/*
 *  /MathJax/config/TeX-AMS_HTML-full.js
 *  
 *  Copyright (c) 2010-2015 The MathJax Consortium
 *
 *  Part of the MathJax library.
 *  See http://www.mathjax.org for details.
 * 
 *  Licensed under the Apache License, Version 2.0;
 *  you may not use this file except in compliance with the License.
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 */

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

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

MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.5.2",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/[:"'<>&]/g,"")},formatURL:function(a){return"#"+escape(a)},useLabelIds:true}}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js");
MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.5.3",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{noReflows:true,matchFontHeight:true,scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",mtextFontInherit:false,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"},".MathJax .MJX-monospace":{"font-family":"monospace"},".MathJax .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px","z-index":401}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g<d;g++){h.appendChild(document.createTextNode(k[g]));if(g<d-1){h.appendChild(document.createElement("br"))}}f.parentNode.insertBefore(h,f)}},(b.config["HTML-CSS"]||{}));if(b.Browser.version!=="0.0"&&!b.Browser.versionAtLeast(a.minBrowserVersion[b.Browser]||0)){c.Translate=a.minBrowserTranslate;b.Config({showProcessingMessages:false});MathJax.Message.Set(["MathJaxNotSupported","Your browser does not support MathJax"],null,4000);b.Startup.signal.Post("MathJax not supported")}},MathJax.Hub,MathJax.OutputJax["HTML-CSS"]]);MathJax.OutputJax["HTML-CSS"].loadComplete("config.js");
MathJax.OutputJax.CommonHTML=MathJax.OutputJax({id:"CommonHTML",version:"2.5.0",directory:MathJax.OutputJax.directory+"/CommonHTML",extensionDir:MathJax.OutputJax.extensionDir+"/CommonHTML",config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.CommonHTML.Register("jax/mml")}MathJax.OutputJax.CommonHTML.loadComplete("config.js");
MathJax.Extension.tex2jax={version:"2.5.0",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],balanceBraces:true,skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c<a;c++){d.push(this.patternQuote(b.inlineMath[c][0]));this.match[b.inlineMath[c][0]]={mode:"",end:b.inlineMath[c][1],pattern:this.endPattern(b.inlineMath[c][1])}}for(c=0,a=b.displayMath.length;c<a;c++){d.push(this.patternQuote(b.displayMath[c][0]));this.match[b.displayMath[c][0]]={mode:"; mode=display",end:b.displayMath[c][1],pattern:this.endPattern(b.displayMath[c][1])}}if(d.length){e.push(d.sort(this.sortLength).join("|"))}if(b.processEnvironments){e.push("\\\\begin\\{([^}]*)\\}")}if(b.processEscapes){e.push("\\\\*\\\\\\$")}if(b.processRefs){e.push("\\\\(eq)?ref\\{[^}]*\\}")}this.start=new RegExp(e.join("|"),"g");this.skipTags=new RegExp("^("+b.skipTags.join("|")+")$","i");var f=[];if(MathJax.Hub.config.preRemoveClass){f.push(MathJax.Hub.config.preRemoveClass)}if(b.ignoreClass){f.push(b.ignoreClass)}this.ignoreClass=(f.length?new RegExp("(^| )("+f.join("|")+")( |$)"):/^$/);this.processClass=new RegExp("(^| )("+b.processClass+")( |$)");return(e.length>0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d<c?-1:1))},scanElement:function(c,b,g){var a,e,d,f;while(c&&c!=b){if(c.nodeName.toLowerCase()==="#text"){if(!g){c=this.scanText(c)}}else{a=(typeof(c.className)==="undefined"?"":c.className);e=(typeof(c.tagName)==="undefined"?"":c.tagName);if(typeof(a)!=="string"){a=String(a)}f=this.processClass.exec(a);if(c.firstChild&&!a.match(/(^| )MathJax/)&&(f||!this.skipTags.exec(e))){d=(g||this.ignoreClass.exec(a))&&!f;this.scanElement(c.firstChild,b,d)}}if(c){c=c.nextSibling}}},scanText:function(b){if(b.nodeValue.replace(/\s+/,"")==""){return b}var a,c;this.search={start:true};this.pattern=this.start;while(b){this.pattern.lastIndex=0;while(b&&b.nodeName.toLowerCase()==="#text"&&(a=this.pattern.exec(b.nodeValue))){if(this.search.start){b=this.startMatch(a,b)}else{b=this.endMatch(a,b)}}if(this.search.matched){b=this.encloseMath(b)}if(b){do{c=b;b=b.nextSibling}while(b&&(b.nodeName.toLowerCase()==="br"||b.nodeName.toLowerCase()==="#comment"));if(!b||b.nodeName!=="#text"){return(this.search.close?this.prevEndMatch():c)}}}return b},startMatch:function(a,b){var f=this.match[a[0]];if(f!=null){this.search={end:f.end,mode:f.mode,pcount:0,open:b,olen:a[0].length,opos:this.pattern.lastIndex-a[0].length};this.switchPattern(f.pattern)}else{if(a[0].substr(0,6)==="\\begin"){this.search={end:"\\end{"+a[1]+"}",mode:"; mode=display",pcount:0,open:b,olen:0,opos:this.pattern.lastIndex-a[0].length,isBeginEnd:true};this.switchPattern(this.endPattern(this.search.end))}else{if(a[0].substr(0,4)==="\\ref"||a[0].substr(0,6)==="\\eqref"){this.search={mode:"",end:"",open:b,pcount:0,olen:0,opos:this.pattern.lastIndex-a[0].length};return this.endMatch([""],b)}else{var d=a[0].substr(0,a[0].length-1),g,c;if(d.length%2===0){c=[d.replace(/\\\\/g,"\\")];g=1}else{c=[d.substr(1).replace(/\\\\/g,"\\"),"$"];g=0}c=MathJax.HTML.Element("span",null,c);var e=MathJax.HTML.TextNode(b.nodeValue.substr(0,a.index));b.nodeValue=b.nodeValue.substr(a.index+a[0].length-g);b.parentNode.insertBefore(c,b);b.parentNode.insertBefore(e,c);this.pattern.lastIndex=g}}}return b},endMatch:function(a,c){var b=this.search;if(a[0]==b.end){if(!b.close||b.pcount===0){b.close=c;b.cpos=this.pattern.lastIndex;b.clen=(b.isBeginEnd?0:a[0].length)}if(b.pcount===0){b.matched=true;c=this.encloseMath(c);this.switchPattern(this.start)}}else{if(a[0]==="{"){b.pcount++}else{if(a[0]==="}"&&b.pcount){b.pcount--}}}return c},prevEndMatch:function(){this.search.matched=true;var a=this.encloseMath(this.search.close);this.switchPattern(this.start);return a},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=(a===this.start)},encloseMath:function(b){var a=this.search,f=a.close,e,c;if(a.cpos===f.length){f=f.nextSibling}else{f=f.splitText(a.cpos)}if(!f){e=f=MathJax.HTML.addText(a.close.parentNode,"")}a.close=f;c=(a.opos?a.open.splitText(a.opos):a.open);while(c.nextSibling&&c.nextSibling!==f){if(c.nextSibling.nodeValue!==null){if(c.nextSibling.nodeName==="#comment"){c.nodeValue+=c.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{c.nodeValue+=c.nextSibling.nodeValue}}else{if(this.msieNewlineBug){c.nodeValue+=(c.nextSibling.nodeName.toLowerCase()==="br"?"\n":" ")}else{c.nodeValue+=" "}}c.parentNode.removeChild(c.nextSibling)}var d=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);if(this.config.preview!=="none"){this.createPreview(a.mode,d)}c=this.createMathTag(a.mode,d);this.search={};this.pattern.lastIndex=0;if(e){e.parentNode.removeChild(e)}return c},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(c,a){var b=this.config.preview;if(b==="none"){return}if(b==="TeX"){b=[this.filterPreview(a)]}if(b){b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b);this.insertNode(b)}},createMathTag:function(c,b){var a=document.createElement("script");a.type="math/tex"+c;MathJax.HTML.setScript(a,b);this.insertNode(a);return a},filterPreview:function(a){return a},msieNewlineBug:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9)};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js");
(function(d,h,l,g,m,b,j){var q="2.5.0";var i=MathJax.Extension;var c=i.MathEvents={version:q};var k=d.config.menuSettings;var p={hover:500,frame:{x:3.5,y:5,bwidth:1,bcolor:"#A6D",hwidth:"15px",hcolor:"#83A"},button:{x:-4,y:-3,wx:-2,src:l.urlRev(b.imageDir+"/MenuArrow-15.png")},fadeinInc:0.2,fadeoutInc:0.05,fadeDelay:50,fadeoutStart:400,fadeoutDelay:15*1000,styles:{".MathJax_Hover_Frame":{"border-radius":".25em","-webkit-border-radius":".25em","-moz-border-radius":".25em","-khtml-border-radius":".25em","box-shadow":"0px 0px 15px #83A","-webkit-box-shadow":"0px 0px 15px #83A","-moz-box-shadow":"0px 0px 15px #83A","-khtml-box-shadow":"0px 0px 15px #83A",border:"1px solid #A6D ! important",display:"inline-block",position:"absolute"},".MathJax_Hover_Arrow":{position:"absolute",width:"15px",height:"11px",cursor:"pointer"}}};var n=c.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",Mousedown:function(r){return n.Handler(r,"Mousedown",this)},Mouseup:function(r){return n.Handler(r,"Mouseup",this)},Mousemove:function(r){return n.Handler(r,"Mousemove",this)},Mouseover:function(r){return n.Handler(r,"Mouseover",this)},Mouseout:function(r){return n.Handler(r,"Mouseout",this)},Click:function(r){return n.Handler(r,"Click",this)},DblClick:function(r){return n.Handler(r,"DblClick",this)},Menu:function(r){return n.Handler(r,"ContextMenu",this)},Handler:function(u,s,t){if(l.loadingMathMenu){return n.False(u)}var r=b[t.jaxID];if(!u){u=window.event}u.isContextMenu=(s==="ContextMenu");if(r[s]){return r[s](u,t)}if(i.MathZoom){return i.MathZoom.HandleEvent(u,s,t)}},False:function(r){if(!r){r=window.event}if(r){if(r.preventDefault){r.preventDefault()}else{r.returnValue=false}if(r.stopPropagation){r.stopPropagation()}r.cancelBubble=true}return false},ContextMenu:function(u,F,x){var C=b[F.jaxID],w=C.getJaxFromMath(F);var G=(C.config.showMathMenu!=null?C:d).config.showMathMenu;if(!G||(k.context!=="MathJax"&&!x)){return}if(c.msieEventBug){u=window.event||u}n.ClearSelection();f.ClearHoverTimer();if(w.hover){if(w.hover.remove){clearTimeout(w.hover.remove);delete w.hover.remove}w.hover.nofade=true}var v=MathJax.Menu;var H,E;if(v){if(v.loadingDomain){return n.False(u)}H=m.loadDomain("MathMenu");if(!H){v.jax=w;var s=v.menu.Find("Show Math As").menu;s.items[0].name=w.sourceMenuTitle;s.items[0].format=(w.sourceMenuFormat||"MathML");s.items[1].name=j[w.inputJax].sourceMenuTitle;s.items[5].disabled=!j[w.inputJax].annotationEncoding;var B=s.items[2];B.disabled=true;var r=B.menu.items;annotationList=MathJax.Hub.Config.semanticsAnnotations;for(var A=0,z=r.length;A<z;A++){var t=r[A].name[1];if(w.root&&w.root.getAnnotation(t)!==null){B.disabled=false;r[A].hidden=false}else{r[A].hidden=true}}var y=v.menu.Find("Math Settings","MathPlayer");y.hidden=!(w.outputJax==="NativeMML"&&d.Browser.hasMathPlayer);return v.menu.Post(u)}v.loadingDomain=true;E=function(){delete v.loadingDomain}}else{if(l.loadingMathMenu){return n.False(u)}l.loadingMathMenu=true;H=l.Require("[MathJax]/extensions/MathMenu.js");E=function(){delete l.loadingMathMenu;if(!MathJax.Menu){MathJax.Menu={}}}}var D={pageX:u.pageX,pageY:u.pageY,clientX:u.clientX,clientY:u.clientY};g.Queue(H,E,["ContextMenu",n,D,F,x]);return n.False(u)},AltContextMenu:function(t,s){var u=b[s.jaxID];var r=(u.config.showMathMenu!=null?u:d).config.showMathMenu;if(r){r=(u.config.showMathMenuMSIE!=null?u:d).config.showMathMenuMSIE;if(k.context==="MathJax"&&!k.mpContext&&r){if(!c.noContextMenuBug||t.button!==n.RIGHTBUTTON){return}}else{if(!t[n.MENUKEY]||t.button!==n.LEFTBUTTON){return}}return u.ContextMenu(t,s,true)}},ClearSelection:function(){if(c.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(document.selection){setTimeout("document.selection.empty()",0)}},getBBox:function(t){t.appendChild(c.topImg);var s=c.topImg.offsetTop,u=t.offsetHeight-s,r=t.offsetWidth;t.removeChild(c.topImg);return{w:r,h:s,d:u}}};var f=c.Hover={Mouseover:function(t,s){if(k.discoverable||k.zoom==="Hover"){var v=t.fromElement||t.relatedTarget,u=t.toElement||t.target;if(v&&u&&(v.isMathJax!=u.isMathJax||d.getJaxFor(v)!==d.getJaxFor(u))){var r=this.getJaxFromMath(s);if(r.hover){f.ReHover(r)}else{f.HoverTimer(r,s)}return n.False(t)}}},Mouseout:function(t,s){if(k.discoverable||k.zoom==="Hover"){var v=t.fromElement||t.relatedTarget,u=t.toElement||t.target;if(v&&u&&(v.isMathJax!=u.isMathJax||d.getJaxFor(v)!==d.getJaxFor(u))){var r=this.getJaxFromMath(s);if(r.hover){f.UnHover(r)}else{f.ClearHoverTimer()}return n.False(t)}}},Mousemove:function(t,s){if(k.discoverable||k.zoom==="Hover"){var r=this.getJaxFromMath(s);if(r.hover){return}if(f.lastX==t.clientX&&f.lastY==t.clientY){return}f.lastX=t.clientX;f.lastY=t.clientY;f.HoverTimer(r,s);return n.False(t)}},HoverTimer:function(r,s){this.ClearHoverTimer();this.hoverTimer=setTimeout(g(["Hover",this,r,s]),p.hover)},ClearHoverTimer:function(){if(this.hoverTimer){clearTimeout(this.hoverTimer);delete this.hoverTimer}},Hover:function(r,v){if(i.MathZoom&&i.MathZoom.Hover({},v)){return}var u=b[r.outputJax],w=u.getHoverSpan(r,v),z=u.getHoverBBox(r,w,v),x=(u.config.showMathMenu!=null?u:d).config.showMathMenu;var B=p.frame.x,A=p.frame.y,y=p.frame.bwidth;if(c.msieBorderWidthBug){y=0}r.hover={opacity:0,id:r.inputID+"-Hover"};var s=h.Element("span",{id:r.hover.id,isMathJax:true,style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{className:"MathJax_Hover_Frame",isMathJax:true,style:{display:"inline-block",position:"absolute",top:this.Px(-z.h-A-y-(z.y||0)),left:this.Px(-B-y+(z.x||0)),width:this.Px(z.w+2*B),height:this.Px(z.h+z.d+2*A),opacity:0,filter:"alpha(opacity=0)"}}]]);var t=h.Element("span",{isMathJax:true,id:r.hover.id+"Menu",style:{display:"inline-block","z-index":1,width:0,height:0,position:"relative"}},[["img",{className:"MathJax_Hover_Arrow",isMathJax:true,math:v,src:p.button.src,onclick:this.HoverMenu,jax:u.id,style:{left:this.Px(z.w+B+y+(z.x||0)+p.button.x),top:this.Px(-z.h-A-y-(z.y||0)-p.button.y),opacity:0,filter:"alpha(opacity=0)"}}]]);if(z.width){s.style.width=t.style.width=z.width;s.style.marginRight=t.style.marginRight="-"+z.width;s.firstChild.style.width=z.width;t.firstChild.style.left="";t.firstChild.style.right=this.Px(p.button.wx)}w.parentNode.insertBefore(s,w);if(x){w.parentNode.insertBefore(t,w)}if(w.style){w.style.position="relative"}this.ReHover(r)},ReHover:function(r){if(r.hover.remove){clearTimeout(r.hover.remove)}r.hover.remove=setTimeout(g(["UnHover",this,r]),p.fadeoutDelay);this.HoverFadeTimer(r,p.fadeinInc)},UnHover:function(r){if(!r.hover.nofade){this.HoverFadeTimer(r,-p.fadeoutInc,p.fadeoutStart)}},HoverFade:function(r){delete r.hover.timer;r.hover.opacity=Math.max(0,Math.min(1,r.hover.opacity+r.hover.inc));r.hover.opacity=Math.floor(1000*r.hover.opacity)/1000;var t=document.getElementById(r.hover.id),s=document.getElementById(r.hover.id+"Menu");t.firstChild.style.opacity=r.hover.opacity;t.firstChild.style.filter="alpha(opacity="+Math.floor(100*r.hover.opacity)+")";if(s){s.firstChild.style.opacity=r.hover.opacity;s.firstChild.style.filter=t.style.filter}if(r.hover.opacity===1){return}if(r.hover.opacity>0){this.HoverFadeTimer(r,r.hover.inc);return}t.parentNode.removeChild(t);if(s){s.parentNode.removeChild(s)}if(r.hover.remove){clearTimeout(r.hover.remove)}delete r.hover},HoverFadeTimer:function(r,t,s){r.hover.inc=t;if(!r.hover.timer){r.hover.timer=setTimeout(g(["HoverFade",this,r]),(s||p.fadeDelay))}},HoverMenu:function(r){if(!r){r=window.event}return b[this.jax].ContextMenu(r,this.math,true)},ClearHover:function(r){if(r.hover.remove){clearTimeout(r.hover.remove)}if(r.hover.timer){clearTimeout(r.hover.timer)}f.ClearHoverTimer();delete r.hover},Px:function(r){if(Math.abs(r)<0.006){return"0px"}return r.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var r=new Image();r.src=p.button.src}}};var a=c.Touch={last:0,delay:500,start:function(s){var r=new Date().getTime();var t=(r-a.last<a.delay&&a.up);a.last=r;a.up=false;if(t){a.timeout=setTimeout(a.menu,a.delay,s,this);s.preventDefault()}},end:function(s){var r=new Date().getTime();a.up=(r-a.last<a.delay);if(a.timeout){clearTimeout(a.timeout);delete a.timeout;a.last=0;a.up=false;s.preventDefault();return n.Handler((s.touches[0]||s.touch),"DblClick",this)}},menu:function(s,r){delete a.timeout;a.last=0;a.up=false;return n.Handler((s.touches[0]||s.touch),"ContextMenu",r)}};if(d.Browser.isMobile){var 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(function(a,d,f,c,j){var k="2.5.0";var i=a.CombineConfig("MathZoom",{styles:{"#MathJax_Zoom":{position:"absolute","background-color":"#F0F0F0",overflow:"auto",display:"block","z-index":301,padding:".5em",border:"1px solid black",margin:0,"font-weight":"normal","font-style":"normal","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","box-shadow":"5px 5px 15px #AAAAAA","-webkit-box-shadow":"5px 5px 15px #AAAAAA","-moz-box-shadow":"5px 5px 15px #AAAAAA","-khtml-box-shadow":"5px 5px 15px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', 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true}if(!h[l]){return true}return h[l](n,m)},Click:function(m,l){if(this.settings.zoom==="Click"){return this.Zoom(m,l)}},DblClick:function(m,l){if(this.settings.zoom==="Double-Click"||this.settings.zoom==="DoubleClick"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(o,u){this.Remove();b.ClearHoverTimer();g.ClearSelection();var s=MathJax.OutputJax[u.jaxID];var p=s.getJaxFromMath(u);if(p.hover){b.UnHover(p)}var q=this.findContainer(u);var l=Math.floor(0.85*q.clientWidth),t=Math.max(document.body.clientHeight,document.documentElement.clientHeight);if(this.getOverflow(q)!=="visible"){t=Math.min(q.clientHeight,t)}t=Math.floor(0.85*t);var n=d.Element("span",{id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var z=n.lastChild,w=z.firstChild,r=n.firstChild;u.parentNode.insertBefore(n,u);u.parentNode.insertBefore(u,n);if(w.addEventListener){w.addEventListener("mousedown",this.Remove,true)}var m=z.offsetWidth||z.clientWidth;l-=m;t-=m;z.style.maxWidth=l+"px";z.style.maxHeight=t+"px";if(this.msieTrapEventBug){var y=d.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});n.insertBefore(y,z)}if(this.msieZIndexBug){var v=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});n.style.position="relative";n.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];n=v}var x=s.Zoom(p,w,u,l,t);if(this.msiePositionBug){if(this.msieSizeBug){z.style.height=x.zH+"px";z.style.width=x.zW+"px"}if(z.offsetHeight>t){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m<l&&z.offsetHeight-m<t){z.style.overflow="visible"}this.Position(z,x);if(this.msieTrapEventBug){y.style.height=z.clientHeight+"px";y.style.width=z.clientWidth+"px";y.style.left=(parseFloat(z.style.left)+z.clientLeft)+"px";y.style.top=(parseFloat(z.style.top)+z.clientTop)+"px"}z.style.visibility="";if(this.settings.zoom==="Hover"){r.onmouseover=this.Remove}if(window.addEventListener){addEventListener("resize",this.Resize,false)}else{if(window.attachEvent){attachEvent("onresize",this.Resize)}else{this.onresize=window.onresize;window.onresize=this.Resize}}a.signal.Post(["math zoomed",p]);return e(o)},Position:function(p,r){p.style.display="none";var q=this.Resize(),m=q.x,s=q.y,l=r.mW;p.style.display="";var o=-l-Math.floor((p.offsetWidth-l)/2),n=r.Y;p.style.left=Math.max(o,10-m)+"px";p.style.top=Math.max(n,10-s)+"px";if(!h.msiePositionBug){h.SetWH()}},Resize:function(m){if(h.onresize){h.onresize(m)}var q=document.getElementById("MathJax_ZoomFrame"),l=document.getElementById("MathJax_ZoomOverlay");var o=h.getXY(q),n=h.findContainer(q);if(h.getOverflow(n)!=="visible"){l.scroll_parent=n;var p=h.getXY(n);o.x-=p.x;o.y-=p.y;p=h.getBorder(n);o.x-=p.x;o.y-=p.y}l.style.left=(-o.x)+"px";l.style.top=(-o.y)+"px";if(h.msiePositionBug){setTimeout(h.SetWH,0)}else{h.SetWH()}return o},SetWH:function(){var l=document.getElementById("MathJax_ZoomOverlay");if(!l){return}l.style.display="none";var m=l.scroll_parent||document.documentElement||document.body;l.style.width=m.scrollWidth+"px";l.style.height=Math.max(m.clientHeight,m.scrollHeight)+"px";l.style.display=""},findContainer:function(l){l=l.parentNode;while(l.parentNode&&l!==document.body&&h.getOverflow(l)==="visible"){l=l.parentNode}return l},getOverflow:(window.getComputedStyle?function(l){return getComputedStyle(l).overflow}:function(l){return(l.currentStyle||{overflow:"visible"}).overflow}),getBorder:function(o){var m={thin:1,medium:2,thick:3};var n=(window.getComputedStyle?getComputedStyle(o):(o.currentStyle||{borderLeftWidth:0,borderTopWidth:0}));var l=n.borderLeftWidth,p=n.borderTopWidth;if(m[l]){l=m[l]}else{l=parseInt(l)}if(m[p]){p=m[p]}else{p=parseInt(p)}return{x:l,y:p}},getXY:function(o){var l=0,n=0,m;m=o;while(m.offsetParent){l+=m.offsetLeft;m=m.offsetParent}if(h.operaPositionBug){o.style.border="1px solid"}m=o;while(m.offsetParent){n+=m.offsetTop;m=m.offsetParent}if(h.operaPositionBug){o.style.border=""}return{x:l,y:n}},Remove:function(n){var p=document.getElementById("MathJax_ZoomFrame");if(p){var o=MathJax.OutputJax[p.previousSibling.jaxID];var l=o.getJaxFromMath(p.previousSibling);a.signal.Post(["math unzoomed",l]);p.parentNode.removeChild(p);p=document.getElementById("MathJax_ZoomTracker");if(p){p.parentNode.removeChild(p)}if(h.operaRefreshBug){var m=d.addElement(document.body,"div",{style:{position:"fixed",left:0,top:0,width:"100%",height:"100%",backgroundColor:"white",opacity:0},id:"MathJax_OperaDiv"});document.body.removeChild(m)}if(window.removeEventListener){removeEventListener("resize",h.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",h.Resize)}else{window.onresize=h.onresize;delete h.onresize}}}return e(n)}};a.Browser.Select({MSIE:function(l){var n=(document.documentMode||0);var m=(n>=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML);
(function(c,g,k,f,b){var q="2.5.0";var j=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:q,signal:j};var o=function(r){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",r]].concat([].slice.call(arguments,1)))};var n=c.Browser.isPC,l=c.Browser.isMSIE,e=((document.documentMode||0)>8);var i=(n?null:"5px");var p=c.CombineConfig("MathMenu",{delay:150,closeImg:k.urlRev(b.imageDir+"/CloseX-31.png"),showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 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#808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(n?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":i,"-webkit-border-radius":i,"-moz-border-radius":i,"-khtml-border-radius":i,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(n?"2px 2em":"1px 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3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(n?"Highlight":"#606872"),color:(n?"HighlightText":"white")},".MathJax_Menu_Close":{position:"absolute",width:"31px",height:"31px",top:"-15px",left:"-15px"}}});var h,d;c.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;d=MathJax.Extension.MathEvents.Hover});var a=MathJax.Menu=MathJax.Object.Subclass({version:q,items:[],posted:false,title:null,margin:5,Init:function(r){this.items=[].slice.call(arguments,0)},With:function(r){if(r){c.Insert(this,r)}return this},Post:function(s,C,A){if(!s){s=window.event}var r=document.getElementById("MathJax_MenuFrame");if(!r){r=a.Background(this);delete m.lastItem;delete m.lastMenu;delete a.skipUp;j.Post(["post",a.jax]);a.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var t=g.Element("div",{onmouseup:a.Mouseup,ondblclick:h,ondragstart:h,onselectstart:h,oncontextmenu:h,menuItem:this,className:"MathJax_Menu"});if(!A){MathJax.Localization.setCSS(t)}for(var v=0,u=this.items.length;v<u;v++){this.items[v].Create(t)}if(a.isMobile){g.addElement(t,"span",{className:"MathJax_Menu_Close",menu:C,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:p.closeImg,style:{width:"100%",height:"100%"}}]])}r.appendChild(t);this.posted=true;t.style.width=(t.offsetWidth+2)+"px";var B=s.pageX,z=s.pageY;if(!B&&!z){B=s.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;z=s.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!C){if(B+t.offsetWidth>document.body.offsetWidth-this.margin){B=document.body.offsetWidth-t.offsetWidth-this.margin}if(a.isMobile){B=Math.max(5,B-Math.floor(t.offsetWidth/2));z-=20}a.skipUp=s.isContextMenu}else{var w="left",D=C.offsetWidth;B=(a.isMobile?30:D-2);z=0;while(C&&C!==r){B+=C.offsetLeft;z+=C.offsetTop;C=C.parentNode}if(!a.isMobile){if((a.isRTL&&B-D-t.offsetWidth>this.margin)||(!a.isRTL&&B+t.offsetWidth>document.body.offsetWidth-this.margin)){w="right";B=Math.max(this.margin,B-D-t.offsetWidth+6)}}if(!n){t.style["borderRadiusTop"+w]=0;t.style["WebkitBorderRadiusTop"+w]=0;t.style["MozBorderRadiusTop"+w]=0;t.style["KhtmlBorderRadiusTop"+w]=0}}t.style.left=B+"px";t.style.top=z+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(s)},Remove:function(r,s){j.Post(["unpost",a.jax]);var t=document.getElementById("MathJax_MenuFrame");if(t){t.parentNode.removeChild(t);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(r)},Find:function(r){return this.FindN(1,r,[].slice.call(arguments,1))},FindId:function(r){return this.FindN(0,r,[].slice.call(arguments,1))},FindN:function(v,s,u){for(var t=0,r=this.items.length;t<r;t++){if(this.items[t].name[v]===s){if(u.length){if(!this.items[t].menu){return null}return this.items[t].menu.FindN(v,u[0],u.slice(1))}return this.items[t]}}return null},IndexOf:function(r){return this.IndexOfN(1,r)},IndexOfId:function(r){return this.IndexOfN(0,r)},IndexOfN:function(u,s){for(var t=0,r=this.items.length;t<r;t++){if(this.items[t].name[u]===s){return t}}return null}},{config:p,div:null,Close:function(r){return a.Event(r,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(r){return a.Event(r,this,"Remove")},Mouseover:function(r){return a.Event(r,this,"Mouseover")},Mouseout:function(r){return a.Event(r,this,"Mouseout")},Mousedown:function(r){return a.Event(r,this,"Mousedown")},Mouseup:function(r){return a.Event(r,this,"Mouseup")},Touchstart:function(r){return a.Event(r,this,"Touchstart")},Touchend:function(r){return a.Event(r,this,"Touchend")},Event:function(t,v,r,u){if(a.skipMouseover&&r==="Mouseover"&&!u){return h(t)}if(a.skipUp){if(r.match(/Mouseup|Touchend/)){delete a.skipUp;return h(t)}if(r==="Touchstart"||(r==="Mousedown"&&!a.skipMousedown)){delete a.skipUp}}if(!t){t=window.event}var s=v.menuItem;if(s&&s[r]){return s[r](t,v)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(s){var t=g.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:s,onmousedown:this.Remove}]]);var r=t.firstChild;if(a.msieBackgroundBug){r.style.backgroundColor="white";r.style.filter="alpha(opacity=0)"}if(a.msieFixedPositionBug){t.width=t.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{r.style.position="fixed"}return t},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var r=document.getElementById("MathJax_MenuFrame");if(r){r=r.firstChild;r.style.width=r.style.height="1px";r.style.width=document.body.scrollWidth+"px";r.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){g.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=g.Cookie.Get("menu")},getImages:function(){if(a.isMobile){var r=new Image();r.src=p.closeImg}}});var m=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(s){if(!this.hidden){var r={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:a.Mousedown,ondragstart:h,onselectstart:h,onselectend:h,ontouchstart:a.Touchstart,ontouchend:a.Touchend,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){r.className+=" MathJax_MenuDisabled"}g.addElement(s,"div",r,this.Label(r,s))}},Name:function(){return o(this.name[0],this.name[1])},Mouseover:function(v,x){if(!this.disabled){this.Activate(x)}if(!this.menu||!this.menu.posted){var 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]/)){a.ITEM.SUBMENU.Augment({marker:"\u00BB"})}})()}a.CreateLocaleMenu();a.CreateAnnotationMenu()});a.showRenderer=function(r){a.cookie.showRenderer=p.showRenderer=r;a.saveCookie();a.menu.Find("Math Settings","Math Renderer").hidden=!r};a.showMathPlayer=function(r){a.cookie.showMathPlayer=p.showMathPlayer=r;a.saveCookie();a.menu.Find("Math Settings","MathPlayer").hidden=!r};a.showFontMenu=function(r){a.cookie.showFontMenu=p.showFontMenu=r;a.saveCookie();a.menu.Find("Math Settings","Font Preference").hidden=!r};a.showContext=function(r){a.cookie.showContext=p.showContext=r;a.saveCookie();a.menu.Find("Math Settings","Contextual Menu").hidden=!r};a.showDiscoverable=function(r){a.cookie.showDiscoverable=p.showDiscoverable=r;a.saveCookie();a.menu.Find("Math Settings","Highlight on Hover").hidden=!r;a.menu.Find("Math 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clarify"])}if(n.type!=="msubsup"){if(m){if(n.type!=="munderover"||n.data[n.under]){if(n.movablelimits&&n.isa(h.mi)){n=this.mi2mo(n)}n=h.munderover(n,null,null).With({movesupsub:true})}l=n.under}else{n=h.msubsup(n,null,null);l=n.sub}}this.Push(b.subsup(n).With({position:l,primes:p,movesupsub:m}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(n){var m=this.stack.Prev();if(!m){m=h.mi()}if(m.type==="msubsup"&&m.data[m.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var l="";this.i--;do{l+=this.PRIME;this.i++,n=this.GetNext()}while(n==="'"||n===this.SMARTQUOTE);l=["","\u2032","\u2033","\u2034","\u2057"][l.length]||l;this.Push(b.prime(m,this.mmlToken(h.mo(l))))},mi2mo:function(l){var m=h.mo();m.Append.apply(m,l.data);var n;for(n in m.defaults){if(m.defaults.hasOwnProperty(n)&&l[n]!=null){m[n]=l[n]}}for(n in h.copyAttributes){if(h.copyAttributes.hasOwnProperty(n)&&l[n]!=null){m[n]=l[n]}}return m},Comment:function(l){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(l){d.Error(["CantUseHash1","You can't use 'macro parameter character #' in math mode"])},Other:function(n){var m,l;if(this.stack.env.font){m={mathvariant:this.stack.env.font}}if(f.remap[n]){n=f.remap[n];if(n instanceof Array){m=n[1];n=n[0]}l=h.mo(h.entity("#x"+n)).With(m)}else{l=h.mo(n).With(m)}if(l.autoDefault("stretchy",true)){l.stretchy=false}if(l.autoDefault("texClass",true)==""){l=h.TeXAtom(l)}this.Push(this.mmlToken(l))},SetFont:function(m,l){this.stack.env.font=l},SetStyle:function(m,l,n,o){this.stack.env.style=l;this.stack.env.level=o;this.Push(b.style().With({styles:{displaystyle:n,scriptlevel:o}}))},SetSize:function(l,m){this.stack.env.size=m;this.Push(b.style().With({styles:{mathsize:m+"em"}}))},Color:function(n){var m=this.GetArgument(n);var l=this.stack.env.color;this.stack.env.color=m;var o=this.ParseArg(n);if(l){this.stack.env.color}else{delete this.stack.env.color}this.Push(h.mstyle(o).With({mathcolor:m}))},Spacer:function(l,m){this.Push(h.mspace().With({width:m,mathsize:h.SIZE.NORMAL,scriptlevel:0}))},LeftRight:function(l){this.Push(b[l.substr(1)]().With({delim:this.GetDelimiter(l)}))},Middle:function(l){var m=this.GetDelimiter(l);if(this.stack.Top().type!=="left"){d.Error(["MisplacedMiddle","%1 must be within \\left and \\right",l])}this.Push(h.mo(m).With({stretchy:true}))},NamedFn:function(m,n){if(!n){n=m.substr(1)}var l=h.mi(n).With({texClass:h.TEXCLASS.OP});this.Push(b.fn(this.mmlToken(l)))},NamedOp:function(m,n){if(!n){n=m.substr(1)}n=n.replace(/&thinsp;/,"\u2006");var l=h.mo(n).With({movablelimits:true,movesupsub:true,form:h.FORM.PREFIX,texClass:h.TEXCLASS.OP});l.useMMLspacing&=~l.SPACE_ATTR.form;this.Push(this.mmlToken(l))},Limits:function(m,l){var o=this.stack.Prev("nopop");if(!o||(o.Get("texClass")!==h.TEXCLASS.OP&&o.movesupsub==null)){d.Error(["MisplacedLimits","%1 is allowed only on operators",m])}var n=this.stack.Top();if(o.type==="munderover"&&!l){o=n.data[n.data.length-1]=h.msubsup.apply(h.subsup,o.data)}else{if(o.type==="msubsup"&&l){o=n.data[n.data.length-1]=h.munderover.apply(h.underover,o.data)}}o.movesupsub=(l?true:false);o.Core().movablelimits=false},Over:function(n,m,o){var l=b.over().With({name:n});if(m||o){l.open=m;l.close=o}else{if(n.match(/withdelims$/)){l.open=this.GetDelimiter(n);l.close=this.GetDelimiter(n)}}if(n.match(/^\\above/)){l.thickness=this.GetDimen(n)}else{if(n.match(/^\\atop/)||m||o){l.thickness=0}}this.Push(l)},Frac:function(m){var l=this.ParseArg(m);var n=this.ParseArg(m);this.Push(h.mfrac(l,n))},Sqrt:function(o){var p=this.GetBrackets(o),l=this.GetArgument(o);if(l==="\\frac"){l+="{"+this.GetArgument(l)+"}{"+this.GetArgument(l)+"}"}var m=d.Parse(l,this.stack.env).mml();if(!p){m=h.msqrt.apply(h,m.array())}else{m=h.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(m){var o=this.GetUpTo(m,"\\of");var l=this.ParseArg(m);this.Push(h.mroot(l,this.parseRoot(o)))},parseRoot:function(q){var m=this.stack.env,l=m.inRoot;m.inRoot=true;var p=d.Parse(q,m);q=p.mml();var o=p.stack.global;if(o.leftRoot||o.upRoot){q=h.mpadded(q);if(o.leftRoot){q.width=o.leftRoot}if(o.upRoot){q.voffset=o.upRoot;q.height=o.upRoot}}m.inRoot=l;return q},MoveRoot:function(l,o){if(!this.stack.env.inRoot){d.Error(["MisplacedMoveRoot","%1 can appear only within a root",l])}if(this.stack.global[o]){d.Error(["MultipleMoveRoot","Multiple use of %1",l])}var m=this.GetArgument(l);if(!m.match(/-?[0-9]+/)){d.Error(["IntegerArg","The argument to %1 must be an integer",l])}m=(m/15)+"em";if(m.substr(0,1)!=="-"){m="+"+m}this.stack.global[o]=m},Accent:function(n,l,q){var p=this.ParseArg(n);var o={accent:true};if(this.stack.env.font){o.mathvariant=this.stack.env.font}var m=this.mmlToken(h.mo(h.entity("#x"+l)).With(o));m.stretchy=(q?true:false);this.Push(h.TeXAtom(h.munderover(p,null,m).With({accent:true})))},UnderOver:function(n,q,l){var p={o:"over",u:"under"}[n.charAt(1)];var o=this.ParseArg(n);if(o.Get("movablelimits")){o.movablelimits=false}if(o.isa(h.munderover)&&o.isEmbellished()){o.Core().With({lspace:0,rspace:0});o=h.mrow(h.mo().With({rspace:0}),o)}var m=h.munderover(o,null,null);m.SetData(m[p],this.mmlToken(h.mo(h.entity("#x"+q)).With({stretchy:true,accent:(p==="under")})));if(l){m=h.TeXAtom(m).With({texClass:h.TEXCLASS.OP,movesupsub:true})}this.Push(m.With({subsupOK:true}))},Overset:function(l){var n=this.ParseArg(l),m=this.ParseArg(l);this.Push(h.mover(m,n))},Underset:function(l){var n=this.ParseArg(l),m=this.ParseArg(l);this.Push(h.munder(m,n))},TeXAtom:function(o,q){var p={texClass:q},n;if(q==h.TEXCLASS.OP){p.movesupsub=p.movablelimits=true;var l=this.GetArgument(o);var m=l.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(m){p.mathvariant=h.VARIANT.NORMAL;n=b.fn(this.mmlToken(h.mi(m[1]).With(p)))}else{n=b.fn(h.TeXAtom(d.Parse(l,this.stack.env).mml()).With(p))}}else{n=h.TeXAtom(this.ParseArg(o)).With(p)}this.Push(n)},MmlToken:function(n){var o=this.GetArgument(n),l=this.GetBrackets(n,"").replace(/^\s+/,""),r=this.GetArgument(n),q={attrNames:[]},m;if(!h[o]||!h[o].prototype.isToken){d.Error(["NotMathMLToken","%1 is not a token element",o])}while(l!==""){m=l.match(/^([a-z]+)\s*=\s*('[^']*'|"[^"]*"|[^ ,]*)\s*,?\s*/i);if(!m){d.Error(["InvalidMathMLAttr","Invalid MathML attribute: %1",l])}if(h[o].prototype.defaults[m[1]]==null&&!this.MmlTokenAllow[m[1]]){d.Error(["UnknownAttrForElement","%1 is not a recognized attribute for %2",m[1],o])}var p=this.MmlFilterAttribute(m[1],m[2].replace(/^(['"])(.*)\1$/,"$2"));if(p){if(p.toLowerCase()==="true"){p=true}else{if(p.toLowerCase()==="false"){p=false}}q[m[1]]=p;q.attrNames.push(m[1])}l=l.substr(m[0].length)}this.Push(this.mmlToken(h[o](r).With(q)))},MmlFilterAttribute:function(l,m){return m},MmlTokenAllow:{fontfamily:1,fontsize:1,fontweight:1,fontstyle:1,color:1,background:1,id:1,"class":1,href:1,style:1},Strut:function(l){this.Push(h.mpadded(h.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(m,l,n){var o=h.mphantom(this.ParseArg(m));if(l||n){o=h.mpadded(o);if(n){o.height=o.depth=0}if(l){o.width=0}}this.Push(h.TeXAtom(o))},Smash:function(n){var m=this.trimSpaces(this.GetBrackets(n,""));var l=h.mpadded(this.ParseArg(n));switch(m){case"b":l.depth=0;break;case"t":l.height=0;break;default:l.height=l.depth=0}this.Push(h.TeXAtom(l))},Lap:function(m){var l=h.mpadded(this.ParseArg(m)).With({width:0});if(m==="\\llap"){l.lspace="-1width"}this.Push(h.TeXAtom(l))},RaiseLower:function(l){var m=this.GetDimen(l);var n=b.position().With({name:l,move:"vertical"});if(m.charAt(0)==="-"){m=m.slice(1);l={raise:"\\lower",lower:"\\raise"}[l.substr(1)]}if(l==="\\lower"){n.dh="-"+m;n.dd="+"+m}else{n.dh="+"+m;n.dd="-"+m}this.Push(n)},MoveLeftRight:function(l){var o=this.GetDimen(l);var n=(o.charAt(0)==="-"?o.slice(1):"-"+o);if(l==="\\moveleft"){var m=o;o=n;n=m}this.Push(b.position().With({name:l,move:"horizontal",left:h.mspace().With({width:o,mathsize:h.SIZE.NORMAL}),right:h.mspace().With({width:n,mathsize:h.SIZE.NORMAL})}))},Hskip:function(l){this.Push(h.mspace().With({width:this.GetDimen(l),mathsize:h.SIZE.NORMAL}))},Rule:function(n,p){var l=this.GetDimen(n),o=this.GetDimen(n),r=this.GetDimen(n);var m,q={width:l,height:o,depth:r};if(p!=="blank"){if(parseFloat(l)&&parseFloat(o)+parseFloat(r)){q.mathbackground=(this.stack.env.color||"black")}m=h.mpadded(h.mrow()).With(q)}else{m=h.mspace().With(q)}this.Push(m)},MakeBig:function(l,o,m){m*=f.p_height;m=String(m).replace(/(\.\d\d\d).+/,"$1")+"em";var n=this.GetDelimiter(l,true);this.Push(h.TeXAtom(h.mo(n).With({minsize:m,maxsize:m,fence:true,stretchy:true,symmetric:true})).With({texClass:o}))},BuildRel:function(l){var m=this.ParseUpTo(l,"\\over");var n=this.ParseArg(l);this.Push(h.TeXAtom(h.munderover(n,null,m)).With({texClass:h.TEXCLASS.REL}))},HBox:function(l,m){this.Push.apply(this,this.InternalMath(this.GetArgument(l),m))},FBox:function(l){this.Push(h.menclose.apply(h,this.InternalMath(this.GetArgument(l))).With({notation:"box"}))},Not:function(l){this.Push(b.not())},Dots:function(l){this.Push(b.dots().With({ldots:this.mmlToken(h.mo(h.entity("#x2026")).With({stretchy:false})),cdots:this.mmlToken(h.mo(h.entity("#x22EF")).With({stretchy:false}))}))},Require:function(l){var m=this.GetArgument(l).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");this.Extension(null,m)},Extension:function(l,m,n){if(l&&!typeof(l)==="string"){l=l.name}m=d.extensionDir+"/"+m;if(!m.match(/\.js$/)){m+=".js"}if(!i.loaded[i.fileURL(m)]){if(l!=null){delete f[n||"macros"][l.replace(/^\\/,"")]}c.RestartAfter(i.Require(m))}},Macro:function(n,q,p,r){if(p){var m=[];if(r!=null){var l=this.GetBrackets(n);m.push(l==null?r:l)}for(var o=m.length;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(m,o,u,q,t,n,l,v,s){var r=this.GetNext();if(r===""){d.Error(["MissingArgFor","Missing argument for %1",m])}if(r==="{"){this.i++}else{this.string=r+"}"+this.string.slice(this.i+1);this.i=0}var p=b.array().With({requireClose:true,arraydef:{rowspacing:(n||"4pt"),columnspacing:(t||"1em")}});if(v){p.isCases=true}if(s){p.isNumbered=true;p.arraydef.side=s}if(o||u){p.open=o;p.close=u}if(l==="D"){p.arraydef.displaystyle=true}if(q!=null){p.arraydef.columnalign=q}this.Push(p)},Entry:function(o){this.Push(b.cell().With({isEntry:true,name:o}));if(this.stack.Top().isCases){var n=this.string;var r=0,p=this.i,l=n.length;while(p<l){var s=n.charAt(p);if(s==="{"){r++;p++}else{if(s==="}"){if(r===0){l=0}else{r--;p++}}else{if(s==="&"&&r===0){d.Error(["ExtraAlignTab","Extra alignment tab in \\cases text"])}else{if(s==="\\"){if(n.substr(p).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){l=0}else{p+=2}}else{p++}}}}}var q=n.substr(this.i,p-this.i);if(!q.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(q,0));this.i=p}}},Cr:function(l){this.Push(b.cell().With({isCR:true,name:l}))},CrLaTeX:function(l){var p;if(this.string.charAt(this.i)==="["){p=this.GetBrackets(l,"").replace(/ /g,"").replace(/,/,".");if(p&&!this.matchDimen(p)){d.Error(["BracketMustBeDimension","Bracket argument to %1 must be a dimension",l])}}this.Push(b.cell().With({isCR:true,name:l,linebreak:true}));var o=this.stack.Top();if(o.isa(b.array)){if(p&&o.arraydef.rowspacing){var m=o.arraydef.rowspacing.split(/ /);if(!o.rowspacing){o.rowspacing=this.dimen2em(m[0])}while(m.length<o.table.length){m.push(this.Em(o.rowspacing))}m[o.table.length-1]=this.Em(Math.max(0,o.rowspacing+this.dimen2em(p)));o.arraydef.rowspacing=m.join(" ")}}else{if(p){this.Push(h.mspace().With({depth:p}))}this.Push(h.mspace().With({linebreak:h.LINEBREAK.NEWLINE}))}},emPerInch:7.2,pxPerInch:72,matchDimen:function(l){return l.match(/^(-?(?:\.\d+|\d+(?:\.\d*)?))(px|pt|em|ex|mu|pc|in|mm|cm)$/)},dimen2em:function(p){var n=this.matchDimen(p);var l=parseFloat(n[1]||"1"),o=n[2];if(o==="em"){return l}if(o==="ex"){return l*0.43}if(o==="pt"){return l/10}if(o==="pc"){return l*1.2}if(o==="px"){return l*this.emPerInch/this.pxPerInch}if(o==="in"){return l*this.emPerInch}if(o==="cm"){return l*this.emPerInch/2.54}if(o==="mm"){return l*this.emPerInch/25.4}if(o==="mu"){return l/18}return 0},Em:function(l){if(Math.abs(l)<0.0006){return"0em"}return l.toFixed(3).replace(/\.?0+$/,"")+"em"},HLine:function(m,n){if(n==null){n="solid"}var o=this.stack.Top();if(!o.isa(b.array)||o.data.length){d.Error(["Misplaced","Misplaced %1",m])}if(o.table.length==0){o.frame.push("top")}else{var l=(o.arraydef.rowlines?o.arraydef.rowlines.split(/ /):[]);while(l.length<o.table.length){l.push("none")}l[o.table.length-1]=n;o.arraydef.rowlines=l.join(" ")}},HFill:function(l){var m=this.stack.Top();if(m.isa(b.array)){m.hfill.push(m.data.length)}else{d.Error(["UnsupportedHFill","Unsupported use of %1",l])}},BeginEnd:function(n){var o=this.GetArgument(n),q=false;if(o.match(/^\\end\\/)){q=true;o=o.substr(5)}if(o.match(/\\/i)){d.Error(["InvalidEnv","Invalid environment name '%1'",o])}var p=this.envFindName(o);if(!p){d.Error(["UnknownEnv","Unknown environment '%1'",o])}if(!(p instanceof Array)){p=[p]}var l=(p[1] instanceof Array?p[1][0]:p[1]);var m=b.begin().With({name:o,end:l,parse:this});if(n==="\\end"){if(!q&&p[1] instanceof Array&&this[p[1][1]]){m=this[p[1][1]].apply(this,[m].concat(p.slice(2)))}else{m=b.end().With({name:o})}}else{if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(p[0]&&this[p[0]]){m=this[p[0]].apply(this,[m].concat(p.slice(2)))}}this.Push(m)},envFindName:function(l){return f.environment[l]},Equation:function(l,m){return m},ExtensionEnv:function(m,l){this.Extension(m.name,l,"environment")},Array:function(m,o,t,r,s,n,l,p){if(!r){r=this.GetArgument("\\begin{"+m.name+"}")}var u=("c"+r).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");r=r.replace(/[^clr]/g,"").split("").join(" ");r=r.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var q=b.array().With({arraydef:{columnalign:r,columnspacing:(s||"1em"),rowspacing:(n||"4pt")}});if(u.match(/[|:]/)){if(u.charAt(0).match(/[|:]/)){q.frame.push("left");q.frame.dashed=u.charAt(0)===":"}if(u.charAt(u.length-1).match(/[|:]/)){q.frame.push("right")}u=u.substr(1,u.length-2);q.arraydef.columnlines=u.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(o){q.open=this.convertDelimiter(o)}if(t){q.close=this.convertDelimiter(t)}if(l==="D"){q.arraydef.displaystyle=true}else{if(l){q.arraydef.displaystyle=false}}if(l==="S"){q.arraydef.scriptlevel=1}if(p){q.arraydef.useHeight=false}this.Push(m);return q},AlignedArray:function(l){var m=this.GetBrackets("\\begin{"+l.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),m)},setArrayAlign:function(m,l){l=this.trimSpaces(l||"");if(l==="t"){m.arraydef.align="baseline 1"}else{if(l==="b"){m.arraydef.align="baseline 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c=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":c,"\u2323":c,"\u25B3":c,"\uE006":c,"\uE007":c,"\uE00C":c,"\uE00D":c,"\uE00E":c,"\uE00F":c,"\uE010":c,"\uE011":c,"\uE016":c,"\uE017":c,"\uE018":c,"\uE019":c,"\uE01A":c,"\uE01B":c,"\uE04B":c,"\uE04F":c}}});MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js");
(function(h,b,d){var g,i=b.Browser.isMobile;var e=function(){var k=[].slice.call(arguments,0);k[0][0]=["HTML-CSS",k[0][0]];return MathJax.Message.Set.apply(MathJax.Message,k)};var f=MathJax.Object.Subclass({timeout:(i?15:8)*1000,comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],FedoraSTIXcheck:{family:"STIXSizeOneSym",testString:"abcABC",noStyleChar:true},Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",width:0,height:0,overflow:"hidden",padding:0,border:0,margin:0}},[["div",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto",padding:0,border:0,margin:0,whiteSpace:"nowrap",textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal",fontSizeAdjust:"none"}},[""]]]).firstChild;this.text=this.div.firstChild},findFont:function(p,l){var o=null;if(l&&this.testCollection(l)){o=l}else{for(var 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q}});var j,a,c;d.Augment({config:{styles:{".MathJax":{display:"inline","font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none",direction:"ltr","max-width":"none","max-height":"none","min-width":0,"min-height":0,border:0,padding:0,margin:0},".MathJax_Display":{position:"relative",display:"block!important","text-indent":0,"max-width":"none","max-height":"none","min-width":0,"min-height":0,width:"100%"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","min-width":0,"min-height":0,"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!important",overflow:"hidden",width:"1px",height:"60ex","min-height":0,"max-height":"none"},".MathJax .MathJax_EmBox":{display:"block!important",overflow:"hidden",width:"1px",height:"60em","min-height":0,"max-height":"none"},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity=0)"},".MathJax .MathJax_HitBox *":{filter:"none",opacity:1,background:"transparent"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",opacity:1,background:"transparent"},"@font-face":{"font-family":"MathJax_Blank",src:"url('about:blank')"}}},settings:b.config.menuSettings,Font:null,webFontDefault:"MathJax_Blank",allowWebFonts:"otf",maxStretchyParts:1000,fontName:{TeXLocal:"TeX",TeXWeb:["","TeX"],TeXImage:["",""],STIXLocal:["STIX","STIX-Web"],STIXWeb:"STIX-Web",AsanaMathWeb:"Asana-Math",GyrePagellaWeb:"Gyre-Pagella",GyreTermesWeb:"Gyre-Termes",LatinModernWeb:"Latin-Modern",NeoEulerWeb:"Neo-Euler"},fontInUse:"generic",FONTDATA:{TeX_factor:1,baselineskip:1.2,lineH:0.8,lineD:0.2,ffLineH:0.8,FONTS:{},VARIANT:{normal:{fonts:[]},"-generic-variant":{},"-largeOp":{},"-smallOp":{}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}},Config:function(){if(!this.require){this.require=[]}this.Font=f();this.SUPER(arguments).Config.call(this);var m=this.settings,l=this.config,k=m.font;if(this.adjustAvailableFonts){this.adjustAvailableFonts(l.availableFonts)}if(m.scale){l.scale=m.scale}if(k&&k!=="Auto"&&this.fontName[k]){l.availableFonts=[];delete l.fonts;if(this.fontName[k] instanceof Array){l.preferredFont=this.fontName[k][0];l.webFont=this.fontName[k][1]}else{l.preferredFont=l.webFont=this.fontName[k]}if(l.preferredFont){l.availableFonts[0]=l.preferredFont}}if(l.fonts){l.availableFonts=l.fonts;l.preferredFont=l.webFont=l.fonts[0];if(l.webFont==="STIX"){l.webFont+="-Web"}}k=this.Font.findFont(l.availableFonts,l.preferredFont);if(!k&&this.allowWebFonts){k=l.webFont;if(k){this.webFonts=true}}if(!k&&this.config.imageFont){k=l.imageFont;this.imgFonts=true}if(k){this.fontInUse=k;this.fontDir+="/"+k;this.webfontDir+="/"+k;this.require.push(this.fontDir+"/fontdata.js");if(this.imgFonts){this.require.push(this.directory+"/imageFonts.js");b.Startup.signal.Post("HTML-CSS Jax - using image fonts")}}else{e(["CantFindFontUsing","Can't find a valid font using %1","["+this.config.availableFonts.join(", ")+"]"],null,3000);b.Startup.signal.Post("HTML-CSS Jax - no valid font")}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=c.Mouseover;this.Mouseout=c.Mouseout;this.Mousemove=c.Mousemove;this.hiddenDiv=this.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=this.addElement(this.hiddenDiv,"div",{id:"MathJax_Hidden"});var l=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=l.offsetWidth/5;this.hiddenDiv.removeChild(l);this.startMarker=this.createStrut(this.Element("span"),10,true);this.endMarker=this.addText(this.Element("span"),"x").parentNode;this.HDspan=this.Element("span");if(this.operaHeightBug){this.createStrut(this.HDspan,0)}if(this.msieInlineBlockAlignBug){this.HDimg=this.addElement(this.HDspan,"img",{style:{height:"0px",width:"1px"}});try{this.HDimg.src="about:blank"}catch(k){}}else{this.HDimg=this.createStrut(this.HDspan,0)}this.EmExSpan=this.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["span",{className:"MathJax_ExBox"}],["span",{className:"MathJax"},[["span",{className:"MathJax_EmBox"}]]]]);this.linebreakSpan=this.Element("span",null,[["hr",{style:{width:"100%",size:1,padding:0,border:0,margin:0}}]]);return h.Styles(this.config.styles,["InitializeHTML",this])},removeSTIXfonts:function(n){for(var l=0,k=n.length;l<k;l++){if(n[l]==="STIX"){n.splice(l,1);k--;l--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=n[0]}},PreloadWebFonts:function(){if(!d.allowWebFonts||!d.config.preloadWebFonts){return}for(var l=0,k=d.config.preloadWebFonts.length;l<k;l++){var n=d.FONTDATA.FONTS[d.config.preloadWebFonts[l]];if(!n.available){d.Font.testFont(n)}}},InitializeHTML:function(){this.PreloadWebFonts();this.getDefaultExEm();if(this.defaultEm){return}var k=MathJax.Callback();h.timer.start(h,function(l){if(l.time(k)){b.signal.Post(["HTML-CSS Jax - no default em size"]);return}d.getDefaultExEm();if(d.defaultEm){k()}else{setTimeout(l,l.delay)}},this.defaultEmDelay,this.defaultEmTimeout);return k},defaultEmDelay:100,defaultEmTimeout:1000,getDefaultExEm:function(){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(q){var p=q.jax[this.id],B,x=p.length,w,E,u,A,s,C,l,D,k,F,t,r=false,y,o=this.config.linebreaks.automatic,v=this.config.linebreaks.width;if(o){r=(v.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)!=null);if(r){v=v.replace(/\s*container\s*/,"")}else{t=this.defaultWidth}if(v===""){v="100%"}}else{t=100000}for(B=0;B<x;B++){E=p[B];if(!E.parentNode){continue}u=E.previousSibling;if(u&&String(u.className).match(/^MathJax(_Display)?( MathJax_Processing)?$/)){u.parentNode.removeChild(u)}l=E.MathJax.elementJax;if(!l){continue}l.HTMLCSS={display:(l.root.Get("display")==="block")};A=s=this.Element("span",{className:"MathJax",id:l.inputID+"-Frame",isMathJax:true,jaxID:this.id,oncontextmenu:j.Menu,onmousedown:j.Mousedown,onmouseover:j.Mouseover,onmouseout:j.Mouseout,onmousemove:j.Mousemove,onclick:j.Click,ondblclick:j.DblClick});if(b.Browser.noContextMenu){A.ontouchstart=a.start;A.ontouchend=a.end}if(l.HTMLCSS.display){s=this.Element("div",{className:"MathJax_Display"});s.appendChild(A)}else{if(this.msieDisappearingBug){A.style.display="inline-block"}}s.className+=" MathJax_Processing";E.parentNode.insertBefore(s,E);E.parentNode.insertBefore(this.EmExSpan.cloneNode(true),E);s.parentNode.insertBefore(this.linebreakSpan.cloneNode(true),s)}var z=[];for(B=0;B<x;B++){E=p[B];if(!E.parentNode){continue}C=E.previousSibling;s=C.previousSibling;l=E.MathJax.elementJax;if(!l){continue}D=C.firstChild.offsetHeight/60;k=C.lastChild.firstChild.offsetHeight/60;y=s.previousSibling.firstChild.offsetWidth;if(r){t=y}if(D===0||D==="NaN"){z.push(s);l.HTMLCSS.isHidden=true;D=this.defaultEx;k=this.defaultEm;y=this.defaultWidth;if(r){t=y}}F=(this.config.matchFontHeight?D/this.TeX.x_height/k:1);F=Math.floor(Math.max(this.config.minScaleAdjust/100,F)*this.config.scale);l.HTMLCSS.scale=F/100;l.HTMLCSS.fontSize=F+"%";l.HTMLCSS.em=l.HTMLCSS.outerEm=k;this.em=k*F/100;l.HTMLCSS.ex=D;l.HTMLCSS.cwidth=y/this.em;l.HTMLCSS.lineWidth=(o?this.length2em(v,1,t/this.em):1000000)}for(B=0,w=z.length;B<w;B++){this.hiddenDiv.appendChild(z[B]);this.addElement(this.hiddenDiv,"br")}for(B=0;B<x;B++){E=p[B];if(!E.parentNode){continue}C=p[B].previousSibling;l=p[B].MathJax.elementJax;if(!l){continue}A=C.previousSibling;if(!l.HTMLCSS.isHidden){A=A.previousSibling}A.parentNode.removeChild(A);C.parentNode.removeChild(C)}q.HTMLCSSeqn=q.HTMLCSSlast=0;q.HTMLCSSi=-1;q.HTMLCSSchunk=this.config.EqnChunk;q.HTMLCSSdelay=false},PHASE:{I:1,II:2,III:3},Translate:function(l,p){if(!l.parentNode){return}if(p.HTMLCSSdelay){p.HTMLCSSdelay=false;b.RestartAfter(MathJax.Callback.Delay(this.config.EqnChunkDelay))}var k=l.MathJax.elementJax,o=k.root,m=document.getElementById(k.inputID+"-Frame"),q=(k.HTMLCSS.display?(m||{}).parentNode:m);if(!q){return}this.getMetrics(k);if(this.scale!==1){m.style.fontSize=k.HTMLCSS.fontSize}this.initImg(m);this.initHTML(o,m);this.savePreview(l);try{o.setTeXclass();k.HTMLCSS.span=m;k.HTMLCSS.div=q;o.toHTML(m,q,this.PHASE.I)}catch(n){if(n.restart){while(m.firstChild){m.removeChild(m.firstChild)}}this.restorePreview(l);throw n}this.restorePreview(l);q.className=q.className.split(/ /)[0]+" MathJax_Processed";b.signal.Post(["New Math Pending",k.inputID]);p.HTMLCSSeqn+=(p.i-p.HTMLCSSi);p.HTMLCSSi=p.i;if(p.HTMLCSSeqn>=p.HTMLCSSlast+p.HTMLCSSchunk){this.postTranslate(p,true);p.HTMLCSSchunk=Math.floor(p.HTMLCSSchunk*this.config.EqnChunkFactor);p.HTMLCSSdelay=true}return false},savePreview:function(k){var l=k.MathJax.preview;if(l){k.MathJax.tmpPreview=document.createElement("span");l.parentNode.replaceChild(k.MathJax.tmpPreview,l)}},restorePreview:function(k){var l=k.MathJax.tmpPreview;if(l){l.parentNode.replaceChild(k.MathJax.preview,l);delete k.MathJax.tmpPreview}},getMetrics:function(k){var l=k.HTMLCSS;this.em=g.mbase.prototype.em=l.em*l.scale;this.outerEm=l.em;this.scale=l.scale;this.cwidth=l.cwidth;this.linebreakWidth=l.lineWidth},postTranslate:function(l,s){var p=l.jax[this.id],t,n,q,o;for(q=l.HTMLCSSlast,o=l.HTMLCSSeqn;q<o;q++){t=p[q];if(t&&t.MathJax.elementJax){var k=t.MathJax.elementJax.HTMLCSS.div;k.className=k.className.split(/ /)[0];if(t.MathJax.preview){t.MathJax.preview.innerHTML=""}}}for(q=l.HTMLCSSlast,o=l.HTMLCSSeqn;q<o;q++){t=p[q];if(t&&t.MathJax.elementJax){n=t.MathJax.elementJax;this.getMetrics(n);n.root.toHTML(n.HTMLCSS.span,n.HTMLCSS.div,this.PHASE.II)}}for(q=l.HTMLCSSlast,o=l.HTMLCSSeqn;q<o;q++){t=p[q];if(t&&t.MathJax.elementJax){n=t.MathJax.elementJax;this.getMetrics(n);n.root.toHTML(n.HTMLCSS.span,n.HTMLCSS.div,this.PHASE.III);if(n.HTMLCSS.isHidden){t.parentNode.insertBefore(n.HTMLCSS.div,t)}delete n.HTMLCSS.span;delete n.HTMLCSS.div;t.MathJax.state=n.STATE.PROCESSED;b.signal.Post(["New Math",t.MathJax.elementJax.inputID])}}if(this.forceReflow){var r=(document.styleSheets||[])[0]||{};r.disabled=true;r.disabled=false}l.HTMLCSSlast=l.HTMLCSSeqn},getJaxFromMath:function(k){if(k.parentNode.className==="MathJax_Display"){k=k.parentNode}do{k=k.nextSibling}while(k&&k.nodeName.toLowerCase()!=="script");return b.getJaxFor(k)},getHoverSpan:function(k,l){return k.root.HTMLspanElement()},getHoverBBox:function(k,n,o){var p=n.bbox,m=k.HTMLCSS.outerEm;var l={w:p.w*m,h:p.h*m,d:p.d*m};if(p.width){l.width=p.width}return l},Zoom:function(l,w,v,k,t){w.className="MathJax";w.style.fontSize=l.HTMLCSS.fontSize;var z=w.appendChild(this.EmExSpan.cloneNode(true));var o=z.lastChild.firstChild.offsetHeight/60;this.em=g.mbase.prototype.em=o;this.outerEm=o/l.HTMLCSS.scale;z.parentNode.removeChild(z);this.scale=l.HTMLCSS.scale;this.linebreakWidth=l.HTMLCSS.lineWidth;this.cwidth=l.HTMLCSS.cwidth;this.zoomScale=parseInt(b.config.menuSettings.zscale)/100;this.idPostfix="-zoom";l.root.toHTML(w,w);this.idPostfix="";this.zoomScale=1;var x=l.root.HTMLspanElement().bbox,n=x.width;if(n){if(x.tw){k=x.tw*o}if(x.w*o<k){k=x.w*o}w.style.width=Math.floor(k-1.5*d.em)+"px";w.style.display="inline-block";var m=(l.root.id||"MathJax-Span-"+l.root.spanID)+"-zoom";var p=document.getElementById(m).firstChild;while(p&&p.style.width!==n){p=p.nextSibling}if(p){var s=p.offsetWidth;p.style.width="100%";if(s>k){w.style.width=(s+100)+"px"}}}p=w.firstChild.firstChild.style;if(x.H!=null&&x.H>x.h){p.marginTop=d.Em(x.H-Math.max(x.h,d.FONTDATA.lineH))}if(x.D!=null&&x.D>x.d){p.marginBottom=d.Em(x.D-Math.max(x.d,d.FONTDATA.lineD))}if(x.lw<0){p.paddingLeft=d.Em(-x.lw)}if(x.rw>x.w){p.marginRight=d.Em(x.rw-x.w)}w.style.position="absolute";if(!n){v.style.position="absolute"}var u=w.offsetWidth,r=w.offsetHeight,y=v.offsetHeight,q=v.offsetWidth;w.style.position=v.style.position="";return{Y:-j.getBBox(w).h,mW:q,mH:y,zW:u,zH:r}},initImg:function(k){},initHTML:function(l,k){},initFont:function(k){var m=d.FONTDATA.FONTS,l=d.config.availableFonts;if(l&&l.length&&d.Font.testFont(m[k])){m[k].available=true;if(m[k].familyFixed){m[k].family=m[k].familyFixed;delete m[k].familyFixed}return null}if(!this.allowWebFonts){return null}m[k].isWebFont=true;if(d.FontFaceBug){m[k].family=k;if(d.msieFontCSSBug){m[k].family+="-Web"}}return h.Styles({"@font-face":this.Font.fontFace(k)})},Remove:function(k){var l=document.getElementById(k.inputID+"-Frame");if(l){if(k.HTMLCSS.display){l=l.parentNode}l.parentNode.removeChild(l)}delete k.HTMLCSS},getHD:function(l,m){if(l.bbox&&this.config.noReflows&&!m){return{h:l.bbox.h,d:l.bbox.d}}var k=l.style.position;l.style.position="absolute";this.HDimg.style.height="0px";l.appendChild(this.HDspan);var n={h:l.offsetHeight};this.HDimg.style.height=n.h+"px";n.d=l.offsetHeight-n.h;n.h-=n.d;n.h/=this.em;n.d/=this.em;l.removeChild(this.HDspan);l.style.position=k;return n},getW:function(o){var l,n,m=(o.bbox||{}).w,p=o;if(o.bbox&&this.config.noReflows&&o.bbox.exactW!==false){if(!o.bbox.exactW){if(o.style.paddingLeft){m+=this.unEm(o.style.paddingLeft)*(o.scale||1)}if(o.style.paddingRight){m+=this.unEm(o.style.paddingRight)*(o.scale||1)}}return m}if(o.bbox&&o.bbox.exactW){return m}if((o.bbox&&m>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug)||this.negativeBBoxes||!o.firstChild){l=o.offsetWidth;n=o.parentNode.offsetHeight}else{if(o.bbox&&m<0&&this.msieNegativeBBoxBug){l=-o.offsetWidth,n=o.parentNode.offsetHeight}else{var k=o.style.position;o.style.position="absolute";p=this.startMarker;o.insertBefore(p,o.firstChild);o.appendChild(this.endMarker);l=this.endMarker.offsetLeft-p.offsetLeft;o.removeChild(this.endMarker);o.removeChild(p);o.style.position=k}}if(n!=null){o.parentNode.HH=n/this.em}return l/this.em},Measured:function(m,l){var n=m.bbox;if(n.width==null&&n.w&&!n.isMultiline){var k=this.getW(m);n.rw+=k-n.w;n.w=k;n.exactW=true}if(!l){l=m.parentNode}if(!l.bbox){l.bbox=n}return m},Remeasured:function(l,k){k.bbox=this.Measured(l,k).bbox},MeasureSpans:function(o){var r=[],t,q,n,u,k,p,l,s;for(q=0,n=o.length;q<n;q++){t=o[q];if(!t){continue}u=t.bbox;s=this.parentNode(t);if(u.exactW||u.width||u.w===0||u.isMultiline||(this.config.noReflows&&u.exactW!==false)){if(!s.bbox){s.bbox=u}continue}if(this.negativeBBoxes||!t.firstChild||(u.w>=0&&!this.initialSkipBug)||(u.w<0&&this.msieNegativeBBoxBug)){r.push([t])}else{if(this.initialSkipBug){k=this.startMarker.cloneNode(true);p=this.endMarker.cloneNode(true);t.insertBefore(k,t.firstChild);t.appendChild(p);r.push([t,k,p,t.style.position]);t.style.position="absolute"}else{p=this.endMarker.cloneNode(true);t.appendChild(p);r.push([t,null,p])}}}for(q=0,n=r.length;q<n;q++){t=r[q][0];u=t.bbox;s=this.parentNode(t);if((u.w>=0&&!this.initialSkipBug)||this.negativeBBoxes||!t.firstChild){l=t.offsetWidth;s.HH=s.offsetHeight/this.em}else{if(u.w<0&&this.msieNegativeBBoxBug){l=-t.offsetWidth,s.HH=s.offsetHeight/this.em}else{l=r[q][2].offsetLeft-((r[q][1]||{}).offsetLeft||0)}}l/=this.em;u.rw+=l-u.w;u.w=l;u.exactW=true;if(!s.bbox){s.bbox=u}}for(q=0,n=r.length;q<n;q++){t=r[q];if(t[1]){t[1].parentNode.removeChild(t[1]),t[0].style.position=t[3]}if(t[2]){t[2].parentNode.removeChild(t[2])}}},Em:function(k){if(Math.abs(k)<0.0006){return"0em"}return k.toFixed(3).replace(/\.?0+$/,"")+"em"},EmRounded:function(k){k=(Math.round(k*d.em)+0.05)/d.em;if(Math.abs(k)<0.0006){return"0em"}return k.toFixed(3).replace(/\.?0+$/,"")+"em"},unEm:function(k){return parseFloat(k)},Px:function(k){k*=this.em;var l=(k<0?"-":"");return l+Math.abs(k).toFixed(1).replace(/\.?0+$/,"")+"px"},unPx:function(k){return parseFloat(k)/this.em},Percent:function(k){return(100*k).toFixed(1).replace(/\.?0+$/,"")+"%"},length2em:function(r,l,p){if(typeof(r)!=="string"){r=r.toString()}if(r===""){return""}if(r===g.SIZE.NORMAL){return 1}if(r===g.SIZE.BIG){return 2}if(r===g.SIZE.SMALL){return 0.71}if(r==="infinity"){return d.BIGDIMEN}var o=this.FONTDATA.TeX_factor,s=(d.zoomScale||1)/d.em;if(r.match(/mathspace$/)){return d.MATHSPACE[r]*o}var n=r.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var k=parseFloat(n[1]||"1"),q=n[2];if(p==null){p=1}if(l==null){l=1}if(q==="em"){return k*o}if(q==="ex"){return k*d.TeX.x_height*o}if(q==="%"){return k/100*p}if(q==="px"){return k*s}if(q==="pt"){return k/10*o}if(q==="pc"){return k*1.2*o}if(q==="in"){return k*this.pxPerInch*s}if(q==="cm"){return k*this.pxPerInch*s/2.54}if(q==="mm"){return k*this.pxPerInch*s/25.4}if(q==="mu"){return k/18*o*l}return k*p},thickness2em:function(l,k){var m=d.TeX.rule_thickness;if(l===g.LINETHICKNESS.MEDIUM){return m}if(l===g.LINETHICKNESS.THIN){return 0.67*m}if(l===g.LINETHICKNESS.THICK){return 1.67*m}return this.length2em(l,k,m)},getPadding:function(l){var n={top:0,right:0,bottom:0,left:0},k=false;for(var o in n){if(n.hasOwnProperty(o)){var m=l.style["padding"+o.charAt(0).toUpperCase()+o.substr(1)];if(m){n[o]=this.length2em(m);k=true}}}return(k?n:false)},getBorders:function(p){var m={top:0,right:0,bottom:0,left:0},n={},l=false;for(var q in m){if(m.hasOwnProperty(q)){var k="border"+q.charAt(0).toUpperCase()+q.substr(1);var o=p.style[k+"Style"];if(o){l=true;m[q]=this.length2em(p.style[k+"Width"]);n[k]=[p.style[k+"Width"],p.style[k+"Style"],p.style[k+"Color"]].join(" ")}}}m.css=n;return(l?m:false)},setBorders:function(k,l){if(l){for(var m in l.css){if(l.css.hasOwnProperty(m)){k.style[m]=l.css[m]}}}},createStrut:function(m,l,n){var k=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:l+"px",width:"1px",marginRight:"-1px"}});if(n){m.insertBefore(k,m.firstChild)}else{m.appendChild(k)}return k},createBlank:function(l,k,m){var n=this.Element("span",{isMathJax:true,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(k)}});if(k<0){n.style.marginRight=n.style.width;n.style.width=0}if(m){l.insertBefore(n,l.firstChild)}else{l.appendChild(n)}return n},createShift:function(l,k,n){var m=this.Element("span",{style:{marginLeft:this.Em(k)},isMathJax:true});if(n){l.insertBefore(m,l.firstChild)}else{l.appendChild(m)}return m},createSpace:function(p,n,o,q,m,s){if(n<-o){o=-n}var r=this.Em(n+o),k=this.Em(-o);if(this.msieInlineBlockAlignBug){k=this.Em(d.getHD(p.parentNode,true).d-o)}if(p.isBox||s){var l=(p.scale==null?1:p.scale);p.bbox={exactW:true,h:n*l,d:o*l,w:q*l,rw:q*l,lw:0};p.style.height=r;p.style.verticalAlign=k;p.HH=(n+o)*l}else{p=this.addElement(p,"span",{style:{height:r,verticalAlign:k},isMathJax:true})}if(q>=0){p.style.width=this.Em(q);p.style.display="inline-block";p.style.overflow="hidden"}else{if(this.msieNegativeSpaceBug){p.style.height=""}p.style.marginLeft=this.Em(q);if(d.safariNegativeSpaceBug&&p.parentNode.firstChild==p){this.createBlank(p,0,true)}}if(m&&m!==g.COLOR.TRANSPARENT){p.style.backgroundColor=m;p.style.position="relative"}return p},createRule:function(r,n,p,s,l){if(n<-p){p=-n}var m=d.TeX.min_rule_thickness,o=1;if(s>0&&s*this.em<m){s=m/this.em}if(n+p>0&&(n+p)*this.em<m){o=1/(n+p)*(m/this.em);n*=o;p*=o}if(!l){l="solid"}else{l="solid "+l}l=this.Em(s)+" "+l;var t=(o===1?this.Em(n+p):m+"px"),k=this.Em(-p);var q=this.addElement(r,"span",{style:{borderLeft:l,display:"inline-block",overflow:"hidden",width:0,height:t,verticalAlign:k},bbox:{h:n,d:p,w:s,rw:s,lw:0,exactW:true},noAdjust:true,HH:n+p,isMathJax:true});if(this.msieRuleBug&&s>0){q.style.width=this.Em(s)}if(r.isBox||r.className=="mspace"){r.bbox=q.bbox,r.HH=n+p}return q},createFrame:function(s,q,r,u,x,l){if(q<-r){r=-q}var p=2*x;if(this.msieFrameSizeBug){if(u<p){u=p}if(q+r<p){q=p-r}}if(this.msieBorderWidthBug){p=0}var v=this.Em(q+r-p),k=this.Em(-r-x),o=this.Em(u-p);var m=this.Em(x)+" "+l;var n=this.addElement(s,"span",{style:{border:m,display:"inline-block",overflow:"hidden",width:o,height:v},bbox:{h:q,d:r,w:u,rw:u,lw:0,exactW:true},noAdjust:true,HH:q+r,isMathJax:true});if(k){n.style.verticalAlign=k}return n},parentNode:function(l){var k=l.parentNode;if(k.nodeName.toLowerCase()==="a"){k=k.parentNode}return k},createStack:function(m,o,l){if(this.msiePaddingWidthBug){this.createStrut(m,0)}var n=String(l).match(/%$/);var k=(!n&&l!=null?l:0);m=this.addElement(m,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(n?"100%":this.Em(k)),height:0}});if(!o){m.parentNode.bbox=m.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:k,lw:this.BIGDIMEN,rw:(!n&&l!=null?l:-this.BIGDIMEN)};if(n){m.bbox.width=l}}return m},createBox:function(l,k){var m=this.addElement(l,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(k!=null){m.style.width=k}return m},addBox:function(k,l){l.style.position="absolute";l.isBox=l.isMathJax=true;return k.appendChild(l)},placeBox:function(u,s,q,o){u.isMathJax=true;var v=d.parentNode(u),C=u.bbox,z=v.bbox;if(this.msiePlaceBoxBug){this.addText(u,this.NBSP)}if(this.imgSpaceBug){this.addText(u,this.imgSpace)}var w,F=0;if(u.HH!=null){w=u.HH}else{if(C){w=Math.max(3,C.h+C.d)}else{w=u.offsetHeight/this.em}}if(!u.noAdjust){w+=1;w=Math.round(w*this.em)/this.em;if(this.msieInlineBlockAlignBug){this.addElement(u,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(w)}})}else{this.addElement(u,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(w)}});if(d.chromeHeightBug){w-=(u.lastChild.offsetHeight-Math.round(w*this.em))/this.em}}}if(C){if(this.initialSkipBug){if(C.lw<0){F=C.lw;d.createBlank(u,-F,true)}if(C.rw>C.w){d.createBlank(u,C.rw-C.w+0.1)}}if(!this.msieClipRectBug&&!C.noclip&&!o){var B=3/this.em;var A=(C.H==null?C.h:C.H),m=(C.D==null?C.d:C.D);var E=w-A-B,p=w+m+B,n=-1000,k=1000;u.style.clip="rect("+this.Em(E)+" "+this.Em(k)+" "+this.Em(p)+" "+this.Em(n)+")"}}u.style.top=this.Em(-q-w);u.style.left=this.Em(s+F);if(C&&z){if(C.H!=null&&(z.H==null||C.H+q>z.H)){z.H=C.H+q}if(C.D!=null&&(z.D==null||C.D-q>z.D)){z.D=C.D-q}if(C.h+q>z.h){z.h=C.h+q}if(C.d-q>z.d){z.d=C.d-q}if(z.H!=null&&z.H<=z.h){delete z.H}if(z.D!=null&&z.D<=z.d){delete z.D}if(C.w+s>z.w){z.w=C.w+s;if(z.width==null){v.style.width=this.Em(z.w)}}if(C.rw+s>z.rw){z.rw=C.rw+s}if(C.lw+s<z.lw){z.lw=C.lw+s}if(C.width!=null&&!C.isFixed){if(z.width==null){v.style.width=z.width="100%";if(C.minWidth){v.style.minWidth=z.minWidth=C.minWidth}}u.style.width=C.width}if(C.tw){z.tw=C.tw}}},alignBox:function(s,o,q,v){if(v==null){v=0}this.placeBox(s,v,q);if(this.msiePlaceBoxBug){var m=s.lastChild;while(m&&m.nodeName!=="#text"){m=m.previousSibling}if(m){s.removeChild(m)}}var u=s.bbox;if(u.isMultiline){return}var t=u.width!=null&&!u.isFixed;var k=0,p=v-u.w/2,n="50%";if(this.initialSkipBug){k=u.w-u.rw-0.1;p+=u.lw}if(this.msieMarginScaleBug){p=(p*this.em)+"px"}else{p=this.Em(p)}if(t){p=(v===0?"":this.Em(v));n=(50-parseFloat(u.width)/2)+"%"}b.Insert(s.style,({right:{left:"",right:this.Em(k-v)},center:{left:n,marginLeft:p}})[o])},setStackWidth:function(l,k){if(typeof(k)==="number"){l.style.width=this.Em(Math.max(0,k));var m=l.bbox;if(m){m.w=k;m.exactW=true}m=l.parentNode.bbox;if(m){m.w=k;m.exactW=true}}else{l.style.width=l.parentNode.style.width="100%";if(l.bbox){l.bbox.width=k}if(l.parentNode.bbox){l.parentNode.bbox.width=k}}},createDelimiter:function(u,k,n,q,o){if(!k){u.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};u.bbox.rw=u.bbox.w;this.createSpace(u,u.bbox.h,u.bbox.d,u.bbox.w);return}if(!q){q=1}if(!(n instanceof Array)){n=[n,n]}var t=n[1];n=n[0];var l={alias:k};while(l.alias){k=l.alias;l=this.FONTDATA.DELIMITERS[k];if(!l){l={HW:[0,this.FONTDATA.VARIANT[g.VARIANT.NORMAL]]}}}if(l.load){b.RestartAfter(h.Require(this.fontDir+"/fontdata-"+l.load+".js"))}for(var s=0,p=l.HW.length;s<p;s++){if(l.HW[s][0]*q>=n-0.01||(s==p-1&&!l.stretch)){if(l.HW[s][2]){q*=l.HW[s][2]}if(l.HW[s][3]){k=l.HW[s][3]}var r=this.addElement(u,"span");this.createChar(r,[k,l.HW[s][1]],q,o);u.bbox=r.bbox;u.offset=0.65*u.bbox.w;u.scale=q;return}}if(l.stretch){this["extendDelimiter"+l.dir](u,t,l.stretch,q,o)}},extendDelimiterV:function(A,t,E,F,w){var o=this.createStack(A,true);var v=this.createBox(o),u=this.createBox(o);this.createChar(v,(E.top||E.ext),F,w);this.createChar(u,(E.bot||E.ext),F,w);var m={bbox:{w:0,lw:0,rw:0}},D=m,p;var B=v.bbox.h+v.bbox.d+u.bbox.h+u.bbox.d;var r=-v.bbox.h;this.placeBox(v,0,r,true);r-=v.bbox.d;if(E.mid){D=this.createBox(o);this.createChar(D,E.mid,F,w);B+=D.bbox.h+D.bbox.d}if(E.min&&t<B*E.min){t=B*E.min}if(t>B){m=this.Element("span");this.createChar(m,E.ext,F,w);var C=m.bbox.h+m.bbox.d,l=C-0.05,x,q,z=(E.mid?2:1);q=x=Math.min(Math.ceil((t-B)/(z*l)),this.maxStretchyParts);if(!E.fullExtenders){l=(t-B)/(z*x)}var s=(x/(x+1))*(C-l);l=C-s;r+=s+l-m.bbox.h;while(z-->0){while(x-->0){if(!this.msieCloneNodeBug){p=m.cloneNode(true)}else{p=this.Element("span");this.createChar(p,E.ext,F,w)}p.bbox=m.bbox;r-=l;this.placeBox(this.addBox(o,p),0,r,true)}r+=s-m.bbox.d;if(E.mid&&z){this.placeBox(D,0,r-D.bbox.h,true);x=q;r+=-(D.bbox.h+D.bbox.d)+s+l-m.bbox.h}}}else{r+=(B-t)/2;if(E.mid){this.placeBox(D,0,r-D.bbox.h,true);r+=-(D.bbox.h+D.bbox.d)}r+=(B-t)/2}this.placeBox(u,0,r-u.bbox.h,true);r-=u.bbox.h+u.bbox.d;A.bbox={w:Math.max(v.bbox.w,m.bbox.w,u.bbox.w,D.bbox.w),lw:Math.min(v.bbox.lw,m.bbox.lw,u.bbox.lw,D.bbox.lw),rw:Math.max(v.bbox.rw,m.bbox.rw,u.bbox.rw,D.bbox.rw),h:0,d:-r,exactW:true};A.scale=F;A.offset=0.55*A.bbox.w;A.isMultiChar=true;this.setStackWidth(o,A.bbox.w)},extendDelimiterH:function(B,o,E,G,y){var r=this.createStack(B,true);var p=this.createBox(r),C=this.createBox(r);this.createChar(p,(E.left||E.rep),G,y);this.createChar(C,(E.right||E.rep),G,y);var l=this.Element("span");this.createChar(l,E.rep,G,y);var D={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},m;this.placeBox(p,-p.bbox.lw,0,true);var u=(p.bbox.rw-p.bbox.lw)+(C.bbox.rw-C.bbox.lw)-0.05,t=p.bbox.rw-p.bbox.lw-0.025,v;if(E.mid){D=this.createBox(r);this.createChar(D,E.mid,G,y);u+=D.bbox.w}if(E.min&&o<u*E.min){o=u*E.min}if(o>u){var F=l.bbox.rw-l.bbox.lw,q=F-0.05,z,s,A=(E.mid?2:1);s=z=Math.min(Math.ceil((o-u)/(A*q)),this.maxStretchyParts);if(!E.fillExtenders){q=(o-u)/(A*z)}v=(z/(z+1))*(F-q);q=F-v;t-=l.bbox.lw+v;while(A-->0){while(z-->0){if(!this.cloneNodeBug){m=l.cloneNode(true)}else{m=this.Element("span");this.createChar(m,E.rep,G,y)}m.bbox=l.bbox;this.placeBox(this.addBox(r,m),t,0,true);t+=q}if(E.mid&&A){this.placeBox(D,t,0,true);t+=D.bbox.w-v;z=s}}}else{t-=(u-o)/2;if(E.mid){this.placeBox(D,t,0,true);t+=D.bbox.w}t-=(u-o)/2}this.placeBox(C,t,0,true);B.bbox={w:t+C.bbox.rw,lw:0,rw:t+C.bbox.rw,H:Math.max(p.bbox.h,l.bbox.h,C.bbox.h,D.bbox.h),D:Math.max(p.bbox.d,l.bbox.d,C.bbox.d,D.bbox.d),h:l.bbox.h,d:l.bbox.d,exactW:true};B.scale=G;B.isMultiChar=true;this.setStackWidth(r,B.bbox.w)},createChar:function(s,p,n,k){s.isMathJax=true;var r=s,t="",o={fonts:[p[1]],noRemap:true};if(k&&k===g.VARIANT.BOLD){o.fonts=[p[1]+"-bold",p[1]]}if(typeof(p[1])!=="string"){o=p[1]}if(p[0] instanceof Array){for(var q=0,l=p[0].length;q<l;q++){t+=String.fromCharCode(p[0][q])}}else{t=String.fromCharCode(p[0])}if(p[4]){n*=p[4]}if(n!==1||p[3]){r=this.addElement(s,"span",{style:{fontSize:this.Percent(n)},scale:n,isMathJax:true});this.handleVariant(r,o,t);s.bbox=r.bbox}else{this.handleVariant(s,o,t)}if(p[2]){s.style.marginLeft=this.Em(p[2])}if(p[3]){s.firstChild.style.verticalAlign=this.Em(p[3]);s.bbox.h+=p[3];if(s.bbox.h<0){s.bbox.h=0}}if(p[5]){s.bbox.h+=p[5]}if(p[6]){s.bbox.d+=p[6]}if(this.AccentBug&&s.bbox.w===0){r.firstChild.nodeValue+=this.NBSP}},positionDelimiter:function(l,k){k-=l.bbox.h;l.bbox.d-=k;l.bbox.h+=k;if(k){if(this.safariVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&l.isMultiChar)){if(l.firstChild.style.display===""&&l.style.top!==""){l=l.firstChild;k-=d.unEm(l.style.top)}l.style.position="relative";l.style.top=this.Em(-k)}else{l.style.verticalAlign=this.Em(k);if(d.ffVerticalAlignBug){d.createRule(l.parentNode,l.bbox.h,0,0);delete l.parentNode.bbox}}}},handleVariant:function(z,o,r){var y="",w,B,s,C,k=z,l=!!z.style.fontFamily;if(r.length===0){return}if(!z.bbox){z.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}}if(!o){o=this.FONTDATA.VARIANT[g.VARIANT.NORMAL]}C=o;for(var A=0,x=r.length;A<x;A++){o=C;w=r.charCodeAt(A);B=r.charAt(A);if(w>=55296&&w<56319){A++;w=(((w-55296)<<10)+(r.charCodeAt(A)-56320))+65536;if(this.FONTDATA.RemapPlane1){var D=this.FONTDATA.RemapPlane1(w,o);w=D.n;o=D.variant}}else{var t,q,u=this.FONTDATA.RANGES;for(t=0,q=u.length;t<q;t++){if(u[t].name==="alpha"&&o.noLowerCase){continue}var p=o["offset"+u[t].offset];if(p&&w>=u[t].low&&w<=u[t].high){if(u[t].remap&&u[t].remap[w]){w=p+u[t].remap[w]}else{w=w-u[t].low+p;if(u[t].add){w+=u[t].add}}if(o["variant"+u[t].offset]){o=this.FONTDATA.VARIANT[o["variant"+u[t].offset]]}break}}}if(o.remap&&o.remap[w]){w=o.remap[w];if(o.remap.variant){o=this.FONTDATA.VARIANT[o.remap.variant]}}else{if(this.FONTDATA.REMAP[w]&&!o.noRemap){w=this.FONTDATA.REMAP[w]}}if(w instanceof Array){o=this.FONTDATA.VARIANT[w[1]];w=w[0]}if(typeof(w)==="string"){r=w+r.substr(A+1);x=r.length;A=-1;continue}s=this.lookupChar(o,w);B=s[w];if(l||(!this.checkFont(s,k.style)&&!B[5].img)){if(y.length){this.addText(k,y);y=""}var v=!!k.style.fontFamily||!!z.style.fontStyle||!!z.style.fontWeight||!s.directory||l;l=false;if(k!==z){v=!this.checkFont(s,z.style);k=z}if(v){k=this.addElement(z,"span",{isMathJax:true,subSpan:true})}this.handleFont(k,s,k!==z)}y=this.handleChar(k,s,B,w,y);if(!(B[5]||{}).space){if(B[0]/1000>z.bbox.h){z.bbox.h=B[0]/1000}if(B[1]/1000>z.bbox.d){z.bbox.d=B[1]/1000}}if(z.bbox.w+B[3]/1000<z.bbox.lw){z.bbox.lw=z.bbox.w+B[3]/1000}if(z.bbox.w+B[4]/1000>z.bbox.rw){z.bbox.rw=z.bbox.w+B[4]/1000}z.bbox.w+=B[2]/1000;if((B[5]||{}).isUnknown){z.bbox.exactW=false}}if(y.length){this.addText(k,y)}if(z.scale&&z.scale!==1){z.bbox.h*=z.scale;z.bbox.d*=z.scale;z.bbox.w*=z.scale;z.bbox.lw*=z.scale;z.bbox.rw*=z.scale}if(r.length==1&&s.skew&&s.skew[w]){z.bbox.skew=s.skew[w]}},checkFont:function(k,l){var m=(l.fontWeight||"normal");if(m.match(/^\d+$/)){m=(parseInt(m)>=600?"bold":"normal")}return(k.family.replace(/'/g,"")===l.fontFamily.replace(/'/g,"")&&(k.style||"normal")===(l.fontStyle||"normal")&&(k.weight||"normal")===m)},handleFont:function(m,k,o){m.style.fontFamily=k.family;if(!k.directory){m.style.fontSize=Math.floor(d.config.scale/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&k.isWebFont)){var l=k.style||"normal",n=k.weight||"normal";if(l!=="normal"||o){m.style.fontStyle=l}if(n!=="normal"||o){m.style.fontWeight=n}}},handleChar:function(l,k,s,r,q){var p=s[5];if(p.space){if(q.length){this.addText(l,q)}d.createShift(l,s[2]/1000);return""}if(p.img){return this.handleImg(l,k,s,r,q)}if(p.isUnknown&&this.FONTDATA.DELIMITERS[r]){if(q.length){this.addText(l,q)}var o=l.scale;d.createDelimiter(l,r,0,1,k);if(this.FONTDATA.DELIMITERS[r].dir==="V"){l.style.verticalAlign=this.Em(l.bbox.d);l.bbox.h+=l.bbox.d;l.bbox.d=0}l.scale=o;s[0]=l.bbox.h*1000;s[1]=l.bbox.d*1000;s[2]=l.bbox.w*1000;s[3]=l.bbox.lw*1000;s[4]=l.bbox.rw*1000;return""}if(p.c==null){if(r<=65535){p.c=String.fromCharCode(r)}else{var m=r-65536;p.c=String.fromCharCode((m>>10)+55296)+String.fromCharCode((m&1023)+56320)}}if(p.rfix){this.addText(l,q+p.c);d.createShift(l,p.rfix/1000);return""}if(s[2]||!this.msieAccentBug||q.length){return q+p.c}d.createShift(l,s[3]/1000);d.createShift(l,(s[4]-s[3])/1000);this.addText(l,p.c);d.createShift(l,-s[4]/1000);return""},handleImg:function(l,k,p,o,m){return m},lookupChar:function(p,s){var o,k;if(!p.FONTS){var r=this.FONTDATA.FONTS;var q=(p.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(q instanceof Array)){q=[q]}if(p.fonts!=q){p.fonts=q}p.FONTS=[];for(o=0,k=q.length;o<k;o++){if(r[q[o]]){p.FONTS.push(r[q[o]]);r[q[o]].name=q[o]}}}for(o=0,k=p.FONTS.length;o<k;o++){var l=p.FONTS[o];if(typeof(l)==="string"){delete p.FONTS;this.loadFont(l)}if(l[s]){if(l[s].length===5){l[s][5]={}}if(d.allowWebFonts&&!l.available){this.loadWebFont(l)}else{return l}}else{this.findBlock(l,s)}}return this.unknownChar(p,s)},unknownChar:function(k,m){var l=(k.defaultFont||{family:d.config.undefinedFamily});if(k.bold){l.weight="bold"}if(k.italic){l.style="italic"}if(!l[m]){l[m]=[800,200,500,0,500,{isUnknown:true}]}b.signal.Post(["HTML-CSS Jax - unknown char",m,k]);return l},findBlock:function(l,q){if(l.Ranges){for(var p=0,k=l.Ranges.length;p<k;p++){if(q<l.Ranges[p][0]){return}if(q<=l.Ranges[p][1]){var o=l.Ranges[p][2];for(var n=l.Ranges.length-1;n>=0;n--){if(l.Ranges[n][2]==o){l.Ranges.splice(n,1)}}this.loadFont(l.directory+"/"+o+".js")}}}},loadFont:function(l){var k=MathJax.Callback.Queue();k.Push(["Require",h,this.fontDir+"/"+l]);if(this.imgFonts){if(!MathJax.isPacked){l=l.replace(/\/([^\/]*)$/,d.imgPacked+"/$1")}k.Push(["Require",h,this.webfontDir+"/png/"+l])}b.RestartAfter(k.Push({}))},loadWebFont:function(k){k.available=k.isWebFont=true;if(d.FontFaceBug){k.family=k.name;if(d.msieFontCSSBug){k.family+="-Web"}}b.RestartAfter(this.Font.loadWebFont(k))},loadWebFontError:function(l,k){b.Startup.signal.Post("HTML-CSS Jax - disable web fonts");l.isWebFont=false;if(this.config.imageFont&&this.config.imageFont===this.fontInUse){this.imgFonts=true;b.Startup.signal.Post("HTML-CSS Jax - switch to image fonts");b.Startup.signal.Post("HTML-CSS Jax - using image fonts");e(["WebFontNotAvailable","Web-Fonts not available -- using image fonts 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l=0,k=this.data.length;l<k;l++){if(this.data[l]){this.data[l].toHTML(o,n)}}if(!o.bbox){o.bbox=this.HTMLzeroBBox()}if(this.data.join("").length!==1){delete o.bbox.skew}this.HTMLhandleSpace(o);this.HTMLhandleColor(o);this.HTMLhandleDir(o);return o}});g.mo.Augment({toHTML:function(v){v=this.HTMLhandleSize(this.HTMLcreateSpan(v));if(this.data.length==0){return v}else{v.bbox=null}var y=this.data.join("");var q=this.HTMLgetVariant();var x=this.getValues("largeop","displaystyle");if(x.largeop){q=d.FONTDATA.VARIANT[x.displaystyle?"-largeOp":"-smallOp"]}var w=this.CoreParent(),o=(w&&w.isa(g.msubsup)&&this!==w.data[w.base]),l=(o?this.remapChars:null);if(y.length===1&&w&&w.isa(g.munderover)&&this.CoreText(w.data[w.base]).length===1){var s=w.data[w.over],u=w.data[w.under];if(s&&this===s.CoreMO()&&w.Get("accent")){l=d.FONTDATA.REMAPACCENT}else{if(u&&this===u.CoreMO()&&w.Get("accentunder")){l=d.FONTDATA.REMAPACCENTUNDER}}}if(o&&y.match(/['`"\u00B4\u2032-\u2037\u2057]/)){q=d.FONTDATA.VARIANT["-"+d.fontInUse+"-variant"]}for(var r=0,n=this.data.length;r<n;r++){if(this.data[r]){this.data[r].toHTML(v,q,this.remap,l)}}if(!v.bbox){v.bbox=this.HTMLzeroBBox()}if(y.length!==1){delete v.bbox.skew}if(d.AccentBug&&v.bbox.w===0&&y.length===1&&v.firstChild){v.firstChild.nodeValue+=d.NBSP;d.createSpace(v,0,0,-v.offsetWidth/d.em)}if(x.largeop){var t=d.TeX.axis_height*this.scale*this.mscale;var k=(v.bbox.h-v.bbox.d)/2-t;if(d.safariVerticalAlignBug&&v.lastChild.nodeName==="IMG"){v.lastChild.style.verticalAlign=d.Em(d.unEm(v.lastChild.style.verticalAlign||0)/d.em-k/v.scale)}else{if(d.konquerorVerticalAlignBug&&v.lastChild.nodeName==="IMG"){v.style.position="relative";v.lastChild.style.position="relative";v.lastChild.style.top=d.Em(k/v.scale)}else{v.style.verticalAlign=d.Em(-k/v.scale)}}v.bbox.h-=k;v.bbox.d+=k;if(v.bbox.rw>v.bbox.w){v.bbox.ic=v.bbox.rw-v.bbox.w;d.createBlank(v,v.bbox.ic/this.mscale);v.bbox.w=v.bbox.rw}}this.HTMLhandleSpace(v);this.HTMLhandleColor(v);this.HTMLhandleDir(v);return v},HTMLcanStretch:function(o){if(!this.Get("stretchy")){return false}var p=this.data.join("");if(p.length>1){return false}var m=this.CoreParent();if(m&&m.isa(g.munderover)&&this.CoreText(m.data[m.base]).length===1){var 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v,s,A,z,u,C,J,O=0;if(p.bbox.ic){O=1.3*p.bbox.ic+0.05}for(M=0,I=this.data.length;M<I;M++){if(this.data[M]!=null){w=r[M];u=d.TeX.big_op_spacing5*P;var 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s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.CHTML.acc=-0.52}else{if(s==="\u2192"){this.CHTML.acc=-0.15;this.CHTML.vec=true}}}},CHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.CHTML.h!==o||this.CHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},CHTMLstretchV:function(p,u){var o=this.CHTMLspanElement(),t=this.CHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXc-right MJXc-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.CHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toCommonHTML:function(u){u=this.CHTMLdefaultSpan(u,{childSpans:true,className:"MJXc-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.CHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.CHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.CHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.CHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.CHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.CHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.CHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},CHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.CHTML[o[0].charAt(0)]:(r?this.CHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toCommonHTML:function(q){var n=this.getValues("displaystyle","accent","accentunder","align");if(!n.displaystyle&&this.data[this.base]!=null&&this.data[this.base].CoreMO().Get("movablelimits")){q=h.msubsup.prototype.toCommonHTML.call(this,q);q.className=q.className.replace(/munderover/,"msubsup");return q}q=this.CHTMLdefaultSpan(q,{childSpans:true,className:"",noBBox:true});var p=this.CHTMLbboxFor(this.over),s=this.CHTMLbboxFor(this.under),u=this.CHTMLbboxFor(this.base),o=this.CHTML,r=p.acc;if(this.data[this.over]){q.lastChild.firstChild.style.marginLeft=p.l=q.lastChild.firstChild.style.marginRight=p.r=0;var t=e.Element("span",{},[["span",{className:"MJXc-over"}]]);t.firstChild.appendChild(q.lastChild);if(q.childNodes.length>(this.data[this.under]?1:0)){t.firstChild.appendChild(q.firstChild)}this.data[this.over].CHTMLhandleScriptlevel(t.firstChild.firstChild);if(r!=null){if(p.vec){t.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}r=r-p.d+0.1;if(u.t!=null){r+=u.t-u.h}t.firstChild.firstChild.style.marginBottom=g.Em(r)}if(q.firstChild){q.insertBefore(t,q.firstChild)}else{q.appendChild(t)}}if(this.data[this.under]){q.lastChild.firstChild.style.marginLeft=s.l=q.lastChild.firstChild.marginRight=s.r=0;this.data[this.under].CHTMLhandleScriptlevel(q.lastChild)}o.w=Math.max(0.8*p.w,0.8*s.w,u.w);o.h=0.8*(p.h+p.d+(r||0))+u.h;o.d=u.d+0.8*(s.h+s.d);return q}});h.msubsup.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.CHTML.h-0.4),u=Math.max(0.2,s.CHTML.d+0.1);var t=this.CHTML;if(n&&p){var r=e.Element("span",{className:"MJXc-script-box",style:{height:g.Em(o+n.CHTML.h*0.8+u+p.CHTML.d*0.8),"vertical-align":g.Em(-u-p.CHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.CHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.CHTML.h-0.05))}}]]]]]]);p.CHTMLhandleScriptlevel(r.firstChild);n.CHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.CHTML.h,n.CHTML.h*0.8+o);t.d=Math.max(s.CHTML.d,p.CHTML.d*0.8+u);t.w=s.CHTML.w+Math.max(n.CHTML.w,p.CHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.CHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.CHTML.h,n.CHTML.h*0.8+o);t.d=Math.max(s.CHTML.d,n.CHTML.d*0.8-o);t.w=s.CHTML.w+n.CHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.CHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.CHTML.h,p.CHTML.h*0.8-u);t.d=Math.max(s.CHTML.d,p.CHTML.d*0.8+u);t.w=s.CHTML.w+p.CHTML.w+0.07}}}return q}});h.mfrac.Augment({toCommonHTML:function(r){r=this.CHTMLdefaultSpan(r,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].CHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].CHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXc-box",style:{"margin-top":"-.8em"}},[["span",{className:"MJXc-denom"},[["span",{},[["span",{className:"MJXc-rule"}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.CHTMLbboxFor(0),p=this.CHTMLbboxFor(1),v=this.CHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-0.9);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}return r}});h.msqrt.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});this.CHTMLlayoutRoot(n,n.firstChild);return n},CHTMLlayoutRoot:function(u,n){var v=this.CHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXc-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXc-root"},[["span",{className:"MJXc-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXc-right MJXc-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.CHTML.h=v.h+0.18;this.CHTML.d=v.d;this.CHTML.w=v.w+p;return u}});h.mroot.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q,{childSpans:true,className:"MJXc-box",forceChild:true,noBBox:true});var p=this.CHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.CHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXc-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.CHTML.w+=Math.max(0,p.w*0.8+s);this.CHTML.h=Math.max(this.CHTML.h,p.h*0.8+o);return q},CHTMLlayoutRoot:h.msqrt.prototype.CHTMLlayoutRoot});h.mfenced.Augment({toCommonHTML:function(q){q=this.CHTMLcreateSpan(q);this.CHTMLhandleStyle(q);this.CHTMLhandleColor(q);this.addFakeNodes();this.CHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;p<n;p++){this.CHTMLaddChild(q,"sep"+p,{});this.CHTMLaddChild(q,p,{})}this.CHTMLaddChild(q,"close",{});var o=this.CHTML.h,r=this.CHTML.d;this.CHTMLstretchChild("open",o,r);for(p=0,n=this.data.length;p<n;p++){this.CHTMLstretchChild("sep"+p,o,r);this.CHTMLstretchChild(p,o,r)}this.CHTMLstretchChild("close",o,r);return q}});h.mrow.Augment({toCommonHTML:function(q){q=this.CHTMLdefaultSpan(q);var p=this.CHTML.h,r=this.CHTML.d;for(var o=0,n=this.data.length;o<n;o++){this.CHTMLstretchChild(o,p,r)}return q}});h.mstyle.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n);this.CHTMLhandleScriptlevel(n);return n}});h.TeXAtom.Augment({toCommonHTML:function(n){n=this.CHTMLdefaultSpan(n);n.className="MJXc-mrow";return n}});h.mtable.Augment({toCommonHTML:function(E){E=this.CHTMLdefaultSpan(E,{noBBox:true});var r=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","width");var u=MathJax.Hub.SplitList,F,A,D,z;var N=u(r.columnspacing),w=u(r.rowspacing),L=u(r.columnalign),t=u(r.rowalign);for(F=0,A=N.length;F<A;F++){N[F]=g.length2em(N[F])}for(F=0,A=w.length;F<A;F++){w[F]=g.length2em(w[F])}var K=e.Element("span");while(E.firstChild){K.appendChild(E.firstChild)}E.appendChild(K);var y=0,s=0;for(F=0,A=this.data.length;F<A;F++){var v=this.data[F];if(v){var J=g.arrayEntry(w,F-1),C=g.arrayEntry(t,F);var x=v.CHTML,q=v.CHTMLspanElement();q.style.verticalAlign=C;var B=(v.type==="mlabeledtr"?1:0);for(D=0,z=v.data.length;D<z-B;D++){var p=v.data[D+B];if(p){var M=g.arrayEntry(N,D-1),G=g.arrayEntry(L,D);var I=p.CHTMLspanElement();if(D){x.w+=M;I.style.paddingLeft=g.Em(M)}if(F){I.style.paddingTop=g.Em(J)}I.style.textAlign=G}}y+=x.h+x.d;if(F){y+=J}if(x.w>s){s=x.w}}}var o=this.CHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({CHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.CHTMLcreateSpan(q);this.CHTMLhandleStyle(q);this.CHTMLhandleColor(q);if(this.isToken){this.CHTMLhandleToken(q)}for(var p=1,n=this.data.length;p<n;p++){this.CHTMLaddChild(q,p,o)}return q}});h.semantics.Augment({toCommonHTML:function(n){n=this.CHTMLcreateSpan(n);if(this.data[0]){this.data[0].toCommonHTML(n);MathJax.Hub.Insert(this.data[0].CHTML||{},this.CHTML)}return n}});h.annotation.Augment({toCommonHTML:function(n){}});h["annotation-xml"].Augment({toCommonHTML:function(n){}});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",g,"jax.js"]),0)})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(b.config.menuSettings.zoom!=="None"){i.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.CommonHTML);
(function(a,e,d){var b=a.config.menuSettings;var c=MathJax.Extension["CHTML-preview"]={version:"2.5.2",config:a.CombineConfig("CHTML-preview",{Chunks:{EqnChunk:10000,EqnChunkFactor:1,EqnChunkDelay:0},color:"inherit!important",updateTime:30,updateDelay:6,messageStyle:"none",disabled:d.isMSIE&&!d.versionAtLeast("8.0")}),Config:function(){a.Config({"HTML-CSS":this.config.Chunks,SVG:this.config.Chunks});MathJax.Ajax.Styles({".MathJax_Preview .MJXc-math":{color:this.config.color}});var k,h,i,f,j;var g=this.config;if(!g.disabled&&b.CHTMLpreview==null){a.Config({menuSettings:{CHTMLpreview:true}})}a.Register.MessageHook("Begin Math Output",function(){if(!f&&b.CHTMLpreview&&b.renderer!=="CommonHTML"){k=a.processUpdateTime;h=a.processUpdateDelay;i=a.config.messageStyle;a.processUpdateTime=g.updateTime;a.processUpdateDelay=g.updateDelay;a.Config({messageStyle:g.messageStyle});MathJax.Message.Clear(0,0);j=true}});a.Register.MessageHook("End Math Output",function(){if(!f&&j){a.processUpdateTime=k;a.processUpdateDelay=h;a.Config({messageStyle:i});f=true}})},Preview:function(f){if(!b.CHTMLpreview||b.renderer==="CommonHTML"){return}var g=f.script.MathJax.preview||f.script.previousSibling;if(!g||g.className!==MathJax.Hub.config.preRemoveClass){g=e.Element("span",{className:MathJax.Hub.config.preRemoveClass});f.script.parentNode.insertBefore(g,f.script);f.script.MathJax.preview=g}g.innerHTML="";g.style.color="inherit";return this.postFilter(g,f)},postFilter:function(h,g){if(!g.math.root.toCommonHTML){var f=MathJax.Callback.Queue();f.Push(["Require",MathJax.Ajax,"[MathJax]/jax/output/CommonHTML/config.js"],["Require",MathJax.Ajax,"[MathJax]/jax/output/CommonHTML/jax.js"]);a.RestartAfter(f.Push({}))}g.math.root.toCommonHTML(h)},Register:function(f){a.Register.StartupHook(f+" Jax Require",function(){var g=MathJax.InputJax[f];g.postfilterHooks.Add(["Preview",MathJax.Extension["CHTML-preview"]],50)})}};c.Register("TeX");c.Register("MathML");c.Register("AsciiMath");a.Register.StartupHook("End Config",["Config",c]);a.Startup.signal.Post("CHTML-preview Ready")})(MathJax.Hub,MathJax.HTML,MathJax.Hub.Browser);MathJax.Ajax.loadComplete("[MathJax]/extensions/CHTML-preview.js");
MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS_HTML-full.js");