/*
 *  /MathJax/config/TeX-AMS_HTML-full.js
 *  
 *  Copyright (c) 2010-11 Design Science, Inc.
 *
 *  Part of the MathJax library.
 *  See http://www.mathjax.org for details.
 * 
 *  Licensed under the Apache License, Version 2.0;
 *  you may not use this file except in compliance with the License.
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 */

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

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

MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"1.1.1",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%"}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js");

MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"1.1.7",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",showMathMenu:true,styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px"}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax.id==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set("Your browser does not support MathJax",null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js");

MathJax.Extension.tex2jax={version:"1.1.3",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,preview:"TeX"},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}this.createPatterns();this.scanElement(a,a.nextSibling)},createPatterns:function(){var d=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c<a;c++){d.push(this.patternQuote(b.inlineMath[c][0]));this.match[b.inlineMath[c][0]]={mode:"",end:b.inlineMath[c][1],pattern:this.endPattern(b.inlineMath[c][1])}}for(c=0,a=b.displayMath.length;c<a;c++){d.push(this.patternQuote(b.displayMath[c][0]));this.match[b.displayMath[c][0]]={mode:"; mode=display",end:b.displayMath[c][1],pattern:this.endPattern(b.displayMath[c][1])}}this.start=new RegExp(d.sort(this.sortLength).join("|")+(b.processEnvironments?"|\\\\begin\\{([^}]*)\\}":"")+(b.processEscapes?"|\\\\*\\\\\\$":""),"g");this.skipTags=new RegExp("^("+b.skipTags.join("|")+")$","i");this.ignoreClass=new RegExp("(^| )("+b.ignoreClass+")( |$)");this.processClass=new RegExp("(^| )("+b.processClass+")( |$)")},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d<c?-1:1))},scanElement:function(c,b,f){var a,e,d;while(c&&c!=b){if(c.nodeName.toLowerCase()==="#text"){if(!f){c=this.scanText(c)}}else{a=(typeof(c.className)==="undefined"?"":c.className);e=(typeof(c.tagName)==="undefined"?"":c.tagName);if(typeof(a)!=="string"){a=String(a)}if(c.firstChild&&!a.match(/(^| )MathJax/)&&!this.skipTags.exec(e)){d=(f||this.ignoreClass.exec(a))&&!this.processClass.exec(a);this.scanElement(c.firstChild,b,d)}}if(c){c=c.nextSibling}}},scanText:function(b){if(b.nodeValue.replace(/\s+/,"")==""){return b}var a,c;this.search={start:true};this.pattern=this.start;while(b){this.pattern.lastIndex=0;while(b&&b.nodeName.toLowerCase()==="#text"&&(a=this.pattern.exec(b.nodeValue))){if(this.search.start){b=this.startMatch(a,b)}else{b=this.endMatch(a,b)}}if(this.search.matched){b=this.encloseMath(b)}if(b){do{c=b;b=b.nextSibling}while(b&&(b.nodeName.toLowerCase()==="br"||b.nodeName.toLowerCase()==="#comment"));if(!b||b.nodeName!=="#text"){return c}}}return b},startMatch:function(a,b){var f=this.match[a[0]];if(f!=null){this.search={end:f.end,mode:f.mode,open:b,olen:a[0].length,opos:this.pattern.lastIndex-a[0].length};this.switchPattern(f.pattern)}else{if(a[0].substr(0,6)==="\\begin"){this.search={end:"\\end{"+a[1]+"}",mode:"; mode=display",open:b,olen:0,opos:this.pattern.lastIndex-a[0].length,isBeginEnd:true};this.switchPattern(this.endPattern(this.search.end))}else{var d=a[0].substr(0,a[0].length-1),g,c;if(d.length%2===0){c=[d.replace(/\\\\/g,"\\")];g=1}else{c=[d.substr(1).replace(/\\\\/g,"\\"),"$"];g=0}c=MathJax.HTML.Element("span",null,c);var e=MathJax.HTML.TextNode(b.nodeValue.substr(0,a.index));b.nodeValue=b.nodeValue.substr(a.index+a[0].length-g);b.parentNode.insertBefore(c,b);b.parentNode.insertBefore(e,c);this.pattern.lastIndex=g}}return b},endMatch:function(a,b){if(a[0]==this.search.end){this.search.close=b;this.search.cpos=this.pattern.lastIndex;this.search.clen=(this.search.isBeginEnd?0:a[0].length);this.search.matched=true;b=this.encloseMath(b);this.switchPattern(this.start)}return b},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=(a===this.start)},encloseMath:function(b){var a=this.search,f=a.close,e,c;if(a.cpos===f.length){f=f.nextSibling}else{f=f.splitText(a.cpos)}if(!f){e=f=MathJax.HTML.addText(a.close.parentNode,"")}a.close=f;c=(a.opos?a.open.splitText(a.opos):a.open);while(c.nextSibling&&c.nextSibling!==f){if(c.nextSibling.nodeValue!==null){if(c.nextSibling.nodeName==="#comment"){c.nodeValue+=c.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{c.nodeValue+=c.nextSibling.nodeValue}}else{if(this.msieNewlineBug){c.nodeValue+=(c.nextSibling.nodeName.toLowerCase()==="br"?"\n":" ")}else{c.nodeValue+=" "}}c.parentNode.removeChild(c.nextSibling)}var d=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);if(this.config.preview!=="none"){this.createPreview(a.mode,d)}c=this.createMathTag(a.mode,d);this.search={};this.pattern.lastIndex=0;if(e){e.parentNode.removeChild(e)}return c},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(c,a){var b;if(this.config.preview==="TeX"){b=[this.filterTeX(a)]}else{if(this.config.preview instanceof Array){b=this.config.preview}}if(b){b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b);this.insertNode(b)}},createMathTag:function(c,b){var a=document.createElement("script");a.type="math/tex"+c;MathJax.HTML.setScript(a,b);this.insertNode(a);return a},filterTeX:function(a){return a},msieNewlineBug:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9)};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js");

(function(a,c,e,b,h){var i="1.1";var g=a.CombineConfig("MathZoom",{delay:400,styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"font-family":"serif","font-size":"85%","font-weight":"normal","font-style":"normal","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","box-shadow":"5px 5px 15px #AAAAAA","-webkit-box-shadow":"5px 5px 15px #AAAAAA","-moz-box-shadow":"5px 5px 15px #AAAAAA","-khtml-box-shadow":"5px 5px 15px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_ZoomOverlay":{position:"absolute",left:0,top:0,"z-index":300,display:"inline-block",width:"100%",height:"100%",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"}}});var d=function(j){if(!j){j=window.event}if(j){if(j.preventDefault){j.preventDefault()}if(j.stopPropagation){j.stopPropagation()}j.cancelBubble=true;j.returnValue=false}return false};var f=MathJax.Extension.MathZoom={version:i,settings:a.config.menuSettings,HandleEvent:function(l,j,k){if(!l){l=window.event}if(f.settings.CTRL&&!l.ctrlKey){return true}if(f.settings.ALT&&!l.altKey){return true}if(f.settings.CMD&&!l.metaKey){return true}if(f.settings.Shift&&!l.shiftKey){return true}return f[j](l,k)},Click:function(k,j){if(this.settings.zoom==="Click"){return this.Zoom(j,k)}},DblClick:function(k,j){if(this.settings.zoom==="Double-Click"){return this.Zoom(j,k)}},Mouseover:function(k,j){if(this.settings.zoom==="Hover"){f.oldMouseOver=j.onmouseover;j.onmouseover=null;j.onmousemove=this.Mousemove;j.onmouseout=this.Mouseout;return f.Timer(k,j)}},Mouseout:function(j){this.onmouseover=f.oldMouseOver;delete f.oldMouseOver;this.onmousemove=this.onmouseout=null;f.ClearTimer();return d(j)},Mousemove:function(j){return f.Timer(j||window.event,this)},Timer:function(k,j){this.ClearTimer();this.timer=setTimeout(MathJax.Callback(["Zoom",this,j,{}]),g.delay);return d(k)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer);delete this.timer}},Zoom:function(s,l){this.ClearTimer();this.Remove();var v=s.parentNode;if(v.className==="MathJax_MathContainer"){v=v.parentNode}if(v.parentNode.className==="MathJax_MathContainer"){v=v.parentNode.parentNode}var q=(String(v.className).match(/^MathJax_(MathML|Display)$/)?v:s).nextSibling;var m=a.getJaxFor(q),r=m.root;var o=(b&&m.outputJax.isa(b.constructor)?"HTMLCSS":(h&&m.outputJax.isa(h.constructor)?"MathML":null));if(!o){return}var j=Math.floor(0.85*document.body.clientWidth),p=Math.floor(0.85*document.body.clientHeight);var k=c.Element("span",{style:{position:"relative",display:"inline-block",height:0,width:0},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":j+"px","max-height":p+"px"}},[["span"]]]]);var x=k.lastChild,u=x.firstChild,n=k.firstChild;s.parentNode.insertBefore(k,s);if(this.msieZIndexBug){var t=c.Element("img",{src:"about:blank",id:"MathJax_ZoomTracker",style:{width:0,height:0,position:"relative"}});document.body.appendChild(k);k.style.position="absolute";k.style.zIndex=g.styles["#MathJax_ZoomOverlay"]["z-index"];k=t}var w=(this["Zoom"+o])(r,u,s);if(this.msiePositionBug){if(this.msieIE8Bug){u.style.position="absolute";x.style.height=u.offsetHeight;u.style.position="";if(x.offsetHeight<=p&&x.offsetWidth<=j){x.style.overflow="visible"}}if(this.msieWidthBug){x.style.width=Math.min(j,w.w)}else{if(w.w>j){x.style.width=j}}if(x.offsetHeight>p){x.style.Height=p+"px"}if(s.nextSibling){s.parentNode.insertBefore(k,s.nextSibling)}else{v.appendChild(k)}}else{if(this.operaPositionBug){x.style.width=Math.min(j,u.offsetWidth)+"px"}}this.Position(x,w,(o==="MathML"&&v.nodeName.toLowerCase()==="div"));x.style.visibility="";if(this.settings.zoom==="Hover"){n.onmouseover=this.Remove}if(window.addEventListener){addEventListener("resize",this.Resize,false)}else{if(window.attachEvent){attachEvent("onresize",this.Resize)}else{this.onresize=window.onresize;window.onresize=this.Resize}}return d(l)},ZoomHTMLCSS:function(o,q,p){q.className="MathJax";b.idPostfix="-zoom";b.getScales(q,q);o.toHTML(q,q);var r=o.HTMLspanElement().bbox;b.idPostfix="";if(r.width&&r.width!=="100%"){var j=Math.floor(0.85*document.body.clientWidth);q.style.width=j+"px";q.style.display="inline-block";var k=(o.id||"MathJax-Span-"+o.spanID)+"-zoom";var l=document.getElementById(k).firstChild;while(l&&l.style.width!==r.width){l=l.nextSibling}if(l){l.style.width="100%"}}q.appendChild(this.topImg);var n=this.topImg.offsetTop;q.removeChild(this.topImg);var m=(this.msieWidthBug?b.getW(p)*b.em:p.offsetWidth);return{w:r.w*b.em,Y:-n,W:m}},ZoomMathML:function(k,l,m){k.toNativeMML(l,l);var n;l.appendChild(this.topImg);n=this.topImg.offsetTop;l.removeChild(this.topImg);var j=(this.ffMMLwidthBug?m.parentNode:m).offsetWidth;return{w:l.offsetWidth,Y:-n,W:j}},Position:function(p,n,r){var k=this.Resize(),m=k.x,l=k.y,j=n.W;if(this.msiePositionBug){j=-j}if(r&&this.ffMMLcenterBug){j=0}var q=-Math.floor((p.offsetWidth-j)/2),o=n.Y;p.style.left=Math.max(q,20-m)+"px";p.style.top=Math.max(o,20-l)+"px"},Resize:function(l){if(f.onresize){f.onresize(l)}var j=0,o=0,n=document.getElementById("MathJax_ZoomFrame"),k=document.getElementById("MathJax_ZoomOverlay");var m=(f.msieZIndexBug?document.getElementById("MathJax_ZoomTracker"):n);if(f.operaPositionBug){n.style.border="1px solid"}if(m.offsetParent){do{j+=m.offsetLeft;o+=m.offsetTop}while(m=m.offsetParent)}if(f.operaPositionBug){n.style.border=""}if(f.msieZIndexBug){n.style.left=j+"px";n.style.top=o+"px"}k.style.left=(-j)+"px";k.style.top=(-o)+"px";if(f.msiePositionBug){setTimeout(f.SetWH,0)}else{f.SetWH()}return{x:j,y:o}},SetWH:function(){var j=document.getElementById("MathJax_ZoomOverlay");j.style.width=j.style.height="1px";j.style.width=document.body.scrollWidth+"px";j.style.height=document.body.scrollHeight+"px"},Remove:function(k){var l=document.getElementById("MathJax_ZoomFrame");if(l){l.parentNode.removeChild(l);l=document.getElementById("MathJax_ZoomTracker");if(l){l.parentNode.removeChild(l)}if(f.operaRefreshBug){var j=c.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(j)}if(window.removeEventListener){removeEventListener("resize",f.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",f.Resize)}else{window.onresize=f.onresize;delete f.onresize}}}return d(k)}};a.Register.StartupHook("HTML-CSS Jax Ready",function(){b=MathJax.OutputJax["HTML-CSS"];b.Augment({HandleEvent:f.HandleEvent})});a.Register.StartupHook("NativeMML Jax Ready",function(){h=MathJax.OutputJax.NativeMML;h.Augment({HandleEvent:f.HandleEvent,MSIEmouseup:function(l,k,j){if(this.trapUp){delete this.trapUp;return true}if(this.MSIEzoomKeys(l)){return true}return false},MSIEclick:function(l,k,j){if(this.trapClick){delete this.trapClick;return true}if(!this.MSIEzoomKeys(l)){return false}if(!this.settings.zoom.match(/Click/)){return false}return(f.Click(l,k)===false)},MSIEdblclick:function(l,k,j){if(!this.MSIEzoomKeys(l)){return false}return(f.DblClick(l,k)===false)},MSIEmouseover:function(l,k,j){if(this.settings.zoom!=="Hover"){return false}f.Timer(l,k);return true},MSIEmouseout:function(l,k,j){if(this.settings.zoom!=="Hover"){return false}f.ClearTimer();return true},MSIEmousemove:function(l,k,j){if(this.settings.zoom!=="Hover"){return false}f.Timer(l,k);return true},MSIEzoomKeys:function(j){if(this.settings.CTRL&&!j.ctrlKey){return false}if(this.settings.CMD&&!j.metaKey){return false}if(this.settings.ALT&&!j.altKey){return false}if(this.settings.Shift&&!j.shiftKey){return false}return true}})});a.Browser.Select({MSIE:function(j){var k=(document.compatMode==="BackCompat");var l=j.versionAtLeast("8.0")&&document.documentMode>7;f.msiePositionBug=true;f.msieWidthBug=!k;f.msieIE8Bug=l;f.msieZIndexBug=!l;f.msieInlineBlockAlignBug=(!l||k);if(document.documentMode>=9){delete g.styles["#MathJax_Zoom"].filter}},Opera:function(j){f.operaPositionBug=true;f.operaRefreshBug=true},Firefox:function(j){f.ffMMLwidthBug=true;f.ffMMLcenterBug=true}});f.topImg=(f.msieInlineBlockAlignBug?c.Element("img",{style:{width:0,height:0},src:"about:blank"}):c.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(f.operaPositionBug){f.topImg.style.border="1px solid"}MathJax.Callback.Queue(["Styles",e,g.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",e,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML);

(function(b,c,f){var k="1.1.6";MathJax.Extension.MathMenu={version:k};var i=b.Browser.isPC,g=b.Browser.isMSIE;var e=(i?null:"5px");var j=b.CombineConfig("MathMenu",{delay:150,helpURL:"http://www.mathjax.org/help/user/",showRenderer:true,showFontMenu:false,showContext:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 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m=this.div.style.fontSize;this.div.style.fontSize=k;if(e.msieItalicWidthBug&&i.style==="italic"){this.text.nodeValue=h=this.compChar;j=this.div.offsetWidth}if(e.safariTextNodeBug){this.div.innerHTML=this.compChar+h}else{this.text.nodeValue=this.compChar+h}var g=this.div.offsetWidth-j;if(e.safariTextNodeBug){this.div.innerHTML=this.styleChar+h}else{this.text.nodeValue=this.styleChar+h}var l=Math.floor((this.div.offsetWidth-j)/g+0.5);if(l===o){if(e.safariTextNodeBug){this.div.innerHTML=this.versionChar+h}else{this.text.nodeValue=this.versionChar+h}i.version=Math.floor((this.div.offsetWidth-j)/g+1.5)/2}this.div.style.fontSize=m;return(l===o)},getComparisonWidths:function(k,j){if(e.FONTDATA&&e.FONTDATA.hasStyleChar&&!j){k+=this.styleChar+" "+this.compChar}if(e.safariTextNodeBug){this.div.innerHTML=k}else{this.text.nodeValue=k}this.div.style.fontFamily=this.comparisonFont[0];var h=this.div.offsetWidth,n=-1;if(e.safariWebFontSerif){this.div.style.fontFamily=e.safariWebFontSerif[0];n=this.div.offsetWidth}for(var l=1,g=this.comparisonFont.length;l<g;l++){this.div.style.fontFamily=this.comparisonFont[l];if(this.div.offsetWidth!=h){return[h,this.div.offsetWidth,l,n]}}return null},loadWebFont:function(h){d.Startup.signal.Post("HTML-CSS Jax - Web-Font "+e.fontInUse+"/"+h.directory);var j=MathJax.Message.File("Web-Font "+e.fontInUse+"/"+h.directory);var g=MathJax.Callback({});var i=MathJax.Callback(["loadComplete",this,h,j,g]);c.timer.start(c,[this.checkWebFont,h,i],1,this.timeout);return g},loadComplete:function(i,k,h,g){MathJax.Message.Clear(k);if(g===c.STATUS.OK){h();return}this.loadError(i);if(d.Browser.isFirefox&&e.allowWebFonts){var j=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){j+=":"+document.location.port}j+="/";if(c.fileURL(e.webfontDir).substr(0,j.length)!==j){this.firefoxFontError(i)}}e.loadWebFontError(i,h)},loadError:function(g){MathJax.Message.Set("Can't load web font "+e.fontInUse+"/"+g.directory,null,2000)},firefoxFontError:function(g){MathJax.Message.Set("Firefox can't load web fonts from a remote host",null,3000)},checkWebFont:function(g,h,i){if(g.time(i)){return}if(e.Font.testFont(h)){i(g.STATUS.OK)}else{setTimeout(g,g.delay)}},fontFace:function(i){var j=e.allowWebFonts;var l=e.FONTDATA.FONTS[i];if(e.msieFontCSSBug&&!l.family.match(/-Web$/)){l.family+="-Web"}var h=c.fileURL(e.webfontDir+"/"+j);var g=i.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!g.match(/-/)){g+="-Regular"}if(j==="svg"){g+=".svg#"+g}else{g+="."+j}var k={"font-family":l.family,src:"url('"+h+"/"+g+"')"};if(j==="svg"){k.src+=" format('svg')"}if(!(e.FontFaceBug&&l.isWebFont)){if(i.match(/-bold/)){k["font-weight"]="bold"}if(i.match(/-italic/)){k["font-style"]="italic"}}return k}});var f={last:0,delay:500,start:function(h){var g=new Date().getTime();var i=(g-f.last<f.delay);f.last=g;if(i){f.timeout=setTimeout(f.menu,f.delay,this,h);h.preventDefault()}},end:function(g){if(f.timeout){clearTimeout(f.timeout);delete f.timeout;f.last=0;g.preventDefault();e.DblClick.call(this,g.touches[0]||g.touch)}},menu:function(h,g){delete f.timeout;f.last=0;e.ContextMenu.call(h,g.touches[0]||even.touch)}};e.Augment({config:{styles:{".MathJax":{display:"inline","font-family":"serif","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"},".MathJax img":{display:"inline ! important"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax .MathJax_HitBox":{cursor:"text"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",background:"transparent"}}},settings:d.config.menuSettings,LEFTBUTTON:(d.Browser.isMSIE?1:0),MENUKEY:"altKey",Touch:f,Font:null,Config:function(){this.Font=b();this.SUPER(arguments).Config.call(this);var h=this.settings;if(this.adjustAvailableFonts){this.adjustAvailableFonts(this.config.availableFonts)}if(h.scale){this.config.scale=h.scale}if(h.font&&h.font!=="Auto"){if(h.font==="TeX (local)"){this.config.availableFonts=["TeX"];this.config.preferredFont="TeX";this.config.webFont="TeX"}else{if(h.font==="STIX (local)"){this.config.availableFonts=["STIX"];this.config.preferredFont="STIX";this.config.webFont="TeX"}else{if(h.font==="TeX (web)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont="TeX"}else{if(h.font==="TeX (image)"){this.config.availableFonts=[];this.config.preferredFont="";this.config.webFont=""}}}}}var g=this.Font.findFont(this.config.availableFonts,this.config.preferredFont);if(!g&&this.allowWebFonts){g=this.config.webFont;if(g){this.webFonts=true}}if(!g&&this.config.imageFont){g=this.config.imageFont;this.imgFonts=true}if(g){this.fontInUse=g;this.fontDir+="/"+g;this.webfontDir+="/"+g;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");d.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{MathJax.Message.Set("Can't find a valid font using ["+this.config.availableFonts.join(", ")+"]",null,3000);this.FONTDATA={TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}};if(MathJax.InputJax.TeX&&MathJax.InputJax.TeX.Definitions){MathJax.InputJax.TeX.Definitions.macros.overline[1]="002D";MathJax.InputJax.TeX.Definitions.macros.underline[1]="002D"}d.Startup.signal.Post("HTML-CSS Jax - no valid font")}},Startup:function(){var j=[],n=this.FONTDATA.VARIANT.normal.fonts;if(!(n instanceof Array)){n=[n]}for(var h=0,g=n.length;h<g;h++){j[h]=this.FONTDATA.FONTS[n[h]].family;if(!j[h]){j[h]=n[h]}}this.config.styles[".MathJax .math span"]=this.config.styles["#MathJax_getScales"]={"font-family":j.join(",")};this.hiddenDiv=this.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=this.addElement(this.hiddenDiv,"div",{id:"MathJax_Hidden"});var l=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=l.offsetWidth/5;this.hiddenDiv.removeChild(l);this.startMarker=e.createStrut(this.Element("span"),10,true);this.endMarker=this.addText(this.Element("span"),"x").parentNode;this.HDspan=this.Element("span");if(this.operaHeightBug){this.createStrut(this.HDspan,0)}if(this.msieInlineBlockAlignBug){this.HDimg=this.addElement(this.HDspan,"img",{style:{height:"0px",width:"1px"}});try{this.HDimg.src="about:blank"}catch(k){}}else{this.HDimg=e.createStrut(this.HDspan,0)}this.HDMspan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}});if(this.msieInlineBlockAlignBug){this.HDMimg=this.addElement(this.HDMspan,"img",{style:{height:"0px",width:"1px","max-width":"none","max-height":"none",border:0,padding:0,margin:0}});try{this.HDMimg.src="about:blank"}catch(k){}}else{this.HDMimg=e.createStrut(this.HDMspan,0);this.HDMimg.style.marginRight=""}this.marginCheck=e.Element("span",null,[["span",{style:{display:"inline-block",width:"5em"}}]]);this.marginMove=e.addElement(this.marginCheck,"span",{style:{display:"inline-block",width:"5em",marginLeft:"-5em"}});return c.Styles(this.config.styles,["PreloadWebFonts",this])},PreloadWebFonts:function(){if(!e.allowWebFonts||!e.config.preloadWebFonts){return}for(var h=0,g=e.config.preloadWebFonts.length;h<g;h++){var j=e.FONTDATA.FONTS[e.config.preloadWebFonts[h]];if(!j.available){e.Font.testFont(j)}}},Translate:function(m){if(!m.parentNode){return}var k=m.previousSibling;if(k&&String(k.className).match(/^MathJax(_MathML|_Display)?$/)){k.parentNode.removeChild(k)}var n=m.MathJax.elementJax.root,o,g,i;o=g=i=this.Element("span",{className:"MathJax",isMathJax:true,oncontextmenu:this.ContextMenu,onmousedown:this.Mousedown,onmouseover:this.Mouseover,onclick:this.Click,ondblclick:this.DblClick});if(MathJax.Hub.Browser.noContextMenu){o.ontouchstart=this.Touch.start;o.ontouchend=this.Touch.end}var j=(n.Get("display")==="block");if(j){g=i=this.Element("div",{className:"MathJax_Display",style:{width:"100%",position:"relative"}});g.appendChild(o)}g.setAttribute("role","textbox");g.setAttribute("aria-readonly","true");if(this.useProcessingFrame){i=this.Element((j?"div":"span"),{className:"MathJax_Processing"});i.appendChild(g)}m.parentNode.insertBefore(i,m);var h;try{this.getScales(o);h=(this.em===0||String(this.em)==="NaN")}catch(l){h=true}if(h){this.hiddenDiv.appendChild(i);this.getScales(o)}this.initImg(o);this.initHTML(n,o);n.setTeXclass();try{n.toHTML(o,g)}catch(l){if(l.restart){i.parentNode.removeChild(i)}throw l}if(h){m.parentNode.insertBefore(i,m)}if(this.useProcessingFrame){i.parentNode.replaceChild(g,i)}},ContextMenu:function(j,k){if(e.config.showMathMenu&&(e.settings.context==="MathJax"||k)){if(e.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(!j||e.msieEventBug){j=window.event}var g=MathJax.Menu;if(g){var i=(this.parentNode.className==="MathJax_Display"?this.parentNode:this);g.jax=d.getJaxFor(i.nextSibling);g.menu.items[1].menu.items[1].name=(g.jax.inputJax.id==="MathML"?"Original":g.jax.inputJax.id);return g.menu.Post(j)}else{if(!c.loadingMathMenu){c.loadingMathMenu=true;var h={pageX:j.pageX,pageY:j.pageY,clientX:j.clientX,clientY:j.clientY};MathJax.Callback.Queue(c.Require("[MathJax]/extensions/MathMenu.js"),function(){delete c.loadingMathMenu},[this,arguments.callee,h,k])}if(j.preventDefault){j.preventDefault()}if(j.stopPropagation){j.stopPropagation()}j.cancelBubble=true;j.returnValue=false;return false}}},Mousedown:function(g){if(e.config.showMathMenu){if(!g){g=window.event}if(e.settings.context==="MathJax"){if(!e.noContextMenuBug||g.button!==2){return}}else{if(!g[e.MENUKEY]||g.button!==e.LEFTBUTTON){return}}return e.ContextMenu.call(this,g,true)}},Mouseover:function(g){e.HandleEvent(g,"Mouseover",this)},Click:function(g){e.HandleEvent(g,"Click",this)},DblClick:function(g){e.HandleEvent(g,"DblClick",this)},HandleEvent:function(i,g,h){},initImg:function(g){},initHTML:function(h,g){},initFont:function(g){var i=e.FONTDATA.FONTS,h=e.config.availableFonts;if(h&&h.length&&e.Font.testFont(i[g])){i[g].available=true;return null}if(!this.allowWebFonts){return null}i[g].isWebFont=true;if(e.FontFaceBug){i[g].family=g;if(e.msieFontCSSBug){i[g].family+="-Web"}}return c.Styles({"@font-face":this.Font.fontFace(g)})},Remove:function(g){var h=g.SourceElement();if(!h){return}h=h.previousSibling;if(!h){return}if(h.className.match(/^MathJax/)){h.parentNode.removeChild(h)}},getScales:function(i){i.parentNode.insertBefore(this.HDMspan,i);this.HDMspan.className="";this.HDMspan.id="";this.HDMspan.style.fontSize="";this.HDMimg.style.height="1px";this.HDMimg.style.width="60ex";var h=this.HDMspan.offsetWidth/60;this.HDMspan.className="MathJax";this.HDMspan.id="MathJax_getScales";this.HDMimg.style.width="60em";var g=this.outerEm=this.HDMspan.offsetWidth/60;this.scale=Math.floor(Math.max(this.config.minScaleAdjust/100,(h/this.TeX.x_height)/g)*this.config.scale);i.style.fontSize=this.HDMspan.style.fontSize=this.scale+"%";this.em=a.mbase.prototype.em=this.HDMspan.offsetWidth/60;if(this.operaFontSizeBug&&g===this.em&&this.scale!==100){this.em=a.mbase.prototype.em=g*this.scale/100}i.parentNode.removeChild(this.HDMspan);this.msieMarginScale=this.getMarginScale(i)},getMarginScale:function(g){return 1},getMSIEmarginScale:function(i){i.appendChild(this.marginCheck);var g=this.marginCheck.offsetWidth,h=this.marginMove.offsetWidth;var j=(2*h-g?h/(2*h-g):1);i.removeChild(this.marginCheck);return j},getHD:function(h){var g=h.style.position;h.style.position="absolute";this.HDimg.style.height="0px";h.appendChild(this.HDspan);var i={h:h.offsetHeight};this.HDimg.style.height=i.h+"px";i.d=h.offsetHeight-i.h;i.h-=i.d;i.h/=this.em;i.d/=this.em;h.removeChild(this.HDspan);h.style.position=g;return i},getW:function(j){var h=j.offsetWidth,i=(j.bbox?j.bbox.w:-1),k=j;if((i<0||this.negativeSkipBug)&&h>=0){if(this.negativeSkipBug){var g=j.style.position;j.style.position="absolute";k=this.startMarker;if(j.firstChild){j.insertBefore(k,j.firstChild)}else{j.appendChild(k)}k=this.startMarker}j.appendChild(this.endMarker);h=this.endMarker.offsetLeft-k.offsetLeft;j.removeChild(this.endMarker);if(this.negativeSkipBug){j.removeChild(k);j.style.position=g}}return h/this.em},Measured:function(i,h){if(i.bbox.width==null&&i.bbox.w&&!i.bbox.isMultiline){var g=this.getW(i);i.bbox.rw+=g-i.bbox.w;i.bbox.w=g}if(!h){h=i.parentNode}if(!h.bbox){h.bbox=i.bbox}return i},Remeasured:function(h,g){g.bbox=this.Measured(h,g).bbox},Em:function(g){if(Math.abs(g)<0.0006){return"0em"}return g.toFixed(3).replace(/\.?0+$/,"")+"em"},Percent:function(g){return(100*g).toFixed(1).replace(/\.?0+$/,"")+"%"},length2percent:function(g){return this.Percent(this.length2em(g))},length2em:function(l,j){if(typeof(l)!=="string"){l=l.toString()}if(l===""){return""}if(l===a.SIZE.NORMAL){return 1}if(l===a.SIZE.BIG){return 2}if(l===a.SIZE.SMALL){return 0.71}if(l==="infinity"){return e.BIGDIMEN}var i=this.FONTDATA.TeX_factor;if(l.match(/mathspace$/)){return e.MATHSPACE[l]*i}var h=l.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var g=parseFloat(h[1]||"1"),k=h[2];if(j==null){j=1}if(k==="em"){return g*i}if(k==="ex"){return g*e.TeX.x_height*i}if(k==="%"){return g/100*j}if(k==="px"){return g/e.em}if(k==="pt"){return g/10*i}if(k==="pc"){return g*1.2*i}if(k==="in"){return g*this.pxPerInch/e.em}if(k==="cm"){return g*this.pxPerInch/e.em/2.54}if(k==="mm"){return g*this.pxPerInch/e.em/25.4}if(k==="mu"){return g/18*i}return g*i*j},thickness2em:function(g){var h=e.TeX.rule_thickness;if(g===a.LINETHICKNESS.MEDIUM){return h}if(g===a.LINETHICKNESS.THIN){return 0.67*h}if(g===a.LINETHICKNESS.THICK){return 1.67*h}return this.length2em(g,h)},createStrut:function(j,i,k){var g=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:i+"px",width:"1px",marginRight:"-1px"}});if(k){j.insertBefore(g,j.firstChild)}else{j.appendChild(g)}return g},createBlank:function(h,g,i){var j=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(g)}});if(i){h.insertBefore(j,h.firstChild)}else{h.appendChild(j)}return j},createShift:function(h,g,j){var i=this.Element("span",{style:{marginLeft:this.Em(g)},isMathJax:true});if(j){h.insertBefore(i,h.firstChild)}else{h.appendChild(i)}return i},createSpace:function(l,k,n,g,i){var j=this.Em(Math.max(0,k+n)),m=this.Em(-n);if(this.msieInlineBlockAlignBug){m=this.Em(e.getHD(l.parentNode).d-n)}if(l.isBox||l.className=="mspace"){l.bbox={h:k*l.scale,d:n*l.scale,w:g*l.scale,rw:g*l.scale,lw:0};l.style.height=j;l.style.verticalAlign=m}else{l=this.addElement(l,"span",{style:{height:j,verticalAlign:m},isMathJax:true})}if(g>=0){l.style.width=this.Em(g);l.style.display="inline-block"}else{if(this.msieNegativeSpaceBug){l.style.height=""}l.style.marginLeft=this.Em(g);if(e.safariNegativeSpaceBug&&l.parentNode.firstChild==l){this.createBlank(l,0,true)}}if(i&&i!==a.COLOR.TRANSPARENT){l.style.backgroundColor=i}return l},createRule:function(o,k,m,p,i){var j=e.TeX.min_rule_thickness;if(p>0&&p*this.em<j){p=j/this.em}if(k+m>0&&(k+m)*this.em<j){var l=1/(k+m)*(j/this.em);k*=l;m*=l}if(!i){i="solid"}else{i="solid "+i}i=this.Em(p)+" "+i;var q=this.Em(k+m),g=this.Em(-m);var n=this.addElement(o,"span",{style:{borderLeft:i,display:"inline-block",overflow:"hidden",width:0,height:q,verticalAlign:g},bbox:{h:k,d:m,w:p,rw:p,lw:0},noAdjust:true,isMathJax:true});if(p>0&&n.offsetWidth==0){n.style.width=this.Em(p)}if(o.isBox||o.className=="mspace"){o.bbox=n.bbox}return n},createFrame:function(p,n,o,q,s,i){var m=(this.msieBorderWidthBug?0:2*s);var r=this.Em(n+o-m),g=this.Em(-o-s),l=this.Em(q-m);var j=this.Em(s)+" "+i;var k=this.addElement(p,"span",{style:{border:j,display:"inline-block",overflow:"hidden",width:l,height:r},bbox:{h:n,d:o,w:q,rw:q,lw:0},noAdjust:true,isMathJax:true});if(g){k.style.verticalAlign=g}return k},createStack:function(i,k,h){if(this.msiePaddingWidthBug){this.createStrut(i,0)}var j=String(h).match(/%$/);var g=(!j&&h!=null?h:0);i=this.addElement(i,"span",{noAdjust:true,isMathJax:true,style:{display:"inline-block",position:"relative",width:(j?"100%":this.Em(g)),height:0}});if(!k){i.parentNode.bbox=i.bbox={h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:g,lw:this.BIGDIMEN,rw:(!j&&h!=null?h:-this.BIGDIMEN)};if(j){i.bbox.width=h}}return i},createBox:function(h,g){var i=this.addElement(h,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(g!=null){i.style.width=g}return i},addBox:function(g,h){h.style.position="absolute";h.isBox=true;return g.appendChild(h)},placeBox:function(o,n,m,j){o.isMathJax=true;var p=o.parentNode,w=o.bbox,s=p.bbox;if(this.msiePlaceBoxBug){this.addText(o,this.NBSP)}if(this.imgSpaceBug){this.addText(o,this.imgSpace)}var q=o.offsetHeight/this.em+1,A=0;if(o.noAdjust){q-=1}else{if(this.msieInlineBlockAlignBug){this.addElement(o,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(q)}})}else{this.addElement(o,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(q)}})}}o.style.top=this.Em(-m-q);o.style.left=this.Em(n+A);if(w){if(this.negativeSkipBug){if(w.lw<0){A=w.lw;e.createBlank(o,-A,true);i=0}if(w.rw>w.w){e.createBlank(o,w.rw-w.w+0.1)}}if(!this.msieClipRectBug&&!w.noclip&&!j){var v=3/this.em;var u=(w.H==null?w.h:w.H),h=(w.D==null?w.d:w.D);var z=q-u-v,k=q+h+v,i=w.lw-3*v,g=1000;if(w.isFixed){g=w.width-i}o.style.clip="rect("+this.Em(z)+" "+this.Em(g)+" "+this.Em(k)+" "+this.Em(i)+")"}}if(w&&s){if(w.H!=null&&(s.H==null||w.H+m>s.H)){s.H=w.H+m}if(w.D!=null&&(s.D==null||w.D-m>s.D)){s.D=w.D-m}if(w.h+m>s.h){s.h=w.h+m}if(w.d-m>s.d){s.d=w.d-m}if(s.H!=null&&s.H<=s.h){delete s.H}if(s.D!=null&&s.D<=s.d){delete s.D}if(w.w+n>s.w){s.w=w.w+n;if(s.width==null){p.style.width=this.Em(s.w)}}if(w.rw+n>s.rw){s.rw=w.rw+n}if(w.lw+n<s.lw){s.lw=w.lw+n}if(w.width!=null&&!w.isFixed){if(s.width==null){p.style.width=s.width="100%"}o.style.width=w.width}}},alignBox:function(i,o,n){this.placeBox(i,0,n);var k=i.bbox;if(k.isMultiline){return}var h=k.width!=null&&!k.isFixed;var j=0,m=-k.w/2,g="50%";if(this.negativeSkipBug){j=k.w-k.rw-0.1;m+=k.lw}m=this.Em(m*this.msieMarginScale);if(h){m="";g=(50-parseFloat(k.width)/2)+"%"}d.Insert(i.style,({right:{left:"",right:this.Em(j)},center:{left:g,marginLeft:m}})[o])},setStackWidth:function(h,g){if(typeof(g)==="number"){h.style.width=this.Em(Math.max(0,g));if(h.bbox){h.bbox.w=g}if(h.parentNode.bbox){h.parentNode.bbox.w=g}}else{h.style.width=h.parentNode.style.width="100%";if(h.bbox){h.bbox.width=g}if(h.parentNode.bbox){h.parentNode.bbox.width=g}}},createDelimiter:function(r,g,j,n,k){if(!g){r.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};r.bbox.rw=r.bbox.w;this.createSpace(r,r.bbox.h,r.bbox.d,r.bbox.w);return}if(!n){n=1}if(!(j instanceof Array)){j=[j,j]}var q=j[1];j=j[0];var h={alias:g};while(h.alias){g=h.alias;h=this.FONTDATA.DELIMITERS[g];if(!h){h={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]}}}for(var p=0,l=h.HW.length;p<l;p++){if(h.HW[p][0]*n>=j-0.01||(p==l-1&&!h.stretch)){if(h.HW[p][2]){n*=h.HW[p][2]}if(h.HW[p][3]){g=h.HW[p][3]}var o=this.addElement(r,"span");this.createChar(o,[g,h.HW[p][1]],n,k);r.bbox=o.bbox;r.offset=0.65*r.bbox.w;r.scale=n;return}}if(h.stretch){this["extendDelimiter"+h.dir](r,q,h.stretch,n,k)}},extendDelimiterV:function(w,q,B,C,t){var j=this.createStack(w,true);var s=this.createBox(j),r=this.createBox(j);this.createChar(s,(B.top||B.ext),C,t);this.createChar(r,(B.bot||B.ext),C,t);var i={bbox:{w:0,lw:0,rw:0}},A=i,l;var x=s.bbox.h+s.bbox.d+r.bbox.h+r.bbox.d;var o=-s.bbox.h;this.placeBox(s,0,o,true);o-=s.bbox.d;if(B.mid){A=this.createBox(j);this.createChar(A,B.mid,C,t);x+=A.bbox.h+A.bbox.d}if(q>x){i=this.Element("span");this.createChar(i,B.ext,C,t);var z=i.bbox.h+i.bbox.d,g=z-0.05,u,m,v=(B.mid?2:1);m=u=Math.ceil((q-x)/(v*g));if(!B.fullExtenders){g=(q-x)/(v*u)}var p=(u/(u+1))*(z-g);g=z-p;o+=p+g-i.bbox.h;while(v-->0){while(u-->0){if(!this.msieCloneNodeBug){l=i.cloneNode(true)}else{l=this.Element("span");this.createChar(l,B.ext,C,t)}o-=g;this.placeBox(this.addBox(j,l),0,o,true)}o+=p-i.bbox.d;if(B.mid&&v){this.placeBox(A,0,o-A.bbox.h,true);u=m;o+=-(A.bbox.h+A.bbox.d)+p+g-i.bbox.h}}}else{o+=(x-q)/2;if(B.mid){this.placeBox(A,0,o-A.bbox.h,true);o+=-(A.bbox.h+A.bbox.d)}o+=(x-q)/2}this.placeBox(r,0,o-r.bbox.h,true);o-=r.bbox.h+r.bbox.d;w.bbox={w:Math.max(s.bbox.w,i.bbox.w,r.bbox.w,A.bbox.w),lw:Math.min(s.bbox.lw,i.bbox.lw,r.bbox.lw,A.bbox.lw),rw:Math.max(s.bbox.rw,i.bbox.rw,r.bbox.rw,A.bbox.rw),h:0,d:-o};w.scale=C;w.offset=0.55*w.bbox.w;w.isMultiChar=true;this.setStackWidth(j,w.bbox.w)},extendDelimiterH:function(v,i,A,C,s){var m=this.createStack(v,true);var j=this.createBox(m),y=this.createBox(m);this.createChar(j,(A.left||A.rep),C,s);this.createChar(y,(A.right||A.rep),C,s);var g=this.Element("span");this.createChar(g,A.rep,C,s);var z={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},h;this.placeBox(j,-j.bbox.lw,0,true);var q=(j.bbox.rw-j.bbox.lw)+(y.bbox.rw-y.bbox.lw)-0.05,p=j.bbox.rw-j.bbox.lw-0.025,r;if(A.mid){z=this.createBox(m);this.createChar(z,A.mid,C,s);q+=z.bbox.w}if(i>q){var B=g.bbox.rw-g.bbox.lw,l=B-0.05,t,o,u=(A.mid?2:1);o=t=Math.ceil((i-q)/(u*l));l=(i-q)/(u*t);r=(t/(t+1))*(B-l);l=B-r;p-=g.bbox.lw+r;while(u-->0){while(t-->0){if(!this.msieCloneNodeBug){h=g.cloneNode(true)}else{h=this.Element("span");this.createChar(h,A.rep,C,s)}this.placeBox(this.addBox(m,h),p,0,true);p+=l}if(A.mid&&u){this.placeBox(z,p,0,true);p+=z.bbox.w-r;t=o}}}else{r=Math.min(q-i,j.bbox.w/2);p-=r/2;if(A.mid){this.placeBox(z,p,0,true);p+=z.bbox.w}p-=r/2}this.placeBox(y,p,0,true);v.bbox={w:p+y.bbox.rw,lw:0,rw:p+y.bbox.rw,H:Math.max(j.bbox.h,g.bbox.h,y.bbox.h,z.bbox.h),D:Math.max(j.bbox.d,g.bbox.d,y.bbox.d,z.bbox.d),h:g.bbox.h,d:g.bbox.d};v.scale=C;v.isMultiChar=true;this.setStackWidth(m,v.bbox.w)},createChar:function(p,l,j,g){p.isMathJax=true;var o=p,q="",k={fonts:[l[1]],noRemap:true};if(g&&g===a.VARIANT.BOLD){k.fonts=[l[1]+"-bold",l[1]]}if(typeof(l[1])!=="string"){k=l[1]}if(l[0] instanceof Array){for(var n=0,h=l[0].length;n<h;n++){q+=String.fromCharCode(l[0][n])}}else{q=String.fromCharCode(l[0])}if(j!==1){o=this.addElement(p,"span",{style:{fontSize:this.Percent(j)},scale:j,isMathJax:true});this.handleVariant(o,k,q);p.bbox=o.bbox}else{this.handleVariant(p,k,q)}if(l[2]){p.style.marginLeft=this.Em(l[2])}if(this.AccentBug&&p.bbox.w===0){o.firstChild.nodeValue+=this.NBSP;e.createSpace(p,0,0,-p.offsetWidth/e.em)}},positionDelimiter:function(i,g){g-=i.bbox.h;i.bbox.d-=g;i.bbox.h+=g;if(g){if(this.safariVerticalAlignBug||this.msieVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&i.isMultiChar)){if(i.firstChild.style.display===""&&i.style.top!==""){i=i.firstChild;g-=parseFloat(i.style.top)}i.style.position="relative";i.style.top=this.Em(-g)}else{i.style.verticalAlign=this.Em(g);if(e.ffVerticalAlignBug){e.createRule(i.parentNode,i.bbox.h,0,0)}}}},handleVariant:function(w,k,p){var v="",t,z,q,h,y,A,g=w;if(p.length===0){return}if(!w.bbox){w.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!k){k=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]}A=k;for(var x=0,u=p.length;x<u;x++){k=A;t=p.charCodeAt(x);z=p.charAt(x);if(z===this.PLANE1){x++;t=p.charCodeAt(x)+119808-56320;if(this.FONTDATA.RemapPlane1){var B=this.FONTDATA.RemapPlane1(t,k);t=B.n;k=B.variant}}else{var r,o,s=this.FONTDATA.RANGES;for(r=0,o=s.length;r<o;r++){if(s[r].name==="alpha"&&k.noLowerCase){continue}var l=k["offset"+s[r].offset];if(l&&t>=s[r].low&&t<=s[r].high){if(s[r].remap&&s[r].remap[t]){t=l+s[r].remap[t]}else{t=t-s[r].low+l;if(s[r].add){t+=s[r].add}}if(k["variant"+s[r].offset]){k=this.FONTDATA.VARIANT[k["variant"+s[r].offset]]}break}}}if(k.remap&&k.remap[t]){if(k.remap[t] instanceof Array){var j=k.remap[t];t=j[0];k=this.FONTDATA.VARIANT[j[1]]}else{t=k.remap[t];if(k.remap.variant){k=this.FONTDATA.VARIANT[k.remap.variant]}}}if(this.FONTDATA.REMAP[t]&&!k.noRemap){t=this.FONTDATA.REMAP[t]}q=this.lookupChar(k,t);z=q[t];if(k!==y&&!z[5].img){if(v.length){this.addText(g,v);v=""}g=w;y=h;if(k!==y){if(y){g=this.addElement(w,"span",{isMathJax:true})}else{h=k}}this.handleFont(g,q,g!==w);y=k}v=this.handleChar(g,q,z,t,v);if(z[0]/1000>w.bbox.h){w.bbox.h=z[0]/1000}if(z[1]/1000>w.bbox.d){w.bbox.d=z[1]/1000}if(w.bbox.w+z[3]/1000<w.bbox.lw){w.bbox.lw=w.bbox.w+z[3]/1000}if(w.bbox.w+z[4]/1000>w.bbox.rw){w.bbox.rw=w.bbox.w+z[4]/1000}w.bbox.w+=z[2]/1000}if(v.length){this.addText(g,v)}if(w.scale&&w.scale!==1){w.bbox.h*=w.scale;w.bbox.d*=w.scale;w.bbox.w*=w.scale;w.bbox.lw*=w.scale;w.bbox.rw*=w.scale}if(p.length==1&&q.skew&&q.skew[t]){w.bbox.skew=q.skew[t]}},handleFont:function(i,g,k){i.style.fontFamily=g.family;if(!(e.FontFaceBug&&g.isWebFont)){var h=g.style||"normal",j=g.weight||"normal";if(h!=="normal"||k){i.style.fontStyle=h}if(j!=="normal"||k){i.style.fontWeight=j}}},handleChar:function(h,g,m,l,k){var j=m[5];if(j.img){return this.handleImg(h,g,m,l,k)}if(j.isUnknown&&this.FONTDATA.DELIMITERS[l]){if(k.length){this.addText(h,k)}var i=h.scale;e.createDelimiter(h,l,0,1,g);h.scale=i;m[0]=h.bbox.h*1000;m[1]=h.bbox.d*1000;m[2]=h.bbox.w*1000;m[3]=h.bbox.lw*1000;m[4]=h.bbox.rw*1000;return""}if(j.c==null){if(l<=65535){j.c=String.fromCharCode(l)}else{j.c=this.PLANE1+String.fromCharCode(l-119808+56320)}}if(m[2]||!this.msieAccentBug||k.length){return k+j.c}e.createShift(h,m[3]/1000);e.createShift(h,(m[4]-m[3])/1000);this.addText(h,j.c);e.createShift(h,-m[4]/1000);return""},handleImg:function(h,g,k,j,i){return i},lookupChar:function(k,q){var j,g;if(!k.FONTS){var p=this.FONTDATA.FONTS;var o=(k.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(o instanceof Array)){o=[o]}if(k.fonts!=o){k.fonts=o}k.FONTS=[];for(j=0,g=o.length;j<g;j++){if(p[o[j]]){k.FONTS.push(p[o[j]]);p[o[j]].name=o[j]}}}for(j=0,g=k.FONTS.length;j<g;j++){var h=k.FONTS[j];if(typeof(h)==="string"){delete k.FONTS;this.loadFont(h)}if(h[q]){if(h[q].length===5){h[q][5]={}}if(e.allowWebFonts&&!h.available){this.loadWebFont(h)}else{return h}}else{this.findBlock(h,q)}}var l=(k.defaultFont||{family:e.config.undefinedFamily});if(k.bold){l.weight="bold"}if(k.italic){l.style="italic"}l[q]=[800,200,500,0,500,{isUnknown:true}];return l},findBlock:function(h,o){if(h.Ranges){for(var n=0,g=h.Ranges.length;n<g;n++){if(o<h.Ranges[n][0]){return}if(o<=h.Ranges[n][1]){var l=h.Ranges[n][2];for(var k=h.Ranges.length-1;k>=0;k--){if(h.Ranges[k][2]==l){h.Ranges.splice(k,1)}}this.loadFont(h.directory+"/"+l+".js")}}}},loadFont:function(h){var g=MathJax.Callback.Queue();g.Push(["Require",c,this.fontDir+"/"+h]);if(this.imgFonts){if(!MathJax.isPacked){h=h.replace(/\/([^\/]*)$/,e.imgPacked+"/$1")}g.Push(["Require",c,this.webfontDir+"/png/"+h])}d.RestartAfter(g.Push({}))},loadWebFont:function(g){g.available=g.isWebFont=true;if(e.FontFaceBug){g.family=g.name;if(e.msieFontCSSBug){g.family+="-Web"}}d.RestartAfter(this.Font.loadWebFont(g))},loadWebFontError:function(h,g){d.Startup.signal.Post("HTML-CSS Jax - disable web fonts");h.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;d.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");d.Startup.signal.Post("HTML-CSS Jax - using image fonts");MathJax.Message.Set("Web-Fonts not available -- using image fonts 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this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:0.430554,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.6,big_op_spacing5:0.1,scriptspace:0.1,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.1,min_rule_thickness:1.25},PLANE1:String.fromCharCode(55349),NBSP:String.fromCharCode(160),rfuzz:0});MathJax.Hub.Register.StartupHook("mml Jax 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j=n.bbox={},o=[];while(k<g){var h=this.data[k];if(!h){continue}if(!l&&h.HTMLcanStretch("Vertical")){o.push(h);h=(h.CoreMO()||h)}this.HTMLcombineBBoxes(h,j);k++}this.HTMLcleanBBox(j);return o},HTMLcombineBBoxes:function(g,h){if(h.w==null){this.HTMLemptyBBox(h)}var j=g.HTMLspanElement();if(!j||!j.bbox){return}var i=j.bbox;if(i.d>h.d){h.d=i.d}if(i.h>h.h){h.h=i.h}if(i.D!=null&&i.D>h.D){h.D=i.D}if(i.H!=null&&i.H>h.H){h.H=i.H}if(j.style.paddingLeft){h.w+=parseFloat(j.style.paddingLeft)*(j.scale||1)}if(h.w+i.lw<h.lw){h.lw=h.w+i.lw}if(h.w+i.rw>h.rw){h.rw=h.w+i.rw}h.w+=i.w;if(j.style.paddingRight){h.w+=parseFloat(j.style.paddingRight)*(j.scale||1)}if(i.width){h.width=i.width}},HTMLemptyBBox:function(g){g.h=g.d=g.H=g.D=g.rw=-e.BIGDIMEN;g.w=0;g.lw=e.BIGDIMEN;return g},HTMLcleanBBox:function(g){if(g.h===this.BIGDIMEN){g.h=g.d=g.H=g.D=g.w=g.rw=g.lw=0}if(g.D<=g.d){delete g.D}if(g.H<=g.h){delete 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