rhodecode/public/js/src/math_jax/config/TeX-AMS_HTML-full.js

/*
 *  /MathJax/config/TeX-AMS_HTML-full.js
 *  
 *  Copyright (c) 2010-2016 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/PreviewHTML/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/PreviewHTML/jax.js",
  "[MathJax]/extensions/fast-preview.js",
  "[MathJax]/extensions/AssistiveMML.js"
);

MathJax.Hub.Config({
  extensions: ['[Contrib]/a11y/accessibility-menu.js']
});

MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.0",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(b,a){return a+"#"+escape(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js");
MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.7.0",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.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.0",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js");
MathJax.Extension.tex2jax={version:"2.7.0",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"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},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&&this.ignoreTags[b.nodeName.toLowerCase()]!=null);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,g=a.close,f,d,c;if(a.cpos===g.length){g=g.nextSibling}else{g=g.splitText(a.cpos)}if(!g){f=g=MathJax.HTML.addText(a.close.parentNode,"")}a.close=g;d=(a.opos?a.open.splitText(a.opos):a.open);while((c=d.nextSibling)&&c!==g){if(c.nodeValue!==null){if(c.nodeName==="#comment"){d.nodeValue+=c.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{d.nodeValue+=c.nodeValue}}else{var h=this.ignoreTags[c.nodeName.toLowerCase()];d.nodeValue+=(h==null?" ":h)}d.parentNode.removeChild(c)}var e=d.nodeValue.substr(a.olen,d.nodeValue.length-a.olen-a.clen);d.parentNode.removeChild(d);if(this.config.preview!=="none"){this.createPreview(a.mode,e)}d=this.createMathTag(a.mode,e);this.search={};this.pattern.lastIndex=0;if(f){f.parentNode.removeChild(f)}return d},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(d,a){var b=MathJax.Hub.config.preRemoveClass;var c=this.config.preview;if(c==="none"){return}if((this.search.close.previousSibling||{}).className===b){return}if(c==="TeX"){c=[this.filterPreview(a)]}if(c){c=MathJax.HTML.Element("span",{className:b},c);this.insertNode(c)}},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}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js");
(function(d,h,l,g,m,b,j){var p="2.7.0";var i=MathJax.Extension;var c=i.MathEvents={version:p};var k=d.config.menuSettings;var o={hover:500,frame:{x:3.5,y:5,bwidth:1,bcolor:"#A6D",hwidth:"15px",hcolor:"#83A"},button:{x:-6,y:-3,wx:-2},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_Menu_Button .MathJax_Hover_Arrow":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"4px","-webkit-border-radius":"4px","-moz-border-radius":"4px","-khtml-border-radius":"4px","font-family":"'Courier New',Courier","font-size":"9px",color:"#F0F0F0"},".MathJax_Menu_Button .MathJax_Hover_Arrow span":{display:"block","background-color":"#AAA",border:"1px solid","border-radius":"3px","line-height":0,padding:"4px"},".MathJax_Hover_Arrow:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_Hover_Arrow:hover span":{"background-color":"#CCC!important"}}};var n=c.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",KEY:{RETURN:13,ESCAPE:27,SPACE:32,LEFT:37,UP:38,RIGHT:39,DOWN:40},Mousedown:function(q){return n.Handler(q,"Mousedown",this)},Mouseup:function(q){return n.Handler(q,"Mouseup",this)},Mousemove:function(q){return n.Handler(q,"Mousemove",this)},Mouseover:function(q){return n.Handler(q,"Mouseover",this)},Mouseout:function(q){return n.Handler(q,"Mouseout",this)},Click:function(q){return n.Handler(q,"Click",this)},DblClick:function(q){return n.Handler(q,"DblClick",this)},Menu:function(q){return n.Handler(q,"ContextMenu",this)},Handler:function(t,r,s){if(l.loadingMathMenu){return n.False(t)}var q=b[s.jaxID];if(!t){t=window.event}t.isContextMenu=(r==="ContextMenu");if(q[r]){return q[r](t,s)}if(i.MathZoom){return i.MathZoom.HandleEvent(t,r,s)}},False:function(q){if(!q){q=window.event}if(q){if(q.preventDefault){q.preventDefault()}else{q.returnValue=false}if(q.stopPropagation){q.stopPropagation()}q.cancelBubble=true}return false},Keydown:function(r,q){if(!r){r=window.event}if(r.keyCode===n.KEY.SPACE){n.ContextMenu(r,this)}},ContextMenu:function(t,E,w){var B=b[E.jaxID],v=B.getJaxFromMath(E);var F=(B.config.showMathMenu!=null?B:d).config.showMathMenu;if(!F||(k.context!=="MathJax"&&!w)){return}if(c.msieEventBug){t=window.event||t}n.ClearSelection();f.ClearHoverTimer();if(v.hover){if(v.hover.remove){clearTimeout(v.hover.remove);delete v.hover.remove}v.hover.nofade=true}var u=MathJax.Menu;var G,D;if(u){if(u.loadingDomain){return n.False(t)}G=m.loadDomain("MathMenu");if(!G){u.jax=v;var r=u.menu.Find("Show Math As").submenu;r.items[0].name=v.sourceMenuTitle;r.items[0].format=(v.sourceMenuFormat||"MathML");r.items[1].name=j[v.inputJax].sourceMenuTitle;r.items[5].disabled=!j[v.inputJax].annotationEncoding;var A=r.items[2];A.disabled=true;var q=A.submenu.items;annotationList=MathJax.Hub.Config.semanticsAnnotations;for(var z=0,y=q.length;z<y;z++){var s=q[z].name[1];if(v.root&&v.root.getAnnotation(s)!==null){A.disabled=false;q[z].hidden=false}else{q[z].hidden=true}}var x=u.menu.Find("Math Settings","MathPlayer");x.hidden=!(v.outputJax==="NativeMML"&&d.Browser.hasMathPlayer);return u.menu.Post(t)}u.loadingDomain=true;D=function(){delete u.loadingDomain}}else{if(l.loadingMathMenu){return n.False(t)}l.loadingMathMenu=true;G=l.Require("[MathJax]/extensions/MathMenu.js");D=function(){delete l.loadingMathMenu;if(!MathJax.Menu){MathJax.Menu={}}}}var C={pageX:t.pageX,pageY:t.pageY,clientX:t.clientX,clientY:t.clientY};g.Queue(G,D,["ContextMenu",n,C,E,w]);return n.False(t)},AltContextMenu:function(s,r){var t=b[r.jaxID];var q=(t.config.showMathMenu!=null?t:d).config.showMathMenu;if(q){q=(t.config.showMathMenuMSIE!=null?t:d).config.showMathMenuMSIE;if(k.context==="MathJax"&&!k.mpContext&&q){if(!c.noContextMenuBug||s.button!==n.RIGHTBUTTON){return}}else{if(!s[n.MENUKEY]||s.button!==n.LEFTBUTTON){return}}return t.ContextMenu(s,r,true)}},ClearSelection:function(){if(c.safariContextMenuBug){setTimeout("window.getSelection().empty()",0)}if(document.selection){setTimeout("document.selection.empty()",0)}},getBBox:function(s){s.appendChild(c.topImg);var r=c.topImg.offsetTop,t=s.offsetHeight-r,q=s.offsetWidth;s.removeChild(c.topImg);return{w:q,h:r,d:t}}};var f=c.Hover={Mouseover:function(s,r){if(k.discoverable||k.zoom==="Hover"){var u=s.fromElement||s.relatedTarget,t=s.toElement||s.target;if(u&&t&&(d.isMathJaxNode(u)!==d.isMathJaxNode(t)||d.getJaxFor(u)!==d.getJaxFor(t))){var q=this.getJaxFromMath(r);if(q.hover){f.ReHover(q)}else{f.HoverTimer(q,r)}return n.False(s)}}},Mouseout:function(s,r){if(k.discoverable||k.zoom==="Hover"){var u=s.fromElement||s.relatedTarget,t=s.toElement||s.target;if(u&&t&&(d.isMathJaxNode(u)!==d.isMathJaxNode(t)||d.getJaxFor(u)!==d.getJaxFor(t))){var q=this.getJaxFromMath(r);if(q.hover){f.UnHover(q)}else{f.ClearHoverTimer()}return n.False(s)}}},Mousemove:function(s,r){if(k.discoverable||k.zoom==="Hover"){var q=this.getJaxFromMath(r);if(q.hover){return}if(f.lastX==s.clientX&&f.lastY==s.clientY){return}f.lastX=s.clientX;f.lastY=s.clientY;f.HoverTimer(q,r);return n.False(s)}},HoverTimer:function(q,r){this.ClearHoverTimer();this.hoverTimer=setTimeout(g(["Hover",this,q,r]),o.hover)},ClearHoverTimer:function(){if(this.hoverTimer){clearTimeout(this.hoverTimer);delete this.hoverTimer}},Hover:function(q,u){if(i.MathZoom&&i.MathZoom.Hover({},u)){return}var t=b[q.outputJax],v=t.getHoverSpan(q,u),y=t.getHoverBBox(q,v,u),w=(t.config.showMathMenu!=null?t:d).config.showMathMenu;var A=o.frame.x,z=o.frame.y,x=o.frame.bwidth;if(c.msieBorderWidthBug){x=0}q.hover={opacity:0,id:q.inputID+"-Hover"};var r=h.Element("span",{id:q.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(-y.h-z-x-(y.y||0)),left:this.Px(-A-x+(y.x||0)),width:this.Px(y.w+2*A),height:this.Px(y.h+y.d+2*z),opacity:0,filter:"alpha(opacity=0)"}}]]);var s=h.Element("span",{isMathJax:true,id:q.hover.id+"Menu",className:"MathJax_Menu_Button",style:{display:"inline-block","z-index":1,width:0,height:0,position:"relative"}},[["span",{className:"MathJax_Hover_Arrow",isMathJax:true,math:u,onclick:this.HoverMenu,jax:t.id,style:{left:this.Px(y.w+A+x+(y.x||0)+o.button.x),top:this.Px(-y.h-z-x-(y.y||0)-o.button.y),opacity:0,filter:"alpha(opacity=0)"}},[["span",{isMathJax:true},"\u25BC"]]]]);if(y.width){r.style.width=s.style.width=y.width;r.style.marginRight=s.style.marginRight="-"+y.width;r.firstChild.style.width=y.width;s.firstChild.style.left="";s.firstChild.style.right=this.Px(o.button.wx)}v.parentNode.insertBefore(r,v);if(w){v.parentNode.insertBefore(s,v)}if(v.style){v.style.position="relative"}this.ReHover(q)},ReHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}q.hover.remove=setTimeout(g(["UnHover",this,q]),o.fadeoutDelay);this.HoverFadeTimer(q,o.fadeinInc)},UnHover:function(q){if(!q.hover.nofade){this.HoverFadeTimer(q,-o.fadeoutInc,o.fadeoutStart)}},HoverFade:function(q){delete q.hover.timer;q.hover.opacity=Math.max(0,Math.min(1,q.hover.opacity+q.hover.inc));q.hover.opacity=Math.floor(1000*q.hover.opacity)/1000;var s=document.getElementById(q.hover.id),r=document.getElementById(q.hover.id+"Menu");s.firstChild.style.opacity=q.hover.opacity;s.firstChild.style.filter="alpha(opacity="+Math.floor(100*q.hover.opacity)+")";if(r){r.firstChild.style.opacity=q.hover.opacity;r.firstChild.style.filter=s.style.filter}if(q.hover.opacity===1){return}if(q.hover.opacity>0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return 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(function(a,d,f,c,j){var k="2.7.0";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","-webkit-box-sizing":"content-box","-moz-box-sizing":"content-box","box-sizing":"content-box","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(f,o,q,e,r){var p="2.7.0";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,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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6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;N<K;N++){this.items[N].Create(v)}if(g.isMobile){o.addElement(v,"span",{className:"MathJax_MenuClose",menu:E,ontouchstart:g.Close,ontouchend:n,onmousedown:g.Close,onmouseup:n},[["span",{},"\u00D7"]])}I.appendChild(v);this.posted=true;if(v.offsetWidth){v.style.width=(v.offsetWidth+2)+"px"}var H=M.pageX,F=M.pageY;var u=document.body.getBoundingClientRect();var C=(window.getComputedStyle?window.getComputedStyle(document.body):{marginLeft:"0px"});var A=u.right-Math.min(0,u.left)+parseFloat(C.marginLeft);if(!H&&!F&&"clientX" in M){H=M.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;F=M.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!E){var L=g.CurrentNode()||M.target;if((M.type==="keydown"||(!H&&!F))&&L){var P=window.pageXOffset||document.documentElement.scrollLeft;var O=window.pageYOffset||document.documentElement.scrollTop;var 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(function(d,c,j){var i,h="\u00A0";var k=function(m){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",m]].concat([].slice.call(arguments,1)))};var f=MathJax.Object.isArray;var e=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o<n;o++){p=arguments[o];if(!p){continue}if(p instanceof i.mbase){p=b.mml(p)}p.global=this.global;q=(this.data.length?this.Top().checkItem(p):true);if(q instanceof Array){this.Pop();this.Push.apply(this,q)}else{if(q instanceof b){this.Pop();this.Push(q)}else{if(q){this.data.push(p);if(p.env){if(p.copyEnv!==false){for(var r in this.env){if(this.env.hasOwnProperty(r)){p.env[r]=this.env[r]}}}this.env=p.env}else{p.env=this.env}}}}}},Pop:function(){var m=this.data.pop();if(!m.isOpen){delete m.env}this.env=(this.data.length?this.Top().env:{});return 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m=this.mmlData();return b.mml(i.TeXAtom(m))}return this.SUPER(arguments).checkItem.call(this,n)}});b.close=b.Subclass({type:"close",isClose:true});b.prime=b.Subclass({type:"prime",checkItem:function(m){if(this.data[0].type!=="msubsup"){return[i.msup(this.data[0],this.data[1]),m]}this.data[0].SetData(this.data[0].sup,this.data[1]);return[this.data[0],m]}});b.subsup=b.Subclass({type:"subsup",stopError:["MissingScript","Missing superscript or subscript argument"],supError:["MissingOpenForSup","Missing open brace for superscript"],subError:["MissingOpenForSub","Missing open brace for subscript"],checkItem:function(m){if(m.type==="open"||m.type==="left"){return true}if(m.type==="mml"){if(this.primes){if(this.position!==2){this.data[0].SetData(2,this.primes)}else{m.data[0]=i.mrow(this.primes.With({variantForm:true}),m.data[0])}}this.data[0].SetData(this.position,m.data[0]);if(this.movesupsub!=null){this.data[0].movesupsub=this.movesupsub}return 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p=0,n=r.length;p<n;p++){if(r[p]===o){continue}if(this.testCollection(r[p])){q=r[p];break}}}if(q==="STIX"&&this.testFont(this.FedoraSTIXcheck)){q=null}return q},testCollection:function(n){var m={testString:"() {} []"};m.family={TeX:"MathJax_Size1",STIX:"STIXSizeOneSym"}[n]||n.replace(/-(Math)?/,"")+"MathJax_Size1";if(n==="STIX"){m.noStyleChar=true}return this.testFont(m)},testFont:function(p){if(p.isWebFont&&d.FontFaceBug){this.div.style.fontWeight=this.div.style.fontStyle="normal"}else{this.div.style.fontWeight=(p.weight||"normal");this.div.style.fontStyle=(p.style||"normal")}var r=p.familyFixed||p.family;if(!p.isWebFont&&!r.match(/^(STIX|MathJax)|'/)){r=r.replace(/_/g," ").replace(/([a-z])([A-Z])/g,"$1 $2").replace(/ Jax/,"Jax")+"','"+r+"','"+r+"-";if(p.weight){r+="Bold"}if(p.style){r+="Italic"}if(!p.weight&&!p.style){r+="Regular"}p.familyFixed=r="'"+r+"'"}var o=this.getComparisonWidths(p.testString,p.noStyleChar);var s=null;if(o){this.div.style.fontFamily=r+","+this.comparisonFont[0];if(this.div.offsetWidth==o[0]){this.div.style.fontFamily=r+","+this.comparisonFont[o[2]];if(this.div.offsetWidth==o[1]){s=false}}if(s===null&&(this.div.offsetWidth!=o[3]||this.div.offsetHeight!=o[4])){if(!p.noStyleChar&&d.FONTDATA&&d.FONTDATA.hasStyleChar){for(var q=0,n=this.testSize.length;q<n;q++){if(this.testStyleChar(p,this.testSize[q])){s=true;n=0}}}else{s=true}}}if(d.safariTextNodeBug){this.div.innerHTML=""}else{this.text.nodeValue=""}return s},styleChar:"\uEFFD",versionChar:"\uEFFE",compChar:"\uEFFF",testStyleChar:function(p,r){var u=3+(p.weight?2:0)+(p.style?4:0);var o="",q=0;var t=this.div.style.fontSize;this.div.style.fontSize=r;if(d.msieItalicWidthBug&&p.style==="italic"){this.text.nodeValue=o=this.compChar;q=this.div.offsetWidth}if(d.safariTextNodeBug){this.div.innerHTML=this.compChar+o}else{this.text.nodeValue=this.compChar+o}var m=this.div.offsetWidth-q;if(d.safariTextNodeBug){this.div.innerHTML=this.styleChar+o}else{this.text.nodeValue=this.styleChar+o}var s=Math.floor((this.div.offsetWidth-q)/m+0.5);if(s===u){if(d.safariTextNodeBug){this.div.innerHTML=this.versionChar+o}else{this.text.nodeValue=this.versionChar+o}p.version=Math.floor((this.div.offsetWidth-q)/m+1.5)/2}this.div.style.fontSize=t;return(s===u)},getComparisonWidths:function(r,p){if(d.FONTDATA&&d.FONTDATA.hasStyleChar&&!p){r+=this.styleChar+" "+this.compChar}if(d.safariTextNodeBug){this.div.innerHTML=r}else{this.text.nodeValue=r}this.div.style.fontFamily=this.comparisonFont[0];var o=this.div.offsetWidth;this.div.style.fontFamily=d.webFontDefault;var t=this.div.offsetWidth,q=this.div.offsetHeight;for(var s=1,n=this.comparisonFont.length;s<n;s++){this.div.style.fontFamily=this.comparisonFont[s];if(this.div.offsetWidth!=o){return[o,this.div.offsetWidth,s,t,q]}}return null},loadWebFont:function(o){b.Startup.signal.Post("HTML-CSS Jax - Web-Font "+d.fontInUse+"/"+o.directory);var q=e(["LoadWebFont","Loading web-font %1",d.fontInUse+"/"+o.directory]);var m=MathJax.Callback({});var p=MathJax.Callback(["loadComplete",this,o,q,m]);j.timer.start(j,[this.checkWebFont,o,p],0,this.timeout);return m},loadComplete:function(p,r,o,m){MathJax.Message.Clear(r);if(m===j.STATUS.OK){this.webFontLoaded=true;o();return}this.loadError(p);if(b.Browser.isFirefox&&d.allowWebFonts){var q=document.location.protocol+"//"+document.location.hostname;if(document.location.port!=""){q+=":"+document.location.port}q+="/";if(j.fileURL(d.webfontDir).substr(0,q.length)!==q){this.firefoxFontError(p)}}if(!this.webFontLoaded){d.loadWebFontError(p,o)}else{o()}},loadError:function(m){e(["CantLoadWebFont","Can't load web font %1",d.fontInUse+"/"+m.directory],null,2000);b.Startup.signal.Post(["HTML-CSS Jax - web font error",d.fontInUse+"/"+m.directory,m])},firefoxFontError:function(m){e(["FirefoxCantLoadWebFont","Firefox can't load web fonts from a remote host"],null,3000);b.Startup.signal.Post("HTML-CSS Jax - Firefox web fonts on remote host error")},checkWebFont:function(m,n,o){if(m.time(o)){return}if(d.Font.testFont(n)){o(m.STATUS.OK)}else{setTimeout(m,m.delay)}},fontFace:function(q){var r=d.allowWebFonts;var t=d.FONTDATA.FONTS[q];if(d.msieFontCSSBug&&!t.family.match(/-Web$/)){t.family+="-Web"}if(t.isWebFont){delete t.familyFixed}var m=d.webfontDir+"/"+r;var p=j.fileURL(m);var o=q.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");if(!o.match(/-/)){o+="-Regular"}if(r==="svg"){o+=".svg#"+o}else{o+="."+r}var n=j.fileRev(m+"/"+o.replace(/#.*/,""));var s={"font-family":t.family,src:"url('"+p+"/"+o+n+"')"};if(r==="otf"){o=o.replace(/otf$/,"woff");n=j.fileRev(m+"/"+o);s.src+=" format('opentype')";p=j.fileURL(d.webfontDir+"/woff");s.src="url('"+p+"/"+o+n+"') format('woff'), "+s.src}else{if(r!=="eot"){s.src+=" format('"+r+"')"}}if(!(d.FontFaceBug&&t.isWebFont)){if(q.match(/-bold/)){s["font-weight"]="bold"}if(q.match(/-italic/)){s["font-style"]="italic"}}return s}});var l,a,c;var g=MathJax.Hub.Browser.isMSIE&&(document.documentMode||0)<8;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:focus, body :focus .MathJax":{display:"inline-table"},".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.MathJax_FullWidth":{"text-align":"center",display:(g?"block":"table-cell")+"!important",width:(g?"100%":"10000em")+"!important"},".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_LineBox":{display:(g?"block":"table")+"!important"},".MathJax_LineBox span":{display:(g?"block":"table-cell")+"!important",width:(g?"100%":"10000em")+"!important","min-width":0,"max-width":"none",padding:0,border:0,margin:0},".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 o=this.settings,n=this.config,m=o.font;if(this.adjustAvailableFonts){this.adjustAvailableFonts(n.availableFonts)}if(o.scale){n.scale=o.scale}if(m&&m!=="Auto"&&this.fontName[m]){n.availableFonts=[];delete n.fonts;if(h(this.fontName[m])){n.preferredFont=this.fontName[m][0];n.webFont=this.fontName[m][1]}else{n.preferredFont=n.webFont=this.fontName[m]}if(n.preferredFont){n.availableFonts[0]=n.preferredFont}}if(n.fonts){n.availableFonts=n.fonts;n.preferredFont=n.webFont=n.fonts[0];if(n.webFont==="STIX"){n.webFont+="-Web"}}m=this.Font.findFont(n.availableFonts,n.preferredFont);if(!m&&this.allowWebFonts){m=n.webFont;if(m){this.webFonts=true}}if(!m&&this.config.imageFont){m=n.imageFont;this.imgFonts=true}if(m){this.fontInUse=m;this.fontDir+="/"+m;this.webfontDir+="/"+m;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(){l=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;c=MathJax.Extension.MathEvents.Hover;this.ContextMenu=l.ContextMenu;this.Mousedown=l.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 n=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;this.hiddenDiv.removeChild(n);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(m){}}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=MathJax.HTML.Element("span",{className:"MathJax_LineBox"},[["span"]]);return j.Styles(this.config.styles,["InitializeHTML",this])},removeSTIXfonts:function(p){for(var o=0,n=p.length;o<n;o++){if(p[o]==="STIX"){p.splice(o,1);n--;o--}}if(this.config.preferredFont==="STIX"){this.config.preferredFont=p[0]}},PreloadWebFonts:function(){if(!d.allowWebFonts||!d.config.preloadWebFonts){return}for(var o=0,n=d.config.preloadWebFonts.length;o<n;o++){var p=d.FONTDATA.FONTS[d.config.preloadWebFonts[o]];if(!p.available){d.Font.testFont(p)}}},InitializeHTML:function(){this.PreloadWebFonts();this.getDefaultExEm();if(this.defaultEm){return}var m=MathJax.Callback();j.timer.start(j,function(n){if(n.time(m)){b.signal.Post(["HTML-CSS Jax - no default em size"]);return}d.getDefaultExEm();if(d.defaultEm){m()}else{setTimeout(n,n.delay)}},this.defaultEmDelay,this.defaultEmTimeout);return m},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(s){var r=s.jax[this.id],D,z=r.length,y,G,w,C,u,E,p,F,o,H,v,t=false,A,q=this.config.linebreaks.automatic,x=this.config.linebreaks.width;if(q){t=(x.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)!=null);if(t){x=x.replace(/\s*container\s*/,"")}else{v=this.defaultWidth}if(x===""){x="100%"}}else{v=100000}for(D=0;D<z;D++){G=r[D];if(!G.parentNode){continue}w=G.previousSibling;if(w&&String(w.className).match(/^MathJax(_Display)?( MathJax_Process(ing|ed))?$/)){w.parentNode.removeChild(w)}if(G.MathJax.preview){G.MathJax.preview.style.display="none"}p=G.MathJax.elementJax;if(!p){continue}p.HTMLCSS={display:(p.root.Get("display")==="block")};C=u=this.Element("span",{className:"MathJax",id:p.inputID+"-Frame",isMathJax:true,jaxID:this.id,oncontextmenu:l.Menu,onmousedown:l.Mousedown,onmouseover:l.Mouseover,onmouseout:l.Mouseout,onmousemove:l.Mousemove,onclick:l.Click,ondblclick:l.DblClick,onkeydown:l.Keydown,tabIndex:b.getTabOrder(p)});if(b.Browser.noContextMenu){C.ontouchstart=a.start;C.ontouchend=a.end}if(p.HTMLCSS.display){u=this.Element("div",{className:"MathJax_Display"});u.appendChild(C)}else{if(this.msieDisappearingBug){C.style.display="inline-block"}}u.className+=" MathJax_Processing";G.parentNode.insertBefore(u,G);p.HTMLCSS.span=C;p.HTMLCSS.div=u;G.parentNode.insertBefore(this.EmExSpan.cloneNode(true),G);u.parentNode.insertBefore(this.linebreakSpan.cloneNode(true),u)}var B=[];for(D=0;D<z;D++){G=r[D];if(!G.parentNode){continue}E=G.previousSibling;u=E.previousSibling;p=G.MathJax.elementJax;if(!p){continue}F=E.firstChild.offsetHeight/60;o=E.lastChild.firstChild.offsetHeight/60;A=Math.max(0,u.previousSibling.firstChild.offsetWidth-2);if(F===0||F==="NaN"){B.push(u);p.HTMLCSS.isHidden=true;F=this.defaultEx;o=this.defaultEm;A=this.defaultWidth}if(t){v=A}H=(this.config.matchFontHeight?F/this.TeX.x_height/o:1);H=Math.floor(Math.max(this.config.minScaleAdjust/100,H)*this.config.scale);p.HTMLCSS.scale=H/100;p.HTMLCSS.fontSize=H+"%";p.HTMLCSS.em=p.HTMLCSS.outerEm=o;this.em=o*H/100;p.HTMLCSS.ex=F;p.HTMLCSS.cwidth=A/this.em;p.HTMLCSS.lineWidth=(q?this.length2em(x,1,v/this.em):1000000)}for(D=0,y=B.length;D<y;D++){this.hiddenDiv.appendChild(B[D]);this.addElement(this.hiddenDiv,"br")}for(D=0;D<z;D++){G=r[D];if(!G.parentNode){continue}E=r[D].previousSibling;p=r[D].MathJax.elementJax;if(!p){continue}C=E.previousSibling;if(!p.HTMLCSS.isHidden){C=C.previousSibling}C.parentNode.removeChild(C);E.parentNode.removeChild(E);if(G.MathJax.preview){G.MathJax.preview.style.display=""}}s.HTMLCSSeqn=s.HTMLCSSlast=0;s.HTMLCSSi=-1;s.HTMLCSSchunk=this.config.EqnChunk;s.HTMLCSSdelay=false},PHASE:{I:1,II:2,III:3},Translate:function(n,r){if(!n.parentNode){return}if(r.HTMLCSSdelay){r.HTMLCSSdelay=false;b.RestartAfter(MathJax.Callback.Delay(this.config.EqnChunkDelay))}var m=n.MathJax.elementJax,q=m.root,s=m.HTMLCSS.div,o=m.HTMLCSS.span;if(!document.getElementById(o.id)){return}this.getMetrics(m);if(this.scale!==1){o.style.fontSize=m.HTMLCSS.fontSize}this.initImg(o);this.initHTML(q,o);this.savePreview(n);try{q.setTeXclass();q.toHTML(o,s,this.PHASE.I)}catch(p){if(p.restart){while(o.firstChild){o.removeChild(o.firstChild)}}this.restorePreview(n);throw p}this.restorePreview(n);s.className=s.className.split(/ /)[0]+" MathJax_Processed";b.signal.Post(["New Math Pending",m.inputID]);r.HTMLCSSeqn+=(r.i-r.HTMLCSSi);r.HTMLCSSi=r.i;if(r.HTMLCSSeqn>=r.HTMLCSSlast+r.HTMLCSSchunk){this.postTranslate(r,true);r.HTMLCSSchunk=Math.floor(r.HTMLCSSchunk*this.config.EqnChunkFactor);r.HTMLCSSdelay=true}return false},savePreview:function(m){var n=m.MathJax.preview;if(n){m.MathJax.tmpPreview=document.createElement("span");n.parentNode.replaceChild(m.MathJax.tmpPreview,n)}},restorePreview:function(m){var n=m.MathJax.tmpPreview;if(n){n.parentNode.replaceChild(m.MathJax.preview,n);delete m.MathJax.tmpPreview}},getMetrics:function(m){var n=m.HTMLCSS;this.em=i.mbase.prototype.em=n.em*n.scale;this.outerEm=n.em;this.scale=n.scale;this.cwidth=n.cwidth;this.linebreakWidth=n.lineWidth},postTranslate:function(o,u){var r=o.jax[this.id],v,p,s,q;for(s=o.HTMLCSSlast,q=o.HTMLCSSeqn;s<q;s++){v=r[s];if(v&&v.parentNode&&v.MathJax.elementJax){var n=(v.MathJax.elementJax.HTMLCSS||{}).div;if(n){n.className=n.className.split(/ /)[0]}if(v.MathJax.preview){v.MathJax.preview.innerHTML="";v.MathJax.preview.style.display="none"}}}for(s=o.HTMLCSSlast,q=o.HTMLCSSeqn;s<q;s++){v=r[s];if(v&&v.parentNode&&v.MathJax.elementJax){p=v.MathJax.elementJax;this.getMetrics(p);if(p.HTMLCSS.span&&p.HTMLCSS.div){p.root.toHTML(p.HTMLCSS.span,p.HTMLCSS.div,this.PHASE.II)}}}for(s=o.HTMLCSSlast,q=o.HTMLCSSeqn;s<q;s++){v=r[s];if(v&&v.parentNode&&v.MathJax.elementJax){p=v.MathJax.elementJax;this.getMetrics(p);if(p.HTMLCSS.span&&p.HTMLCSS.div){p.root.toHTML(p.HTMLCSS.span,p.HTMLCSS.div,this.PHASE.III);if(p.HTMLCSS.isHidden){v.parentNode.insertBefore(p.HTMLCSS.div,v)}delete p.HTMLCSS.span;delete p.HTMLCSS.div;v.MathJax.state=p.STATE.PROCESSED;b.signal.Post(["New Math",v.MathJax.elementJax.inputID])}}}if(this.forceReflow){var t=(document.styleSheets||[])[0]||{};t.disabled=true;t.disabled=false}o.HTMLCSSlast=o.HTMLCSSeqn},getJaxFromMath:function(m){if(m.parentNode.className.match(/MathJax_Display/)){m=m.parentNode}do{m=m.nextSibling}while(m&&m.nodeName.toLowerCase()!=="script");return b.getJaxFor(m)},getHoverSpan:function(m,n){return m.root.HTMLspanElement()},getHoverBBox:function(m,p,q){var r=p.bbox,o=m.HTMLCSS.outerEm;var n={w:r.w*o,h:r.h*o,d:r.d*o};if(r.width){n.width=r.width}return n},Zoom:function(n,y,x,m,v){y.className="MathJax";y.style.fontSize=n.HTMLCSS.fontSize;var B=y.appendChild(this.EmExSpan.cloneNode(true));var q=B.lastChild.firstChild.offsetHeight/60;this.em=i.mbase.prototype.em=q;this.outerEm=q/n.HTMLCSS.scale;B.parentNode.removeChild(B);this.scale=n.HTMLCSS.scale;this.linebreakWidth=n.HTMLCSS.lineWidth;this.cwidth=n.HTMLCSS.cwidth;this.zoomScale=parseInt(b.config.menuSettings.zscale)/100;this.idPostfix="-zoom";n.root.toHTML(y,y);this.idPostfix="";this.zoomScale=1;var z=n.root.HTMLspanElement().bbox,p=z.width;if(p){if(z.tw){m=z.tw*q}if(z.w*q<m){m=z.w*q}y.style.width=Math.floor(m-1.5*d.em)+"px";y.style.display="inline-block";var o=(n.root.id||"MathJax-Span-"+n.root.spanID)+"-zoom";var r=document.getElementById(o).firstChild;while(r&&r.style.width!==p){r=r.nextSibling}if(r){var u=r.offsetWidth;r.style.width="100%";if(u>m){y.style.width=(u+100)+"px"}}}r=y.firstChild.firstChild.style;if(z.H!=null&&z.H>z.h){r.marginTop=d.Em(z.H-Math.max(z.h,d.FONTDATA.lineH))}if(z.D!=null&&z.D>z.d){r.marginBottom=d.Em(z.D-Math.max(z.d,d.FONTDATA.lineD))}if(z.lw<0){r.paddingLeft=d.Em(-z.lw)}if(z.rw>z.w){r.marginRight=d.Em(z.rw-z.w)}y.style.position="absolute";if(!p){x.style.position="absolute"}var w=y.offsetWidth,t=y.offsetHeight,A=x.offsetHeight,s=x.offsetWidth;y.style.position=x.style.position="";return{Y:-l.getBBox(y).h,mW:s,mH:A,zW:w,zH:t}},initImg:function(m){},initHTML:function(n,m){},initFont:function(m){var 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m={display:"inline-block",overflow:"hidden",verticalAlign:this.Em(-r)};if(u>p+r){m.borderTop=this.Px(p+r)+" "+n;m.width=this.Em(u);m.height=(this.msieRuleBug&&p+r>0?this.Em(p+r):0)}else{m.borderLeft=this.Px(u)+" "+n;m.width=(this.msieRuleBug&&u>0?this.Em(u):0);m.height=this.Em(p+r)}var s=this.addElement(t,"span",{style:m,noAdjust:true,HH:p+r,isMathJax:true,bbox:{h:p,d:r,w:u,rw:u,lw:0,exactW:true}});if(t.isBox||t.className=="mspace"){t.bbox=s.bbox,t.HH=p+r}return s},createFrame:function(v,s,u,x,z,n){if(s<-u){u=-s}var r=2*z;if(this.msieFrameSizeBug){if(x<r){x=r}if(s+u<r){s=r-u}}if(this.msieBorderWidthBug){r=0}var y=this.Em(s+u-r),m=this.Em(-u-z),q=this.Em(x-r);var o=this.Px(z)+" "+n;var p=this.addElement(v,"span",{style:{border:o,display:"inline-block",overflow:"hidden",width:q,height:y},bbox:{h:s,d:u,w:x,rw:x,lw:0,exactW:true},noAdjust:true,HH:s+u,isMathJax:true});if(m){p.style.verticalAlign=m}return p},parentNode:function(n){var m=n.parentNode;if(m.nodeName.toLowerCase()==="a"){m=m.parentNode}return m},createStack:function(o,q,n){if(this.msiePaddingWidthBug){this.createStrut(o,0)}var p=String(n).match(/%$/);var m=(!p&&n!=null?n:0);o=this.addElement(o,"span",{noAdjust:true,HH:0,isMathJax:true,style:{display:"inline-block",position:"relative",width:(p?"100%":this.Em(m)),height:0}});if(!q){o.parentNode.bbox=o.bbox={exactW:true,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:m,lw:this.BIGDIMEN,rw:(!p&&n!=null?n:-this.BIGDIMEN)};if(p){o.bbox.width=n}}return o},createBox:function(n,m){var o=this.addElement(n,"span",{style:{position:"absolute"},isBox:true,isMathJax:true});if(m!=null){o.style.width=m}return o},addBox:function(m,n){n.style.position="absolute";n.isBox=n.isMathJax=true;return m.appendChild(n)},placeBox:function(v,u,s,p){v.isMathJax=true;var w=d.parentNode(v),E=v.bbox,A=w.bbox;if(this.msiePlaceBoxBug){this.addText(v,this.NBSP)}if(this.imgSpaceBug){this.addText(v,this.imgSpace)}var z,G=0;if(v.HH!=null){z=v.HH}else{if(E){z=Math.max(3,E.h+E.d)}else{z=v.offsetHeight/this.em}}if(!v.noAdjust){z+=1;z=Math.round(z*this.em)/this.em;if(this.msieInlineBlockAlignBug){this.addElement(v,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:true,style:{width:0,height:this.Em(z)}})}else{this.addElement(v,"span",{isMathJax:true,style:{display:"inline-block",width:0,height:this.Em(z)}});if(d.chromeHeightBug){z-=(v.lastChild.offsetHeight-Math.round(z*this.em))/this.em}}}if(E){if(this.initialSkipBug){if(E.lw<0){G=E.lw;d.createBlank(v,-G,true)}if(E.rw>E.w){d.createBlank(v,E.rw-E.w+0.1)}}if(!this.msieClipRectBug&&!E.noclip&&!p){var C=3/this.em;var B=(E.H==null?E.h:E.H),n=(E.D==null?E.d:E.D);var F=z-B-C,q=z+n+C,o=-1000,m=E.rw+1000;v.style.clip="rect("+this.Em(F)+" "+this.Em(m)+" "+this.Em(q)+" 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m=0,q=x-v.w/2,o="50%";if(this.initialSkipBug){m=v.w-v.rw-0.1;q+=v.lw}if(this.msieMarginScaleBug){q=(q*this.em)+"px"}else{q=this.Em(q)}if(u){q=(x===0?"":this.Em(x));o=(50-parseFloat(v.width)/2)+"%"}b.Insert(t.style,({right:{left:"",right:this.Em(m-x)},center:{left:o,marginLeft:q}})[p])},setStackWidth:function(n,m){if(typeof(m)==="number"){n.style.width=this.Em(Math.max(0,m));var o=n.bbox;if(o){o.w=m;o.exactW=true}o=n.parentNode.bbox;if(o){o.w=m;o.exactW=true}}else{n.style.width=n.parentNode.style.width="100%";if(n.bbox){n.bbox.width=m}if(n.parentNode.bbox){n.parentNode.bbox.width=m}}},createDelimiter:function(w,n,p,s,q){if(!n){w.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0};w.bbox.rw=w.bbox.w;this.createSpace(w,w.bbox.h,w.bbox.d,w.bbox.w);return}if(!s){s=1}if(!(p instanceof Array)){p=[p,p]}var v=p[1];p=p[0];var o={alias:n};while(o.alias){n=o.alias;o=this.FONTDATA.DELIMITERS[n];if(!o){o={HW:[0,this.FONTDATA.VARIANT[i.VARIANT.NORMAL]]}}}if(o.load){b.RestartAfter(j.Require(this.fontDir+"/fontdata-"+o.load+".js"))}for(var u=0,r=o.HW.length;u<r;u++){if(o.HW[u][0]*s>=p-0.01||(u==r-1&&!o.stretch)){if(o.HW[u][2]){s*=o.HW[u][2]}if(o.HW[u][3]){n=o.HW[u][3]}var t=this.addElement(w,"span");this.createChar(t,[n,o.HW[u][1]],s,q);w.bbox=t.bbox;w.offset=0.65*w.bbox.w;w.scale=s;return}}if(o.stretch){this["extendDelimiter"+o.dir](w,v,o.stretch,s,q)}},extendDelimiterV:function(B,u,F,G,x){var p=this.createStack(B,true);var w=this.createBox(p),v=this.createBox(p);this.createChar(w,(F.top||F.ext),G,x);this.createChar(v,(F.bot||F.ext),G,x);var o={bbox:{w:0,lw:0,rw:0}},E=o,q;var C=w.bbox.h+w.bbox.d+v.bbox.h+v.bbox.d;var s=-w.bbox.h;this.placeBox(w,0,s,true);s-=w.bbox.d;if(F.mid){E=this.createBox(p);this.createChar(E,F.mid,G,x);C+=E.bbox.h+E.bbox.d}if(F.min&&u<C*F.min){u=C*F.min}if(u>C){o=this.Element("span");this.createChar(o,F.ext,G,x);var D=o.bbox.h+o.bbox.d,m=D-0.05,z,r,A=(F.mid?2:1);r=z=Math.min(Math.ceil((u-C)/(A*m)),this.maxStretchyParts);if(!F.fullExtenders){m=(u-C)/(A*z)}var t=(z/(z+1))*(D-m);m=D-t;s+=t+m-o.bbox.h;while(A-->0){while(z-->0){if(!this.msieCloneNodeBug){q=o.cloneNode(true)}else{q=this.Element("span");this.createChar(q,F.ext,G,x)}q.bbox=o.bbox;s-=m;this.placeBox(this.addBox(p,q),0,s,true)}s+=t-o.bbox.d;if(F.mid&&A){this.placeBox(E,0,s-E.bbox.h,true);z=r;s+=-(E.bbox.h+E.bbox.d)+t+m-o.bbox.h}}}else{s+=(C-u)/2;if(F.mid){this.placeBox(E,0,s-E.bbox.h,true);s+=-(E.bbox.h+E.bbox.d)}s+=(C-u)/2}this.placeBox(v,0,s-v.bbox.h,true);s-=v.bbox.h+v.bbox.d;B.bbox={w:Math.max(w.bbox.w,o.bbox.w,v.bbox.w,E.bbox.w),lw:Math.min(w.bbox.lw,o.bbox.lw,v.bbox.lw,E.bbox.lw),rw:Math.max(w.bbox.rw,o.bbox.rw,v.bbox.rw,E.bbox.rw),h:0,d:-s,exactW:true};B.scale=G;B.offset=0.55*B.bbox.w;B.isMultiChar=true;this.setStackWidth(p,B.bbox.w)},extendDelimiterH:function(C,p,F,H,z){var s=this.createStack(C,true);var q=this.createBox(s),D=this.createBox(s);this.createChar(q,(F.left||F.rep),H,z);this.createChar(D,(F.right||F.rep),H,z);var m=this.Element("span");this.createChar(m,F.rep,H,z);var E={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}},o;this.placeBox(q,-q.bbox.lw,0,true);var v=(q.bbox.rw-q.bbox.lw)+(D.bbox.rw-D.bbox.lw)-0.05,u=q.bbox.rw-q.bbox.lw-0.025,y;if(F.mid){E=this.createBox(s);this.createChar(E,F.mid,H,z);v+=E.bbox.w}if(F.min&&p<v*F.min){p=v*F.min}if(p>v){var G=m.bbox.rw-m.bbox.lw,r=G-0.05,A,t,B=(F.mid?2:1);t=A=Math.min(Math.ceil((p-v)/(B*r)),this.maxStretchyParts);if(!F.fillExtenders){r=(p-v)/(B*A)}y=(A/(A+1))*(G-r);r=G-y;u-=m.bbox.lw+y;while(B-->0){while(A-->0){if(!this.cloneNodeBug){o=m.cloneNode(true)}else{o=this.Element("span");this.createChar(o,F.rep,H,z)}o.bbox=m.bbox;this.placeBox(this.addBox(s,o),u,0,true);u+=r}if(F.mid&&B){this.placeBox(E,u,0,true);u+=E.bbox.w-y;A=t}}}else{u-=(v-p)/2;if(F.mid){this.placeBox(E,u,0,true);u+=E.bbox.w}u-=(v-p)/2}this.placeBox(D,u,0,true);C.bbox={w:u+D.bbox.rw,lw:0,rw:u+D.bbox.rw,h:Math.max(q.bbox.h,m.bbox.h,D.bbox.h,E.bbox.h),d:Math.max(q.bbox.d,m.bbox.d,D.bbox.d,E.bbox.d),exactW:true};C.scale=H;C.isMultiChar=true;this.setStackWidth(s,C.bbox.w)},createChar:function(u,r,p,n){u.isMathJax=true;var t=u,v="",q={fonts:[r[1]],noRemap:true};if(n&&n===i.VARIANT.BOLD){q.fonts=[r[1]+"-bold",r[1]]}if(typeof(r[1])!=="string"){q=r[1]}if(r[0] instanceof Array){for(var s=0,o=r[0].length;s<o;s++){v+=String.fromCharCode(r[0][s])}}else{v=String.fromCharCode(r[0])}if(r[4]){p*=r[4]}if(p!==1||r[3]){t=this.addElement(u,"span",{style:{fontSize:this.Percent(p)},scale:p,isMathJax:true});this.handleVariant(t,q,v);u.bbox=t.bbox}else{this.handleVariant(u,q,v)}if(r[2]){u.style.marginLeft=this.Em(r[2])}if(r[3]){u.firstChild.style.verticalAlign=this.Em(r[3]);u.bbox.h+=r[3];if(u.bbox.h<0){u.bbox.h=0}}if(r[5]){u.bbox.h+=r[5]}if(r[6]){u.bbox.d+=r[6]}if(this.AccentBug&&u.bbox.w===0){t.firstChild.nodeValue+=this.NBSP}},positionDelimiter:function(n,m){m-=n.bbox.h;n.bbox.d-=m;n.bbox.h+=m;if(m){if(this.safariVerticalAlignBug||this.konquerorVerticalAlignBug||(this.operaVerticalAlignBug&&n.isMultiChar)){if(n.firstChild.style.display===""&&n.style.top!==""){n=n.firstChild;m-=d.unEm(n.style.top)}n.style.position="relative";n.style.top=this.Em(-m)}else{n.style.verticalAlign=this.Em(m);if(d.ffVerticalAlignBug){d.createRule(n.parentNode,n.bbox.h,0,0);delete 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r=q["offset"+w[v].offset];if(r&&y>=w[v].low&&y<=w[v].high){if(w[v].remap&&w[v].remap[y]){y=r+w[v].remap[y]}else{y=y-w[v].low+r;if(w[v].add){y+=w[v].add}}if(q["variant"+w[v].offset]){q=this.FONTDATA.VARIANT[q["variant"+w[v].offset]]}break}}}if(q.remap&&q.remap[y]){y=q.remap[y];if(q.remap.variant){q=this.FONTDATA.VARIANT[q.remap.variant]}}else{if(this.FONTDATA.REMAP[y]&&!q.noRemap){y=this.FONTDATA.REMAP[y]}}if(h(y)){q=this.FONTDATA.VARIANT[y[1]];y=y[0]}if(typeof(y)==="string"){t=y+t.substr(C+1);z=t.length;C=-1;continue}u=this.lookupChar(q,y);D=u[y];if(p||(!this.checkFont(u,o.style)&&!D[5].img)){if(A.length){this.addText(o,A);A=""}var x=!!o.style.fontFamily||!!B.style.fontStyle||!!B.style.fontWeight||!u.directory||p;p=false;if(o!==B){x=!this.checkFont(u,B.style);o=B}if(x){o=this.addElement(B,"span",{isMathJax:true,subSpan:true})}this.handleFont(o,u,o!==B)}A=this.handleChar(o,u,D,y,A);if(!(D[5]||{}).space){if(D[0]/1000>B.bbox.h){B.bbox.h=D[0]/1000}if(D[1]/1000>B.bbox.d){B.bbox.d=D[1]/1000}}if(B.bbox.w+D[3]/1000<B.bbox.lw){B.bbox.lw=B.bbox.w+D[3]/1000}if(B.bbox.w+D[4]/1000>B.bbox.rw){B.bbox.rw=B.bbox.w+D[4]/1000}B.bbox.w+=D[2]/1000;if((D[5]||{}).isUnknown){B.bbox.exactW=false}}if(A.length){this.addText(o,A)}if(B.scale&&B.scale!==1){B.bbox.h*=B.scale;B.bbox.d*=B.scale;B.bbox.w*=B.scale;B.bbox.lw*=B.scale;B.bbox.rw*=B.scale}if(t.length==1&&u.skew&&u.skew[y]){B.bbox.skew=u.skew[y]}},checkFont:function(m,n){var o=(n.fontWeight||"normal");if(o.match(/^\d+$/)){o=(parseInt(o)>=600?"bold":"normal")}return(m.family.replace(/'/g,"")===n.fontFamily.replace(/'/g,"")&&(m.style||"normal")===(n.fontStyle||"normal")&&(m.weight||"normal")===o)},handleFont:function(o,m,q){o.style.fontFamily=m.family;if(!m.directory){o.style.fontSize=Math.floor(d.config.scale/d.scale+0.5)+"%"}if(!(d.FontFaceBug&&m.isWebFont)){var n=m.style||"normal",p=m.weight||"normal";if(n!=="normal"||q){o.style.fontStyle=n}if(p!=="normal"||q){o.style.fontWeight=p}}},handleChar:function(o,m,u,t,s){var r=u[5];if(r.space){if(s.length){this.addText(o,s)}d.createShift(o,u[2]/1000);return""}if(r.img){return this.handleImg(o,m,u,t,s)}if(r.isUnknown&&this.FONTDATA.DELIMITERS[t]){if(s.length){this.addText(o,s)}var q=o.scale;d.createDelimiter(o,t,0,1,m);if(this.FONTDATA.DELIMITERS[t].dir==="V"){o.style.verticalAlign=this.Em(o.bbox.d);o.bbox.h+=o.bbox.d;o.bbox.d=0}o.scale=q;u[0]=o.bbox.h*1000;u[1]=o.bbox.d*1000;u[2]=o.bbox.w*1000;u[3]=o.bbox.lw*1000;u[4]=o.bbox.rw*1000;return""}if(r.c==null){if(t<=65535){r.c=String.fromCharCode(t)}else{var p=t-65536;r.c=String.fromCharCode((p>>10)+55296)+String.fromCharCode((p&1023)+56320)}}if(d.ffFontOptimizationBug&&u[4]-u[2]>125){o.style.textRendering="optimizeLegibility"}if(r.rfix){this.addText(o,s+r.c);d.createShift(o,r.rfix/1000);return""}if(u[2]||!this.msieAccentBug||s.length){return s+r.c}d.createShift(o,u[3]/1000);d.createShift(o,(u[4]-u[3])/1000);this.addText(o,r.c);d.createShift(o,-u[4]/1000);return""},handleImg:function(o,m,r,q,p){return p},lookupChar:function(r,u){var q,o;if(!r.FONTS){var t=this.FONTDATA.FONTS;var s=(r.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(s instanceof 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n=this.HTMLspanElement();if(n&&(n.parentNode===m||(n.parentNode||{}).parentNode===m)){while(n.firstChild){n.removeChild(n.firstChild)}n.bbox=this.HTMLzeroBBox();n.scale=1;n.isMultChar=n.HH=null;n.style.cssText="";return n}}if(this.href){m=d.addElement(m,"a",{href:this.href,isMathJax:true})}m=d.addElement(m,"span",{className:this.type,isMathJax:true});if(d.imgHeightBug){m.style.display="inline-block"}if(this["class"]){m.className+=" "+this["class"]}if(!this.spanID){this.spanID=d.GetID()}m.id=(this.id||"MathJax-Span-"+this.spanID)+d.idPostfix;m.bbox=this.HTMLzeroBBox();this.styles={};if(this.style){m.style.cssText=this.style;if(m.style.fontSize){this.mathsize=m.style.fontSize;m.style.fontSize=""}this.styles={border:d.getBorders(m),padding:d.getPadding(m)};if(this.styles.border){m.style.border=""}if(this.styles.padding){m.style.padding=""}}if(this.href){m.parentNode.bbox=m.bbox}this.HTMLaddAttributes(m);return m},HTMLaddAttributes:function(p){if(this.attrNames){var u=this.attrNames,q=i.nocopyAttributes,t=b.config.ignoreMMLattributes;var r=(this.type==="mstyle"?i.math.prototype.defaults:this.defaults);for(var o=0,n=u.length;o<n;o++){var s=u[o];if(t[s]==false||(!q[s]&&!t[s]&&r[s]==null&&typeof(p[s])==="undefined")){p.setAttribute(s,this.attr[s])}}}},HTMLspanElement:function(){if(!this.spanID){return null}return document.getElementById((this.id||"MathJax-Span-"+this.spanID)+d.idPostfix)},HTMLhandleVariant:function(n,m,o){d.handleVariant(n,m,o)},HTMLhandleSize:function(m){if(!m.scale){m.scale=this.HTMLgetScale();if(m.scale!==1){m.style.fontSize=d.Percent(m.scale)}}return m},HTMLhandleDir:function(n){var m=this.Get("dir",true);if(m){n.dir=m}return n},HTMLhandleColor:function(y){var A=this.getValues("mathcolor","color");if(this.mathbackground){A.mathbackground=this.mathbackground}if(this.background){A.background=this.background}if(this.style&&y.style.backgroundColor){A.mathbackground=y.style.backgroundColor;y.style.backgroundColor="transparent"}var 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m=d.createStack(q);var r=d.createBox(m);var t=this.data[0].toHTML(r);if(s!=null){d.Remeasured(this.data[0].HTMLstretchV(r,o,s),r)}else{if(o!=null){d.Remeasured(this.data[0].HTMLstretchH(r,o),r)}else{d.Measured(t,r)}}var n=d.TeX.axis_height*this.HTMLgetScale();d.placeBox(r,0,n-(r.bbox.h+r.bbox.d)/2+r.bbox.d)}else{var p=this.data[0].toHTML(q,o,s);if(s!=null){p=this.data[0].HTMLstretchV(r,o,s)}else{if(o!=null){p=this.data[0].HTMLstretchH(r,o)}}q.bbox=p.bbox}}this.HTMLhandleSpace(q);this.HTMLhandleColor(q);return q},HTMLstretchH:i.mbase.HTMLstretchH,HTMLstretchV:i.mbase.HTMLstretchV});b.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",d,"jax.js"]),0)})});b.Register.StartupHook("End Config",function(){b.Browser.Select({MSIE:function(m){var q=(document.documentMode||0);var p=m.versionAtLeast("7.0");var o=m.versionAtLeast("8.0")&&q>7;var n=(document.compatMode==="BackCompat");if(q<9){d.config.styles[".MathJax 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n=o.MathJax.elementJax,r=n.root,p=document.getElementById(n.inputID+"-Frame"),t=(n.PHTML.display?p.parentNode:p);this.initPHTML(r,p);try{r.toPreviewHTML(p)}catch(q){if(q.restart){while(p.firstChild){p.removeChild(p.firstChild)}}throw q}t.className=t.className.split(/ /)[0];if(this.hideProcessedMath){t.className+=" MathJax_Processed";if(o.MathJax.preview){n.PHTML.preview=o.MathJax.preview;delete o.MathJax.preview}}},postTranslate:function(s){var o=s.jax[this.id];if(!this.hideProcessedMath){return}for(var q=0,n=o.length;q<n;q++){var p=o[q];if(p&&p.MathJax.elementJax){p.previousSibling.className=p.previousSibling.className.split(/ /)[0];var r=p.MathJax.elementJax.PHTML;if(r.preview){r.preview.innerHTML="";r.preview.style.display="none";p.MathJax.preview=r.preview;delete r.preview}}}},getJaxFromMath:function(n){if(n.parentNode.className.match(/MathJax_PHTML_Display/)){n=n.parentNode}do{n=n.nextSibling}while(n&&n.nodeName.toLowerCase()!=="script");return 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t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" 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t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var 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.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch: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.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;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="MJXp-right MJXp-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({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(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.PHTML;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({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(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},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(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.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;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="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-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="MJXp-right MJXp-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.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-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.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;p<n;p++){this.PHTMLaddChild(q,"sep"+p,{});this.PHTMLaddChild(q,p,{})}this.PHTMLaddChild(q,"close",{});var o=this.PHTML.h,r=this.PHTML.d;this.PHTMLstretchChild("open",o,r);for(p=0,n=this.data.length;p<n;p++){this.PHTMLstretchChild("sep"+p,o,r);this.PHTMLstretchChild(p,o,r)}this.PHTMLstretchChild("close",o,r);return q}});h.mrow.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var p=this.PHTML.h,r=this.PHTML.d;for(var o=0,n=this.data.length;o<n;o++){this.PHTMLstretchChild(o,p,r)}return q}});h.mstyle.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);this.PHTMLhandleScriptlevel(n);return n}});h.TeXAtom.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);n.className="MJXp-mrow";return n}});h.mtable.Augment({toPreviewHTML:function(E){E=this.PHTMLdefaultSpan(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.PHTML,q=v.PHTMLspanElement();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.PHTMLspanElement();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.PHTML;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({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p<n;p++){this.PHTMLaddChild(q,p,o)}return q}});h.semantics.Augment({toPreviewHTML:function(n){n=this.PHTMLcreateSpan(n);if(this.data[0]){this.data[0].toPreviewHTML(n);MathJax.Hub.Insert(this.data[0].PHTML||{},this.PHTML)}return n}});h.annotation.Augment({toPreviewHTML:function(n){}});h["annotation-xml"].Augment({toPreviewHTML: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.PreviewHTML);
(function(b,g,f){var c=b.config.menuSettings;var e=MathJax.OutputJax;var a=f.isMSIE&&(document.documentMode||0)<8;var d=MathJax.Extension["fast-preview"]={version:"2.7.0",enabled:true,config:b.CombineConfig("fast-preview",{Chunks:{EqnChunk:10000,EqnChunkFactor:1,EqnChunkDelay:0},color:"inherit!important",updateTime:30,updateDelay:6,messageStyle:"none",disabled:f.isMSIE&&!f.versionAtLeast("8.0")}),Config:function(){if(b.config["CHTML-preview"]){MathJax.Hub.Config({"fast-preview":b.config["CHTML-preview"]})}var m,j,k,h,l;var i=this.config;if(!i.disabled&&c.FastPreview==null){b.Config({menuSettings:{FastPreview:true}})}if(c.FastPreview){MathJax.Ajax.Styles({".MathJax_Preview .MJXf-math":{color:i.color}});b.Config({"HTML-CSS":i.Chunks,CommonHTML:i.Chunks,SVG:i.Chunks})}b.Register.MessageHook("Begin Math Output",function(){if(!h&&d.Active()){m=b.processUpdateTime;j=b.processUpdateDelay;k=b.config.messageStyle;b.processUpdateTime=i.updateTime;b.processUpdateDelay=i.updateDelay;b.Config({messageStyle:i.messageStyle});MathJax.Message.Clear(0,0);l=true}});b.Register.MessageHook("End Math Output",function(){if(!h&&l){b.processUpdateTime=m;b.processUpdateDelay=j;b.Config({messageStyle:k});h=true}})},Disable:function(){this.enabled=false},Enable:function(){this.enabled=true},Active:function(){return c.FastPreview&&this.enabled&&!(e[c.renderer]||{}).noFastPreview},Preview:function(h){if(!this.Active()||!h.script.parentNode){return}var i=h.script.MathJax.preview||h.script.previousSibling;if(!i||i.className!==MathJax.Hub.config.preRemoveClass){i=g.Element("span",{className:MathJax.Hub.config.preRemoveClass});h.script.parentNode.insertBefore(i,h.script);h.script.MathJax.preview=i}i.innerHTML="";i.style.color=(a?"black":"inherit");return this.postFilter(i,h)},postFilter:function(j,i){if(!i.math.root.toPreviewHTML){var h=MathJax.Callback.Queue();h.Push(["Require",MathJax.Ajax,"[MathJax]/jax/output/PreviewHTML/config.js"],["Require",MathJax.Ajax,"[MathJax]/jax/output/PreviewHTML/jax.js"]);b.RestartAfter(h.Push({}))}i.math.root.toPreviewHTML(j)},Register:function(h){b.Register.StartupHook(h+" Jax Require",function(){var i=MathJax.InputJax[h];i.postfilterHooks.Add(["Preview",MathJax.Extension["fast-preview"]],50)})}};d.Register("TeX");d.Register("MathML");d.Register("AsciiMath");b.Register.StartupHook("End Config",["Config",d]);b.Startup.signal.Post("fast-preview Ready")})(MathJax.Hub,MathJax.HTML,MathJax.Hub.Browser);MathJax.Ajax.loadComplete("[MathJax]/extensions/fast-preview.js");
(function(a,e,b,f){var c=b.config.menuSettings;var d=MathJax.Extension.AssistiveMML={version:"2.7.0",config:b.CombineConfig("AssistiveMML",{disabled:false,styles:{".MJX_Assistive_MathML":{position:"absolute!important",top:0,left:0,clip:(b.Browser.isMSIE&&(document.documentMode||0)<8?"rect(1px 1px 1px 1px)":"rect(1px, 1px, 1px, 1px)"),padding:"1px 0 0 0!important",border:"0!important",height:"1px!important",width:"1px!important",overflow:"hidden!important",display:"block!important","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none"},".MJX_Assistive_MathML.MJX_Assistive_MathML_Block":{width:"100%!important"}}}),Config:function(){if(!this.config.disabled&&c.assistiveMML==null){b.Config({menuSettings:{assistiveMML:true}})}a.Styles(this.config.styles);b.Register.MessageHook("End Math",function(g){if(c.assistiveMML){return d.AddAssistiveMathML(g[1])}})},AddAssistiveMathML:function(g){var h={jax:b.getAllJax(g),i:0,callback:MathJax.Callback({})};this.HandleMML(h);return h.callback},RemoveAssistiveMathML:function(k){var h=b.getAllJax(k),l;for(var j=0,g=h.length;j<g;j++){l=document.getElementById(h[j].inputID+"-Frame");if(l&&l.getAttribute("data-mathml")){l.removeAttribute("data-mathml");if(l.lastChild&&l.lastChild.className.match(/MJX_Assistive_MathML/)){l.removeChild(l.lastChild)}}}},HandleMML:function(l){var g=l.jax.length,h,i,n,j;while(l.i<g){h=l.jax[l.i];n=document.getElementById(h.inputID+"-Frame");if(h.outputJax!=="NativeMML"&&h.outputJax!=="PlainSource"&&n&&!n.getAttribute("data-mathml")){try{i=h.root.toMathML("").replace(/\n */g,"").replace(/<!--.*?-->/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])});
MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS_HTML-full.js");