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e=t.charCodeAt(0);return e>=55296&&e<56319},findBlock:function(t,e){if(t.Ranges)for(var i=0,a=t.Ranges.length;i<a;i++){if(e<t.Ranges[i][0])return;if(e<=t.Ranges[i][1]){for(var s=t.Ranges[i][2],n=t.Ranges.length-1;n>=0;n--)t.Ranges[n][2]==s&&t.Ranges.splice(n,1);this.loadFont(t.directory+"/"+s+".js")}}},loadFont:function(i){e.RestartAfter(t.Require(this.fontDir+"/"+i))},createDelimiter:function(i,n,h,r){h||(h=1);var l=c.G();if(!i)return l.Clean(),delete l.element,l.w=l.r=this.TeX.nulldelimiterspace*h,l;n instanceof Array||(n=[n,n]);var o=n[1];n=n[0];for(var d={alias:i};d.alias;)i=d.alias,(d=this.FONTDATA.DELIMITERS[i])||(d={HW:[0,this.FONTDATA.VARIANT[s.VARIANT.NORMAL]]});d.load&&e.RestartAfter(t.Require(this.fontDir+"/fontdata-"+d.load+".js"));for(var m=0,f=d.HW.length;m<f;m++)if(d.HW[m][0]*h>=n-10-a.config.blacker||m==f-1&&!d.stretch)return d.HW[m][2]&&(h*=d.HW[m][2]),d.HW[m][3]&&(i=d.HW[m][3]),this.createChar(h,[i,d.HW[m][1]],r).With({stretched:!0});return 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i.mid?(o-=(l-e)/2,t.Add(d,o,0),o+=d.w-(l-e)/2):o-=l-e;t.Add(r,o-r.l,0),t.Clean(),t.scale=s,t.isMultiChar=!0},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:430.554,quad:1e3,num1:676.508,num2:393.732,num3:443.73,denom1:685.951,denom2:344.841,sup1:412.892,sup2:362.892,sup3:288.888,sub1:150,sub2:247.217,sup_drop:386.108,sub_drop:50,delim1:2390,delim2:1e3,axis_height:250,rule_thickness:60,big_op_spacing1:111.111,big_op_spacing2:166.666,big_op_spacing3:200,big_op_spacing4:600,big_op_spacing5:100,scriptspace:100,nulldelimiterspace:120,delimiterfactor:901,delimitershortfall:300,min_rule_thickness:1.25,min_root_space:1.5},BIGDIMEN:1e7,NBSP:" "});var c=a.BBOX=MathJax.Object.Subclass({type:"g",removeable:!0,Init:function(t){this.h=this.d=-a.BIGDIMEN,this.H=this.D=0,this.w=this.r=0,this.l=a.BIGDIMEN,this.x=this.y=0,this.scale=1,this.n=0,this.type&&(this.element=a.Element(this.type,t))},With:function(t){return e.Insert(this,t)},Add:function(t,e,i,a,s){if(e&&(t.x+=e),i&&(t.y+=i),t.element){if(t.removeable&&1===t.element.childNodes.length&&1===t.n){var n=t.element.firstChild,h=n.nodeName.toLowerCase();if("use"===h||"rect"===h){t.element=n,t.scale=t.childScale;var r=t.childX,l=t.childY;t.x+=r,t.y+=l,t.h-=l,t.d+=l,t.H-=l,t.D+=l,t.w-=r,t.r-=r,t.l+=r,t.removeable=!1,n.setAttribute("x",Math.floor(t.x/t.scale)),n.setAttribute("y",Math.floor(t.y/t.scale))}}if(Math.abs(t.x)<1&&Math.abs(t.y)<1)t.remove=t.removeable;else if("g"===(h=t.element.nodeName.toLowerCase()))t.element.firstChild?t.element.setAttribute("transform","translate("+Math.floor(t.x)+","+Math.floor(t.y)+")"):t.remove=t.removeable;else if("line"===h||"polygon"===h||"path"===h||"a"===h){var o=t.element.getAttribute("transform")||"";o&&(o=" "+o),o="translate("+Math.floor(t.x)+","+Math.floor(t.y)+")"+o,t.element.setAttribute("transform",o)}else t.element.setAttribute("x",Math.floor(t.x/t.scale)),t.element.setAttribute("y",Math.floor(t.y/t.scale));if(t.remove)for(this.n+=t.n;t.element.firstChild;)s&&this.element.firstChild?this.element.insertBefore(t.element.firstChild,this.element.firstChild):this.element.appendChild(t.element.firstChild);else s?this.element.insertBefore(t.element,this.element.firstChild):this.element.appendChild(t.element);delete t.element}return t.hasIndent&&(this.hasIndent=t.hasIndent),null!=t.tw&&(this.tw=t.tw),t.d-t.y>this.d&&(this.d=t.d-t.y,this.d>this.D&&(this.D=this.d)),t.y+t.h>this.h&&(this.h=t.y+t.h,this.h>this.H&&(this.H=this.h)),t.D-t.y>this.D&&(this.D=t.D-t.y),t.y+t.H>this.H&&(this.H=t.y+t.H),t.x+t.l<this.l&&(this.l=t.x+t.l),t.x+t.r>this.r&&(this.r=t.x+t.r),(a||t.x+t.w+(t.X||0)>this.w)&&(this.w=t.x+t.w+(t.X||0)),this.childScale=t.scale,this.childX=t.x,this.childY=t.y,this.n++,t},Align:function(t,e,i,a,s){i={left:i,center:(this.w-t.w)/2,right:this.w-t.w-i}[e]||0;var n=this.w;this.Add(t,i+(s||0),a),this.w=n},Clean:function(){return this.h===-a.BIGDIMEN&&(this.h=this.d=this.l=0),this}});c.ROW=c.Subclass({Init:function(){this.SUPER(arguments).Init.call(this),this.svg=[],this.sh=this.sd=0},Check:function(t){var e=t.toSVG();this.svg.push(e),t.SVGcanStretch("Vertical")&&(e.mml=t),e.h+e.y>this.sh&&(this.sh=e.h+e.y),e.d-e.y>this.sd&&(this.sd=e.d-e.y)},Stretch:function(){for(var t=0,e=this.svg.length;t<e;t++){var i=this.svg[t],a=i.mml;a&&((a.forceStretch||a.SVGdata.h!==this.sh||a.SVGdata.d!==this.sd)&&(i=a.SVGstretchV(this.sh,this.sd)),a.SVGdata.HW=this.sh,a.SVGdata.D=this.sd),i.ic?this.ic=i.ic:delete this.ic,this.Add(i,this.w,0,!0)}delete this.svg}}),c.RECT=c.Subclass({type:"rect",removeable:!1,Init:function(t,e,i,a){null==a&&(a={stroke:"none"}),a.width=Math.floor(i),a.height=Math.floor(t+e),this.SUPER(arguments).Init.call(this,a),this.w=this.r=i,this.h=this.H=t+e,this.d=this.D=this.l=0,this.y=-e}}),c.FRAME=c.Subclass({type:"rect",removeable:!1,Init:function(t,e,i,s,n,h,r){null==r&&(r={}),r.fill="none",r["stroke-width"]=a.Fixed(s,2),r.width=Math.floor(i-s),r.height=Math.floor(t+e-s),r.transform="translate("+Math.floor(s/2)+","+Math.floor(s/2-e)+")","dashed"===n&&(r["stroke-dasharray"]=[Math.floor(6*a.em),Math.floor(6*a.em)].join(" 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h=Math.floor(Math.max(0,t-e)/(6*e)),r=Math.floor(Math.max(0,t-e)/(2*h+1));n["stroke-dasharray"]=r+" "+r}"dotted"===i&&(n["stroke-dasharray"]=[1,Math.max(150,Math.floor(2*e))].join(" "),n["stroke-linecap"]="round"),this.SUPER(arguments).Init.call(this,n),this.w=this.r=e,this.l=0,this.h=this.H=t,this.d=this.D=0}}),c.TEXT=c.Subclass({type:"text",removeable:!1,Init:function(t,e,i){i||(i={}),i.stroke="none",""===i["font-style"]&&delete i["font-style"],""===i["font-weight"]&&delete i["font-weight"],this.SUPER(arguments).Init.call(this,i),a.addText(this.element,e),a.textSVG.appendChild(this.element);var s=this.element.getBBox();a.textSVG.removeChild(this.element),t*=1e3/a.em,this.element.setAttribute("transform","scale("+a.Fixed(t)+") matrix(1 0 0 -1 0 0)"),this.w=this.r=s.width*t,this.l=0,this.h=this.H=-s.y*t,this.d=this.D=(s.height+s.y)*t}}),c.G=c,c.NULL=c.Subclass({Init:function(){this.SUPER(arguments).Init.apply(this,arguments),this.Clean()}}),c.GLYPH=c.Subclass({type:"path",removeable:!1,Init:function(t,e,i,s,n,h,r,l){var o,f=a.config.blacker,S=c.GLYPH,u=a.config.useFontCache,p=1===t?null:"scale("+a.Fixed(t)+")";u&&!a.config.useGlobalCache&&(e="E"+S.n+"-"+e),u&&S.glyphs[e]||(o={"stroke-width":f},u?o.id=e:p&&(o.transform=p),o.d=l?"M"+l+"Z":"",this.SUPER(arguments).Init.call(this,o),u&&(S.defs.appendChild(this.element),S.glyphs[e]=!0)),u&&(o={},p&&(o.transform=p),this.element=a.Element("use",o),this.element.setAttributeNS(d,"href",m+"#"+e)),this.h=(i+f)*t,this.d=(s+f)*t,this.w=(n+f/2)*t,this.l=(h+f/2)*t,this.r=(r+f/2)*t,this.H=Math.max(0,this.h),this.D=Math.max(0,this.d),this.x=this.y=0,this.scale=t}},{glyphs:{},defs:null,n:0}),e.Register.StartupHook("mml Jax Ready",(function(){(s=MathJax.ElementJax.mml).mbase.Augment({SVG:c,toSVG:function(){this.SVGgetStyles();var t=this.SVGgetVariant(),e=this.SVG();this.SVGgetScale(e),this.SVGhandleSpace(e);for(var i=0,s=this.data.length;i<s;i++)if(this.data[i]){var n=e.Add(this.data[i].toSVG(t,e.scale),e.w,0,!0);n.skew&&(e.skew=n.skew)}e.Clean();var h=this.data.join("");return e.skew&&!a.isChar(h)&&delete e.skew,e.r>e.w&&a.isChar(h)&&!t.noIC&&(e.ic=e.r-e.w,e.w=e.r),this.SVGhandleColor(e),this.SVGsaveData(e),e},SVGchildSVG:function(t){return this.data[t]?this.data[t].toSVG():c()},SVGdataStretched:function(t,e,i){return this.SVGdata={HW:e,D:i},this.data[t]?null!=i?this.data[t].SVGstretchV(e,i):null!=e?this.data[t].SVGstretchH(e):this.data[t].toSVG():c()},SVGsaveData:function(t){this.SVGdata||(this.SVGdata={}),this.SVGdata.w=t.w,this.SVGdata.x=t.x,this.SVGdata.h=t.h,this.SVGdata.d=t.d,t.y&&(this.SVGdata.h+=t.y,this.SVGdata.d-=t.y),null!=t.X&&(this.SVGdata.X=t.X),null!=t.tw&&(this.SVGdata.tw=t.tw),t.skew&&(this.SVGdata.skew=t.skew),t.ic&&(this.SVGdata.ic=t.ic),this.class&&(t.removeable=!1,a.Element(t.element,{class:this.class})),this.id&&(t.removeable=!1,a.Element(t.element,{id:this.id})),this.href&&this.SVGaddHref(t),a.config.addMMLclasses&&(this.SVGaddClass(t.element,"mjx-svg-"+this.type),t.removeable=!1);var e=this.style;e&&t.element&&(t.element.style.cssText=e,t.element.style.fontSize&&(t.element.style.fontSize=""),t.element.style.border=t.element.style.padding="",t.removeable&&(t.removeable=""===t.element.style.cssText)),this.SVGaddAttributes(t)},SVGaddClass:function(t,e){var i=t.getAttribute("class");t.setAttribute("class",(i?i+" ":"")+e)},SVGaddAttributes:function(t){if(this.attrNames)for(var i=this.attrNames,a=s.nocopyAttributes,n=e.config.ignoreMMLattributes,h="mstyle"===this.type?s.math.prototype.defaults:this.defaults,r=0,l=i.length;r<l;r++){var o=i[r];0!=n[o]&&(a[o]||n[o]||null!=h[o]||void 0!==t.element[o])||(t.element.setAttribute(o,this.attr[o]),t.removeable=!1)}},SVGaddHref:function(t){var e=a.Element("a",{class:"mjx-svg-href"});if(e.setAttributeNS(d,"href",this.href),e.onclick=this.SVGlink,a.addElement(e,"rect",{width:t.w,height:t.h+t.d,y:-t.d,fill:"none",stroke:"none","pointer-events":"all"}),"svg"===t.type){for(var i=t.element.firstChild;i.firstChild;)e.appendChild(i.firstChild);i.appendChild(e)}else e.appendChild(t.element),t.element=e;t.removeable=!1},SVGlink:function(){var t=this.href.animVal;if("#"===t.charAt(0)){var e=a.hashCheck(document.getElementById(t.substr(1)));e&&e.scrollIntoView&&setTimeout((function(){e.parentNode.scrollIntoView(!0)}),1)}document.location=t},SVGgetStyles:function(){if(this.style){var t=i.Element("span");t.style.cssText=this.style,this.styles=this.SVGprocessStyles(t.style)}},SVGprocessStyles:function(t){var e={border:a.getBorders(t),padding:a.getPadding(t)};return e.border||delete e.border,e.padding||delete e.padding,t.fontSize&&(e.fontSize=t.fontSize),t.color&&(e.color=t.color),t.backgroundColor&&(e.background=t.backgroundColor),t.fontStyle&&(e.fontStyle=t.fontStyle),t.fontWeight&&(e.fontWeight=t.fontWeight),t.fontFamily&&(e.fontFamily=t.fontFamily),e.fontWeight&&e.fontWeight.match(/^\d+$/)&&(e.fontWeight=parseInt(e.fontWeight)>600?"bold":"normal"),e},SVGhandleSpace:function(t){if(this.hasMMLspacing()){if("mo"!==this.type)return;var e=this.getValues("scriptlevel","lspace","rspace");if(e.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var i=this.SVGgetMu(t);e.lspace=Math.max(0,a.length2em(e.lspace,i)),e.rspace=Math.max(0,a.length2em(e.rspace,i));for(var s=this,n=this.Parent();n&&n.isEmbellished()&&n.Core()===s;)s=n,n=n.Parent();e.lspace&&(t.x+=e.lspace),e.rspace&&(t.X=e.rspace)}}else{var h=this.texSpacing();this.SVGgetScale(),""!==h&&(t.x+=a.length2em(h,this.scale)*this.mscale)}},SVGhandleColor:function(t){var e=this.getValues("mathcolor","color");this.styles&&this.styles.color&&!e.color&&(e.color=this.styles.color),e.color&&!this.mathcolor&&(e.mathcolor=e.color),e.mathcolor&&(a.Element(t.element,{fill:e.mathcolor,stroke:e.mathcolor}),t.removeable=!1);var i,n=(this.styles||{}).border,h=(this.styles||{}).padding,r=(n||{}).left||0,l=(h||{}).left||0;if(e.background=this.mathbackground||this.background||(this.styles||{}).background||s.COLOR.TRANSPARENT,r+l){var o=c();for(i in t)t.hasOwnProperty(i)&&(o[i]=t[i]);o.x=0,o.y=0,t.element=a.Element("g"),t.removeable=!0,t.Add(o,r+l,0)}if(h&&(t.w+=h.right||0,t.h+=h.top||0,t.d+=h.bottom||0),n&&(t.w+=n.right||0,t.h+=n.top||0,t.d+=n.bottom||0),e.background!==s.COLOR.TRANSPARENT){var d=t.element.nodeName.toLowerCase();if("g"!==d&&"svg"!==d){var m=a.Element("g");m.appendChild(t.element),t.element=m,t.removeable=!0}t.Add(c.RECT(t.h,t.d,t.w,{fill:e.background,stroke:"none"}),0,0,!1,!0)}if(n){var f={left:["V",t.h+t.d,-5,-t.d],right:["V",t.h+t.d,t.w-n.right+5,-t.d],top:["H",t.w,0,t.h-n.top+5],bottom:["H",t.w,0,-t.d-5]};for(i in f)if(f.hasOwnProperty(i)&&n[i]){var S=f[i],u=c[S[0]+"LINE"];t.Add(u(S[1],n[i],n[i+"Style"],n[i+"Color"]),S[2],S[3])}}},SVGhandleVariant:function(t,e,i){return a.HandleVariant(t,e,i)},SVGgetVariant:function(){var t=this.getValues("mathvariant","fontfamily","fontweight","fontstyle"),e=t.mathvariant;return this.variantForm&&(e="-"+a.fontInUse+"-variant"),t.hasVariant=this.Get("mathvariant",!0),t.hasVariant||(t.family=t.fontfamily,t.weight=t.fontweight,t.style=t.fontstyle),this.styles&&(!t.style&&this.styles.fontStyle&&(t.style=this.styles.fontStyle),!t.weight&&this.styles.fontWeight&&(t.weight=this.styles.fontWeight),!t.family&&this.styles.fontFamily&&(t.family=this.styles.fontFamily)),t.family&&!t.hasVariant?(!t.weight&&t.mathvariant.match(/bold/)&&(t.weight="bold"),!t.style&&t.mathvariant.match(/italic/)&&(t.style="italic"),e={forceFamily:!0,font:{"font-family":t.family}},t.style&&(e.font["font-style"]=t.style),t.weight&&(e.font["font-weight"]=t.weight),e):("bold"===t.weight?e={normal:s.VARIANT.BOLD,italic:s.VARIANT.BOLDITALIC,fraktur:s.VARIANT.BOLDFRAKTUR,script:s.VARIANT.BOLDSCRIPT,"sans-serif":s.VARIANT.BOLDSANSSERIF,"sans-serif-italic":s.VARIANT.SANSSERIFBOLDITALIC}[e]||e:"normal"===t.weight&&(e={bold:s.VARIANT.normal,"bold-italic":s.VARIANT.ITALIC,"bold-fraktur":s.VARIANT.FRAKTUR,"bold-script":s.VARIANT.SCRIPT,"bold-sans-serif":s.VARIANT.SANSSERIF,"sans-serif-bold-italic":s.VARIANT.SANSSERIFITALIC}[e]||e),"italic"===t.style?e={normal:s.VARIANT.ITALIC,bold:s.VARIANT.BOLDITALIC,"sans-serif":s.VARIANT.SANSSERIFITALIC,"bold-sans-serif":s.VARIANT.SANSSERIFBOLDITALIC}[e]||e:"normal"===t.style&&(e={italic:s.VARIANT.NORMAL,"bold-italic":s.VARIANT.BOLD,"sans-serif-italic":s.VARIANT.SANSSERIF,"sans-serif-bold-italic":s.VARIANT.BOLDSANSSERIF}[e]||e),e 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t.scale&&1!==t.scale&&(e=1/t.scale),0!==i.scriptlevel&&(i.scriptlevel>2&&(i.scriptlevel=2),e=Math.sqrt(Math.pow(i.scriptsizemultiplier,i.scriptlevel))),e},SVGnotEmpty:function(t){for(;t;){if("mrow"!==t.type&&"texatom"!==t.type||t.data.length>1)return!0;t=t.data[0]}return!1},SVGcanStretch:function(t){var e=!1;if(this.isEmbellished()){var i=this.Core();i&&i!==this&&(e=i.SVGcanStretch(t))&&i.forceStretch&&(this.forceStretch=!0)}return e},SVGstretchV:function(t,e){return this.toSVG(t,e)},SVGstretchH:function(t){return this.toSVG(t)},SVGlineBreaks:function(){return!1}},{SVGemptySVG:function(){var t=this.SVG();return t.Clean(),this.SVGsaveData(t),t},SVGautoload:function(){this.constructor.Augment({toSVG:s.mbase.SVGautoloadFail});var i=a.autoloadDir+"/"+this.type+".js";e.RestartAfter(t.Require(i))},SVGautoloadFail:function(){throw Error("SVG can't autoload '"+this.type+"'")},SVGautoloadList:{},SVGautoloadFile:function(i){if(s.mbase.SVGautoloadList.hasOwnProperty(i))throw Error("SVG can't 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t=i.Element("span",{style:a.config.merrorStyle});this.styles=this.SVGprocessStyles(t.style),this.style&&(t.style.cssText=this.style,e.Insert(this.styles,this.SVGprocessStyles(t.style)))}}),s.ms.Augment({toSVG:s.mbase.SVGautoload}),s.mglyph.Augment({toSVG:s.mbase.SVGautoload}),s.mspace.Augment({toSVG:function(){this.SVGgetStyles();var t=this.getValues("height","depth","width");t.mathbackground=this.mathbackground,this.background&&!this.mathbackground&&(t.mathbackground=this.background);var e=this.SVG();this.SVGgetScale(e);var i=this.mscale,s=this.SVGgetMu(e);return e.h=a.length2em(t.height,s)*i,e.d=a.length2em(t.depth,s)*i,e.w=e.r=a.length2em(t.width,s)*i,e.w<0&&(e.x=e.w,e.w=e.r=0),e.h<-e.d&&(e.d=-e.h),e.l=0,e.Clean(),this.SVGhandleColor(e),this.SVGsaveData(e),e}}),s.mphantom.Augment({toSVG:function(t,e){this.SVGgetStyles();var i=this.SVG();if(this.SVGgetScale(i),null!=this.data[0]){for(this.SVGhandleSpace(i),i.Add(this.SVGdataStretched(0,t,e)),i.Clean();i.element.firstChild;)i.element.removeChild(i.element.firstChild);i.D=i.d,i.H=i.h,i.r=Math.max(0,Math.min(i.w,i.r)),i.l=Math.max(0,Math.min(i.w,i.l))}return this.SVGhandleColor(i),this.SVGsaveData(i),i.removeable&&!i.element.firstChild&&delete i.element,i}}),s.mpadded.Augment({toSVG:function(t,e){this.SVGgetStyles();var i=this.SVG();if(null!=this.data[0]){this.SVGgetScale(i),this.SVGhandleSpace(i);var a=this.SVGdataStretched(0,t,e),s=this.SVGgetMu(i),n=this.getValues("height","depth","width","lspace","voffset"),h=0,r=0;n.lspace&&(h=this.SVGlength2em(a,n.lspace,s)),n.voffset&&(r=this.SVGlength2em(a,n.voffset,s));var 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this.SVGlineBreaks(i)&&(i=this.SVGmultiline(i)),this.SVGhandleColor(i),this.SVGsaveData(i),i},SVGlineBreaks:function(t){return!!this.parent.linebreakContainer&&(a.config.linebreaks.automatic&&t.w>a.linebreakWidth||this.hasNewline())},SVGmultiline:function(t){s.mbase.SVGautoloadFile("multiline")},SVGstretchH:function(t){var e=this.SVG();this.SVGhandleSpace(e);for(var i=0,a=this.data.length;i<a;i++)e.Add(this.SVGdataStretched(i,t),e.w,0);return e.Clean(),this.SVGhandleColor(e),this.SVGsaveData(e),e}}),s.mstyle.Augment({toSVG:function(t,e){this.SVGgetStyles();var i=this.SVG();if(null!=this.data[0]){this.SVGhandleSpace(i);var a=i.Add(this.data[0].toSVG(t,e));i.Clean(),a.ic&&(i.ic=a.ic),this.SVGhandleColor(i)}return this.SVGsaveData(i),i}}),s.mfrac.Augment({toSVG:function(){this.SVGgetStyles();var t=this.SVG(),e=this.SVGgetScale(t),i=c();i.scale=t.scale,this.SVGhandleSpace(i);var s=this.SVGchildSVG(0),n=this.SVGchildSVG(1),h=this.getValues("displaystyle","linethickness","numalign","denomalign","bevelled"),r=h.displaystyle,l=a.TeX.axis_height*e;if(h.bevelled){var o=r?400:150,d=Math.max(s.h+s.d,n.h+n.d)+2*o,m=a.createDelimiter(47,d);i.Add(s,0,(s.d-s.h)/2+l+o),i.Add(m,s.w-o/2,(m.d-m.h)/2+l),i.Add(n,s.w+m.w-o,(n.d-n.h)/2+l-o)}else{var f,S,u,p,g=Math.max(s.w,n.w),V=a.thickness2em(h.linethickness,this.scale)*this.mscale,G=a.TeX.min_rule_thickness/a.em*1e3;r?(u=a.TeX.num1,p=a.TeX.denom1):(u=0===V?a.TeX.num3:a.TeX.num2,p=a.TeX.denom2),u*=e,p*=e,0===V?(f=Math.max((r?7:3)*a.TeX.rule_thickness,2*G),(S=u-s.d-(n.h-p))<f&&(u+=(f-S)/2,p+=(f-S)/2),i.w=g,V=0):(f=Math.max((r?2:0)*G+V,V/2+1.5*G),(S=u-s.d-(l+V/2))<f&&(u+=f-S),(S=l-V/2-(n.h-p))<f&&(p+=f-S),i.Add(c.RECT(V/2,V/2,g+2*V),0,l)),i.Align(s,h.numalign,V,u),i.Align(n,h.denomalign,V,-p)}return 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h=this.data[1].toSVG();h.x=0;var r=this.SVGrootHeight(e.h+e.d,s,h)-a,l=Math.min(h.w,h.r);i=Math.max(l,n),t.Add(h,i-l,r)}else n=i;return i-n},SVGrootHeight:function(t,e,i){return.45*(t-900*e)+600*e+Math.max(0,i.d-75)}}),s.mfenced.Augment({SVG:c.ROW,toSVG:function(){this.SVGgetStyles();var t=this.SVG();this.SVGhandleSpace(t),this.data.open&&t.Check(this.data.open),null!=this.data[0]&&t.Check(this.data[0]);for(var e=1,i=this.data.length;e<i;e++)this.data[e]&&(this.data["sep"+e]&&t.Check(this.data["sep"+e]),t.Check(this.data[e]));return this.data.close&&t.Check(this.data.close),t.Stretch(),t.Clean(),this.SVGhandleColor(t),this.SVGsaveData(t),t}}),s.menclose.Augment({toSVG:s.mbase.SVGautoload}),s.maction.Augment({toSVG:s.mbase.SVGautoload}),s.semantics.Augment({toSVG:function(){this.SVGgetStyles();var t=this.SVG();return null!=this.data[0]?(this.SVGhandleSpace(t),t.Add(this.data[0].toSVG()),t.Clean()):t.Clean(),this.SVGsaveData(t),t},SVGstretchH:function(t){return null!=this.data[0]?this.data[0].SVGstretchH(t):c.NULL()},SVGstretchV:function(t,e){return null!=this.data[0]?this.data[0].SVGstretchV(t,e):c.NULL()}}),s.munderover.Augment({toSVG:function(t,e){this.SVGgetStyles();var i=this.getValues("displaystyle","accent","accentunder","align"),n=this.data[this.base];if(!i.displaystyle&&null!=n&&(n.movablelimits||n.CoreMO().Get("movablelimits")))return s.msubsup.prototype.toSVG.call(this);var h=this.SVG(),r=this.SVGgetScale(h);this.SVGhandleSpace(h);var l,o,d,m,f=[],S=[],u=-a.BIGDIMEN,p=u;for(o=0,d=this.data.length;o<d;o++)null!=this.data[o]&&(o==this.base?(l=f[o]=this.SVGdataStretched(o,t,e),S[o]=(null!=e||null==t)&&this.data[o].SVGcanStretch("Horizontal"),this.data[this.over]&&i.accent&&(l.h=Math.max(l.h,r*a.TeX.x_height))):((l=f[o]=this.data[o].toSVG()).x=0,delete 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C=o!=this.base&&i[this.ACCENTS[o]];C&&l.w<=1&&(l.x=-l.l,f[o]=c.G().With({removeable:!1}),f[o].Add(l),f[o].Clean(),f[o].w=-l.l,l=f[o]),g={left:0,center:(p-(m=l.w+l.x+(l.X||0)))/2,right:p-m}[i.align],V=0,o==this.over?(C?(x=A*r,y=0,n.skew&&(g+=n.skew,h.skew=n.skew,g+m>p&&(h.skew+=(p-m-g)/2))):(G=a.TeX.big_op_spacing1*r,v=a.TeX.big_op_spacing3*r,x=Math.max(G,v-Math.max(0,l.d))),x=Math.max(x,1500/a.em),g+=b/2,V=n.y+n.h+l.d+x,l.h+=y,l.h>l.H&&(l.H=l.h)):o==this.under&&(C?(x=3*A*r,y=0):(G=a.TeX.big_op_spacing2*r,v=a.TeX.big_op_spacing4*r,x=Math.max(G,v-l.h)),x=Math.max(x,1500/a.em),g-=b/2,V=n.y-(n.d+l.h+x),l.d+=y,l.d>l.D&&(l.D=l.d)),h.Add(l,g,V)}return h.Clean(),this.SVGhandleColor(h),this.SVGsaveData(h),h}}),s.msubsup.Augment({toSVG:function(t,e){this.SVGgetStyles();var i=this.SVG(),s=this.SVGgetScale(i);this.SVGhandleSpace(i);var n,h,r=this.SVGgetMu(i),l=i.Add(this.SVGdataStretched(this.base,t,e)),o=(this.data[this.sup]||this.data[this.sub]||this).SVGgetScale(),d=a.TeX.x_height*s,m=a.TeX.scriptspace*s;this.SVGnotEmpty(this.data[this.sup])&&((n=this.data[this.sup].toSVG()).w+=m,n.r=Math.max(n.w,n.r)),this.SVGnotEmpty(this.data[this.sub])&&((h=this.data[this.sub].toSVG()).w+=m,h.r=Math.max(h.w,h.r));var c,f=a.TeX.sup_drop*o,S=a.TeX.sub_drop*o,u=l.h+(l.y||0)-f,p=l.d-(l.y||0)+S,g=0;l.ic&&(l.w-=l.ic,g=1.3*l.ic+.05),!this.data[this.base]||"mi"!==this.data[this.base].type&&"mo"!==this.data[this.base].type||!a.isChar(this.data[this.base].data.join(""))||1!==l.scale||l.stretched||this.data[this.base].Get("largeop")||(u=p=0);var V=this.getValues("subscriptshift","superscriptshift");V.subscriptshift=""===V.subscriptshift?0:a.length2em(V.subscriptshift,r),V.superscriptshift=""===V.superscriptshift?0:a.length2em(V.superscriptshift,r);var G=l.w+l.x;if(n)if(h){p=Math.max(p,a.TeX.sub2*s);var v=a.TeX.rule_thickness*s;u-n.d-(h.h-p)<3*v&&(p=3*v-u+n.d+h.h,(f=.8*d-(u-n.d))>0&&(u+=f,p-=f)),i.Add(n,G+g,Math.max(u,V.superscriptshift)),i.Add(h,G,-Math.max(p,V.subscriptshift)),this.data[this.sup].SVGdata.dx=g,this.data[this.sup].SVGdata.dy=Math.max(u,V.superscriptshift),this.data[this.sub].SVGdata.dy=-Math.max(p,V.subscriptshift)}else{var y=this.getValues("displaystyle","texprimestyle");c=a.TeX[y.displaystyle?"sup1":y.texprimestyle?"sup3":"sup2"],u=Math.max(u,c*s,n.d+1/4*d,V.superscriptshift),i.Add(n,G+g,u),this.data[this.sup].SVGdata.dx=g,this.data[this.sup].SVGdata.dy=u}else h&&(p=Math.max(p,a.TeX.sub1*s,h.h-.8*d,V.subscriptshift),i.Add(h,G,-p),this.data[this.sub].SVGdata.dy=-p);return i.Clean(),this.SVGhandleColor(i),this.SVGsaveData(i),i}}),s.mmultiscripts.Augment({toSVG:s.mbase.SVGautoload}),s.mtable.Augment({toSVG:s.mbase.SVGautoload}),s["annotation-xml"].Augment({toSVG:s.mbase.SVGautoload}),s.math.Augment({SVG:c.Subclass({type:"svg",removeable:!1}),toSVG:function(t,i){var n=a.config;if(this.data[0]){this.SVGgetStyles(),s.mbase.prototype.displayAlign=e.config.displayAlign,s.mbase.prototype.displayIndent=e.config.displayIndent,String(e.config.displayIndent).match(/^0($|[a-z%])/i)&&(s.mbase.prototype.displayIndent="0");var h=c.G();h.Add(this.data[0].toSVG(),0,0,!0),h.Clean(),this.SVGhandleColor(h),a.Element(h.element,{stroke:"currentColor",fill:"currentColor","stroke-width":0,transform:"matrix(1 0 0 -1 0 0)"}),h.removeable=!1;var r=this.SVG();if(r.element.setAttribute("xmlns:xlink",d),n.useFontCache&&!n.useGlobalCache&&r.element.appendChild(c.GLYPH.defs),r.Add(h),r.Clean(),this.SVGsaveData(r),!t)return r.element=r.element.firstChild,r.element.removeAttribute("transform"),r.removable=!0,r;var l=Math.max(-r.l,0),o=Math.max(r.r-r.w,0),m=r.element.style,f=a.TeX.x_height/a.ex,S=(Math.ceil(r.H/f)+1)*f+a.HFUZZ,u=(Math.ceil(r.D/f)+1)*f+a.DFUZZ,p=l+r.w+o;r.element.setAttribute("width",a.Ex(p)),r.element.setAttribute("height",a.Ex(S+u)),m.verticalAlign=a.Ex(-u),l&&(m.marginLeft=a.Ex(-l)),o&&(m.marginRight=a.Ex(-o)),r.element.setAttribute("viewBox",a.Fixed(-l,1)+" "+a.Fixed(-S,1)+" "+a.Fixed(p,1)+" "+a.Fixed(S+u,1)),r.H>r.h&&(m.marginTop=a.Ex(r.h-S)),r.D>r.d&&(m.marginBottom=a.Ex(r.d-u),m.verticalAlign=a.Ex(-r.d)),Math.abs(p-a.cwidth)<10&&(m.maxWidth=a.Fixed(a.cwidth*a.em/1e3*a.config.scale)+"px");var g=this.Get("alttext");if(g&&!r.element.getAttribute("aria-label")&&r.element.setAttribute("aria-label",g),r.element.getAttribute("role")||r.element.setAttribute("role","img"),r.element.setAttribute("focusable","false"),t.appendChild(r.element),r.element=null,!this.isMultiline&&"block"===this.Get("display")&&!r.hasIndent){var V=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");V.indentalignfirst!==s.INDENTALIGN.INDENTALIGN&&(V.indentalign=V.indentalignfirst),V.indentalign===s.INDENTALIGN.AUTO&&(V.indentalign=this.displayAlign),V.indentshiftfirst!==s.INDENTSHIFT.INDENTSHIFT&&(V.indentshift=V.indentshiftfirst),"auto"===V.indentshift&&(V.indentshift="0");var G=a.length2em(V.indentshift,1,a.cwidth);if("0"!==this.displayIndent){var v=a.length2em(this.displayIndent,1,a.cwidth);G+=V.indentalign===s.INDENTALIGN.RIGHT?-v:v}i.style.textAlign=V.indentalign,G&&e.Insert(m,{left:{marginLeft:a.Ex(G)},right:{marginRight:a.Ex(-G),marginLeft:a.Ex(Math.max(0,G-p))},center:{marginLeft:a.Ex(G),marginRight:a.Ex(-G)}}[V.indentalign])}}return t}}),s.TeXAtom.Augment({toSVG:function(t,e){this.SVGgetStyles();var i=this.SVG();if(this.SVGhandleSpace(i),null!=this.data[0]){var n=this.SVGdataStretched(0,t,e),h=0;this.texClass===s.TEXCLASS.VCENTER&&(h=a.TeX.axis_height-(n.h+n.d)/2+n.d),i.Add(n,0,h),i.ic=n.ic,i.skew=n.skew}return this.SVGhandleColor(i),this.SVGsaveData(i),i}}),s.maligngroup.Augment({toSVG:s.mbase.SVGemptySVG}),s.malignmark.Augment({toSVG:s.mbase.SVGemptySVG}),s.mprescripts.Augment({toSVG:s.mbase.SVGemptySVG}),s.none.Augment({toSVG:s.mbase.SVGemptySVG}),e.Register.StartupHook("onLoad",(function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)}))})),e.Browser.Select({Opera:function(t){a.Augment({operaZoomRefresh:!0})}}),e.Register.StartupHook("End Cookie",(function(){"None"!==e.config.menuSettings.zoom&&t.Require("[MathJax]/extensions/MathZoom.js")})),document.createElementNS||(document.namespaces.svg||document.namespaces.add("svg",o),a.Augment({Element:function(t,e){var i="string"==typeof t?document.createElement("svg:"+t):t;if(i.isMathJax=!0,e)for(var a in e)e.hasOwnProperty(a)&&i.setAttribute(a,e[a].toString());return i}}))}(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.SVG);