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e=document.documentMode||0,i=t.versionAtLeast("8.0");l.msieBorderWidthBug="BackCompat"===document.compatMode,l.msieEventBug=t.isIE9,l.msieAlignBug=!i||e<8,e<9&&(d.LEFTBUTTON=1)},Safari:function(t){l.safariContextMenuBug=!0},Opera:function(t){l.operaPositionBug=!0},Konqueror:function(t){l.noContextMenuBug=!0}}),l.topImg=l.msieAlignBug?e.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):e.Element("span",{style:{width:0,height:0,display:"inline-block"}}),l.operaPositionBug&&(l.topImg.style.border="1px solid"),l.config=u=t.CombineConfig("MathEvents",u),a.Queue(t.Register.StartupHook("End Config",{}),[function(){var t=u.styles[".MathJax_Hover_Frame"];t.border=u.frame.bwidth+"px solid "+u.frame.bcolor+" ! important",t["box-shadow"]=t["-webkit-box-shadow"]=t["-moz-box-shadow"]=t["-khtml-box-shadow"]="0px 0px "+u.frame.hwidth+" "+u.frame.hcolor}],["getImages",c],["Styles",i,u.styles],["Post",t.Startup.signal,"MathEvents 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h=MathJax.Extension.MathZoom={version:"2.7.9",settings:t.config.menuSettings,scrollSize:18,HandleEvent:function(t,e,i){return!(!h.settings.CTRL||t.ctrlKey)||!(!h.settings.ALT||t.altKey)||!(!h.settings.CMD||t.metaKey)||!(!h.settings.Shift||t.shiftKey)||!h[e]||h[e](t,i)},Click:function(t,e){if("Click"===this.settings.zoom)return this.Zoom(t,e)},DblClick:function(t,e){if("Double-Click"===this.settings.zoom||"DoubleClick"===this.settings.zoom)return this.Zoom(t,e)},Hover:function(t,e){return"Hover"===this.settings.zoom&&(this.Zoom(t,e),!0)},Zoom:function(i,a){this.Remove(),o.ClearHoverTimer(),r.ClearSelection();var n=MathJax.OutputJax[a.jaxID],h=n.getJaxFromMath(a);h.hover&&o.UnHover(h);var u=this.findContainer(a),d=Math.floor(.85*u.clientWidth),c=Math.max(document.body.clientHeight,document.documentElement.clientHeight);"visible"!==this.getOverflow(u)&&(c=Math.min(u.clientHeight,c)),c=Math.floor(.85*c);var 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i=this.Resize(),a=i.x,n=i.y,s=e.mW;t.style.display="";var o=-s-Math.floor((t.offsetWidth-s)/2),r=e.Y;t.style.left=Math.max(o,10-a)+"px",t.style.top=Math.max(r,10-n)+"px",h.msiePositionBug||h.SetWH()},Resize:function(t){h.onresize&&h.onresize(t);var e=document.getElementById("MathJax_ZoomFrame"),i=document.getElementById("MathJax_ZoomOverlay"),a=h.getXY(e),n=h.findContainer(e);if("visible"!==h.getOverflow(n)){i.scroll_parent=n;var s=h.getXY(n);a.x-=s.x,a.y-=s.y,s=h.getBorder(n),a.x-=s.x,a.y-=s.y}return i.style.left=-a.x+"px",i.style.top=-a.y+"px",h.msiePositionBug?setTimeout(h.SetWH,0):h.SetWH(),a},SetWH:function(){var t=document.getElementById("MathJax_ZoomOverlay");if(t){t.style.display="none";var 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a=document.getElementById("MathJax_ZoomFrame");if(a){var n=MathJax.OutputJax[a.previousSibling.jaxID].getJaxFromMath(a.previousSibling);if(t.signal.Post(["math unzoomed",n]),a.parentNode.removeChild(a),(a=document.getElementById("MathJax_ZoomTracker"))&&a.parentNode.removeChild(a),h.operaRefreshBug){var o=e.addElement(document.body,"div",{style:{position:"fixed",left:0,top:0,width:"100%",height:"100%",backgroundColor:"white",opacity:0},id:"MathJax_OperaDiv"});document.body.removeChild(o)}window.removeEventListener?removeEventListener("resize",h.Resize,!1):window.detachEvent?detachEvent("onresize",h.Resize):(window.onresize=h.onresize,delete h.onresize)}return s(i)}};t.Browser.Select({MSIE:function(t){var e=document.documentMode||0,i=e>=9;h.msiePositionBug=!i,h.msieSizeBug=t.versionAtLeast("7.0")&&(!document.documentMode||7===e||8===e),h.msieZIndexBug=e<=7,h.msieInlineBlockAlignBug=e<=7,h.msieTrapEventBug=!window.addEventListener,"BackCompat"===document.compatMode&&(h.scrollSize=52),i&&delete l.styles["#MathJax_Zoom"].filter},Opera:function(t){h.operaPositionBug=!0,h.operaRefreshBug=!0}}),h.topImg=h.msieInlineBlockAlignBug?e.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):e.Element("span",{style:{width:0,height:0,display:"inline-block"}}),(h.operaPositionBug||h.msieTopBug)&&(h.topImg.style.border="1px solid"),MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",i,l.styles],["Post",t.Startup.signal,"MathZoom Ready"],["loadComplete",i,"[MathJax]/extensions/MathZoom.js"])}(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML),function(t,e,i,a,n){var 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Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics."))}else document.body.appendChild(this.EmExSpan),this.defaultEx=this.EmExSpan.firstChild.offsetWidth/60,this.defaultMEx=this.EmExSpan.lastChild.offsetWidth/60,document.body.removeChild(this.EmExSpan)},preTranslate:function(t){var e,i,n,s,o,r,l,u,d,c,m=t.jax[this.id],p=m.length;for(e=0;e<p;e++)if((i=m[e]).parentNode&&(this.initialized||this.InitializeMML(),(n=i.previousSibling)&&"MathJax_MathML"===n.className&&n.parentNode.removeChild(n),l=i.MathJax.elementJax)){r=l.root,l.NativeMML={};var f="block"===r.Get("display")?"div":"span";s=a.Element(f,{className:"MathJax_MathML",id:l.inputID+"-Frame"},[["span",{className:"MathJax_MathContainer",isMathJax:!0,jaxID:this.id,style:{position:"relative",display:"inline-block","white-space":"nowrap"}},[["span",{isMathJax:!0,style:{display:"inline-block"}}]]]]),i.parentNode.insertBefore(s,i),h||i.parentNode.insertBefore(this.EmExSpan.cloneNode(!0),i)}for(e=0;e<p;e++)(i=m[e]).parentNode&&(l=i.MathJax.elementJax)&&(h?c=100:(u=(o=i.previousSibling).firstChild.offsetWidth/60,d=o.lastChild.offsetWidth/60,0!==u&&"NaN"!==u||(u=this.defaultEx,d=this.defaultMEx),c=this.config.matchFontHeight&&d>1?u/d:1,c=Math.floor(Math.max(this.config.minScaleAdjust/100,c)*this.config.scale),l.NativeMML.ex=u,l.NativeMML.mex=d),l.NativeMML.fontSize=c+"%",l.NativeMML.scale=c/100);if(!h)for(e=0;e<p;e++)(i=m[e]).parentNode&&i.MathJax.elementJax&&i.parentNode.removeChild(i.previousSibling)},Translate:function(t){if(t.parentNode){var i=t.MathJax.elementJax,a=i.root,n=document.getElementById(i.inputID+"-Frame");if(n){var r=n.firstChild,l=r.firstChild;this.ex=i.NativeMML.ex||this.defaultEx,this.scale=i.NativeMML.scale||1,1!==this.scale&&(n.style.fontSize=i.NativeMML.fontSize);try{a.toNativeMML(l,i)}catch(t){if(t.restart)for(;l.firstChild;)l.removeChild(l.firstChild);throw t}if(h)if(r.addEventListener)for(var u in this.MSIE9events)this.MSIE9events.hasOwnProperty(u)&&r.addEventListener(u,this.MSIE9event,!0);else!(null!=this.config.showMathMenuMSIE?this:e).config.showMathMenuMSIE||this.settings.mpContext||this.settings.mpMouse?(r.style.position="",l.firstChild.onmousedown=this.MSIEaltMenu):this.MSIEoverlay(r);else r.oncontextmenu=s.Menu,r.onmouseover=s.Mouseover,r.onmouseout=s.Mouseout,r.onmousedown=s.Mousedown,r.onclick=s.Click,r.ondblclick=s.DblClick,r.onkeydown=s.Keydown,r.tabIndex=e.getTabOrder(i),e.Browser.noContextMenu&&(r.ontouchstart=o.start,r.ontouchend=o.end)}}},postTranslate:function(t){if(this.forceReflow){var e=(document.styleSheets||[])[0]||{};e.disabled=!0,e.disabled=!1}},Remove:function(t){var e=t.SourceElement();e&&(e=e.previousSibling)&&e.className.match(/MathJax_MathML/)&&e.parentNode.removeChild(e)},MMLnamespace:"http://www.w3.org/1998/Math/MathML",isFullWidth:function(t){if(t){var e=t.getAttribute("width")||(String(t.getAttribute("style")).match(/(?:^| )width: *([^; ]*)/)||[])[1];if(e)return!!e.match(/%/);if(t.nodeName.match(/^(semantics|math|mstyle)$/))e=this.isFullWidth(t.firstChild);else if("mrow"===t.nodeName.toLowerCase())for(var i=0,a=t.childNodes.length;i<a&&!e;i++)e=this.isFullWidth(t.childNodes[i]);if(e){var n="width:100%; "+(t.getAttribute("style")||"");t.setAttribute("style",n.replace(/ +$/,""))}return e}},MSIEoverlay:function(t){var i=t.firstChild;"span"===i.nodeName.toLowerCase()&&(i=i.firstChild);var n=this.getHoverBBox(null,i,{});a.addElement(t,"span",{style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{isMathJax:!0,className:"MathJax_MathPlayer_Overlay",style:{display:"inline-block",position:"absolute",left:r.Px(-n.w),top:r.Px(-n.h-(n.y||0)-1),width:r.Px(n.w),height:r.Px(n.h+n.d),cursor:"pointer","background-color":"white",filter:"alpha(opacity=0)"}}]]),e.Insert(t,{msieMath:i,onmousedown:this.MSIEevent,oncontextmenu:this.MSIEevent,onclick:this.MSIEevent,onmouseup:this.MSIEevent,onmousemove:this.MSIEevent,ondblclick:this.MSIEevent,onmouseover:this.MSIEevent,onmouseout:this.MSIEevent})},MSIEevents:{mousedown:"Mousedown",contextmenu:"ContextMenu",click:"Click",mouseup:"Mouseup",mousemove:"Mousemove",dblclick:"DblClick",mouseover:"Mouseover",mouseout:"Mouseout"},MSIEevent:function(){var e=window.event,i=t.MSIEevents[e.type];return(!t[i]||!1!==t[i](e,this))&&(!l||!1!==l.HandleEvent(e,i,this))&&("MathJax_MathPlayer_Overlay"===e.srcElement.className&&this.msieMath.fireEvent&&("ContextMenu"!==i&&"Mouseover"!==i&&"Mouseout"!==i||this.msieMath.fireEvent("on"+e.type,e)),s.False(e))},MSIEaltMenu:function(){for(var t=this.parentNode.parentNode;!t.jaxID;)t=t.parentNode;s.AltContextMenu(window.event,t)},MSIE9events:{contextmenu:"Menu",click:"Click",dblclick:"DblClick",mouseup:"False",mouseover:"Mouseover",mouseout:"Mouseout"},MSIE9event:function(e){if("contextmenu"===e.type&&t.settings.mpContext)return!0;if("mouseup"===e.type&&t.settings.mpMouse)return!0;if("click"===e.type&&t.settings.mpContext)return s.AltContextMenu(e,this);var i=t.MSIE9events[e.type];return s[i].call(this,e)},getJaxFromMath:function(t){t=t.parentNode;do{t=t.nextSibling}while(t&&"script"!==t.nodeName.toLowerCase());return e.getJaxFor(t)},getHoverSpan:function(t,e){return e.firstChild},getHoverBBox:function(t,e,i){return s.getBBox(e.parentNode)},Zoom:function(e,i,a,n,o){e.root.toNativeMML(i),this.msieIE8HeightBug&&(i.style.position="absolute"),t.widthBug&&(i.style.width=i.parentNode.style.width=""),i.parentNode.style.width.match(/%$/)&&(i.parentNode.style.minWidth=Math.ceil(3*o/4)+"px");var r=a.offsetWidth||a.scrollWidth,l=a.offsetHeight||a.scrollHeight,h=i.offsetWidth,u=i.offsetHeight;if(t.widthBug||i.style.width.match(/%/)){var d=i.firstChild.firstChild.scrollWidth;d>h&&(h=d,i.parentNode.style.width=i.style.minWidth=h+"px")}return this.msieIE8HeightBug&&(i.style.position=""),{Y:-s.getBBox(i.parentNode).h,mW:r,mH:l,zW:h,zH:u}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em",veryverythinmathspace:".0556em",verythinmathspace:".1111em",thinmathspace:".1667em",mediummathspace:".2222em",thickmathspace:".2778em",verythickmathspace:".3333em",veryverythickmathspace:".3889em"}}),e.Register.StartupHook("mml Jax Ready",(function(){if((n=MathJax.ElementJax.mml).mbase.Augment({toNativeMML:function(t){var e=this.NativeMMLelement(this.type);this.NativeMMLattributes(e);for(var i=0,a=this.data.length;i<a;i++)this.data[i]?this.data[i].toNativeMML(e):e.appendChild(this.NativeMMLelement("mrow"));t.appendChild(e)},NativeMMLattributes:function(t){var e="mstyle"===this.type?n.math.prototype.defaults:this.defaults,i=this.attrNames||n.copyAttributeNames,a=n.skipAttributes,s=n.copyAttributes;if(!this.attrNames)for(var o in e)a[o]||s[o]||!e.hasOwnProperty(o)||null!=this[o]&&this[o]!==e[o]&&this.Get(o,null,1)!==this[o]&&t.setAttribute(o,this.NativeMMLattribute(this[o]));for(var r=0,l=i.length;r<l;r++)if(1!==s[i[r]]||e.hasOwnProperty(i[r])){var h=(this.attr||{})[i[r]];null==h&&(h=this[i[r]]),null!=h&&t.setAttribute(i[r],this.NativeMMLattribute(h))}this.NativeMMLclass(t)},NativeMMLclass:function(t){var e=[];if(this.class&&e.push(this.class),this.isa(n.TeXAtom)){var i=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];i&&(e.push("MJX-TeXAtom-"+i),"OP"!==i||this.movablelimits||e.push("MJX-fixedlimits"))}this.mathvariant&&this.NativeMMLvariants[this.mathvariant]&&e.push("MJX"+this.mathvariant),this.variantForm&&e.push("MJX-variant"),e.length&&t.setAttribute("class",e.join(" "))},NativeMMLattribute:function(e){return e=String(e),t.NAMEDSPACE[e]?e=t.NAMEDSPACE[e]:e.match(/^\s*(([-+])?(\d+(\.\d*)?|\.\d+))\s*mu\s*$/)?e=(RegExp.$2||"")+(1/18*RegExp.$3).toFixed(3).replace(/\.?0+$/,"")+"em":this.NativeMMLvariants[e]&&(e=this.NativeMMLvariants[e]),e},NativeMMLvariants:{"-tex-caligraphic":n.VARIANT.SCRIPT,"-tex-caligraphic-bold":n.VARIANT.BOLDSCRIPT,"-tex-oldstyle":n.VARIANT.NORMAL,"-tex-oldstyle-bold":n.VARIANT.BOLD,"-tex-mathit":n.VARIANT.ITALIC},NativeMMLelement:function(i){var a=e.Browser.mpNamespace?document.createElement("m:"+i):document.createElementNS?document.createElementNS(t.MMLnamespace,i):document.createElement(i);return a.isMathJax=!0,a}}),n.mrow.Augment({toNativeMML:function(e){var i,a;if(this.inferred&&this.parent.inferRow)for(i=0,a=this.data.length;i<a;i++)this.data[i]?this.data[i].toNativeMML(e):e.appendChild(this.NativeMMLelement("mrow"));else if(t.stretchyMoBug&&(this.open||this.close)){var n=this.NativeMMLelement("mfenced");this.NativeMMLattributes(n),i=0,a=this.data.length,this.open&&(n.setAttribute("open",this.open),i++),this.close&&(n.setAttribute("close",this.close),a--);var s=n;for(a-i+1>1&&(s=this.NativeMMLelement("mrow"),e.appendChild(n),e=n);i<a;i++)this.data[i]?this.data[i].toNativeMML(s):s.appendChild(this.NativeMMLelement("mrow"));e.appendChild(s)}else this.SUPER(arguments).toNativeMML.call(this,e)}}),n.msubsup.Augment({toNativeMML:function(t){var e=this.type;null==this.data[this.sup]&&(e="msub"),null==this.data[this.sub]&&(e="msup");var i=this.NativeMMLelement(e);this.NativeMMLattributes(i),this.data[0]&&delete this.data[0].inferred;for(var a=0,n=this.data.length;a<n;a++)this.data[a]&&this.data[a].toNativeMML(i);t.appendChild(i)}}),n.munderover.Augment({toNativeMML:function(t){var e=this.type,i=this.data[this.base];i&&i.isa(n.TeXAtom)&&i.movablelimits&&!i.Get("displaystyle")?(e="msubsup",null==this.data[this.under]&&(e="msup"),null==this.data[this.over]&&(e="msub")):(null==this.data[this.under]&&(e="mover"),null==this.data[this.over]&&(e="munder"));var a=this.NativeMMLelement(e);this.NativeMMLattributes(a),this.data[0]&&delete this.data[0].inferred;for(var s=0,o=this.data.length;s<o;s++)this.data[s]&&this.data[s].toNativeMML(a);t.appendChild(a)}}),!h){var s=e.SplitList;n.mtable.Augment({toNativeMML:function(i){var a,o;if(t.tableSpacingBug){var r=this.getValues("rowspacing","columnspacing");this.nMMLtopPadding=s("0px "+r.rowspacing),this.nMMLleftPadding=s("0px "+r.columnspacing);var l=this.nMMLtopPadding,h=l.length;for(a=0,o=this.data.length;a<o;a++)this.data[a]&&(this.data[a].nMMLtopPadding=l[a<h?a:h-1])}if(t.tableLabelBug)for(a=0,o=this.data.length;a<o;a++)if(this.data[a]&&this.data[a].isa(n.mlabeledtr)){var u=e.config.displayAlign.charAt(0),d=this.Get("side").charAt(0);this.nMMLhasLabels=!0,this.nMMLlaMatch=u===d,this.nMMLforceWidth="c"===u||!!(this.width||"").match("%");break}if(this.width&&this.ffTableWidthBug){var c=(this.style||"").replace(/;\s*$/,"").split(";");""===c[0]&&c.shift(),c.push("width:"+this.width),this.style=c.join(";")}if(this.SUPER(arguments).toNativeMML.call(this,i),this.nMMLhasLabels){var m=i.firstChild;if(this.nMMLforceWidth||"r"!==d){var p=("l"!==u?1:0)+("l"===d?1:0);if(p){var f={columnalign:"left",columnwidth:"auto",columnspacing:"0px",columnlines:"none"};for(var M in f)if(f.hasOwnProperty(M)&&this[M]){var g=[f[M],f[M]].slice(2-p).join(" ")+" ";m.setAttribute(M,g+m.getAttribute(M))}}}!this.nMMLforceWidth&&this.nMMLlaMatch||m.setAttribute("width","100%")}}}),n.mtr.Augment({toNativeMML:function(i){this.SUPER(arguments).toNativeMML.call(this,i);var a=i.lastChild;if(t.tableSpacingBug)for(var n=this.parent.nMMLleftPadding,s=n.length,o=a.firstChild,r=0;o;o=o.nextSibling,r++)d(o,this.nMMLtopPadding,n[r<s?r:s-1]);if(t.tableLabelBug){var l=this.parent.nMMLforceWidth,h=this.parent.Get("side").charAt(0),c=e.config.displayAlign.charAt(0);this.parent.nMMLhasLabels&&a.firstChild&&((l||"r"!==h)&&(u("Left",a.firstChild),"l"!==c&&a.insertBefore(this.NativeMMLelement("mtd"),a.firstChild).setAttribute("style","padding:0"),"l"===h&&a.insertBefore(this.NativeMMLelement("mtd"),a.firstChild).setAttribute("style","padding:0")),(l||"l"!==h)&&u("Right",a.lastChild))}}}),n.mlabeledtr.Augment({toNativeMML:function(i){var a=this.NativeMMLelement("mtr");this.NativeMMLattributes(a);for(var n=1,s=this.data.length;n<s;n++)this.data[n]?this.data[n].toNativeMML(a):a.appendChild(this.NativeMMLelement("mtd"));if(t.tableSpacingBug){var o=this.parent.nMMLleftPadding,r=o.length;n=0;for(var l=a.firstChild;l;l=l.nextSibling,n++)d(l,this.nMMLtopPadding,o[n<r?n:r-1])}if(t.tableLabelBug&&this.data[0]){var h=this.parent.Get("side").charAt(0),c=e.config.displayAlign.charAt(0),m=e.config.displayIndent;this.data[0].toNativeMML(a);var p=a.lastChild,f=p;h===c?(p.setAttribute("style","width:"+m),p.setAttribute("columnalign",e.config.displayAlign)):((f=this.NativeMMLelement("mpadded")).setAttribute("style","width:0"),f.setAttribute("width","0px"),f.appendChild(p.firstChild),p.appendChild(f)),u("",p),a.removeChild(p);var M=100,g=this.parent.nMMLforceWidth;(this.parent.width||"").match(/%/)&&(M-=parseFloat(this.parent.width));var x=M;(g||"r"!==h)&&(u("Left",a.firstChild),"l"!==c&&("c"===c&&(x/=2),M-=x,a.insertBefore(this.NativeMMLelement("mtd"),a.firstChild).setAttribute("style","padding:0;width:"+x+"%")),"l"===h&&a.insertBefore(p,a.firstChild)),(g||"l"!==h)&&(u("Right",a.lastChild),"r"!==c&&a.appendChild(this.NativeMMLelement("mtd")).setAttribute("style","padding:0;width:"+M+"%"),"r"===h&&(h!==c&&f.setAttribute("lspace","-1width"),a.appendChild(p)))}i.appendChild(a)}}),n.mtd.Augment({toNativeMML:function(e){var i=e.appendChild(this.NativeMMLelement(this.type));this.NativeMMLattributes(i),t.mtdWidthBug&&(t.adjustWidths.push(i),i=i.appendChild(this.NativeMMLelement("mrow")));for(var a=0,n=this.data.length;a<n;a++)this.data[a]?this.data[a].toNativeMML(i):i.appendChild(this.NativeMMLelement("mrow"))}}),n.mspace.Augment({toNativeMML:function(e){if(this.SUPER(arguments).toNativeMML.call(this,e),t.spaceWidthBug&&this.width){var i=e.lastChild,a=i.getAttribute("width"),n=(i.getAttribute("style")||"").replace(/;?\s*/,"; ");i.setAttribute("style",n+"width:"+a)}}}),n.mn.Augment({NativeMMLremapMinus:function(t){return t.replace(/^-/,"−")},toNativeMML:function(t){var e=this.NativeMMLelement(this.type);this.NativeMMLattributes(e);for(var i=this.NativeMMLremapMinus,a=0,n=this.data.length;a<n;a++)this.data[a]&&(this.data[a].toNativeMML(e,i),i=null);t.appendChild(e)}});var o=i.fileURL(MathJax.OutputJax.fontDir+"/HTML-CSS/TeX/otf");t.Augment({config:{styles:{'[class="MJX-tex-oldstyle"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB"},'[class="MJX-tex-oldstyle-bold"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB","font-weight":"bold"},'[class="MJX-tex-caligraphic"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB"},'[class="MJX-tex-caligraphic-bold"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB","font-weight":"bold"},"@font-face /*1*/":{"font-family":"MathJax_Caligraphic-WEB",src:"url('"+o+"/MathJax_Caligraphic-Regular.otf')"},"@font-face /*2*/":{"font-family":"MathJax_Caligraphic-WEB","font-weight":"bold",src:"url('"+o+"/MathJax_Caligraphic-Bold.otf')"}}}}),this.handlesVariants||t.Augment({config:{styles:{'[mathvariant="double-struck"]':{"font-family":"MathJax_AMS, MathJax_AMS-WEB"},'[mathvariant="script"]':{"font-family":"MathJax_Script, MathJax_Script-WEB"},'[mathvariant="fraktur"]':{"font-family":"MathJax_Fraktur, MathJax_Fraktur-WEB"},'[mathvariant="bold-script"]':{"font-family":"MathJax_Script, MathJax_Caligraphic-WEB","font-weight":"bold"},'[mathvariant="bold-fraktur"]':{"font-family":"MathJax_Fraktur, MathJax_Fraktur-WEB","font-weight":"bold"},'[mathvariant="monospace"]':{"font-family":"monospace"},'[mathvariant="sans-serif"]':{"font-family":"sans-serif"},'[mathvariant="bold-sans-serif"]':{"font-family":"sans-serif","font-weight":"bold"},'[mathvariant="sans-serif-italic"]':{"font-family":"sans-serif","font-style":"italic"},'[mathvariant="sans-serif-bold-italic"]':{"font-family":"sans-serif","font-style":"italic","font-weight":"bold"},"@font-face /*3*/":{"font-family":"MathJax_AMS-WEB",src:"url('"+o+"/MathJax_AMS-Regular.otf')"},"@font-face /*4*/":{"font-family":"MathJax_Script-WEB",src:"url('"+o+"/MathJax_Script-Regular.otf')"},"@font-face /*5*/":{"font-family":"MathJax_Fraktur-WEB",src:"url('"+o+"/MathJax_Fraktur-Regular.otf')"},"@font-face /*6*/":{"font-family":"MathJax_Fraktur-WEB","font-weight":"bold",src:"url('"+o+"/MathJax_Fraktur-Bold.otf')"}}}})}n.math.Augment({toNativeMML:function(i,a){var n,s,o=this.NativeMMLelement(this.type),r=o,l=a?MathJax.InputJax[a.inputJax].annotationEncoding:null;if(t.adjustWidths=[],o.setAttribute("xmlns",t.MMLnamespace),this.NativeMMLattributes(o),t.widthBug&&(o=o.appendChild(this.NativeMMLelement("mrow"))),l){(o=o.appendChild(this.NativeMMLelement("semantics"))).appendChild(this.NativeMMLelement("mrow"));var h=o.appendChild(this.NativeMMLelement("annotation"));h.appendChild(document.createTextNode(a.originalText)),h.setAttribute("encoding",l),o=o.firstChild}for(n=0,s=this.data.length;n<s;n++)this.data[n]?this.data[n].toNativeMML(o):o.appendChild(this.NativeMMLelement("mrow"));var u=(this.data[0]||{data:[]}).data[0]||{};u.nMMLhasLabels&&(!u.nMMLforceWidth&&u.nMMLlaMatch||(o.setAttribute("style","width:100%"),l&&o.parentNode.setAttribute("style","width:100%")),u.nMMLlaMatch&&"div"===i.parentNode.parentNode.nodeName.toLowerCase()&&i.parentNode.parentNode.style.setProperty("margin-"+e.config.displayAlign,"0px","important"));var d=t.isFullWidth(r);if(d&&(i.style.width=i.parentNode.style.width="100%"),i.appendChild(r),t.widthBug&&!d&&(i.style.width=(r.firstChild.scrollWidth/t.ex/t.scale).toFixed(3)+"ex",a&&(a.NativeMML.scrollWidth=r.firstChild.scrollWidth)),t.adjustWidths.length){var c=[];for(n=0,s=t.adjustWidths.length;n<s;n++){var m=(o=t.adjustWidths[n]).getAttribute("style")||"";if(!m.match(/(^|;)\s*min-width:/)){var p=o.firstChild.scrollWidth;c.push(p),p=(p/t.ex).toFixed(3)+"ex",m=m.replace(/;?\s*$/,"; "),o.setAttribute("style",m+"min-width:"+p)}}a||(a=e.getJaxFor(i)),a&&(a.NativeMML.mtds=c),r.MathJaxMtds=t.adjustWidths,t.adjustWidths=[]}}}),n.mfenced.Augment({toNativeMML:function(i){if(t.mfencedBug){var a,n,s,o=e.Browser.isOpera,r=this.getValues("open","close","separators");if(r.open=r.open.replace(/^\s+/,"").replace(/\s+$/,""),r.close=r.close.replace(/^\s+/,"").replace(/\s+$/,""),r.separators=r.separators.replace(/\s+/g,"").split(""),0==r.separators.length)r.separators=null;else if(r.separators.length<this.data.length-1){var l=r.separators[r.separators.length-1];for(a=this.data.length-1-r.separators.length;a>0;a--)r.separators.push(l)}var h=this.NativeMMLelement(o?this.type:"mrow");for(this.NativeMMLattributes(h),h.removeAttribute("separators"),o?(h.setAttribute("open",r.open),h.setAttribute("close",r.close),this.data.length>1&&(i.appendChild(h),i=h,h=this.NativeMMLelement("mrow"))):(h.removeAttribute("open"),h.removeAttribute("close")),o||((s=this.NativeMMLelement("mo")).setAttribute("fence","true"),s.textContent=r.open,h.appendChild(s)),a=0,n=this.data.length;a<n;a++)r.separators&&a>0&&((s=this.NativeMMLelement("mo")).setAttribute("separator","true"),s.textContent=r.separators[a-1],h.appendChild(s)),this.data[a]?this.data[a].toNativeMML(h):h.appendChild(this.NativeMMLelement("mrow"));o||((s=this.NativeMMLelement("mo")).setAttribute("fence","true"),s.textContent=r.close,h.appendChild(s)),i.appendChild(h)}else this.SUPER(arguments).toNativeMML.call(this,i)}}),n.TeXAtom.Augment({toNativeMML:function(t){var e=this.NativeMMLelement("mrow");this.NativeMMLattributes(e),this.data[0].toNativeMML(e),t.appendChild(e)}}),n.chars.Augment({toNativeMML:function(t,e){var i=this.toString();e&&(i=e(i)),t.appendChild(document.createTextNode(i))}}),n.entity.Augment({toNativeMML:function(t){t.appendChild(document.createTextNode(this.toString()))}}),n.xml.Augment({toNativeMML:function(t){for(var e=0,i=this.data.length;e<i;e++)t.appendChild(this.data[e].cloneNode(!0))}}),n.mi.Augment({toNativeMML:function(e){if(this.SUPER(arguments).toNativeMML.call(this,e),t.miItalicBug&&this.Get("mathvariant")===n.VARIANT.NORMAL){var i=e.lastChild;i.setAttribute("mathvariant",n.VARIANT.NORMAL)}}}),n.mo.Augment({toNativeMML:function(e){if(this.SUPER(arguments).toNativeMML.call(this,e),t.webkitMoSpacingBug){var i=0,n=0,s=this.parent;if(s&&"mrow"===s.type&&(s.inferred||!s.isEmbellished())){var o=this.getValues("lspace","rspace");i=o.lspace,n=o.rspace,t.NAMEDSPACE[i]&&(i=t.NAMEDSPACE[i]),t.NAMEDSPACE[n]&&(n=t.NAMEDSPACE[n])}var r=e.lastChild,l=a.Element("span");l.style.cssText=r.getAttribute("style")||"",l.style.setProperty("-webkit-margin-start",i),l.style.setProperty("-webkit-margin-end",n),r.setAttribute("style",l.style.cssText)}}}),n.mmultiscripts.Augment({toNativeMML:function(e){if(t.mmultiscriptsBug&&0!==this.data.length){var i=this.NativeMMLelement("mrow");this.NativeMMLattributes(i),this.data[0]?this.data[0].toNativeMML(i):i.appendChild(this.NativeMMLelement("mrow"));var a,n,s=i.removeChild(i.lastChild),o=this.data.length;for(a=1;a<o&&"mprescripts"!==this.data[a].type;a+=2)(n=this.NativeMMLelement("msubsup")).appendChild(s),this.data[a]?this.data[a].toNativeMML(n):n.appendChild(this.NativeMMLelement("mrow")),a+1<o&&this.data[a+1]?this.data[a+1].toNativeMML(n):n.appendChild(this.NativeMMLelement("mrow")),s=n;for(i.appendChild(s),a++;a<o;a+=2)(n=this.NativeMMLelement("msubsup")).appendChild(this.NativeMMLelement("mrow")),this.data[a]?this.data[a].toNativeMML(n):n.appendChild(this.NativeMMLelement("mrow")),a+1<o&&this.data[a+1]?this.data[a+1].toNativeMML(n):n.appendChild(this.NativeMMLelement("mrow")),i.insertBefore(n,s);e.appendChild(i)}else this.SUPER(arguments).toNativeMML.call(this,e)}}),e.Register.StartupHook("TeX mathchoice Ready",(function(){n.TeXmathchoice.Augment({toNativeMML:function(t){this.Core().toNativeMML(t)}})})),setTimeout(MathJax.Callback(["loadComplete",t,"jax.js"]),0)})),e.Browser.Select({MSIE:function(e){var i=document.documentMode||0;t.msieIE8HeightBug=8===i},Opera:function(e){t.stretchyMoBug=!0,t.tableLabelBug=!0,t.mfencedBug=!0,t.miBug=!0,t.mmultiscriptsBug=!0},Firefox:function(e){var i=e.versionAtLeast("29.0");t.ffTableWidthBug=!e.versionAtLeast("13.0"),t.forceReflow=!i,t.widthBug=!i,t.mtdWidthBug=!0,t.handlesVariants=i,t.spaceWidthBug=!e.versionAtLeast("20.0"),t.tableSpacingBug=!e.versionAtLeast("33.0"),t.tableLabelBug=!0,t.mfencedBug=!0},Chrome:function(e){t.tableSpacingBug=!0,t.tableLabelBug=!0,t.mfencedBug=!0},Safari:function(e){t.tableSpacingBug=!0,t.tableLabelBug=!0,t.mfencedBug=!0,t.miItalicBug=!0,t.webkitMoSpacingBug=!0,t.spaceWidthBug=!0,t.mmultiscriptsBug=!0}}),e.Register.StartupHook("End Cookie",(function(){"None"!==e.config.menuSettings.zoom&&i.Require("[MathJax]/extensions/MathZoom.js")}))}(MathJax.OutputJax.NativeMML,MathJax.Hub,MathJax.Ajax,MathJax.HTML),function(t,e,i){var a,n,s,o,r=e.Browser.isMobile,l=MathJax.Object.isArray,h=function(){var t=[].slice.call(arguments,0);return t[0][0]=["HTML-CSS",t[0][0]],MathJax.Message.Set.apply(MathJax.Message,t)},u=MathJax.Object.Subclass({timeout:1e3*(r?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,n=t.length;a<n;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),n=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]&&(n=!1)),null===n&&(this.div.offsetWidth!=a[3]||this.div.offsetHeight!=a[4])))if(!t.noStyleChar&&i.FONTDATA&&i.FONTDATA.hasStyleChar)for(var s=0,o=this.testSize.length;s<o;s++)this.testStyleChar(t,this.testSize[s])&&(n=!0,o=0);else n=!0;return i.safariTextNodeBug?this.div.innerHTML="":this.text.nodeValue="",n},styleChar:"",versionChar:"",compChar:"",testStyleChar:function(t,e){var a=3+(t.weight?2:0)+(t.style?4:0),n="",s=0,o=this.div.style.fontSize;this.div.style.fontSize=e,i.msieItalicWidthBug&&"italic"===t.style&&(this.text.nodeValue=n=this.compChar,s=this.div.offsetWidth),i.safariTextNodeBug?this.div.innerHTML=this.compChar+n:this.text.nodeValue=this.compChar+n;var r=this.div.offsetWidth-s;i.safariTextNodeBug?this.div.innerHTML=this.styleChar+n:this.text.nodeValue=this.styleChar+n;var l=Math.floor((this.div.offsetWidth-s)/r+.5);return l===a&&(i.safariTextNodeBug?this.div.innerHTML=this.versionChar+n:this.text.nodeValue=this.versionChar+n,t.version=Math.floor((this.div.offsetWidth-s)/r+1.5)/2),this.div.style.fontSize=o,l===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 n=this.div.offsetWidth,s=this.div.offsetHeight,o=1,r=this.comparisonFont.length;o<r;o++)if(this.div.style.fontFamily=this.comparisonFont[o],this.div.offsetWidth!=a)return[a,this.div.offsetWidth,o,n,s];return null},loadWebFont:function(a){e.Startup.signal.Post("HTML-CSS Jax - Web-Font "+i.fontInUse+"/"+a.directory);var n=h(["LoadWebFont","Loading web-font %1",i.fontInUse+"/"+a.directory]),s=MathJax.Callback({}),o=MathJax.Callback(["loadComplete",this,a,n,s]);return t.timer.start(t,[this.checkWebFont,a,o],0,this.timeout),s},loadComplete:function(a,n,s,o){if(MathJax.Message.Clear(n),o===t.STATUS.OK)return this.webFontLoaded=!0,void s();if(this.loadError(a),e.Browser.isFirefox&&i.allowWebFonts){var r=document.location.protocol+"//"+document.location.hostname;""!=document.location.port&&(r+=":"+document.location.port),r+="/",t.fileURL(i.webfontDir).substr(0,r.length)!==r&&this.firefoxFontError(a)}this.webFontLoaded?s():i.loadWebFontError(a,s)},loadError:function(t){h(["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){h(["FirefoxCantLoadWebFont","Firefox can't load web fonts from a remote host"],null,3e3),e.Startup.signal.Post("HTML-CSS Jax - Firefox web 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.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:(d?"block":"table-cell")+"!important",width:(d?"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:(d?"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:(d?"block":"table-cell")+"!important",width:(d?"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=u(),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,l(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"))):(h(["CantFindFontUsing","Can't find a valid font using 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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,r,l,h,u,d,c,m,p,f,M,g=t.jax[this.id],x=g.length,b=!1,v=this.config.linebreaks.automatic,T=this.config.linebreaks.width;for(v?((b=null!=T.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/))?T=T.replace(/\s*container\s*/,""):f=this.defaultWidth,""===T&&(T="100%")):f=1e5,i=0;i<x;i++)(o=g[i]).parentNode&&((r=o.previousSibling)&&String(r.className).match(/^MathJax(_Display)?( MathJax_Process(ing|ed))?$/)&&r.parentNode.removeChild(r),o.MathJax.preview&&(o.MathJax.preview.style.display="none"),(d=o.MathJax.elementJax)&&(d.HTMLCSS={display:"block"===d.root.Get("display")},l=h=this.Element("span",{className:"MathJax",id:d.inputID+"-Frame",isMathJax:!0,jaxID:this.id,oncontextmenu:n.Menu,onmousedown:n.Mousedown,onmouseover:n.Mouseover,onmouseout:n.Mouseout,onmousemove:n.Mousemove,onclick:n.Click,ondblclick:n.DblClick,onkeydown:n.Keydown,tabIndex:e.getTabOrder(d)}),e.Browser.noContextMenu&&(l.ontouchstart=s.start,l.ontouchend=s.end),d.HTMLCSS.display?(h=this.Element("div",{className:"MathJax_Display"})).appendChild(l):this.msieDisappearingBug&&(l.style.display="inline-block"),h.className+=" MathJax_Processing",o.parentNode.insertBefore(h,o),d.HTMLCSS.span=l,d.HTMLCSS.div=h,(u=this.TestSpan.cloneNode(!0)).className+=" mjx-test-"+(d.HTMLCSS.display?"display":"inline"),o.parentNode.insertBefore(u,o)));var y=[];for(i=0;i<x;i++)(o=g[i]).parentNode&&(h=(u=o.previousSibling).previousSibling,(d=o.MathJax.elementJax)&&(c=u.childNodes[1].offsetHeight/60,m=u.childNodes[2].offsetHeight/60,M=Math.max(0,d.HTMLCSS.display?u.lastChild.offsetWidth-1:u.lastChild.offsetLeft-u.firstChild.offsetLeft-2),0!==c&&"NaN"!==c||(y.push(h),d.HTMLCSS.isHidden=!0,c=this.defaultEx,m=this.defaultEm,M=this.defaultWidth),0!==M||d.HTMLCSS.display||(M=this.defaultWidth),b&&(f=M),p=this.config.matchFontHeight?c/this.TeX.x_height/m:1,p=Math.floor(Math.max(this.config.minScaleAdjust/100,p)*this.config.scale),d.HTMLCSS.scale=p/100,d.HTMLCSS.fontSize=p+"%",d.HTMLCSS.em=d.HTMLCSS.outerEm=m,this.em=m*p/100,d.HTMLCSS.ex=c,d.HTMLCSS.cwidth=M/this.em,d.HTMLCSS.lineWidth=v?this.length2em(T,1,f/this.em):1e6));for(i=0,a=y.length;i<a;i++)this.hiddenDiv.appendChild(y[i]),this.addElement(this.hiddenDiv,"br");for(i=0;i<x;i++)(o=g[i]).parentNode&&(d=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,n=a.root,s=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(n,o),this.savePreview(t);try{n.setTeXclass(),n.toHTML(o,s,this.PHASE.I)}catch(e){if(e.restart)for(;o.firstChild;)o.removeChild(o.firstChild);throw this.restorePreview(t),e}return this.restorePreview(t),s.className=s.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,n,s,o,r=t.jax[this.id];for(s=t.HTMLCSSlast,o=t.HTMLCSSeqn;s<o;s++)if((a=r[s])&&a.parentNode&&a.MathJax.elementJax){var l=(a.MathJax.elementJax.HTMLCSS||{}).div;l&&(l.className=l.className.split(/ /)[0]),a.MathJax.preview&&(a.MathJax.preview.innerHTML="")}for(s=t.HTMLCSSlast,o=t.HTMLCSSeqn;s<o;s++)(a=r[s])&&a.parentNode&&a.MathJax.elementJax&&(n=a.MathJax.elementJax,this.getMetrics(n),n.HTMLCSS.span&&n.HTMLCSS.div&&n.root.toHTML(n.HTMLCSS.span,n.HTMLCSS.div,this.PHASE.II));for(s=t.HTMLCSSlast,o=t.HTMLCSSeqn;s<o;s++)(a=r[s])&&a.parentNode&&a.MathJax.elementJax&&(n=a.MathJax.elementJax,this.getMetrics(n),n.HTMLCSS.span&&n.HTMLCSS.div&&(n.root.toHTML(n.HTMLCSS.span,n.HTMLCSS.div,this.PHASE.III),n.HTMLCSS.isHidden&&a.parentNode.insertBefore(n.HTMLCSS.div,a),delete n.HTMLCSS.span,delete n.HTMLCSS.div,a.MathJax.state=n.STATE.PROCESSED,e.signal.Post(["New Math",a.MathJax.elementJax.inputID])));if(this.forceReflow){var h=(document.styleSheets||[])[0]||{};h.disabled=!0,h.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,n=t.HTMLCSS.outerEm,s={w:a.w*n,h:a.h*n,d:a.d*n};return a.width&&(s.width=a.width),s},Zoom:function(t,s,o,r,l){s.className="MathJax",s.style.fontSize=t.HTMLCSS.fontSize;var h=s.appendChild(this.TestSpan.cloneNode(!0)),u=h.childNodes[2].offsetHeight/60;this.em=a.mbase.prototype.em=u,this.outerEm=u/t.HTMLCSS.scale,h.parentNode.removeChild(h),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(s,s),this.idPostfix="",this.zoomScale=1;var d=t.root.HTMLspanElement().bbox,c=d.width;if(c){d.tw&&(r=d.tw*u),d.w*u<r&&(r=d.w*u),s.style.width=Math.floor(r-1.5*i.em)+"px",s.style.display="inline-block";for(var m=(t.root.id||"MathJax-Span-"+t.root.spanID)+"-zoom",p=document.getElementById(m).firstChild;p&&p.style.width!==c;)p=p.nextSibling;if(p){var f=p.offsetWidth;p.style.width="100%",f>r&&(s.style.width=f+100+"px")}}p=s.firstChild.firstChild.style,null!=d.H&&d.H>d.h&&(p.marginTop=i.Em(d.H-Math.max(d.h,i.FONTDATA.lineH))),null!=d.D&&d.D>d.d&&(p.marginBottom=i.Em(d.D-Math.max(d.d,i.FONTDATA.lineD))),d.lw<0&&(p.paddingLeft=i.Em(-d.lw)),d.rw>d.w&&(p.marginRight=i.Em(d.rw-d.w)),s.style.position="absolute",c||(o.style.position="absolute");var M=s.offsetWidth,g=s.offsetHeight,x=o.offsetHeight,b=o.offsetWidth;return s.style.position=o.style.position="",{Y:-n.getBBox(s).h,mW:b,mH:x,zW:M,zH:g}},initImg:function(t){},initHTML:function(t,e){},initFont:function(e){var a=i.FONTDATA.FONTS,n=i.config.availableFonts;return n&&n.length&&i.Font.testFont(a[e])?(a[e].available=!0,a[e].familyFixed&&(a[e].family=a[e].familyFixed,delete a[e].familyFixed),null):this.allowWebFonts?(a[e].isWebFont=!0,i.FontFaceBug&&(a[e].family=e,i.msieFontCSSBug&&(a[e].family+="-Web")),t.Styles({"@font-face":this.Font.fontFace(e)})):null},Remove:function(t){var e=document.getElementById(t.inputID+"-Frame");e&&(t.HTMLCSS.display&&(e=e.parentNode),e.parentNode.removeChild(e)),delete t.HTMLCSS},getHD:function(t,e){if(t.bbox&&this.config.noReflows&&!e)return{h:t.bbox.h,d:t.bbox.d};var i=t.style.position;t.style.position="absolute",this.HDimg.style.height="0px",t.appendChild(this.HDspan);var a={h:t.offsetHeight};return this.HDimg.style.height=a.h+"px",a.d=t.offsetHeight-a.h,a.h-=a.d,a.h/=this.em,a.d/=this.em,t.removeChild(this.HDspan),t.style.position=i,a},getW:function(t){var e,i,a=(t.bbox||{}).w,n=t;if(t.bbox&&this.config.noReflows&&!1!==t.bbox.exactW)return t.bbox.exactW||(t.style.paddingLeft&&(a+=this.unEm(t.style.paddingLeft)*(t.scale||1)),t.style.paddingRight&&(a+=this.unEm(t.style.paddingRight)*(t.scale||1))),a;if(t.bbox&&t.bbox.exactW)return a;if(t.bbox&&a>=0&&!this.initialSkipBug&&!this.msieItalicWidthBug||this.negativeBBoxes||!t.firstChild)e=t.offsetWidth,i=t.parentNode.offsetHeight;else if(t.bbox&&a<0&&this.msieNegativeBBoxBug)e=-t.offsetWidth,i=t.parentNode.offsetHeight;else{var s=t.style.position;t.style.position="absolute",n=this.startMarker,t.insertBefore(n,t.firstChild),t.appendChild(this.endMarker),e=this.endMarker.offsetLeft-n.offsetLeft,t.removeChild(this.endMarker),t.removeChild(n),t.style.position=s}return null!=i&&(t.parentNode.HH=i/this.em),e/this.em},Measured:function(t,e){var i=t.bbox;if(null==i.width&&i.w&&!i.isMultiline){var a=this.getW(t);i.rw+=a-i.w,i.w=a,i.exactW=!0}return e||(e=t.parentNode),e.bbox||(e.bbox=i),t},Remeasured:function(t,e){e.bbox=this.Measured(t,e).bbox},MeasureSpans:function(t){var e,i,a,n,s,o,r,l,h=[];for(i=0,a=t.length;i<a;i++)(e=t[i])&&(n=e.bbox,l=this.parentNode(e),n.exactW||n.width||0===n.w||n.isMultiline||this.config.noReflows&&!1!==n.exactW?l.bbox||(l.bbox=n):this.negativeBBoxes||!e.firstChild||n.w>=0&&!this.initialSkipBug||n.w<0&&this.msieNegativeBBoxBug?h.push([e]):this.initialSkipBug?(s=this.startMarker.cloneNode(!0),o=this.endMarker.cloneNode(!0),e.insertBefore(s,e.firstChild),e.appendChild(o),h.push([e,s,o,e.style.position]),e.style.position="absolute"):(o=this.endMarker.cloneNode(!0),e.appendChild(o),h.push([e,null,o])));for(i=0,a=h.length;i<a;i++)n=(e=h[i][0]).bbox,l=this.parentNode(e),n.w>=0&&!this.initialSkipBug||this.negativeBBoxes||!e.firstChild?(r=e.offsetWidth,l.HH=l.offsetHeight/this.em):n.w<0&&this.msieNegativeBBoxBug?(r=-e.offsetWidth,l.HH=l.offsetHeight/this.em):r=h[i][2].offsetLeft-((h[i][1]||{}).offsetLeft||0),r/=this.em,n.rw+=r-n.w,n.w=r,n.exactW=!0,l.bbox||(l.bbox=n);for(i=0,a=h.length;i<a;i++)(e=h[i])[1]&&(e[1].parentNode.removeChild(e[1]),e[0].style.position=e[3]),e[2]&&e[2].parentNode.removeChild(e[2])},Em:function(t){return Math.abs(t)<6e-4?"0em":t.toFixed(3).replace(/\.?0+$/,"")+"em"},EmRounded:function(t){return Math.abs(t)<6e-4?"0em":(t=(Math.round(t*i.em)+.05)/i.em).toFixed(3).replace(/\.?0+$/,"")+"em"},unEm:function(t){return parseFloat(t)},Px:function(t){return((t*=this.em)<0?"-":"")+Math.abs(t).toFixed(1).replace(/\.?0+$/,"")+"px"},unPx:function(t){return parseFloat(t)/this.em},Percent:function(t){return(100*t).toFixed(1).replace(/\.?0+$/,"")+"%"},length2em:function(t,e,n){if("string"!=typeof t&&(t=t.toString()),""===t)return"";if(t===a.SIZE.NORMAL)return 1;if(t===a.SIZE.BIG)return 2;if(t===a.SIZE.SMALL)return.71;if("infinity"===t)return i.BIGDIMEN;var s=this.FONTDATA.TeX_factor,o=(i.zoomScale||1)/i.em;if(t.match(/mathspace$/))return i.MATHSPACE[t]*s;var r=t.match(/^\s*([-+]?(?:\.\d+|\d+(?:\.\d*)?))?(pt|em|ex|mu|px|pc|in|mm|cm|%)?/),l=parseFloat(r[1]||"1"),h=r[2];return null==n&&(n=1),null==e&&(e=1),"em"===h?l*s:"ex"===h?l*i.TeX.x_height*s:"%"===h?l/100*n:"px"===h?l*o:"pt"===h?l/10*s:"pc"===h?1.2*l*s:"in"===h?l*this.pxPerInch*o:"cm"===h?l*this.pxPerInch*o/2.54:"mm"===h?l*this.pxPerInch*o/25.4:"mu"===h?l/18*s*e:l*n},thickness2em:function(t,e){var n=i.TeX.rule_thickness;return t===a.LINETHICKNESS.MEDIUM?n:t===a.LINETHICKNESS.THIN?.67*n:t===a.LINETHICKNESS.THICK?1.67*n:this.length2em(t,e,n)},border2em:function(t,e){return t===a.LINETHICKNESS.THIN&&(t="1px"),t===a.LINETHICKNESS.MEDIUM&&(t="3px"),t===a.LINETHICKNESS.THICK&&(t="5px"),this.length2em(t,e)},getPadding:function(t){var e={top:0,right:0,bottom:0,left:0},i=!1;for(var a in e)if(e.hasOwnProperty(a)){var n=t.style["padding"+a.charAt(0).toUpperCase()+a.substr(1)];n&&(e[a]=this.length2em(n),i=!0)}return!!i&&e},getBorders:function(t){var e={top:0,right:0,bottom:0,left:0},i={},n=!1;for(var s in e)if(e.hasOwnProperty(s)){var o="border"+s.charAt(0).toUpperCase()+s.substr(1);t.style[o+"Style"]&&(n=!0,e[s]=this.border2em(t.style[o+"Width"]||a.LINETHICKNESS.MEDIUM),i[o]=[t.style[o+"Width"],t.style[o+"Style"],t.style[o+"Color"]].join(" "))}return e.css=i,!!n&&e},setBorders:function(t,e){if(e)for(var i in e.css)e.css.hasOwnProperty(i)&&(t.style[i]=e.css[i])},createStrut:function(t,e,i){var a=this.Element("span",{isMathJax:!0,style:{display:"inline-block",overflow:"hidden",height:e+"px",width:"1px",marginRight:"-1px"}});return i?t.insertBefore(a,t.firstChild):t.appendChild(a),a},createBlank:function(t,e,i){var a=this.Element("span",{isMathJax:!0,style:{display:"inline-block",overflow:"hidden",height:"1px",width:this.Em(e)}});return e<0&&(a.style.marginRight=a.style.width,a.style.width=0),i?t.insertBefore(a,t.firstChild):t.appendChild(a),a},createShift:function(t,e,i){var a=this.Element("span",{style:{marginLeft:this.Em(e)},isMathJax:!0});return i?t.insertBefore(a,t.firstChild):t.appendChild(a),a},createSpace:function(t,e,n,s,o,r){e<-n&&(n=-e);var l=this.Em(e+n),h=this.Em(-n);if(this.msieInlineBlockAlignBug&&(h=this.Em(i.getHD(t.parentNode,!0).d-n)),t.isBox||r){var u=null==t.scale?1:t.scale;t.bbox={exactW:!0,h:e*u,d:n*u,w:s*u,rw:s*u,lw:0},t.style.height=l,t.style.verticalAlign=h,t.HH=(e+n)*u}else t=this.addElement(t,"span",{style:{height:l,verticalAlign:h},isMathJax:!0});return s>=0?(t.style.width=this.Em(s),t.style.display="inline-block",t.style.overflow="hidden"):(this.msieNegativeSpaceBug&&(t.style.height=""),t.style.marginLeft=this.Em(s),i.safariNegativeSpaceBug&&t.parentNode.firstChild==t&&this.createBlank(t,0,!0)),o&&o!==a.COLOR.TRANSPARENT&&(t.style.backgroundColor=o,t.style.position="relative"),t},createRule:function(t,e,a,n,s){e<-a&&(a=-e);var o=i.TeX.min_rule_thickness,r=1;n>0&&n*this.em<o&&(n=o/this.em),e+a>0&&(e+a)*this.em<o&&(e*=r=1/(e+a)*(o/this.em),a*=r),s=s?"solid "+s:"solid";var l={display:"inline-block",overflow:"hidden",verticalAlign:this.Em(-a)};n>e+a?(l.borderTop=this.Px(e+a)+" "+s,l.width=this.Em(n),l.height=this.msieRuleBug&&e+a>0?this.Em(e+a):0):(l.borderLeft=this.Px(n)+" "+s,l.width=this.msieRuleBug&&n>0?this.Em(n):0,l.height=this.Em(e+a));var h=this.addElement(t,"span",{style:l,noAdjust:!0,HH:e+a,isMathJax:!0,bbox:{h:e,d:a,w:n,rw:n,lw:0,exactW:!0}});return(t.isBox||"mspace"==t.className)&&(t.bbox=h.bbox,t.HH=e+a),h},createFrame:function(t,e,i,a,n,s){e<-i&&(i=-e);var o=2*n;this.msieFrameSizeBug&&(a<o&&(a=o),e+i<o&&(e=o-i)),this.msieBorderWidthBug&&(o=0);var r=this.Em(e+i-o),l=this.Em(-i-n),h=this.Em(a-o),u=this.Px(n)+" "+s,d=this.addElement(t,"span",{style:{border:u,display:"inline-block",overflow:"hidden",width:h,height:r},bbox:{h:e,d:i,w:a,rw:a,lw:0,exactW:!0},noAdjust:!0,HH:e+i,isMathJax:!0});return l&&(d.style.verticalAlign=l),d},parentNode:function(t){var e=t.parentNode;return"a"===e.nodeName.toLowerCase()&&(e=e.parentNode),e},createStack:function(t,e,i){this.msiePaddingWidthBug&&this.createStrut(t,0);var a=String(i).match(/%$/),n=a||null==i?0:i;return t=this.addElement(t,"span",{noAdjust:!0,HH:0,isMathJax:!0,style:{display:"inline-block",position:"relative",width:a?"100%":this.Em(n),height:0}}),e||(t.parentNode.bbox=t.bbox={exactW:!0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,w:n,lw:this.BIGDIMEN,rw:a||null==i?-this.BIGDIMEN:i},a&&(t.bbox.width=i)),t},createBox:function(t,e){var i=this.addElement(t,"span",{style:{position:"absolute"},isBox:!0,isMathJax:!0});return null!=e&&(i.style.width=e),i},addBox:function(t,e){return e.style.position="absolute",e.isBox=e.isMathJax=!0,t.appendChild(e)},placeBox:function(t,e,a,n){t.isMathJax=!0;var s=i.parentNode(t),o=t.bbox,r=s.bbox;this.msiePlaceBoxBug&&this.addText(t,this.NBSP),this.imgSpaceBug&&this.addText(t,this.imgSpace);var l,h=0;if(null!=t.HH)l=t.HH;else if(o){var u=t.firstChild;l=Math.max(3,3*(u&&u.scale||1),o.h+o.d)}else l=t.offsetHeight/this.em;if(t.noAdjust||(l+=1,l=Math.round(l*this.em)/this.em,this.msieInlineBlockAlignBug?this.addElement(t,"img",{className:"MathJax_strut",border:0,src:"about:blank",isMathJax:!0,style:{width:0,height:this.Em(l)}}):(this.addElement(t,"span",{isMathJax:!0,style:{display:"inline-block",width:0,height:this.Em(l)}}),i.chromeHeightBug&&(l-=(t.lastChild.offsetHeight-Math.round(l*this.em))/this.em))),o&&(this.initialSkipBug&&(o.lw<0&&(h=o.lw,i.createBlank(t,-h,!0)),o.rw>o.w&&i.createBlank(t,o.rw-o.w+.1)),!this.msieClipRectBug&&!o.noclip&&!n)){var d=3/this.em,c=l-(null==o.H?o.h:o.H)-d,m=l+(null==o.D?o.d:o.D)+d,p=o.rw+1e3;t.style.clip="rect("+this.Em(c)+" "+this.Em(p)+" "+this.Em(m)+" "+this.Em(-1e3)+")"}t.style.top=this.Em(-a-l),t.style.left=this.Em(e+h),o&&r&&(null!=o.H&&(null==r.H||o.H+a>r.H)&&(r.H=o.H+a),null!=o.D&&(null==r.D||o.D-a>r.D)&&(r.D=o.D-a),o.h+a>r.h&&(r.h=o.h+a),o.d-a>r.d&&(r.d=o.d-a),null!=r.H&&r.H<=r.h&&delete r.H,null!=r.D&&r.D<=r.d&&delete r.D,o.w+e>r.w&&(r.w=o.w+e,null==r.width&&(s.style.width=this.Em(r.w))),o.rw+e>r.rw&&(r.rw=o.rw+e),o.lw+e<r.lw&&(r.lw=o.lw+e),null==o.width||o.isFixed||(null==r.width&&(s.style.width=r.width="100%",o.minWidth&&(s.style.minWidth=r.minWidth=o.minWidth)),t.style.width=o.width),o.tw&&(r.tw=o.tw))},alignBox:function(t,i,a,n,s){if(null==n&&(n=0),this.placeBox(t,n,a),this.msiePlaceBoxBug){for(var o=t.lastChild;o&&"#text"!==o.nodeName;)o=o.previousSibling;o&&t.removeChild(o)}var r=t.bbox;if(!r.isMultiline||s){var l=null!=r.width&&!r.isFixed,h=0,u=n-r.w/2,d="50%";this.initialSkipBug&&(h=r.w-r.rw-.1,u+=r.lw),u=this.msieMarginScaleBug?u*this.em+"px":this.Em(u),l&&(u=0===n?"":this.Em(n),d=50-parseFloat(r.width)/2+"%"),e.Insert(t.style,{right:{left:"",right:this.Em(h-n)},center:{left:d,marginLeft:u}}[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,n,s,o,r){if(!n)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),s instanceof Array||(s=[s,s]);var l=s[1];s=s[0];for(var h={alias:n};h.alias;)n=h.alias,(h=this.FONTDATA.DELIMITERS[n])||(h={HW:[0,this.FONTDATA.VARIANT[a.VARIANT.NORMAL]]});h.load&&e.RestartAfter(t.Require(this.fontDir+"/fontdata-"+h.load+".js"));for(var u=0,d=h.HW.length;u<d;u++)if(h.HW[u][0]*o>=s-.01||u==d-1&&!h.stretch){h.HW[u][2]&&(o*=h.HW[u][2]),h.HW[u][3]&&(n=h.HW[u][3]);var c=this.addElement(i,"span");return this.createChar(c,[n,h.HW[u][1]],o,r),i.bbox=c.bbox,i.offset=.65*i.bbox.w,void(i.scale=o)}h.stretch&&this["extendDelimiter"+h.dir](i,l,h.stretch,o,r)},extendDelimiterV:function(t,e,i,a,n){var s=this.createStack(t,!0),o=this.createBox(s),r=this.createBox(s);this.createChar(o,i.top||i.ext,a,n),this.createChar(r,i.bot||i.ext,a,n);var l,h={bbox:{w:0,lw:0,rw:0}},u=h,d=o.bbox.h+o.bbox.d+r.bbox.h+r.bbox.d,c=-o.bbox.h;if(this.placeBox(o,0,c,!0),c-=o.bbox.d,i.mid&&(u=this.createBox(s),this.createChar(u,i.mid,a,n),d+=u.bbox.h+u.bbox.d),i.min&&e<d*i.min&&(e=d*i.min),e>d){h=this.Element("span"),this.createChar(h,i.ext,a,n);var m,p,f=h.bbox.h+h.bbox.d,M=f-.05,g=i.mid?2:1;p=m=Math.min(Math.ceil((e-d)/(g*M)),this.maxStretchyParts),i.fullExtenders||(M=(e-d)/(g*m));var x=m/(m+1)*(f-M);for(c+=x+(M=f-x)-h.bbox.h;g-- >0;){for(;m-- >0;)this.msieCloneNodeBug?(l=this.Element("span"),this.createChar(l,i.ext,a,n)):l=h.cloneNode(!0),l.bbox=h.bbox,c-=M,this.placeBox(this.addBox(s,l),0,c,!0);c+=x-h.bbox.d,i.mid&&g&&(this.placeBox(u,0,c-u.bbox.h,!0),m=p,c+=-(u.bbox.h+u.bbox.d)+x+M-h.bbox.h)}}else c+=(d-e)/2,i.mid&&(this.placeBox(u,0,c-u.bbox.h,!0),c+=-(u.bbox.h+u.bbox.d)),c+=(d-e)/2;this.placeBox(r,0,c-r.bbox.h,!0),c-=r.bbox.h+r.bbox.d,t.bbox={w:Math.max(o.bbox.w,h.bbox.w,r.bbox.w,u.bbox.w),lw:Math.min(o.bbox.lw,h.bbox.lw,r.bbox.lw,u.bbox.lw),rw:Math.max(o.bbox.rw,h.bbox.rw,r.bbox.rw,u.bbox.rw),h:0,d:-c,exactW:!0},t.scale=a,t.offset=.55*t.bbox.w,t.isMultiChar=!0,this.setStackWidth(s,t.bbox.w)},extendDelimiterH:function(t,e,i,a,n){var s=this.createStack(t,!0),o=this.createBox(s),r=this.createBox(s);this.createChar(o,i.left||i.rep,a,n),this.createChar(r,i.right||i.rep,a,n);var l=this.Element("span");this.createChar(l,i.rep,a,n);var h,u={bbox:{h:-this.BIGDIMEN,d:-this.BIGDIMEN}};this.placeBox(o,-o.bbox.lw,0,!0);var d,c=o.bbox.rw-o.bbox.lw+(r.bbox.rw-r.bbox.lw)-.05,m=o.bbox.rw-o.bbox.lw-.025;if(i.mid&&(u=this.createBox(s),this.createChar(u,i.mid,a,n),c+=u.bbox.w),i.min&&e<c*i.min&&(e=c*i.min),e>c){var p,f,M=l.bbox.rw-l.bbox.lw,g=M-.05,x=i.mid?2:1;for(f=p=Math.min(Math.ceil((e-c)/(x*g)),this.maxStretchyParts),i.fillExtenders||(g=(e-c)/(x*p)),g=M-(d=p/(p+1)*(M-g)),m-=l.bbox.lw+d;x-- >0;){for(;p-- >0;)this.cloneNodeBug?(h=this.Element("span"),this.createChar(h,i.rep,a,n)):h=l.cloneNode(!0),h.bbox=l.bbox,this.placeBox(this.addBox(s,h),m,0,!0),m+=g;i.mid&&x&&(this.placeBox(u,m,0,!0),m+=u.bbox.w-d,p=f)}}else m-=(c-e)/2,i.mid&&(this.placeBox(u,m,0,!0),m+=u.bbox.w),m-=(c-e)/2;m-=r.bbox.lw,this.placeBox(r,m,0,!0),t.bbox={w:m+r.bbox.rw,lw:0,rw:m+r.bbox.rw,h:Math.max(o.bbox.h,l.bbox.h,r.bbox.h,u.bbox.h),d:Math.max(o.bbox.d,l.bbox.d,r.bbox.d,u.bbox.d),exactW:!0},t.scale=a,t.isMultiChar=!0,this.setStackWidth(s,t.bbox.w)},createChar:function(t,e,i,n){t.isMathJax=!0;var s=t,o="",r={fonts:[e[1]],noRemap:!0};if(n&&n===a.VARIANT.BOLD&&(r.fonts=[e[1]+"-bold",e[1]]),"string"!=typeof e[1]&&(r=e[1]),e[0]instanceof Array)for(var l=0,h=e[0].length;l<h;l++)o+=String.fromCharCode(e[0][l]);else o=String.fromCharCode(e[0]);e[4]&&(i*=e[4]),1!==i||e[3]?(s=this.addElement(t,"span",{style:{fontSize:this.Percent(i)},scale:i,isMathJax:!0}),this.handleVariant(s,r,o),t.bbox=s.bbox):this.handleVariant(t,r,o),e[2]&&(t.style.marginLeft=this.Em(e[2])),e[3]&&(t.firstChild.style.verticalAlign=this.Em(e[3]),t.bbox.h+=e[3],t.bbox.h<0&&(t.bbox.h=0)),e[5]&&(t.bbox.h+=e[5]),e[6]&&(t.bbox.d+=e[6]),this.AccentBug&&0===t.bbox.w&&(s.firstChild.nodeValue+=this.NBSP)},positionDelimiter:function(t,e){e-=t.bbox.h,t.bbox.d-=e,t.bbox.h+=e,e&&(this.safariVerticalAlignBug||this.konquerorVerticalAlignBug||this.operaVerticalAlignBug&&t.isMultiChar?(""===t.firstChild.style.display&&""!==t.style.top&&(t=t.firstChild,e-=i.unEm(t.style.top)),t.style.position="relative",t.style.top=this.Em(-e)):(t.style.verticalAlign=this.Em(e),i.ffVerticalAlignBug&&(i.createRule(t.parentNode,t.bbox.h,0,0),delete t.parentNode.bbox)))},handleVariant:function(t,e,n){var s,o,r,h,u="",d=t,c=!!t.style.fontFamily;if(0!==n.length){t.bbox||(t.bbox={w:0,h:-this.BIGDIMEN,d:-this.BIGDIMEN,rw:-this.BIGDIMEN,lw:this.BIGDIMEN}),e||(e=this.FONTDATA.VARIANT[a.VARIANT.NORMAL]),h=e;for(var m=0,p=n.length;m<p;m++){if(e=h,s=n.charCodeAt(m),n.charAt(m),s>=55296&&s<56319){if(m++,s=(s-55296<<10)+(n.charCodeAt(m)-56320)+65536,this.FONTDATA.RemapPlane1){var f=this.FONTDATA.RemapPlane1(s,e);s=f.n,e=f.variant}}else{var M,g,x=this.FONTDATA.RANGES;for(M=0,g=x.length;M<g;M++)if("alpha"!==x[M].name||!e.noLowerCase){var b=e["offset"+x[M].offset];if(b&&s>=x[M].low&&s<=x[M].high){if(x[M].remap&&x[M].remap[s])s=b+x[M].remap[s];else{if(x[M].remapOnly)break;s=s-x[M].low+b,x[M].add&&(s+=x[M].add)}e["variant"+x[M].offset]&&(e=this.FONTDATA.VARIANT[e["variant"+x[M].offset]]);break}}}if(e.remap&&e.remap[s]?(s=e.remap[s],e.remap.variant&&(e=this.FONTDATA.VARIANT[e.remap.variant])):this.FONTDATA.REMAP[s]&&!e.noRemap&&(s=this.FONTDATA.REMAP[s]),l(s)&&(e=this.FONTDATA.VARIANT[s[1]],s=s[0]),"string"!=typeof s){if(o=(r=this.lookupChar(e,s))[s],c||!this.checkFont(r,d.style)&&!o[5].img){u.length&&(this.addText(d,u),u="");var v=!!d.style.fontFamily||!!t.style.fontStyle||!!t.style.fontWeight||!r.directory||c;c=!1,d!==t&&(v=!this.checkFont(r,t.style),d=t),v&&(d=this.addElement(t,"span",{isMathJax:!0,subSpan:!0})),this.handleFont(d,r,d!==t)}u=this.handleChar(d,r,o,s,u),(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 p=(n=s+n.substr(m+1)).length,m=-1}u.length&&this.addText(d,u),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(n)&&r.skew&&r.skew[s]&&(t.bbox.skew=r.skew[s])}},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 n=e.style||"normal",s=e.weight||"normal";("normal"!==n||a)&&(t.style.fontStyle=n),("normal"!==s||a)&&(t.style.fontWeight=s)}},handleChar:function(t,e,a,n,s){var o=a[5];if(o.space)return s.length&&this.addText(t,s),i.createShift(t,a[2]/1e3),"";if(o.img)return this.handleImg(t,e,a,n,s);if(o.isUnknown&&this.FONTDATA.DELIMITERS[n]){s.length&&this.addText(t,s);var r=t.scale;return i.createDelimiter(t,n,0,1,e),"V"===this.FONTDATA.DELIMITERS[n].dir&&(t.style.verticalAlign=this.Em(t.bbox.d),t.bbox.h+=t.bbox.d,t.bbox.d=0),t.scale=r,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(n<=65535)o.c=String.fromCharCode(n);else{var l=n-65536;o.c=String.fromCharCode(55296+(l>>10))+String.fromCharCode(56320+(1023&l))}return i.ffFontOptimizationBug&&a[4]-a[2]>125&&(t.style.textRendering="optimizeLegibility"),o.rfix?(this.addText(t,s+o.c),i.createShift(t,o.rfix/1e3),""):a[2]||!this.msieAccentBug&&!this.combiningCharBug||s.length?s+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,n){return n},lookupChar:function(t,e){var a,n;if(!t.FONTS){var s=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,n=o.length;a<n;a++)s[o[a]]&&(t.FONTS.push(s[o[a]]),s[o[a]].name=o[a])}for(a=0,n=t.FONTS.length;a<n;a++){var r=t.FONTS[a];if("string"==typeof r&&(delete t.FONTS,this.loadFont(r)),r[e]){if(5===r[e].length&&(r[e][5]={}),!i.allowWebFonts||r.available)return r;this.loadWebFont(r)}else this.findBlock(r,e)}return this.unknownChar(t,e)},unknownChar:function(t,a){var n=t.defaultFont||{family:i.config.undefinedFamily};return t.bold&&(n.weight="bold"),t.italic&&(n.style="italic"),n[a]||(n[a]=[800,200,500,0,500,{isUnknown:!0}]),e.signal.Post(["HTML-CSS Jax - unknown char",a,t]),n},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 n=t.Ranges[i][2],s=t.Ranges.length-1;s>=0;s--)t.Ranges[s][2]==n&&t.Ranges.splice(s,1);this.loadFont(t.directory+"/"+n+".js")}}},loadFont:function(a){var n=MathJax.Callback.Queue();n.Push(["Require",t,this.fontDir+"/"+a]),this.imgFonts&&(MathJax.isPacked||(a=a.replace(/\/([^\/]*)$/,i.imgPacked+"/$1")),n.Push(["Require",t,this.webfontDir+"/png/"+a])),e.RestartAfter(n.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"),h(["WebFontNotAvailable","Web-Fonts not available -- using image fonts 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this.ID++,this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:.430554,quad:1,num1:.676508,num2:.393732,num3:.44373,denom1:.685951,denom2:.344841,sup1:.412892,sup2:.362892,sup3:.288888,sub1:.15,sub2:.247217,sup_drop:.386108,sub_drop:.05,delim1:2.39,delim2:1,axis_height:.25,rule_thickness:.06,big_op_spacing1:.111111,big_op_spacing2:.166666,big_op_spacing3:.2,big_op_spacing4:.6,big_op_spacing5:.1,scriptspace:.1,nulldelimiterspace:.12,delimiterfactor:901,delimitershortfall:.3,min_rule_thickness:1.25},NBSP:" ",rfuzz:0}),MathJax.Hub.Register.StartupHook("mml Jax Ready",(function(){(a=MathJax.ElementJax.mml).mbase.Augment({toHTML:function(t){t=this.HTMLcreateSpan(t),"mrow"!=this.type&&(t=this.HTMLhandleSize(t));for(var e=0,i=this.data.length;e<i;e++)this.data[e]&&this.data[e].toHTML(t);var a,n=this.HTMLcomputeBBox(t),s=t.bbox.h,o=t.bbox.d,r=!1;for(e=0,i=n.length;e<i;e++)a=n[e].HTMLspanElement().bbox,n[e].forceStretch||a.h!==s||a.d!==o?(n[e].HTMLstretchV(t,s,o),r=!0):n[e].needsBBox&&(r=!0);return r&&this.HTMLcomputeBBox(t,!0),this.HTMLlineBreaks(t)&&(t=this.HTMLmultiline(t)),this.HTMLhandleSpace(t),this.HTMLhandleColor(t),1===this.data.length&&this.data[0]&&(a=this.data[0].HTMLspanElement().bbox).skew&&(t.bbox.skew=a.skew),t},HTMLlineBreaks:function(){return!1},HTMLmultiline:function(){a.mbase.HTMLautoloadFile("multiline")},HTMLcomputeBBox:function(t,e,i,a){null==i&&(i=0),null==a&&(a=this.data.length);for(var n=t.bbox={exactW:!0},s=[];i<a;){var o=this.data[i];o&&(!e&&o.HTMLcanStretch("Vertical")&&(s.push(o),o=o.CoreMO()||o,s[s.length-1].needsBBox=o!==this.data[i]),this.HTMLcombineBBoxes(o,n),i++)}return this.HTMLcleanBBox(n),s},HTMLcombineBBoxes:function(t,e){null==e.w&&this.HTMLemptyBBox(e);var a=t.bbox?t:t.HTMLspanElement();if(a&&a.bbox){var n=a.bbox;n.d>e.d&&(e.d=n.d),n.h>e.h&&(e.h=n.h),null!=n.D&&n.D>e.D&&(e.D=n.D),null!=n.H&&n.H>e.H&&(e.H=n.H),a.style.paddingLeft&&(e.w+=i.unEm(a.style.paddingLeft)*(a.scale||1)),e.w+n.lw<e.lw&&(e.lw=e.w+n.lw),e.w+n.rw>e.rw&&(e.rw=e.w+n.rw),e.w+=n.w,a.style.paddingRight&&(e.w+=i.unEm(a.style.paddingRight)*(a.scale||1)),n.width&&(e.width=n.width,e.minWidth=n.minWidth),n.tw&&(e.tw=n.tw),n.ic?e.ic=n.ic:delete e.ic,e.exactW&&!n.exactW&&(e.exactW=n.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 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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,n=a.nocopyAttributes,s=e.config.ignoreMMLattributes,o="mstyle"===this.type?a.math.prototype.defaults:this.defaults,r=0,l=i.length;r<l;r++){var h=i[r];0!=s[h]&&(n[h]||s[h]||null!=o[h]||void 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n=(this.styles||{}).border,s=(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||n||s){var o=t.bbox,r=o.exact?0:1/i.em,l=0,h=0,u=t.style.paddingLeft,d=t.style.paddingRight;this.isToken&&(l=o.lw,h=o.rw-o.w),""!==u&&(l+=i.unEm(u)*(t.scale||1)),""!==d&&(h-=i.unEm(d)*(t.scale||1));var c=i.PaddingWidthBug||o.keepPadding||o.exactW?0:h-l,m=Math.max(0,i.getW(t)+c),p=o.h+o.d,f=-o.d,M=0,g=0;m>0&&(m+=2*r,l-=r),p>0&&(p+=2*r,f-=r),h=-m-l,n&&(h-=n.right,f-=n.bottom,M+=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),s&&(p+=s.top+s.bottom,m+=s.left+s.right,h-=s.right,f-=s.bottom,M+=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),g&&(t.style.paddingRight=i.Em(g));var x=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(p),verticalAlign:i.Em(f),marginLeft:i.Em(l),marginRight:i.Em(h)}});return i.setBorders(x,n),o.width&&(x.style.width=o.width,x.style.marginRight="-"+o.width),i.msieInlineBlockAlignBug&&(x.style.position="relative",x.style.width=x.style.height=0,x.style.verticalAlign=x.style.marginLeft=x.style.marginRight="",x.style.border=x.style.padding="",n&&i.msieBorderWidthBug&&(p+=n.top+n.bottom,m+=n.left+n.right),x.style.width=i.Em(M+r),i.placeBox(i.addElement(x,"span",{noAdjust:!0,isMathJax:!0,style:{display:"inline-block",position:"absolute",overflow:"hidden",background:e.mathbackground||"transparent",width:i.Em(m),height:i.Em(p)}}),l,o.h+r),i.setBorders(x.firstChild,n)),t.parentNode.insertBefore(x,t),i.msieColorPositionBug&&(t.style.position="relative"),x}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 n=this,s=this.Parent();s&&s.isEmbellished()&&s.Core()===n;)n=s,s=s.Parent(),t=n.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 n=t.mathvariant;return this.variantForm&&(n="-"+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?n={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}[n]||n:"normal"===t.weight&&(n={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}[n]||n),"italic"===t.style?n={normal:a.VARIANT.ITALIC,bold:a.VARIANT.BOLDITALIC,"sans-serif":a.VARIANT.SANSSERIFITALIC,"bold-sans-serif":a.VARIANT.SANSSERIFBOLDITALIC}[n]||n:"normal"===t.style&&(n={italic:a.VARIANT.NORMAL,"bold-italic":a.VARIANT.BOLD,"sans-serif-italic":a.VARIANT.SANSSERIF,"sans-serif-bold-italic":a.VARIANT.BOLDSANSSERIF}[n]||n),n 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s=i.autoloadDir+"/"+n+".js";e.RestartAfter(t.Require(s))},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,n){var s=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(a&&(s=a(s,n)),e.fontInherit){var o=Math.floor(i.config.scale/i.scale+.5)+"%";i.addElement(t,"span",{style:{"font-size":o}},[s]),e.bold&&(t.lastChild.style.fontWeight="bold"),e.italic&&(t.lastChild.style.fontStyle="italic"),t.bbox=null;var r=i.getHD(t),l=i.getW(t);t.bbox={h:r.h,d:r.d,w:l,lw:0,rw:l,exactW:!0}}else this.HTMLhandleVariant(t,e,s)}}),a.entity.Augment({toHTML:function(t,e,a,n){var s=this.toString().replace(/[\u2061-\u2064]/g,"");if(a&&(s=a(s,n)),e.fontInherit){var o=Math.floor(i.config.scale/i.scale+.5)+"%";i.addElement(t,"span",{style:{"font-size":o}},[s]),e.bold&&(t.lastChild.style.fontWeight="bold"),e.italic&&(t.lastChild.style.fontStyle="italic"),delete t.bbox;var r=i.getHD(t),l=i.getW(t);t.bbox={h:r.h,d:r.d,w:l,lw:0,rw:l,exactW:!0}}else this.HTMLhandleVariant(t,e,s)}}),a.mi.Augment({toHTML:function(t){(t=this.HTMLhandleSize(this.HTMLcreateSpan(t))).bbox=null;for(var e=this.HTMLgetVariant(),a=0,n=this.data.length;a<n;a++)this.data[a]&&this.data[a].toHTML(t,e);t.bbox||(t.bbox=this.HTMLzeroBBox());var s=this.data.join(""),o=t.bbox;return o.skew&&!i.isChar(s)&&delete o.skew,o.rw>o.w&&i.isChar(s)&&!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,n=0,s=this.data.length;n<s;n++)this.data[n]&&(this.data[n].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(""),n=this.HTMLgetVariant(),s=this.getValues("largeop","displaystyle");s.largeop&&(n=i.FONTDATA.VARIANT[s.displaystyle?"-largeOp":"-smallOp"]);var o=this.CoreParent(),r=o&&o.isa(a.msubsup)&&this!==o.data[o.base],l=r?this.remapChars:null;if(i.isChar(e)&&o&&o.isa(a.munderover)&&i.isChar(this.CoreText(o.data[o.base]))){var h=o.data[o.over],u=o.data[o.under];h&&this===h.CoreMO()&&o.Get("accent")?l=i.FONTDATA.REMAPACCENT:u&&this===u.CoreMO()&&o.Get("accentunder")&&(l=i.FONTDATA.REMAPACCENTUNDER)}r&&e.match(/['`"\u00B4\u2032-\u2037\u2057]/)&&(n=i.FONTDATA.VARIANT["-"+i.fontInUse+"-variant"]);for(var d=0,c=this.data.length;d<c;d++)this.data[d]&&this.data[d].toHTML(t,n,this.remap,l);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)),s.largeop){var m=i.TeX.axis_height*this.scale*this.mscale,p=(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-p/t.scale):i.konquerorVerticalAlignBug&&"IMG"===t.lastChild.nodeName?(t.style.position="relative",t.lastChild.style.position="relative",t.lastChild.style.top=i.Em(p/t.scale)):t.style.verticalAlign=i.Em(-p/t.scale),t.bbox.h-=p,t.bbox.d+=p,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 n=this.CoreParent();if(n&&n.isa(a.munderover)&&i.isChar(this.CoreText(n.data[n.base]))){var s=n.data[n.over],o=n.data[n.under];s&&this===s.CoreMO()&&n.Get("accent")?e=i.FONTDATA.REMAPACCENT[e]||e:o&&this===o.CoreMO()&&n.Get("accentunder")&&(e=i.FONTDATA.REMAPACCENTUNDER[e]||e)}var r=(e=i.FONTDATA.DELIMITERS[e.charCodeAt(0)])&&e.dir===t.substr(0,1);return this.forceStretch=r&&(this.Get("minsize",!0)||this.Get("maxsize",!0)),r},HTMLstretchV:function(t,e,a){this.HTMLremoveColor();var n,s=this.getValues("symmetric","maxsize","minsize"),o=this.HTMLspanElement(),r=this.HTMLgetMu(o),l=this.HTMLgetScale(),h=i.TeX.axis_height*l;return n=s.symmetric?2*Math.max(e-h,a+h):e+a,s.maxsize=i.length2em(s.maxsize,r,o.bbox.h+o.bbox.d),s.minsize=i.length2em(s.minsize,r,o.bbox.h+o.bbox.d),(n=Math.max(s.minsize,Math.min(s.maxsize,n)))!=s.minsize&&(n=[Math.max(n*i.TeX.delimiterfactor/1e3,n-i.TeX.delimitershortfall),n]),o=this.HTMLcreateSpan(t),i.createDelimiter(o,this.data.join("").charCodeAt(0),n,l),n=s.symmetric?(o.bbox.h+o.bbox.d)/2+h:(o.bbox.h+o.bbox.d)*e/(e+a),i.positionDelimiter(o,n),this.HTMLhandleSpace(o),this.HTMLhandleColor(o),o},HTMLstretchH:function(t,e){this.HTMLremoveColor();var n=this.getValues("maxsize","minsize","mathvariant","fontweight");("bold"===n.fontweight||parseInt(n.fontweight)>=600)&&!this.Get("mathvariant",!0)&&(n.mathvariant=a.VARIANT.BOLD);var s=this.HTMLspanElement(),o=this.HTMLgetMu(s),r=s.scale;return n.maxsize=i.length2em(n.maxsize,o,s.bbox.w),n.minsize=i.length2em(n.minsize,o,s.bbox.w),e=Math.max(n.minsize,Math.min(n.maxsize,e)),s=this.HTMLcreateSpan(t),i.createDelimiter(s,this.data.join("").charCodeAt(0),e,r,n.mathvariant),this.HTMLhandleSpace(s),this.HTMLhandleColor(s),s}}),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 n=0,s=this.data.length;n<s;n++)this.data[n]&&this.data[n].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),n=i.getW(e);return e.bbox={h:a.h,d:a.d,w:n,lw:0,rw:n,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 n=i.length2em(e.height,a)*this.mscale,s=i.length2em(e.depth,a)*this.mscale,o=i.length2em(e.width,a)*this.mscale;return i.createSpace(t,n,s,o,e.mathbackground,!0),t}}),a.mphantom.Augment({toHTML:function(t,e,a){if(t=this.HTMLcreateSpan(t),null!=this.data[0]){var n=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):n=i.Measured(n,t),t.bbox={w:n.bbox.w,h:n.bbox.h,d:n.bbox.d,lw:0,rw:0,exactW:!0};for(var s=0,o=t.childNodes.length;s<o;s++)t.childNodes[s].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 n=i.createStack(t,!0),s=i.createBox(n),o=this.data[0].toHTML(s);null!=a?i.Remeasured(this.data[0].HTMLstretchV(s,e,a),s):null!=e?i.Remeasured(this.data[0].HTMLstretchH(s,e),s):i.Measured(o,s);var r=this.getValues("height","depth","width","lspace","voffset"),l=0,h=0,u=this.HTMLgetMu(t);this.HTMLgetScale(),r.lspace&&(l=this.HTMLlength2em(s,r.lspace,u)),r.voffset&&(h=this.HTMLlength2em(s,r.voffset,u)),i.placeBox(s,l,h),l/=this.mscale,h/=this.mscale,t.bbox={h:s.bbox.h,d:s.bbox.d,w:s.bbox.w,exactW:!0,lw:s.bbox.lw+l,rw:s.bbox.rw+l,H:Math.max(null==s.bbox.H?-i.BIGDIMEN:s.bbox.H+h,s.bbox.h+h),D:Math.max(null==s.bbox.D?-i.BIGDIMEN:s.bbox.D-h,s.bbox.d-h)},""!==r.height&&(t.bbox.h=this.HTMLlength2em(s,r.height,u,"h",0)),""!==r.depth&&(t.bbox.d=this.HTMLlength2em(s,r.depth,u,"d",0)),""!==r.width&&(t.bbox.w=this.HTMLlength2em(s,r.width,u,"w",0)),t.bbox.H<=t.bbox.h&&delete t.bbox.H,t.bbox.D<=t.bbox.d&&delete t.bbox.D;var d=/^\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||d.exec(r.height)||d.exec(r.width)||d.exec(r.depth)),i.setStackWidth(n,t.bbox.w)}return this.HTMLhandleSpace(t),this.HTMLhandleColor(t),t},HTMLlength2em:function(t,e,a,n,s){null==s&&(s=-i.BIGDIMEN);var o=String(e).match(/width|height|depth/),r=o?t.bbox[o[0].charAt(0)]:n?t.bbox[n]:0,l=i.length2em(e,a,r/this.mscale)*this.mscale;return n&&String(e).match(/^\s*[-+]/)?Math.max(s,t.bbox[n]+l):l},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),n=i.createBox(e);i.MeasureSpans([this.HTMLboxChild(0,a),this.HTMLboxChild(1,n)]);var s=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled"),o=this.HTMLgetScale(),r=s.displaystyle,l=i.TeX.axis_height*o;if(s.bevelled){var h=r?.4:.15,u=Math.max(a.bbox.h+a.bbox.d,n.bbox.h+n.bbox.d)+2*h,d=i.createBox(e);i.createDelimiter(d,47,u),i.placeBox(a,0,(a.bbox.d-a.bbox.h)/2+l+h),i.placeBox(d,a.bbox.w-h/2,(d.bbox.d-d.bbox.h)/2+l),i.placeBox(n,a.bbox.w+d.bbox.w-h,(n.bbox.d-n.bbox.h)/2+l-h)}else{var c,m,p,f,M=Math.max(a.bbox.w,n.bbox.w),g=i.thickness2em(s.linethickness,this.scale)*this.mscale,x=i.TeX.min_rule_thickness/this.em;if(r?(p=i.TeX.num1,f=i.TeX.denom1):(p=0===g?i.TeX.num3:i.TeX.num2,f=i.TeX.denom2),p*=o,f*=o,0===g)c=Math.max((r?7:3)*i.TeX.rule_thickness,2*x),(m=p-a.bbox.d-(n.bbox.h-f))<c&&(p+=(c-m)/2,f+=(c-m)/2);else{c=Math.max((r?2:0)*x+g,g/2+1.5*x),(m=p-a.bbox.d-(l+g/2))<c&&(p+=c-m),(m=l-g/2-(n.bbox.h-f))<c&&(f+=c-m);var b=i.createBox(e);i.createRule(b,g,0,M+2*g),i.placeBox(b,0,l-g/2)}i.alignBox(a,s.numalign,p,0,!0),i.alignBox(n,s.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,n,s,o=i.createStack(t),r=i.createBox(o),l=i.createBox(o),h=i.createBox(o),u=this.HTMLgetScale(),d=i.TeX.rule_thickness*u;e=this.Get("displaystyle")?i.TeX.x_height*u:d,a=Math.max(d+e/4,1.5*i.TeX.min_rule_thickness/this.em);var c=this.HTMLboxChild(0,r);n=c.bbox.h+c.bbox.d+a+d,i.createDelimiter(h,8730,n,u),i.MeasureSpans([c,h]),s=c.bbox.w;var m=0;(h.isMultiChar||i.AdjustSurd&&i.imgFonts)&&(h.bbox.w*=.95),h.bbox.h+h.bbox.d>n&&(a=(h.bbox.h+h.bbox.d-(n-d))/2);var p=i.FONTDATA.DELIMITERS[i.FONTDATA.RULECHAR];return!p||s<(p.HW[0]||[0])[0]*u||u<.75?(i.createRule(l,0,d,s),l.bbox.h=-d):i.createDelimiter(l,i.FONTDATA.RULECHAR,s,u),a=(n=c.bbox.h+a+d)*i.rfuzz,h.isMultiChar&&(a=i.rfuzz),m=this.HTMLaddRoot(o,h,m,h.bbox.h+h.bbox.d-n,u),i.placeBox(h,m,n-h.bbox.h),i.placeBox(l,m+h.bbox.w,n-l.bbox.h+a),i.placeBox(r,m+h.bbox.w,0),this.HTMLhandleSpace(t),this.HTMLhandleColor(t),t},HTMLaddRoot:function(t,e,i,a,n){return i}}),a.mroot.Augment({toHTML:a.msqrt.prototype.toHTML,HTMLaddRoot:function(t,e,a,n,s){var o=i.createBox(t);if(this.data[1]){var r=this.data[1].toHTML(o);r.style.paddingRight=r.style.paddingLeft="",i.Measured(r,o)}else o.bbox=this.HTMLzeroBBox();var l=this.HTMLrootHeight(e.bbox.h+e.bbox.d,s,o)-n,h=Math.min(o.bbox.w,o.bbox.rw);return a=Math.max(h,e.offset),i.placeBox(o,a-h,l),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),n=t.bbox.h,s=t.bbox.d;for(e=0,i=a.length;e<i;e++)a[e].HTMLstretchV(t,n,s);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 n=1,s=this.data.length;n<s;n++)this.data[n]&&(this.HTMLcheckStretchy(this.data["sep"+n],i,a,e),this.HTMLcheckStretchy(this.data[n],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,n){var s=this.getValues("displaystyle","accent","accentunder","align"),o=this.data[this.base];if(!s.displaystyle&&null!=o&&(o.movablelimits||o.CoreMO().Get("movablelimits")))return a.msubsup.prototype.toHTML.call(this,t);t=this.HTMLcreateSpan(t);var r,l,h,u=this.HTMLgetScale(),d=i.createStack(t),c=[],m=[],p=[];for(l=0,h=this.data.length;l<h;l++)null!=this.data[l]&&(r=c[l]=i.createBox(d),m[l]=this.data[l].toHTML(r),l==this.base?(null!=n?this.data[this.base].HTMLstretchV(r,e,n):null!=e&&this.data[this.base].HTMLstretchH(r,e),p[l]=(null!=n||null==e)&&this.data[l].HTMLcanStretch("Horizontal"),this.data[this.over]&&s.accent&&(m[l].bbox.h=Math.max(m[l].bbox.h,u*i.TeX.x_height))):(p[l]=this.data[l].HTMLcanStretch("Horizontal"),m[l].style.paddingLeft=m[l].style.paddingRight=""));i.MeasureSpans(m);var f=-i.BIGDIMEN,M=f;for(l=0,h=this.data.length;l<h;l++)this.data[l]&&(c[l].bbox.w>M&&(M=c[l].bbox.w),!p[l]&&M>f&&(f=M));for(null==n&&null!=e?f=e:f==-i.BIGDIMEN&&(f=M),l=M=0,h=this.data.length;l<h;l++)this.data[l]&&(r=c[l],p[l]&&(r.bbox=this.data[l].HTMLstretchH(r,f).bbox,l!==this.base&&(m[l].style.paddingLeft=m[l].style.paddingRight="")),r.bbox.w>M&&(M=r.bbox.w));var g,x,b,v,T,y,C=i.TeX.rule_thickness*this.mscale,L=i.FONTDATA.TeX_factor,E=0;for((o=c[this.base]||{bbox:this.HTMLzeroBBox()}).bbox.ic&&(E=1.3*o.bbox.ic+.05),l=0,h=this.data.length;l<h;l++)if(null!=this.data[l]){r=c[l],T=i.TeX.big_op_spacing5*u;var S=l!=this.base&&s[this.ACCENTS[l]];S&&r.bbox.w<=1/i.em+1e-4&&(r.bbox.w=r.bbox.rw-r.bbox.lw,r.bbox.noclip=!0,r.bbox.lw&&r.insertBefore(i.createSpace(r.parentNode,0,0,-r.bbox.lw),r.firstChild),i.createBlank(r,0,0,r.bbox.rw+.1)),g={left:0,center:(M-r.bbox.w)/2,right:M-r.bbox.w}[s.align],x=0,l==this.over?(S?(y=Math.max(C*u*L,2.5/this.em),T=0,o.bbox.skew&&(g+=o.bbox.skew,t.bbox.skew=o.bbox.skew,g+r.bbox.w>M&&(t.bbox.skew+=(M-r.bbox.w-g)/2))):(b=i.TeX.big_op_spacing1*u*L,v=i.TeX.big_op_spacing3*u*L,y=Math.max(b,v-Math.max(0,r.bbox.d))),y=Math.max(y,1.5/this.em),g+=E/2,x=o.bbox.h+r.bbox.d+y,r.bbox.h+=T):l==this.under&&(S?(y=3*C*u*L,T=0):(b=i.TeX.big_op_spacing2*u*L,v=i.TeX.big_op_spacing4*u*L,y=Math.max(b,v-r.bbox.h)),y=Math.max(y,1.5/this.em),g-=E/2,x=-(o.bbox.d+r.bbox.h+y),r.bbox.d+=T),i.placeBox(r,g,x)}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 n,s=this.HTMLgetScale(),o=this.HTMLgetMu(t),r=i.createStack(t),l=[],h=i.createBox(r);this.data[this.base]?(l.push(this.data[this.base].toHTML(h)),null!=a?this.data[this.base].HTMLstretchV(h,e,a):null!=e&&this.data[this.base].HTMLstretchH(h,e)):h.bbox=this.HTMLzeroBBox();var u,d,c=i.TeX.x_height*s,m=i.TeX.scriptspace*s*.75;this.HTMLnotEmpty(this.data[this.sup])&&(u=i.createBox(r),l.push(this.data[this.sup].toHTML(u))),this.HTMLnotEmpty(this.data[this.sub])&&(d=i.createBox(r),l.push(this.data[this.sub].toHTML(d))),i.MeasureSpans(l),u&&(u.bbox.w+=m,u.bbox.rw=Math.max(u.bbox.w,u.bbox.rw)),d&&(d.bbox.w+=m,d.bbox.rw=Math.max(d.bbox.w,d.bbox.rw)),i.placeBox(h,0,0);var p=s;u?p=this.data[this.sup].HTMLgetScale():d&&(p=this.data[this.sub].HTMLgetScale());var f,M=i.TeX.sup_drop*p,g=i.TeX.sub_drop*p,x=h.bbox.h-M,b=h.bbox.d+g,v=0;h.bbox.ic&&(h.bbox.w-=h.bbox.ic,v=1.3*h.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===l[0].scale&&!this.data[this.base].Get("largeop")&&(x=b=0);var T=this.getValues("subscriptshift","superscriptshift");if(T.subscriptshift=""===T.subscriptshift?0:i.length2em(T.subscriptshift,o),T.superscriptshift=""===T.superscriptshift?0:i.length2em(T.superscriptshift,o),u)if(d){b=Math.max(b,i.TeX.sub2*s);var y=i.TeX.rule_thickness*s;x-u.bbox.d-(d.bbox.h-b)<3*y&&(b=3*y-x+u.bbox.d+d.bbox.h,(M=.8*c-(x-u.bbox.d))>0&&(x+=M,b-=M)),i.placeBox(u,h.bbox.w+v,Math.max(x,T.superscriptshift)),i.placeBox(d,h.bbox.w,-Math.max(b,T.subscriptshift))}else n=this.getValues("displaystyle","texprimestyle"),f=i.TeX[n.displaystyle?"sup1":n.texprimestyle?"sup3":"sup2"],x=Math.max(x,f*s,u.bbox.d+1/4*c,T.superscriptshift),i.placeBox(u,h.bbox.w+v,x,u.bbox);else d&&(b=Math.max(b,i.TeX.sub1*s,d.bbox.h-.8*c,T.subscriptshift),i.placeBox(d,h.bbox.w,-b,d.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,n,s){var o,r,l,h,u=t;if(s&&s!==i.PHASE.I)t=t.firstChild.firstChild,this.href&&(t=t.firstChild),"relative"!==(o=t.firstChild).style.position&&(o=o.nextSibling),l=(r=o.firstChild).firstChild;else{var d=i.addElement(t,"nobr",{isMathJax:!0});t=this.HTMLcreateSpan(d);var c=this.Get("alttext");c&&!t.getAttribute("aria-label")&&t.setAttribute("aria-label",c),o=i.createStack(t),r=i.createBox(o),o.style.fontSize=d.parentNode.style.fontSize,d.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"),(l=this.data[0].toHTML(r)).bbox.exactW=!1)}if(h=s&&s!==i.PHASE.II?l:i.Measured(l,r),!s||s===i.PHASE.III){i.placeBox(r,0,0);var m=h.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 p=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),h&&null!=h.bbox.width&&(t.style.minWidth=h.bbox.minWidth||t.style.width,t.style.width=h.bbox.width,r.style.width=o.style.width="100%",u.className+=" 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e=this.getValues("displaystyle","accent","accentunder","align"),s=this.data[this.base];if(!e.displaystyle&&null!=s&&(s.movablelimits||s.CoreMO().Get("movablelimits")))return(t=n.msubsup.prototype.toPreviewHTML.call(this,t)).className=t.className.replace(/munderover/,"msubsup"),t;t=this.PHTMLdefaultSpan(t,{childSpans:!0,className:"",noBBox:!0});var o=this.PHTMLbboxFor(this.over),r=this.PHTMLbboxFor(this.under),l=this.PHTMLbboxFor(this.base),h=this.PHTML,u=o.acc;if(this.data[this.over]){t.lastChild.firstChild&&(t.lastChild.firstChild.style.marginLeft=o.l=t.lastChild.firstChild.style.marginRight=o.r=0);var d=i.Element("span",{},[["span",{className:"MJXp-over"}]]);d.firstChild.appendChild(t.lastChild),t.childNodes.length>(this.data[this.under]?1:0)&&d.firstChild.appendChild(t.firstChild),this.data[this.over].PHTMLhandleScriptlevel(d.firstChild.firstChild),null!=u&&(o.vec&&(d.firstChild.firstChild.firstChild.style.fontSize="60%",o.h*=.6,o.d*=.6,o.w*=.6),u=u-o.d+.1,null!=l.t&&(u+=l.t-l.h),d.firstChild.firstChild.style.marginBottom=a.Em(u)),t.firstChild?t.insertBefore(d,t.firstChild):t.appendChild(d)}return this.data[this.under]&&(t.lastChild.firstChild&&(t.lastChild.firstChild.style.marginLeft=r.l=t.lastChild.firstChild.marginRight=r.r=0),this.data[this.under].PHTMLhandleScriptlevel(t.lastChild)),h.w=Math.max(.8*o.w,.8*r.w,l.w),h.h=.8*(o.h+o.d+(u||0))+l.h,h.d=l.d+.8*(r.h+r.d),t}}),n.msubsup.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t,{noBBox:!0}),this.data[this.base]||(t.firstChild?t.insertBefore(i.Element("span"),t.firstChild):t.appendChild(i.Element("span")));var e=this.data[this.base],n=this.data[this.sub],s=this.data[this.sup];e||(e={bbox:{h:.8,d:.2}}),t.firstChild.style.marginRight=".05em";var o=Math.max(.4,e.PHTML.h-.4),r=Math.max(.2,e.PHTML.d+.1),l=this.PHTML;if(s&&n){var h=i.Element("span",{className:"MJXp-script-box",style:{height:a.Em(o+.8*s.PHTML.h+r+.8*n.PHTML.d),"vertical-align":a.Em(-r-.8*n.PHTML.d)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":a.Em(-(s.PHTML.d-.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":a.Em(-(s.PHTML.h-.05))}}]]]]]]);n.PHTMLhandleScriptlevel(h.firstChild),s.PHTMLhandleScriptlevel(h.lastChild),h.firstChild.firstChild.firstChild.appendChild(t.lastChild),h.lastChild.firstChild.firstChild.appendChild(t.lastChild),t.appendChild(h),l.h=Math.max(e.PHTML.h,.8*s.PHTML.h+o),l.d=Math.max(e.PHTML.d,.8*n.PHTML.d+r),l.w=e.PHTML.w+Math.max(s.PHTML.w,n.PHTML.w)+.07}else s?(t.lastChild.style.verticalAlign=a.Em(o),s.PHTMLhandleScriptlevel(t.lastChild),l.h=Math.max(e.PHTML.h,.8*s.PHTML.h+o),l.d=Math.max(e.PHTML.d,.8*s.PHTML.d-o),l.w=e.PHTML.w+s.PHTML.w+.07):n&&(t.lastChild.style.verticalAlign=a.Em(-r),n.PHTMLhandleScriptlevel(t.lastChild),l.h=Math.max(e.PHTML.h,.8*n.PHTML.h-r),l.d=Math.max(e.PHTML.d,.8*n.PHTML.d+r),l.w=e.PHTML.w+n.PHTML.w+.07);return t}}),n.mfrac.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t,{childSpans:!0,className:"MJXp-box",forceChild:!0,noBBox:!0});var e=this.getValues("linethickness","displaystyle");e.displaystyle||(this.data[0]&&this.data[0].PHTMLhandleScriptlevel(t.firstChild),this.data[1]&&this.data[1].PHTMLhandleScriptlevel(t.lastChild));var n=i.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(t.lastChild),t.appendChild(n);var s=this.PHTMLbboxFor(0),o=this.PHTMLbboxFor(1),r=this.PHTML;if(r.w=.8*Math.max(s.w,o.w),r.h=s.h+s.d+.1+.25,r.d=o.h+o.d-.25,r.l=r.r=.125,e.linethickness=Math.max(0,a.length2em(e.linethickness||"0",0)),e.linethickness){var l=n.firstChild.firstChild.firstChild,h=a.Em(e.linethickness);l.style.borderTop="none",l.style.borderBottom=(e.linethickness<.15?"1px":h)+" solid",l.style.margin=h+" 0",h=e.linethickness,n.style.marginTop=a.Em(3*h-1.2),t.style.verticalAlign=a.Em(1.5*h+.1),r.h+=1.5*h-.1,r.d+=1.5*h}else n.style.marginTop="-.7em";return t}}),n.msqrt.Augment({toPreviewHTML:function(t){return t=this.PHTMLdefaultSpan(t,{childSpans:!0,className:"MJXp-box",forceChild:!0,noBBox:!0}),this.PHTMLlayoutRoot(t,t.firstChild),t},PHTMLlayoutRoot:function(t,e){var n=this.PHTMLbboxFor(0),s=Math.ceil(100*(n.h+n.d+.14)),o=a.Em(14/s),r=i.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":s+"%","margin-top":o}},["√"]]]),l=i.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]),h=1.2/2.2*s/100;if(s>150){var u=Math.ceil(150/s*10);r.firstChild.className="MJXp-right MJXp-scale"+u,r.firstChild.style.marginLeft=a.Em(h*(u/10-1)/s*100),h=h*u/10,l.firstChild.style.borderTopWidth=a.Em(.08/Math.sqrt(u/10))}return l.appendChild(e),t.appendChild(r),t.appendChild(l),this.PHTML.h=n.h+.18,this.PHTML.d=n.d,this.PHTML.w=n.w+h,t}}),n.mroot.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t,{childSpans:!0,className:"MJXp-box",forceChild:!0,noBBox:!0});var e=this.PHTMLbboxFor(1),n=t.removeChild(t.lastChild),s=this.PHTMLlayoutRoot(i.Element("span"),t.firstChild);n.className="MJXp-script";var o=parseInt(s.firstChild.firstChild.style.fontSize),r=o/120*.55+.8*e.d,l=o/120*-.6;return o>150&&(l*=.95*Math.ceil(150/o*10)/10),n.style.marginRight=a.Em(l),n.style.verticalAlign=a.Em(r),-l>.8*e.w&&(n.style.marginLeft=a.Em(-l-.8*e.w)),t.appendChild(n),t.appendChild(s),this.PHTML.w+=Math.max(0,.8*e.w+l),this.PHTML.h=Math.max(this.PHTML.h,.8*e.h+r),t},PHTMLlayoutRoot:n.msqrt.prototype.PHTMLlayoutRoot}),n.mfenced.Augment({toPreviewHTML:function(t){t=this.PHTMLcreateSpan(t),this.PHTMLhandleStyle(t),this.PHTMLhandleColor(t),this.addFakeNodes(),this.PHTMLaddChild(t,"open",{});for(var e=0,i=this.data.length;e<i;e++)this.PHTMLaddChild(t,"sep"+e,{}),this.PHTMLaddChild(t,e,{});this.PHTMLaddChild(t,"close",{});var a=this.PHTML.h,n=this.PHTML.d;for(this.PHTMLstretchChild("open",a,n),e=0,i=this.data.length;e<i;e++)this.PHTMLstretchChild("sep"+e,a,n),this.PHTMLstretchChild(e,a,n);return this.PHTMLstretchChild("close",a,n),t}}),n.mrow.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t);for(var e=this.PHTML.h,i=this.PHTML.d,a=0,n=this.data.length;a<n;a++)this.PHTMLstretchChild(a,e,i);return t}}),n.mstyle.Augment({toPreviewHTML:function(t){return t=this.PHTMLdefaultSpan(t),this.PHTMLhandleScriptlevel(t),t}}),n.TeXAtom.Augment({toPreviewHTML:function(t){return(t=this.PHTMLdefaultSpan(t)).className="MJXp-mrow",t}}),n.mtable.Augment({toPreviewHTML:function(t){t=this.PHTMLdefaultSpan(t,{noBBox:!0});var e,n,s,o,r=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","width"),l=MathJax.Hub.SplitList,h=l(r.columnspacing),u=l(r.rowspacing),d=l(r.columnalign),c=l(r.rowalign);for(e=0,n=h.length;e<n;e++)h[e]=a.length2em(h[e]);for(e=0,n=u.length;e<n;e++)u[e]=a.length2em(u[e]);for(var m=i.Element("span");t.firstChild;)m.appendChild(t.firstChild);t.appendChild(m);var p=0,f=0;for(e=0,n=this.data.length;e<n;e++){var M=this.data[e];if(M){var g=a.arrayEntry(u,e-1),x=a.arrayEntry(c,e),b=M.PHTML;M.PHTMLspanElement().style.verticalAlign=x;var v="mlabeledtr"===M.type?1:0;for(s=0,o=M.data.length;s<o-v;s++){var T=M.data[s+v];if(T){var y=a.arrayEntry(h,s-1),C=a.arrayEntry(d,s),L=T.PHTMLspanElement();s&&(b.w+=y,L.style.paddingLeft=a.Em(y)),e&&(L.style.paddingTop=a.Em(g)),L.style.textAlign=C}}p+=b.h+b.d,e&&(p+=g),b.w>f&&(f=b.w)}}var E=this.PHTML;return E.w=f,E.h=p/2+.25,E.d=p/2-.25,E.l=E.r=.125,t}}),n.mlabeledtr.Augment({PHTMLdefaultSpan:function(t,e){e||(e={}),t=this.PHTMLcreateSpan(t),this.PHTMLhandleStyle(t),this.PHTMLhandleColor(t),this.isToken&&this.PHTMLhandleToken(t);for(var i=1,a=this.data.length;i<a;i++)this.PHTMLaddChild(t,i,e);return t}}),n.semantics.Augment({toPreviewHTML:function(t){return t=this.PHTMLcreateSpan(t),this.data[0]&&(this.data[0].toPreviewHTML(t),MathJax.Hub.Insert(this.data[0].PHTML||{},this.PHTML)),t}}),n.annotation.Augment({toPreviewHTML:function(t){}}),n["annotation-xml"].Augment({toPreviewHTML:function(t){}}),MathJax.Hub.Register.StartupHook("onLoad",(function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)}))})),MathJax.Hub.Register.StartupHook("End Cookie",(function(){"None"!==e.config.menuSettings.zoom&&t.Require("[MathJax]/extensions/MathZoom.js")}))}(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.PreviewHTML),function(t,e,i){var a=t.config.menuSettings,n=MathJax.OutputJax,s=i.isMSIE&&(document.documentMode||0)<8,o=MathJax.Extension["fast-preview"]={version:"2.7.9",enabled:!0,config:t.CombineConfig("fast-preview",{Chunks:{EqnChunk:1e4,EqnChunkFactor:1,EqnChunkDelay:0},color:"inherit!important",updateTime:30,updateDelay:6,messageStyle:"none",disabled:i.isMSIE&&!i.versionAtLeast("8.0")}),Config:function(){var e,i,n,s,r;t.config["CHTML-preview"]&&MathJax.Hub.Config({"fast-preview":t.config["CHTML-preview"]});var l=this.config;l.disabled||null!=a.FastPreview||t.Config({menuSettings:{FastPreview:!0}}),a.FastPreview&&(MathJax.Ajax.Styles({".MathJax_Preview .MJXf-math":{color:l.color}}),t.Config({"HTML-CSS":l.Chunks,CommonHTML:l.Chunks,SVG:l.Chunks})),t.Register.MessageHook("Begin Math Output",(function(){!s&&o.Active()&&(e=t.processUpdateTime,i=t.processUpdateDelay,n=t.config.messageStyle,t.processUpdateTime=l.updateTime,t.processUpdateDelay=l.updateDelay,t.Config({messageStyle:l.messageStyle}),MathJax.Message.Clear(0,0),r=!0)})),t.Register.MessageHook("End Math Output",(function(){!s&&r&&(t.processUpdateTime=e,t.processUpdateDelay=i,t.Config({messageStyle:n}),s=!0)}))},Disable:function(){this.enabled=!1},Enable:function(){this.enabled=!0},Active:function(){return a.FastPreview&&this.enabled&&!(n[a.renderer]||{}).noFastPreview},Preview:function(t){if(this.Active()&&t.script.parentNode){var i=t.script.MathJax.preview||t.script.previousSibling;return i&&i.className===MathJax.Hub.config.preRemoveClass||(i=e.Element("span",{className:MathJax.Hub.config.preRemoveClass}),t.script.parentNode.insertBefore(i,t.script),t.script.MathJax.preview=i),i.innerHTML="",i.style.color=s?"black":"inherit",this.postFilter(i,t)}},postFilter:function(e,i){if(!i.math.root.toPreviewHTML){var a=MathJax.Callback.Queue();a.Push(["Require",MathJax.Ajax,"[MathJax]/jax/output/PreviewHTML/config.js"],["Require",MathJax.Ajax,"[MathJax]/jax/output/PreviewHTML/jax.js"]),t.RestartAfter(a.Push({}))}i.math.root.toPreviewHTML(e)},Register:function(e){t.Register.StartupHook(e+" Jax Require",(function(){MathJax.InputJax[e].postfilterHooks.Add(["Preview",MathJax.Extension["fast-preview"]],50)}))}};o.Register("TeX"),o.Register("MathML"),o.Register("AsciiMath"),t.Register.StartupHook("End Config",["Config",o]),t.Startup.signal.Post("fast-preview Ready")}(MathJax.Hub,MathJax.HTML,MathJax.Hub.Browser),MathJax.Ajax.loadComplete("[MathJax]/extensions/fast-preview.js"),function(t,e,i,a){var n=i.config.menuSettings,s=MathJax.Extension.AssistiveMML={version:"2.7.9",config:i.CombineConfig("AssistiveMML",{disabled:!1,styles:{".MJX_Assistive_MathML":{position:"absolute!important",top:0,left:0,clip:i.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(){this.config.disabled||null!=n.assistiveMML||i.Config({menuSettings:{assistiveMML:!0}}),t.Styles(this.config.styles),i.Register.MessageHook("End Math",(function(t){if(n.assistiveMML)return s.AddAssistiveMathML(t[1])}))},AddAssistiveMathML:function(t){var e={jax:i.getAllJax(t),i:0,callback:MathJax.Callback({})};return this.HandleMML(e),e.callback},RemoveAssistiveMathML:function(t){for(var e,a=i.getAllJax(t),n=0,s=a.length;n<s;n++)(e=document.getElementById(a[n].inputID+"-Frame"))&&e.getAttribute("data-mathml")&&(e.removeAttribute("data-mathml"),e.lastChild&&e.lastChild.className.match(/MJX_Assistive_MathML/)&&e.removeChild(e.lastChild))},HandleMML:function(t){var e,i,n,s,o=t.jax.length,r=MathJax.ElementJax.mml;for(r.copyAttributes.id=1;t.i<o;){if(e=t.jax[t.i],n=document.getElementById(e.inputID+"-Frame"),"NativeMML"!==e.outputJax&&"PlainSource"!==e.outputJax&&n&&!n.getAttribute("data-mathml")){try{i=e.root.toMathML("").replace(/\n */g,"").replace(/<!--.*?-->/g,"")}catch(e){if(r.copyAttributes.id=!0,!e.restart)throw e;return MathJax.Callback.After(["HandleMML",this,t],e.restart)}n.setAttribute("data-mathml",i),s=a.addElement(n,"span",{isMathJax:!0,unselectable:"on",className:"MJX_Assistive_MathML"+("block"===e.root.Get("display")?" MJX_Assistive_MathML_Block":"")});try{s.innerHTML=i}catch(t){}n.style.position="relative",n.setAttribute("role","presentation"),n.firstChild.setAttribute("aria-hidden","true"),s.setAttribute("role","presentation")}t.i++}r.copyAttributes.id=!0,t.callback()}};i.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])})),function(t,e){var i,a,n=t.config.menuSettings,s=Function.prototype.bind?function(t,e){return t.bind(e)}:function(t,e){return function(){t.apply(e,arguments)}},o=Object.keys||function(t){var e=[];for(var i in t)t.hasOwnProperty(i)&&e.push(i);return e},r=MathJax.Ajax.config.path;r.a11y||(r.a11y=t.config.root+"/extensions/a11y");var l=e["accessibility-menu"]={version:"1.6.0",prefix:"",defaults:{},modules:[],MakeOption:function(t){return l.prefix+t},GetOption:function(t){return n[l.MakeOption(t)]},AddDefaults:function(){for(var t,e=o(l.defaults),i=0;t=e[i];i++){var a=l.MakeOption(t);void 0===n[a]&&(n[a]=l.defaults[t])}},AddMenu:function(){for(var t,e=Array(this.modules.length),n=0;t=this.modules[n];n++)e[n]=t.placeHolder;var s,o,r=a.FindId("Accessibility");r?(e.unshift(i.RULE()),r.submenu.items.push.apply(r.submenu.items,e)):((s=(a.FindId("Settings","Renderer")||{}).submenu)&&(e.unshift(i.RULE()),e.unshift(s.items.pop()),e.unshift(s.items.pop())),e.unshift("Accessibility"),r=i.SUBMENU.apply(i.SUBMENU,e),(o=a.IndexOfId("Locale"))?a.items.splice(o,0,r):a.items.push(i.RULE(),r))},Register:function(t){l.defaults[t.option]=!1,l.modules.push(t)},Startup:function(){i=MathJax.Menu.ITEM,a=MathJax.Menu.menu;for(var t,e=0;t=this.modules[e];e++)t.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var e,i=[],a=0;e=this.modules[a];a++)n[e.option]&&i.push(e.module);return i.length?t.Startup.loadArray(i):null}},h=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(t,e,i,a,n){this.option=t,this.name=[e.replace(/ /g,""),e],this.module=i,this.extension=a,this.submenu=n||!1},CreateMenu:function(){var t=s(this.Load,this);this.submenu?this.placeHolder=i.SUBMENU(this.name,i.CHECKBOX(["Activate","Activate"],l.MakeOption(this.option),{action:t}),i.RULE(),i.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=i.CHECKBOX(this.name,l.MakeOption(this.option),{action:t})},Load:function(){t.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(t){var e=MathJax.Extension[this.extension];e&&(e.Enable(!0,!0),MathJax.Menu.saveCookie())}});l.Register(h("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),l.Register(h("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),l.Register(h("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),l.AddDefaults(),t.Register.StartupHook("End Extensions",(function(){t.Register.StartupHook("MathMenu Ready",(function(){l.Startup(),t.Startup.signal.Post("Accessibility Menu Ready")}),5)}),5),MathJax.Hub.Register.StartupHook("End Cookie",(function(){MathJax.Callback.Queue(["LoadExtensions",l],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])}))}(MathJax.Hub,MathJax.Extension),MathJax.Ajax.loadComplete("[MathJax]/config/AM_HTMLorMML-full.js");