/*
 *  /MathJax/config/TeX-AMS_CHTML-full.js
 *  
 *  Copyright (c) 2010-2018 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/CommonHTML/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/CommonHTML/jax.js",
  "[MathJax]/jax/output/CommonHTML/autoload/mtable.js",
  "[MathJax]/jax/output/PreviewHTML/jax.js",
  "[MathJax]/extensions/fast-preview.js",
  "[MathJax]/extensions/AssistiveMML.js"
);

MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.9",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(/\s/g,"_")},formatURL:function(b,a){return a+"#"+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js");
MathJax.OutputJax.CommonHTML=MathJax.OutputJax({id:"CommonHTML",version:"2.7.9",directory:MathJax.OutputJax.directory+"/CommonHTML",extensionDir:MathJax.OutputJax.extensionDir+"/CommonHTML",autoloadDir:MathJax.OutputJax.directory+"/CommonHTML/autoload",fontDir:MathJax.OutputJax.directory+"/CommonHTML/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{matchFontHeight:true,scale:100,minScaleAdjust:50,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Cambria Math','Arial Unicode MS',serif",EqnChunk:(MathJax.Hub.Browser.isMobile?20:100),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.CommonHTML.Register("jax/mml")}MathJax.OutputJax.CommonHTML.loadComplete("config.js");
MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.9",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:"2.7.9",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],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(c){if(c.nodeValue.replace(/\s+/,"")==""){return c}var b,d,e=0,a;this.search={start:true};this.pattern=this.start;while(c){a=null;this.pattern.lastIndex=e;e=0;while(c&&c.nodeName.toLowerCase()==="#text"&&(b=this.pattern.exec(c.nodeValue))){if(this.search.start){c=this.startMatch(b,c)}else{c=this.endMatch(b,c)}}if(this.search.matched){c=this.encloseMath(c)}else{if(!this.search.start&&!this.search.close){a=this.search}}if(c){do{d=c;c=c.nextSibling}while(c&&this.ignoreTags[c.nodeName.toLowerCase()]!=null);if(!c||c.nodeName!=="#text"){if(!a){return(this.search.close?this.prevEndMatch():d)}c=a.open;e=a.opos+a.olen+(a.blen||0);this.search={start:true};this.pattern=this.start}}}return c},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,blen:a[1].length+3,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)}}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="2.7.9";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,LESS:188,GREATER:190,DASH:189},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 b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.last<a.delay&&a.up);a.last=q;a.up=false;if(s){a.timeout=setTimeout(a.menu,a.delay,r,this);r.preventDefault()}},end:function(r){var q=new Date().getTime();a.up=(q-a.last<a.delay);if(a.timeout){clearTimeout(a.timeout);delete a.timeout;a.last=0;a.up=false;r.preventDefault();return n.Handler((r.touches[0]||r.touch),"DblClick",this)}},menu:function(r,q){delete a.timeout;a.last=0;a.up=false;return n.Handler((r.touches[0]||r.touch),"ContextMenu",q)}};d.Browser.Select({MSIE:function(q){var s=(document.documentMode||0);var r=q.versionAtLeast("8.0");c.msieBorderWidthBug=(document.compatMode==="BackCompat");c.msieEventBug=q.isIE9;c.msieAlignBug=(!r||s<8);if(s<9){n.LEFTBUTTON=1}},Safari:function(q){c.safariContextMenuBug=true},Opera:function(q){c.operaPositionBug=true},Konqueror:function(q){c.noContextMenuBug=true}});c.topImg=(c.msieAlignBug?h.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):h.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(c.operaPositionBug){c.topImg.style.border="1px solid"}c.config=o=d.CombineConfig("MathEvents",o);var e=function(){var q=o.styles[".MathJax_Hover_Frame"];q.border=o.frame.bwidth+"px solid "+o.frame.bcolor+" ! important";q["box-shadow"]=q["-webkit-box-shadow"]=q["-moz-box-shadow"]=q["-khtml-box-shadow"]="0px 0px "+o.frame.hwidth+" "+o.frame.hcolor};g.Queue(d.Register.StartupHook("End Config",{}),[e],["getImages",f],["Styles",l,o.styles],["Post",d.Startup.signal,"MathEvents Ready"],["loadComplete",l,"[MathJax]/extensions/MathEvents.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.Callback,MathJax.Localization,MathJax.OutputJax,MathJax.InputJax);
(function(a,d,f,c,j){var k="2.7.9";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', Positive='true')"},"#MathJax_ZoomOverlay":{position:"absolute",left:0,top:0,"z-index":300,display:"inline-block",width:"100%",height:"100%",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"},"#MathJax_ZoomFrame":{position:"relative",display:"inline-block",height:0,width:0},"#MathJax_ZoomEventTrap":{position:"absolute",left:0,top:0,"z-index":302,display:"inline-block",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"}}});var e,b,g;MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){g=MathJax.Extension.MathEvents.Event;e=MathJax.Extension.MathEvents.Event.False;b=MathJax.Extension.MathEvents.Hover});var h=MathJax.Extension.MathZoom={version:k,settings:a.config.menuSettings,scrollSize:18,HandleEvent:function(n,l,m){if(h.settings.CTRL&&!n.ctrlKey){return true}if(h.settings.ALT&&!n.altKey){return true}if(h.settings.CMD&&!n.metaKey){return true}if(h.settings.Shift&&!n.shiftKey){return 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);
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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 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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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i.mrow.apply(i,this.data).With((m?{inferred:true}:{}))},checkItem:function(m){if(m.type==="over"&&this.isOpen){m.num=this.mmlData(false);this.data=[]}if(m.type==="cell"&&this.isOpen){if(m.linebreak){return false}d.Error(["Misplaced","Misplaced %1",m.name])}if(m.isClose&&this[m.type+"Error"]){d.Error(this[m.type+"Error"])}if(!m.isNotStack){return true}this.Push(m.data[0]);return false},With:function(m){for(var n in m){if(m.hasOwnProperty(n)){this[n]=m[n]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:true,Init:function(m){this.SUPER(arguments).Init.call(this);this.global=m},checkItem:function(m){if(m.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,m)}});b.stop=b.Subclass({type:"stop",isClose:true});b.open=b.Subclass({type:"open",isOpen:true,stopError:["ExtraOpenMissingClose","Extra open brace or missing close brace"],checkItem:function(n){if(n.type==="close"){var 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b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,m)){d.Error(this[["","subError","supError"][this.position]])}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:true,name:"\\over",checkItem:function(o,m){if(o.type==="over"){d.Error(["AmbiguousUseOf","Ambiguous use of %1",o.name])}if(o.isClose){var n=i.mfrac(this.num,this.mmlData(false));if(this.thickness!=null){n.linethickness=this.thickness}if(this.open||this.close){n.texWithDelims=true;n=d.fixedFence(this.open,n,this.close)}return[b.mml(n),o]}return this.SUPER(arguments).checkItem.call(this,o)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:true,delim:"(",stopError:["ExtraLeftMissingRight","Extra \\left or missing \\right"],checkItem:function(m){if(m.type==="right"){return b.mml(d.fenced(this.delim,this.mmlData(),m.delim))}return this.SUPER(arguments).checkItem.call(this,m)}});b.right=b.Subclass({type:"right",isClose:true,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:true,checkItem:function(m){if(m.type==="end"){if(m.name!==this.name){d.Error(["EnvBadEnd","\\begin{%1} ended with \\end{%2}",this.name,m.name])}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(m.type==="stop"){d.Error(["EnvMissingEnd","Missing \\end{%1}",this.name])}return this.SUPER(arguments).checkItem.call(this,m)}});b.end=b.Subclass({type:"end",isClose:true});b.style=b.Subclass({type:"style",checkItem:function(n){if(!n.isClose){return this.SUPER(arguments).checkItem.call(this,n)}var m=i.mstyle.apply(i,this.data).With(this.styles);return[b.mml(m),n]}});b.position=b.Subclass({type:"position",checkItem:function(n){if(n.isClose){d.Error(["MissingBoxFor","Missing box for %1",this.name])}if(n.isNotStack){var m=n.mmlData();switch(this.move){case"vertical":m=i.mpadded(m).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(m)];case"horizontal":return[b.mml(this.left),n,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,n)}});b.array=b.Subclass({type:"array",isOpen:true,copyEnv:false,arraydef:{},Init:function(){this.table=[];this.row=[];this.frame=[];this.hfill=[];this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(n){if(n.isClose&&n.type!=="over"){if(n.isEntry){this.EndEntry();this.clearEnv();return false}if(n.isCR){this.EndEntry();this.EndRow();this.clearEnv();return false}this.EndTable();this.clearEnv();var o=this.arraydef.scriptlevel;delete this.arraydef.scriptlevel;var m=i.mtable.apply(i,this.table).With(this.arraydef);if(this.frame.length===4){m.frame=(this.frame.dashed?"dashed":"solid")}else{if(this.frame.length){m.hasFrame=true;if(this.arraydef.rowlines){this.arraydef.rowlines=this.arraydef.rowlines.replace(/none( 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m=i.mtr;if(this.isNumbered&&this.row.length===3){this.row.unshift(this.row.pop());m=i.mlabeledtr}this.table.push(m.apply(i,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var m=this.arraydef.rowlines.split(/ /);if(m.length===this.table.length){this.frame.push("bottom");m.pop();this.arraydef.rowlines=m.join(" ")}else{if(m.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}if(this.rowspacing){var n=this.arraydef.rowspacing.split(/ /);while(n.length<this.table.length){n.push(this.rowspacing+"em")}this.arraydef.rowspacing=n.join(" ")}},clearEnv:function(){for(var m in this.env){if(this.env.hasOwnProperty(m)){delete this.env[m]}}}});b.cell=b.Subclass({type:"cell",isClose:true});b.mml=b.Subclass({type:"mml",isNotStack:true,Add:function(){this.data.push.apply(this.data,arguments);return this}});b.fn=b.Subclass({type:"fn",checkItem:function(n){if(this.data[0]){if(n.isOpen){return true}if(n.type!=="fn"){if(n.type!=="mml"||!n.data[0]){return[this.data[0],n]}if(n.data[0].isa(i.mspace)){return[this.data[0],n]}var m=n.data[0];if(m.isEmbellished()){m=m.CoreMO()}if([0,0,1,1,0,1,1,0,0,0][m.Get("texClass")]){return[this.data[0],n]}}return[this.data[0],i.mo(i.entity("#x2061")).With({texClass:i.TEXCLASS.NONE}),n]}return this.SUPER(arguments).checkItem.apply(this,arguments)}});b.not=b.Subclass({type:"not",checkItem:function(n){var m,o;if(n.type==="open"||n.type==="left"){return true}if(n.type==="mml"&&n.data[0].type.match(/^(mo|mi|mtext)$/)){m=n.data[0],o=m.data.join("");if(o.length===1&&!m.movesupsub&&m.data.length===1){o=b.not.remap[o.charCodeAt(0)];if(o){m.SetData(0,i.chars(String.fromCharCode(o)))}else{m.Append(i.chars("\u0338"))}return 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clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.under]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.under}else{o=i.msubsup(o,null,null);m=o.sub}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(o){var n=this.stack.Prev();if(!n){n=i.mi()}if(n.type==="msubsup"&&n.data[n.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=["","\u2032","\u2033","\u2034","\u2057"][m.length]||m;this.Push(b.prime(n,this.mmlToken(i.mo(m))))},mi2mo:function(m){var n=i.mo();n.Append.apply(n,m.data);var o;for(o in n.defaults){if(n.defaults.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}for(o in i.copyAttributes){if(i.copyAttributes.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}n.lspace=n.rspace="0";n.useMMLspacing&=~(n.SPACE_ATTR.lspace|n.SPACE_ATTR.rspace);return n},Comment:function(m){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(m){d.Error(["CantUseHash1","You can't use 'macro parameter character #' in math mode"])},Other:function(o){var n,m;if(this.stack.env.font){n={mathvariant:this.stack.env.font}}if(g.remap.hasOwnProperty(o)){o=g.remap[o];if(f(o)){n=o[1];o=o[0]}m=i.mo(i.entity("#x"+o)).With(n)}else{m=i.mo(o).With(n)}if(m.autoDefault("stretchy",true)){m.stretchy=false}if(m.autoDefault("texClass",true)==""){m=i.TeXAtom(m)}this.Push(this.mmlToken(m))},SetFont:function(n,m){this.stack.env.font=m},SetStyle:function(n,m,o,p){this.stack.env.style=m;this.stack.env.level=p;this.Push(b.style().With({styles:{displaystyle:o,scriptlevel:p}}))},SetSize:function(m,n){this.stack.env.size=n;this.Push(b.style().With({styles:{mathsize:n+"em"}}))},Color:function(o){var n=this.GetArgument(o);var m=this.stack.env.color;this.stack.env.color=n;var p=this.ParseArg(o);if(m){this.stack.env.color=m}else{delete this.stack.env.color}this.Push(i.mstyle(p).With({mathcolor:n}))},Spacer:function(m,n){this.Push(i.mspace().With({width:n,mathsize:i.SIZE.NORMAL,scriptlevel:0}))},LeftRight:function(m){this.Push(b[m.substr(1)]().With({delim:this.GetDelimiter(m)}))},Middle:function(m){var n=this.GetDelimiter(m);this.Push(i.TeXAtom().With({texClass:i.TEXCLASS.CLOSE}));if(this.stack.Top().type!=="left"){d.Error(["MisplacedMiddle","%1 must be within \\left and \\right",m])}this.Push(i.mo(n).With({stretchy:true}));this.Push(i.TeXAtom().With({texClass:i.TEXCLASS.OPEN}))},NamedFn:function(n,o){if(!o){o=n.substr(1)}var m=i.mi(o).With({texClass:i.TEXCLASS.OP});this.Push(b.fn(this.mmlToken(m)))},NamedOp:function(n,o){if(!o){o=n.substr(1)}o=o.replace(/&thinsp;/,"\u2006");var m=i.mo(o).With({movablelimits:true,movesupsub:true,form:i.FORM.PREFIX,texClass:i.TEXCLASS.OP});this.Push(this.mmlToken(m))},Limits:function(n,m){var p=this.stack.Prev("nopop");if(!p||(p.Get("texClass")!==i.TEXCLASS.OP&&p.movesupsub==null)){d.Error(["MisplacedLimits","%1 is allowed only on operators",n])}var o=this.stack.Top();if(p.type==="munderover"&&!m){p=o.data[o.data.length-1]=i.msubsup.apply(i.subsup,p.data)}else{if(p.type==="msubsup"&&m){p=o.data[o.data.length-1]=i.munderover.apply(i.underover,p.data)}}p.movesupsub=(m?true:false);p.Core().movablelimits=false;if(p.movablelimits){p.movablelimits=false}},Over:function(o,n,p){var m=b.over().With({name:o});if(n||p){m.open=n;m.close=p}else{if(o.match(/withdelims$/)){m.open=this.GetDelimiter(o);m.close=this.GetDelimiter(o)}}if(o.match(/^\\above/)){m.thickness=this.GetDimen(o)}else{if(o.match(/^\\atop/)||n||p){m.thickness=0}}this.Push(m)},Frac:function(n){var m=this.ParseArg(n);var o=this.ParseArg(n);this.Push(i.mfrac(m,o))},Sqrt:function(p){var q=this.GetBrackets(p),m=this.GetArgument(p);if(m==="\\frac"){m+="{"+this.GetArgument(m)+"}{"+this.GetArgument(m)+"}"}var o=d.Parse(m,this.stack.env).mml();if(!q){o=i.msqrt.apply(i,o.array())}else{o=i.mroot(o,this.parseRoot(q))}this.Push(o)},Root:function(o){var p=this.GetUpTo(o,"\\of");var m=this.ParseArg(o);this.Push(i.mroot(m,this.parseRoot(p)))},parseRoot:function(r){var o=this.stack.env,m=o.inRoot;o.inRoot=true;var q=d.Parse(r,o);r=q.mml();var p=q.stack.global;if(p.leftRoot||p.upRoot){r=i.mpadded(r);if(p.leftRoot){r.width=p.leftRoot}if(p.upRoot){r.voffset=p.upRoot;r.height=p.upRoot}}o.inRoot=m;return r},MoveRoot:function(m,p){if(!this.stack.env.inRoot){d.Error(["MisplacedMoveRoot","%1 can appear only within a root",m])}if(this.stack.global[p]){d.Error(["MultipleMoveRoot","Multiple use of %1",m])}var o=this.GetArgument(m);if(!o.match(/-?[0-9]+/)){d.Error(["IntegerArg","The argument to %1 must be an integer",m])}o=(o/15)+"em";if(o.substr(0,1)!=="-"){o="+"+o}this.stack.global[p]=o},Accent:function(o,m,s){var r=this.ParseArg(o);var q={accent:true};if(this.stack.env.font){q.mathvariant=this.stack.env.font}var n=this.mmlToken(i.mo(i.entity("#x"+m)).With(q));n.stretchy=(s?true:false);var p=(r.isEmbellished()?r.CoreMO():r);if(p.isa(i.mo)){p.movablelimits=false}this.Push(i.TeXAtom(i.munderover(r,null,n).With({accent:true})))},UnderOver:function(o,s,m,q){var r={o:"over",u:"under"}[o.charAt(1)];var p=this.ParseArg(o);if(p.Get("movablelimits")){p.movablelimits=false}if(p.isa(i.munderover)&&p.isEmbellished()){p.Core().With({lspace:0,rspace:0});p=i.mrow(i.mo().With({rspace:0}),p)}var n=i.munderover(p,null,null);n.SetData(n[r],this.mmlToken(i.mo(i.entity("#x"+s)).With({stretchy:true,accent:!q})));if(m){n=i.TeXAtom(n).With({texClass:i.TEXCLASS.OP,movesupsub:true})}this.Push(n.With({subsupOK:true}))},Overset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);n.movablelimits=false;this.Push(i.mover(n,o))},Underset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);n.movablelimits=false;this.Push(i.munder(n,o))},TeXAtom:function(p,r){var q={texClass:r},o;if(r==i.TEXCLASS.OP){q.movesupsub=q.movablelimits=true;var m=this.GetArgument(p);var n=m.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(n){q.mathvariant=i.VARIANT.NORMAL;o=b.fn(this.mmlToken(i.mi(n[1]).With(q)))}else{o=b.fn(i.TeXAtom(d.Parse(m,this.stack.env).mml()).With(q))}}else{o=i.TeXAtom(this.ParseArg(p)).With(q)}this.Push(o)},MmlToken:function(o){var p=this.GetArgument(o),m=this.GetBrackets(o,"").replace(/^\s+/,""),s=this.GetArgument(o),r={attrNames:[]},n;if(!i[p]||!i[p].prototype.isToken){d.Error(["NotMathMLToken","%1 is not a token element",p])}while(m!==""){n=m.match(/^([a-z]+)\s*=\s*('[^']*'|"[^"]*"|[^ ,]*)\s*,?\s*/i);if(!n){d.Error(["InvalidMathMLAttr","Invalid MathML attribute: %1",m])}if(i[p].prototype.defaults[n[1]]==null&&!this.MmlTokenAllow[n[1]]){d.Error(["UnknownAttrForElement","%1 is not a recognized attribute for %2",n[1],p])}var q=this.MmlFilterAttribute(n[1],n[2].replace(/^(['"])(.*)\1$/,"$2"));if(q){if(q.toLowerCase()==="true"){q=true}else{if(q.toLowerCase()==="false"){q=false}}r[n[1]]=q;r.attrNames.push(n[1])}m=m.substr(n[0].length)}this.Push(this.mmlToken(i[p](s).With(r)))},MmlFilterAttribute:function(m,n){return n},MmlTokenAllow:{fontfamily:1,fontsize:1,fontweight:1,fontstyle:1,color:1,background:1,id:1,"class":1,href:1,style:1},Strut:function(m){this.Push(i.mpadded(i.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(o,m,p){var n=this.ParseArg(o);if(m||p){n=i.mpadded(n);if(p){n.height=n.depth=0}if(m){n.width=0}}this.Push(i.TeXAtom(i.mphantom(n)))},Smash:function(o){var n=this.trimSpaces(this.GetBrackets(o,""));var m=i.mpadded(this.ParseArg(o));switch(n){case"b":m.depth=0;break;case"t":m.height=0;break;default:m.height=m.depth=0}this.Push(i.TeXAtom(m))},Lap:function(n){var m=i.mpadded(this.ParseArg(n)).With({width:0});if(n==="\\llap"){m.lspace="-1width"}this.Push(i.TeXAtom(m))},RaiseLower:function(m){var n=this.GetDimen(m);var o=b.position().With({name:m,move:"vertical"});if(n.charAt(0)==="-"){n=n.slice(1);m={raise:"\\lower",lower:"\\raise"}[m.substr(1)]}if(m==="\\lower"){o.dh="-"+n;o.dd="+"+n}else{o.dh="+"+n;o.dd="-"+n}this.Push(o)},MoveLeftRight:function(m){var p=this.GetDimen(m);var o=(p.charAt(0)==="-"?p.slice(1):"-"+p);if(m==="\\moveleft"){var n=p;p=o;o=n}this.Push(b.position().With({name:m,move:"horizontal",left:i.mspace().With({width:p,mathsize:i.SIZE.NORMAL}),right:i.mspace().With({width:o,mathsize:i.SIZE.NORMAL})}))},Hskip:function(m){this.Push(i.mspace().With({width:this.GetDimen(m),mathsize:i.SIZE.NORMAL}))},Rule:function(n,p){var m=this.GetDimen(n),o=this.GetDimen(n),r=this.GetDimen(n);var q={width:m,height:o,depth:r};if(p!=="blank"){q.mathbackground=(this.stack.env.color||"black")}this.Push(i.mspace().With(q))},rule:function(p){var n=this.GetBrackets(p),m=this.GetDimen(p),q=this.GetDimen(p);var o=i.mspace().With({width:m,height:q,mathbackground:(this.stack.env.color||"black")});if(n){o=i.mpadded(o).With({voffset:n});if(n.match(/^\-/)){o.height=n;o.depth="+"+n.substr(1)}else{o.height="+"+n}}this.Push(o)},MakeBig:function(m,p,n){n*=g.p_height;n=String(n).replace(/(\.\d\d\d).+/,"$1")+"em";var o=this.GetDelimiter(m,true);this.Push(i.mstyle(i.TeXAtom(i.mo(o).With({minsize:n,maxsize:n,fence:true,stretchy:true,symmetric:true})).With({texClass:p})).With({scriptlevel:0}))},BuildRel:function(m){var n=this.ParseUpTo(m,"\\over");var o=this.ParseArg(m);this.Push(i.TeXAtom(i.munderover(o,null,n)).With({texClass:i.TEXCLASS.REL}))},HBox:function(m,n){this.Push.apply(this,this.InternalMath(this.GetArgument(m),n))},FBox:function(m){this.Push(i.menclose.apply(i,this.InternalMath(this.GetArgument(m))).With({notation:"box"}))},Not:function(m){this.Push(b.not())},Dots:function(m){this.Push(b.dots().With({ldots:this.mmlToken(i.mo(i.entity("#x2026")).With({stretchy:false})),cdots:this.mmlToken(i.mo(i.entity("#x22EF")).With({stretchy:false}))}))},Require:function(m){var n=this.GetArgument(m).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");this.Extension(null,n)},Extension:function(m,n,o){if(m&&!typeof(m)==="string"){m=m.name}n=d.extensionDir+"/"+n;if(!n.match(/\.js$/)){n+=".js"}if(!j.loaded[j.fileURL(n)]){if(m!=null){delete g[o||"macros"][m.replace(/^\\/,"")]}c.RestartAfter(j.Require(n))}},Macro:function(o,r,q,s){if(q){var n=[];if(s!=null){var m=this.GetBrackets(o);n.push(m==null?s:m)}for(var p=n.length;p<q;p++){n.push(this.GetArgument(o))}r=this.SubstituteArgs(n,r)}this.string=this.AddArgs(r,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(n,p,v,r,u,o,m,w,t){var s=this.GetNext();if(s===""){d.Error(["MissingArgFor","Missing argument for %1",n])}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:true,arraydef:{rowspacing:(o||"4pt"),columnspacing:(u||"1em")}});if(w){q.isCases=true}if(t){q.isNumbered=true;q.arraydef.side=t}if(p||v){q.open=p;q.close=v}if(m==="D"){q.arraydef.displaystyle=true}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:true,name:p}));if(this.stack.Top().isCases){var o=this.string;var t=0,s=-1,q=this.i,n=o.length;while(q<n){var u=o.charAt(q);if(u==="{"){t++;q++}else{if(u==="}"){if(t===0){n=0}else{t--;if(t===0&&s<0){s=q-this.i}q++}}else{if(u==="&"&&t===0){d.Error(["ExtraAlignTab","Extra alignment tab in \\cases text"])}else{if(u==="\\"){if(o.substr(q).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){n=0}else{q+=2}}else{q++}}}}}var r=o.substr(this.i,q-this.i);if(!r.match(/^\s*\\text[^a-zA-Z]/)||s!==r.replace(/\s+$/,"").length-1){this.Push.apply(this,this.InternalMath(r,0));this.i=q}}},Cr:function(m){this.Push(b.cell().With({isCR:true,name:m}))},CrLaTeX:function(o,m){var r;if(!m&&this.string.charAt(this.i)==="["){r=this.GetBrackets(o,"").replace(/ /g,"").replace(/,/,".");if(r&&!this.matchDimen(r)){d.Error(["BracketMustBeDimension","Bracket argument to %1 must be a dimension",o])}}this.Push(b.cell().With({isCR:true,name:o,linebreak:true}));var q=this.stack.Top();if(q.isa(b.array)){if(r&&q.arraydef.rowspacing){var p=q.arraydef.rowspacing.split(/ /);if(!q.rowspacing){q.rowspacing=this.dimen2em(p[0])}while(p.length<q.table.length){p.push(this.Em(q.rowspacing))}p[q.table.length-1]=this.Em(Math.max(0,q.rowspacing+this.dimen2em(r)));q.arraydef.rowspacing=p.join(" ")}}else{if(r){this.Push(i.mspace().With({depth:r}))}this.Push(i.mspace().With({linebreak:i.LINEBREAK.NEWLINE}))}},emPerInch:7.2,pxPerInch:72,matchDimen:function(m){return m.match(/^(-?(?:\.\d+|\d+(?:\.\d*)?))(px|pt|em|ex|mu|pc|in|mm|cm)$/)},dimen2em:function(q){var o=this.matchDimen(q);var n=parseFloat(o[1]||"1"),p=o[2];if(p==="em"){return n}if(p==="ex"){return n*0.43}if(p==="pt"){return n/10}if(p==="pc"){return n*1.2}if(p==="px"){return n*this.emPerInch/this.pxPerInch}if(p==="in"){return n*this.emPerInch}if(p==="cm"){return n*this.emPerInch/2.54}if(p==="mm"){return n*this.emPerInch/25.4}if(p==="mu"){return n/18}return 0},Em:function(n){if(Math.abs(n)<0.0006){return"0em"}return n.toFixed(3).replace(/\.?0+$/,"")+"em"},HLine:function(n,o){if(o==null){o="solid"}var p=this.stack.Top();if(!p.isa(b.array)||p.data.length){d.Error(["Misplaced","Misplaced %1",n])}if(p.table.length==0){p.frame.push("top")}else{var m=(p.arraydef.rowlines?p.arraydef.rowlines.split(/ /):[]);while(m.length<p.table.length){m.push("none")}m[p.table.length-1]=o;p.arraydef.rowlines=m.join(" ")}},HFill:function(m){var n=this.stack.Top();if(n.isa(b.array)){n.hfill.push(n.data.length)}else{d.Error(["UnsupportedHFill","Unsupported use of %1",m])}},BeginEnd:function(o){var p=this.GetArgument(o),r=false;if(p.match(/^\\end\\/)){r=true;p=p.substr(5)}if(p.match(/\\/i)){d.Error(["InvalidEnv","Invalid environment name '%1'",p])}var q=this.envFindName(p);if(!q){d.Error(["UnknownEnv","Unknown environment '%1'",p])}if(!f(q)){q=[q]}var m=(f(q[1])?q[1][0]:q[1]);var n=b.begin().With({name:p,end:m,parse:this});if(o==="\\end"){if(!r&&f(q[1])&&this[q[1][1]]){n=this[q[1][1]].apply(this,[n].concat(q.slice(2)))}else{n=b.end().With({name:p})}}else{if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(q[0]&&this[q[0]]){n=this[q[0]].apply(this,[n].concat(q.slice(2)))}}this.Push(n)},envFindName:function(m){return(g.environment.hasOwnProperty(m)?g.environment[m]:null)},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(n,p,u,s,t,o,m,q){if(!s){s=this.GetArgument("\\begin{"+n.name+"}")}var v=("c"+s).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");s=s.replace(/[^clr]/g,"").split("").join(" ");s=s.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var 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F=x[this.base],C=this.CHTML;C.w=v;C.h=F.h;C.d=F.d;if(F.h<0.35){u.style.marginTop=a.Em(F.h-0.35)}if(E.accent&&F.h<a.TEX.x_height){C.h+=a.TEX.x_height-F.h;u.style.marginTop=a.Em(a.TEX.x_height-Math.max(F.h,0.35));F.h=a.TEX.x_height}var A=u,D=0;if(F.ic){D=1.3*F.ic+0.05}if(this.data[this.over]){A=this.CHTMLaddOverscript(z,x,E,D,u,t)}if(this.data[this.under]){this.CHTMLaddUnderscript(B,x,E,D,w,A,t)}else{if(!t){w.appendChild(A)}}this.CHTMLplaceBoxes(u,B,z,E,x);return w},CHTMLgetBBoxes:function(A,x,v){var y,t=this.data.length,z,u=-i,s=u;for(y=0;y<t;y++){A[y]=this.CHTMLbboxFor(y);A[y].x=A[y].y=0;if(this.data[y]){A[y].stretch=this.data[y].CHTMLcanStretch("Horizontal")}z=(y===this.base?1:A[y].rscale);if(y!==this.base){delete A[y].L;delete 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C=x*(z[y].w+(z[y].L||0)+(z[y].R||0));z[y].x+={left:0,center:(t-C)/2,right:t-C}[E.align];if(z[y].x<F){F=z[y].x}}for(y=0;y<v;y++){if(this.data[y]){x=(y===this.base?1:z[y].rscale);if(z[y].x-F){var u=(y===this.base?s:y===this.over?A:B);u.style.paddingLeft=a.Em((z[y].x-F)/x)}D.combine(z[y],z[y].x-F,z[y].y)}}this.CHTML=D},CHTMLstretchV:d.mbase.CHTMLstretchV,CHTMLstretchH:d.mbase.CHTMLstretchH,CHTMLchildNode:function(u,t){var s=["mjx-op","mjx-under","mjx-over"];if(this.over===1){s[1]=s[2]}return a.getNode(u,s[t])}});d.msubsup.Augment({toCommonHTML:function(S,C){var A=this.getValues("displaystyle","subscriptshift","superscriptshift","texprimestyle");var D,H,z;if(C&&C.stretch){if(this.data[this.base]){D=a.getNode(S,"mjx-base")}if(this.data[this.sub]){H=a.getNode(S,"mjx-sub")}if(this.data[this.sup]){z=a.getNode(S,"mjx-sup")}E=a.getNode(S,"mjx-stack")}else{var K=["mjx-base","mjx-sub","mjx-sup"];if(this.sup===1){K[1]=K[2]}S=this.CHTMLdefaultNode(S,{childNodes:K,noBBox:true,forceChild:true,minChildren:3});D=S.childNodes[this.base];H=S.childNodes[this.sub];z=S.childNodes[this.sup];if(!this.CHTMLnotEmpty(this.data[this.sub])){S.removeChild(H);H=null}if(!this.CHTMLnotEmpty(this.data[this.sup])){S.removeChild(z);z=null}if(S.childNodes.length===3){var E=a.addElement(S,"mjx-stack");E.appendChild(z);E.appendChild(H)}}var F=[],G=a.BBOX.empty(this.CHTML);for(var V=0,T=this.data.length;V<T;V++){F[V]=this.CHTMLbboxFor(V)}var y=F[this.base]||a.BBOX.empty(),P=F[this.sub],W=F[this.sup];var B=(H?P.rscale:1),w=(z?W.rscale:1);G.combine(y,0,0);var X=a.TEX.x_height,N=a.TEX.scriptspace;var Q=a.TEX.sup_drop*w,O=a.TEX.sub_drop*B;var L=y.h-Q,J=y.d+O,Y=0,R;if(y.ic){G.w-=y.ic;D.style.marginRight=a.Em(-y.ic);Y=1.3*y.ic+0.05}var 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M=a.TEX.rule_thickness;if((L-w*W.d)-(B*P.h-J)<3*M){J=3*M-L+w*W.d+B*P.h;Q=(4/5)*X-(L-w*W.d);if(Q>0){L+=Q;J-=Q}}L=Math.max(L,A.superscriptshift);J=Math.max(J,A.subscriptshift);H.style.paddingRight=a.Em(N/B);z.style.paddingBottom=a.Em(L/w+J/B-W.d-P.h/B*w);z.style.paddingLeft=a.Em(Y/w);z.style.paddingRight=a.Em(N/w);E.style.verticalAlign=a.Em(-J);G.combine(W,I+Y,L);G.combine(P,I,-J)}}G.clean();return S},CHTMLstretchV:d.mbase.CHTMLstretchV,CHTMLstretchH:d.mbase.CHTMLstretchH,CHTMLchildNode:function(u,t){var s=["mjx-base","mjx-sub","mjx-sup"];if(this.over===1){s[1]=s[2]}return a.getNode(u,s[t])}});d.mfrac.Augment({toCommonHTML:function(N){N=this.CHTMLdefaultNode(N,{childNodes:["mjx-numerator","mjx-denominator"],childOptions:{autowidth:true},forceChild:true,noBBox:true,minChildren:2});var x=this.getValues("linethickness","displaystyle","numalign","denomalign","bevelled");var O=x.displaystyle;var D=N.firstChild,w=N.lastChild;var y=a.addElement(N,"mjx-box");y.appendChild(D);y.appendChild(w);N.appendChild(y);if(x.numalign!=="center"){D.style.textAlign=x.numalign}if(x.denomalign!=="center"){w.style.textAlign=x.denomalign}var P=this.CHTMLbboxFor(0),B=this.CHTMLbboxFor(1),C=a.BBOX.empty(this.CHTML),F=P.rscale,z=B.rscale;x.linethickness=Math.max(0,a.thickness2em(x.linethickness||"0",C.scale));var M=a.TEX.min_rule_thickness/a.em,T=a.TEX.axis_height;var J=x.linethickness,L,K,I,G;if(x.bevelled){y.className+=" MJXc-bevelled";var S=(O?0.4:0.15);var E=Math.max(F*(P.h+P.d),z*(B.h+B.d))+2*S;var R=a.Element("mjx-bevel");y.insertBefore(R,w);var s=a.createDelimiter(R,47,E);I=F*(P.d-P.h)/2+T+S;G=z*(B.d-B.h)/2+T-S;if(I){D.style.verticalAlign=a.Em(I/F)}if(G){w.style.verticalAlign=a.Em(G/z)}R.style.marginLeft=R.style.marginRight=a.Em(-S/2);C.combine(P,0,I);C.combine(s,F*P.w-S/2,0);C.combine(B,F*P.w+s.w-S,G);C.clean()}else{y.className+=" 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t=this.CHTML.h,w=this.CHTML.d;this.CHTMLstretchChildV("open",t,w);for(u=0,s=this.data.length;u<s;u++){this.CHTMLstretchChildV("sep"+u,t,w);this.CHTMLstretchChildV(u,t,w)}this.CHTMLstretchChildV("close",t,w);this.CHTMLhandleSpace(v);this.CHTMLhandleBBox(v);this.CHTMLhandleColor(v);return v}});d.mrow.Augment({toCommonHTML:function(w,t){t=t||{};w=this.CHTMLdefaultNode(w);var z=this.CHTML,v=z.h,x=z.d,y;for(var u=0,s=this.data.length;u<s;u++){this.CHTMLstretchChildV(u,v,x);if(this.data[u]&&this.data[u].CHTML&&this.data[u].CHTML.w<0){y=true}}if(this.CHTMLlineBreaks()){this.CHTMLmultiline(w);if(t.autowidth){w.style.width=""}}else{if(y&&z.w){w.style.width=a.Em(Math.max(0,z.w))}if(z.w<0){w.style.marginRight=a.Em(z.w)}}return w},CHTMLlineBreaks:function(){if(!this.parent.linebreakContainer){return false}return(c.automatic&&this.CHTML.w>a.linebreakWidth)||this.hasNewline()},CHTMLstretchV:function(s,t){this.CHTMLstretchChildV(this.CoreIndex(),s,t);return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLstretchChildH(this.CoreIndex(),s,t);return this.CHTML}});d.TeXAtom.Augment({toCommonHTML:function(x,w){if(!w||!w.stretch){x=this.CHTMLdefaultNode(x)}if(this.texClass===d.TEXCLASS.VCENTER){var s=a.TEX.axis_height,u=this.CHTML;var t=s-(u.h+u.d)/2+u.d;if(Math.abs(t)>0.001){x.style.verticalAlign=a.Em(t);u.h+=t;u.t+=t;u.d-=t;u.b-=t}}return x},CHTMLstretchV:function(s,t){this.CHTMLupdateFrom(this.Core().CHTMLstretchV(s,t));this.toCommonHTML(this.CHTMLnodeElement(),{stretch:true});return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,s));this.toCommonHTML(t,{stretch:true});return this.CHTML}});d.semantics.Augment({toCommonHTML:function(s){s=this.CHTMLcreateNode(s);if(this.data[0]){this.data[0].toCommonHTML(s);this.CHTMLupdateFrom(this.data[0].CHTML);this.CHTMLhandleBBox(s)}return s}});d.annotation.Augment({toCommonHTML:function(s){return this.CHTMLcreateNode(s)}});d["annotation-xml"].Augment({toCommonHTML:d.mbase.CHTMLautoload});d.ms.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mglyph.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.menclose.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.maction.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mmultiscripts.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mtable.Augment({toCommonHTML:d.mbase.CHTMLautoload});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(f.config.menuSettings.zoom!=="None"){o.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.CommonHTML);
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i=this.CHTML;i.w=i.r=m.R;i.h=i.t=m.T-m.B;i.d=i.b=m.B;if(!h.frame&&!i.pwidth){l.style.padding="0 "+e.Em(1/6);i.L=i.R=1/6}this.CHTMLhandleSpace(l);this.CHTMLhandleBBox(l);this.CHTMLhandleColor(l);return l},CHTMLgetBoxSizes:function(z,k){var r=e.FONTDATA.lineH*z.useHeight,t=e.FONTDATA.lineD*z.useHeight;var y=[],h=[],l=[],w=-1,q,n;for(q=0,n=this.data.length;q<n;q++){var B=this.data[q],A=(B.type==="mtr"?0:c);y[q]=r;h[q]=t;for(var p=A,v=B.data.length+A;p<v;p++){if(l[p]==null){l[p]=-f;if(p>w){w=p}}var u=B.data[p-A].CHTML;if(u.h>y[q]){y[q]=u.h}if(u.d>h[q]){h[q]=u.d}if(u.w>l[p]){l[p]=u.w}}}if(z.equalrows){k.HD=true;var x=Math.max.apply(Math,y);var o=Math.max.apply(Math,h);for(q=0,n=y.length;q<n;q++){y[q]=x;h[q]=o}}k.H=y;k.D=h;k.W=l,k.J=w},CHTMLgetAttributes:function(v,j){var l=d(v.columnspacing),x=d(v.rowspacing),t=d(v.columnalign),r=d(v.rowalign),k=d(v.columnlines),w=d(v.rowlines),o=d(v.columnwidth),n=[],q,p,u=j.J,s=j.rows.length-1;for(q=0,p=l.length;q<p;q++){l[q]=this.CHTMLlength2em(l[q])}for(q=0,p=x.length;q<p;q++){x[q]=this.CHTMLlength2em(x[q])}while(l.length<u){l.push(l[l.length-1])}while(t.length<=u){t.push(t[t.length-1])}while(k.length<u){k.push(k[k.length-1])}while(o.length<=u){o.push(o[o.length-1])}while(x.length<s){x.push(x[x.length-1])}while(r.length<=s){r.push(r[r.length-1])}while(w.length<s){w.push(w[w.length-1])}t[c]=(v.side.substr(0,1)==="l"?"left":"right");for(q=0;q<=s;q++){var y=this.data[q];n[q]=[];if(y.rowalign){r[q]=y.rowalign}if(y.columnalign){n[q]=d(y.columnalign);while(n[q].length<=u){n[q].push(n[q][n[q].length-1])}}}var h=d(v.framespacing);if(h.length!=2){h=d(this.defaults.framespacing)}h[0]=Math.max(0,this.CHTMLlength2em(h[0]));h[1]=Math.max(0,this.CHTMLlength2em(h[1]));if(v.columnlines.replace(/none/g,"").replace(/ 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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 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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:"2.7.9",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:"2.7.9",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(n){var h=n.jax.length,i,j,o,k;var g=MathJax.ElementJax.mml;g.copyAttributes.id=1;while(n.i<h){i=n.jax[n.i];o=document.getElementById(i.inputID+"-Frame");if(i.outputJax!=="NativeMML"&&i.outputJax!=="PlainSource"&&o&&!o.getAttribute("data-mathml")){try{j=i.root.toMathML("").replace(/\n */g,"").replace(/<!--.*?-->/g,"")}catch(l){g.copyAttributes.id=true;if(!l.restart){throw l}return MathJax.Callback.After(["HandleMML",this,n],l.restart)}o.setAttribute("data-mathml",j);k=f.addElement(o,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(i.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{k.innerHTML=j}catch(l){}o.style.position="relative";o.setAttribute("role","presentation");o.firstChild.setAttribute("aria-hidden","true");k.setAttribute("role","presentation")}n.i++}g.copyAttributes.id=true;n.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_CHTML-full.js");