/*
 *  /MathJax/config/MML_CHTML-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/MathML/config.js",
  "[MathJax]/jax/output/CommonHTML/config.js",
  "[MathJax]/jax/output/PreviewHTML/config.js",
  "[MathJax]/extensions/mml2jax.js",
  "[MathJax]/extensions/MathEvents.js",
  "[MathJax]/extensions/MathZoom.js",
  "[MathJax]/extensions/MathMenu.js",
  "[MathJax]/jax/element/mml/jax.js",
  "[MathJax]/extensions/toMathML.js",
  "[MathJax]/jax/input/MathML/jax.js",
  "[MathJax]/jax/output/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.Hub.Config({
  extensions: ['[Contrib]/a11y/accessibility-menu.js']
});

MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.0",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js");
MathJax.OutputJax.CommonHTML=MathJax.OutputJax({id:"CommonHTML",version:"2.7.0",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:"2.7.0",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.mml2jax={version:"2.7.0",config:{preview:"mathml"},MMLnamespace:"http://www.w3.org/1998/Math/MathML",PreProcess:function(e){if(!this.configured){this.config=MathJax.Hub.CombineConfig("mml2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.InitBrowser();this.configured=true}if(typeof(e)==="string"){e=document.getElementById(e)}if(!e){e=document.body}var h=[];this.PushMathElements(h,e,"math");this.PushMathElements(h,e,"math",this.MMLnamespace);var d,b;if(typeof(document.namespaces)!=="undefined"){try{for(d=0,b=document.namespaces.length;d<b;d++){var f=document.namespaces[d];if(f.urn===this.MMLnamespace){this.PushMathElements(h,e,f.name+":math")}}}catch(g){}}else{var c=document.getElementsByTagName("html")[0];if(c){for(d=0,b=c.attributes.length;d<b;d++){var a=c.attributes[d];if(a.nodeName.substr(0,6)==="xmlns:"&&a.nodeValue===this.MMLnamespace){this.PushMathElements(h,e,a.nodeName.substr(6)+":math")}}}}this.ProcessMathArray(h)},PushMathElements:function(f,d,a,c){var h,g=MathJax.Hub.config.preRemoveClass;if(c){if(!d.getElementsByTagNameNS){return}h=d.getElementsByTagNameNS(c,a)}else{h=d.getElementsByTagName(a)}for(var e=0,b=h.length;e<b;e++){var j=h[e].parentNode;if(j&&j.className!==g&&!j.isMathJax&&!h[e].prefix===!c){f.push(h[e])}}},ProcessMathArray:function(c){var b,a=c.length;if(a){if(this.MathTagBug){for(b=0;b<a;b++){if(c[b].nodeName==="MATH"){this.ProcessMathFlattened(c[b])}else{this.ProcessMath(c[b])}}}else{for(b=0;b<a;b++){this.ProcessMath(c[b])}}}},ProcessMath:function(e){var d=e.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var a=document.createElement("script");a.type="math/mml";d.insertBefore(a,e);if(this.AttributeBug){var b=this.OuterHTML(e);if(this.CleanupHTML){b=b.replace(/<\?import .*?>/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/&nbsp;/g,"&#xA0;")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"</math>";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c="<!--"+e.nodeValue+"-->"}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b<a;b++){var d=e.attributes[b];if(d.specified&&d.nodeName.substr(0,10)!=="_moz-math-"){c+=" "+d.nodeName.toLowerCase().replace(/xmlns:xmlns/,"xmlns")+"=";var f=d.nodeValue;if(f==null&&d.nodeName==="style"&&e.style){f=e.style.cssText}c+='"'+this.quoteHTML(f)+'"'}}c+=">";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b<a;b++){c+=this.OuterHTML(e.childNodes[b])}c+="</"+e.nodeName.toLowerCase()+">"}}}return c},OuterHTML:function(d){if(d.nodeName.charAt(0)==="#"){return this.NodeHTML(d)}if(!this.AttributeBug){return d.outerHTML}var c=this.NodeHTML(d);for(var b=0,a=d.childNodes.length;b<a;b++){c+=this.OuterHTML(d.childNodes[b])}c+="</"+d.nodeName.toLowerCase()+">";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&#x26;").replace(/</g,"&lt;").replace(/>/g,"&gt;").replace(/\"/g,"&quot;")},createPreview:function(g,f){var e=this.config.preview;if(e==="none"){return}var i=false;var c=MathJax.Hub.config.preRemoveClass;if((f.previousSibling||{}).className===c){return}if(e==="mathml"){i=true;if(this.MathTagBug){e="alttext"}else{e=g.cloneNode(true)}}if(e==="alttext"||e==="altimg"){i=true;var d=this.filterPreview(g.getAttribute("alttext"));if(e==="alttext"){if(d!=null){e=MathJax.HTML.TextNode(d)}else{e=null}}else{var a=g.getAttribute("altimg");if(a!=null){var b={width:g.getAttribute("altimg-width"),height:g.getAttribute("altimg-height")};e=MathJax.HTML.Element("img",{src:a,alt:d,style:b})}else{e=null}}}if(e){var h;if(i){h=MathJax.HTML.Element("span",{className:c});h.appendChild(e)}else{h=MathJax.HTML.Element("span",{className:c},e)}f.parentNode.insertBefore(h,f)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"<math><mi>x</mi><mspace /></math>"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="&lt;"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax],5);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.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 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="2.7.0";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', 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 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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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w=window.innerHeight||z.clientHeight||z.scrollHeight||0;if(g.prototype.msieAboutBug){x.style.width="20em";x.style.position="absolute";x.style.left=Math.floor((document.documentElement.scrollWidth-x.offsetWidth)/2)+"px";x.style.top=(Math.floor((w-x.offsetHeight)/3)+document.body.scrollTop)+"px"}else{x.style.marginLeft=Math.floor(-x.offsetWidth/2)+"px";x.style.top=Math.floor((w-x.offsetHeight)/3)+"px"}};g.About.Remove=function(u){if(g.About.div){document.body.removeChild(g.About.div);delete g.About.div}};g.About.Keydown=function(u){if(u.keyCode===b.ESCAPE||(this.id==="MathJax_AboutClose"&&(u.keyCode===b.SPACE||u.keyCode===b.RETURN))){g.About.Remove(u);g.CurrentNode().focus();n(u)}},g.About.GetJax=function(v,A,y,x){var z=[];for(var B in A){if(A.hasOwnProperty(B)&&A[B]){if((x&&A[B].version)||(A[B].isa&&A[B].isa(A))){z.push(t(y[0],y[1],(A[B].id||B),A[B].version))}}}z.sort();for(var w=0,u=z.length;w<u;w++){v.push(z[w],["br"])}return v};g.About.GetFont=function(){var 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B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w<u;w++){v=r[z[w]];if(v){y=v.config.scale;break}}var x=prompt(t("ScaleMath","Scale all mathematics (compared to surrounding text) by"),y+"%");if(x){if(x.match(/^\s*\d+(\.\d*)?\s*%?\s*$/)){x=parseFloat(x);if(x){if(x!==y){for(w=0;w<u;w++){v=r[z[w]];if(v){v.config.scale=x}}g.cookie.scale=f.config.scale=x;g.saveCookie();f.Queue(["Rerender",f])}}else{alert(t("NonZeroScale","The scale should not be 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Switching to SVG output will cause the mathematics to not display properly."]}};g.AssistiveMML=function(w,u){var v=MathJax.Extension.AssistiveMML;if(!v){if(!u){q.Require("[MathJax]/extensions/AssistiveMML.js",["AssistiveMML",g,w,true])}return}MathJax.Hub.Queue([(s.settings.assistiveMML?"Add":"Remove")+"AssistiveMathML",v])};g.Font=function(){var u=r["HTML-CSS"];if(!u){return}document.location.reload()};g.Locale=function(){MathJax.Localization.setLocale(s.settings.locale);MathJax.Hub.Queue(["Reprocess",MathJax.Hub])};g.LoadLocale=function(){var u=prompt(t("LoadURL","Load translation data from this URL:"));if(u){if(!u.match(/\.js$/)){alert(t("BadURL","The URL should be for a javascript file that defines MathJax translation data.  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s=r.MathJax.preview;if(s&&s.parentNode){r.MathJax.tmpPreview=document.createElement("span");s.parentNode.replaceChild(r.MathJax.tmpPreview,s)}},restorePreview:function(r){var s=r.MathJax.tmpPreview;if(s){s.parentNode.replaceChild(r.MathJax.preview,s);delete r.MathJax.tmpPreview}},getMetrics:function(r){var s=r.CHTML;this.jax=r;this.em=s.em;this.outerEm=s.outerEm;this.scale=s.scale;this.cwidth=s.cwidth;this.linebreakWidth=s.lineWidth},postTranslate:function(w){var s=w.jax[this.id];for(var u=w.CHTMLlast,r=w.CHTMLeqn;u<r;u++){var t=s[u];if(t&&t.MathJax.elementJax){t.previousSibling.className=t.previousSibling.className.replace(/ [^ ]+$/,"");var v=t.MathJax.elementJax.CHTML;if(v.preview){v.preview.innerHTML="";v.preview.style.display="none";t.MathJax.preview=v.preview;delete v.preview}}}w.CHTMLlast=w.CHTMLeqn},getJaxFromMath:function(r){if(r.parentNode.className.match(/MJXc-display/)){r=r.parentNode}do{r=r.nextSibling}while(r&&r.nodeName.toLowerCase()!=="script");return c.getJaxFor(r)},getHoverSpan:function(r,s){return r.root.CHTMLnodeElement()},getHoverBBox:function(r,u,v){var w=r.root.CHTML,t=r.CHTML.outerEm;var s={w:w.w*t,h:w.h*t,d:w.d*t};if(w.width){s.width=w.width}return s},Zoom:function(t,A,z,r,x){this.getMetrics(t);var u=h.addElement(A,"mjx-chtml",{style:{"font-size":Math.floor(h.scale*100)+"%"},isMathJax:false});h.CHTMLnode=u;this.idPostfix="-zoom";t.root.toCommonHTML(u);this.idPostfix="";var s=u.style,B=t.root.CHTML;if(B.t>B.h){s.marginTop=h.Em(B.t-B.h)}if(B.b>B.d){s.marginBottom=h.Em(B.b-B.d)}if(B.l<0){s.paddingLeft=h.Em(-B.l)}if(B.r>B.w){s.marginRight=h.Em(B.r-B.w)}s.position="absolute";var y=u.offsetWidth,w=u.offsetHeight,C=z.firstChild.offsetHeight,v=z.firstChild.offsetWidth;u.style.position="";return{Y:-m.getBBox(A).h,mW:v,mH:C,zW:y,zH:w}},Remove:function(r){var s=document.getElementById(r.inputID+"-Frame");if(s&&r.CHTML.display){s=s.parentNode}if(s){s.parentNode.removeChild(s)}delete r.CHTML},ID:0,idPostfix:"",GetID:function(){this.ID++;return 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String.fromCharCode(r)}r-=65536;return String.fromCharCode((r>>10)+55296)+String.fromCharCode((r&1023)+56320)},getUnicode:function(r){var s=r.text.charCodeAt(r.i);r.i++;if(s>=55296&&s<56319){s=(((s-55296)<<10)+(r.text.charCodeAt(r.i)-56320))+65536;r.i++}return s},getCharList:function(v,u){var t,A,y=[],s=v.cache,D=u;if(s[u]){return s[u]}if(u>65535&&this.FONTDATA.RemapPlane1){var z=this.FONTDATA.RemapPlane1(u,v);u=z.n;v=z.variant}var r=this.FONTDATA.RANGES,C=this.FONTDATA.VARIANT;if(u>=r[0].low&&u<=r[r.length-1].high){for(t=0,A=r.length;t<A;t++){if(r[t].name==="alpha"&&v.noLowerCase){continue}var x=v["offset"+r[t].offset];if(x&&u>=r[t].low&&u<=r[t].high){if(r[t].remap&&r[t].remap[u]){u=x+r[t].remap[u]}else{u=u-r[t].low+x;if(r[t].add){u+=r[t].add}}if(v["variant"+r[t].offset]){v=C[v["variant"+r[t].offset]]}break}}}if(v.remap&&v.remap[u]){u=v.remap[u];if(v.remap.variant){v=C[v.remap.variant]}}else{if(this.FONTDATA.REMAP[u]&&!v.noRemap){u=this.FONTDATA.REMAP[u]}}if(g(u)){v=C[u[1]];u=u[0]}if(typeof(u)==="string"){var w={text:u,i:0,length:u.length};while(w.i<w.length){u=this.getUnicode(w);var B=this.getCharList(v,u);if(B){y.push.apply(y,B)}}}else{if(v.cache[u]){y=v.cache[u]}else{v.cache[u]=y=[this.lookupChar(v,u)]}}s[D]=y;return y},lookupChar:function(u,x){var w=u;while(u){for(var t=0,r=u.fonts.length;t<r;t++){var s=this.FONTDATA.FONTS[u.fonts[t]];if(typeof(s)==="string"){this.loadFont(s)}var v=s[x];if(v){if(v.length===5){v[5]={}}if(v.c==null){v[0]/=1000;v[1]/=1000;v[2]/=1000;v[3]/=1000;v[4]/=1000;v.c=this.unicodeChar(x)}if(v[5].space){return{type:"space",w:v[2],font:s}}return{type:"char",font:s,n:x}}else{if(s.Extra){this.findBlock(s,x)}}}u=this.FONTDATA.VARIANT[u.chain]}return this.unknownChar(w,x)},findBlock:function(t,x){var s=t.Extra,u=t.file,w;for(var v=0,r=s.length;v<r;v++){if(typeof(s[v])==="number"){if(x===s[v]){w=u;break}}else{if(x<s[v][0]){return}if(x<=s[v][1]){w=u;break}}}if(w){delete t.Extra;this.loadFont(u)}},unknownChar:function(r,u){c.signal.Post(["CommonHTML Jax - unknown char",u,r]);var t="";if(r.bold){t+="B"}if(r.italic){t+="I"}var s=this.FONTDATA.UNKNOWN[t||"R"];if(!s[u]){this.getUnknownChar(s,u)}return{type:"unknown",n:u,font:s}},getUnknownChar:function(s,u){var t=this.unicodeChar(u);var r=this.getHDW(t,s.className);s[u]=[0.8,0.2,r.w,0,r.w,{a:Math.max(0,(r.h-r.d)/2),h:r.h,d:r.d}];s[u].c=t},styledText:function(s,v){c.signal.Post(["CommonHTML Jax - styled 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z=document.body.appendChild(document.createElement("div"));z.appendChild(s);z.appendChild(r);D=s.offsetHeight,B=r.offsetHeight,v=s.offsetWidth;document.body.removeChild(z)}var y=(B-1000)/u,C=v/u,x=D/u-y;return{h:x,d:y,w:C}},addCharList:function(u,w,x){var v={text:"",className:null,a:0};for(var s=0,r=w.length;s<r;s++){var t=w[s];if(this.charList[t.type]){(this.charList[t.type])(t,u,x,v,r)}}if(v.text!==""){if(u.childNodes.length){this.charList.flushText(u,v)}else{f.addText(u,v.text);if(u.className){u.className+=" "+v.className}else{u.className=v.className}}}x.b=(v.flushed?0:x.a)},charList:{"char":function(u,t,x,v,r){var s=u.font;if(v.className&&s.className!==v.className){this.flushText(t,v)}if(!v.a){v.a=s.centerline/1000}if(v.a>(x.a||0)){x.a=v.a}var w=s[u.n];v.text+=w.c;v.className=s.className;if(x.h<w[0]+k){x.t=x.h=w[0]+k}if(x.d<w[1]+a){x.b=x.d=w[1]+a}if(x.l>x.w+w[3]){x.l=x.w+w[3]}if(x.r<x.w+w[4]){x.r=x.w+w[4]}x.w+=w[2]*(u.rscale||1);if(r==1&&s.skew&&s.skew[u.n]){x.skew=s.skew[u.n]}if(w[5].rfix){this.flushText(t,v).style.marginRight=h.Em(w[5].rfix/1000)}},space:function(s,r,u,t){if(s.w){if(t.text===""){t.className=s.font.className}this.flushText(r,t).style.marginRight=h.Em(s.w);u.w+=s.w}},unknown:function(s,r,v,t){(this["char"])(s,r,v,t,0);var u=s.font[s.n];if(u[5].a){t.a=u[5].a;if(v.a==null||t.a>v.a){v.a=t.a}}r=this.flushText(r,t,s.style);r.style.width=h.Em(u[2])},flushText:function(s,t,r){s=h.addElement(s,"mjx-charbox",{className:t.className,style:r},[t.text]);if(t.a){s.style.paddingBottom=h.Em(t.a)}t.text="";t.className=null;t.a=0;t.flushed=true;return s}},handleText:function(t,w,s,v){if(t.childNodes.length===0){h.addElement(t,"mjx-char");v=h.BBOX.empty(v)}if(typeof(s)==="string"){s=this.FONTDATA.VARIANT[s]}if(!s){s=this.FONTDATA.VARIANT[i.VARIANT.NORMAL]}var r={text:w,i:0,length:w.length},u=[];if(s.style&&r.length){u.push(this.styledText(s,w))}else{while(r.i<r.length){var x=this.getUnicode(r);u.push.apply(u,this.getCharList(s,x))}}if(u.length){this.addCharList(t.firstChild,u,v)}v.clean();if(v.d<0){v.D=v.d;v.d=0}if(v.h-v.a){t.firstChild.style[v.h-v.a<0?"marginTop":"paddingTop"]=this.EmRounded(v.h-v.a)}if(v.d>-v.b){t.firstChild.style.paddingBottom=this.EmRounded(v.d+v.b)}return v},createDelimiter:function(w,r,t,z,u){if(!r){var A=this.BBOX.zero();A.w=A.r=this.TEX.nulldelimiterspace;h.addElement(w,"mjx-box",{style:{width:A.w}});return A}if(!(t instanceof Array)){t=[t,t]}var y=t[1];t=t[0];var s={alias:r};while(s.alias){r=s.alias;s=this.FONTDATA.DELIMITERS[r];if(!s){s={HW:[0,this.FONTDATA.VARIANT[i.VARIANT.NORMAL]]}}}if(s.load){c.RestartAfter(j.Require(this.fontDir+"/TeX/fontdata-"+s.load+".js"))}for(var x=0,v=s.HW.length;x<v;x++){if(s.HW[x][0]>=t-0.01||(x==v-1&&!s.stretch)){if(s.HW[x][3]){r=s.HW[x][3]}A=this.createChar(w,[r,s.HW[x][1]],(s.HW[x][2]||1),u);A.offset=0.6*A.w;if(z){A.scale=z.scale;z.rscale=z.rscale}return A}}if(!s.stretch){return A}return this["extendDelimiter"+s.dir](w,y,s.stretch,z,u)},extendDelimiterV:function(D,w,O,v,B){D=h.addElement(D,"mjx-delim-v");var M=h.Element("span");var A,z,N,u,G,s,E,x,F=1,L;G=this.createChar(M,(O.top||O.ext),1,B);A=M.removeChild(M.firstChild);s=this.createChar(M,(O.bot||O.ext),1,B);z=M.removeChild(M.firstChild);E=x=h.BBOX.zero();var I=G.h+G.d+s.h+s.d-q;D.appendChild(A);if(O.mid){E=this.createChar(M,O.mid,1,B);N=M.removeChild(M.firstChild);I+=E.h+E.d;F=2}if(O.min&&w<I*O.min){w=I*O.min}if(w>I){x=this.createChar(M,O.ext,1,B);u=M.removeChild(M.firstChild);var K=x.h+x.d,t=K-q;var C=Math.min(Math.ceil((w-I)/(F*t)),this.maxStretchyParts);if(O.fullExtenders){w=C*F*t+I}else{t=(w-I)/(F*C)}L=x.d+x.a-K/2;u.style.margin=u.style.padding="";u.style.lineHeight=h.Em(t);u.style.marginBottom=h.Em(L-q/2/F);u.style.marginTop=h.Em(-L-q/2/F);var J=u.textContent,y="\n"+J;while(--C>0){J+=y}u.textContent=J;D.appendChild(u);if(O.mid){D.appendChild(N);D.appendChild(u.cloneNode(true))}}else{L=(w-I-q)/F;A.style.marginBottom=h.Em(L+parseFloat(A.style.marginBottom||"0"));if(O.mid){D.appendChild(N)}z.style.marginTop=h.Em(L+parseFloat(z.style.marginTop||"0"))}D.appendChild(z);var r=h.BBOX({w:Math.max(G.w,x.w,s.w,E.w),l:Math.min(G.l,x.l,s.l,E.l),r:Math.max(G.r,x.r,s.r,E.r),h:w-s.d,d:s.d,t:w-s.d,b:s.d});r.offset=0.5*r.w;if(v){r.scale=v.scale;r.rscale=v.rscale}return r},extendDelimiterH:function(E,r,O,u,C){E=h.addElement(E,"mjx-delim-h");var M=h.Element("span");var s,L,N,t,J,B,v,F,y,G=1;B=this.createChar(M,(O.left||O.rep),1,C);s=M.removeChild(M.firstChild);v=this.createChar(M,(O.right||O.rep),1,C);L=M.removeChild(M.firstChild);y=this.createChar(M,O.rep,1,C);t=M.removeChild(M.firstChild);s.style.marginLeft=h.Em(-B.l);L.style.marginRight=h.Em(v.r-v.w);E.appendChild(s);var P=h.BBOX.zero();P.h=Math.max(B.h,v.h,y.h);P.d=Math.max(B.D||B.d,v.D||v.d,y.D||y.d);var x=(B.r-B.l)+(v.r-v.l)-q;if(O.mid){F=this.createChar(M,O.mid,1,C);N=M.removeChild(M.firstChild);N.style.marginleft=h.Em(-F.l);N.style.marginRight=h.Em(F.r-F.w);x+=F.r-F.l+q;G=2;if(F.h>P.h){P.h=F.h}if(F.d>P.d){P.d=F.d}}if(O.min&&r<x*O.min){r=x*O.min}P.w=P.r=r;if(r>x){var A=y.r-y.l,I=A-q;var D=Math.min(Math.ceil((r-x)/(G*I)),this.maxStretchyParts);if(O.fullExtenders){r=D*G*I+x}else{I=(r-x)/(G*D)}var K=(A-I+q/G)/2;t.style.marginLeft=h.Em(-y.l-K);t.style.marginRight=h.Em(y.r-y.w+K);t.style.letterSpacing=h.Em(-(y.w-I));s.style.marginRight=h.Em(B.r-B.w);L.style.marginleft=h.Em(-v.l);var H=t.textContent,z=H;while(--D>0){H+=z}t.textContent=H;E.appendChild(t);if(O.mid){E.appendChild(N);J=E.appendChild(t.cloneNode(true))}}else{K=(r-x-q/G)/2;s.style.marginRight=h.Em(B.r-B.w+K);if(O.mid){E.appendChild(N)}L.style.marginLeft=h.Em(-v.l+K)}E.appendChild(L);this.adjustHeights([s,t,N,J,L],[B,y,F,y,v],P);if(u){P.scale=u.scale;P.rscale=u.rscale}return P},adjustHeights:function(s,v,w){var t=w.h,x=w.d;if(w.d<0){x=-w.d;w.D=w.d;w.d=0}for(var u=0,r=s.length;u<r;u++){if(s[u]){s[u].style.paddingTop=h.Em(t-v[u].a);s[u].style.paddingBottom=h.Em(x+v[u].a);s[u].style.marginTop=s[u].style.marginBottom=0}}},createChar:function(t,x,v,s){var A="",w={fonts:[x[1]],noRemap:true,cache:{}};if(s&&s===i.VARIANT.BOLD&&this.FONTDATA.FONTS[x[1]+"-Bold"]){w.fonts=[x[1]+"-Bold",x[1]]}if(typeof(x[1])!=="string"){w=x[1]}if(x[0] instanceof Array){for(var y=0,u=x[0].length;y<u;y++){A+=String.fromCharCode(x[0][y])}}else{A=String.fromCharCode(x[0])}if(x[4]){v*=x[4]}var z=this.handleText(t,A,w),r=t.firstChild.style;if(v!==1){r.fontSize=this.Percent(v)}if(x[2]){r.paddingLeft=this.Em(x[2]);z.w+=x[2];z.r+=x[2]}if(x[3]){r.verticalAlign=this.Em(x[3]);z.h+=x[3];if(z.h<0){z.h=0}}if(x[5]){r.marginTop=this.Em(x[5]);z.h+=x[5];z.t+=x[5]}if(x[6]){r.marginBottom=this.Em(x[6]);z.d+=x[6];z.b+=x[6]}return z},length2em:function(v,t,w){if(typeof(v)!=="string"){v=v.toString()}if(v===""){return""}if(v===i.SIZE.NORMAL){return 1}if(v===i.SIZE.BIG){return 2}if(v===i.SIZE.SMALL){return 0.71}if(this.MATHSPACE[v]){return this.MATHSPACE[v]}var s=v.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/);var 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r.toFixed(1).replace(/\.0$/,"")+"px"},Percent:function(r){return(100*r).toFixed(1).replace(/\.?0+$/,"")+"%"},Transform:function(u,s,r){var t=u.style;t.transform=t.WebkitTransform=t.MozTransform=t["-ms-transform"]=s;if(r){t.transformOrigin=t.WebkitTransformOrigin=t.MozTransformOrigin=t["-ms-transform-origin"]=r}},arrayEntry:function(r,s){return r[Math.max(0,Math.min(s,r.length-1))]},removeStyles:["fontSize","fontFamily","fontWeight","fontStyle","fontVariant","font"]});h.BBOX=MathJax.Object.Subclass({Init:function(r){for(var s in r){if(r.hasOwnProperty(s)){this[s]=r[s]}}},clean:function(){if(this.h===-n){this.h=0}if(this.d===-n){this.d=0}if(this.l===n){this.l=0}if(this.r===-n){this.r=0}if(this.t===-n){this.t=0}if(this.b===-n){this.b=0}if(this.D&&this.d>0){delete this.D}},rescale:function(r){this.w*=r;this.h*=r;this.d*=r;this.l*=r;this.r*=r;this.t*=r;this.b*=r;if(this.L){this.L*=r}if(this.R){this.R*=r}if(this.D){this.D*=r}},combine:function(s,r,t){s.X=r;s.Y=t;scale=s.rscale;if(r+scale*s.r>this.r){this.r=r+scale*s.r}if(r+scale*s.l<this.l){this.l=r+scale*s.l}if(r+scale*(s.w+(s.L||0)+(s.R||0))>this.w){this.w=r+scale*(s.w+(s.L||0)+(s.R||0))}if(t+scale*s.h>this.h){this.h=t+scale*s.h}if(s.D&&(this.D==null||scale*s.D-t>this.D)&&scale*s.D>this.d){this.D=scale*s.D-t}else{if(s.D==null&&this.D){delete this.D}}if(scale*s.d-t>this.d){this.d=scale*s.d-t}if(t+scale*s.t>this.t){this.t=t+scale*s.t}if(scale*s.b-t>this.b){this.b=scale*s.b-t}},append:function(s){scale=s.rscale;var r=this.w;if(r+scale*s.r>this.r){this.r=r+scale*s.r}if(r+scale*s.l<this.l){this.l=r+scale*s.l}this.w+=scale*(s.w+(s.L||0)+(s.R||0));if(scale*s.h>this.h){this.h=scale*s.h}if(s.D&&(this.D==null||scale*s.D>this.D)&&scale*s.D>this.d){this.D=scale*s.D}else{if(s.D==null&&this.D){delete this.D}}if(scale*s.d>this.d){this.d=scale*s.d}if(scale*s.t>this.t){this.t=scale*s.t}if(scale*s.b>this.b){this.b=scale*s.b}},updateFrom:function(r){this.h=r.h;this.d=r.d;this.w=r.w;this.r=r.r;this.l=r.l;this.t=r.t;this.b=r.b;if(r.pwidth){this.pwidth=r.pwidth}if(r.D){this.D=r.D}else{delete this.D}},adjust:function(s,r,u,t){this[r]+=h.length2em(s,1,this.scale);if(t==null){if(this[r]>this[u]){this[u]=this[r]}}else{if(this[u]<t){this[u]=t}}}},{zero:function(){return h.BBOX({h:0,d:0,w:0,l:0,r:0,t:0,b:0,scale:1,rscale:1})},empty:function(r){if(!r){r=h.BBOX.zero()}r.h=r.d=r.r=r.t=r.b=-n;r.w=0;r.l=n;delete r.pwidth;return r},styleAdjust:[["borderTopWidth","h","t"],["borderRightWidth","w","r"],["borderBottomWidth","d","b"],["borderLeftWidth","w","l",0],["paddingTop","h","t"],["paddingRight","w","r"],["paddingBottom","d","b"],["paddingLeft","w","l",0],]});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){i=MathJax.ElementJax.mml;i.mbase.Augment({toCommonHTML:function(s,r){return this.CHTMLdefaultNode(s,r)},CHTMLmultiline:function(){i.mbase.CHTMLautoloadFile("multiline")},CHTMLdefaultNode:function(u,s){if(!s){s={}}u=this.CHTMLcreateNode(u);this.CHTML=h.BBOX.empty();this.CHTMLhandleStyle(u);if(this.isToken){this.CHTMLgetVariant()}this.CHTMLhandleScale(u);var r=Math.max((s.minChildren||0),this.data.length);for(var t=0;t<r;t++){this.CHTMLaddChild(u,t,s)}if(!s.noBBox){this.CHTML.clean()}this.CHTMLhandleSpace(u);this.CHTMLhandleBBox(u);this.CHTMLhandleColor(u);return u},CHTMLaddChild:function(w,s,r){var y=this.data[s],v;var t=r.childNodes;if(t instanceof Array){t=t[s]||"span"}if(y){if(t){w=h.addElement(w,t)}v=y.toCommonHTML(w,r.childOptions);if(t&&y.CHTML.rscale!==1){w.style.fontSize=w.firstChild.style.fontSize;w.firstChild.style.fontSize=""}if(!r.noBBox){var x=this.CHTML,u=y.CHTML;x.append(u);if(u.ic){x.ic=u.ic}else{delete x.ic}if(u.skew){x.skew=u.skew}if(u.pwidth){x.pwidth=u.pwidth}}}else{if(r.forceChild){v=h.addElement(w,(t||"mjx-box"))}}return v},CHTMLchildNode:function(s,r){s=s.childNodes[r];if(s.nodeName.toLowerCase()==="a"){s=s.firstChild}return s},CHTMLcoreNode:function(r){if(this.inferRow&&this.data[0]){return this.data[0].CHTMLcoreNode(r.firstChild)}return this.CHTMLchildNode(r,this.CoreIndex())},CHTMLstretchChildV:function(u,t,x){var v=this.data[u];if(v){var y=this.CHTML,s=v.CHTML;if(s.stretch||(s.stretch==null&&v.CHTMLcanStretch("Vertical",t,x))){var r=s.w;s=v.CHTMLstretchV(t,x);y.w+=s.w-r;if(y.w>y.r){y.r=y.w}if(s.h>y.h){y.h=s.h}if(s.d>y.d){y.d=s.d}if(s.t>y.t){y.t=s.t}if(s.b>y.b){y.b=s.b}}}},CHTMLstretchChildH:function(u,r,v){var x=this.data[u];if(x){var y=this.CHTML,t=x.CHTML;if(t.stretch||(t.stretch==null&&x.CHTMLcanStretch("Horizontal",r))){var s=t.w;t=x.CHTMLstretchH(this.CHTMLchildNode(v,u),r);y.w+=t.w-s;if(y.w>y.r){y.r=y.w}if(t.h>y.h){y.h=t.h}if(t.d>y.d){y.d=t.d}if(t.t>y.t){y.t=t.t}if(t.b>y.b){y.b=t.b}}}},CHTMLcanStretch:function(v,t,u){var s=false;if(this.isEmbellished()){var r=this.Core();if(r&&r!==this){s=r.CHTMLcanStretch(v,t,u)}}this.CHTML.stretch=s;return s},CHTMLstretchV:function(r,s){this.CHTML.updateFrom(this.Core().CHTMLstretchV(r,s));return this.CHTML},CHTMLstretchH:function(s,r){this.CHTML.updateFrom(this.CHTMLstretchCoreH(s,r));return this.CHTML},CHTMLstretchCoreH:function(s,r){return this.Core().CHTMLstretchH(this.CHTMLcoreNode(s),r)},CHTMLcreateNode:function(r){if(!this.CHTML){this.CHTML={}}this.CHTML=h.BBOX.zero();if(this.href){r=h.addElement(r,"a",{href:this.href,isMathJax:true})}if(!this.CHTMLnodeID){this.CHTMLnodeID=h.GetID()}var s=(this.id||"MJXc-Node-"+this.CHTMLnodeID)+h.idPostfix;return this.CHTMLhandleAttributes(h.addElement(r,"mjx-"+this.type,{id:s}))},CHTMLnodeElement:function(){if(!this.CHTMLnodeID){return null}return document.getElementById((this.id||"MJXc-Node-"+this.CHTMLnodeID)+h.idPostfix)},CHTMLlength2em:function(s,r){return h.length2em(s,r,this.CHTML.scale)},CHTMLhandleAttributes:function(u){if(this["class"]){if(u.className){u.className+=" "+this["class"]}else{u.className=this["class"]}}if(this.attrNames){var y=this.attrNames,t=i.nocopyAttributes,x=c.config.ignoreMMLattributes;var v=(this.type==="mstyle"?i.math.prototype.defaults:this.defaults);for(var s=0,r=y.length;s<r;s++){var w=y[s];if(x[w]==false||(!t[w]&&!x[w]&&v[w]==null&&typeof(u[w])==="undefined")){u.setAttribute(w,this.attr[w])}}}return u},CHTMLhandleScale:function(u){var w=1,t=this.parent,v=(t?t.CHTML.scale:1);var r=this.getValues("scriptlevel","fontsize");r.mathsize=this.Get("mathsize",null,!this.isToken);if(r.scriptlevel!==0){if(r.scriptlevel>2){r.scriptlevel=2}w=Math.pow(this.Get("scriptsizemultiplier"),r.scriptlevel);r.scriptminsize=h.length2em(this.Get("scriptminsize"),0.8,1);if(w<r.scriptminsize){w=r.scriptminsize}}if(this.removedStyles&&this.removedStyles.fontSize&&!r.fontsize){r.fontsize=this.removedStyles.fontSize}if(r.fontsize&&!this.mathsize){r.mathsize=r.fontsize}if(r.mathsize!==1){w*=h.length2em(r.mathsize,1,1)}var s=this.CHTMLvariant;if(s&&s.style&&s.style["font-family"]){w*=(h.config.scale/100)/h.scale}this.CHTML.scale=w;v=this.CHTML.rscale=w/v;if(Math.abs(v-1)<0.001){v=1}if(u&&v!==1){u.style.fontSize=h.Percent(v)}return w},CHTMLhandleStyle:function(u){if(!this.style){return}var t=u.style;t.cssText=this.style;this.removedStyles={};for(var s=0,r=h.removeStyles.length;s<r;s++){var v=h.removeStyles[s];if(t[v]){this.removedStyles[v]=t[v];t[v]=""}}},CHTMLhandleBBox:function(v){var s=this.CHTML,u=v.style;if(this.data.length===1&&(this.data[0].CHTML||{}).pwidth){s.pwidth=this.data[0].CHTML.pwidth;s.mwidth=this.data[0].CHTML.mwidth;u.width="100%"}else{if(s.pwidth){s.mwidth=h.Em(s.w);u.width="100%"}else{if(s.w<0){u.width="0px";u.marginRight=h.Em(s.w)}}}if(!this.style){return}for(var t=0,r=h.BBOX.styleAdjust.length;t<r;t++){var w=h.BBOX.styleAdjust[t];if(w&&u[w[0]]){s.adjust(u[w[0]],w[1],w[2],w[3])}}},CHTMLhandleColor:function(r){if(this.mathcolor){r.style.color=this.mathcolor}else{if(this.color){r.style.color=this.color}}if(this.mathbackground){r.style.backgroundColor=this.mathbackground}else{if(this.background){r.style.backgroundColor=this.background}}},CHTMLhandleSpace:function(r){if(!this.useMMLspacing){var s=this.texSpacing();if(s!==""){this.CHTML.L=this.CHTMLlength2em(s);r.className+=" "+h.SPACECLASS[s]}}},CHTMLhandleText:function(s,t,r){if(s.firstChild&&!this.CHTML){this.CHTML=h.BBOX.empty()}this.CHTML=h.handleText(s,t,r,this.CHTML)},CHTMLgetVariant:function(){var r=this.getValues("mathvariant","fontfamily","fontweight","fontstyle"),t;r.hasVariant=this.Get("mathvariant",true);if(this.removedStyles){t=this.removedStyles;if(t.fontFamily){r.family=t.fontFamily}if(t.fontWeight){r.weight=t.fontWeight}if(t.fontStyle){r.style=t.fontStyle}}if(!r.hasVariant){if(r.fontfamily){r.family=r.fontfamily}if(r.fontweight){r.weight=r.fontweight}if(r.fontstyle){r.style=r.fontstyle}}if(r.weight&&r.weight.match(/^\d+$/)){r.weight=(parseInt(r.weight)>600?"bold":"normal")}var s=r.mathvariant;if(this.variantForm){s="-TeX-variant"}if(r.family&&!r.hasVariant){if(!r.weight&&r.mathvariant.match(/bold/)){r.weight="bold"}if(!r.style&&r.mathvariant.match(/italic/)){r.style="italic"}this.CHTMLvariant={fonts:[],noRemap:true,cache:{},style:{"font-family":r.family,"font-weight":r.weight||"normal","font-style":r.style||"normal"}};return}if(r.weight==="bold"){s={normal:i.VARIANT.BOLD,italic:i.VARIANT.BOLDITALIC,fraktur:i.VARIANT.BOLDFRAKTUR,script:i.VARIANT.BOLDSCRIPT,"sans-serif":i.VARIANT.BOLDSANSSERIF,"sans-serif-italic":i.VARIANT.SANSSERIFBOLDITALIC}[s]||s}else{if(r.weight==="normal"){s={bold:i.VARIANT.normal,"bold-italic":i.VARIANT.ITALIC,"bold-fraktur":i.VARIANT.FRAKTUR,"bold-script":i.VARIANT.SCRIPT,"bold-sans-serif":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.SANSSERIFITALIC}[s]||s}}if(r.style==="italic"){s={normal:i.VARIANT.ITALIC,bold:i.VARIANT.BOLDITALIC,"sans-serif":i.VARIANT.SANSSERIFITALIC,"bold-sans-serif":i.VARIANT.SANSSERIFBOLDITALIC}[s]||s}else{if(r.style==="normal"){s={italic:i.VARIANT.NORMAL,"bold-italic":i.VARIANT.BOLD,"sans-serif-italic":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.BOLDSANSSERIF}[s]||s}}this.CHTMLvariant=h.FONTDATA.VARIANT[s]||h.FONTDATA.VARIANT[i.VARIANT.NORMAL]},CHTMLbboxFor:function(r){if(this.data[r]&&this.data[r].CHTML){return this.data[r].CHTML}return h.BBOX.zero()},CHTMLdrawBBox:function(s,t){if(!t){t=this.CHTML}var r=h.Element("mjx-box",{style:{opacity:0.25,"margin-left":h.Em(-(t.w+(t.R||0)))}},[["mjx-box",{style:{height:h.Em(t.h),width:h.Em(t.w),"background-color":"red"}}],["mjx-box",{style:{height:h.Em(t.d),width:h.Em(t.w),"margin-left":h.Em(-t.w),"vertical-align":h.Em(-t.d),"background-color":"green"}}]]);if(s.nextSibling){s.parentNode.insertBefore(r,s.nextSibling)}else{s.parentNode.appendChild(r)}},CHTMLnotEmpty:function(r){while(r&&r.data.length<2&&(r.type==="mrow"||r.type==="texatom")){r=r.data[0]}return !!r}},{CHTMLautoload:function(){var r=h.autoloadDir+"/"+this.type+".js";c.RestartAfter(j.Require(r))},CHTMLautoloadFile:function(r){var s=h.autoloadDir+"/"+r+".js";c.RestartAfter(j.Require(s))},CHTMLstretchV:function(r,s){this.Core().CHTMLstretchV(r,s);this.toCommonHTML(this.CHTMLnodeElement(),{stretch:true});return this.CHTML},CHTMLstretchH:function(s,r){this.CHTMLstretchCoreH(s,r);this.toCommonHTML(s,{stretch:true});return this.CHTML}});i.chars.Augment({toCommonHTML:function(s,r){if(r==null){r={}}var t=this.toString();if(r.remap){t=r.remap(t,r.remapchars)}this.CHTMLhandleText(s,t,r.variant||this.parent.CHTMLvariant)}});i.entity.Augment({toCommonHTML:function(s,r){if(r==null){r={}}var t=this.toString();if(r.remapchars){t=r.remap(t,r.remapchars)}this.CHTMLhandleText(s,t,r.variant||this.parent.CHTMLvariant)}});i.math.Augment({toCommonHTML:function(w){w=this.CHTMLdefaultNode(w);if(this.CHTML.w<0){w.parentNode.style.width="0px";w.parentNode.style.marginRight=h.Em(this.CHTML.w)}var u=this.Get("alttext");if(u&&!w.getAttribute("aria-label")){w.setAttribute("aria-label",u)}if(this.CHTML.pwidth){w.parentNode.style.minWidth=this.CHTML.mwidth||h.Em(this.CHTML.w);w.parentNode.className="mjx-full-width "+w.parentNode.className;w.style.width=this.CHTML.pwidth}else{if(!this.isMultiline&&this.Get("display")==="block"){var t=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(t.indentalignfirst!==i.INDENTALIGN.INDENTALIGN){t.indentalign=t.indentalignfirst}if(t.indentalign===i.INDENTALIGN.AUTO){t.indentalign=o.displayAlign}if(t.indentshiftfirst!==i.INDENTSHIFT.INDENTSHIFT){t.indentshift=t.indentshiftfirst}if(t.indentshift==="auto"){t.indentshift="0"}var s=this.CHTMLlength2em(t.indentshift,h.cwidth);if(o.displayIndent!=="0"){var r=this.CHTMLlength2em(o.displayIndent,h.cwidth);s+=(t.indentalign===i.INDENTALIGN.RIGHT?-r:r)}var v=w.parentNode.parentNode.style;w.parentNode.style.textAlign=v.textAlign=t.indentalign;if(s){s*=h.em/h.outerEm;c.Insert(v,({left:{marginLeft:h.Em(s)},right:{marginRight:h.Em(-s)},center:{marginLeft:h.Em(s),marginRight:h.Em(-s)}})[t.indentalign])}}}return w}});i.mi.Augment({toCommonHTML:function(r){r=this.CHTMLdefaultNode(r);var t=this.CHTML,s=this.data.join("");if(t.skew!=null&&s.length!==1){delete t.skew}if(t.r>t.w&&s.length===1&&!this.CHTMLvariant.noIC){t.ic=t.r-t.w;t.w=t.r;r.lastChild.style.paddingRight=h.Em(t.ic)}return r}});i.mn.Augment({CHTMLremapMinus:function(r){return r.replace(/^-/,"\u2212")},toCommonHTML:function(r){r=this.CHTMLdefaultNode(r,{childOptions:{remap:this.CHTMLremapMinus}});var t=this.CHTML,s=this.data.join("");if(t.skew!=null&&s.length!==1){delete t.skew}if(t.r>t.w&&s.length===1&&!this.CHTMLvariant.noIC){t.ic=t.r-t.w;t.w=t.r;r.lastChild.style.paddingRight=h.Em(t.ic)}return r}});i.mo.Augment({toCommonHTML:function(u){u=this.CHTMLcreateNode(u);this.CHTMLhandleStyle(u);this.CHTMLgetVariant();this.CHTMLhandleScale(u);h.BBOX.empty(this.CHTML);var s=this.getValues("displaystyle","largeop");s.variant=this.CHTMLvariant;s.text=this.data.join("");if(s.text==""){if(this.fence){u.style.width=h.Em(h.TEX.nulldelimiterspace)}}else{this.CHTMLadjustAccent(s);this.CHTMLadjustVariant(s);for(var t=0,r=this.data.length;t<r;t++){this.CHTMLaddChild(u,t,{childOptions:{variant:s.mathvariant,remap:this.remap,remapchars:s.remapchars}})}if(s.text.length!==1){delete this.CHTML.skew}else{if(this.CHTML.w===0&&this.CHTML.l<0){this.CHTMLfixCombiningChar(u)}}if(s.largeop){this.CHTMLcenterOp(u)}}this.CHTML.clean();this.CHTMLhandleBBox(u);this.CHTMLhandleSpace(u);this.CHTMLhandleColor(u);return u},CHTMLhandleSpace:function(u){if(this.useMMLspacing){var s=this.getValues("scriptlevel","lspace","rspace");s.lspace=Math.max(0,this.CHTMLlength2em(s.lspace));s.rspace=Math.max(0,this.CHTMLlength2em(s.rspace));if(s.scriptlevel>0){if(!this.hasValue("lspace")){s.lspace=0.15}if(!this.hasValue("rspace")){s.rspace=0.15}}var r=this,t=this.Parent();while(t&&t.isEmbellished()&&t.Core()===r){r=t;t=t.Parent();u=r.CHTMLnodeElement()}if(s.lspace){u.style.paddingLeft=h.Em(s.lspace)}if(s.rspace){u.style.paddingRight=h.Em(s.rspace)}this.CHTML.L=s.lspace;this.CHTML.R=s.rspace}else{this.SUPER(arguments).CHTMLhandleSpace.apply(this,arguments)}},CHTMLadjustAccent:function(t){var s=this.CoreParent();t.parent=s;if(t.text.length===1&&s&&s.isa(i.munderover)&&this.CoreText(s.data[s.base]).length===1){var u=s.data[s.over],r=s.data[s.under];if(u&&this===u.CoreMO()&&s.Get("accent")){t.remapchars=h.FONTDATA.REMAPACCENT}else{if(r&&this===r.CoreMO()&&s.Get("accentunder")){t.remapchars=h.FONTDATA.REMAPACCENTUNDER}}}},CHTMLadjustVariant:function(s){var r=s.parent,t=(r&&r.isa(i.msubsup)&&this!==r.data[r.base]);if(s.largeop){s.mathvariant=(s.displaystyle?"-largeOp":"-smallOp")}if(t){s.remapchars=this.remapChars;if(s.text.match(/['`"\u00B4\u2032-\u2037\u2057]/)){s.mathvariant="-TeX-variant"}}},CHTMLfixCombiningChar:function(r){r=r.firstChild;var s=h.Element("mjx-box",{style:{width:".25em","margin-left":"-.25em"}});r.insertBefore(s,r.firstChild)},CHTMLcenterOp:function(r){var t=this.CHTML;var s=(t.h-t.d)/2-h.TEX.axis_height;if(Math.abs(s)>0.001){r.style.verticalAlign=h.Em(-s)}t.h-=s;t.d+=s;if(t.r>t.w){t.ic=t.r-t.w;t.w=t.r;r.style.paddingRight=h.Em(t.ic)}},CHTMLcanStretch:function(v,t,u){if(!this.Get("stretchy")){return false}var w=this.data.join("");if(w.length!==1){return false}var s={text:w};this.CHTMLadjustAccent(s);if(s.remapchars){w=s.remapchars[w]||w}w=h.FONTDATA.DELIMITERS[w.charCodeAt(0)];var r=(w&&w.dir===v.substr(0,1));if(r){r=(this.CHTML.h!==t||this.CHTML.d!==u||!!this.Get("minsize",true)||!!this.Get("maxsize",true));if(r){this.CHTML.stretch=true}}return r},CHTMLstretchV:function(u,x){var v=this.CHTMLnodeElement(),w=this.CHTML;var s=this.getValues("symmetric","maxsize","minsize");var t,r=h.TEX.axis_height;if(s.symmetric){t=2*Math.max(u-r,x+r)}else{t=u+x}s.maxsize=this.CHTMLlength2em(s.maxsize,w.h+w.d);s.minsize=this.CHTMLlength2em(s.minsize,w.h+w.d);t=Math.max(s.minsize,Math.min(s.maxsize,t));if(t!==w.sH){if(t!=s.minsize){t=[Math.max(t*h.TEX.delimiterfactor/1000,t-h.TEX.delimitershortfall),t]}while(v.firstChild){v.removeChild(v.firstChild)}this.CHTML=w=h.createDelimiter(v,this.data.join("").charCodeAt(0),t,w);w.sH=(t instanceof Array?t[1]:t);if(s.symmetric){t=(w.h+w.d)/2+r}else{t=(w.h+w.d)*u/(u+x)}t-=w.h;if(Math.abs(t)>0.05){v.style.verticalAlign=h.Em(t);w.h+=t;w.d-=t;w.t+=t;w.b-=t}}return this.CHTML},CHTMLstretchH:function(t,r){var u=this.CHTML;var s=this.getValues("maxsize","minsize","mathvariant","fontweight");if((s.fontweight==="bold"||(this.removedStyles||{}).fontWeight==="bold"||parseInt(s.fontweight)>=600)&&!this.Get("mathvariant",true)){s.mathvariant=i.VARIANT.BOLD}s.maxsize=this.CHTMLlength2em(s.maxsize,u.w);s.minsize=this.CHTMLlength2em(s.minsize,u.w);r=Math.max(s.minsize,Math.min(s.maxsize,r));if(r!==u.sW){while(t.firstChild){t.removeChild(t.firstChild)}this.CHTML=u=h.createDelimiter(t,this.data.join("").charCodeAt(0),r,u,s.mathvariant);u.sW=r}return this.CHTML}});i.mtext.Augment({CHTMLgetVariant:function(){if(h.config.mtextFontInherit||this.Parent().type==="merror"){var t=(h.config.scale/100)/h.scale;var s={cache:{},fonts:[],className:"MJXc-font-inherit",rscale:t,style:{"font-size":h.Percent(t)}};var r=this.Get("mathvariant");if(r.match(/bold/)){s.style["font-weight"]="bold"}if(r.match(/italic|-tex-mathit/)){s.style["font-style"]="italic"}if(r==="monospace"){s.className+=" MJXc-monospace-font"}if(r==="double-struck"){s.className+=" MJXc-double-struck-font"}if(r.match(/fraktur/)){s.className+=" MJXc-fraktur-font"}if(r.match(/sans-serif/)){s.className+=" MJXc-sans-serif-font"}if(r.match(/script/)){s.className+=" MJXc-script-font"}this.CHTMLvariant=s}else{this.SUPER(arguments).CHTMLgetVariant.call(this)}}});i.merror.Augment({toCommonHTML:function(r){r=this.CHTMLdefaultNode(r);var s=this.CHTML;s.rescale(0.9);s.h+=3/h.em;if(s.h>s.t){s.t=s.h}s.d+=3/h.em;if(s.d>s.b){s.b=s.d}s.w+=8/h.em;s.r=s.w;s.l=0;return r}});i.mspace.Augment({toCommonHTML:function(u){u=this.CHTMLcreateNode(u);this.CHTMLhandleStyle(u);this.CHTMLhandleScale(u);var s=this.getValues("height","depth","width");var r=this.CHTMLlength2em(s.width),t=this.CHTMLlength2em(s.height),x=this.CHTMLlength2em(s.depth);var v=this.CHTML;v.w=v.r=r;v.h=v.t=t;v.d=v.b=x;v.l=0;if(r<0){u.style.marginRight=h.Em(r);r=0}u.style.width=h.Em(r);u.style.height=h.Em(Math.max(0,t+x));if(x){u.style.verticalAlign=h.Em(-x)}this.CHTMLhandleBBox(u);this.CHTMLhandleColor(u);return u}});i.mpadded.Augment({toCommonHTML:function(s,E){var r;if(E&&E.stretch){s=s.firstChild;r=s.firstChild}else{s=this.CHTMLdefaultNode(s,{childNodes:"mjx-box",forceChild:true});r=s.firstChild;s=h.addElement(s,"mjx-block");s.appendChild(r);h.addElement(s,"mjx-strut")}var v=this.CHTMLbboxFor(0);var C=this.getValues("width","height","depth","lspace","voffset");var A=0,z=0,B=v.w,t=v.h,u=v.d;r.style.width=0;r.style.margin=h.Em(-t)+" 0 "+h.Em(-u);if(C.width!==""){B=this.CHTMLdimen(C.width,"w",B,0)}if(C.height!==""){t=this.CHTMLdimen(C.height,"h",t,0)}if(C.depth!==""){u=this.CHTMLdimen(C.depth,"d",u,0)}if(C.voffset!==""){z=this.CHTMLdimen(C.voffset);if(z){r.style.position="relative";r.style.top=h.Em(-z)}}if(C.lspace!==""){A=this.CHTMLdimen(C.lspace);if(A){r.style.position="relative";r.style.left=h.Em(A)}}s.style.width=0;s.style.marginTop=h.Em(t-e);s.style.padding="0 "+h.Em(B)+" "+h.Em(u)+" 0";var D=h.BBOX({w:B,h:t,d:u,l:0,r:B,t:t,b:u,scale:this.CHTML.scale,rscale:this.CHTML.rscale});D.combine(v,A,z);D.w=B;D.h=t;D.d=u;this.CHTML=D;return s.parentNode},CHTMLstretchV:i.mbase.CHTMLstretchV,CHTMLstretchH:i.mbase.CHTMLstretchH,CHTMLdimen:function(v,x,w,r){if(r==null){r=-n}v=String(v);var s=v.match(/width|height|depth/);var t=(s?this.CHTML[s[0].charAt(0)]:(x?this.CHTML[x]:0));var u=(this.CHTMLlength2em(v,t)||0);if(v.match(/^[-+]/)&&w!=null){u+=w}if(r!=null){u=Math.max(r,u)}return u}});i.munderover.Augment({toCommonHTML:function(v,F){var D=this.getValues("displaystyle","accent","accentunder","align");var t=this.data[this.base];if(!D.displaystyle&&t!=null&&(t.movablelimits||t.CoreMO().Get("movablelimits"))){return i.msubsup.prototype.toCommonHTML.call(this,v,s)}var A,y,r=[],s=false;if(F&&F.stretch){if(this.data[this.base]){t=h.getNode(v,"mjx-op")}if(this.data[this.under]){A=h.getNode(v,"mjx-under")}if(this.data[this.over]){y=h.getNode(v,"mjx-over")}r[0]=t;r[1]=A||y;r[2]=y;s=true}else{var x=["mjx-op","mjx-under","mjx-over"];if(this.over===1){x[1]=x[2]}v=this.CHTMLdefaultNode(v,{childNodes:x,noBBox:true,forceChild:true,minChildren:2});r[0]=t=v.removeChild(v.firstChild);r[1]=A=y=v.removeChild(v.firstChild);if(v.firstChild){r[2]=y=v.removeChild(v.firstChild)}}var w=[],u=this.CHTMLgetBBoxes(w,r,D);var E=w[this.base],B=this.CHTML;B.w=u;B.h=E.h;B.d=E.d;var z=t,C=0;if(E.ic){C=1.3*E.ic+0.05}if(this.data[this.over]){z=this.CHTMLaddOverscript(y,w,D,C,t,s)}if(this.data[this.under]){this.CHTMLaddUnderscript(A,w,D,C,v,z,s)}else{if(!s){v.appendChild(z)}}this.CHTMLplaceBoxes(t,A,y,D,w);return v},CHTMLgetBBoxes:function(z,v,u){var x,s=this.data.length,y,t=-n,r=t;for(x=0;x<s;x++){z[x]=this.CHTMLbboxFor(x);z[x].x=z[x].y=0;if(this.data[x]){z[x].stretch=this.data[x].CHTMLcanStretch("Horizontal")}y=(x===this.base?1:z[x].rscale);if(x!==this.base){delete z[x].L;delete z[x].R}r=Math.max(r,y*(z[x].w+(z[x].L||0)+(z[x].R||0)));if(!z[x].stretch&&r>t){t=r}}if(t===-n){t=r}for(x=0;x<s;x++){if(z[x].stretch){y=(x===this.base?1:z[x].rscale);z[x]=this.data[x].CHTMLstretchH(v[x].firstChild,t/y);z[x].x=z[x].y=0;r=Math.max(r,y*(z[x].w+(z[x].L||0)+(z[x].R||0)))}}if(!z[this.base]){z[this.base]=h.BBOX.empty()}return r},CHTMLaddOverscript:function(A,y,E,D,s,r){var C=this.CHTML;var x,w,v=h.TEX.big_op_spacing5,u;var z=y[this.over],F=y[this.base],t=z.rscale;if(!r){var B=h.Element("mjx-stack");B.appendChild(A);B.appendChild(s)}if(z.D){z.d=z.D}if(z.d<0){A.firstChild.style.verticalAlign="top";A.style.height=h.Em(z.h+z.d)}z.x=0;if(E.accent){if(z.w<0.001){z.x+=(z.r-z.l)/2}u=h.TEX.rule_thickness;v=0;if(F.skew){z.x+=t*F.skew;C.skew=t*F.skew;if(z.x+t*z.w>C.w){C.skew+=(C.w-(z.x+t*z.w))/2}}}else{x=h.TEX.big_op_spacing1;w=h.TEX.big_op_spacing3;u=Math.max(x,w-Math.max(0,t*z.d))}z.x+=D/2;z.y=C.h+u+v+t*z.d;if(u){A.style.paddingBottom=h.Em(u/t)}if(v){A.style.paddingTop=h.Em(v/t)}return B},CHTMLaddUnderscript:function(A,y,D,C,s,z,r){var B=this.CHTML;var x,w,v=h.TEX.big_op_spacing5,u;var E=y[this.under],t=E.rscale;if(!r){h.addElement(s,"mjx-itable",{},[["mjx-row",{},[["mjx-cell"]]],["mjx-row"]]);s.firstChild.firstChild.firstChild.appendChild(z);s.firstChild.lastChild.appendChild(A)}if(E.D){E.d=E.D}if(E.d<0){A.firstChild.style.verticalAlign="top";s.firstChild.style.marginBottom=h.Em(E.d)}if(D.accentunder){u=2*h.TEX.rule_thickness;v=0}else{x=h.TEX.big_op_spacing2;w=h.TEX.big_op_spacing4;u=Math.max(x,w-t*E.h)}E.x=-C/2;E.y=-(B.d+u+v+t*E.h);if(u){A.style.paddingTop=h.Em(u/t)}if(v){A.style.paddingBottom=h.Em(v/t)}},CHTMLplaceBoxes:function(r,A,z,D,y){var s=this.CHTML.w,x,u=y.length,v;var C=h.BBOX.zero();C.scale=this.CHTML.scale;C.rscale=this.CHTML.rscale;y[this.base].x=y[this.base].y=0;var E=n;for(x=0;x<u;x++){v=(x===this.base?1:y[x].rscale);var B=v*(y[x].w+(y[x].L||0)+(y[x].R||0));y[x].x+={left:0,center:(s-B)/2,right:s-B}[D.align];if(y[x].x<E){E=y[x].x}}for(x=0;x<u;x++){if(this.data[x]){v=(x===this.base?1:y[x].rscale);if(y[x].x-E){var t=(x===this.base?r:x===this.over?z:A);t.style.paddingLeft=h.Em((y[x].x-E)/v)}C.combine(y[x],y[x].x-E,y[x].y)}}this.CHTML=C},CHTMLstretchV:i.mbase.CHTMLstretchV,CHTMLstretchH:i.mbase.CHTMLstretchH,CHTMLchildNode:function(t,s){var r=["mjx-op","mjx-under","mjx-over"];if(this.over===1){r[1]=r[2]}return h.getNode(t,r[s])}});i.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=h.getNode(S,"mjx-base")}if(this.data[this.sub]){H=h.getNode(S,"mjx-sub")}if(this.data[this.sup]){z=h.getNode(S,"mjx-sup")}E=h.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=h.addElement(S,"mjx-stack");E.appendChild(z);E.appendChild(H)}}var F=[],G=h.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]||h.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=h.TEX.x_height,N=h.TEX.scriptspace;var Q=h.TEX.sup_drop*w,O=h.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=h.Em(-y.ic);Y=1.3*y.ic+0.05}var U=this.data[this.base];if(U){if((U.type==="mrow"||U.type==="mstyle")&&U.data.length===1){U=U.data[0]}if(U.type==="mi"||U.type==="mo"){if(U.data.join("").length===1&&y.rscale===1&&!y.sH&&!U.Get("largeop")){L=J=0}}}A.subscriptshift=(A.subscriptshift===""?0:this.CHTMLlength2em(A.subscriptshift));A.superscriptshift=(A.superscriptshift===""?0:this.CHTMLlength2em(A.superscriptshift));var I=G.w;if(H){P.w+=N}if(z){W.w+=N}if(!z){if(H){J=Math.max(J,h.TEX.sub1,B*P.h-(4/5)*X,A.subscriptshift);H.style.verticalAlign=h.Em(-J/B);H.style.paddingRight=h.Em(N/B);G.combine(P,I,-J)}}else{if(!H){R=h.TEX[(A.displaystyle?"sup1":(A.texprimestyle?"sup3":"sup2"))];L=Math.max(L,R,w*W.d+(1/4)*X,A.superscriptshift);z.style.verticalAlign=h.Em(L/w);z.style.paddingLeft=h.Em(Y/w);z.style.paddingRight=h.Em(N/w);G.combine(W,I+Y,L)}else{J=Math.max(J,h.TEX.sub2);var M=h.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=h.Em(N/B);z.style.paddingBottom=h.Em(L/w+J/B-W.d-P.h/B*w);z.style.paddingLeft=h.Em(Y/w);z.style.paddingRight=h.Em(N/w);E.style.verticalAlign=h.Em(-J);G.combine(W,I+Y,L);G.combine(P,I,-J)}}G.clean();return S},CHTMLstretchV:i.mbase.CHTMLstretchV,CHTMLstretchH:i.mbase.CHTMLstretchH,CHTMLchildNode:function(t,s){var r=["mjx-base","mjx-sub","mjx-sup"];if(this.over===1){r[1]=r[2]}return h.getNode(t,r[s])}});i.mfrac.Augment({toCommonHTML:function(M){M=this.CHTMLdefaultNode(M,{childNodes:["mjx-numerator","mjx-denominator"],childOptions:{autowidth:true},forceChild:true,noBBox:true,minChildren:2});var w=this.getValues("linethickness","displaystyle","numalign","denomalign","bevelled");var N=w.displaystyle;var C=M.firstChild,s=M.lastChild;var x=h.addElement(M,"mjx-box");x.appendChild(C);x.appendChild(s);M.appendChild(x);if(w.numalign!=="center"){C.style.textAlign=w.numalign}if(w.denomalign!=="center"){s.style.textAlign=w.denomalign}var O=this.CHTMLbboxFor(0),A=this.CHTMLbboxFor(1),B=h.BBOX.empty(this.CHTML),E=O.rscale,y=A.rscale;w.linethickness=Math.max(0,h.thickness2em(w.linethickness||"0",B.scale));var L=h.TEX.min_rule_thickness/h.em,S=h.TEX.axis_height;var I=w.linethickness,K,J,G,F;if(w.bevelled){x.className+=" MJXc-bevelled";var R=(N?0.4:0.15);var D=Math.max(E*(O.h+O.d),y*(A.h+A.d))+2*R;var Q=h.Element("mjx-bevel");x.insertBefore(Q,s);var r=h.createDelimiter(Q,47,D);G=E*(O.d-O.h)/2+S+R;F=y*(A.d-A.h)/2+S-R;if(G){C.style.verticalAlign=h.Em(G/E)}if(F){s.style.verticalAlign=h.Em(F/y)}Q.style.marginLeft=Q.style.marginRight=h.Em(-R/2);B.combine(O,0,G);B.combine(r,E*O.w-R/2,0);B.combine(A,E*O.w+r.w-R,F);B.clean()}else{x.className+=" MJXc-stacked";if(N){G=h.TEX.num1;F=h.TEX.denom1}else{G=(I===0?h.TEX.num3:h.TEX.num2);F=h.TEX.denom2}if(I===0){K=Math.max((N?7:3)*h.TEX.rule_thickness,2*L);J=(G-O.d*E)-(A.h*y-F);if(J<K){G+=(K-J)/2;F+=(K-J)/2}}else{K=Math.max((N?2:0)*L+I,I/2+1.5*L);I=Math.max(I,L);J=(G-O.d*E)-(S+I/2);if(J<K){G+=(K-J)}J=(S-I/2)-(A.h*y-F);if(J<K){F+=(K-J)}O.L=O.R=A.L=A.R=0.1;var z=h.addElement(x,"mjx-line",{style:{"border-bottom":h.Px(I*B.scale,1)+" solid",top:h.Em(-I/2-S)}})}B.combine(O,0,G);B.combine(A,0,-F);B.clean();x.style.width=h.Em(B.w);C.style.width=h.Em(B.w/E);s.style.width=h.Em(B.w/y);if(z){z.style.width=x.style.width}C.style.top=h.Em(-B.h/E);s.style.bottom=h.Em(-B.d/y);h.addElement(M,"mjx-vsize",{style:{height:h.Em(B.h+B.d),verticalAlign:h.Em(-B.d)}})}if(!this.texWithDelims&&!this.useMMLspacing){var P=h.TEX.nulldelimiterspace;x.style.padding="0 "+h.Em(P);B.l+=P;B.r+=P;B.w+=2*P}return M},CHTMLcanStretch:function(r){return false}});i.msqrt.Augment({toCommonHTML:function(v){v=this.CHTMLdefaultNode(v,{childNodes:["mjx-box","mjx-root"],forceChild:true,noBBox:true});var u=v.firstChild||h.Element("mjx-box");var D=h.addElement(v,"mjx-box");D.appendChild(u);var E=this.CHTMLbboxFor(0),B=h.BBOX.empty(this.CHTML);var F=h.TEX.rule_thickness,w=h.TEX.surd_height,s=F,r,C;if(this.Get("displaystyle")){s=h.TEX.x_height}r=F+s/4;C=E.h+E.d+r+F;var y=h.Element("mjx-surd");D.insertBefore(y,u);var z=h.createDelimiter(y,8730,[C-0.04,C]);if(z.h+z.d>C){r=((z.h+z.d)-(C-F))/2}C=E.h+r+F;var A=this.CHTMLaddRoot(v,z,z.h+z.d-C);u.style.paddingTop=h.Em(r);u.style.borderTop=h.Px(w*E.scale,1)+" solid";D.style.paddingTop=h.Em(2*F-w);E.h+=r+2*F;B.combine(z,A,C-z.h);B.combine(E,A+z.w,0);B.clean();return v},CHTMLaddRoot:function(){return 0}});i.mroot.Augment({toCommonHTML:i.msqrt.prototype.toCommonHTML,CHTMLaddRoot:function(z,t,u){if(!this.data[1]){return}var y=this.CHTML,A=this.data[1].CHTML,v=z.firstChild;var r=A.rscale;var s=this.CHTMLrootHeight(A,t,r)-u;var x=Math.min(A.w,A.r);var B=Math.max(x,t.offset/r);if(s){v.style.verticalAlign=h.Em(s/r)}if(B>x){v.firstChild.style.paddingLeft=h.Em(B-x)}B-=t.offset/r;v.style.width=h.Em(B);y.combine(A,0,s);return B*r},CHTMLrootHeight:function(t,r,s){return 0.45*(r.h+r.d-0.9)+r.offset+Math.max(0,t.d-0.075)}});i.mfenced.Augment({toCommonHTML:function(u){u=this.CHTMLcreateNode(u);this.CHTMLhandleStyle(u);this.CHTMLhandleScale(u);this.CHTMLaddChild(u,"open",{});for(var t=0,r=this.data.length;t<r;t++){this.CHTMLaddChild(u,"sep"+t,{});this.CHTMLaddChild(u,t,{})}this.CHTMLaddChild(u,"close",{});var s=this.CHTML.h,v=this.CHTML.d;this.CHTMLstretchChildV("open",s,v);for(t=0,r=this.data.length;t<r;t++){this.CHTMLstretchChildV("sep"+t,s,v);this.CHTMLstretchChildV(t,s,v)}this.CHTMLstretchChildV("close",s,v);this.CHTMLhandleSpace(u);this.CHTMLhandleBBox(u);this.CHTMLhandleColor(u);return u}});i.mrow.Augment({toCommonHTML:function(v,s){s=s||{};v=this.CHTMLdefaultNode(v);var y=this.CHTML,u=y.h,w=y.d,x;for(var t=0,r=this.data.length;t<r;t++){this.CHTMLstretchChildV(t,u,w);if(this.data[t]&&this.data[t].CHTML&&this.data[t].CHTML.w<0){x=true}}if(this.CHTMLlineBreaks()){this.CHTMLmultiline(v);if(s.autowidth){v.style.width=""}}else{if(x&&y.w){v.style.width=h.Em(Math.max(0,y.w))}if(y.w<0){v.style.marginRight=h.Em(y.w)}}return v},CHTMLlineBreaks:function(){if(!this.parent.linebreakContainer){return false}return(l.automatic&&this.CHTML.w>h.linebreakWidth)||this.hasNewline()},CHTMLstretchV:function(r,s){this.CHTMLstretchChildV(this.CoreIndex(),r,s);return this.CHTML},CHTMLstretchH:function(s,r){this.CHTMLstretchChildH(this.CoreIndex(),r,s);return this.CHTML}});i.mstyle.Augment({toCommonHTML:function(r){r=this.CHTMLdefaultNode(r);if(this.scriptlevel&&this.data[0]){this.CHTML.rescale(this.data[0].CHTML.rscale)}return r}});i.TeXAtom.Augment({toCommonHTML:function(w,u){if(!u||!u.stretch){w=this.CHTMLdefaultNode(w)}if(this.texClass===i.TEXCLASS.VCENTER){var r=h.TEX.axis_height,t=this.CHTML;var s=r-(t.h+t.d)/2+t.d;if(Math.abs(s)>0.001){w.style.verticalAlign=h.Em(s);t.h+=s;t.t+=s;t.d-=s;t.b-=s}}return w},CHTMLstretchV:function(r,s){this.CHTML.updateFrom(this.Core().CHTMLstretchV(r,s));this.toCommonHTML(this.CHTMLnodeElement(),{stretch:true});return this.CHTML},CHTMLstretchH:function(s,r){this.CHTML.updateFrom(this.CHTMLstretchCoreH(s,r));this.toCommonHTML(s,{stretch:true});return this.CHTML}});i.semantics.Augment({toCommonHTML:function(r){r=this.CHTMLcreateNode(r);if(this.data[0]){this.data[0].toCommonHTML(r);this.CHTML.updateFrom(this.data[0].CHTML);this.CHTMLhandleBBox(r)}return r}});i.annotation.Augment({toCommonHTML:function(r){return this.CHTMLcreateNode(r)}});i["annotation-xml"].Augment({toCommonHTML:i.mbase.CHTMLautoload});i.ms.Augment({toCommonHTML:i.mbase.CHTMLautoload});i.mglyph.Augment({toCommonHTML:i.mbase.CHTMLautoload});i.menclose.Augment({toCommonHTML:i.mbase.CHTMLautoload});i.maction.Augment({toCommonHTML:i.mbase.CHTMLautoload});i.mmultiscripts.Augment({toCommonHTML:i.mbase.CHTMLautoload});i.mtable.Augment({toCommonHTML:i.mbase.CHTMLautoload});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",h,"jax.js"]),0)})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(c.config.menuSettings.zoom!=="None"){j.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.CommonHTML);
MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var g="2.7.0";var b=MathJax.ElementJax.mml,a=MathJax.Hub.config,e=MathJax.OutputJax.CommonHTML,d=MathJax.Hub.SplitList;var c=-1,f=1000000;b.mtable.Augment({toCommonHTML:function(l){var m={rows:[],labels:[],labeled:false};l=this.CHTMLdefaultNode(l,{noBBox:true,childOptions:m});var k=e.Element("mjx-table");while(l.firstChild){k.appendChild(l.firstChild)}l.appendChild(k);var h=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","width","side","minlabelspacing","useHeight");var j=e.TEX.min_rule_thickness/e.em;m.t=e.Px(j*this.CHTML.scale,1);this.CHTMLgetBoxSizes(h,m);this.CHTMLgetAttributes(h,m);this.CHTMLadjustCells(h,m);if(h.frame){k.style.border=m.t+" "+h.frame}this.CHTMLalignV(h,m,l);this.CHTMLcolumnWidths(h,m,l);this.CHTMLstretchCells(h,m);if(m.labeled){this.CHTMLaddLabels(h,m,l,k)}var 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(/ /g,"")!==""||v.rowlines.replace(/none/g,"").replace(/ /g,"")!==""){v.fspace=true}if(v.frame===b.LINES.NONE){delete v.frame}else{v.fspace=true}if(v.frame){h[0]=Math.max(0,h[0]);h[1]=Math.max(0,h[1])}if(v.fspace){l[u]=h[0];x[s]=h[1]}else{l[u]=x[s]=0}k[u]=w[s]=b.LINES.NONE;j.CSPACE=l;j.RSPACE=x;j.CALIGN=t;j.RALIGN=r;j.CLINES=k;j.RLINES=w;j.CWIDTH=o;j.RCALIGN=n;j.FSPACE=h},CHTMLadjustCells:function(k,q){var P=q.rows,U=q.CSPACE,n=q.CLINES,w=q.RSPACE,E=q.RLINES,S=q.CALIGN,p=q.RALIGN,F=q.RCALIGN;U[q.J]*=2;w[P.length-1]*=2;var o="0",G,r,y,J,l,N,Q=0;if(k.fspace){Q=q.FSPACE[1];o=e.Em(q.FSPACE[1])}q.RHD=[];q.RH=[];for(var O=0,I=P.length;O<I;O++){var v=P[O],u=this.data[O];G=w[O]/2;J=null;y="0";if(E[O]!==b.LINES.NONE&&E[O]!==""){J=q.t+" "+E[O]}q.RH[O]=Q+q.H[O];Q=Math.max(0,G);q.RHD[O]=q.RH[O]+Q+q.D[O];G=e.Em(Q);if(k.fspace){y=e.Em(q.FSPACE[0])}for(var K=0,x=v.length;K<x;K++){var C=(u.type==="mtr"?0:c);cell=v[K].style;l=u.data[K-C].CHTML;r=U[K]/2;if(n[K]!==b.LINES.NONE){cell.borderRight=q.t+" "+n[K];r-=1/e.em/2}r=e.Em(Math.max(0,r));cell.padding=o+" "+r+" 0px "+y;if(J){cell.borderBottom=J}y=r;N=(u.data[K-C].rowalign||this.data[O].rowalign||p[O]);var z=Math.max(1,l.h),A=Math.max(0.2,l.d),h=(q.H[O]+q.D[O])-(z+A),t=v[K].firstChild.style;if(N===b.ALIGN.TOP){if(h){t.marginBottom=e.Em(h)}cell.verticalAlign="top"}else{if(N===b.ALIGN.BOTTOM){cell.verticalAlign="bottom";if(h){t.marginTop=e.Em(h)}}else{if(N===b.ALIGN.CENTER){if(h){t.marginTop=t.marginBottom=e.Em(h/2)}cell.verticalAlign="middle"}else{if(z!==q.H[O]){t.marginTop=e.Em(q.H[O]-z)}}}}N=(u.data[K-C].columnalign||F[O][K]||S[K]);if(N!==b.ALIGN.CENTER){cell.textAlign=N}}v.node.style.height=e.Em(q.RHD[O]);o=G}U[q.J]/=2;w[P.length-1]/=2},CHTMLalignV:function(w,k,o){var m,t=k.rows.length,v=k.H,j=k.D,x=k.RSPACE;if(typeof(w.align)!=="string"){w.align=String(w.align)}if(w.align.match(/(top|bottom|center|baseline|axis)( +(-?\d+))?/)){m=parseInt(RegExp.$3||"0");w.align=RegExp.$1;if(m<0){m+=k.rows.length+1}if(m>t||m<=0){m=null}}else{w.align=this.defaults.align}var p=0,l=0,u=e.TEX.axis_height;if(w.fspace){p+=k.FSPACE[1]}if(w.frame){p+=2/e.em;l+=1/e.em}for(var q=0;q<t;q++){var r=v[q],s=j[q];p+=r+s+x[q];if(m){if(q===m-1){l+=({top:r+s,bottom:0,center:(r+s)/2,baseline:s,axis:u+s})[w.align]+x[q]}if(q>=m){l+=r+s+x[q]}}}if(!m){l=({top:p,bottom:0,center:p/2,baseline:p/2,axis:p/2-u})[w.align]}if(l){o.style.verticalAlign=e.Em(-l)}k.T=p;k.B=l},CHTMLcolumnWidths:function(l,r,A){var I=r.CWIDTH,K=r.CSPACE,u=r.J,F;var G=0,n=false,y=l.width.match(/%$/);var H,B,v;if(l.width!=="auto"&&!y){G=Math.max(0,this.CHTMLlength2em(l.width,r.R));n=true}if(l.equalcolumns){if(y){var z=e.Percent(1/(u+1));for(F=0;F<=u;F++){I[F]=z}}else{v=Math.max.apply(Math,r.W);if(l.width!=="auto"){var q=(l.fspace?r.FSPACE[0]+(l.frame?2/e.em:0):0);for(F=0;F<=u;F++){q+=K[F]}v=Math.max((G-q)/(u+1),v)}v=e.Em(v);for(F=0;F<=u;F++){I[F]=v}}n=true}var E=0;if(l.fspace){E=r.FSPACE[0]}var s=[],D=[],h=[],o=[];var t=r.rows[0];for(F=0;F<=u;F++){o[F]=r.W[F];if(I[F]==="auto"){s.push(F)}else{if(I[F]==="fit"){D.push(F)}else{if(I[F].match(/%$/)){h.push(F)}else{o[F]=this.CHTMLlength2em(I[F],o[F])}}}E+=o[F]+K[F];if(t[F]){t[F].style.width=e.Em(o[F])}}if(l.frame){E+=2/e.em}var C=(D.length>0);if(n){if(y){for(F=0;F<=u;F++){cell=t[F].style;if(I[F]==="auto"&&!C){cell.width=""}else{if(I[F]==="fit"){cell.width=""}else{if(I[F].match(/%$/)){cell.width=I[F]}else{cell.minWidth=cell.maxWidth=cell.width}}}}}else{if(G>E){var k=0;for(H=0,B=h.length;H<B;H++){F=h[H];v=Math.max(o[F],this.CHTMLlength2em(I[F],G));k+=v-o[F];o[F]=v;t[F].style.width=e.Em(v)}E+=k}if(!C){D=s}if(G>E&&D.length){var x=(G-E)/D.length;for(H=0,B=D.length;H<B;H++){F=D[H];o[F]+=x;t[F].style.width=e.Em(o[F])}E=G}}}o[c]=r.W[c];r.W=o;r.R=E;if(y){this.CHTML.pwidth=l.width;this.CHTML.mwidth=e.Em(E);A.style.width=A.firstChild.style.width="100%"}},CHTMLstretchCells:function(x,l){var 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s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.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/MML_CHTML-full.js");