!function(t,e,i){var a,s,n,o,h=e.Browser.isMobile,r=MathJax.Object.isArray,l=function(){var t=[].slice.call(arguments,0);return t[0][0]=["HTML-CSS",t[0][0]],MathJax.Message.Set.apply(MathJax.Message,t)},d=MathJax.Object.Subclass({timeout:1e3*(h?15:8),comparisonFont:["sans-serif","monospace","script","Times","Courier","Arial","Helvetica"],testSize:["40px","50px","60px","30px","20px"],FedoraSTIXcheck:{family:"STIXSizeOneSym",testString:"abcABC",noStyleChar:!0},Init:function(){this.div=MathJax.HTML.addElement(document.body,"div",{style:{position:"absolute",width:0,height:0,overflow:"hidden",padding:0,border:0,margin:0}},[["div",{id:"MathJax_Font_Test",style:{position:"absolute",visibility:"hidden",top:0,left:0,width:"auto","min-width":0,"max-width":"none",padding:0,border:0,margin:0,whiteSpace:"nowrap",textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal",fontSize:this.testSize[0],fontWeight:"normal",fontStyle:"normal",fontSizeAdjust:"none"}},[""]]]).firstChild,this.text=this.div.firstChild},findFont:function(t,e){var i=null;if(e&&this.testCollection(e))i=e;else for(var a=0,s=t.length;a<s;a++)if(t[a]!==e&&this.testCollection(t[a])){i=t[a];break}return"STIX"===i&&this.testFont(this.FedoraSTIXcheck)&&(i=null),i},testCollection:function(t){var e={testString:"() {} []"};return e.family={TeX:"MathJax_Size1",STIX:"STIXSizeOneSym"}[t]||t.replace(/-(Math)?/,"")+"MathJax_Size1","STIX"===t&&(e.noStyleChar=!0),this.testFont(e)},testFont:function(t){t.isWebFont&&i.FontFaceBug?this.div.style.fontWeight=this.div.style.fontStyle="normal":(this.div.style.fontWeight=t.weight||"normal",this.div.style.fontStyle=t.style||"normal");var e=t.familyFixed||t.family;t.isWebFont||e.match(/^(STIX|MathJax)|'/)||(e=e.replace(/_/g," ").replace(/([a-z])([A-Z])/g,"$1 $2").replace(/ Jax/,"Jax")+"','"+e+"','"+e+"-",t.weight&&(e+="Bold"),t.style&&(e+="Italic"),t.weight||t.style||(e+="Regular"),t.familyFixed=e="'"+e+"'");var a=this.getComparisonWidths(t.testString,t.noStyleChar),s=null;if(a&&(this.div.style.fontFamily=e+","+this.comparisonFont[0],this.div.offsetWidth==a[0]&&(this.div.style.fontFamily=e+","+this.comparisonFont[a[2]],this.div.offsetWidth==a[1]&&(s=!1)),null===s&&(this.div.offsetWidth!=a[3]||this.div.offsetHeight!=a[4])))if(!t.noStyleChar&&i.FONTDATA&&i.FONTDATA.hasStyleChar)for(var n=0,o=this.testSize.length;n<o;n++)this.testStyleChar(t,this.testSize[n])&&(s=!0,o=0);else s=!0;return i.safariTextNodeBug?this.div.innerHTML="":this.text.nodeValue="",s},styleChar:"",versionChar:"",compChar:"",testStyleChar:function(t,e){var a=3+(t.weight?2:0)+(t.style?4:0),s="",n=0,o=this.div.style.fontSize;this.div.style.fontSize=e,i.msieItalicWidthBug&&"italic"===t.style&&(this.text.nodeValue=s=this.compChar,n=this.div.offsetWidth),i.safariTextNodeBug?this.div.innerHTML=this.compChar+s:this.text.nodeValue=this.compChar+s;var h=this.div.offsetWidth-n;i.safariTextNodeBug?this.div.innerHTML=this.styleChar+s:this.text.nodeValue=this.styleChar+s;var r=Math.floor((this.div.offsetWidth-n)/h+.5);return r===a&&(i.safariTextNodeBug?this.div.innerHTML=this.versionChar+s:this.text.nodeValue=this.versionChar+s,t.version=Math.floor((this.div.offsetWidth-n)/h+1.5)/2),this.div.style.fontSize=o,r===a},getComparisonWidths:function(t,e){i.FONTDATA&&i.FONTDATA.hasStyleChar&&!e&&(t+=this.styleChar+" "+this.compChar),i.safariTextNodeBug?this.div.innerHTML=t:this.text.nodeValue=t,this.div.style.fontFamily=this.comparisonFont[0];var a=this.div.offsetWidth;this.div.style.fontFamily=i.webFontDefault;for(var s=this.div.offsetWidth,n=this.div.offsetHeight,o=1,h=this.comparisonFont.length;o<h;o++)if(this.div.style.fontFamily=this.comparisonFont[o],this.div.offsetWidth!=a)return[a,this.div.offsetWidth,o,s,n];return null},loadWebFont:function(a){e.Startup.signal.Post("HTML-CSS Jax - Web-Font "+i.fontInUse+"/"+a.directory);var s=l(["LoadWebFont","Loading web-font %1",i.fontInUse+"/"+a.directory]),n=MathJax.Callback({}),o=MathJax.Callback(["loadComplete",this,a,s,n]);return t.timer.start(t,[this.checkWebFont,a,o],0,this.timeout),n},loadComplete:function(a,s,n,o){if(MathJax.Message.Clear(s),o===t.STATUS.OK)return this.webFontLoaded=!0,void n();if(this.loadError(a),e.Browser.isFirefox&&i.allowWebFonts){var h=document.location.protocol+"//"+document.location.hostname;""!=document.location.port&&(h+=":"+document.location.port),h+="/",t.fileURL(i.webfontDir).substr(0,h.length)!==h&&this.firefoxFontError(a)}this.webFontLoaded?n():i.loadWebFontError(a,n)},loadError:function(t){l(["CantLoadWebFont","Can't load web font %1",i.fontInUse+"/"+t.directory],null,2e3),e.Startup.signal.Post("HTML-CSS Jax - web font error for "+i.fontInUse+"/"+t.directory)},firefoxFontError:function(t){l(["FirefoxCantLoadWebFont","Firefox can't load web fonts from a remote host"],null,3e3),e.Startup.signal.Post("HTML-CSS Jax - Firefox web fonts on remote host error")},checkWebFont:function(t,e,a){t.time(a)||(i.Font.testFont(e)?a(t.STATUS.OK):setTimeout(t,t.delay))},fontFace:function(e){var a=i.allowWebFonts,s=i.FONTDATA.FONTS[e];i.msieFontCSSBug&&!s.family.match(/-Web$/)&&(s.family+="-Web"),s.isWebFont&&delete s.familyFixed;var n=i.webfontDir+"/"+a,o=t.fileURL(n),h=e.replace(/-b/,"-B").replace(/-i/,"-I").replace(/-Bold-/,"-Bold");h.match(/-/)||(h+="-Regular"),h+="svg"===a?".svg#"+h:"."+a;var r=t.fileRev(n+"/"+h.replace(/#.*/,"")),l={"font-family":s.family,src:"url('"+o+"/"+h+r+"')"};return"otf"===a?(h=h.replace(/otf$/,"woff"),r=t.fileRev(n+"/"+h),l.src+=" format('opentype')",o=t.fileURL(i.webfontDir+"/woff"),l.src="url('"+o+"/"+h+r+"') format('woff'), "+l.src):"eot"!==a&&(l.src+=" format('"+a+"')"),i.FontFaceBug&&s.isWebFont||(e.match(/-bold/)&&(l["font-weight"]="bold"),e.match(/-italic/)&&(l["font-style"]="italic")),l}}),c=MathJax.Hub.Browser.isMSIE&&(document.documentMode||0)<8;i.Augment({config:{styles:{".MathJax":{display:"inline","font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap",float:"none",direction:"ltr","max-width":"none","max-height":"none","min-width":0,"min-height":0,border:0,padding:0,margin:0},".MathJax:focus, body :focus .MathJax":{display:"inline-table"},".MathJax_Display":{position:"relative",display:"block!important","text-indent":0,"max-width":"none","max-height":"none","min-width":0,"min-height":0,width:"100%"},".MathJax.MathJax_FullWidth":{"text-align":"center",display:(c?"block":"table-cell")+"!important",width:(c?"100%":"10000em")+"!important"},".MathJax img, .MathJax nobr, .MathJax a":{border:0,padding:0,margin:0,"max-width":"none","max-height":"none","min-width":0,"min-height":0,"vertical-align":0,"line-height":"normal","text-decoration":"none"},"img.MathJax_strut":{border:"0!important",padding:"0!important",margin:"0!important","vertical-align":"0!important"},".MathJax span":{display:"inline",position:"static",border:0,padding:0,margin:0,"vertical-align":0,"line-height":"normal","text-decoration":"none","box-sizing":"content-box"},".MathJax nobr":{"white-space":"nowrap!important"},".MathJax img":{display:"inline!important",float:"none!important"},".MathJax *":{transition:"none","-webkit-transition":"none","-moz-transition":"none","-ms-transition":"none","-o-transition":"none"},".MathJax_Processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MathJax_Processed":{display:"none!important"},".MathJax_test":{"font-style":"normal","font-weight":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-transform":"none","letter-spacing":"normal","word-spacing":"normal",overflow:"hidden",height:"1px"},".MathJax_test.mjx-test-display":{display:(c?"block":"table")+"!important"},".MathJax_test.mjx-test-inline":{display:"inline!important","margin-right":"-1px"},".MathJax_test.mjx-test-default":{display:"block!important",clear:"both"},".MathJax_ex_box":{display:"inline-block!important",position:"absolute",overflow:"hidden","min-height":0,"max-height":"none",padding:0,border:0,margin:0,width:"1px",height:"60ex"},".MathJax_em_box":{display:"inline-block!important",position:"absolute",overflow:"hidden","min-height":0,"max-height":"none",padding:0,border:0,margin:0,width:"1px",height:"60em"},".mjx-test-inline .MathJax_left_box":{display:"inline-block",width:0,float:"left"},".mjx-test-inline .MathJax_right_box":{display:"inline-block",width:0,float:"right"},".mjx-test-display .MathJax_right_box":{display:(c?"block":"table-cell")+"!important",width:(c?"100%":"10000em")+"!important","min-width":0,"max-width":"none",padding:0,border:0,margin:0},".MathJax .MathJax_HitBox":{cursor:"text",background:"white",opacity:0,filter:"alpha(opacity=0)"},".MathJax .MathJax_HitBox *":{filter:"none",opacity:1,background:"transparent"},"#MathJax_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"},"#MathJax_Tooltip *":{filter:"none",opacity:1,background:"transparent"},"@font-face":{"font-family":"MathJax_Blank",src:"url('about:blank')"}}},settings:e.config.menuSettings,Font:null,webFontDefault:"MathJax_Blank",allowWebFonts:"otf",maxStretchyParts:1e3,fontName:{TeXLocal:"TeX",TeXWeb:["","TeX"],TeXImage:["",""],STIXLocal:["STIX","STIX-Web"],STIXWeb:"STIX-Web",AsanaMathWeb:"Asana-Math",GyrePagellaWeb:"Gyre-Pagella",GyreTermesWeb:"Gyre-Termes",LatinModernWeb:"Latin-Modern",NeoEulerWeb:"Neo-Euler"},fontInUse:"generic",FONTDATA:{TeX_factor:1,baselineskip:1.2,lineH:.8,lineD:.2,ffLineH:.8,FONTS:{},VARIANT:{normal:{fonts:[]},"-generic-variant":{},"-largeOp":{},"-smallOp":{}},RANGES:[],DELIMITERS:{},RULECHAR:45,REMAP:{}},Config:function(){this.require||(this.require=[]),this.Font=d(),this.SUPER(arguments).Config.call(this);var t=this.settings,i=this.config,a=t.font;this.adjustAvailableFonts&&this.adjustAvailableFonts(i.availableFonts),t.scale&&(i.scale=t.scale),a&&"Auto"!==a&&this.fontName[a]&&(i.availableFonts=[],delete i.fonts,r(this.fontName[a])?(i.preferredFont=this.fontName[a][0],i.webFont=this.fontName[a][1]):i.preferredFont=i.webFont=this.fontName[a],i.preferredFont&&(i.availableFonts[0]=i.preferredFont)),i.fonts&&(i.availableFonts=i.fonts,i.preferredFont=i.webFont=i.fonts[0],"STIX"===i.webFont&&(i.webFont+="-Web")),!(a=this.Font.findFont(i.availableFonts,i.preferredFont))&&this.allowWebFonts&&(a=i.webFont)&&(this.webFonts=!0),!a&&this.config.imageFont&&(a=i.imageFont,this.imgFonts=!0),a?(this.fontInUse=a,this.fontDir+="/"+a,this.webfontDir+="/"+a,this.require.push(this.fontDir+"/fontdata.js"),this.imgFonts&&(this.require.push(this.directory+"/imageFonts.js"),e.Startup.signal.Post("HTML-CSS Jax - using image fonts"))):(l(["CantFindFontUsing","Can't find a valid font using %1","["+this.config.availableFonts.join(", ")+"]"],null,3e3),e.Startup.signal.Post("HTML-CSS Jax - no valid font")),this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){s=MathJax.Extension.MathEvents.Event,n=MathJax.Extension.MathEvents.Touch,o=MathJax.Extension.MathEvents.Hover,this.ContextMenu=s.ContextMenu,this.Mousedown=s.AltContextMenu,this.Mouseover=o.Mouseover,this.Mouseout=o.Mouseout,this.Mousemove=o.Mousemove,this.hiddenDiv=this.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}}),document.body.firstChild?document.body.insertBefore(this.hiddenDiv,document.body.firstChild):document.body.appendChild(this.hiddenDiv),this.hiddenDiv=this.addElement(this.hiddenDiv,"div",{id:"MathJax_Hidden"});var e=this.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});if(this.pxPerInch=e.offsetWidth/5,this.hiddenDiv.removeChild(e),this.startMarker=this.createStrut(this.Element("span"),10,!0),this.endMarker=this.addText(this.Element("span"),"x").parentNode,this.HDspan=this.Element("span"),this.operaHeightBug&&this.createStrut(this.HDspan,0),this.msieInlineBlockAlignBug){this.HDimg=this.addElement(this.HDspan,"img",{style:{height:"0px",width:"1px"}});try{this.HDimg.src="about:blank"}catch(t){}}else this.HDimg=this.createStrut(this.HDspan,0);return this.TestSpan=this.Element("span",{className:"MathJax_test"},[["span",{className:"MathJax_left_box"}],["span",{className:"MathJax_ex_box"}],["span",{className:"MathJax_em_box"}],["span",{className:"MathJax_right_box"}]]),t.Styles(this.config.styles,["InitializeHTML",this])},removeSTIXfonts:function(t){for(var e=0,i=t.length;e<i;e++)"STIX"===t[e]&&(t.splice(e,1),i--,e--);"STIX"===this.config.preferredFont&&(this.config.preferredFont=t[0])},PreloadWebFonts:function(){if(i.allowWebFonts&&i.config.preloadWebFonts)for(var t=0,e=i.config.preloadWebFonts.length;t<e;t++){var a=i.FONTDATA.FONTS[i.config.preloadWebFonts[t]];a.available||i.Font.testFont(a)}},InitializeHTML:function(){if(this.PreloadWebFonts(),this.getDefaultExEm(),!this.defaultEm){var a=MathJax.Callback();return t.timer.start(t,(function(t){t.time(a)?e.signal.Post(["HTML-CSS Jax - no default em size"]):(i.getDefaultExEm(),i.defaultEm?a():setTimeout(t,t.delay))}),this.defaultEmDelay,this.defaultEmTimeout),a}},defaultEmDelay:100,defaultEmTimeout:1e3,getDefaultExEm:function(){var t=document.body.appendChild(this.TestSpan.cloneNode(!0));t.className+=" mjx-test-inline mjx-test-default",this.defaultEx=t.childNodes[1].offsetHeight/60,this.defaultEm=t.childNodes[2].offsetHeight/60,this.defaultWidth=Math.max(0,t.lastChild.offsetLeft-t.firstChild.offsetLeft-2),document.body.removeChild(t)},preTranslate:function(t){var i,a,o,h,r,l,d,c,b,m,u,f,x,g=t.jax[this.id],p=g.length,M=!1,T=this.config.linebreaks.automatic,H=this.config.linebreaks.width;for(T?((M=null!=H.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/))?H=H.replace(/\s*container\s*/,""):f=this.defaultWidth,""===H&&(H="100%")):f=1e5,i=0;i<p;i++)(o=g[i]).parentNode&&((h=o.previousSibling)&&String(h.className).match(/^MathJax(_Display)?( MathJax_Process(ing|ed))?$/)&&h.parentNode.removeChild(h),o.MathJax.preview&&(o.MathJax.preview.style.display="none"),(c=o.MathJax.elementJax)&&(c.HTMLCSS={display:"block"===c.root.Get("display")},r=l=this.Element("span",{className:"MathJax",id:c.inputID+"-Frame",isMathJax:!0,jaxID:this.id,oncontextmenu:s.Menu,onmousedown:s.Mousedown,onmouseover:s.Mouseover,onmouseout:s.Mouseout,onmousemove:s.Mousemove,onclick:s.Click,ondblclick:s.DblClick,onkeydown:s.Keydown,tabIndex:e.getTabOrder(c)}),e.Browser.noContextMenu&&(r.ontouchstart=n.start,r.ontouchend=n.end),c.HTMLCSS.display?(l=this.Element("div",{className:"MathJax_Display"})).appendChild(r):this.msieDisappearingBug&&(r.style.display="inline-block"),l.className+=" MathJax_Processing",o.parentNode.insertBefore(l,o),c.HTMLCSS.span=r,c.HTMLCSS.div=l,(d=this.TestSpan.cloneNode(!0)).className+=" mjx-test-"+(c.HTMLCSS.display?"display":"inline"),o.parentNode.insertBefore(d,o)));var L=[];for(i=0;i<p;i++)(o=g[i]).parentNode&&(l=(d=o.previousSibling).previousSibling,(c=o.MathJax.elementJax)&&(b=d.childNodes[1].offsetHeight/60,m=d.childNodes[2].offsetHeight/60,x=Math.max(0,c.HTMLCSS.display?d.lastChild.offsetWidth-1:d.lastChild.offsetLeft-d.firstChild.offsetLeft-2),0!==b&&"NaN"!==b||(L.push(l),c.HTMLCSS.isHidden=!0,b=this.defaultEx,m=this.defaultEm,x=this.defaultWidth),0!==x||c.HTMLCSS.display||(x=this.defaultWidth),M&&(f=x),u=this.config.matchFontHeight?b/this.TeX.x_height/m:1,u=Math.floor(Math.max(this.config.minScaleAdjust/100,u)*this.config.scale),c.HTMLCSS.scale=u/100,c.HTMLCSS.fontSize=u+"%",c.HTMLCSS.em=c.HTMLCSS.outerEm=m,this.em=m*u/100,c.HTMLCSS.ex=b,c.HTMLCSS.cwidth=x/this.em,c.HTMLCSS.lineWidth=T?this.length2em(H,1,f/this.em):1e6));for(i=0,a=L.length;i<a;i++)this.hiddenDiv.appendChild(L[i]),this.addElement(this.hiddenDiv,"br");for(i=0;i<p;i++)(o=g[i]).parentNode&&(c=g[i].MathJax.elementJax)&&(o.parentNode.removeChild(o.previousSibling),o.MathJax.preview&&(o.MathJax.preview.style.display=""));t.HTMLCSSeqn=t.HTMLCSSlast=0,t.HTMLCSSi=-1,t.HTMLCSSchunk=this.config.EqnChunk,t.HTMLCSSdelay=!1},PHASE:{I:1,II:2,III:3},Translate:function(t,i){if(t.parentNode){i.HTMLCSSdelay&&(i.HTMLCSSdelay=!1,e.RestartAfter(MathJax.Callback.Delay(this.config.EqnChunkDelay)));var a=t.MathJax.elementJax,s=a.root,n=a.HTMLCSS.div,o=a.HTMLCSS.span;if(document.getElementById(o.id)){this.getMetrics(a),1!==this.scale&&(o.style.fontSize=a.HTMLCSS.fontSize),this.initImg(o),this.initHTML(s,o),this.savePreview(t);try{s.setTeXclass(),s.toHTML(o,n,this.PHASE.I)}catch(e){if(e.restart)for(;o.firstChild;)o.removeChild(o.firstChild);throw this.restorePreview(t),e}return this.restorePreview(t),n.className=n.className.split(/ /)[0]+" MathJax_Processed",e.signal.Post(["New Math Pending",a.inputID]),i.HTMLCSSeqn+=i.i-i.HTMLCSSi,i.HTMLCSSi=i.i,i.HTMLCSSeqn>=i.HTMLCSSlast+i.HTMLCSSchunk&&(this.postTranslate(i,!0),i.HTMLCSSchunk=Math.floor(i.HTMLCSSchunk*this.config.EqnChunkFactor),i.HTMLCSSdelay=!0),!1}}},savePreview:function(t){var e=t.MathJax.preview;e&&(t.MathJax.tmpPreview=document.createElement("span"),e.parentNode.replaceChild(t.MathJax.tmpPreview,e))},restorePreview:function(t){var e=t.MathJax.tmpPreview;e&&(e.parentNode.replaceChild(t.MathJax.preview,e),delete t.MathJax.tmpPreview)},getMetrics:function(t){var e=t.HTMLCSS;this.em=a.mbase.prototype.em=e.em*e.scale,this.outerEm=e.em,this.scale=e.scale,this.cwidth=e.cwidth,this.linebreakWidth=e.lineWidth},postTranslate:function(t,i){var a,s,n,o,h=t.jax[this.id];for(n=t.HTMLCSSlast,o=t.HTMLCSSeqn;n<o;n++)if((a=h[n])&&a.parentNode&&a.MathJax.elementJax){var r=(a.MathJax.elementJax.HTMLCSS||{}).div;r&&(r.className=r.className.split(/ /)[0]),a.MathJax.preview&&(a.MathJax.preview.innerHTML="")}for(n=t.HTMLCSSlast,o=t.HTMLCSSeqn;n<o;n++)(a=h[n])&&a.parentNode&&a.MathJax.elementJax&&(s=a.MathJax.elementJax,this.getMetrics(s),s.HTMLCSS.span&&s.HTMLCSS.div&&s.root.toHTML(s.HTMLCSS.span,s.HTMLCSS.div,this.PHASE.II));for(n=t.HTMLCSSlast,o=t.HTMLCSSeqn;n<o;n++)(a=h[n])&&a.parentNode&&a.MathJax.elementJax&&(s=a.MathJax.elementJax,this.getMetrics(s),s.HTMLCSS.span&&s.HTMLCSS.div&&(s.root.toHTML(s.HTMLCSS.span,s.HTMLCSS.div,this.PHASE.III),s.HTMLCSS.isHidden&&a.parentNode.insertBefore(s.HTMLCSS.div,a),delete s.HTMLCSS.span,delete s.HTMLCSS.div,a.MathJax.state=s.STATE.PROCESSED,e.signal.Post(["New Math",a.MathJax.elementJax.inputID])));if(this.forceReflow){var l=(document.styleSheets||[])[0]||{};l.disabled=!0,l.disabled=!1}t.HTMLCSSlast=t.HTMLCSSeqn},getJaxFromMath:function(t){t.parentNode.className.match(/MathJax_Display/)&&(t=t.parentNode);do{t=t.nextSibling}while(t&&"script"!==t.nodeName.toLowerCase());return e.getJaxFor(t)},getHoverSpan:function(t,e){return t.root.HTMLspanElement()},getHoverBBox:function(t,e,i){var a=e.bbox,s=t.HTMLCSS.outerEm,n={w:a.w*s,h:a.h*s,d:a.d*s};return a.width&&(n.width=a.width),n},Zoom:function(t,n,o,h,r){n.className="MathJax",n.style.fontSize=t.HTMLCSS.fontSize;var l=n.appendChild(this.TestSpan.cloneNode(!0)),d=l.childNodes[2].offsetHeight/60;this.em=a.mbase.prototype.em=d,this.outerEm=d/t.HTMLCSS.scale,l.parentNode.removeChild(l),this.scale=t.HTMLCSS.scale,this.linebreakWidth=t.HTMLCSS.lineWidth,this.cwidth=t.HTMLCSS.cwidth,this.zoomScale=parseInt(e.config.menuSettings.zscale)/100,this.idPostfix="-zoom",t.root.toHTML(n,n),this.idPostfix="",this.zoomScale=1;var c=t.root.HTMLspanElement().bbox,b=c.width;if(b){c.tw&&(h=c.tw*d),c.w*d<h&&(h=c.w*d),n.style.width=Math.floor(h-1.5*i.em)+"px",n.style.display="inline-block";for(var m=(t.root.id||"MathJax-Span-"+t.root.spanID)+"-zoom",u=document.getElementById(m).firstChild;u&&u.style.width!==b;)u=u.nextSibling;if(u){var 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r=null!=h.width&&!h.isFixed,l=0,d=s-h.w/2,c="50%";this.initialSkipBug&&(l=h.w-h.rw-.1,d+=h.lw),d=this.msieMarginScaleBug?d*this.em+"px":this.Em(d),r&&(d=0===s?"":this.Em(s),c=50-parseFloat(h.width)/2+"%"),e.Insert(t.style,{right:{left:"",right:this.Em(l-s)},center:{left:c,marginLeft:d}}[i])}},setStackWidth:function(t,e){if("number"==typeof e){t.style.width=this.Em(Math.max(0,e));var i=t.bbox;i&&(i.w=e,i.exactW=!0),(i=t.parentNode.bbox)&&(i.w=e,i.exactW=!0)}else t.style.width=t.parentNode.style.width="100%",t.bbox&&(t.bbox.width=e),t.parentNode.bbox&&(t.parentNode.bbox.width=e)},createDelimiter:function(i,s,n,o,h){if(!s)return i.bbox={h:0,d:0,w:this.TeX.nulldelimiterspace,lw:0},i.bbox.rw=i.bbox.w,void this.createSpace(i,i.bbox.h,i.bbox.d,i.bbox.w);o||(o=1),n instanceof Array||(n=[n,n]);var r=n[1];n=n[0];for(var l={alias:s};l.alias;)s=l.alias,(l=this.FONTDATA.DELIMITERS[s])||(l={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]});l.load&&e.RestartAfter(t.Require(this.fontDir+"/fontdata-"+l.load+".js"));for(var d=0,c=l.HW.length;d<c;d++)if(l.HW[d][0]*o>=n-.01||d==c-1&&!l.stretch){l.HW[d][2]&&(o*=l.HW[d][2]),l.HW[d][3]&&(s=l.HW[d][3]);var b=this.addElement(i,"span");return this.createChar(b,[s,l.HW[d][1]],o,h),i.bbox=b.bbox,i.offset=.65*i.bbox.w,void(i.scale=o)}l.stretch&&this["extendDelimiter"+l.dir](i,r,l.stretch,o,h)},extendDelimiterV:function(t,e,i,a,s){var n=this.createStack(t,!0),o=this.createBox(n),h=this.createBox(n);this.createChar(o,i.top||i.ext,a,s),this.createChar(h,i.bot||i.ext,a,s);var r,l={bbox:{w:0,lw:0,rw:0}},d=l,c=o.bbox.h+o.bbox.d+h.bbox.h+h.bbox.d,b=-o.bbox.h;if(this.placeBox(o,0,b,!0),b-=o.bbox.d,i.mid&&(d=this.createBox(n),this.createChar(d,i.mid,a,s),c+=d.bbox.h+d.bbox.d),i.min&&e<c*i.min&&(e=c*i.min),e>c){l=this.Element("span"),this.createChar(l,i.ext,a,s);var 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n=this.createStack(t,!0),o=this.createBox(n),h=this.createBox(n);this.createChar(o,i.left||i.rep,a,s),this.createChar(h,i.right||i.rep,a,s);var r=this.Element("span");this.createChar(r,i.rep,a,s);var l,d={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}};this.placeBox(o,-o.bbox.lw,0,!0);var c,b=o.bbox.rw-o.bbox.lw+(h.bbox.rw-h.bbox.lw)-.05,m=o.bbox.rw-o.bbox.lw-.025;if(i.mid&&(d=this.createBox(n),this.createChar(d,i.mid,a,s),b+=d.bbox.w),i.min&&e<b*i.min&&(e=b*i.min),e>b){var u,f,x=r.bbox.rw-r.bbox.lw,g=x-.05,p=i.mid?2:1;for(f=u=Math.min(Math.ceil((e-b)/(p*g)),this.maxStretchyParts),i.fillExtenders||(g=(e-b)/(p*u)),g=x-(c=u/(u+1)*(x-g)),m-=r.bbox.lw+c;p-- >0;){for(;u-- >0;)this.cloneNodeBug?(l=this.Element("span"),this.createChar(l,i.rep,a,s)):l=r.cloneNode(!0),l.bbox=r.bbox,this.placeBox(this.addBox(n,l),m,0,!0),m+=g;i.mid&&p&&(this.placeBox(d,m,0,!0),m+=d.bbox.w-c,u=f)}}else 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M=e["offset"+p[x].offset];if(M&&n>=p[x].low&&n<=p[x].high){if(p[x].remap&&p[x].remap[n])n=M+p[x].remap[n];else{if(p[x].remapOnly)break;n=n-p[x].low+M,p[x].add&&(n+=p[x].add)}e["variant"+p[x].offset]&&(e=this.FONTDATA.VARIANT[e["variant"+p[x].offset]]);break}}}if(e.remap&&e.remap[n]?(n=e.remap[n],e.remap.variant&&(e=this.FONTDATA.VARIANT[e.remap.variant])):this.FONTDATA.REMAP[n]&&!e.noRemap&&(n=this.FONTDATA.REMAP[n]),r(n)&&(e=this.FONTDATA.VARIANT[n[1]],n=n[0]),"string"!=typeof n){if(o=(h=this.lookupChar(e,n))[n],b||!this.checkFont(h,c.style)&&!o[5].img){d.length&&(this.addText(c,d),d="");var T=!!c.style.fontFamily||!!t.style.fontStyle||!!t.style.fontWeight||!h.directory||b;b=!1,c!==t&&(T=!this.checkFont(h,t.style),c=t),T&&(c=this.addElement(t,"span",{isMathJax:!0,subSpan:!0})),this.handleFont(c,h,c!==t)}d=this.handleChar(c,h,o,n,d),(o[5]||{}).space||(o[0]/1e3>t.bbox.h&&(t.bbox.h=o[0]/1e3),o[1]/1e3>t.bbox.d&&(t.bbox.d=o[1]/1e3)),t.bbox.w+o[3]/1e3<t.bbox.lw&&(t.bbox.lw=t.bbox.w+o[3]/1e3),t.bbox.w+o[4]/1e3>t.bbox.rw&&(t.bbox.rw=t.bbox.w+o[4]/1e3),t.bbox.w+=o[2]/1e3,(o[5]||{}).isUnknown&&(t.bbox.exactW=!1)}else u=(s=n+s.substr(m+1)).length,m=-1}d.length&&this.addText(c,d),t.scale&&1!==t.scale&&(t.bbox.h*=t.scale,t.bbox.d*=t.scale,t.bbox.w*=t.scale,t.bbox.lw*=t.scale,t.bbox.rw*=t.scale),i.isChar(s)&&h.skew&&h.skew[n]&&(t.bbox.skew=h.skew[n])}},checkFont:function(t,e){var i=e.fontWeight||"normal";return i.match(/^\d+$/)&&(i=parseInt(i)>=600?"bold":"normal"),t.family.replace(/'/g,"")===e.fontFamily.replace(/'/g,"")&&((t.style||"normal")===(e.fontStyle||"normal")&&(t.weight||"normal")===i||this.FontFaceBug&&""!==e.fontFamily)},handleFont:function(t,e,a){if(t.style.fontFamily=e.family,e.directory||(t.style.fontSize=Math.floor(i.config.scale/i.scale+.5)+"%"),!i.FontFaceBug||!e.isWebFont){var s=e.style||"normal",n=e.weight||"normal";("normal"!==s||a)&&(t.style.fontStyle=s),("normal"!==n||a)&&(t.style.fontWeight=n)}},handleChar:function(t,e,a,s,n){var o=a[5];if(o.space)return n.length&&this.addText(t,n),i.createShift(t,a[2]/1e3),"";if(o.img)return this.handleImg(t,e,a,s,n);if(o.isUnknown&&this.FONTDATA.DELIMITERS[s]){n.length&&this.addText(t,n);var h=t.scale;return i.createDelimiter(t,s,0,1,e),"V"===this.FONTDATA.DELIMITERS[s].dir&&(t.style.verticalAlign=this.Em(t.bbox.d),t.bbox.h+=t.bbox.d,t.bbox.d=0),t.scale=h,a[0]=1e3*t.bbox.h,a[1]=1e3*t.bbox.d,a[2]=1e3*t.bbox.w,a[3]=1e3*t.bbox.lw,a[4]=1e3*t.bbox.rw,""}if(null==o.c)if(s<=65535)o.c=String.fromCharCode(s);else{var r=s-65536;o.c=String.fromCharCode(55296+(r>>10))+String.fromCharCode(56320+(1023&r))}return i.ffFontOptimizationBug&&a[4]-a[2]>125&&(t.style.textRendering="optimizeLegibility"),o.rfix?(this.addText(t,n+o.c),i.createShift(t,o.rfix/1e3),""):a[2]||!this.msieAccentBug&&!this.combiningCharBug||n.length?n+o.c:this.combiningCharBug?(i.addElement(t,"span",{style:{marginLeft:i.Em(a[3]/1e3)}},[o.c]),""):(i.createShift(t,a[3]/1e3),i.createShift(t,(a[4]-a[3])/1e3),this.addText(t,o.c),i.createShift(t,-a[4]/1e3),"")},handleImg:function(t,e,i,a,s){return s},lookupChar:function(t,e){var a,s;if(!t.FONTS){var n=this.FONTDATA.FONTS,o=t.fonts||this.FONTDATA.VARIANT.normal.fonts;for(o instanceof Array||(o=[o]),t.fonts!=o&&(t.fonts=o),t.FONTS=[],a=0,s=o.length;a<s;a++)n[o[a]]&&(t.FONTS.push(n[o[a]]),n[o[a]].name=o[a])}for(a=0,s=t.FONTS.length;a<s;a++){var h=t.FONTS[a];if("string"==typeof h&&(delete t.FONTS,this.loadFont(h)),h[e]){if(5===h[e].length&&(h[e][5]={}),!i.allowWebFonts||h.available)return h;this.loadWebFont(h)}else this.findBlock(h,e)}return this.unknownChar(t,e)},unknownChar:function(t,a){var s=t.defaultFont||{family:i.config.undefinedFamily};return t.bold&&(s.weight="bold"),t.italic&&(s.style="italic"),s[a]||(s[a]=[800,200,500,0,500,{isUnknown:!0}]),e.signal.Post(["HTML-CSS Jax - unknown char",a,t]),s},isChar:function(t){if(1===t.length)return!0;if(2!==t.length)return!1;var e=t.charCodeAt(0);return e>=55296&&e<56319},findBlock:function(t,e){if(t.Ranges)for(var i=0,a=t.Ranges.length;i<a;i++){if(e<t.Ranges[i][0])return;if(e<=t.Ranges[i][1]){for(var s=t.Ranges[i][2],n=t.Ranges.length-1;n>=0;n--)t.Ranges[n][2]==s&&t.Ranges.splice(n,1);this.loadFont(t.directory+"/"+s+".js")}}},loadFont:function(a){var s=MathJax.Callback.Queue();s.Push(["Require",t,this.fontDir+"/"+a]),this.imgFonts&&(MathJax.isPacked||(a=a.replace(/\/([^\/]*)$/,i.imgPacked+"/$1")),s.Push(["Require",t,this.webfontDir+"/png/"+a])),e.RestartAfter(s.Push({}))},loadWebFont:function(t){t.available=t.isWebFont=!0,i.FontFaceBug&&(t.family=t.name,i.msieFontCSSBug&&(t.family+="-Web")),e.RestartAfter(this.Font.loadWebFont(t))},loadWebFontError:function(i,a){e.Startup.signal.Post("HTML-CSS Jax - disable web fonts"),i.isWebFont=!1,this.config.imageFont&&this.config.imageFont===this.fontInUse?(this.imgFonts=!0,e.Startup.signal.Post("HTML-CSS Jax - switch to image fonts"),e.Startup.signal.Post("HTML-CSS Jax - using image fonts"),l(["WebFontNotAvailable","Web-Fonts not available -- using image fonts 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o=this.data[i];o&&(!e&&o.HTMLcanStretch("Vertical")&&(n.push(o),o=o.CoreMO()||o,n[n.length-1].needsBBox=o!==this.data[i]),this.HTMLcombineBBoxes(o,s),i++)}return this.HTMLcleanBBox(s),n},HTMLcombineBBoxes:function(t,e){null==e.w&&this.HTMLemptyBBox(e);var a=t.bbox?t:t.HTMLspanElement();if(a&&a.bbox){var s=a.bbox;s.d>e.d&&(e.d=s.d),s.h>e.h&&(e.h=s.h),null!=s.D&&s.D>e.D&&(e.D=s.D),null!=s.H&&s.H>e.H&&(e.H=s.H),a.style.paddingLeft&&(e.w+=i.unEm(a.style.paddingLeft)*(a.scale||1)),e.w+s.lw<e.lw&&(e.lw=e.w+s.lw),e.w+s.rw>e.rw&&(e.rw=e.w+s.rw),e.w+=s.w,a.style.paddingRight&&(e.w+=i.unEm(a.style.paddingRight)*(a.scale||1)),s.width&&(e.width=s.width,e.minWidth=s.minWidth),s.tw&&(e.tw=s.tw),s.ic?e.ic=s.ic:delete e.ic,e.exactW&&!s.exactW&&(e.exactW=s.exactW)}},HTMLemptyBBox:function(t){return t.h=t.d=t.H=t.D=t.rw=-i.BIGDIMEN,t.w=0,t.lw=i.BIGDIMEN,t},HTMLcleanBBox:function(t){t.h===this.BIGDIMEN&&(t.h=t.d=t.H=t.D=t.w=t.rw=t.lw=0),t.D<=t.d&&delete t.D,t.H<=t.h&&delete t.H},HTMLzeroBBox:function(){return{h:0,d:0,w:0,lw:0,rw:0}},HTMLcanStretch:function(t){if(this.isEmbellished()){var e=this.Core();if(e&&e!==this)return e.HTMLcanStretch(t)}return!1},HTMLstretchH:function(t,e){return this.HTMLspanElement()},HTMLstretchV:function(t,e,i){return this.HTMLspanElement()},HTMLnotEmpty:function(t){for(;t;){if("mrow"!==t.type&&"texatom"!==t.type||t.data.length>1)return!0;t=t.data[0]}return!1},HTMLmeasureChild:function(t,e){this.data[t]?i.Measured(this.data[t].toHTML(e),e):e.bbox=this.HTMLzeroBBox()},HTMLboxChild:function(t,e){return this.data[t]||this.SetData(t,a.mrow()),this.data[t].toHTML(e)},HTMLcreateSpan:function(t){if(this.spanID){var e=this.HTMLspanElement();if(e&&(e.parentNode===t||(e.parentNode||{}).parentNode===t)){for(;e.firstChild;)e.removeChild(e.firstChild);return e.bbox=this.HTMLzeroBBox(),e.scale=1,e.isMultChar=e.HH=null,e.style.cssText="",e}}return this.href&&(t=i.addElement(t,"a",{href:this.href,isMathJax:!0})),t=i.addElement(t,"span",{className:this.type,isMathJax:!0}),i.imgHeightBug&&(t.style.display="inline-block"),this.class&&(t.className+=" "+this.class),this.spanID||(this.spanID=i.GetID()),t.id=(this.id||"MathJax-Span-"+this.spanID)+i.idPostfix,t.bbox=this.HTMLzeroBBox(),this.styles={},this.style&&(t.style.cssText=this.style,t.style.fontSize&&(this.mathsize=t.style.fontSize,t.style.fontSize=""),this.styles={border:i.getBorders(t),padding:i.getPadding(t)},this.styles.border&&(t.style.border=""),this.styles.padding&&(t.style.padding="")),this.href&&(t.parentNode.bbox=t.bbox),this.HTMLaddAttributes(t),t},HTMLaddAttributes:function(t){if(this.attrNames)for(var i=this.attrNames,s=a.nocopyAttributes,n=e.config.ignoreMMLattributes,o="mstyle"===this.type?a.math.prototype.defaults:this.defaults,h=0,r=i.length;h<r;h++){var l=i[h];0!=n[l]&&(s[l]||n[l]||null!=o[l]||void 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s=(this.styles||{}).border,n=(this.styles||{}).padding;if(e.color&&!this.mathcolor&&(e.mathcolor=e.color),e.background&&!this.mathbackground&&(e.mathbackground=e.background),e.mathcolor&&(t.style.color=e.mathcolor),e.mathbackground&&e.mathbackground!==a.COLOR.TRANSPARENT||s||n){var o=t.bbox,h=o.exact?0:1/i.em,r=0,l=0,d=t.style.paddingLeft,c=t.style.paddingRight;this.isToken&&(r=o.lw,l=o.rw-o.w),""!==d&&(r+=i.unEm(d)*(t.scale||1)),""!==c&&(l-=i.unEm(c)*(t.scale||1));var b=i.PaddingWidthBug||o.keepPadding||o.exactW?0:l-r,m=Math.max(0,i.getW(t)+b),u=o.h+o.d,f=-o.d,x=0,g=0;m>0&&(m+=2*h,r-=h),u>0&&(u+=2*h,f-=h),l=-m-r,s&&(l-=s.right,f-=s.bottom,x+=s.left,g+=s.right,o.h+=s.top,o.d+=s.bottom,o.w+=s.left+s.right,o.lw-=s.left,o.rw+=s.right),n&&(u+=n.top+n.bottom,m+=n.left+n.right,l-=n.right,f-=n.bottom,x+=n.left,g+=n.right,o.h+=n.top,o.d+=n.bottom,o.w+=n.left+n.right,o.lw-=n.left,o.rw+=n.right),g&&(t.style.paddingRight=i.Em(g));var p=i.Element("span",{id:"MathJax-Color-"+this.spanID+i.idPostfix,isMathJax:!0,style:{display:"inline-block",backgroundColor:e.mathbackground,width:i.Em(m),height:i.Em(u),verticalAlign:i.Em(f),marginLeft:i.Em(r),marginRight:i.Em(l)}});return i.setBorders(p,s),o.width&&(p.style.width=o.width,p.style.marginRight="-"+o.width),i.msieInlineBlockAlignBug&&(p.style.position="relative",p.style.width=p.style.height=0,p.style.verticalAlign=p.style.marginLeft=p.style.marginRight="",p.style.border=p.style.padding="",s&&i.msieBorderWidthBug&&(u+=s.top+s.bottom,m+=s.left+s.right),p.style.width=i.Em(x+h),i.placeBox(i.addElement(p,"span",{noAdjust:!0,isMathJax:!0,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:e.mathbackground||"transparent",width:i.Em(m),height:i.Em(u)}}),r,o.h+h),i.setBorders(p.firstChild,s)),t.parentNode.insertBefore(p,t),i.msieColorPositionBug&&(t.style.position="relative"),p}return null},HTMLremoveColor:function(){var t=document.getElementById("MathJax-Color-"+this.spanID+i.idPostfix);t&&t.parentNode.removeChild(t)},HTMLhandleSpace:function(t){if(this.hasMMLspacing()){if("mo"!==this.type)return;var e=this.getValues("scriptlevel","lspace","rspace");if(e.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var a=this.HTMLgetMu(t);e.lspace=Math.max(0,i.length2em(e.lspace,a)),e.rspace=Math.max(0,i.length2em(e.rspace,a));for(var s=this,n=this.Parent();n&&n.isEmbellished()&&n.Core()===s;)s=n,n=n.Parent(),t=s.HTMLspanElement();e.lspace&&(t.style.paddingLeft=i.Em(e.lspace)),e.rspace&&(t.style.paddingRight=i.Em(e.rspace))}}else{var o=this.texSpacing();""!==o&&(this.HTMLgetScale(),o=i.length2em(o,this.scale)/(t.scale||1)*this.mscale,t.style.paddingLeft&&(o+=i.unEm(t.style.paddingLeft)),t.style.paddingLeft=i.Em(o))}},HTMLgetScale:function(){if(this.scale)return this.scale*this.mscale;var t=1,e=this.getValues("scriptlevel","fontsize");if(e.mathsize=(this.isToken?this:this.Parent()).Get("mathsize"),this.style){var a=this.HTMLspanElement();""!=a.style.fontSize&&(e.fontsize=a.style.fontSize)}return e.fontsize&&!this.mathsize&&(e.mathsize=e.fontsize),0!==e.scriptlevel&&(e.scriptlevel>2&&(e.scriptlevel=2),t=Math.pow(this.Get("scriptsizemultiplier"),e.scriptlevel),e.scriptminsize=i.length2em(this.Get("scriptminsize")),t<e.scriptminsize&&(t=e.scriptminsize)),this.scale=t,this.mscale=i.length2em(e.mathsize),t*this.mscale},HTMLgetMu:function(t){var e=1,i=this.getValues("scriptlevel","scriptsizemultiplier");return t.scale&&1!==t.scale&&(e=1/t.scale),0!==i.scriptlevel&&(i.scriptlevel>2&&(i.scriptlevel=2),e=Math.sqrt(Math.pow(i.scriptsizemultiplier,i.scriptlevel))),e},HTMLgetVariant:function(){var t=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");if(t.hasVariant=this.Get("mathvariant",!0),t.hasVariant||(t.family=t.fontfamily,t.weight=t.fontweight,t.style=t.fontstyle),this.style){var e=this.HTMLspanElement();!t.family&&e.style.fontFamily&&(t.family=e.style.fontFamily),!t.weight&&e.style.fontWeight&&(t.weight=e.style.fontWeight),!t.style&&e.style.fontStyle&&(t.style=e.style.fontStyle)}t.weight&&t.weight.match(/^\d+$/)&&(t.weight=parseInt(t.weight)>600?"bold":"normal");var s=t.mathvariant;return this.variantForm&&(s="-"+i.fontInUse+"-variant"),t.family&&!t.hasVariant?(!t.weight&&t.mathvariant.match(/bold/)&&(t.weight="bold"),!t.style&&t.mathvariant.match(/italic/)&&(t.style="italic"),{FONTS:[],fonts:[],noRemap:!0,defaultFont:{family:t.family,style:t.style,weight:t.weight}}):("bold"===t.weight?s={normal:a.VARIANT.BOLD,italic:a.VARIANT.BOLDITALIC,fraktur:a.VARIANT.BOLDFRAKTUR,script:a.VARIANT.BOLDSCRIPT,"sans-serif":a.VARIANT.BOLDSANSSERIF,"sans-serif-italic":a.VARIANT.SANSSERIFBOLDITALIC}[s]||s:"normal"===t.weight&&(s={bold:a.VARIANT.normal,"bold-italic":a.VARIANT.ITALIC,"bold-fraktur":a.VARIANT.FRAKTUR,"bold-script":a.VARIANT.SCRIPT,"bold-sans-serif":a.VARIANT.SANSSERIF,"sans-serif-bold-italic":a.VARIANT.SANSSERIFITALIC}[s]||s),"italic"===t.style?s={normal:a.VARIANT.ITALIC,bold:a.VARIANT.BOLDITALIC,"sans-serif":a.VARIANT.SANSSERIFITALIC,"bold-sans-serif":a.VARIANT.SANSSERIFBOLDITALIC}[s]||s:"normal"===t.style&&(s={italic:a.VARIANT.NORMAL,"bold-italic":a.VARIANT.BOLD,"sans-serif-italic":a.VARIANT.SANSSERIF,"sans-serif-bold-italic":a.VARIANT.BOLDSANSSERIF}[s]||s),s 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n=i.autoloadDir+"/"+s+".js";e.RestartAfter(t.Require(n))},HTMLstretchH:function(t,e){return this.HTMLremoveColor(),this.toHTML(t,e)},HTMLstretchV:function(t,e,i){return this.HTMLremoveColor(),this.toHTML(t,e,i)}}),a.chars.Augment({toHTML:function(t,e,a,s){var n=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(a&&(n=a(n,s)),e.fontInherit){var o=Math.floor(i.config.scale/i.scale+.5)+"%";i.addElement(t,"span",{style:{"font-size":o}},[n]),e.bold&&(t.lastChild.style.fontWeight="bold"),e.italic&&(t.lastChild.style.fontStyle="italic"),t.bbox=null;var h=i.getHD(t),r=i.getW(t);t.bbox={h:h.h,d:h.d,w:r,lw:0,rw:r,exactW:!0}}else this.HTMLhandleVariant(t,e,n)}}),a.entity.Augment({toHTML:function(t,e,a,s){var n=this.toString().replace(/[\u2061-\u2064]/g,"");if(a&&(n=a(n,s)),e.fontInherit){var o=Math.floor(i.config.scale/i.scale+.5)+"%";i.addElement(t,"span",{style:{"font-size":o}},[n]),e.bold&&(t.lastChild.style.fontWeight="bold"),e.italic&&(t.lastChild.style.fontStyle="italic"),delete t.bbox;var h=i.getHD(t),r=i.getW(t);t.bbox={h:h.h,d:h.d,w:r,lw:0,rw:r,exactW:!0}}else this.HTMLhandleVariant(t,e,n)}}),a.mi.Augment({toHTML:function(t){(t=this.HTMLhandleSize(this.HTMLcreateSpan(t))).bbox=null;for(var e=this.HTMLgetVariant(),a=0,s=this.data.length;a<s;a++)this.data[a]&&this.data[a].toHTML(t,e);t.bbox||(t.bbox=this.HTMLzeroBBox());var n=this.data.join(""),o=t.bbox;return o.skew&&!i.isChar(n)&&delete o.skew,o.rw>o.w&&i.isChar(n)&&!e.noIC&&(o.ic=o.rw-o.w,i.createBlank(t,o.ic/this.mscale),o.w=o.rw),this.HTMLhandleSpace(t),this.HTMLhandleColor(t),this.HTMLhandleDir(t),t}}),a.mn.Augment({HTMLremapMinus:function(t){return t.replace(/^-/,"−")},toHTML:function(t){(t=this.HTMLhandleSize(this.HTMLcreateSpan(t))).bbox=null;for(var e=this.HTMLgetVariant(),a=this.HTMLremapMinus,s=0,n=this.data.length;s<n;s++)this.data[s]&&(this.data[s].toHTML(t,e,a),a=null);return t.bbox||(t.bbox=this.HTMLzeroBBox()),i.isChar(this.data.join(""))||delete t.bbox.skew,this.HTMLhandleSpace(t),this.HTMLhandleColor(t),this.HTMLhandleDir(t),t}}),a.mo.Augment({toHTML:function(t){if(t=this.HTMLhandleSize(this.HTMLcreateSpan(t)),0==this.data.length)return t;t.bbox=null;var e=this.data.join(""),s=this.HTMLgetVariant(),n=this.getValues("largeop","displaystyle");n.largeop&&(s=i.FONTDATA.VARIANT[n.displaystyle?"-largeOp":"-smallOp"]);var o=this.CoreParent(),h=o&&o.isa(a.msubsup)&&this!==o.data[o.base],r=h?this.remapChars:null;if(i.isChar(e)&&o&&o.isa(a.munderover)&&i.isChar(this.CoreText(o.data[o.base]))){var l=o.data[o.over],d=o.data[o.under];l&&this===l.CoreMO()&&o.Get("accent")?r=i.FONTDATA.REMAPACCENT:d&&this===d.CoreMO()&&o.Get("accentunder")&&(r=i.FONTDATA.REMAPACCENTUNDER)}h&&e.match(/['`"\u00B4\u2032-\u2037\u2057]/)&&(s=i.FONTDATA.VARIANT["-"+i.fontInUse+"-variant"]);for(var c=0,b=this.data.length;c<b;c++)this.data[c]&&this.data[c].toHTML(t,s,this.remap,r);if(t.bbox||(t.bbox=this.HTMLzeroBBox()),i.isChar(e)||delete t.bbox.skew,i.AccentBug&&0===t.bbox.w&&i.isChar(e)&&t.firstChild&&(t.firstChild.nodeValue+=i.NBSP,i.createSpace(t,0,0,-t.offsetWidth/i.em)),n.largeop){var m=i.TeX.axis_height*this.scale*this.mscale,u=(t.bbox.h-t.bbox.d)/2-m;i.safariVerticalAlignBug&&"IMG"===t.lastChild.nodeName?t.lastChild.style.verticalAlign=i.Em(i.unEm(t.lastChild.style.verticalAlign||0)/i.em-u/t.scale):i.konquerorVerticalAlignBug&&"IMG"===t.lastChild.nodeName?(t.style.position="relative",t.lastChild.style.position="relative",t.lastChild.style.top=i.Em(u/t.scale)):t.style.verticalAlign=i.Em(-u/t.scale),t.bbox.h-=u,t.bbox.d+=u,t.bbox.rw>t.bbox.w&&(t.bbox.ic=t.bbox.rw-t.bbox.w,i.createBlank(t,t.bbox.ic/this.mscale),t.bbox.w=t.bbox.rw)}return this.HTMLhandleSpace(t),this.HTMLhandleColor(t),this.HTMLhandleDir(t),t},HTMLcanStretch:function(t){if(!this.Get("stretchy"))return!1;var e=this.data.join("");if(e.length>1)return!1;var s=this.CoreParent();if(s&&s.isa(a.munderover)&&i.isChar(this.CoreText(s.data[s.base]))){var n=s.data[s.over],o=s.data[s.under];n&&this===n.CoreMO()&&s.Get("accent")?e=i.FONTDATA.REMAPACCENT[e]||e:o&&this===o.CoreMO()&&s.Get("accentunder")&&(e=i.FONTDATA.REMAPACCENTUNDER[e]||e)}var h=(e=i.FONTDATA.DELIMITERS[e.charCodeAt(0)])&&e.dir===t.substr(0,1);return this.forceStretch=h&&(this.Get("minsize",!0)||this.Get("maxsize",!0)),h},HTMLstretchV:function(t,e,a){this.HTMLremoveColor();var s,n=this.getValues("symmetric","maxsize","minsize"),o=this.HTMLspanElement(),h=this.HTMLgetMu(o),r=this.HTMLgetScale(),l=i.TeX.axis_height*r;return s=n.symmetric?2*Math.max(e-l,a+l):e+a,n.maxsize=i.length2em(n.maxsize,h,o.bbox.h+o.bbox.d),n.minsize=i.length2em(n.minsize,h,o.bbox.h+o.bbox.d),(s=Math.max(n.minsize,Math.min(n.maxsize,s)))!=n.minsize&&(s=[Math.max(s*i.TeX.delimiterfactor/1e3,s-i.TeX.delimitershortfall),s]),o=this.HTMLcreateSpan(t),i.createDelimiter(o,this.data.join("").charCodeAt(0),s,r),s=n.symmetric?(o.bbox.h+o.bbox.d)/2+l:(o.bbox.h+o.bbox.d)*e/(e+a),i.positionDelimiter(o,s),this.HTMLhandleSpace(o),this.HTMLhandleColor(o),o},HTMLstretchH:function(t,e){this.HTMLremoveColor();var s=this.getValues("maxsize","minsize","mathvariant","fontweight");("bold"===s.fontweight||parseInt(s.fontweight)>=600)&&!this.Get("mathvariant",!0)&&(s.mathvariant=a.VARIANT.BOLD);var n=this.HTMLspanElement(),o=this.HTMLgetMu(n),h=n.scale;return s.maxsize=i.length2em(s.maxsize,o,n.bbox.w),s.minsize=i.length2em(s.minsize,o,n.bbox.w),e=Math.max(s.minsize,Math.min(s.maxsize,e)),n=this.HTMLcreateSpan(t),i.createDelimiter(n,this.data.join("").charCodeAt(0),e,h,s.mathvariant),this.HTMLhandleSpace(n),this.HTMLhandleColor(n),n}}),a.mtext.Augment({toHTML:function(t){t=this.HTMLhandleSize(this.HTMLcreateSpan(t));var e=this.HTMLgetVariant();if(i.config.mtextFontInherit||"merror"===this.Parent().type){var a=this.Get("mathvariant");"monospace"===a?t.className+=" MJX-monospace":a.match(/sans-serif/)&&(t.className+=" MJX-sans-serif"),e={bold:e.bold,italic:e.italic,fontInherit:!0}}for(var s=0,n=this.data.length;s<n;s++)this.data[s]&&this.data[s].toHTML(t,e);return t.bbox||(t.bbox=this.HTMLzeroBBox()),i.isChar(this.data.join(""))||delete t.bbox.skew,this.HTMLhandleSpace(t),this.HTMLhandleColor(t),this.HTMLhandleDir(t),t}}),a.merror.Augment({toHTML:function(t){var e=MathJax.HTML.addElement(t,"span",{style:{display:"inline-block"}});t=this.SUPER(arguments).toHTML.call(this,e);var a=i.getHD(e),s=i.getW(e);return e.bbox={h:a.h,d:a.d,w:s,lw:0,rw:s,exactW:!0},e.id=t.id,t.id=null,e}}),a.ms.Augment({toHTML:a.mbase.HTMLautoload}),a.mglyph.Augment({toHTML:a.mbase.HTMLautoload}),a.mspace.Augment({toHTML:function(t){t=this.HTMLcreateSpan(t);var e=this.getValues("height","depth","width"),a=this.HTMLgetMu(t);this.HTMLgetScale(),e.mathbackground=this.mathbackground,this.background&&!this.mathbackground&&(e.mathbackground=this.background);var s=i.length2em(e.height,a)*this.mscale,n=i.length2em(e.depth,a)*this.mscale,o=i.length2em(e.width,a)*this.mscale;return i.createSpace(t,s,n,o,e.mathbackground,!0),t}}),a.mphantom.Augment({toHTML:function(t,e,a){if(t=this.HTMLcreateSpan(t),null!=this.data[0]){var s=this.data[0].toHTML(t);null!=a?i.Remeasured(this.data[0].HTMLstretchV(t,e,a),t):null!=e?i.Remeasured(this.data[0].HTMLstretchH(t,e),t):s=i.Measured(s,t),t.bbox={w:s.bbox.w,h:s.bbox.h,d:s.bbox.d,lw:0,rw:0,exactW:!0};for(var n=0,o=t.childNodes.length;n<o;n++)t.childNodes[n].style.visibility="hidden"}return this.HTMLhandleSpace(t),this.HTMLhandleColor(t),t},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV}),a.mpadded.Augment({toHTML:function(t,e,a){if(t=this.HTMLcreateSpan(t),null!=this.data[0]){var s=i.createStack(t,!0),n=i.createBox(s),o=this.data[0].toHTML(n);null!=a?i.Remeasured(this.data[0].HTMLstretchV(n,e,a),n):null!=e?i.Remeasured(this.data[0].HTMLstretchH(n,e),n):i.Measured(o,n);var h=this.getValues("height","depth","width","lspace","voffset"),r=0,l=0,d=this.HTMLgetMu(t);this.HTMLgetScale(),h.lspace&&(r=this.HTMLlength2em(n,h.lspace,d)),h.voffset&&(l=this.HTMLlength2em(n,h.voffset,d)),i.placeBox(n,r,l),r/=this.mscale,l/=this.mscale,t.bbox={h:n.bbox.h,d:n.bbox.d,w:n.bbox.w,exactW:!0,lw:n.bbox.lw+r,rw:n.bbox.rw+r,H:Math.max(null==n.bbox.H?-i.BIGDIMEN:n.bbox.H+l,n.bbox.h+l),D:Math.max(null==n.bbox.D?-i.BIGDIMEN:n.bbox.D-l,n.bbox.d-l)},""!==h.height&&(t.bbox.h=this.HTMLlength2em(n,h.height,d,"h",0)),""!==h.depth&&(t.bbox.d=this.HTMLlength2em(n,h.depth,d,"d",0)),""!==h.width&&(t.bbox.w=this.HTMLlength2em(n,h.width,d,"w",0)),t.bbox.H<=t.bbox.h&&delete t.bbox.H,t.bbox.D<=t.bbox.d&&delete t.bbox.D;var c=/^\s*(\d+(\.\d*)?|\.\d+)\s*(pt|em|ex|mu|px|pc|in|mm|cm)\s*$/;t.bbox.exact=!!(this.data[0]&&0==this.data[0].data.length||c.exec(h.height)||c.exec(h.width)||c.exec(h.depth)),i.setStackWidth(s,t.bbox.w)}return this.HTMLhandleSpace(t),this.HTMLhandleColor(t),t},HTMLlength2em:function(t,e,a,s,n){null==n&&(n=-i.BIGDIMEN);var o=String(e).match(/width|height|depth/),h=o?t.bbox[o[0].charAt(0)]:s?t.bbox[s]:0,r=i.length2em(e,a,h/this.mscale)*this.mscale;return s&&String(e).match(/^\s*[-+]/)?Math.max(n,t.bbox[s]+r):r},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV}),a.mrow.Augment({HTMLlineBreaks:function(t){return!!this.parent.linebreakContainer&&(i.config.linebreaks.automatic&&t.bbox.w>i.linebreakWidth||this.hasNewline())},HTMLstretchH:function(t,e){this.HTMLremoveColor();var i=this.HTMLspanElement();return this.data[this.core].HTMLstretchH(i,e),this.HTMLcomputeBBox(i,!0),this.HTMLhandleColor(i),i},HTMLstretchV:function(t,e,i){this.HTMLremoveColor();var a=this.HTMLspanElement();return this.data[this.core].HTMLstretchV(a,e,i),this.HTMLcomputeBBox(a,!0),this.HTMLhandleColor(a),a}}),a.mstyle.Augment({toHTML:function(t,e,i){if(t=this.HTMLcreateSpan(t),null!=this.data[0]){var a=this.data[0].toHTML(t);null!=i?this.data[0].HTMLstretchV(t,e,i):null!=e&&this.data[0].HTMLstretchH(t,e),t.bbox=a.bbox}return this.HTMLhandleSpace(t),this.HTMLhandleColor(t),t},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV}),a.mfrac.Augment({toHTML:function(t){t=this.HTMLcreateSpan(t);var e=i.createStack(t),a=i.createBox(e),s=i.createBox(e);i.MeasureSpans([this.HTMLboxChild(0,a),this.HTMLboxChild(1,s)]);var n=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled"),o=this.HTMLgetScale(),h=n.displaystyle,r=i.TeX.axis_height*o;if(n.bevelled){var l=h?.4:.15,d=Math.max(a.bbox.h+a.bbox.d,s.bbox.h+s.bbox.d)+2*l,c=i.createBox(e);i.createDelimiter(c,47,d),i.placeBox(a,0,(a.bbox.d-a.bbox.h)/2+r+l),i.placeBox(c,a.bbox.w-l/2,(c.bbox.d-c.bbox.h)/2+r),i.placeBox(s,a.bbox.w+c.bbox.w-l,(s.bbox.d-s.bbox.h)/2+r-l)}else{var b,m,u,f,x=Math.max(a.bbox.w,s.bbox.w),g=i.thickness2em(n.linethickness,this.scale)*this.mscale,p=i.TeX.min_rule_thickness/this.em;if(h?(u=i.TeX.num1,f=i.TeX.denom1):(u=0===g?i.TeX.num3:i.TeX.num2,f=i.TeX.denom2),u*=o,f*=o,0===g)b=Math.max((h?7:3)*i.TeX.rule_thickness,2*p),(m=u-a.bbox.d-(s.bbox.h-f))<b&&(u+=(b-m)/2,f+=(b-m)/2);else{b=Math.max((h?2:0)*p+g,g/2+1.5*p),(m=u-a.bbox.d-(r+g/2))<b&&(u+=b-m),(m=r-g/2-(s.bbox.h-f))<b&&(f+=b-m);var M=i.createBox(e);i.createRule(M,g,0,x+2*g),i.placeBox(M,0,r-g/2)}i.alignBox(a,n.numalign,u,0,!0),i.alignBox(s,n.denomalign,-f,0,!0)}return this.HTMLhandleSpace(t),this.HTMLhandleColor(t),t},HTMLcanStretch:function(t){return!1},HTMLhandleSpace:function(t){if(!this.texWithDelims){var e=i.TeX.nulldelimiterspace*this.mscale,a=t.childNodes[i.msiePaddingWidthBug?1:0].style;a.marginLeft=a.marginRight=i.Em(e),t.bbox.w+=2*e,t.bbox.rw+=2*e}this.SUPER(arguments).HTMLhandleSpace.call(this,t)}}),a.msqrt.Augment({toHTML:function(t){t=this.HTMLcreateSpan(t);var e,a,s,n,o=i.createStack(t),h=i.createBox(o),r=i.createBox(o),l=i.createBox(o),d=this.HTMLgetScale(),c=i.TeX.rule_thickness*d;e=this.Get("displaystyle")?i.TeX.x_height*d:c,a=Math.max(c+e/4,1.5*i.TeX.min_rule_thickness/this.em);var b=this.HTMLboxChild(0,h);s=b.bbox.h+b.bbox.d+a+c,i.createDelimiter(l,8730,s,d),i.MeasureSpans([b,l]),n=b.bbox.w;var m=0;(l.isMultiChar||i.AdjustSurd&&i.imgFonts)&&(l.bbox.w*=.95),l.bbox.h+l.bbox.d>s&&(a=(l.bbox.h+l.bbox.d-(s-c))/2);var u=i.FONTDATA.DELIMITERS[i.FONTDATA.RULECHAR];return!u||n<(u.HW[0]||[0])[0]*d||d<.75?(i.createRule(r,0,c,n),r.bbox.h=-c):i.createDelimiter(r,i.FONTDATA.RULECHAR,n,d),a=(s=b.bbox.h+a+c)*i.rfuzz,l.isMultiChar&&(a=i.rfuzz),m=this.HTMLaddRoot(o,l,m,l.bbox.h+l.bbox.d-s,d),i.placeBox(l,m,s-l.bbox.h),i.placeBox(r,m+l.bbox.w,s-r.bbox.h+a),i.placeBox(h,m+l.bbox.w,0),this.HTMLhandleSpace(t),this.HTMLhandleColor(t),t},HTMLaddRoot:function(t,e,i,a,s){return i}}),a.mroot.Augment({toHTML:a.msqrt.prototype.toHTML,HTMLaddRoot:function(t,e,a,s,n){var o=i.createBox(t);if(this.data[1]){var h=this.data[1].toHTML(o);h.style.paddingRight=h.style.paddingLeft="",i.Measured(h,o)}else o.bbox=this.HTMLzeroBBox();var r=this.HTMLrootHeight(e.bbox.h+e.bbox.d,n,o)-s,l=Math.min(o.bbox.w,o.bbox.rw);return a=Math.max(l,e.offset),i.placeBox(o,a-l,r),a-e.offset},HTMLrootHeight:function(t,e,i){return.45*(t-.9*e)+.6*e+Math.max(0,i.bbox.d-.075)}}),a.mfenced.Augment({toHTML:function(t){t=this.HTMLcreateSpan(t),this.data.open&&this.data.open.toHTML(t),null!=this.data[0]&&this.data[0].toHTML(t);for(var e=1,i=this.data.length;e<i;e++)this.data[e]&&(this.data["sep"+e]&&this.data["sep"+e].toHTML(t),this.data[e].toHTML(t));this.data.close&&this.data.close.toHTML(t);var a=this.HTMLcomputeBBox(t),s=t.bbox.h,n=t.bbox.d;for(e=0,i=a.length;e<i;e++)a[e].HTMLstretchV(t,s,n);return a.length&&this.HTMLcomputeBBox(t,!0),this.HTMLhandleSpace(t),this.HTMLhandleColor(t),t},HTMLcomputeBBox:function(t,e){var i=t.bbox={},a=[];this.HTMLcheckStretchy(this.data.open,i,a,e),this.HTMLcheckStretchy(this.data[0],i,a,e);for(var s=1,n=this.data.length;s<n;s++)this.data[s]&&(this.HTMLcheckStretchy(this.data["sep"+s],i,a,e),this.HTMLcheckStretchy(this.data[s],i,a,e));return this.HTMLcheckStretchy(this.data.close,i,a,e),this.HTMLcleanBBox(i),a},HTMLcheckStretchy:function(t,e,i,a){t&&(!a&&t.HTMLcanStretch("Vertical")&&(i.push(t),t=t.CoreMO()||t),this.HTMLcombineBBoxes(t,e))}}),a.menclose.Augment({toHTML:a.mbase.HTMLautoload}),a.maction.Augment({toHTML:a.mbase.HTMLautoload}),a.semantics.Augment({toHTML:function(t,e,i){if(t=this.HTMLcreateSpan(t),null!=this.data[0]){var a=this.data[0].toHTML(t);null!=i?this.data[0].HTMLstretchV(t,e,i):null!=e&&this.data[0].HTMLstretchH(t,e),t.bbox=a.bbox}return this.HTMLhandleSpace(t),t},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV}),a.munderover.Augment({toHTML:function(t,e,s){var n=this.getValues("displaystyle","accent","accentunder","align"),o=this.data[this.base];if(!n.displaystyle&&null!=o&&(o.movablelimits||o.CoreMO().Get("movablelimits")))return a.msubsup.prototype.toHTML.call(this,t);t=this.HTMLcreateSpan(t);var h,r,l,d=this.HTMLgetScale(),c=i.createStack(t),b=[],m=[],u=[];for(r=0,l=this.data.length;r<l;r++)null!=this.data[r]&&(h=b[r]=i.createBox(c),m[r]=this.data[r].toHTML(h),r==this.base?(null!=s?this.data[this.base].HTMLstretchV(h,e,s):null!=e&&this.data[this.base].HTMLstretchH(h,e),u[r]=(null!=s||null==e)&&this.data[r].HTMLcanStretch("Horizontal"),this.data[this.over]&&n.accent&&(m[r].bbox.h=Math.max(m[r].bbox.h,d*i.TeX.x_height))):(u[r]=this.data[r].HTMLcanStretch("Horizontal"),m[r].style.paddingLeft=m[r].style.paddingRight=""));i.MeasureSpans(m);var f=-i.BIGDIMEN,x=f;for(r=0,l=this.data.length;r<l;r++)this.data[r]&&(b[r].bbox.w>x&&(x=b[r].bbox.w),!u[r]&&x>f&&(f=x));for(null==s&&null!=e?f=e:f==-i.BIGDIMEN&&(f=x),r=x=0,l=this.data.length;r<l;r++)this.data[r]&&(h=b[r],u[r]&&(h.bbox=this.data[r].HTMLstretchH(h,f).bbox,r!==this.base&&(m[r].style.paddingLeft=m[r].style.paddingRight="")),h.bbox.w>x&&(x=h.bbox.w));var g,p,M,T,H,L,S=i.TeX.rule_thickness*this.mscale,w=i.FONTDATA.TeX_factor,y=0;for((o=b[this.base]||{bbox:this.HTMLzeroBBox()}).bbox.ic&&(y=1.3*o.bbox.ic+.05),r=0,l=this.data.length;r<l;r++)if(null!=this.data[r]){h=b[r],H=i.TeX.big_op_spacing5*d;var v=r!=this.base&&n[this.ACCENTS[r]];v&&h.bbox.w<=1/i.em+1e-4&&(h.bbox.w=h.bbox.rw-h.bbox.lw,h.bbox.noclip=!0,h.bbox.lw&&h.insertBefore(i.createSpace(h.parentNode,0,0,-h.bbox.lw),h.firstChild),i.createBlank(h,0,0,h.bbox.rw+.1)),g={left:0,center:(x-h.bbox.w)/2,right:x-h.bbox.w}[n.align],p=0,r==this.over?(v?(L=Math.max(S*d*w,2.5/this.em),H=0,o.bbox.skew&&(g+=o.bbox.skew,t.bbox.skew=o.bbox.skew,g+h.bbox.w>x&&(t.bbox.skew+=(x-h.bbox.w-g)/2))):(M=i.TeX.big_op_spacing1*d*w,T=i.TeX.big_op_spacing3*d*w,L=Math.max(M,T-Math.max(0,h.bbox.d))),L=Math.max(L,1.5/this.em),g+=y/2,p=o.bbox.h+h.bbox.d+L,h.bbox.h+=H):r==this.under&&(v?(L=3*S*d*w,H=0):(M=i.TeX.big_op_spacing2*d*w,T=i.TeX.big_op_spacing4*d*w,L=Math.max(M,T-h.bbox.h)),L=Math.max(L,1.5/this.em),g-=y/2,p=-(o.bbox.d+h.bbox.h+L),h.bbox.d+=H),i.placeBox(h,g,p)}return this.HTMLhandleSpace(t),this.HTMLhandleColor(t),t},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV}),a.msubsup.Augment({toHTML:function(t,e,a){t=this.HTMLcreateSpan(t);var s,n=this.HTMLgetScale(),o=this.HTMLgetMu(t),h=i.createStack(t),r=[],l=i.createBox(h);this.data[this.base]?(r.push(this.data[this.base].toHTML(l)),null!=a?this.data[this.base].HTMLstretchV(l,e,a):null!=e&&this.data[this.base].HTMLstretchH(l,e)):l.bbox=this.HTMLzeroBBox();var d,c,b=i.TeX.x_height*n,m=i.TeX.scriptspace*n*.75;this.HTMLnotEmpty(this.data[this.sup])&&(d=i.createBox(h),r.push(this.data[this.sup].toHTML(d))),this.HTMLnotEmpty(this.data[this.sub])&&(c=i.createBox(h),r.push(this.data[this.sub].toHTML(c))),i.MeasureSpans(r),d&&(d.bbox.w+=m,d.bbox.rw=Math.max(d.bbox.w,d.bbox.rw)),c&&(c.bbox.w+=m,c.bbox.rw=Math.max(c.bbox.w,c.bbox.rw)),i.placeBox(l,0,0);var u=n;d?u=this.data[this.sup].HTMLgetScale():c&&(u=this.data[this.sub].HTMLgetScale());var f,x=i.TeX.sup_drop*u,g=i.TeX.sub_drop*u,p=l.bbox.h-x,M=l.bbox.d+g,T=0;l.bbox.ic&&(l.bbox.w-=l.bbox.ic,T=1.3*l.bbox.ic+.05),!this.data[this.base]||null!=e||null!=a||"mi"!==this.data[this.base].type&&"mo"!==this.data[this.base].type||i.isChar(this.data[this.base].data.join(""))&&1===r[0].scale&&!this.data[this.base].Get("largeop")&&(p=M=0);var H=this.getValues("subscriptshift","superscriptshift");if(H.subscriptshift=""===H.subscriptshift?0:i.length2em(H.subscriptshift,o),H.superscriptshift=""===H.superscriptshift?0:i.length2em(H.superscriptshift,o),d)if(c){M=Math.max(M,i.TeX.sub2*n);var L=i.TeX.rule_thickness*n;p-d.bbox.d-(c.bbox.h-M)<3*L&&(M=3*L-p+d.bbox.d+c.bbox.h,(x=.8*b-(p-d.bbox.d))>0&&(p+=x,M-=x)),i.placeBox(d,l.bbox.w+T,Math.max(p,H.superscriptshift)),i.placeBox(c,l.bbox.w,-Math.max(M,H.subscriptshift))}else s=this.getValues("displaystyle","texprimestyle"),f=i.TeX[s.displaystyle?"sup1":s.texprimestyle?"sup3":"sup2"],p=Math.max(p,f*n,d.bbox.d+1/4*b,H.superscriptshift),i.placeBox(d,l.bbox.w+T,p,d.bbox);else c&&(M=Math.max(M,i.TeX.sub1*n,c.bbox.h-.8*b,H.subscriptshift),i.placeBox(c,l.bbox.w,-M,c.bbox));return this.HTMLhandleSpace(t),this.HTMLhandleColor(t),t},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV}),a.mmultiscripts.Augment({toHTML:a.mbase.HTMLautoload}),a.mtable.Augment({toHTML:a.mbase.HTMLautoload}),a["annotation-xml"].Augment({toHTML:a.mbase.HTMLautoload}),a.annotation.Augment({toHTML:function(t){return this.HTMLcreateSpan(t)}}),a.math.Augment({toHTML:function(t,s,n){var o,h,r,l,d=t;if(n&&n!==i.PHASE.I)t=t.firstChild.firstChild,this.href&&(t=t.firstChild),"relative"!==(o=t.firstChild).style.position&&(o=o.nextSibling),r=(h=o.firstChild).firstChild;else{var c=i.addElement(t,"nobr",{isMathJax:!0});t=this.HTMLcreateSpan(c);var b=this.Get("alttext");b&&!t.getAttribute("aria-label")&&t.setAttribute("aria-label",b),o=i.createStack(t),h=i.createBox(o),o.style.fontSize=c.parentNode.style.fontSize,c.parentNode.style.fontSize="",null!=this.data[0]&&(a.mbase.prototype.displayAlign=e.config.displayAlign,a.mbase.prototype.displayIndent=e.config.displayIndent,String(e.config.displayIndent).match(/^0($|[a-z%])/i)&&(a.mbase.prototype.displayIndent="0"),(r=this.data[0].toHTML(h)).bbox.exactW=!1)}if(l=n&&n!==i.PHASE.II?r:i.Measured(r,h),!n||n===i.PHASE.III){i.placeBox(h,0,0);var m=l.bbox.w;m=Math.abs(m)<.006?0:Math.max(0,Math.round(m*this.em)+.25),t.style.width=i.EmRounded(m/i.outerEm),t.style.display="inline-block";var u=1/i.em,f=i.em/i.outerEm;i.em/=f,t.bbox.h*=f,t.bbox.d*=f,t.bbox.w*=f,t.bbox.lw*=f,t.bbox.rw*=f,t.bbox.H&&(t.bbox.H*=f),t.bbox.D&&(t.bbox.D*=f),l&&null!=l.bbox.width&&(t.style.minWidth=l.bbox.minWidth||t.style.width,t.style.width=l.bbox.width,h.style.width=o.style.width="100%",d.className+=" 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T=parseFloat(x.style.marginLeft||"0")+p,H=parseFloat(x.style.marginRight||"0")-p;x.style.marginLeft=i.Em(T),x.style.marginRight=i.Em(H+("right"===g.indentalign?t.bbox.w+p-t.bbox.w:0)),i.msieColorBug&&"right"===g.indentalign&&(parseFloat(x.style.marginLeft)>0&&(MathJax.HTML.addElement(x.parentNode,"span").style.marginLeft=i.Em(H+Math.min(0,t.bbox.w+p)),x.nextSibling.style.marginRight="0em"),x.nextSibling.style.marginLeft="0em",x.style.marginRight=x.style.marginLeft="0em")}}}return t},HTMLspanElement:a.mbase.prototype.HTMLspanElement}),a.TeXAtom.Augment({toHTML:function(t,e,s){if(t=this.HTMLcreateSpan(t),null!=this.data[0])if(this.texClass===a.TEXCLASS.VCENTER){var n=i.createStack(t),o=i.createBox(n),h=this.data[0].toHTML(o);null!=s?i.Remeasured(this.data[0].HTMLstretchV(o,e,s),o):null!=e?i.Remeasured(this.data[0].HTMLstretchH(o,e),o):i.Measured(h,o);var r=i.TeX.axis_height*this.HTMLgetScale();i.placeBox(o,0,r-(o.bbox.h+o.bbox.d)/2+o.bbox.d)}else{var l=this.data[0].toHTML(t,e,s);null!=s?l=this.data[0].HTMLstretchV(o,e,s):null!=e&&(l=this.data[0].HTMLstretchH(o,e)),t.bbox=l.bbox}return this.HTMLhandleSpace(t),this.HTMLhandleColor(t),t},HTMLstretchH:a.mbase.HTMLstretchH,HTMLstretchV:a.mbase.HTMLstretchV}),e.Register.StartupHook("onLoad",(function(){setTimeout(MathJax.Callback(["loadComplete",i,"jax.js"]),0)}))})),e.Register.StartupHook("End Config",(function(){e.Browser.Select({MSIE:function(t){var e=document.documentMode||0,a=t.versionAtLeast("7.0"),s=t.versionAtLeast("8.0")&&e>7,n="BackCompat"===document.compatMode;e<9&&(i.config.styles[".MathJax .MathJax_HitBox"]["background-color"]="white",i.config.styles[".MathJax .MathJax_HitBox"].opacity=0,i.config.styles[".MathJax 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