/*
 *  /MathJax-v2/jax/output/HTML-CSS/autoload/menclose.js
 *
 *  Copyright (c) 2009-2018 The MathJax Consortium
 *
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *  you may not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 */

MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var d="2.7.9";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];var c="http://www.w3.org/2000/svg";var f="urn:schemas-microsoft-com:vml";var e="mjxvml";a.menclose.Augment({toHTML:function(ac){var j=this.getValues("notation","thickness","padding","mathcolor","color");if(j.color&&!this.mathcolor){j.mathcolor=j.color}if(j.thickness==null){j.thickness=".075em"}if(j.padding==null){j.padding=".2em"}ac=this.HTMLcreateSpan(ac);var V=this.HTMLgetMu(ac),af=this.HTMLgetScale();var X=b.length2em(j.padding,V,1/b.em)*af;var N=b.length2em(j.thickness,V,1/b.em)*af;N=Math.max(1/b.em,N);var E=b.Em(N)+" solid";var z=b.createStack(ac);var v=b.createBox(z);this.HTMLmeasureChild(0,v);var K=v.bbox.h+X+N,P=v.bbox.d+X+N,o=v.bbox.w+2*(X+N);var O=b.createFrame(z,K+P,0,o,N,"none");O.id="MathJax-frame-"+this.spanID;b.addBox(z,O);z.insertBefore(O,v);var s=0,U=0,u=0,A=0,M=0,J=0;var S,g;var I,ad,Q;if(!j.mathcolor){j.mathcolor="currentColor"}else{ac.style.color=j.mathcolor}var k=MathJax.Hub.SplitList(j.notation),q={};for(var ab=0,Z=k.length;ab<Z;ab++){q[k[ab]]=true}if(q[a.NOTATION.UPDIAGONALARROW]){q[a.NOTATION.UPDIAGONALSTRIKE]=false}var G;for(var Y in q){if(!q.hasOwnProperty(Y)||!q[Y]){continue}switch(Y){case a.NOTATION.BOX:O.style.border=E;if(!b.msieBorderWidthBug){s=U=A=u=N}break;case a.NOTATION.ROUNDEDBOX:if(b.useVML){if(!g){g=this.HTMLvml(z,K,P,o,N,j.mathcolor)}Q=Math.floor(1000*Math.min(o,K+P)-2*N);I=Math.floor(4000*(o-2*N)),ad=Math.floor(4000*(K+P-2*N));this.HTMLvmlElement(g,"shape",{style:{width:this.HTMLpx(o-2*N),height:this.HTMLpx(K+P-2*N),left:this.HTMLpx(N,0.5),top:this.HTMLpx(N,0.5)},path:"m "+Q+",0 qx 0,"+Q+" l 0,"+(ad-Q)+" qy "+Q+","+ad+" l "+(I-Q)+","+ad+" qx "+I+","+(ad-Q)+" l "+I+","+Q+" qy "+(I-Q)+",0 x e",coordsize:I+","+ad})}else{if(!S){S=this.HTMLsvg(z,K,P,o,N,j.mathcolor)}this.HTMLsvgElement(S.firstChild,"rect",{x:1,y:1,width:this.HTMLpx(o-N)-1,height:this.HTMLpx(K+P-N)-1,rx:this.HTMLpx(Math.min(K+P,o)/4)})}break;case a.NOTATION.CIRCLE:if(b.useVML){if(!g){g=this.HTMLvml(z,K,P,o,N,j.mathcolor)}this.HTMLvmlElement(g,"oval",{style:{width:this.HTMLpx(o-2*N),height:this.HTMLpx(K+P-2*N),left:this.HTMLpx(N,0.5),top:this.HTMLpx(N,0.5)}})}else{if(!S){S=this.HTMLsvg(z,K,P,o,N,j.mathcolor)}this.HTMLsvgElement(S.firstChild,"ellipse",{rx:this.HTMLpx(o/2-N),ry:this.HTMLpx((K+P)/2-N),cx:this.HTMLpx(o/2),cy:this.HTMLpx((K+P)/2)})}break;case a.NOTATION.LEFT:O.style.borderLeft=E;if(!b.msieBorderWidthBug){A=N}break;case a.NOTATION.ACTUARIAL:O.style.borderTop=E;if(!b.msieBorderWidthBug){s=N;O.bbox.w+=X-N}case a.NOTATION.RIGHT:O.style.borderRight=E;if(!b.msieBorderWidthBug){u=N}break;case a.NOTATION.VERTICALSTRIKE:G=b.createRule(z,K+P-N/2,0,N);b.addBox(z,G);b.placeBox(G,X+N+v.bbox.w/2,-P,true);break;case a.NOTATION.TOP:O.style.borderTop=E;if(!b.msieBorderWidthBug){s=N}break;case a.NOTATION.BOTTOM:O.style.borderBottom=E;if(!b.msieBorderWidthBug){U=N}break;case a.NOTATION.HORIZONTALSTRIKE:G=b.createRule(z,N,0,o-N/2);b.addBox(z,G);b.placeBox(G,0,(K+P)/2-P,true);break;case a.NOTATION.UPDIAGONALSTRIKE:if(b.useVML){if(!g){g=this.HTMLvml(z,K,P,o,N,j.mathcolor)}G=this.HTMLvmlElement(g,"line",{from:"0,"+this.HTMLpx(K+P-N),to:this.HTMLpx(o)+",0"})}else{if(!S){S=this.HTMLsvg(z,K,P,o,N,j.mathcolor)}this.HTMLsvgElement(S.firstChild,"line",{x1:1,y1:this.HTMLpx(K+P-N),x2:this.HTMLpx(o-N),y2:this.HTMLpx(N)})}break;case a.NOTATION.UPDIAGONALARROW:if(b.useVML){if(!g){g=this.HTMLvml(z,K,P,o,N,j.mathcolor)}G=this.HTMLvmlElement(g,"line",{from:"0,"+this.HTMLpx(K+P-N),to:this.HTMLpx(o)+","+this.HTMLpx(N)});this.HTMLvmlElement(G,"stroke",{endarrow:"classic"})}else{if(!S){S=this.HTMLsvg(z,K,P,o,N,j.mathcolor)}var aa=Math.sqrt(o*o+(K+P)*(K+P)),ae=1/aa*10*this.scale/b.em*N/0.075;I=o*ae;ad=(K+P)*ae;var F=o-N/2,C=N/2;if(C+ad-0.4*I<0){C=0.4*I-ad}this.HTMLsvgElement(S.firstChild,"line",{x1:1,y1:this.HTMLpx(K+P-N),x2:this.HTMLpx(F-0.7*I),y2:this.HTMLpx(C+0.7*ad)});this.HTMLsvgElement(S.firstChild,"polygon",{points:this.HTMLpx(F)+","+this.HTMLpx(C)+" "+this.HTMLpx(F-I-0.4*ad)+","+this.HTMLpx(C+ad-0.4*I)+" "+this.HTMLpx(F-0.7*I)+","+this.HTMLpx(C+0.7*ad)+" "+this.HTMLpx(F-I+0.4*ad)+","+this.HTMLpx(C+ad+0.4*I)+" "+this.HTMLpx(F)+","+this.HTMLpx(C),fill:j.mathcolor,stroke:"none"})}break;case a.NOTATION.DOWNDIAGONALSTRIKE:if(b.useVML){if(!g){g=this.HTMLvml(z,K,P,o,N,j.mathcolor)}this.HTMLvmlElement(g,"line",{from:"0,0",to:this.HTMLpx(o)+","+this.HTMLpx(K+P-N)})}else{if(!S){S=this.HTMLsvg(z,K,P,o,N,j.mathcolor)}this.HTMLsvgElement(S.firstChild,"line",{x1:1,y1:this.HTMLpx(N),x2:this.HTMLpx(o-N),y2:this.HTMLpx(K+P-N)})}break;case a.NOTATION.PHASORANGLE:o-=2*X;X=(K+P)/2;o+=X;if(b.useVML){if(!g){g=this.HTMLvml(z,K,P,o,N,j.mathcolor)}this.HTMLvmlElement(g,"shape",{style:{width:this.HTMLpx(o),height:this.HTMLpx(K+P)},path:"m "+this.HTMLpt(X+N/2,N/2)+" l "+this.HTMLpt(N/2,K+P-N)+" "+this.HTMLpt(o-N/2,K+P-N)+" e",coordsize:this.HTMLpt(o,K+P)})}else{if(!S){S=this.HTMLsvg(z,K,P,o,N,j.mathcolor)}this.HTMLsvgElement(S.firstChild,"path",{d:"M "+this.HTMLpx(X)+",1L 1,"+this.HTMLpx(K+P-N)+" L "+this.HTMLpx(o)+","+this.HTMLpx(K+P-N)});b.placeBox(S.parentNode,0,-P,true)}break;case a.NOTATION.MADRUWB:O.style.borderBottom=E;O.style.borderRight=E;if(!b.msieBorderWidthBug){U=u=N}break;case a.NOTATION.RADICAL:if(b.useVML){if(!g){g=this.HTMLvml(z,K,P,o,N,j.mathcolor)}this.HTMLvmlElement(g,"shape",{style:{width:this.HTMLpx(o),height:this.HTMLpx(K+P)},path:"m "+this.HTMLpt(N/2,0.6*(K+P))+" l "+this.HTMLpt(X,K+P-N)+" "+this.HTMLpt(2*X,N/2)+" "+this.HTMLpt(o,N/2)+" e",coordsize:this.HTMLpt(o,K+P)});M=X}else{if(!S){S=this.HTMLsvg(z,K,P,o,N,j.mathcolor)}this.HTMLsvgElement(S.firstChild,"path",{d:"M 1,"+this.HTMLpx(0.6*(K+P))+" L "+this.HTMLpx(X)+","+this.HTMLpx(K+P)+" L "+this.HTMLpx(2*X)+",1 L "+this.HTMLpx(o)+",1"});b.placeBox(S.parentNode,0,X/2-P,true);M=X;J=N}break;case a.NOTATION.LONGDIV:if(b.useVML){if(!g){g=this.HTMLvml(z,K,P,o,N,j.mathcolor)}this.HTMLvmlElement(g,"line",{from:"0,"+this.HTMLpx(N/2),to:this.HTMLpx(o-N)+","+this.HTMLpx(N/2)});this.HTMLvmlElement(g,"arc",{style:{width:this.HTMLpx(2*X),height:this.HTMLpx(K+P-2*N),left:this.HTMLpx(-X),top:this.HTMLpx(N)},startangle:"10",endangle:"170"});M=X}else{if(!S){S=this.HTMLsvg(z,K,P,o,N,j.mathcolor)}this.HTMLsvgElement(S.firstChild,"path",{d:"M "+this.HTMLpx(o)+",1 L 1,1 a"+this.HTMLpx(X)+","+this.HTMLpx((K+P)/2-N)+" 0 0,1 1,"+this.HTMLpx(K+P-2*N)});b.placeBox(S.parentNode,0,N-P,true);M=X;J=N}break}}O.style.width=b.Em(o-A-u);O.style.height=b.Em(K+P-s-U);b.placeBox(O,0,J-P,true);b.placeBox(v,M+X+N,0);this.HTMLhandleSpace(ac);this.HTMLhandleColor(ac);return ac},HTMLpx:function(g){return(g*b.em)},HTMLpt:function(g,h){return Math.floor(1000*g)+","+Math.floor(1000*h)},HTMLhandleColor:function(h){var i=document.getElementById("MathJax-frame-"+this.spanID);if(i){var g=this.getValues("mathbackground","background");if(this.style&&h.style.backgroundColor){g.mathbackground=h.style.backgroundColor;h.style.backgroundColor=""}if(g.background&&!this.mathbackground){g.mathbackground=g.background}if(g.mathbackground&&g.mathbackground!==a.COLOR.TRANSPARENT){i.style.backgroundColor=g.mathbackground}}else{this.SUPER(arguments).HTMLhandleColor.call(this,h)}},HTMLsvg:function(h,l,m,g,k,j){var i=document.createElementNS(c,"svg");if(i.style){i.style.width=b.Em(g);i.style.height=b.Em(l+m)}var n=b.createBox(h);n.appendChild(i);b.placeBox(n,0,-m,true);this.HTMLsvgElement(i,"g",{fill:"none",stroke:j,"stroke-width":k*b.em});return i},HTMLsvgElement:function(g,h,i){var j=document.createElementNS(c,h);j.isMathJax=true;if(i){for(var k in i){if(i.hasOwnProperty(k)){j.setAttributeNS(null,k,i[k].toString())}}}g.appendChild(j);return j},HTMLvml:function(i,l,m,h,k,j){var g=b.createFrame(i,l+m,0,h,0,"none");b.addBox(i,g);b.placeBox(g,0,-m,true);this.constructor.VMLcolor=j;this.constructor.VMLthickness=this.HTMLpx(k);return g},HTMLvmlElement:function(g,h,i){var j=b.addElement(g,e+":"+h,{isMathJax:true});j.style.position="absolute";j.style.left=j.style.top=0;MathJax.Hub.Insert(j,i);if(!i.fillcolor){j.fillcolor="none"}if(!i.strokecolor){j.strokecolor=this.constructor.VMLcolor}if(!i.strokeweight){j.strokeweight=this.constructor.VMLthickness}return j}});MathJax.Hub.Browser.Select({MSIE:function(g){if((document.documentMode||0)<9){a.menclose.Augment({HTMLpx:function(i,h){return(i*b.em+(h||0))+"px"}});b.useVML=true;if(!document.namespaces[e]){if(document.documentMode&&document.documentMode===8){document.namespaces.add(e,f,"#default#VML")}else{document.namespaces.add(e,f);document.createStyleSheet().addRule(e+"\\: *","{behavior: url(#default#VML)}")}}}}});MathJax.Hub.Startup.signal.Post("HTML-CSS menclose Ready");MathJax.Ajax.loadComplete(b.autoloadDir+"/menclose.js")});