r].bbox.w>g&&(g=l[r].bbox.w),!p[r]&&g>m&&(m=g));null==d&&null!=c?m=c:m==-b.BIGDIMEN&&(m=g);r=g=0;for(q=this.data.length;r<q;r++)this.data[r]&&(n=l[r],p[r]&&(n.bbox=this.data[r].HTMLstretchH(n,m).bbox),n.bbox.w>g&&(g=n.bbox.w));c=b.TeX.rule_thickness;d=b.FONTDATA.TeX_factor;var p=l[this.base]||{bbox:this.HTMLzeroBBox()},C,w,z,y=0;p.bbox.ic&&(y=1.3*p.bbox.ic+.05);r=0;for(q=this.data.length;r<q;r++)null!=this.data[r]&&(n=l[r],m=b.TeX.big_op_spacing5*e,(z=r!=this.base&&f[this.ACCENTS[r]])&&n.bbox.w<=1/b.em+1E-4&&(n.bbox.w=n.bbox.rw-n.bbox.lw,n.bbox.noclip=!0,n.bbox.lw&&n.insertBefore(b.createSpace(n.parentNode,0,0,-n.bbox.lw),n.firstChild),b.createBlank(n,0,0,n.bbox.rw+.1)),C={left:0,center:(g-n.bbox.w)/2,right:g-n.bbox.w}[f.align],w=0,r==this.over?(z?(z=Math.max(c*e*d,2.5/this.em),m=0,p.bbox.skew&&(C+=p.bbox.skew)):(z=b.TeX.big_op_spacing1*e*d,w=b.TeX.big_op_spacing3*e*d,z=Math.max(z,w-Math.max(0,n.bbox.d))),z=Math.max(z,1.5/this.em),C+=y/2,w=p.bbox.h+n.bbox.d+z,n.bbox.h+=m):r==this.under&&(z?(z=3*c*e*d,m=0):(z=b.TeX.big_op_spacing2*e*d,w=b.TeX.big_op_spacing4*e*d,z=Math.max(z,w-n.bbox.h)),z=Math.max(z,1.5/this.em),C-=y/2,w=-(p.bbox.d+n.bbox.h+z),n.bbox.d+=m),b.placeBox(n,C,w));this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLstretchH:k.mbase.HTMLstretchH,HTMLstretchV:k.mbase.HTMLstretchV});k.msubsup.Augment({toHTML:function(a,c,d){a=this.HTMLcreateSpan(a);var f=this.HTMLgetScale(),e=this.HTMLgetMu(a),g=b.createStack(a),k,l=[],m=b.createBox(g);this.data[this.base]?(l.push(this.data[this.base].toHTML(m)),null!=d?this.data[this.base].HTMLstretchV(m,c,d):null!=c&&this.data[this.base].HTMLstretchH(m,c)):m.bbox=this.HTMLzeroBBox();c=b.TeX.x_height*f;d=b.TeX.scriptspace*f*.75;var n;this.HTMLnotEmpty(this.data[this.sup])&&(n=b.createBox(g),l.push(this.data[this.sup].toHTML(n)));this.HTMLnotEmpty(this.data[this.sub])&&(k=b.createBox(g),l.push(this.data[this.sub].toHTML(k)));b.MeasureSpans(l);n&&(n.bbox.w+=d,n.bbox.rw=Math.max(n.bbox.w,n.bbox.rw));k&&(k.bbox.w+=d,k.bbox.rw=Math.max(k.bbox.w,k.bbox.rw));b.placeBox(m,0,0);var l=n?this.data[this.sup].HTMLgetScale():k?this.data[this.sub].HTMLgetScale():this.HTMLgetScale(),p=b.TeX.sup_drop*l,g=m.bbox.h-p,q=m.bbox.d+b.TeX.sub_drop*l,l=0;m.bbox.ic&&(m.bbox.w-=m.bbox.ic,l=1.3*m.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!==m.bbox.scale||this.data[this.base].Get("largeop")||(g=q=0);d=this.getValues("subscriptshift","superscriptshift");d.subscriptshift=""===d.subscriptshift?0:b.length2em(d.subscriptshift,e);d.superscriptshift=""===d.superscriptshift?0:b.length2em(d.superscriptshift,e);n?k?(q=Math.max(q,b.TeX.sub2*f),f*=b.TeX.rule_thickness,g-n.bbox.d-(k.bbox.h-q)<3*f&&(q=3*f-g+n.bbox.d+k.bbox.h,p=.8*c-(g-n.bbox.d),0<p&&(g+=p,q-=p)),b.placeBox(n,m.bbox.w+l,Math.max(g,d.superscriptshift)),b.placeBox(k,m.bbox.w,-Math.max(q,d.subscriptshift))):(k=this.getValues("displaystyle","texprimestyle"),k=b.TeX[k.displaystyle?"sup1":k.texprimestyle?"sup3":"sup2"],g=Math.max(g,k*f,n.bbox.d+.25*c,d.superscriptshift),b.placeBox(n,m.bbox.w+l,g,n.bbox)):k&&(q=Math.max(q,b.TeX.sub1*f,k.bbox.h-.8*c,d.subscriptshift),b.placeBox(k,m.bbox.w,-q,k.bbox));this.HTMLhandleSpace(a);this.HTMLhandleColor(a);return a},HTMLstretchH:k.mbase.HTMLstretchH,HTMLstretchV:k.mbase.HTMLstretchV});k.mmultiscripts.Augment({toHTML:k.mbase.HTMLautoload});k.mtable.Augment({toHTML:k.mbase.HTMLautoload});k["annotation-xml"].Augment({toHTML:k.mbase.HTMLautoload});k.math.Augment({toHTML:function(a,c){var d=this.Get("alttext");d&&""!==d&&c.setAttribute("aria-label",d);var l=b.addElement(a,"nobr",{isMathJax:!0});a=this.HTMLcreateSpan(l);var d=b.createStack(a),e=b.createBox(d),g;d.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)),k.mbase.prototype.displayAlign=f.config.displayAlign,k.mbase.prototype.displayIndent=f.config.displayIndent,g=this.data[0].toHTML(e),g.bbox.exactW=!1,g=b.Measured(g,e));b.placeBox(e,0,0);a.style.width=b.Em((Math.round(g.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;g&&null!=g.bbox.width&&(a.style.minWidth=g.bbox.minWidth||a.style.width,a.style.width=d.style.width=g.bbox.width,e.style.width="100%");this.HTMLhandleColor(a);g&&b.createRule(a,(g.bbox.h+l)*m,(g.bbox.d+l)*m,0);this.isMultiline||"block"!==this.Get("display")||null!=a.bbox.width||(d=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift"),d.indentalignfirst!==k.INDENTALIGN.INDENTALIGN&&(d.indentalign=d.indentalignfirst),d.indentalign===k.INDENTALIGN.AUTO&&(d.indentalign=this.displayAlign),c.style.textAlign=d.indentalign,d.indentshiftfirst!==k.INDENTSHIFT.INDENTSHIFT&&(d.indentshift=d.indentshiftfirst),"auto"===d.indentshift&&(d.indentshift=this.displayIndent),d.indentshift&&d.indentalign!==k.INDENTALIGN.CENTER&&(a.style[{left:"marginLeft",right:"marginRight"}[d.indentalign]]=b.Em(b.length2em(d.indentshift))));return a},HTMLspanElement:k.mbase.prototype.HTMLspanElement});k.TeXAtom.Augment({toHTML:function(a){a=this.HTMLcreateSpan(a);if(null!=this.data[0])if(this.texClass===k.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)})});f.Register.StartupHook("End Config",function(){f.Browser.Select({MSIE:function(a){var c=document.documentMode||0,d=a.versionAtLeast("7.0"),f=a.versionAtLeast("8.0")&&7<c,e="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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