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h=c.Element("span",{id:t.hover.id,isMathJax:!0,style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{className:"MathJax_Hover_Frame",isMathJax:!0,style:{display:"inline-block",position:"absolute",top:this.Px(-s.h-o-l-(s.y||0)),left:this.Px(-r-l+(s.x||0)),width:this.Px(s.w+2*r),height:this.Px(s.h+s.d+2*o),opacity:0,filter:"alpha(opacity=0)"}}]]),m=c.Element("span",{isMathJax:!0,id:t.hover.id+"Menu",className:"MathJax_Menu_Button",style:{display:"inline-block","z-index":1,width:0,height:0,position:"relative"}},[["span",{className:"MathJax_Hover_Arrow",isMathJax:!0,math:e,onclick:this.HoverMenu,jax:a.id,style:{left:this.Px(s.w+r+l+(s.x||0)+u.button.x),top:this.Px(-s.h-o-l-(s.y||0)-u.button.y),opacity:0,filter:"alpha(opacity=0)"}},[["span",{isMathJax:!0},"▼"]]]]);s.width&&(h.style.width=m.style.width=s.width,h.style.marginRight=m.style.marginRight="-"+s.width,h.firstChild.style.width=s.width,m.firstChild.style.left="",m.firstChild.style.right=this.Px(u.button.wx)),i.parentNode.insertBefore(h,i),n&&i.parentNode.insertBefore(m,i),i.style&&(i.style.position="relative"),this.ReHover(t)}},ReHover:function(t){t.hover.remove&&clearTimeout(t.hover.remove),t.hover.remove=setTimeout(M(["UnHover",this,t]),u.fadeoutDelay),this.HoverFadeTimer(t,u.fadeinInc)},UnHover:function(t){t.hover.nofade||this.HoverFadeTimer(t,-u.fadeoutInc,u.fadeoutStart)},HoverFade:function(t){delete t.hover.timer,t.hover.opacity=Math.max(0,Math.min(1,t.hover.opacity+t.hover.inc)),t.hover.opacity=Math.floor(1e3*t.hover.opacity)/1e3;var e=document.getElementById(t.hover.id),a=document.getElementById(t.hover.id+"Menu");e.firstChild.style.opacity=t.hover.opacity,e.firstChild.style.filter="alpha(opacity="+Math.floor(100*t.hover.opacity)+")",a&&(a.firstChild.style.opacity=t.hover.opacity,a.firstChild.style.filter=e.style.filter),1!==t.hover.opacity&&(0<t.hover.opacity?this.HoverFadeTimer(t,t.hover.inc):(e.parentNode.removeChild(e),a&&a.parentNode.removeChild(a),t.hover.remove&&clearTimeout(t.hover.remove),delete t.hover))},HoverFadeTimer:function(t,e,a){t.hover.inc=e,t.hover.timer||(t.hover.timer=setTimeout(M(["HoverFade",this,t]),a||u.fadeDelay))},HoverMenu:function(t){return t||(t=window.event),T[this.jax].ContextMenu(t,this.math,!0)},ClearHover:function(t){t.hover.remove&&clearTimeout(t.hover.remove),t.hover.timer&&clearTimeout(t.hover.timer),v.ClearHoverTimer(),delete 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e=document.documentMode||0,a=t.versionAtLeast("8.0");C.msieBorderWidthBug="BackCompat"===document.compatMode,C.msieEventBug=t.isIE9,C.msieAlignBug=!a||e<8,e<9&&(b.LEFTBUTTON=1)},Safari:function(t){C.safariContextMenuBug=!0},Opera:function(t){C.operaPositionBug=!0},Konqueror:function(t){C.noContextMenuBug=!0}}),C.topImg=C.msieAlignBug?c.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):c.Element("span",{style:{width:0,height:0,display:"inline-block"}}),C.operaPositionBug&&(C.topImg.style.border="1px solid"),C.config=u=f.CombineConfig("MathEvents",u);M.Queue(f.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",v],["Styles",x,u.styles],["Post",f.Startup.signal,"MathEvents 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Positive='true')"},"#MathJax_ZoomOverlay":{position:"absolute",left:0,top:0,"z-index":300,display:"inline-block",width:"100%",height:"100%",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"},"#MathJax_ZoomFrame":{position:"relative",display:"inline-block",height:0,width:0},"#MathJax_ZoomEventTrap":{position:"absolute",left:0,top:0,"z-index":302,display:"inline-block",border:0,padding:0,margin:0,"background-color":"white",opacity:0,filter:"alpha(opacity=0)"}}});MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){T=MathJax.Extension.MathEvents.Event,M=MathJax.Extension.MathEvents.Event.False,g=MathJax.Extension.MathEvents.Hover});var l=MathJax.Extension.MathZoom={version:"2.7.5",settings:f.config.menuSettings,scrollSize:18,HandleEvent:function(t,e,a){return!(!l.settings.CTRL||t.ctrlKey)||(!(!l.settings.ALT||t.altKey)||(!(!l.settings.CMD||t.metaKey)||(!(!l.settings.Shift||t.shiftKey)||(!l[e]||l[e](t,a)))))},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(t,e){this.Remove(),g.ClearHoverTimer(),T.ClearSelection();var a=MathJax.OutputJax[e.jaxID],i=a.getJaxFromMath(e);i.hover&&g.UnHover(i);var s=this.findContainer(e),n=Math.floor(.85*s.clientWidth),r=Math.max(document.body.clientHeight,document.documentElement.clientHeight);"visible"!==this.getOverflow(s)&&(r=Math.min(s.clientHeight,r)),r=Math.floor(.85*r);var o=x.Element("span",{id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]),l=o.lastChild,h=l.firstChild,m=o.firstChild;e.parentNode.insertBefore(o,e),e.parentNode.insertBefore(e,o),h.addEventListener&&h.addEventListener("mousedown",this.Remove,!0);var c=l.offsetWidth||l.clientWidth;if(n-=c,r-=c,l.style.maxWidth=n+"px",l.style.maxHeight=r+"px",this.msieTrapEventBug){var d=x.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});o.insertBefore(d,l)}if(this.msieZIndexBug){var u=x.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});o.style.position="relative",o.style.zIndex=E.styles["#MathJax_ZoomOverlay"]["z-index"],o=u}var p=a.Zoom(i,h,e,n,r);return this.msiePositionBug&&(this.msieSizeBug&&(l.style.height=p.zH+"px",l.style.width=p.zW+"px"),l.offsetHeight>r&&(l.style.height=r+"px",l.style.width=p.zW+this.scrollSize+"px"),l.offsetWidth>n&&(l.style.width=n+"px",l.style.height=p.zH+this.scrollSize+"px")),this.operaPositionBug&&(l.style.width=Math.min(n,p.zW)+"px"),l.offsetWidth>c&&l.offsetWidth-c<n&&l.offsetHeight-c<r&&(l.style.overflow="visible"),this.Position(l,p),this.msieTrapEventBug&&(d.style.height=l.clientHeight+"px",d.style.width=l.clientWidth+"px",d.style.left=parseFloat(l.style.left)+l.clientLeft+"px",d.style.top=parseFloat(l.style.top)+l.clientTop+"px"),l.style.visibility="","Hover"===this.settings.zoom&&(m.onmouseover=this.Remove),window.addEventListener?addEventListener("resize",this.Resize,!1):window.attachEvent?attachEvent("onresize",this.Resize):(this.onresize=window.onresize,window.onresize=this.Resize),f.signal.Post(["math zoomed",i]),M(t)},Position:function(t,e){t.style.display="none";var a=this.Resize(),i=a.x,s=a.y,n=e.mW;t.style.display="";var r=-n-Math.floor((t.offsetWidth-n)/2),o=e.Y;t.style.left=Math.max(r,10-i)+"px",t.style.top=Math.max(o,10-s)+"px",l.msiePositionBug||l.SetWH()},Resize:function(t){l.onresize&&l.onresize(t);var e=document.getElementById("MathJax_ZoomFrame"),a=document.getElementById("MathJax_ZoomOverlay"),i=l.getXY(e),s=l.findContainer(e);if("visible"!==l.getOverflow(s)){a.scroll_parent=s;var n=l.getXY(s);i.x-=n.x,i.y-=n.y,n=l.getBorder(s),i.x-=n.x,i.y-=n.y}return a.style.left=-i.x+"px",a.style.top=-i.y+"px",l.msiePositionBug?setTimeout(l.SetWH,0):l.SetWH(),i},SetWH:function(){var t=document.getElementById("MathJax_ZoomOverlay");if(t){t.style.display="none";var e=t.scroll_parent||document.documentElement||document.body;t.style.width=e.scrollWidth+"px",t.style.height=Math.max(e.clientHeight,e.scrollHeight)+"px",t.style.display=""}},findContainer:function(t){for(t=t.parentNode;t.parentNode&&t!==document.body&&"visible"===l.getOverflow(t);)t=t.parentNode;return t},getOverflow:window.getComputedStyle?function(t){return getComputedStyle(t).overflow}:function(t){return(t.currentStyle||{overflow:"visible"}).overflow},getBorder:function(t){var e={thin:1,medium:2,thick:3},a=window.getComputedStyle?getComputedStyle(t):t.currentStyle||{borderLeftWidth:0,borderTopWidth:0},i=a.borderLeftWidth,s=a.borderTopWidth;return{x:i=e[i]?e[i]:parseInt(i),y:s=e[s]?e[s]:parseInt(s)}},getXY:function(t){var e,a=0,i=0;for(e=t;e.offsetParent;)a+=e.offsetLeft,e=e.offsetParent;for(l.operaPositionBug&&(t.style.border="1px solid"),e=t;e.offsetParent;)i+=e.offsetTop,e=e.offsetParent;return l.operaPositionBug&&(t.style.border=""),{x:a,y:i}},Remove:function(t){var e=document.getElementById("MathJax_ZoomFrame");if(e){var a=MathJax.OutputJax[e.previousSibling.jaxID].getJaxFromMath(e.previousSibling);if(f.signal.Post(["math unzoomed",a]),e.parentNode.removeChild(e),(e=document.getElementById("MathJax_ZoomTracker"))&&e.parentNode.removeChild(e),l.operaRefreshBug){var i=x.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(i)}window.removeEventListener?removeEventListener("resize",l.Resize,!1):window.detachEvent?detachEvent("onresize",l.Resize):(window.onresize=l.onresize,delete l.onresize)}return M(t)}};f.Browser.Select({MSIE:function(t){var e=document.documentMode||0,a=9<=e;l.msiePositionBug=!a,l.msieSizeBug=t.versionAtLeast("7.0")&&(!document.documentMode||7===e||8===e),l.msieZIndexBug=e<=7,l.msieInlineBlockAlignBug=e<=7,l.msieTrapEventBug=!window.addEventListener,"BackCompat"===document.compatMode&&(l.scrollSize=52),a&&delete E.styles["#MathJax_Zoom"].filter},Opera:function(t){l.operaPositionBug=!0,l.operaRefreshBug=!0}}),l.topImg=l.msieInlineBlockAlignBug?x.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):x.Element("span",{style:{width:0,height:0,display:"inline-block"}}),(l.operaPositionBug||l.msieTopBug)&&(l.topImg.style.border="1px solid"),MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",t,E.styles],["Post",f.Startup.signal,"MathZoom Ready"],["loadComplete",t,"[MathJax]/extensions/MathZoom.js"])}(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML),function(o,E,s,n,r){var C=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:"2.7.5",signal:C};var L,i,a,l=function(t){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",t]].concat([].slice.call(arguments,1)))},h=MathJax.Object.isArray,b=o.Browser.isPC,t=o.Browser.isMSIE,m=8<(document.documentMode||0),e=b?null:"5px",v=o.CombineConfig("MathMenu",{delay:150,showRenderer:!0,showMathPlayer:!0,showFontMenu:!1,showContext:!1,showDiscoverable:!1,showLocale:!0,showLocaleURL:!1,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 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#808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:b?"2px":"5px 0px",border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap",float:"none","z-index":201,"border-radius":e,"-webkit-border-radius":e,"-moz-border-radius":e,"-khtml-border-radius":e,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:b?"2px 2em":"1px 2em",background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":t?"'Arial unicode MS'":null,"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":t?"'Arial unicode MS'":null},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:b?"1em":".7em"},".MathJax_MenuRadioCheck.RTL":{right:b?"1em":".7em",left:"auto"},".MathJax_MenuLabel":{padding:b?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em","font-style":"italic"},".MathJax_MenuRule":{"border-top":b?"1px solid #CCCCCC":"1px solid #DDDDDD",margin:b?"4px 1px 0px":"4px 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6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});o.Register.StartupHook("MathEvents Ready",function(){L=MathJax.Extension.MathEvents.Event.False,i=MathJax.Extension.MathEvents.Hover,a=MathJax.Extension.MathEvents.Event.KEY});var c=MathJax.Object.Subclass({Keydown:function(t,e){switch(t.keyCode){case a.ESCAPE:this.Remove(t,e);break;case a.RIGHT:this.Right(t,e);break;case a.LEFT:this.Left(t,e);break;case a.UP:this.Up(t,e);break;case a.DOWN:this.Down(t,e);break;case a.RETURN:case a.SPACE:this.Space(t,e);break;default:return}return 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t,e,a,i=r.outerHeight-r.innerHeight||30,s=r.outerWidth-r.innerWidth||30;s=Math.max(140,Math.min(Math.floor(.5*screen.width),o.offsetWidth+s+25)),i=Math.max(40,Math.min(Math.floor(.5*screen.height),o.offsetHeight+i+25)),y.prototype.msieHeightBug&&(i+=35),r.resizeTo(s,i);try{a=n.screenX}catch(t){}n&&null!=a&&(t=Math.max(0,Math.min(n.screenX-Math.floor(s/2),screen.width-s-20)),e=Math.max(0,Math.min(n.screenY-Math.floor(i/2),screen.height-i-20)),r.moveTo(t,e))},50)}},y.Scale=function(){var t,e,a=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],i=a.length,s=100;for(t=0;t<i;t++)if(e=r[a[t]]){s=e.config.scale;break}var n=prompt(l("ScaleMath","Scale all mathematics (compared to surrounding text) by"),s+"%");if(n)if(n.match(/^\s*\d+(\.\d*)?\s*%?\s*$/))if(n=parseFloat(n)){if(n!==s){for(t=0;t<i;t++)(e=r[a[t]])&&(e.config.scale=n);y.cookie.scale=o.config.scale=n,y.saveCookie(),o.Queue(["Rerender",o])}}else alert(l("NonZeroScale","The scale should not be zero"));else 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Events"],"mpMouse",{action:y.MPEvents,hidden:m})),N.SUBMENU(["FontPrefs","Font Preference"],{hidden:!v.showFontMenu},N.LABEL(["ForHTMLCSS","For HTML-CSS:"]),N.RADIO(["Auto","Auto"],"font",{action:y.Font}),N.RULE(),N.RADIO(["TeXLocal","TeX (local)"],"font",{action:y.Font}),N.RADIO(["TeXWeb","TeX (web)"],"font",{action:y.Font}),N.RADIO(["TeXImage","TeX (image)"],"font",{action:y.Font}),N.RULE(),N.RADIO(["STIXLocal","STIX (local)"],"font",{action:y.Font}),N.RADIO(["STIXWeb","STIX (web)"],"font",{action:y.Font}),N.RULE(),N.RADIO(["AsanaMathWeb","Asana Math (web)"],"font",{action:y.Font}),N.RADIO(["GyrePagellaWeb","Gyre Pagella (web)"],"font",{action:y.Font}),N.RADIO(["GyreTermesWeb","Gyre Termes (web)"],"font",{action:y.Font}),N.RADIO(["LatinModernWeb","Latin Modern (web)"],"font",{action:y.Font}),N.RADIO(["NeoEulerWeb","Neo Euler (web)"],"font",{action:y.Font})),N.SUBMENU(["ContextMenu","Contextual 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Trigger").submenu).items[0].disabled=e.items[1].disabled=!0,"Hover"!==t.zoom&&"Click"!=t.zoom||(t.zoom="None"),e.items=e.items.slice(0,4),navigator.appVersion.match(/[ (]Android[) ]/)&&y.ITEM.SUBMENU.Augment({marker:"»"})),y.CreateLocaleMenu(),y.CreateAnnotationMenu()}),y.showRenderer=function(t){y.cookie.showRenderer=v.showRenderer=t,y.saveCookie(),y.menu.Find("Math Settings","Math Renderer").hidden=!t},y.showMathPlayer=function(t){y.cookie.showMathPlayer=v.showMathPlayer=t,y.saveCookie(),y.menu.Find("Math Settings","MathPlayer").hidden=!t},y.showFontMenu=function(t){y.cookie.showFontMenu=v.showFontMenu=t,y.saveCookie(),y.menu.Find("Math Settings","Font Preference").hidden=!t},y.showContext=function(t){y.cookie.showContext=v.showContext=t,y.saveCookie(),y.menu.Find("Math Settings","Contextual Menu").hidden=!t},y.showDiscoverable=function(t){y.cookie.showDiscoverable=v.showDiscoverable=t,y.saveCookie(),y.menu.Find("Math Settings","Highlight on Hover").hidden=!t,y.menu.Find("Math 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this.toMathMLclass(s),s.length?" 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t:"§",sharp:"♯",sigma:"σ",sigmav:"ς",simne:"≆",smile:"⌣",spades:"♠",sub:"⊂",subE:"⫅",subnE:"⫋",subne:"⊊",supE:"⫆",supnE:"⫌",supne:"⊋",swarr:"↙",tau:"τ",theta:"θ",thetav:"ϑ",tilde:"˜",times:"×",triangle:"▵",triangleq:"≜",upsi:"υ",upuparrows:"⇈",veebar:"⊻",vellip:"⋮",weierp:"℘",xi:"ξ",yen:"¥",zeta:"ζ",zigrarr:"⇝"},y.loadComplete("jax.js"),A=MathJax.InputJax.MathML,MathJax.Hub.Insert(A.Parse.Entity,{Ascr:"𝒜",Bscr:"ℬ",Cscr:"𝒞",Dscr:"𝒟",Escr:"ℰ",Fscr:"ℱ",Gscr:"𝒢",Hscr:"ℋ",Iscr:"ℐ",Jscr:"𝒥",Kscr:"𝒦",Lscr:"ℒ",Mscr:"ℳ",Nscr:"𝒩",Oscr:"𝒪",Pscr:"𝒫",Qscr:"𝒬",Rscr:"ℛ",Sscr:"𝒮",Tscr:"𝒯",Uscr:"𝒰",Vscr:"𝒱",Wscr:"𝒲",Xscr:"𝒳",Yscr:"𝒴",Zscr:"𝒵",ascr:"𝒶",bscr:"𝒷",cscr:"𝒸",dscr:"𝒹",escr:"ℯ",fscr:"𝒻",gscr:"ℊ",hscr:"𝒽",iscr:"𝒾",jscr:"𝒿",kscr:"𝓀",lscr:"𝓁",mscr:"𝓂",nscr:"𝓃",oscr:"ℴ",pscr:"𝓅",qscr:"𝓆",rscr:"𝓇",sscr:"𝓈",tscr:"𝓉",uscr:"𝓊",vscr:"𝓋",wscr:"𝓌",xscr:"𝓍",yscr:"𝓎",zscr:"𝓏"}),MathJax.Ajax.loadComplete(A.entityDir+"/scr.js"),w=MathJax.InputJax.MathML,MathJax.Hub.Insert(w.Parse.Entity,{Aopf:"𝔸",Bopf:"𝔹",Copf:"ℂ",Dopf:"𝔻",Eopf:"𝔼",Fopf:"𝔽",Gopf:"𝔾",Hopf:"ℍ",Iopf:"𝕀",Jopf:"𝕁",Kopf:"𝕂",Lopf:"𝕃",Mopf:"𝕄",Nopf:"ℕ",Oopf:"𝕆",Popf:"ℙ",Qopf:"ℚ",Ropf:"ℝ",Sopf:"𝕊",Topf:"𝕋",Uopf:"𝕌",Vopf:"𝕍",Wopf:"𝕎",Xopf:"𝕏",Yopf:"𝕐",Zopf:"ℤ",aopf:"𝕒",bopf:"𝕓",copf:"𝕔",dopf:"𝕕",eopf:"𝕖",fopf:"𝕗",gopf:"𝕘",hopf:"𝕙",iopf:"𝕚",jopf:"𝕛",kopf:"𝕜",lopf:"𝕝",mopf:"𝕞",nopf:"𝕟",oopf:"𝕠",popf:"𝕡",qopf:"𝕢",ropf:"𝕣",sopf:"𝕤",topf:"𝕥",uopf:"𝕦",vopf:"𝕧",wopf:"𝕨",xopf:"𝕩",yopf:"𝕪",zopf:"𝕫"}),MathJax.Ajax.loadComplete(w.entityDir+"/opf.js"),S=MathJax.InputJax.MathML,MathJax.Hub.Insert(S.Parse.Entity,{ZHcy:"Ж",Zacute:"Ź",Zcaron:"Ž",Zcy:"З",Zdot:"Ż",ZeroWidthSpace:"​",Zeta:"Ζ",zacute:"ź",zcaron:"ž",zcy:"з",zdot:"ż",zeetrf:"ℨ",zhcy:"ж",zwj:"‍",zwnj:"‌"}),MathJax.Ajax.loadComplete(S.entityDir+"/z.js"),I=MathJax.InputJax.MathML,MathJax.Hub.Insert(I.Parse.Entity,{GJcy:"Ѓ",GT:">",Gammad:"Ϝ",Gbreve:"Ğ",Gcedil:"Ģ",Gcirc:"Ĝ",Gcy:"Г",Gdot:"Ġ",GreaterGreater:"⪢",Gt:"≫",gE:"≧",gacute:"ǵ",gammad:"ϝ",gbreve:"ğ",gcirc:"ĝ",gcy:"г",gdot:"ġ",ge:"≥",gel:"⋛",geq:"≥",geqq:"≧",geqslant:"⩾",ges:"⩾",gescc:"⪩",gesdot:"⪀",gesdoto:"⪂",gesdotol:"⪄",gesl:"⋛︀",gesles:"⪔",gg:"≫",ggg:"⋙",gjcy:"ѓ",gl:"≷",glE:"⪒",gla:"⪥",glj:"⪤",gnapprox:"⪊",gneq:"⪈",gneqq:"≩",grave:"`",gsim:"≳",gsime:"⪎",gsiml:"⪐",gtcc:"⪧",gtcir:"⩺",gtlPar:"⦕",gtquest:"⩼",gtrapprox:"⪆",gtrarr:"⥸",gtrdot:"⋗",gtreqless:"⋛",gtreqqless:"⪌",gtrless:"≷",gtrsim:"≳",gvertneqq:"≩︀",gvnE:"≩︀"}),MathJax.Ajax.loadComplete(I.entityDir+"/g.js"),J=MathJax.InputJax.MathML,MathJax.Hub.Insert(J.Parse.Entity,{RBarr:"⤐",REG:"®",Racute:"Ŕ",Rang:"⟫",Rarrtl:"⤖",Rcaron:"Ř",Rcedil:"Ŗ",Rcy:"Р",ReverseElement:"∋",ReverseUpEquilibrium:"⥯",Rho:"Ρ",RightArrowBar:"⇥",RightDoubleBracket:"⟧",RightDownTeeVector:"⥝",RightDownVectorBar:"⥕",RightTeeVector:"⥛",RightTriangleBar:"⧐",RightUpDownVector:"⥏",RightUpTeeVector:"⥜",RightUpVectorBar:"⥔",RightVectorBar:"⥓",RoundImplies:"⥰",RuleDelayed:"⧴",rAarr:"⇛",rArr:"⇒",rAtail:"⤜",rBarr:"⤏",rHar:"⥤",race:"∽̱",racute:"ŕ",radic:"√",raemptyv:"⦳",rang:"⟩",rangd:"⦒",range:"⦥",rangle:"⟩",raquo:"»",rarr:"→",rarrap:"⥵",rarrb:"⇥",rarrbfs:"⤠",rarrc:"⤳",rarrfs:"⤞",rarrhk:"↪",rarrlp:"↬",rarrpl:"⥅",rarrsim:"⥴",rarrw:"↝",ratail:"⤚",ratio:"∶",rationals:"ℚ",rbarr:"⤍",rbbrk:"❳",rbrke:"⦌",rbrksld:"⦎",rbrkslu:"⦐",rcaron:"ř",rcedil:"ŗ",rceil:"⌉",rcub:"}",rcy:"р",rdca:"⤷",rdldhar:"⥩",rdquo:"”",rdquor:"”",rdsh:"↳",real:"ℜ",realine:"ℛ",realpart:"ℜ",reals:"ℝ",rect:"▭",reg:"®",rfisht:"⥽",rfloor:"⌋",rhard:"⇁",rharu:"⇀",rharul:"⥬",rightarrow:"→",rightarrowtail:"↣",rightharpoondown:"⇁",rightharpoonup:"⇀",rightleftarrows:"⇄",rightleftharpoons:"⇌",rightsquigarrow:"↝",risingdotseq:"≓",rlarr:"⇄",rlhar:"⇌",rlm:"‏",rmoustache:"⎱",rnmid:"⫮",roang:"⟭",roarr:"⇾",robrk:"⟧",ropar:"⦆",roplus:"⨮",rotimes:"⨵",rpar:")",rpargt:"⦔",rppolint:"⨒",rrarr:"⇉",rsaquo:"›",rsh:"↱",rsqb:"]",rsquo:"’",rsquor:"’",rthree:"⋌",rtrie:"⊵",rtrif:"▸",rtriltri:"⧎",ruluhar:"⥨",rx:"℞"}),MathJax.Ajax.loadComplete(J.entityDir+"/r.js"),k=MathJax.InputJax.MathML,MathJax.Hub.Insert(k.Parse.Entity,{Pcy:"П",Poincareplane:"ℌ",Pr:"⪻",Prime:"″",Proportion:"∷",par:"∥",para:"¶",parallel:"∥",parsim:"⫳",parsl:"⫽",part:"∂",pcy:"п",percnt:"%",permil:"‰",perp:"⊥",pertenk:"‱",phmmat:"ℳ",phone:"☎",pitchfork:"⋔",planck:"ℏ",planckh:"ℎ",plankv:"ℏ",plus:"+",plusacir:"⨣",plusb:"⊞",pluscir:"⨢",plusdo:"∔",plusdu:"⨥",pluse:"⩲",plusmn:"±",plussim:"⨦",plustwo:"⨧",pm:"±",pointint:"⨕",pound:"£",pr:"≺",prE:"⪳",prcue:"≼",pre:"⪯",prec:"≺",precapprox:"⪷",preccurlyeq:"≼",preceq:"⪯",precsim:"≾",primes:"ℙ",prnE:"⪵",prnap:"⪹",prnsim:"⋨",prod:"∏",profalar:"⌮",profline:"⌒",profsurf:"⌓",prop:"∝",propto:"∝",prsim:"≾",prurel:"⊰",puncsp:" "}),MathJax.Ajax.loadComplete(k.entityDir+"/p.js"),O=MathJax.InputJax.MathML,MathJax.Hub.Insert(O.Parse.Entity,{Map:"⤅",Mcy:"М",MediumSpace:" ",Mellintrf:"ℳ",Mu:"Μ",mDDot:"∺",male:"♂",maltese:"✠",map:"↦",mapsto:"↦",mapstodown:"↧",mapstoleft:"↤",mapstoup:"↥",marker:"▮",mcomma:"⨩",mcy:"м",mdash:"—",measuredangle:"∡",micro:"µ",mid:"∣",midast:"*",midcir:"⫰",middot:"·",minus:"−",minusb:"⊟",minusd:"∸",minusdu:"⨪",mlcp:"⫛",mldr:"…",mnplus:"∓",models:"⊧",mp:"∓",mstpos:"∾",mumap:"⊸"}),MathJax.Ajax.loadComplete(O.entityDir+"/m.js"),D=MathJax.InputJax.MathML,MathJax.Hub.Insert(D.Parse.Entity,{QUOT:'"',qint:"⨌",qprime:"⁗",quaternions:"ℍ",quatint:"⨖",quest:"?",questeq:"≟",quot:'"'}),MathJax.Ajax.loadComplete(D.entityDir+"/q.js"),B=MathJax.InputJax.MathML,MathJax.Hub.Insert(B.Parse.Entity,{THORN:"Þ",TRADE:"™",TSHcy:"Ћ",TScy:"Ц",Tab:"\t",Tau:"Τ",Tcaron:"Ť",Tcedil:"Ţ",Tcy:"Т",ThickSpace:"  ",ThinSpace:" ",TripleDot:"⃛",Tstrok:"Ŧ",target:"⌖",tbrk:"⎴",tcaron:"ť",tcedil:"ţ",tcy:"т",tdot:"⃛",telrec:"⌕",there4:"∴",therefore:"∴",thetasym:"ϑ",thickapprox:"≈",thicksim:"∼",thinsp:" ",thkap:"≈",thksim:"∼",thorn:"þ",timesb:"⊠",timesbar:"⨱",timesd:"⨰",tint:"∭",toea:"⤨",top:"⊤",topbot:"⌶",topcir:"⫱",topfork:"⫚",tosa:"⤩",tprime:"‴",trade:"™",triangledown:"▿",triangleleft:"◃",trianglelefteq:"⊴",triangleright:"▹",trianglerighteq:"⊵",tridot:"◬",trie:"≜",triminus:"⨺",triplus:"⨹",trisb:"⧍",tritime:"⨻",trpezium:"⏢",tscy:"ц",tshcy:"ћ",tstrok:"ŧ",twixt:"≬",twoheadleftarrow:"↞",twoheadrightarrow:"↠"}),MathJax.Ajax.loadComplete(B.entityDir+"/t.js"),P=MathJax.InputJax.MathML,MathJax.Hub.Insert(P.Parse.Entity,{Wcirc:"Ŵ",wcirc:"ŵ",wedbar:"⩟",wedge:"∧",wedgeq:"≙",wp:"℘",wr:"≀",wreath:"≀"}),MathJax.Ajax.loadComplete(P.entityDir+"/w.js"),j=MathJax.InputJax.MathML,MathJax.Hub.Insert(j.Parse.Entity,{Fcy:"Ф",FilledSmallSquare:"◼",Fouriertrf:"ℱ",fallingdotseq:"≒",fcy:"ф",female:"♀",ffilig:"ﬃ",fflig:"ﬀ",ffllig:"ﬄ",filig:"ﬁ",fjlig:"fj",fllig:"ﬂ",fltns:"▱",fnof:"ƒ",forall:"∀",forkv:"⫙",fpartint:"⨍",frac12:"½",frac13:"⅓",frac14:"¼",frac15:"⅕",frac16:"⅙",frac18:"⅛",frac23:"⅔",frac25:"⅖",frac34:"¾",frac35:"⅗",frac38:"⅜",frac45:"⅘",frac56:"⅚",frac58:"⅝",frac78:"⅞",frasl:"⁄"}),MathJax.Ajax.loadComplete(j.entityDir+"/f.js"),F=MathJax.InputJax.MathML,MathJax.Hub.Insert(F.Parse.Entity,{VDash:"⊫",Vbar:"⫫",Vcy:"В",Vdashl:"⫦",Verbar:"‖",Vert:"‖",VerticalLine:"|",VerticalSeparator:"❘",VeryThinSpace:" ",vArr:"⇕",vBar:"⫨",vBarv:"⫩",vDash:"⊨",vangrt:"⦜",varepsilon:"ϵ",varkappa:"ϰ",varnothing:"∅",varphi:"ϕ",varpi:"ϖ",varpropto:"∝",varr:"↕",varrho:"ϱ",varsigma:"ς",varsubsetneq:"⊊︀",varsubsetneqq:"⫋︀",varsupsetneq:"⊋︀",varsupsetneqq:"⫌︀",vartheta:"ϑ",vartriangleleft:"⊲",vartriangleright:"⊳",vcy:"в",vdash:"⊢",vee:"∨",veeeq:"≚",verbar:"|",vert:"|",vltri:"⊲",vnsub:"⊂⃒",vnsup:"⊃⃒",vprop:"∝",vrtri:"⊳",vsubnE:"⫋︀",vsubne:"⊊︀",vsupnE:"⫌︀",vsupne:"⊋︀",vzigzag:"⦚"}),MathJax.Ajax.loadComplete(F.entityDir+"/v.js"),X=MathJax.InputJax.MathML,MathJax.Hub.Insert(X.Parse.Entity,{ENG:"Ŋ",ETH:"Ð",Eacute:"É",Ecaron:"Ě",Ecirc:"Ê",Ecy:"Э",Edot:"Ė",Egrave:"È",Emacr:"Ē",EmptySmallSquare:"◻",EmptyVerySmallSquare:"▫",Eogon:"Ę",Epsilon:"Ε",Equal:"⩵",Esim:"⩳",Eta:"Η",Euml:"Ë",eDDot:"⩷",eDot:"≑",eacute:"é",easter:"⩮",ecaron:"ě",ecirc:"ê",ecolon:"≕",ecy:"э",edot:"ė",ee:"ⅇ",eg:"⪚",egrave:"è",egsdot:"⪘",el:"⪙",elinters:"⏧",elsdot:"⪗",emacr:"ē",emptyset:"∅",emptyv:"∅",emsp:" ",emsp13:" ",emsp14:" ",eng:"ŋ",ensp:" ",eogon:"ę",epar:"⋕",eparsl:"⧣",eplus:"⩱",epsilon:"ε",eqcirc:"≖",eqcolon:"≕",eqsim:"≂",eqslantgtr:"⪖",eqslantless:"⪕",equals:"=",equest:"≟",equiv:"≡",equivDD:"⩸",eqvparsl:"⧥",erarr:"⥱",esdot:"≐",esim:"≂",euml:"ë",euro:"€",excl:"!",exist:"∃",expectation:"ℰ",exponentiale:"ⅇ"}),MathJax.Ajax.loadComplete(X.entityDir+"/e.js"),W=MathJax.InputJax.MathML,MathJax.Hub.Insert(W.Parse.Entity,{KHcy:"Х",KJcy:"Ќ",Kappa:"Κ",Kcedil:"Ķ",Kcy:"К",kcedil:"ķ",kcy:"к",kgreen:"ĸ",khcy:"х",kjcy:"ќ"}),MathJax.Ajax.loadComplete(W.entityDir+"/k.js"),V=MathJax.InputJax.MathML,MathJax.Hub.Insert(V.Parse.Entity,{xcap:"⋂",xcirc:"◯",xcup:"⋃",xdtri:"▽",xhArr:"⟺",xharr:"⟷",xlArr:"⟸",xlarr:"⟵",xmap:"⟼",xnis:"⋻",xodot:"⨀",xoplus:"⨁",xotime:"⨂",xrArr:"⟹",xrarr:"⟶",xsqcup:"⨆",xuplus:"⨄",xutri:"△",xvee:"⋁",xwedge:"⋀"}),MathJax.Ajax.loadComplete(V.entityDir+"/x.js"),U=MathJax.InputJax.MathML,MathJax.Hub.Insert(U.Parse.Entity,{CHcy:"Ч",COPY:"©",Cacute:"Ć",CapitalDifferentialD:"ⅅ",Cayleys:"ℭ",Ccaron:"Č",Ccedil:"Ç",Ccirc:"Ĉ",Cconint:"∰",Cdot:"Ċ",Cedilla:"¸",Chi:"Χ",ClockwiseContourIntegral:"∲",CloseCurlyDoubleQuote:"”",CloseCurlyQuote:"’",Colon:"∷",Colone:"⩴",Conint:"∯",CounterClockwiseContourIntegral:"∳",cacute:"ć",capand:"⩄",capbrcup:"⩉",capcap:"⩋",capcup:"⩇",capdot:"⩀",caps:"∩︀",caret:"⁁",caron:"ˇ",ccaps:"⩍",ccaron:"č",ccedil:"ç",ccirc:"ĉ",ccups:"⩌",ccupssm:"⩐",cdot:"ċ",cedil:"¸",cemptyv:"⦲",cent:"¢",centerdot:"·",chcy:"ч",checkmark:"✓",cir:"○",cirE:"⧃",cire:"≗",cirfnint:"⨐",cirmid:"⫯",cirscir:"⧂",clubsuit:"♣",colone:"≔",coloneq:"≔",comma:",",commat:"@",compfn:"∘",complement:"∁",complexes:"ℂ",cong:"≅",congdot:"⩭",conint:"∮",coprod:"∐",copy:"©",copysr:"℗",crarr:"↵",cross:"✗",csub:"⫏",csube:"⫑",csup:"⫐",csupe:"⫒",cudarrl:"⤸",cudarrr:"⤵",cularrp:"⤽",cupbrcap:"⩈",cupcap:"⩆",cupcup:"⩊",cupdot:"⊍",cupor:"⩅",cups:"∪︀",curarrm:"⤼",curlyeqprec:"⋞",curlyeqsucc:"⋟",curren:"¤",curvearrowleft:"↶",curvearrowright:"↷",cuvee:"⋎",cuwed:"⋏",cwconint:"∲",cwint:"∱",cylcty:"⌭"}),MathJax.Ajax.loadComplete(U.entityDir+"/c.js"),_=MathJax.InputJax.MathML,MathJax.Hub.Insert(_.Parse.Entity,{NJcy:"Њ",Nacute:"Ń",Ncaron:"Ň",Ncedil:"Ņ",Ncy:"Н",NegativeMediumSpace:"​",NegativeThickSpace:"​",NegativeThinSpace:"​",NegativeVeryThinSpace:"​",NewLine:"\n",NoBreak:"⁠",NonBreakingSpace:" ",Not:"⫬",NotCongruent:"≢",NotCupCap:"≭",NotEqualTilde:"≂̸",NotGreaterFullEqual:"≧̸",NotGreaterGreater:"≫̸",NotGreaterLess:"≹",NotGreaterSlantEqual:"⩾̸",NotGreaterTilde:"≵",NotHumpDownHump:"≎̸",NotHumpEqual:"≏̸",NotLeftTriangleBar:"⧏̸",NotLessGreater:"≸",NotLessLess:"≪̸",NotLessSlantEqual:"⩽̸",NotLessTilde:"≴",NotNestedGreaterGreater:"⪢̸",NotNestedLessLess:"⪡̸",NotPrecedesEqual:"⪯̸",NotReverseElement:"∌",NotRightTriangleBar:"⧐̸",NotSquareSubset:"⊏̸",NotSquareSubsetEqual:"⋢",NotSquareSuperset:"⊐̸",NotSquareSupersetEqual:"⋣",NotSubset:"⊂⃒",NotSucceedsEqual:"⪰̸",NotSucceedsTilde:"≿̸",NotSuperset:"⊃⃒",NotTildeEqual:"≄",NotTildeFullEqual:"≇",NotTildeTilde:"≉",Ntilde:"Ñ",Nu:"Ν",nGg:"⋙̸",nGt:"≫⃒",nGtv:"≫̸",nLl:"⋘̸",nLt:"≪⃒",nLtv:"≪̸",nabla:"∇",nacute:"ń",nang:"∠⃒",nap:"≉",napE:"⩰̸",napid:"≋̸",napos:"ŉ",napprox:"≉",natural:"♮",naturals:"ℕ",nbsp:" ",nbump:"≎̸",nbumpe:"≏̸",ncap:"⩃",ncaron:"ň",ncedil:"ņ",ncong:"≇",ncongdot:"⩭̸",ncup:"⩂",ncy:"н",ndash:"–",ne:"≠",neArr:"⇗",nearhk:"⤤",nearrow:"↗",nedot:"≐̸",nequiv:"≢",nesear:"⤨",nesim:"≂̸",nexist:"∄",nexists:"∄",ngE:"≧̸",nge:"≱",ngeq:"≱",ngeqq:"≧̸",ngeqslant:"⩾̸",nges:"⩾̸",ngsim:"≵",ngt:"≯",ngtr:"≯",nhArr:"⇎",nhpar:"⫲",ni:"∋",nis:"⋼",nisd:"⋺",niv:"∋",njcy:"њ",nlArr:"⇍",nlE:"≦̸",nldr:"‥",nle:"≰",nleftarrow:"↚",nleftrightarrow:"↮",nleq:"≰",nleqq:"≦̸",nleqslant:"⩽̸",nles:"⩽̸",nless:"≮",nlsim:"≴",nlt:"≮",nltri:"⋪",nltrie:"⋬",nmid:"∤",notin:"∉",notinE:"⋹̸",notindot:"⋵̸",notinva:"∉",notinvb:"⋷",notinvc:"⋶",notni:"∌",notniva:"∌",notnivb:"⋾",notnivc:"⋽",npar:"∦",nparallel:"∦",nparsl:"⫽⃥",npart:"∂̸",npolint:"⨔",npr:"⊀",nprcue:"⋠",npre:"⪯̸",nprec:"⊀",npreceq:"⪯̸",nrArr:"⇏",nrarrc:"⤳̸",nrarrw:"↝̸",nrightarrow:"↛",nrtri:"⋫",nrtrie:"⋭",nsc:"⊁",nsccue:"⋡",nsce:"⪰̸",nshortmid:"∤",nshortparallel:"∦",nsim:"≁",nsime:"≄",nsimeq:"≄",nsmid:"∤",nspar:"∦",nsqsube:"⋢",nsqsupe:"⋣",nsub:"⊄",nsubE:"⫅̸",nsube:"⊈",nsubset:"⊂⃒",nsubseteq:"⊈",nsubseteqq:"⫅̸",nsucc:"⊁",nsucceq:"⪰̸",nsup:"⊅",nsupE:"⫆̸",nsupe:"⊉",nsupset:"⊃⃒",nsupseteq:"⊉",nsupseteqq:"⫆̸",ntgl:"≹",ntilde:"ñ",ntlg:"≸",ntriangleleft:"⋪",ntrianglelefteq:"⋬",ntriangleright:"⋫",ntrianglerighteq:"⋭",num:"#",numero:"№",numsp:" ",nvHarr:"⤄",nvap:"≍⃒",nvge:"≥⃒",nvgt:">⃒",nvinfin:"⧞",nvlArr:"⤂",nvle:"≤⃒",nvlt:"<⃒",nvltrie:"⊴⃒",nvrArr:"⤃",nvrtrie:"⊵⃒",nvsim:"∼⃒",nwArr:"⇖",nwarhk:"⤣",nwarrow:"↖",nwnear:"⤧"}),MathJax.Ajax.loadComplete(_.entityDir+"/n.js"),q=MathJax.InputJax.MathML,MathJax.Hub.Insert(q.Parse.Entity,{AElig:"Æ",AMP:"&",Aacute:"Á",Abreve:"Ă",Acirc:"Â",Acy:"А",Agrave:"À",Alpha:"Α",Amacr:"Ā",And:"⩓",Aogon:"Ą",Aring:"Å",Assign:"≔",Atilde:"Ã",Auml:"Ä",aacute:"á",abreve:"ă",ac:"∾",acE:"∾̳",acd:"∿",acirc:"â",acy:"а",aelig:"æ",af:"⁡",agrave:"à",alefsym:"ℵ",amacr:"ā",amp:"&",andand:"⩕",andd:"⩜",andslope:"⩘",andv:"⩚",ange:"⦤",angle:"∠",angmsdaa:"⦨",angmsdab:"⦩",angmsdac:"⦪",angmsdad:"⦫",angmsdae:"⦬",angmsdaf:"⦭",angmsdag:"⦮",angmsdah:"⦯",angrt:"∟",angrtvb:"⊾",angrtvbd:"⦝",angst:"Å",angzarr:"⍼",aogon:"ą",ap:"≈",apE:"⩰",apacir:"⩯",apid:"≋",apos:"'",approx:"≈",approxeq:"≊",aring:"å",ast:"*",asymp:"≈",asympeq:"≍",atilde:"ã",auml:"ä",awconint:"∳",awint:"⨑"}),MathJax.Ajax.loadComplete(q.entityDir+"/a.js"),z=MathJax.InputJax.MathML,MathJax.Hub.Insert(z.Parse.Entity,{Jcirc:"Ĵ",Jcy:"Й",Jsercy:"Ј",Jukcy:"Є",jcirc:"ĵ",jcy:"й",jsercy:"ј",jukcy:"є"}),MathJax.Ajax.loadComplete(z.entityDir+"/j.js"),G=MathJax.InputJax.MathML,MathJax.Hub.Insert(G.Parse.Entity,{Uacute:"Ú",Uarr:"↟",Uarrocir:"⥉",Ubrcy:"Ў",Ubreve:"Ŭ",Ucirc:"Û",Ucy:"У",Udblac:"Ű",Ugrave:"Ù",Umacr:"Ū",UnderBracket:"⎵",UnderParenthesis:"⏝",Uogon:"Ų",UpArrowBar:"⤒",UpArrowDownArrow:"⇅",UpEquilibrium:"⥮",UpTeeArrow:"↥",UpperLeftArrow:"↖",UpperRightArrow:"↗",Upsi:"ϒ",Uring:"Ů",Utilde:"Ũ",Uuml:"Ü",uArr:"⇑",uHar:"⥣",uacute:"ú",uarr:"↑",ubrcy:"ў",ubreve:"ŭ",ucirc:"û",ucy:"у",udarr:"⇅",udblac:"ű",udhar:"⥮",ufisht:"⥾",ugrave:"ù",uharl:"↿",uharr:"↾",uhblk:"▀",ulcorn:"⌜",ulcorner:"⌜",ulcrop:"⌏",ultri:"◸",umacr:"ū",uml:"¨",uogon:"ų",uparrow:"↑",updownarrow:"↕",upharpoonleft:"↿",upharpoonright:"↾",uplus:"⊎",upsih:"ϒ",upsilon:"υ",urcorn:"⌝",urcorner:"⌝",urcrop:"⌎",uring:"ů",urtri:"◹",utdot:"⋰",utilde:"ũ",utri:"▵",utrif:"▴",uuarr:"⇈",uuml:"ü",uwangle:"⦧"}),MathJax.Ajax.loadComplete(G.entityDir+"/u.js"),$=MathJax.InputJax.MathML,MathJax.Hub.Insert($.Parse.Entity,{Barv:"⫧",Barwed:"⌆",Bcy:"Б",Bernoullis:"ℬ",Beta:"Β",Bumpeq:"≎",bNot:"⫭",backcong:"≌",backepsilon:"϶",barvee:"⊽",barwed:"⌅",barwedge:"⌅",bbrk:"⎵",bbrktbrk:"⎶",bcong:"≌",bcy:"б",bdquo:"„",becaus:"∵",because:"∵",bemptyv:"⦰",bepsi:"϶",bernou:"ℬ",bigcap:"⋂",bigcup:"⋃",bigvee:"⋁",bigwedge:"⋀",bkarow:"⤍",blacksquare:"▪",blacktriangleright:"▸",blank:"␣",blk12:"▒",blk14:"░",blk34:"▓",block:"█",bne:"=⃥",bnequiv:"≡⃥",bnot:"⌐",bot:"⊥",bottom:"⊥",boxDL:"╗",boxDR:"╔",boxDl:"╖",boxDr:"╓",boxH:"═",boxHD:"╦",boxHU:"╩",boxHd:"╤",boxHu:"╧",boxUL:"╝",boxUR:"╚",boxUl:"╜",b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x=h.h+h.d+m.h+m.d-.1;if(t.appendChild(n),a.mid&&(c=this.createChar(p,a.mid,1,s),o=p.removeChild(p.firstChild),x+=c.h+c.d,f=2),a.min&&e<x*a.min&&(e=x*a.min),x<e){d=this.createChar(p,a.ext,1,s),l=p.removeChild(p.firstChild);var M=d.h+d.d,g=M-.1,T=Math.min(Math.ceil((e-x)/(f*g)),this.maxStretchyParts);a.fullExtenders?e=T*f*g+x:g=(e-x)/(f*T),u=d.d+d.a-M/2,l.style.margin=l.style.padding="",l.style.lineHeight=ot.Em(g),l.style.marginBottom=ot.Em(u-.05/f),l.style.marginTop=ot.Em(-u-.05/f);for(var E=l.textContent,C="\n"+E;0<--T;)E+=C;l.textContent=E,t.appendChild(l),a.mid&&(t.appendChild(o),t.appendChild(l.cloneNode(!0)))}else u=(e-x-.1)/f,n.style.marginBottom=ot.Em(u+parseFloat(n.style.marginBottom||"0")),a.mid&&t.appendChild(o),r.style.marginTop=ot.Em(u+parseFloat(r.style.marginTop||"0"));t.appendChild(r);var L=ot.BBOX({w:Math.max(h.w,d.w,m.w,c.w),l:Math.min(h.l,d.l,m.l,c.l),r:Math.max(h.r,d.r,m.r,c.r),h:e-m.d,d:m.d,t:e-m.d,b:m.d});return 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i=t.style;i.transform=i.WebkitTransform=i.MozTransform=i["-ms-transform"]=e,a&&(i.transformOrigin=i.WebkitTransformOrigin=i.MozTransformOrigin=i["-ms-transform-origin"]=a)},arrayEntry:function(t,e){return t[Math.max(0,Math.min(e,t.length-1))]},removeStyles:["fontSize","fontFamily","fontWeight","fontStyle","fontVariant","font"]}),ot.BBOX=MathJax.Object.Subclass({Init:function(t){for(var e in t)t.hasOwnProperty(e)&&(this[e]=t[e])},clean:function(){this.h===-pt&&(this.h=0),this.d===-pt&&(this.d=0),this.l===pt&&(this.l=0),this.r===-pt&&(this.r=0),this.t===-pt&&(this.t=0),this.b===-pt&&(this.b=0),this.D&&0<this.d&&delete this.D},rescale:function(t){this.w*=t,this.h*=t,this.d*=t,this.l*=t,this.r*=t,this.t*=t,this.b*=t,this.L&&(this.L*=t),this.R&&(this.R*=t),this.D&&(this.D*=t)},combine:function(t,e,a){t.X=e,t.Y=a;var i=t.rscale;e+i*t.r>this.r&&(this.r=e+i*t.r),e+i*t.l<this.l&&(this.l=e+i*t.l),e+i*(t.w+(t.L||0)+(t.R||0))>this.w&&(this.w=e+i*(t.w+(t.L||0)+(t.R||0))),a+i*t.h>this.h&&(this.h=a+i*t.h),t.D&&(null==this.D||i*t.D-a>this.D)&&i*t.D>this.d?this.D=i*t.D-a:null==t.D&&this.D&&delete this.D,i*t.d-a>this.d&&(this.d=i*t.d-a),a+i*t.t>this.t&&(this.t=a+i*t.t),i*t.b-a>this.b&&(this.b=i*t.b-a)},append:function(t){var e=t.rscale,a=this.w;a+e*t.r>this.r&&(this.r=a+e*t.r),a+e*t.l<this.l&&(this.l=a+e*t.l),this.w+=e*(t.w+(t.L||0)+(t.R||0)),e*t.h>this.h&&(this.h=e*t.h),t.D&&(null==this.D||e*t.D>this.D)&&e*t.D>this.d?this.D=e*t.D:null==t.D&&this.D&&delete this.D,e*t.d>this.d&&(this.d=e*t.d),e*t.t>this.t&&(this.t=e*t.t),e*t.b>this.b&&(this.b=e*t.b)},updateFrom:function(t){this.h=t.h,this.d=t.d,this.w=t.w,this.r=t.r,this.l=t.l,this.t=t.t,this.b=t.b,t.pwidth&&(this.pwidth=t.pwidth),t.D?this.D=t.D:delete this.D},adjust:function(t,e,a,i){this[e]+=ot.length2em(t,1,this.scale),null==i?this[e]>this[a]&&(this[a]=this[e]):this[a]<i&&(this[a]=i)}},{zero:function(){return ot.BBOX({h:0,d:0,w:0,l:0,r:0,t:0,b:0,scale:1,rscale:1})},empty:function(t){return t||(t=ot.BBOX.zero()),t.h=t.d=t.r=t.t=t.b=-pt,t.w=0,t.l=pt,delete t.pwidth,t},styleAdjust:[["borderTopWidth","h","t"],["borderRightWidth","w","r"],["borderBottomWidth","d","b"],["borderLeftWidth","w","l",0],["paddingTop","h","t"],["paddingRight","w","r"],["paddingBottom","d","b"],["paddingLeft","w","l",0]]}),MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){(lt=MathJax.ElementJax.mml).mbase.Augment({toCommonHTML:function(t,e){return this.CHTMLdefaultNode(t,e)},CHTMLmultiline:function(){lt.mbase.CHTMLautoloadFile("multiline")},CHTMLdefaultNode:function(t,e){e||(e={}),t=this.CHTMLcreateNode(t),this.CHTML=ot.BBOX.empty(),this.CHTMLhandleStyle(t),this.isToken&&this.CHTMLgetVariant(),this.CHTMLhandleScale(t);for(var a=Math.max(e.minChildren||0,this.data.length),i=0;i<a;i++)this.CHTMLaddChild(t,i,e);return e.noBBox||this.CHTML.clean(),this.CHTMLhandleSpace(t),this.CHTMLhandleBBox(t),this.CHTMLhandleColor(t),t},CHTMLaddChild:function(t,e,a){var i,s=this.data[e],n=a.childNodes;if(n instanceof Array&&(n=n[e]||"span"),s){if(n&&(t=ot.addElement(t,n)),i=s.toCommonHTML(t,a.childOptions),n&&1!==s.CHTML.rscale&&(t.style.fontSize=t.firstChild.style.fontSize,t.firstChild.style.fontSize=""),!a.noBBox){var r=this.CHTML,o=s.CHTML;r.append(o),1===this.data.length?(o.ic&&(r.ic=o.ic),o.skew&&(r.skew=o.skew)):(delete r.ic,delete r.skew),o.pwidth&&(r.pwidth=o.pwidth)}}else a.forceChild&&(i=ot.addElement(t,n||"mjx-box"));return i},CHTMLchildNode:function(t,e){return"a"===(t=t.childNodes[e]).nodeName.toLowerCase()&&(t=t.firstChild),t},CHTMLcoreNode:function(t){return this.inferRow&&this.data[0]?this.data[0].CHTMLcoreNode(t.firstChild):this.CHTMLchildNode(t,this.CoreIndex())},CHTMLstretchChildV:function(t,e,a){var i=this.data[t];if(i){var s=this.CHTML,n=i.CHTML;if(n.stretch||null==n.stretch&&i.CHTMLcanStretch("Vertical",e,a)){var r=n.w;n=i.CHTMLstretchV(e,a),s.w+=n.w-r,s.w>s.r&&(s.r=s.w),n.h>s.h&&(s.h=n.h),n.d>s.d&&(s.d=n.d),n.t>s.t&&(s.t=n.t),n.b>s.b&&(s.b=n.b)}}},CHTMLstretchChildH:function(t,e,a){var i=this.data[t];if(i){var s=this.CHTML,n=i.CHTML;if(n.stretch||null==n.stretch&&i.CHTMLcanStretch("Horizontal",e)){var r=n.w;n=i.CHTMLstretchH(this.CHTMLchildNode(a,t),e),s.w+=n.w-r,s.w>s.r&&(s.r=s.w),n.h>s.h&&(s.h=n.h),n.d>s.d&&(s.d=n.d),n.t>s.t&&(s.t=n.t),n.b>s.b&&(s.b=n.b)}}},CHTMLupdateFrom:function(t){this.CHTML.updateFrom(t),this.inferRow&&this.data[0].CHTML.updateFrom(t)},CHTMLcanStretch:function(t,e,a){var i=!1;if(this.isEmbellished()){var s=this.Core();s&&s!==this&&(i=s.CHTMLcanStretch(t,e,a))}return this.CHTML.stretch=i},CHTMLstretchV:function(t,e){return this.CHTMLupdateFrom(this.Core().CHTMLstretchV(t,e)),this.CHTML},CHTMLstretchH:function(t,e){return this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,e)),this.CHTML},CHTMLstretchCoreH:function(t,e){return this.Core().CHTMLstretchH(this.CHTMLcoreNode(t),e)},CHTMLcreateNode:function(t){this.CHTML||(this.CHTML={}),this.CHTML=ot.BBOX.zero(),this.href&&(t=ot.addElement(t,"a",{href:this.href,isMathJax:!0})),this.CHTMLnodeID||(this.CHTMLnodeID=ot.GetID());var e=(this.id||"MJXc-Node-"+this.CHTMLnodeID)+ot.idPostfix;return this.CHTMLhandleAttributes(ot.addElement(t,"mjx-"+this.type,{id:e}))},CHTMLnodeElement:function(){return this.CHTMLnodeID?document.getElementById((this.id||"MJXc-Node-"+this.CHTMLnodeID)+ot.idPostfix):null},CHTMLlength2em:function(t,e){return ot.length2em(t,e,this.CHTML.scale)},CHTMLhandleAttributes:function(t){if(this.class&&(t.className?t.className+=" "+this.class:t.className=this.class),this.attrNames)for(var e=this.attrNames,a=lt.nocopyAttributes,i=nt.config.ignoreMMLattributes,s="mstyle"===this.type?lt.math.prototype.defaults:this.defaults,n=0,r=e.length;n<r;n++){var o=e[n];0!=i[o]&&(a[o]||i[o]||null!=s[o]||void 0!==t[o])||t.setAttribute(o,this.attr[o])}return t},CHTMLhandleScale:function(t){var e=1,a=this.parent,i=a?a.CHTML.scale:1,s=this.getValues("scriptlevel","fontsize");s.mathsize=this.Get("mathsize",null,!this.isToken),0!==s.scriptlevel&&(2<s.scriptlevel&&(s.scriptlevel=2),e=Math.pow(this.Get("scriptsizemultiplier"),s.scriptlevel),s.scriptminsize=ot.length2em(this.Get("scriptminsize"),.8,1),e<s.scriptminsize&&(e=s.scriptminsize)),this.removedStyles&&this.removedStyles.fontSize&&!s.fontsize&&(s.fontsize=this.removedStyles.fontSize),s.fontsize&&!this.mathsize&&(s.mathsize=s.fontsize),1!==s.mathsize&&(e*=ot.length2em(s.mathsize,1,1));var n=this.CHTMLvariant;return n&&n.style&&n.style["font-family"]&&(e*=ot.config.scale/100/ot.scale),this.CHTML.scale=e,i=this.CHTML.rscale=e/i,Math.abs(i-1)<.001&&(i=1),t&&1!==i&&(t.style.fontSize=ot.Percent(i)),e},CHTMLhandleStyle:function(t){if(this.style){var e=t.style;e.cssText=this.style,this.removedStyles={};for(var a=0,i=ot.removeStyles.length;a<i;a++){var s=ot.removeStyles[a];e[s]&&(this.removedStyles[s]=e[s],e[s]="")}}},CHTMLhandleBBox:function(t){var e=this.CHTML,a=t.style;if(1===this.data.length&&(this.data[0].CHTML||{}).pwidth?(e.pwidth=this.data[0].CHTML.pwidth,e.mwidth=this.data[0].CHTML.mwidth,a.width="100%"):e.pwidth?(e.mwidth=ot.Em(e.w),a.width="100%"):e.w<0&&(a.width="0px",a.marginRight=ot.Em(e.w)),this.style)for(var i=0,s=ot.BBOX.styleAdjust.length;i<s;i++){var n=ot.BBOX.styleAdjust[i];n&&a[n[0]]&&e.adjust(a[n[0]],n[1],n[2],n[3])}},CHTMLhandleColor:function(t){this.mathcolor?t.style.color=this.mathcolor:this.color&&(t.style.color=this.color),this.mathbackground?t.style.backgroundColor=this.mathbackground:this.background&&(t.style.backgroundColor=this.background)},CHTMLhandleSpace:function(t){if(!this.useMMLspacing){var e=this.texSpacing();""!==e&&(this.CHTML.L=this.CHTMLlength2em(e),t.className+=" "+ot.SPACECLASS[e])}},CHTMLhandleText:function(t,e,a){t.firstChild&&!this.CHTML&&(this.CHTML=ot.BBOX.empty()),this.CHTML=ot.handleText(t,e,a,this.CHTML)},CHTMLgetVariant:function(){var t,e=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");e.hasVariant=this.Get("mathvariant",!0),this.removedStyles&&((t=this.removedStyles).fontFamily&&(e.family=t.fontFamily),t.fontWeight&&(e.weight=t.fontWeight),t.fontStyle&&(e.style=t.fontStyle)),e.hasVariant||(e.fontfamily&&(e.family=e.fontfamily),e.fontweight&&(e.weight=e.fontweight),e.fontstyle&&(e.style=e.fontstyle)),e.weight&&e.weight.match(/^\d+$/)&&(e.weight=600<parseInt(e.weight)?"bold":"normal");var a=e.mathvariant;if(this.variantForm&&(a="-TeX-variant"),e.family&&!e.hasVariant)return!e.weight&&e.mathvariant.match(/bold/)&&(e.weight="bold"),!e.style&&e.mathvariant.match(/italic/)&&(e.style="italic"),void(this.CHTMLvariant={fonts:[],noRemap:!0,cache:{},style:{"font-family":e.family,"font-weight":e.weight||"normal","font-style":e.style||"normal"}});"bold"===e.weight?a={normal:lt.VARIANT.BOLD,italic:lt.VARIANT.BOLDITALIC,fraktur:lt.VARIANT.BOLDFRAKTUR,script:lt.VARIANT.BOLDSCRIPT,"sans-serif":lt.VARIANT.BOLDSANSSERIF,"sans-serif-italic":lt.VARIANT.SANSSERIFBOLDITALIC}[a]||a:"normal"===e.weight&&(a={bold:lt.VARIANT.normal,"bold-italic":lt.VARIANT.ITALIC,"bold-fraktur":lt.VARIANT.FRAKTUR,"bold-script":lt.VARIANT.SCRIPT,"bold-sans-serif":lt.VARIANT.SANSSERIF,"sans-serif-bold-italic":lt.VARIANT.SANSSERIFITALIC}[a]||a),"italic"===e.style?a={normal:lt.VARIANT.ITALIC,bold:lt.VARIANT.BOLDITALIC,"sans-serif":lt.VARIANT.SANSSERIFITALIC,"bold-sans-serif":lt.VARIANT.SANSSERIFBOLDITALIC}[a]||a:"normal"===e.style&&(a={italic:lt.VARIANT.NORMAL,"bold-italic":lt.VARIANT.BOLD,"sans-serif-italic":lt.VARIANT.SANSSERIF,"sans-serif-bold-italic":lt.VARIANT.BOLDSANSSERIF}[a]||a),this.CHTMLvariant=ot.FONTDATA.VARIANT[a]||ot.FONTDATA.VARIANT[lt.VARIANT.NORMAL]},CHTMLbboxFor:function(t){return this.data[t]&&this.data[t].CHTML?this.data[t].CHTML:ot.BBOX.zero()},CHTMLdrawBBox:function(t,e){e||(e=this.CHTML);var a=ot.Element("mjx-box",{style:{opacity:.25,"margin-left":ot.Em(-(e.w+(e.R||0)))}},[["mjx-box",{style:{height:ot.Em(e.h),width:ot.Em(e.w),"background-color":"red"}}],["mjx-box",{style:{height:ot.Em(e.d),width:ot.Em(e.w),"margin-left":ot.Em(-e.w),"vertical-align":ot.Em(-e.d),"background-color":"green"}}]]);t.nextSibling?t.parentNode.insertBefore(a,t.nextSibling):t.parentNode.appendChild(a)},CHTMLnotEmpty:function(t){for(;t&&t.data.length<2&&("mrow"===t.type||"texatom"===t.type);)t=t.data[0];return!!t}},{CHTMLautoload:function(){this.constructor.Augment({toCommonHTML:lt.mbase.CHTMLautoloadFail});var t=ot.autoloadDir+"/"+this.type+".js";nt.RestartAfter(st.Require(t))},CHTMLautoloadFail:function(){throw Error("CommonHTML can't autoload '"+this.type+"'")},CHTMLautoloadList:{},CHTMLautoloadFile:function(t){if(lt.mbase.CHTMLautoloadList.hasOwnProperty(t))throw Error("CommonHTML can't autoload file '"+t+"'");lt.mbase.CHTMLautoloadList[t]=!0;var e=ot.autoloadDir+"/"+t+".js";nt.RestartAfter(st.Require(e))},CHTMLstretchV:function(t,e){return this.Core().CHTMLstretchV(t,e),this.toCommonHTML(this.CHTMLnodeElement(),{stretch:!0}),this.CHTML},CHTMLstretchH:function(t,e){return this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,e)),this.toCommonHTML(t,{stretch:!0}),this.CHTML}}),lt.chars.Augment({toCommonHTML:function(t,e){(this.CHTML=null)==e&&(e={});var a=this.toString();e.remap&&(a=e.remap(a,e.remapchars)),this.CHTMLhandleText(t,a,e.variant||this.parent.CHTMLvariant)}}),lt.entity.Augment({toCommonHTML:function(t,e){null==e&&(e={});var a=this.toString();e.remapchars&&(a=e.remap(a,e.remapchars)),this.CHTMLhandleText(t,a,e.variant||this.parent.CHTMLvariant)}}),lt.math.Augment({toCommonHTML:function(t){t=this.CHTMLdefaultNode(t),this.CHTML.w<0&&(t.parentNode.style.width="0px",t.parentNode.style.marginRight=ot.Em(this.CHTML.w));var e=this.Get("alttext");if(e&&!t.getAttribute("aria-label")&&t.setAttribute("aria-label",e),this.CHTML.pwidth)t.parentNode.style.minWidth=this.CHTML.mwidth||ot.Em(this.CHTML.w),t.parentNode.className="mjx-full-width "+t.parentNode.className,t.style.width=this.CHTML.pwidth;else if(!this.isMultiline&&"block"===this.Get("display")){var a=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");a.indentalignfirst!==lt.INDENTALIGN.INDENTALIGN&&(a.indentalign=a.indentalignfirst),a.indentalign===lt.INDENTALIGN.AUTO&&(a.indentalign=xt.displayAlign),a.indentshiftfirst!==lt.INDENTSHIFT.INDENTSHIFT&&(a.indentshift=a.indentshiftfirst),"auto"===a.indentshift&&(a.indentshift="0");var i=this.CHTMLlength2em(a.indentshift,ot.cwidth);if("0"!==xt.displayIndent){var s=this.CHTMLlength2em(xt.displayIndent,ot.cwidth);i+=a.indentalign===lt.INDENTALIGN.RIGHT?-s:s}var n=t.parentNode.parentNode.style;t.parentNode.style.textAlign=n.textAlign=a.indentalign,i&&(i*=ot.em/ot.outerEm,nt.Insert(n,{left:{marginLeft:ot.Em(i)},right:{marginRight:ot.Em(-i)},center:{marginLeft:ot.Em(i),marginRight:ot.Em(-i)}}[a.indentalign]))}return t}}),lt.mi.Augment({toCommonHTML:function(t){t=this.CHTMLdefaultNode(t);var e=this.CHTML,a=this.data.join("");return null==e.skew||ot.isChar(a)||delete e.skew,e.r>e.w&&ot.isChar(a)&&!this.CHTMLvariant.noIC&&(e.ic=e.r-e.w,e.w=e.r,t.lastChild.style.paddingRight=ot.Em(e.ic)),t}}),lt.mn.Augment({CHTMLremapMinus:function(t){return t.replace(/^-/,"−")},toCommonHTML:function(t){t=this.CHTMLdefaultNode(t,{childOptions:{remap:this.CHTMLremapMinus}});var e=this.CHTML,a=this.data.join("");return null==e.skew||ot.isChar(a)||delete e.skew,e.r>e.w&&ot.isChar(a)&&!this.CHTMLvariant.noIC&&(e.ic=e.r-e.w,e.w=e.r,t.lastChild.style.paddingRight=ot.Em(e.ic)),t}}),lt.mo.Augment({toCommonHTML:function(t){t=this.CHTMLcreateNode(t),this.CHTMLhandleStyle(t),this.CHTMLgetVariant(),this.CHTMLhandleScale(t),ot.BBOX.empty(this.CHTML);var e=this.getValues("displaystyle","largeop");if(e.variant=this.CHTMLvariant,e.text=this.data.join(""),""==e.text)this.fence&&(t.style.width=ot.Em(ot.TEX.nulldelimiterspace));else{this.CHTMLadjustAccent(e),this.CHTMLadjustVariant(e);for(var a=0,i=this.data.length;a<i;a++)this.CHTMLaddChild(t,a,{childOptions:{variant:e.mathvariant,remap:this.remap,remapchars:e.remapchars}});ot.isChar(e.text)?0===this.CHTML.w&&this.CHTML.l<0&&this.CHTMLfixCombiningChar(t):delete this.CHTML.skew,e.largeop&&this.CHTMLcenterOp(t)}return this.CHTML.clean(),this.CHTMLhandleBBox(t),this.CHTMLhandleSpace(t),this.CHTMLhandleColor(t),t},CHTMLhandleSpace:function(t){if(this.hasMMLspacing()){var e=this.getValues("scriptlevel","lspace","rspace");e.lspace=Math.max(0,this.CHTMLlength2em(e.lspace)),e.rspace=Math.max(0,this.CHTMLlength2em(e.rspace)),0<e.scriptlevel&&(this.hasValue("lspace")||(e.lspace=.15),this.hasValue("rspace")||(e.rspace=.15));for(var a=this,i=this.Parent();i&&i.isEmbellished()&&i.Core()===a;)i=(a=i).Parent(),t=a.CHTMLnodeElement();e.lspace&&(t.style.paddingLeft=ot.Em(e.lspace)),e.rspace&&(t.style.paddingRight=ot.Em(e.rspace)),this.CHTML.L=e.lspace,this.CHTML.R=e.rspace}else this.SUPER(arguments).CHTMLhandleSpace.apply(this,arguments)},CHTMLadjustAccent:function(t){var e=this.CoreParent();if(t.parent=e,ot.isChar(t.text)&&e&&e.isa(lt.munderover)){var a=e.data[e.over],i=e.data[e.under];a&&this===a.CoreMO()&&e.Get("accent")?t.remapchars=ot.FONTDATA.REMAPACCENT:i&&this===i.CoreMO()&&e.Get("accentunder")&&(t.remapchars=ot.FONTDATA.REMAPACCENTUNDER)}},CHTMLadjustVariant:function(t){var e=t.parent,a=e&&e.isa(lt.msubsup)&&this!==e.data[e.base];t.largeop&&(t.mathvariant=t.displaystyle?"-largeOp":"-smallOp"),a&&(t.remapchars=this.remapChars,t.text.match(/['`"\u00B4\u2032-\u2037\u2057]/)&&(t.mathvariant="-TeX-variant"))},CHTMLfixCombiningChar:function(t){t=t.firstChild;var e=ot.Element("mjx-box",{style:{width:".25em","margin-left":"-.25em"}});t.insertBefore(e,t.firstChild)},CHTMLcenterOp:function(t){var e=this.CHTML,a=(e.h-e.d)/2-ot.TEX.axis_height;.001<Math.abs(a)&&(t.style.verticalAlign=ot.Em(-a)),e.h-=a,e.d+=a,e.r>e.w&&(e.ic=e.r-e.w,e.w=e.r,t.style.paddingRight=ot.Em(e.ic))},CHTMLcanStretch:function(t,e,a){if(!this.Get("stretchy"))return!1;var i=this.data.join("");if(!ot.isChar(i))return!1;var s={text:i};this.CHTMLadjustAccent(s),s.remapchars&&(i=s.remapchars[i]||i);var n=(i=ot.FONTDATA.DELIMITERS[i.charCodeAt(0)])&&i.dir===t.substr(0,1);return n&&(n=this.CHTML.h!==e||this.CHTML.d!==a||!!this.Get("minsize",!0)||!!this.Get("maxsize",!0))&&(this.CHTML.stretch=!0),n},CHTMLstretchV:function(t,e){var a,i=this.CHTMLnodeElement(),s=this.CHTML,n=this.getValues("symmetric","maxsize","minsize"),r=ot.TEX.axis_height;if(a=n.symmetric?2*Math.max(t-r,e+r):t+e,n.maxsize=this.CHTMLlength2em(n.maxsize,s.h+s.d),n.minsize=this.CHTMLlength2em(n.minsize,s.h+s.d),(a=Math.max(n.minsize,Math.min(n.maxsize,a)))!==s.sH){for(a!=n.minsize&&(a=[Math.max(a*ot.TEX.delimiterfactor/1e3,a-ot.TEX.delimitershortfall),a]);i.firstChild;)i.removeChild(i.firstChild);this.CHTML=s=ot.createDelimiter(i,this.data.join("").charCodeAt(0),a,s),s.sH=a instanceof Array?a[1]:a,a=n.symmetric?(s.h+s.d)/2+r:(s.h+s.d)*t/(t+e),a-=s.h,.05<Math.abs(a)&&(i.style.verticalAlign=ot.Em(a),s.h+=a,s.d-=a,s.t+=a,s.b-=a)}return this.CHTML},CHTMLstretchH:function(t,e){var a=this.CHTML,i=this.getValues("maxsize","minsize","mathvariant","fontweight");if(("bold"===i.fontweight||"bold"===(this.removedStyles||{}).fontWeight||600<=parseInt(i.fontweight))&&!this.Get("mathvariant",!0)&&(i.mathvariant=lt.VARIANT.BOLD),i.maxsize=this.CHTMLlength2em(i.maxsize,a.w),i.minsize=this.CHTMLlength2em(i.minsize,a.w),(e=Math.max(i.minsize,Math.min(i.maxsize,e)))!==a.sW){for(;t.firstChild;)t.removeChild(t.firstChild);this.CHTML=a=ot.createDelimiter(t,this.data.join("").charCodeAt(0),e,a,i.mathvariant),a.sW=e}return this.CHTML}}),lt.mtext.Augment({CHTMLgetVariant:function(){if(ot.config.mtextFontInherit||"merror"===this.Parent().type){var t=ot.config.scale/100/ot.scale,e={cache:{},fonts:[],className:"MJXc-font-inherit",rscale:t,style:{"font-size":ot.Percent(t)}},a=this.Get("mathvariant");a.match(/bold/)&&(e.style["font-weight"]="bold"),a.match(/italic|-tex-mathit/)&&(e.style["font-style"]="italic"),"monospace"===a&&(e.className+=" MJXc-monospace-font"),"double-struck"===a&&(e.className+=" MJXc-double-struck-font"),a.match(/fraktur/)&&(e.className+=" MJXc-fraktur-font"),a.match(/sans-serif/)&&(e.className+=" MJXc-sans-serif-font"),a.match(/script/)&&(e.className+=" MJXc-script-font"),this.CHTMLvariant=e}else this.SUPER(arguments).CHTMLgetVariant.call(this)}}),lt.merror.Augment({toCommonHTML:function(t){t=this.CHTMLdefaultNode(t);var e=this.CHTML;return e.rescale(.9),e.h+=3/ot.em,e.h>e.t&&(e.t=e.h),e.d+=3/ot.em,e.d>e.b&&(e.b=e.d),e.w+=8/ot.em,e.r=e.w,e.l=0,t}}),lt.mspace.Augment({toCommonHTML:function(t){t=this.CHTMLcreateNode(t),this.CHTMLhandleStyle(t),this.CHTMLhandleScale(t);var e=this.getValues("height","depth","width"),a=this.CHTMLlength2em(e.width),i=this.CHTMLlength2em(e.height),s=this.CHTMLlength2em(e.depth),n=this.CHTML;return n.w=n.r=a,n.h=n.t=i,n.d=n.b=s,a<(n.l=0)&&(t.style.marginRight=ot.Em(a),a=0),t.style.width=ot.Em(a),t.style.height=ot.Em(Math.max(0,i+s)),s&&(t.style.verticalAlign=ot.Em(-s)),this.CHTMLhandleBBox(t),this.CHTMLhandleColor(t),t}}),lt.mpadded.Augment({toCommonHTML:function(t,e){var a;e&&e.stretch?a=(t=t.firstChild).firstChild:(a=(t=this.CHTMLdefaultNode(t,{childNodes:"mjx-box",forceChild:!0})).firstChild,(t=ot.addElement(t,"mjx-block")).appendChild(a),ot.addElement(t,"mjx-strut"));var i=this.CHTMLbboxFor(0),s=this.getValues("width","height","depth","lspace","voffset"),n=0,r=0,o=i.w,l=i.h,h=i.d;a.style.width=0,a.style.margin=ot.Em(-l)+" 0 "+ot.Em(-h),""!==s.width&&(o=this.CHTMLdimen(s.width,"w",o,0)),""!==s.height&&(l=this.CHTMLdimen(s.height,"h",l,0)),""!==s.depth&&(h=this.CHTMLdimen(s.depth,"d",h,0)),""!==s.voffset&&(r=this.CHTMLdimen(s.voffset))&&(a.style.position="relative",a.style.top=ot.Em(-r)),""!==s.lspace&&(n=this.CHTMLdimen(s.lspace))&&(a.style.position="relative",a.style.left=ot.Em(n)),t.style.width=0,t.style.marginTop=ot.Em(l-1),t.style.padding="0 "+ot.Em(o)+" "+ot.Em(h)+" 0";var m=ot.BBOX({w:o,h:l,d:h,l:0,r:o,t:l,b:h,scale:this.CHTML.scale,rscale:this.CHTML.rscale});return m.combine(i,n,r),m.w=o,m.h=l,m.d=h,this.CHTML=m,t.parentNode},CHTMLstretchV:lt.mbase.CHTMLstretchV,CHTMLstretchH:lt.mbase.CHTMLstretchH,CHTMLdimen:function(t,e,a,i){null==i&&(i=-pt);var s=(t=String(t)).match(/width|height|depth/),n=s?this.CHTML[s[0].charAt(0)]:e?this.CHTML[e]:0,r=this.CHTMLlength2em(t,n)||0;return t.match(/^[-+]/)&&null!=a&&(r+=a),null!=i&&(r=Math.max(i,r)),r}}),lt.munderover.Augment({toCommonHTML:function(t,e){var a=this.getValues("displaystyle","accent","accentunder","align"),i=this.data[this.base];if(!a.displaystyle&&null!=i&&(i.movablelimits||i.CoreMO().Get("movablelimits")))return lt.msubsup.prototype.toCommonHTML.call(this,t,o);var s,n,r=[],o=!1;if(e&&e.stretch)this.data[this.base]&&(i=ot.getNode(t,"mjx-op")),this.data[this.under]&&(s=ot.getNode(t,"mjx-under")),this.data[this.over]&&(n=ot.getNode(t,"mjx-over")),r[0]=i,r[1]=s||n,r[2]=n,o=!0;else{var l=["mjx-op","mjx-under","mjx-over"];1===this.over&&(l[1]=l[2]),t=this.CHTMLdefaultNode(t,{childNodes:l,noBBox:!0,forceChild:!0,minChildren:2}),r[0]=i=t.removeChild(t.firstChild),r[1]=s=n=t.removeChild(t.firstChild),t.firstChild&&(r[2]=n=t.removeChild(t.firstChild))}var h=[],m=this.CHTMLgetBBoxes(h,r,a),c=h[this.base],d=this.CHTML;d.w=m,d.h=c.h,d.d=c.d,c.h<.35&&(i.style.marginTop=ot.Em(c.h-.35)),a.accent&&c.h<ot.TEX.x_height&&(d.h+=ot.TEX.x_height-c.h,i.style.marginTop=ot.Em(ot.TEX.x_height-Math.max(c.h,.35)),c.h=ot.TEX.x_height);var u=i,p=0;return c.ic&&(p=1.3*c.ic+.05),this.data[this.over]&&(u=this.CHTMLaddOverscript(n,h,a,p,i,o)),this.data[this.under]?this.CHTMLaddUnderscript(s,h,a,p,t,u,o):o||t.appendChild(u),this.CHTMLplaceBoxes(i,s,n,a,h),t},CHTMLgetBBoxes:function(t,e,a){var i,s,n=this.data.length,r=-pt,o=r;for(i=0;i<n;i++)t[i]=this.CHTMLbboxFor(i),t[i].x=t[i].y=0,this.data[i]&&(t[i].stretch=this.data[i].CHTMLcanStretch("Horizontal")),s=i===this.base?1:t[i].rscale,i!==this.base&&(delete t[i].L,delete t[i].R),o=Math.max(o,s*(t[i].w+(t[i].L||0)+(t[i].R||0))),!t[i].stretch&&r<o&&(r=o);for(r===-pt&&(r=o),i=0;i<n;i++)t[i].stretch&&(s=i===this.base?1:t[i].rscale,t[i]=this.data[i].CHTMLstretchH(e[i].firstChild,r/s),t[i].x=t[i].y=0,o=Math.max(o,s*(t[i].w+(t[i].L||0)+(t[i].R||0))));return t[this.base]||(t[this.base]=ot.BBOX.empty()),o},CHTMLaddOverscript:function(t,e,a,i,s,n){var r,o,l,h=this.CHTML,m=ot.TEX.big_op_spacing5,c=e[this.over],d=e[this.base],u=c.rscale;if(!n){var p=ot.Element("mjx-stack");p.appendChild(t),p.appendChild(s)}return c.D&&(c.d=c.D),c.d<0&&(t.firstChild.style.verticalAlign="top",t.style.height=ot.Em(c.h+c.d)),c.x=0,a.accent?(c.w<.001&&(c.x+=(c.r-c.l)/2),l=ot.TEX.rule_thickness,m=0,d.skew&&(c.x+=u*d.skew,h.skew=u*d.skew,c.x+u*c.w>h.w&&(h.skew+=(h.w-(c.x+u*c.w))/2))):(r=ot.TEX.big_op_spacing1,o=ot.TEX.big_op_spacing3,l=Math.max(r,o-Math.max(0,u*c.d))),c.x+=i/2,c.y=h.h+l+m+u*c.d,l&&(t.style.paddingBottom=ot.Em(l/u)),m&&(t.style.paddingTop=ot.Em(m/u)),p},CHTMLaddUnderscript:function(t,e,a,i,s,n,r){var o,l,h,m=this.CHTML,c=ot.TEX.big_op_spacing5,d=e[this.under],u=d.rscale;r||(ot.addElement(s,"mjx-itable",{},[["mjx-row",{},[["mjx-cell"]]],["mjx-row"]]),s.firstChild.firstChild.firstChild.appendChild(n),s.firstChild.lastChild.appendChild(t)),d.D&&(d.d=d.D),d.d<0&&(t.firstChild.style.verticalAlign="top",s.firstChild.style.marginBottom=ot.Em(d.d)),a.accentunder?(h=2*ot.TEX.rule_thickness,c=0):(o=ot.TEX.big_op_spacing2,l=ot.TEX.big_op_spacing4,h=Math.max(o,l-u*d.h)),d.x=-i/2,d.y=-(m.d+h+c+u*d.h),h&&(t.style.paddingTop=ot.Em(h/u)),c&&(t.style.paddingBottom=ot.Em(c/u))},CHTMLplaceBoxes:function(t,e,a,i,s){var n,r,o=this.CHTML.w,l=s.length,h=ot.BBOX.zero();h.scale=this.CHTML.scale,h.rscale=this.CHTML.rscale,s[this.base].x=s[this.base].y=0;var m=pt;for(n=0;n<l;n++){var c=(r=n===this.base?1:s[n].rscale)*(s[n].w+(s[n].L||0)+(s[n].R||0));s[n].x+={left:0,center:(o-c)/2,right:o-c}[i.align],s[n].x<m&&(m=s[n].x)}for(n=0;n<l;n++)this.data[n]&&(r=n===this.base?1:s[n].rscale,s[n].x-m&&((n===this.base?t:n===this.over?a:e).style.paddingLeft=ot.Em((s[n].x-m)/r)),h.combine(s[n],s[n].x-m,s[n].y));this.CHTML=h},CHTMLstretchV:lt.mbase.CHTMLstretchV,CHTMLstretchH:lt.mbase.CHTMLstretchH,CHTMLchildNode:function(t,e){var a=["mjx-op","mjx-under","mjx-over"];return 1===this.over&&(a[1]=a[2]),ot.getNode(t,a[e])}}),lt.msubsup.Augment({toCommonHTML:function(t,e){var a,i,s,n=this.getValues("displaystyle","subscriptshift","superscriptshift","texprimestyle");if(e&&e.stretch)this.data[this.base]&&(a=ot.getNode(t,"mjx-base")),this.data[this.sub]&&(i=ot.getNode(t,"mjx-sub")),this.data[this.sup]&&(s=ot.getNode(t,"mjx-sup")),o=ot.getNode(t,"mjx-stack");else{var r=["mjx-base","mjx-sub","mjx-sup"];if(1===this.sup&&(r[1]=r[2]),a=(t=this.CHTMLdefaultNode(t,{childNodes:r,noBBox:!0,forceChild:!0,minChildren:3})).childNodes[this.base],i=t.childNodes[this.sub],s=t.childNodes[this.sup],this.CHTMLnotEmpty(this.data[this.sub])||(t.removeChild(i),i=null),this.CHTMLnotEmpty(this.data[this.sup])||(t.removeChild(s),s=null),3===t.childNodes.length){var o=ot.addElement(t,"mjx-stack");o.appendChild(s),o.appendChild(i)}}for(var l=[],h=ot.BBOX.empty(this.CHTML),m=0,c=this.data.length;m<c;m++)l[m]=this.CHTMLbboxFor(m);var d=l[this.base]||ot.BBOX.empty(),u=l[this.sub],p=l[this.sup],f=i?u.rscale:1,x=s?p.rscale:1;h.combine(d,0,0);var M,g=ot.TEX.x_height,T=ot.TEX.scriptspace,E=ot.TEX.sup_drop*x,C=ot.TEX.sub_drop*f,L=d.h-E,b=d.d+C,v=0;d.ic&&(h.w-=d.ic,a.style.marginRight=ot.Em(-d.ic),v=1.3*d.ic+.05);var y=this.data[this.base];y&&("mrow"!==y.type&&"mstyle"!==y.type||1!==y.data.length||(y=y.data[0]),"mi"!==y.type&&"mo"!==y.type||!ot.isChar(y.data.join(""))||1!==d.rscale||d.sH||y.Get("largeop")||(L=b=0)),n.subscriptshift=""===n.subscriptshift?0:this.CHTMLlength2em(n.subscriptshift),n.superscriptshift=""===n.superscriptshift?0:this.CHTMLlength2em(n.superscriptshift);var N=h.w;if(i&&(u.w+=T),s&&(p.w+=T),s)if(i){b=Math.max(b,ot.TEX.sub2);var R=ot.TEX.rule_thickness;L-x*p.d-(f*u.h-b)<3*R&&(b=3*R-L+x*p.d+f*u.h,0<(E=.8*g-(L-x*p.d))&&(L+=E,b-=E)),L=Math.max(L,n.superscriptshift),b=Math.max(b,n.subscriptshift),i.style.paddingRight=ot.Em(T/f),s.style.paddingBottom=ot.Em(L/x+b/f-p.d-u.h/f*x),s.style.paddingLeft=ot.Em(v/x),s.style.paddingRight=ot.Em(T/x),o.style.verticalAlign=ot.Em(-b),h.combine(p,N+v,L),h.combine(u,N,-b)}else M=ot.TEX[n.displaystyle?"sup1":n.texprimestyle?"sup3":"sup2"],L=Math.max(L,M,x*p.d+.25*g,n.superscriptshift),s.style.verticalAlign=ot.Em(L/x),s.style.paddingLeft=ot.Em(v/x),s.style.paddingRight=ot.Em(T/x),h.combine(p,N+v,L);else i&&(b=Math.max(b,ot.TEX.sub1,f*u.h-.8*g,n.subscriptshift),i.style.verticalAlign=ot.Em(-b/f),i.style.paddingRight=ot.Em(T/f),h.combine(u,N,-b));return h.clean(),t},CHTMLstretchV:lt.mbase.CHTMLstretchV,CHTMLstretchH:lt.mbase.CHTMLstretchH,CHTMLchildNode:function(t,e){var a=["mjx-base","mjx-sub","mjx-sup"];return 1===this.over&&(a[1]=a[2]),ot.getNode(t,a[e])}}),lt.mfrac.Augment({toCommonHTML:function(t){t=this.CHTMLdefaultNode(t,{childNodes:["mjx-numerator","mjx-denominator"],childOptions:{autowidth:!0},forceChild:!0,noBBox:!0,minChildren:2});var e=this.getValues("linethickness","displaystyle","numalign","denomalign","bevelled"),a=e.displaystyle,i=t.firstChild,s=t.lastChild,n=ot.addElement(t,"mjx-box");n.appendChild(i),n.appendChild(s),t.appendChild(n),"center"!==e.numalign&&(i.style.textAlign=e.numalign),"center"!==e.denomalign&&(s.style.textAlign=e.denomalign);var r=this.CHTMLbboxFor(0),o=this.CHTMLbboxFor(1),l=ot.BBOX.empty(this.CHTML),h=r.rscale,m=o.rscale;e.linethickness=Math.max(0,ot.thickness2em(e.linethickness||"0",l.scale));var c,d,u,p,f=ot.TEX.min_rule_thickness/ot.em,x=ot.TEX.axis_height,M=e.linethickness;if(e.bevelled){n.className+=" MJXc-bevelled";var g=a?.4:.15,T=Math.max(h*(r.h+r.d),m*(o.h+o.d))+2*g,E=ot.Element("mjx-bevel");n.insertBefore(E,s);var C=ot.createDelimiter(E,47,T);u=h*(r.d-r.h)/2+x+g,p=m*(o.d-o.h)/2+x-g,u&&(i.style.verticalAlign=ot.Em(u/h)),p&&(s.style.verticalAlign=ot.Em(p/m)),E.style.marginLeft=E.style.marginRight=ot.Em(-g/2),l.combine(r,0,u),l.combine(C,h*r.w-g/2,0),l.combine(o,h*r.w+C.w-g,p),l.clean()}else{if(n.className+=" MJXc-stacked",a?(u=ot.TEX.num1,p=ot.TEX.denom1):(u=0===M?ot.TEX.num3:ot.TEX.num2,p=ot.TEX.denom2),0===M)c=Math.max((a?7:3)*ot.TEX.rule_thickness,2*f),(d=u-r.d*h-(o.h*m-p))<c&&(u+=(c-d)/2,p+=(c-d)/2);else{c=Math.max((a?2:0)*f+M,M/2+1.5*f),M=Math.max(M,f),(d=u-r.d*h-(x+M/2))<c&&(u+=c-d),(d=x-M/2-(o.h*m-p))<c&&(p+=c-d),r.L=r.R=o.L=o.R=.1;var L=ot.addElement(n,"mjx-line",{style:{"border-bottom":ot.Px(M*l.scale,1)+" solid",top:ot.Em(-M/2-x)}})}l.combine(r,0,u),l.combine(o,0,-p),l.clean(),n.style.width=ot.Em(l.w),i.style.width=ot.Em(l.w/h),s.style.width=ot.Em(l.w/m),L&&(L.style.width=n.style.width),i.style.top=ot.Em(-l.h/h),s.style.bottom=ot.Em(-l.d/m),ot.addElement(t,"mjx-vsize",{style:{height:ot.Em(l.h+l.d),verticalAlign:ot.Em(-l.d)}})}if(!this.texWithDelims){var b=ot.TEX.nulldelimiterspace;n.style.padding="0 "+ot.Em(b),l.l+=b,l.r+=b,l.w+=2*b}return t},CHTMLcanStretch:function(t){return!1}}),lt.msqrt.Augment({toCommonHTML:function(t){var e=(t=this.CHTMLdefaultNode(t,{childNodes:["mjx-box","mjx-root"],forceChild:!0,noBBox:!0})).firstChild||ot.Element("mjx-box"),a=ot.addElement(t,"mjx-box");a.appendChild(e);var i,s,n=this.CHTMLbboxFor(0),r=ot.BBOX.empty(this.CHTML),o=ot.TEX.rule_thickness,l=ot.TEX.surd_height,h=o;this.Get("displaystyle")&&(h=ot.TEX.x_height),i=o+h/4,s=n.h+n.d+i+o;var m=ot.Element("mjx-surd");a.insertBefore(m,e);var c=ot.createDelimiter(m,8730,[s-.04,s]);c.h+c.d>s&&(i=(c.h+c.d-(s-o))/2),s=n.h+i+o;var d=this.CHTMLaddRoot(t,c,c.h+c.d-s);return e.style.paddingTop=ot.Em(i),e.style.borderTop=ot.Px(l*n.scale,1)+" solid",a.style.paddingTop=ot.Em(2*o-l),n.h+=i+2*o,r.combine(c,d,s-c.h),r.combine(n,d+c.w,0),r.clean(),t},CHTMLaddRoot:function(){return 0},CHTMLhandleBBox:function(t){delete this.CHTMLbboxFor(0).pwidth,this.SUPER(arguments).CHTMLhandleBBox.apply(this,arguments)}}),lt.mroot.Augment({toCommonHTML:lt.msqrt.prototype.toCommonHTML,CHTMLhandleBBox:lt.msqrt.prototype.CHTMLhandleBBox,CHTMLaddRoot:function(t,e,a){if(this.data[1]){var i=this.CHTML,s=this.data[1].CHTML,n=t.firstChild,r=s.rscale,o=this.CHTMLrootHeight(s,e,r)-a,l=Math.min(s.w,s.r),h=Math.max(l,e.offset/r);return o&&(n.style.verticalAlign=ot.Em(o/r)),l<h&&(n.firstChild.style.paddingLeft=ot.Em(h-l)),h-=e.offset/r,n.style.width=ot.Em(h),i.combine(s,0,o),h*r}},CHTMLrootHeight:function(t,e,a){return.45*(e.h+e.d-.9)+e.offset+Math.max(0,t.d-.075)}}),lt.mfenced.Augment({toCommonHTML:function(t){t=this.CHTMLcreateNode(t),this.CHTMLhandleStyle(t),this.CHTMLhandleScale(t),this.CHTMLaddChild(t,"open",{});for(var e=0,a=this.data.length;e<a;e++)this.CHTMLaddChild(t,"sep"+e,{}),this.CHTMLaddChild(t,e,{});this.CHTMLaddChild(t,"close",{});var i=this.CHTML.h,s=this.CHTML.d;for(this.CHTMLstretchChildV("open",i,s),e=0,a=this.data.length;e<a;e++)this.CHTMLstretchChildV("sep"+e,i,s),this.CHTMLstretchChildV(e,i,s);return this.CHTMLstretchChildV("close",i,s),this.CHTMLhandleSpace(t),this.CHTMLhandleBBox(t),this.CHTMLhandleColor(t),t}}),lt.mrow.Augment({toCommonHTML:function(t,e){e=e||{},t=this.CHTMLdefaultNode(t);for(var a,i=this.CHTML,s=i.h,n=i.d,r=0,o=this.data.length;r<o;r++)this.CHTMLstretchChildV(r,s,n),this.data[r]&&this.data[r].CHTML&&this.data[r].CHTML.w<0&&(a=!0);return this.CHTMLlineBreaks()?(this.CHTMLmultiline(t),e.autowidth&&(t.style.width="")):(a&&i.w&&(t.style.width=ot.Em(Math.max(0,i.w))),i.w<0&&(t.style.marginRight=ot.Em(i.w))),t},CHTMLlineBreaks:function(){return!!this.parent.linebreakContainer&&(ft.automatic&&this.CHTML.w>ot.linebreakWidth||this.hasNewline())},CHTMLstretchV:function(t,e){return this.CHTMLstretchChildV(this.CoreIndex(),t,e),this.CHTML},CHTMLstretchH:function(t,e){return this.CHTMLstretchChildH(this.CoreIndex(),e,t),this.CHTML}}),lt.TeXAtom.Augment({toCommonHTML:function(t,e){if(e&&e.stretch||(t=this.CHTMLdefaultNode(t)),this.texClass===lt.TEXCLASS.VCENTER){var a=ot.TEX.axis_height,i=this.CHTML,s=a-(i.h+i.d)/2+i.d;.001<Math.abs(s)&&(t.style.verticalAlign=ot.Em(s),i.h+=s,i.t+=s,i.d-=s,i.b-=s)}return t},CHTMLstretchV:function(t,e){return this.CHTMLupdateFrom(this.Core().CHTMLstretchV(t,e)),this.toCommonHTML(this.CHTMLnodeElement(),{stretch:!0}),this.CHTML},CHTMLstretchH:function(t,e){return this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,e)),this.toCommonHTML(t,{stretch:!0}),this.CHTML}}),lt.semantics.Augment({toCommonHTML:function(t){return t=this.CHTMLcreateNode(t),this.data[0]&&(this.data[0].toCommonHTML(t),this.CHTMLupdateFrom(this.data[0].CHTML),this.CHTMLhandleBBox(t)),t}}),lt.annotation.Augment({toCommonHTML:function(t){return this.CHTMLcreateNode(t)}}),lt["annotation-xml"].Augment({toCommonHTML:lt.mbase.CHTMLautoload}),lt.ms.Augment({toCommonHTML:lt.mbase.CHTMLautoload}),lt.mglyph.Augment({toCommonHTML:lt.mbase.CHTMLautoload}),lt.menclose.Augment({toCommonHTML:lt.mbase.CHTMLautoload}),lt.maction.Augment({toCommonHTML:lt.mbase.CHTMLautoload}),lt.mmultiscripts.Augment({toCommonHTML:lt.mbase.CHTMLautoload}),lt.mtable.Augment({toCommonHTML:lt.mbase.CHTMLautoload}),MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",ot,"jax.js"]),0)})}),MathJax.Hub.Register.StartupHook("End Cookie",function(){"None"!==nt.config.menuSettings.zoom&&st.Require("[MathJax]/extensions/MathZoom.js")}),MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var t=MathJax.ElementJax.mml,l=MathJax.OutputJax.CommonHTML;t["annotation-xml"].Augment({toCommonHTML:function(t){var e=this.Get("encoding");return t=this.CHTMLdefaultNode(t,{childOptions:{encoding:e}}),1!==this.CHTML.rscale&&this.CHTML.rescale(1/this.CHTML.rscale),t}}),t.xml.Augment({toCommonHTML:function(t,e){for(var a=this.CHTML=l.BBOX.zero(),i=0,s=this.data.length;i<s;i++)t.appendChild(this.data[i].cloneNode(!0));var n=t.offsetWidth,r=t.offsetHeight,o=l.addElement(t,"mjx-hd-test",{style:{height:r+"px"}});a.d=a.b=(t.offsetHeight-r)/l.em,a.w=a.r=n/l.em,a.h=a.t=r/l.em-a.d,t.removeChild(o)}}),MathJax.Hub.Startup.signal.Post("CommonHTML annotation-xml Ready"),MathJax.Ajax.loadComplete(l.autoloadDir+"/annotation-xml.js")}),MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var t,n,r,e=MathJax.ElementJax.mml,o=MathJax.OutputJax.CommonHTML,l=o.config.tooltip=MathJax.Hub.Insert({delayPost:600,delayClear:600,offsetX:10,offsetY:5},o.config.tooltip||{});e.maction.Augment({CHTMLtooltip:o.addElement(document.body,"div",{id:"MathJax_CHTML_Tooltip"}),toCommonHTML:function(t){var e=this.Get("selection");t=this.CHTMLcreateNode(t),this.CHTML=o.BBOX.empty(),this.CHTMLhandleStyle(t),this.CHTMLhandleScale(t),this.CHTMLaddChild(t,e-1,{}),this.CHTML.clean(),this.CHTMLhandleSpace(t),this.CHTMLhandleBBox(t),this.CHTMLhandleColor(t);var a=this.Get("actiontype");return this.CHTMLaction[a]&&this.CHTMLaction.hasOwnProperty(a)&&this.CHTMLaction[a].call(this,t,e),t},CHTMLcoreNode:function(t){return this.CHTMLchildNode(t,0)},CHTMLaction:{toggle:function(t,e){this.selection=e,t.onclick=MathJax.Callback(["CHTMLclick",this,o.jax]),t.style.cursor="pointer"},statusline:function(t,e){t.onmouseover=MathJax.Callback(["CHTMLsetStatus",this]),t.onmouseout=MathJax.Callback(["CHTMLclearStatus",this]),t.onmouseover.autoReset=t.onmouseout.autoReset=!0},tooltip:function(t,e){this.data[1]&&this.data[1].isToken?t.title=t.alt=this.data[1].data.join(""):(t.onmouseover=MathJax.Callback(["CHTMLtooltipOver",this,o.jax]),t.onmouseout=MathJax.Callback(["CHTMLtooltipOut",this,o.jax]),t.onmouseover.autoReset=t.onmouseout.autoReset=!0)}},CHTMLclick:function(t,e){this.selection++,this.selection>this.data.length&&(this.selection=1);var a=!!t.hover;if(t.Update(),a){var i=document.getElementById(t.inputID+"-Span");MathJax.Extension.MathEvents.Hover.Hover(t,i)}return MathJax.Extension.MathEvents.Event.False(e)},CHTMLsetStatus:function(t){this.messageID=MathJax.Message.Set(this.data[1]&&this.data[1].isToken?this.data[1].data.join(""):this.data[1].toString())},CHTMLclearStatus:function(t){this.messageID&&MathJax.Message.Clear(this.messageID,0),delete this.messageID},CHTMLtooltipOver:function(t,e){e||(e=window.event),r&&(clearTimeout(r),r=null),n&&clearTimeout(n);var a=e.pageX,i=e.pageY;null==a&&(a=e.clientX+document.body.scrollLeft+document.documentElement.scrollLeft,i=e.clientY+document.body.scrollTop+document.documentElement.scrollTop);var s=MathJax.Callback(["CHTMLtooltipPost",this,t,a+l.offsetX,i+l.offsetY]);n=setTimeout(s,l.delayPost)},CHTMLtooltipOut:function(t,e){n&&(clearTimeout(n),n=null),r&&clearTimeout(r);var a=MathJax.Callback(["CHTMLtooltipClear",this,80]);r=setTimeout(a,l.delayClear)},CHTMLtooltipPost:function(e,a,i){n=null,r&&(clearTimeout(r),r=null);var s=this.CHTMLtooltip;if(s.style.display="block",s.style.opacity="",this!==t){s.style.left=a+"px",s.style.top=i+"px",s.innerHTML='<span class="mjx-chtml"><span class="mjx-math"></span></span>',o.getMetrics(e);try{this.data[1].toCommonHTML(s.firstChild.firstChild)}catch(t){if(!t.restart)throw t;return s.style.display="none",void MathJax.Callback.After(["CHTMLtooltipPost",this,e,a,i],t.restart)}t=this}},CHTMLtooltipClear:function(t){var e=this.CHTMLtooltip;t<=0?(e.style.display="none",e.style.opacity=e.style.filter="",r=null):(e.style.opacity=t/100,e.style.filter="alpha(opacity="+t+")",r=setTimeout(MathJax.Callback(["CHTMLtooltipClear",this,t-20]),50))}}),MathJax.Hub.Startup.signal.Post("CommonHTML maction Ready"),MathJax.Ajax.loadComplete(o.autoloadDir+"/maction.js")}),MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var p=MathJax.ElementJax.mml,f=MathJax.OutputJax.CommonHTML,n="http://www.w3.org/2000/svg";p.menclose.Augment({toCommonHTML:function(t){var e=this.getValues("notation","thickness","padding");null==e.thickness&&(e.thickness=".075em"),null==e.padding&&(e.padding=".2em");var a=(t=this.CHTMLdefaultNode(t,{childNodes:"mjx-box",forceChild:!0})).firstChild,i=this.CHTMLbboxFor(0),s=this.CHTMLlength2em(e.padding,1/f.em),n=this.CHTMLlength2em(e.thickness,1/f.em);n=Math.max(1,Math.round(n*f.em))/f.em;var r=f.Px(n)+" solid",o={L:s,R:s,T:s,B:s,H:i.h+s,D:i.d+s,W:i.w+2*s};a.style.padding=f.Em(s);for(var l=MathJax.Hub.SplitList(e.notation),h={},m=0,c=l.length;m<c;m++)h[l[m]]=!0;for(var d in h[p.NOTATION.UPDIAGONALARROW]&&delete h[p.NOTATION.UPDIAGONALSTRIKE],h)h.hasOwnProperty(d)&&this.CHTMLnotation[d]&&this.CHTMLnotation.hasOwnProperty(d)&&this.CHTMLnotation[d].call(this,a,i,o,s,n,r);var u=this.CHTML;return u.w+=o.L+o.R,u.r+=u.L,u.w>u.r&&(u.r=u.w),u.h+=o.T,u.h>u.t&&(u.t=u.h),u.d+=o.B,u.d>u.b&&(u.b=u.d),t},CHTMLnotation:{box:function(t,e,a,i,s,n){i-=s,t.style.padding=f.Em(i),t.style.border=n},roundedbox:function(t,e,a,i,s,n){var r=Math.min(e.w,e.h+e.d+2*i)/4;f.addElement(t.parentNode,"mjx-box",{style:{padding:f.Em(i-s),border:n,"border-radius":f.Em(r),height:f.Em(e.h+e.d),"vertical-align":f.Em(-a.D),width:f.Em(e.w),"margin-left":f.Em(-a.W)}})},circle:function(t,e,a,i,s,n){var r=a.H,o=a.D,l=a.W,h=this.CHTMLsvg(t,a,s);this.CHTMLsvgElement(h.firstChild,"ellipse",{rx:f.Px(l/2-s/2),ry:f.Px((r+o)/2-s/2),cx:f.Px(l/2),cy:f.Px((r+o)/2)})},left:function(t,e,a,i,s,n){t.style.borderLeft=n,t.style.paddingLeft=f.Em(i-s)},right:function(t,e,a,i,s,n){t.style.borderRight=n,t.style.paddingRight=f.Em(i-s)},top:function(t,e,a,i,s,n){t.style.borderTop=n,t.style.paddingTop=f.Em(i-s)},bottom:function(t,e,a,i,s,n){t.style.borderBottom=n,t.style.paddingBottom=f.Em(i-s)},actuarial:function(t,e,a,i,s,n){t.style.borderTop=t.style.borderRight=n,t.style.paddingTop=t.style.paddingRight=f.Em(i-s)},madruwb:function(t,e,a,i,s,n){t.style.borderBottom=t.style.borderRight=n,t.style.paddingBottom=t.style.paddingRight=f.Em(i-s)},verticalstrike:function(t,e,a,i,s,n){f.addElement(t.parentNode,"mjx-box",{style:{"border-left":n,height:f.Em(a.H+a.D),"vertical-align":f.Em(-a.D),width:f.Em(e.w/2+i-s/2),"margin-left":f.Em(-e.w/2-i-s/2)}})},horizontalstrike:function(t,e,a,i,s,n){f.addElement(t.parentNode,"mjx-box",{style:{"border-top":n,height:f.Em((a.H+a.D)/2-s/2),"vertical-align":f.Em(-a.D),width:f.Em(a.W),"margin-left":f.Em(-a.W)}})},updiagonalstrike:function(t,e,a,i,s,n){var r=a.H,o=a.D,l=a.W,h=this.CHTMLsvg(t,a,s);this.CHTMLsvgElement(h.firstChild,"line",{x1:f.Px(s/2),y1:f.Px(r+o-s),x2:f.Px(l-s),y2:f.Px(s/2)})},downdiagonalstrike:function(t,e,a,i,s,n){var r=a.H,o=a.D,l=a.W,h=this.CHTMLsvg(t,a,s);this.CHTMLsvgElement(h.firstChild,"line",{x1:f.Px(s/2),y1:f.Px(s/2),x2:f.Px(l-s),y2:f.Px(r+o-s)})},updiagonalarrow:function(t,e,a,i,s,n){var r=a.H+a.D-s,o=a.W-s/2,l=Math.atan2(r,o)*(-180/Math.PI).toFixed(3),h=Math.sqrt(r*r+o*o),m=this.CHTMLsvg(t,a,s),c=this.CHTMLsvgElement(m.firstChild,"g",{fill:"currentColor",transform:"translate("+this.CHTMLpx(s/2)+" "+this.CHTMLpx(r+s/2)+") rotate("+l+")"}),d=4*s,u=1*s,p=2*s;this.CHTMLsvgElement(c,"line",{x1:f.Px(s/2),y1:0,x2:f.Px(h-d),y2:0}),this.CHTMLsvgElement(c,"path",{d:"M "+this.CHTMLpx(h-d)+",0 L "+this.CHTMLpx(h-d-u)+","+this.CHTMLpx(p)+"L "+this.CHTMLpx(h)+",0 L "+this.CHTMLpx(h-d-u)+","+this.CHTMLpx(-p),stroke:"none"})},phasorangle:function(t,e,a,i,s,n){var r=i,o=a.H,l=a.D;i=(o+l)/2;var h=a.W+i-r;a.W=h,a.L=i,t.style.margin="0 0 0 "+f.Em(i-r);var m=this.CHTMLsvg(t,a,s);this.CHTMLsvgElement(m.firstChild,"path",{d:"M "+this.CHTMLpx(i)+",1 L 1,"+this.CHTMLpx(o+l-s)+" L "+this.CHTMLpx(h)+","+this.CHTMLpx(o+l-s)})},longdiv:function(t,e,a,i,s,n){a.W+=1.5*i,a.L+=1.5*i;var r=a.H,o=a.D,l=a.W;t.style.margin="0 0 0 "+f.Em(1.5*i);var h=this.CHTMLsvg(t,a,s);this.CHTMLsvgElement(h.firstChild,"path",{d:"M "+this.CHTMLpx(l)+",1 L 1,1 a"+this.CHTMLpx(i)+","+this.CHTMLpx((r+o)/2-s/2)+" 0 0,1 1,"+this.CHTMLpx(r+o-1.5*s)})},radical:function(t,e,a,i,s,n){a.W+=1.5*i,a.L+=1.5*i;var r=a.H,o=a.D,l=a.W;t.style.margin="0 0 0 "+f.Em(1.5*i);var h=this.CHTMLsvg(t,a,s);this.CHTMLsvgElement(h.firstChild,"path",{d:"M 1,"+this.CHTMLpx(.6*(r+o))+" L "+this.CHTMLpx(i)+","+this.CHTMLpx(r+o)+" L "+this.CHTMLpx(2*i)+",1 L "+this.CHTMLpx(l)+",1"})}},CHTMLpx:function(t){return t*=f.em,Math.abs(t)<.1?"0":t.toFixed(1).replace(/\.0$/,"")},CHTMLsvg:function(t,e,a){if(!i){var i=document.createElementNS(n,"svg");i.style&&(i.style.width=f.Em(e.W),i.style.height=f.Em(e.H+e.D),i.style.verticalAlign=f.Em(-e.D),i.style.marginLeft=f.Em(-e.W)),this.CHTMLsvgElement(i,"g",{"stroke-width":f.Px(a)}),t.parentNode.appendChild(i)}return i},CHTMLsvgElement:function(t,e,a){var i=document.createElementNS(n,e);if(i.isMathJax=!0,a)for(var s in a)a.hasOwnProperty(s)&&i.setAttributeNS(null,s,a[s].toString());return t.appendChild(i),i}}),document.createElementNS||delete p.menclose.prototype.toCommonHTML,MathJax.Hub.Startup.signal.Post("CommonHTML menclose Ready"),MathJax.Ajax.loadComplete(f.autoloadDir+"/menclose.js")}),MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var u=MathJax.ElementJax.mml,p=MathJax.OutputJax.CommonHTML,f=MathJax.Localization;u.mglyph.Augment({toCommonHTML:function(t,e){var a=this.getValues("src","width","height","valign","alt");if(t=this.CHTMLcreateNode(t),this.CHTMLhandleStyle(t),this.CHTMLhandleScale(t),""===a.src){var i=this.Get("index");this.CHTMLgetVariant(),i&&this.CHTMLvariant.style&&this.CHTMLhandleText(t,String.fromCharCode(i),this.CHTMLvariant)}else{var s=this.CHTML;if(s.img||(s.img=u.mglyph.GLYPH[a.src]),s.img||(s.img=u.mglyph.GLYPH[a.src]={img:new Image,status:"pending"},s.img.img.onload=MathJax.Callback(["CHTMLimgLoaded",this]),s.img.img.onerror=MathJax.Callback(["CHTMLimgError",this]),s.img.img.src=a.src,MathJax.Hub.RestartAfter(s.img.img.onload)),"OK"!==s.img.status){var n=u.Error(f._(["MathML","BadMglyph"],"Bad mglyph: %1",a.src));n.data[0].data[0].mathsize="75%",this.Append(n),n.toCommonHTML(t),this.data.pop(),s.combine(n.CHTML,0,0,1)}else{var r=p.addElement(t,"img",{isMathJax:!0,src:a.src,alt:a.alt,title:a.alt}),o=a.width,l=a.height,h=s.img.img.width/p.em,m=s.img.img.height/p.em,c=h,d=m;""!==o&&(h=this.CHTMLlength2em(o,c),m=c?h/c*d:0),""!==l&&(m=this.CHTMLlength2em(l,d),""===o&&(h=d?m/d*c:0)),r.style.width=p.Em(h),s.w=s.r=h,r.style.height=p.Em(m),s.h=s.t=m,a.valign&&(s.d=s.b=-this.CHTMLlength2em(a.valign,d),r.style.verticalAlign=p.Em(-s.d),s.h-=s.d,s.t=s.h)}}return this.CHTMLhandleSpace(t),this.CHTMLhandleBBox(t),this.CHTMLhandleColor(t),t},CHTMLimgLoaded:function(t,e){"string"==typeof t&&(e=t),this.CHTML.img.status=e||"OK"},CHTMLimgError:function(){this.CHTML.img.img.onload("error")}},{GLYPH:{}}),MathJax.Hub.Startup.signal.Post("CommonHTML mglyph Ready"),MathJax.Ajax.loadComplete(p.autoloadDir+"/mglyph.js")}),MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var t=MathJax.ElementJax.mml,S=MathJax.OutputJax.CommonHTML;t.mmultiscripts.Augment({toCommonHTML:function(t,e){var a,i,s=(e||{}).stretch;s||(t=this.CHTMLcreateNode(t),this.CHTMLhandleStyle(t),this.CHTMLgetVariant(),this.CHTMLhandleScale(t)),S.BBOX.empty(this.CHTML),s?a=S.getNode(t,"mjx-base"):(this.CHTMLaddChild(t,0,{type:"mjx-base",noBBox:!0,forceChild:!0}),a=t.firstChild),(i=this.CHTMLbboxFor(0)).ic&&(i.R-=i.ic,s||(a.style.marginRight=S.Em(-i.ic)),v=1.3*i.ic+.05);var n={},r={};this.CHTMLgetScripts(n,r,s,t);var o=n.sub,l=n.sup,h=n.presub,m=n.presup,c=r.sub,d=r.sup,u=r.presub,p=r.presup;s||this.CHTMLaddBoxes(t,a,n);var f,x=this.getValues("scriptlevel","scriptsizemultiplier"),M=this.Get("scriptlevel")<3?x.scriptsizemultiplier:1,g=S.TEX.x_height,T=S.TEX.scriptspace,E=S.TEX.sup_drop*M,C=S.TEX.sub_drop*M,L=i.h-E,b=i.d+C,v=0,y=this.data[this.base];!y||"mi"!==y.type&&"mo"!==y.type||!S.isChar(y.data.join(""))||1!==i.rscale||i.sH||y.Get("largeop")||(L=b=0),(x=this.getValues("displaystyle","subscriptshift","superscriptshift","texprimestyle")).subscriptshift=""===x.subscriptshift?0:this.CHTMLlength2em(x.subscriptshift),x.superscriptshift=""===x.superscriptshift?0:this.CHTMLlength2em(x.superscriptshift);var N=h?T+u.w:m?T+p.w-v:0;this.CHTML.combine(i,N,0);var R=this.CHTML.w;if(l||m)if(o||h){b=Math.max(b,S.TEX.sub2);var H=S.TEX.rule_thickness,A=(c||u).h,w=(d||p).d;h&&(A=Math.max(A,u.h)),m&&(w=Math.max(w,p.d)),L-w-(A-b)<3*H&&(b=3*H-L+w+A,0<(E=.8*g-(L-w))&&(L+=E,b-=E)),L=Math.max(L,x.superscriptshift),b=Math.max(b,x.subscriptshift),l?o?this.CHTMLplaceSubSup(o,c,l,d,R,v,L,b,T):this.CHTMLplaceSupOnly(l,d,R,v,L,T):o&&this.CHTMLplaceSubOnly(o,c,R,b,T),m?h?this.CHTMLplacePresubPresup(h,u,m,p,v,L,b,T):this.CHTMLplacePresupOnly(m,p,v,L,T):h&&this.CHTMLplacePresubOnly(h,u,b,T)}else f=S.TEX[x.displaystyle?"sup1":x.texprimestyle?"sup3":"sup2"],L=Math.max(L,f,x.superscriptshift),l&&(L=Math.max(L,d.d+.25*g)),m&&(L=Math.max(L,p.d+.25*g)),l&&this.CHTMLplaceSupOnly(l,d,R,v,L,T),m&&this.CHTMLplacePresupOnly(m,p,v,L,T);else b=Math.max(b,S.TEX.sub1,x.subscriptshift),o&&(b=Math.max(b,c.h-.8*g)),h&&(b=Math.max(b,u.h-.8*g)),o&&this.CHTMLplaceSubOnly(o,c,R,b,T),h&&this.CHTMLplacePresubOnly(h,u,b,T);return 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n&&"none"!==n.type&&"mprescripts"!==n.type&&((i=e.BOX[t])||(i=e.BOX[t]=S.addElement(a,"mjx-"+t),s=e.BBOX[t]=S.BBOX.empty(),e.w&&(i.style.paddingLeft=S.Em(e.w),s.w=s.r=e.w,s.x=e.w)),n.toCommonHTML(i),s=n.CHTML),n&&"mprescripts"!==n.type&&e.i++,s},CHTMLpadScript:function(t,e,a,i){a||(a={w:0,fake:1,rscale:1});var s=i.BBOX[t],n=0,r=0;if(s){if(a.rscale*a.w<e){var o=i.BOX[t];r=e-a.rscale*a.w;var l=S.Element("mjx-spacer",{style:{width:S.Em(r)}});"pre"!==t.substr(0,3)||a.fake?o.appendChild(l):(o.insertBefore(l,o.lastChild),n=r,r=0)}a.fake?s.w+=n:s.combine(a,s.w+n,0),s.w+=r}},CHTMLaddBoxes:function(t,e,a){var i=a.sub,s=a.sup,n=a.presub,r=a.presup;if(n&&r){var o=S.Element("mjx-prestack");t.insertBefore(o,e),o.appendChild(r),o.appendChild(n)}else n&&t.insertBefore(n,e),r&&t.insertBefore(r,e);if(i&&s){var l=S.addElement(t,"mjx-stack");l.appendChild(s),l.appendChild(i)}else 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mmultiscripts Ready"),MathJax.Ajax.loadComplete(S.autoloadDir+"/mmultiscripts.js")}),MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var t=MathJax.ElementJax.mml,i=MathJax.OutputJax.CommonHTML;t.ms.Augment({toCommonHTML:function(t){t=this.CHTMLcreateNode(t),this.CHTMLhandleStyle(t),this.CHTMLgetVariant(),this.CHTMLhandleScale(t),i.BBOX.empty(this.CHTML);var e=this.getValues("lquote","rquote","mathvariant");this.hasValue("lquote")&&'"'!==e.lquote||(e.lquote="“"),this.hasValue("rquote")&&'"'!==e.rquote||(e.rquote="”"),"“"===e.lquote&&"monospace"===e.mathvariant&&(e.lquote='"'),"”"===e.rquote&&"monospace"===e.mathvariant&&(e.rquote='"');var a=e.lquote+this.data.join("")+e.rquote;return this.CHTMLhandleText(t,a,this.CHTMLvariant),this.CHTML.clean(),this.CHTMLhandleSpace(t),this.CHTMLhandleBBox(t),this.CHTMLhandleColor(t),t}}),MathJax.Hub.Startup.signal.Post("CommonHTML ms 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n=this.CHTML;return n.w=n.r=e.R,n.h=n.t=e.T-e.B,n.d=n.b=e.B,i.frame||n.pwidth||(t.style.padding="0 "+I.Em(1/6),n.L=n.R=1/6),this.CHTMLhandleSpace(t),this.CHTMLhandleBBox(t),this.CHTMLhandleColor(t),t},CHTMLgetBoxSizes:function(t,e){var a,i,s=I.FONTDATA.lineH*t.useHeight,n=I.FONTDATA.lineD*t.useHeight,r=[],o=[],l=[],h=-1;for(a=0,i=this.data.length;a<i;a++){var m=this.data[a],c="mtr"===m.type?0:-1;r[a]=s,o[a]=n;for(var d=c,u=m.data.length+c;d<u;d++){null==l[d]&&(l[d]=-1e6,h<d&&(h=d));var p=m.data[d-c].CHTML;p.h>r[a]&&(r[a]=p.h),p.d>o[a]&&(o[a]=p.d),p.w>l[d]&&(l[d]=p.w)}}if(t.equalrows){e.HD=!0;var f=Math.max.apply(Math,r),x=Math.max.apply(Math,o);for(a=0,i=r.length;a<i;a++)r[a]=f,o[a]=x}e.H=r,e.D=o,e.W=l,e.J=h},CHTMLgetAttributes:function(t,e){var a,i,s=x(t.columnspacing),n=x(t.rowspacing),r=x(t.columnalign),o=x(t.rowalign),l=x(t.columnlines),h=x(t.rowlines),m=x(t.columnwidth),c=[],d=e.J,u=e.rows.length-1;for(a=0,i=s.length;a<i;a++)s[a]=this.CHTMLlength2em(s[a]);for(a=0,i=n.length;a<i;a++)n[a]=this.CHTMLlength2em(n[a]);for(;s.length<d;)s.push(s[s.length-1]);for(;r.length<=d;)r.push(r[r.length-1]);for(;l.length<d;)l.push(l[l.length-1]);for(;m.length<=d;)m.push(m[m.length-1]);for(;n.length<u;)n.push(n[n.length-1]);for(;o.length<=u;)o.push(o[o.length-1]);for(;h.length<u;)h.push(h[h.length-1]);for(r[-1]="l"===t.side.substr(0,1)?"left":"right",a=0;a<=u;a++){var p=this.data[a];if(c[a]=[],p.rowalign&&(o[a]=p.rowalign),p.columnalign)for(c[a]=x(p.columnalign);c[a].length<=d;)c[a].push(c[a][c[a].length-1])}var f=x(t.framespacing);2!=f.length&&(f=x(this.defaults.framespacing)),f[0]=Math.max(0,this.CHTMLlength2em(f[0])),f[1]=Math.max(0,this.CHTMLlength2em(f[1])),""===t.columnlines.replace(/none/g,"").replace(/ 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v="mtr"===C.type?0:-1,y=C.data[L-v]||{CHTML:I.BBOX.zero()},N=E[L].style;p=y.CHTML,c=i[L]/2,s[L]!==S.LINES.NONE&&(N.borderRight=e.t+" "+s[L],c-=1/I.em/2),c=I.Em(Math.max(0,c)),N.padding=x+" "+c+" 0px "+d,u&&(N.borderBottom=u),d=c,f=y.rowalign||(this.data[g]||{}).rowalign||l[g];var R=Math.max(1,p.h),H=Math.max(.2,p.d),A=e.H[g]+e.D[g]-(R+H),w=E[L].firstChild.style;f===S.ALIGN.TOP?(A&&(w.marginBottom=I.Em(A)),N.verticalAlign="top"):f===S.ALIGN.BOTTOM?(N.verticalAlign="bottom",A&&(w.marginTop=I.Em(A))):f===S.ALIGN.CENTER?(A&&(w.marginTop=w.marginBottom=I.Em(A/2)),N.verticalAlign="middle"):R!==e.H[g]&&(w.marginTop=I.Em(e.H[g]-R)),(f=y.columnalign||h[g][L]||o[L])!==S.ALIGN.CENTER&&(N.textAlign=f)}E.node.style.height=I.Em(e.RHD[g]),x=m}i[e.J]/=2,n[a.length-1]/=2},CHTMLalignV:function(t,e,a){var i,s=e.rows.length,n=e.H,r=e.D,o=e.RSPACE;"string"!=typeof t.align&&(t.align=String(t.align)),t.align.match(/(top|bottom|center|baseline|axis)( 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x=[],M=[],g=[],T=[],E=e.rows[0];for(i=0;i<=h;i++)T[i]=e.W[i],"auto"===o[i]?x.push(i):"fit"===o[i]?M.push(i):o[i].match(/%$/)?g.push(i):T[i]=this.CHTMLlength2em(o[i],T[i]),f+=T[i]+l[i],E[i]&&(E[i].style.width=I.Em(T[i]));t.frame&&(f+=2/I.em);var C=0<M.length;if(c)if(d)for(i=0;i<=h;i++)cell=E[i].style,"auto"!==o[i]||C?"fit"===o[i]?cell.width="":o[i].match(/%$/)?cell.width=o[i]:cell.minWidth=cell.maxWidth=cell.width:cell.width="";else{if(f<m){var L=0;for(s=0,n=g.length;s<n;s++)i=g[s],L+=(r=Math.max(T[i],this.CHTMLlength2em(o[i],m)))-T[i],T[i]=r,E[i].style.width=I.Em(r);f+=L}if(C||(M=x),f<m&&M.length){var b=(m-f)/M.length;for(s=0,n=M.length;s<n;s++)T[i=M[s]]+=b,E[i].style.width=I.Em(T[i]);f=m}}T[-1]=e.W[-1],e.W=T,e.R=f,d&&(a.style.width=this.CHTML.pwidth="100%",this.CHTML.mwidth=I.Em(f),a.firstChild.style.width=t.width,a.firstChild.style.margin="auto")},CHTMLstretchCells:function(t,e){for(var a=e.rows,i=e.H,s=e.D,n=e.W,r=e.J,o=a.length-1,l=0;l<=o;l++)for(var h=a[l],m=this.data[l],c=i[l],d=s[l],u=0;u<=r;u++){var p=h[u],f=m.data[u];f&&("V"===f.CHTML.stretch?f.CHTMLstretchV(c,d):"H"===f.CHTML.stretch&&f.CHTMLstretchH(p,n[u]))}},CHTMLaddLabels:function(t,e,a,i){var s=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");s.indentalignfirst!==S.INDENTALIGN.INDENTALIGN&&(s.indentalign=s.indentalignfirst),s.indentalign===S.INDENTALIGN.AUTO&&(s.indentalign=T.displayAlign),s.indentshiftfirst!==S.INDENTSHIFT.INDENTSHIFT&&(s.indentshift=s.indentshiftfirst),"auto"===s.indentshift&&(s.indentshift="0");var n=this.CHTMLlength2em(s.indentshift,I.cwidth),r=this.CHTMLlength2em(t.minlabelspacing,.8)+e.W[-1],o=0,l=e.R,h=this.CHTMLlength2em(T.displayIndent,I.cwidth),m=e.CALIGN[-1]===S.INDENTALIGN.RIGHT?-1:1;s.indentalign===S.INDENTALIGN.CENTER?(l+=2*(r-m*(n+h)),n+=h):e.CALIGN[-1]===s.indentalign?(h<0&&(o=m*h,h=0),m*(n+=m*h)<r&&(n=m*r),n+=o,l+=n*=m):(l+=r-m*n+h,n-=m*h,n*=-m);var 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