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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=h=t.CombineConfig("MathEvents",h),a.Queue(t.Register.StartupHook("End Config",{}),[function(){var t=h.styles[".MathJax_Hover_Frame"];t.border=h.frame.bwidth+"px solid "+h.frame.bcolor+" ! important",t["box-shadow"]=t["-webkit-box-shadow"]=t["-moz-box-shadow"]=t["-khtml-box-shadow"]="0px 0px "+h.frame.hwidth+" "+h.frame.hcolor}],["getImages",p],["Styles",i,h.styles],["Post",t.Startup.signal,"MathEvents 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u=MathJax.Extension.MathZoom={version:"2.7.9",settings:t.config.menuSettings,scrollSize:18,HandleEvent:function(t,e,i){return!(!u.settings.CTRL||t.ctrlKey)||!(!u.settings.ALT||t.altKey)||!(!u.settings.CMD||t.metaKey)||!(!u.settings.Shift||t.shiftKey)||!u[e]||u[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(),s.ClearHoverTimer(),r.ClearSelection();var n=MathJax.OutputJax[a.jaxID],u=n.getJaxFromMath(a);u.hover&&s.UnHover(u);var h=this.findContainer(a),d=Math.floor(.85*h.clientWidth),p=Math.max(document.body.clientHeight,document.documentElement.clientHeight);"visible"!==this.getOverflow(h)&&(p=Math.min(h.clientHeight,p)),p=Math.floor(.85*p);var c=e.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"}}]]]]),m=c.lastChild,f=m.firstChild,M=c.firstChild;a.parentNode.insertBefore(c,a),a.parentNode.insertBefore(a,c),f.addEventListener&&f.addEventListener("mousedown",this.Remove,!0);var x=m.offsetWidth||m.clientWidth;if(d-=x,p-=x,m.style.maxWidth=d+"px",m.style.maxHeight=p+"px",this.msieTrapEventBug){var g=e.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});c.insertBefore(g,m)}if(this.msieZIndexBug){var v=e.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});c.style.position="relative",c.style.zIndex=l.styles["#MathJax_ZoomOverlay"]["z-index"],c=v}var b=n.Zoom(u,f,a,d,p);return 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i=this.Resize(),a=i.x,n=i.y,o=e.mW;t.style.display="";var s=-o-Math.floor((t.offsetWidth-o)/2),r=e.Y;t.style.left=Math.max(s,10-a)+"px",t.style.top=Math.max(r,10-n)+"px",u.msiePositionBug||u.SetWH()},Resize:function(t){u.onresize&&u.onresize(t);var e=document.getElementById("MathJax_ZoomFrame"),i=document.getElementById("MathJax_ZoomOverlay"),a=u.getXY(e),n=u.findContainer(e);if("visible"!==u.getOverflow(n)){i.scroll_parent=n;var o=u.getXY(n);a.x-=o.x,a.y-=o.y,o=u.getBorder(n),a.x-=o.x,a.y-=o.y}return i.style.left=-a.x+"px",i.style.top=-a.y+"px",u.msiePositionBug?setTimeout(u.SetWH,0):u.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),u.operaRefreshBug){var s=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(s)}window.removeEventListener?removeEventListener("resize",u.Resize,!1):window.detachEvent?detachEvent("onresize",u.Resize):(window.onresize=u.onresize,delete u.onresize)}return o(i)}};t.Browser.Select({MSIE:function(t){var e=document.documentMode||0,i=e>=9;u.msiePositionBug=!i,u.msieSizeBug=t.versionAtLeast("7.0")&&(!document.documentMode||7===e||8===e),u.msieZIndexBug=e<=7,u.msieInlineBlockAlignBug=e<=7,u.msieTrapEventBug=!window.addEventListener,"BackCompat"===document.compatMode&&(u.scrollSize=52),i&&delete l.styles["#MathJax_Zoom"].filter},Opera:function(t){u.operaPositionBug=!0,u.operaRefreshBug=!0}}),u.topImg=u.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"}}),(u.operaPositionBug||u.msieTopBug)&&(u.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 o="2.7.9",s=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:o,signal:s};var r,l,u,h=function(t){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",t]].concat([].slice.call(arguments,1)))},d=MathJax.Object.isArray,p=t.Browser.isPC,c=t.Browser.isMSIE,m=(document.documentMode||0)>8,f=p?null:"5px",M=t.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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e&&t.Insert(this,e),this},Post:function(t,i,a){t||(t=window.event||{});var n=document.getElementById("MathJax_MenuFrame");n||(n=g.Background(this),delete v.lastItem,delete v.lastMenu,delete g.skipUp,s.Post(["post",g.jax]),g.isRTL="rtl"===MathJax.Localization.fontDirection());var o=e.Element("div",{onmouseup:g.Mouseup,ondblclick:r,ondragstart:r,onselectstart:r,oncontextmenu:r,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});"contextmenu"!==t.type&&"mouseover"!==t.type||(o.className+=" MathJax_ContextMenu"),a||MathJax.Localization.setCSS(o);for(var l=0,u=this.items.length;l<u;l++)this.items[l].Create(o);g.isMobile&&e.addElement(o,"span",{className:"MathJax_MenuClose",menu:i,ontouchstart:g.Close,ontouchend:r,onmousedown:g.Close,onmouseup:r},[["span",{},"×"]]),n.appendChild(o),this.posted=!0,o.offsetWidth&&(o.style.width=o.offsetWidth+2+"px");var h=t.pageX,d=t.pageY,c=document.body.getBoundingClientRect(),m=window.getComputedStyle?window.getComputedStyle(document.body):{marginLeft:"0px"},f=c.right-Math.min(0,c.left)+parseFloat(m.marginLeft);if(h||d||!("clientX"in t)||(h=t.clientX+document.body.scrollLeft+document.documentElement.scrollLeft,d=t.clientY+document.body.scrollTop+document.documentElement.scrollTop),i){var x="left",b=i.offsetWidth;for(h=g.isMobile?30:b-2,d=0;i&&i!==n;)h+=i.offsetLeft,d+=i.offsetTop,i=i.parentNode;g.isMobile||(g.isRTL&&h-b-o.offsetWidth>this.margin||!g.isRTL&&h+o.offsetWidth>f-this.margin)&&(x="right",h=Math.max(this.margin,h-b-o.offsetWidth+6)),p||(o.style["borderRadiusTop"+x]=0,o.style["WebkitBorderRadiusTop"+x]=0,o.style["MozBorderRadiusTop"+x]=0,o.style["KhtmlBorderRadiusTop"+x]=0)}else{var C=g.CurrentNode()||t.target;if(("keydown"===t.type||!h&&!d)&&C){var T=window.pageXOffset||document.documentElement.scrollLeft,E=window.pageYOffset||document.documentElement.scrollTop,y=C.getBoundingClientRect();h=(y.right+y.left)/2+T,d=(y.bottom+y.top)/2+E}h+o.offsetWidth>f-this.margin&&(h=f-o.offsetWidth-this.margin),g.isMobile&&(h=Math.max(5,h-Math.floor(o.offsetWidth/2)),d-=20),g.skipUp=t.isContextMenu}o.style.left=h+"px",o.style.top=d+"px",document.selection&&document.selection.empty&&document.selection.empty();var L=window.pageXOffset||document.documentElement.scrollLeft,A=window.pageYOffset||document.documentElement.scrollTop;return g.Focus(o),"keydown"===t.type&&(g.skipMouseoverFromKey=!0,setTimeout((function(){delete g.skipMouseoverFromKey}),M.delay)),window.scrollTo(L,A),r(t)},Remove:function(t,e){s.Post(["unpost",g.jax]);var i=document.getElementById("MathJax_MenuFrame");return i&&(i.parentNode.removeChild(i),this.msieFixedPositionBug&&detachEvent("onresize",g.Resize)),g.jax.hover&&(delete 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this.Remove(t,e)},DeactivateSubmenus:function(t){for(var e=document.getElementById("MathJax_MenuFrame").childNodes,i=v.GetMenuNode(t).childNodes,a=0,n=i.length;a<n;a++){var o=i[a].menuItem;o&&o.submenu&&o.submenu.posted&&o!==t.menuItem&&o.Deactivate(i[a])}this.RemoveSubmenus(t,e)},RemoveSubmenus:function(t,e){for(var i=(e=e||document.getElementById("MathJax_MenuFrame").childNodes).length-1;i>=0&&v.GetMenuNode(t).menuItem!==e[i].menuItem;)e[i].menuItem.posted=!1,e[i].parentNode.removeChild(e[i]),i--},Touchstart:function(t,e){return this.TouchEvent(t,e,"Mousedown")},Touchend:function(t,e){return this.TouchEvent(t,e,"Mouseup")},TouchEvent:function(t,e,i){return this!==v.lastItem&&(v.lastMenu&&g.Event(t,v.lastMenu,"Mouseout"),g.Event(t,e,"Mouseover",!0),v.lastItem=this,v.lastMenu=e),this.nativeTouch?null:(g.Event(t,e,i),!1)},Remove:function(t,e){return(e=e.parentNode.menuItem).Remove(t,e)},With:function(e){return e&&t.Insert(this,e),this},isRTL:function(){return g.isRTL},rtlClass:function(){return this.isRTL()?" 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n=v.GetMenuNode(e);if(n.menuItem===g.menu&&t.shiftKey&&i(t,e),!a){n.menuItem!==g.menu&&this.Deactivate(e);for(var o=n.previousSibling.childNodes,s=o.length;s--;){var r=o[s];if(r.menuItem.submenu&&r.menuItem.submenu===n.menuItem){g.Focus(r);break}}this.RemoveSubmenus(e)}},Space:function(t,e){this.Mouseup(t,e)},Activate:function(t,e){this.Deactivate(e),this.disabled||(e.className+=" MathJax_MenuActive"),this.DeactivateSubmenus(e),g.Focus(e)},Deactivate:function(t){t.className=t.className.replace(/ MathJax_MenuActive/,"")}}),g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(t,e,i){d(t)||(t=[t,t]),this.name=t,this.action=e,this.With(i)},Label:function(t,e){return[this.Name()]},Mouseup:function(t,e){return this.disabled||(this.Remove(t,e),s.Post(["command",this]),this.action.call(this,t)),r(t)}}),g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"►",markerRTL:"◄",Attributes:function(e){return e=t.Insert({"aria-haspopup":"true"},e),this.SUPER(arguments).Attributes.call(this,e)},Init:function(t,e){d(t)||(t=[t,t]),this.name=t;var i=1;e instanceof g.ITEM||(this.With(e),i++),this.submenu=g.apply(g,[].slice.call(arguments,i))},Label:function(t,e){return this.submenu.posted=!1,[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(t,e){this.ClearTimer(),t={type:t.type,clientX:t.clientX,clientY:t.clientY},this.timer=setTimeout(a(["Mouseup",this,t,e]),M.delay)},ClearTimer:function(){this.timer&&clearTimeout(this.timer)},Touchend:function(t,e){var i=this.submenu.posted,a=this.SUPER(arguments).Touchend.apply(this,arguments);return i&&(this.Deactivate(e),delete v.lastItem,delete v.lastMenu),a},Mouseout:function(t,e){this.submenu.posted||this.Deactivate(e),this.ClearTimer()},Mouseover:function(t,e){this.Activate(t,e)},Mouseup:function(t,e){return this.disabled||(this.submenu.posted?this.DeactivateSubmenus(e):(this.ClearTimer(),this.submenu.Post(t,e,this.ltr),g.Focus(e))),r(t)},Activate:function(t,e){this.disabled||(this.Deactivate(e),e.className+=" MathJax_MenuActive"),this.submenu.posted||(this.DeactivateSubmenus(e),g.isMobile||this.Timer(t,e)),g.Focus(e)},MoveVertical:function(t,e,i){this.ClearTimer(),this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(t,e,i,a){if(a){if(!this.disabled)if(this.submenu.posted){var n=v.GetMenuNode(e).nextSibling.childNodes;n.length>0&&this.submenu.items[0].Activate(t,n[0])}else this.Activate(t,e)}else this.SUPER(arguments).MoveHorizontal.apply(this,arguments)}}),g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:p?"●":"✓",role:"menuitemradio",Attributes:function(e){var i=M.settings[this.variable]===this.value?"true":"false";return e=t.Insert({"aria-checked":i},e),this.SUPER(arguments).Attributes.call(this,e)},Init:function(t,e,i){d(t)||(t=[t,t]),this.name=t,this.variable=e,this.With(i),null==this.value&&(this.value=this.name[0])},Label:function(t,e){var i={className:"MathJax_MenuRadioCheck"+this.rtlClass()};return M.settings[this.variable]!==this.value&&(i={style:{display:"none"}}),[["span",i,[this.marker]]," "+this.Name()]},Mouseup:function(t,e){if(!this.disabled){for(var i=e.parentNode.childNodes,a=0,n=i.length;a<n;a++){var o=i[a].menuItem;o&&o.variable===this.variable&&(i[a].firstChild.style.display="none")}e.firstChild.display="",M.settings[this.variable]=this.value,g.cookie[this.variable]=M.settings[this.variable],g.saveCookie(),s.Post(["radio button",this])}return this.Remove(t,e),this.action&&!this.disabled&&this.action.call(g,this),r(t)}}),g.ITEM.CHECKBOX=g.ENTRY.Subclass({variable:null,marker:"✓",role:"menuitemcheckbox",Attributes:function(e){var i=M.settings[this.variable]?"true":"false";return e=t.Insert({"aria-checked":i},e),this.SUPER(arguments).Attributes.call(this,e)},Init:function(t,e,i){d(t)||(t=[t,t]),this.name=t,this.variable=e,this.With(i)},Label:function(t,e){var i={className:"MathJax_MenuCheck"+this.rtlClass()};return M.settings[this.variable]||(i={style:{display:"none"}}),[["span",i,[this.marker]]," "+this.Name()]},Mouseup:function(t,e){return this.disabled||(e.firstChild.display=M.settings[this.variable]?"none":"",M.settings[this.variable]=!M.settings[this.variable],g.cookie[this.variable]=M.settings[this.variable],g.saveCookie(),s.Post(["checkbox",this])),this.Remove(t,e),this.action&&!this.disabled&&this.action.call(g,this),r(t)}}),g.ITEM.LABEL=g.ENTRY.Subclass({role:"menuitem",Init:function(t,e){d(t)||(t=[t,t]),this.name=t,this.With(e)},Label:function(t,e){return t.className+=" 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r=document.documentElement||{},l=window.innerHeight||r.clientHeight||r.scrollHeight||0;g.prototype.msieAboutBug?(s.style.width="20em",s.style.position="absolute",s.style.left=Math.floor((document.documentElement.scrollWidth-s.offsetWidth)/2)+"px",s.style.top=Math.floor((l-s.offsetHeight)/3)+document.body.scrollTop+"px"):(s.style.marginLeft=Math.floor(-s.offsetWidth/2)+"px",s.style.top=Math.floor((l-s.offsetHeight)/3)+"px")},g.About.Remove=function(t){g.About.div&&(document.body.removeChild(g.About.div),delete g.About.div)},g.About.Keydown=function(t){t.keyCode!==u.ESCAPE&&("MathJax_AboutClose"!==this.id||t.keyCode!==u.SPACE&&t.keyCode!==u.RETURN)||(g.About.Remove(t),g.CurrentNode().focus(),r(t))},g.About.GetJax=function(t,e,i,a){var n=[];for(var o in e)e.hasOwnProperty(o)&&e[o]&&(a&&e[o].version||e[o].isa&&e[o].isa(e))&&n.push(h(i[0],i[1],e[o].id||o,e[o].version));n.sort();for(var s=0,r=n.length;s<r;s++)t.push(n[s],["br"]);return t},g.About.GetFont=function(){var t=MathJax.Hub.outputJax["jax/mml"][0]||{};return({SVG:"web SVG",CommonHTML:"web TeX","HTML-CSS":t.imgFonts?"image":(t.webFonts?"web":"local")+" "+t.fontInUse}[t.id]||"generic")+" fonts"},g.About.GetFormat=function(){var t=MathJax.Hub.outputJax["jax/mml"][0]||{};if("HTML-CSS"===t.id&&t.webFonts&&!t.imgFonts)return t.allowWebFonts.replace(/otf/,"woff or otf")+" fonts"},g.Help=function(t){i.Require("[MathJax]/extensions/HelpDialog.js",(function(){MathJax.Extension.Help.Dialog({type:t.type})}))},g.ShowSource=function(t){t||(t=window.event);var e={screenX:t.screenX,screenY:t.screenY};if(g.jax)if("MathML"===this.format){var n=MathJax.ElementJax.mml;if(n&&void 0!==n.mbase.prototype.toMathML)try{g.ShowSource.Text(g.jax.root.toMathML("",g.jax),t)}catch(t){if(!t.restart)throw t;a.After([this,g.ShowSource,e],t.restart)}else if(!i.loadingToMathML)return i.loadingToMathML=!0,g.ShowSource.Window(t),void a.Queue(i.Require("[MathJax]/extensions/toMathML.js"),(function(){delete i.loadingToMathML,n.mbase.prototype.toMathML||(n.mbase.prototype.toMathML=function(){})}),[this,g.ShowSource,e])}else if("Error"===this.format)g.ShowSource.Text(g.jax.errorText,t);else if(M.semanticsAnnotations[this.format]){var o=g.jax.root.getAnnotation(this.format);o.data[0]&&g.ShowSource.Text(o.data[0].toString())}else{if(null==g.jax.originalText)return void alert(h("NoOriginalForm","No original form available"));g.ShowSource.Text(g.jax.originalText,t)}},g.ShowSource.Window=function(t){if(!g.ShowSource.w){var e=[],i=M.windowSettings;for(var a in i)i.hasOwnProperty(a)&&e.push(a+"="+i[a]);g.ShowSource.w=window.open("","_blank",e.join(","))}return g.ShowSource.w},g.ShowSource.Text=function(t,e){var i=g.ShowSource.Window(e);delete g.ShowSource.w,t=(t=t.replace(/^\s*/,"").replace(/\s*$/,"")).replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;");var a=h("EqSource","MathJax Equation Source");if(g.isMobile)i.document.open(),i.document.write("<html><head><meta name='viewport' content='width=device-width, initial-scale=1.0' /><title>"+a+"</title></head><body style='font-size:85%'>"),i.document.write("<pre>"+t+"</pre>"),i.document.write("<hr><input type='button' value='"+h("Close","Close")+"' onclick='window.close()' />"),i.document.write("</body></html>"),i.document.close();else{i.document.open(),i.document.write("<html><head><title>"+a+"</title></head><body style='font-size:85%'>"),i.document.write("<table><tr><td><pre>"+t+"</pre></td></tr></table>"),i.document.write("</body></html>"),i.document.close();var n=i.document.body.firstChild;setTimeout((function(){var t,a,o,s=i.outerHeight-i.innerHeight||30,r=i.outerWidth-i.innerWidth||30;r=Math.max(140,Math.min(Math.floor(.5*screen.width),n.offsetWidth+r+25)),s=Math.max(40,Math.min(Math.floor(.5*screen.height),n.offsetHeight+s+25)),g.prototype.msieHeightBug&&(s+=35),i.resizeTo(r,s);try{o=e.screenX}catch(t){}e&&null!=o&&(t=Math.max(0,Math.min(e.screenX-Math.floor(r/2),screen.width-r-20)),a=Math.max(0,Math.min(e.screenY-Math.floor(s/2),screen.height-s-20)),i.moveTo(t,a))}),50)}},g.Scale=function(){var e,i,a=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],o=a.length,s=100;for(e=0;e<o;e++)if(i=n[a[e]]){s=i.config.scale;break}var r=prompt(h("ScaleMath","Scale all mathematics (compared to surrounding text) by"),s+"%");if(r)if(r.match(/^\s*\d+(\.\d*)?\s*%?\s*$/))if(r=parseFloat(r)){if(r!==s){for(e=0;e<o;e++)(i=n[a[e]])&&(i.config.scale=r);g.cookie.scale=t.config.scale=r,g.saveCookie(),t.Queue(["Rerender",t])}}else alert(h("NonZeroScale","The scale should not be zero"));else alert(h("PercentScale","The scale should be a percentage (e.g., 120%%)"))},g.Zoom=function(){MathJax.Extension.MathZoom||i.Require("[MathJax]/extensions/MathZoom.js")},g.Renderer=function(){var i=t.outputJax["jax/mml"];if(i[0]!==M.settings.renderer){var a,n,o=t.Browser,s=g.Renderer.Messages;switch(M.settings.renderer){case"NativeMML":M.settings.warnedMML||(o.isChrome&&"24."!==o.version.substr(0,3)||o.isSafari&&!o.versionAtLeast("5.0")?a=s.MML.WebKit:o.isMSIE?o.hasMathPlayer||(a=s.MML.MSIE):a=o.isEdge?s.MML.WebKit:s.MML[o],n="warnedMML");break;case"SVG":M.settings.warnedSVG||o.isMSIE&&!m&&(a=s.SVG.MSIE)}if(a){if(a=h(a[0],a[1]),a+="\n\n",a+=h("SwitchAnyway","Switch the renderer anyway?\n\n(Press OK to switch, CANCEL to continue with the current renderer)"),g.cookie.renderer=i[0].id,g.saveCookie(),!confirm(a))return g.cookie.renderer=M.settings.renderer=e.Cookie.Get("menu").renderer,void g.saveCookie();n&&(g.cookie.warned=M.settings.warned=!0),g.cookie.renderer=M.settings.renderer,g.saveCookie()}t.Queue(["setRenderer",t,M.settings.renderer,"jax/mml"],["Rerender",t])}},g.Renderer.Messages={MML:{WebKit:["WebkitNativeMMLWarning","Your browser doesn't seem to support MathML natively, so switching to MathML output may cause the mathematics on the page to become unreadable."],MSIE:["MSIENativeMMLWarning","Internet Explorer requires the MathPlayer plugin in order to process MathML output."],Opera:["OperaNativeMMLWarning","Opera's support for MathML is limited, so switching to MathML output may cause some expressions to render poorly."],Safari:["SafariNativeMMLWarning","Your browser's native MathML does not implement all the features used by MathJax, so some expressions may not render properly."],Firefox:["FirefoxNativeMMLWarning","Your browser's native MathML does not implement all the features used by MathJax, so some expressions may not render 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o=this.PHTMLbboxFor(0),s=this.PHTMLbboxFor(1),r=this.PHTML;if(r.w=.8*Math.max(o.w,s.w),r.h=o.h+o.d+.1+.25,r.d=s.h+s.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,u=a.Em(e.linethickness);l.style.borderTop="none",l.style.borderBottom=(e.linethickness<.15?"1px":u)+" solid",l.style.margin=u+" 0",u=e.linethickness,n.style.marginTop=a.Em(3*u-1.2),t.style.verticalAlign=a.Em(1.5*u+.1),r.h+=1.5*u-.1,r.d+=1.5*u}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),o=Math.ceil(100*(n.h+n.d+.14)),s=a.Em(14/o),r=i.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":o+"%","margin-top":s}},["√"]]]),l=i.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]),u=1.2/2.2*o/100;if(o>150){var h=Math.ceil(150/o*10);r.firstChild.className="MJXp-right MJXp-scale"+h,r.firstChild.style.marginLeft=a.Em(u*(h/10-1)/o*100),u=u*h/10,l.firstChild.style.borderTopWidth=a.Em(.08/Math.sqrt(h/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+u,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),o=this.PHTMLlayoutRoot(i.Element("span"),t.firstChild);n.className="MJXp-script";var s=parseInt(o.firstChild.firstChild.style.fontSize),r=s/120*.55+.8*e.d,l=s/120*-.6;return s>150&&(l*=.95*Math.ceil(150/s*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(o),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,o,s,r=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","width"),l=MathJax.Hub.SplitList,u=l(r.columnspacing),h=l(r.rowspacing),d=l(r.columnalign),p=l(r.rowalign);for(e=0,n=u.length;e<n;e++)u[e]=a.length2em(u[e]);for(e=0,n=h.length;e<n;e++)h[e]=a.length2em(h[e]);for(var c=i.Element("span");t.firstChild;)c.appendChild(t.firstChild);t.appendChild(c);var m=0,f=0;for(e=0,n=this.data.length;e<n;e++){var M=this.data[e];if(M){var x=a.arrayEntry(h,e-1),g=a.arrayEntry(p,e),v=M.PHTML;M.PHTMLspanElement().style.verticalAlign=g;var b="mlabeledtr"===M.type?1:0;for(o=0,s=M.data.length;o<s-b;o++){var C=M.data[o+b];if(C){var T=a.arrayEntry(u,o-1),E=a.arrayEntry(d,o),y=C.PHTMLspanElement();o&&(v.w+=T,y.style.paddingLeft=a.Em(T)),e&&(y.style.paddingTop=a.Em(x)),y.style.textAlign=E}}m+=v.h+v.d,e&&(m+=x),v.w>f&&(f=v.w)}}var L=this.PHTML;return L.w=f,L.h=m/2+.25,L.d=m/2-.25,L.l=L.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,o=i.isMSIE&&(document.documentMode||0)<8,s=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,o,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(){!o&&s.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(){!o&&r&&(t.processUpdateTime=e,t.processUpdateDelay=i,t.Config({messageStyle:n}),o=!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=o?"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)}))}};s.Register("TeX"),s.Register("MathML"),s.Register("AsciiMath"),t.Register.StartupHook("End Config",["Config",s]),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,o=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 o.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,o=a.length;n<o;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,o,s=t.jax.length,r=MathJax.ElementJax.mml;for(r.copyAttributes.id=1;t.i<s;){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),o=a.addElement(n,"span",{isMathJax:!0,unselectable:"on",className:"MJX_Assistive_MathML"+("block"===e.root.Get("display")?" MJX_Assistive_MathML_Block":"")});try{o.innerHTML=i}catch(t){}n.style.position="relative",n.setAttribute("role","presentation"),n.firstChild.setAttribute("aria-hidden","true"),o.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,o=Function.prototype.bind?function(t,e){return t.bind(e)}:function(t,e){return function(){t.apply(e,arguments)}},s=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=s(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 o,s,r=a.FindId("Accessibility");r?(e.unshift(i.RULE()),r.submenu.items.push.apply(r.submenu.items,e)):((o=(a.FindId("Settings","Renderer")||{}).submenu)&&(e.unshift(i.RULE()),e.unshift(o.items.pop()),e.unshift(o.items.pop())),e.unshift("Accessibility"),r=i.SUBMENU.apply(i.SUBMENU,e),(s=a.IndexOfId("Locale"))?a.items.splice(s,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}},u=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=o(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(u("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),l.Register(u("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),l.Register(u("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.js");